Centralizers of semisimple elements in E8(q)
--------------------------------------------

|G(q)| = q^120 phi1^8 phi2^8 phi3^4 phi4^4 phi5^2 phi6^4 phi7 phi8^2 phi9 phi1\
0^2 phi12^2 phi14 phi15 phi18 phi20 phi24 phi30

Semisimple class types:
i = 1: Pi = [ 1, 2, 3, 4, 5, 6, 7, 8 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [1,1,1]
      Dynkin type is E_8(q)
      Order of center |Z^F|: 1
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1
        q congruent 2 modulo 60:   1
        q congruent 3 modulo 60:   1
        q congruent 4 modulo 60:   1
        q congruent 5 modulo 60:   1
        q congruent 7 modulo 60:   1
        q congruent 8 modulo 60:   1
        q congruent 9 modulo 60:   1
        q congruent 11 modulo 60:   1
        q congruent 13 modulo 60:   1
        q congruent 16 modulo 60:   1
        q congruent 17 modulo 60:   1
        q congruent 19 modulo 60:   1
        q congruent 21 modulo 60:   1
        q congruent 23 modulo 60:   1
        q congruent 25 modulo 60:   1
        q congruent 27 modulo 60:   1
        q congruent 29 modulo 60:   1
        q congruent 31 modulo 60:   1
        q congruent 32 modulo 60:   1
        q congruent 37 modulo 60:   1
        q congruent 41 modulo 60:   1
        q congruent 43 modulo 60:   1
        q congruent 47 modulo 60:   1
        q congruent 49 modulo 60:   1
        q congruent 53 modulo 60:   1
        q congruent 59 modulo 60:   1
      Fusion of maximal tori of C^F in those of G^F:
        [ 1 .. 112 ]
      elements of other class types in center:
[  ]

i = 2: Pi = [ 1, 2, 3, 4, 5, 6, 7, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [2,1,1]
      Dynkin type is E_7(q) + A_1(q)
      Order of center |Z^F|: 1 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1
        q congruent 7 modulo 60:   1
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1
        q congruent 11 modulo 60:   1
        q congruent 13 modulo 60:   1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1
        q congruent 19 modulo 60:   1
        q congruent 21 modulo 60:   1
        q congruent 23 modulo 60:   1
        q congruent 25 modulo 60:   1
        q congruent 27 modulo 60:   1
        q congruent 29 modulo 60:   1
        q congruent 31 modulo 60:   1
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1
        q congruent 41 modulo 60:   1
        q congruent 43 modulo 60:   1
        q congruent 47 modulo 60:   1
        q congruent 49 modulo 60:   1
        q congruent 53 modulo 60:   1
        q congruent 59 modulo 60:   1
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 5, 67, 3, 69, 4, 68, 7, 69, 8, 77, 12, 79, 14, 83, 16, 73, 
  19, 72, 20, 71, 18, 74, 19, 76, 23, 93, 31, 78, 28, 82, 33, 86, 30, 81, 38, 
  84, 35, 88, 40, 88, 41, 103, 43, 90, 44, 91, 46, 105, 51, 94, 59, 95, 60, 
  98, 57, 101, 62, 111, 67, 2, 66, 4, 68, 3, 69, 5, 68, 7, 78, 9, 80, 13, 84, 
  15, 74, 17, 72, 20, 70, 19, 73, 18, 76, 20, 94, 24, 77, 30, 81, 27, 85, 34, 
  82, 31, 83, 37, 87, 35, 87, 40, 104, 42, 89, 43, 91, 45, 106, 47, 93, 50, 
  96, 60, 97, 59, 102, 58, 112, 63 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]

i = 3: Pi = [ 1, 2, 3, 4, 5, 6, 8, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [3,1,1]
      Dynkin type is E_6(q) + A_2(q)
      Order of center |Z^F|: 1 times
        1, q congruent 0 modulo 3
        3, q congruent 1 modulo 3
        1, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   1
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1
        q congruent 16 modulo 60:   1
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 8, 3, 69, 27, 4, 68, 30, 12, 79, 10, 8, 77, 14, 14, 83, 12, 
  16, 73, 53, 19, 76, 59, 23, 93, 62, 33, 86, 29, 28, 82, 36, 35, 88, 34, 30, 
  81, 37, 46, 105, 48, 57, 101, 55, 66, 4, 77, 68, 7, 81, 72, 20, 95, 70, 19, 
  97, 77, 30, 83, 83, 37, 79, 87, 40, 85, 89, 43, 109, 93, 50, 111, 96, 60, 
  99 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]

    k = 2: F-action on Pi is (  1,  6)(  3,  5)(  8,240)      [3,1,2]
      Dynkin type is ^2E_6(q) + ^2A_2(q)
      Order of center |Z^F|: 1 times
        1, q congruent 0 modulo 3
        1, q congruent 1 modulo 3
        3, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   1
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   1
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   1
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   1
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   1
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   1
        q congruent 59 modulo 60:   1
      Fusion of maximal tori of C^F in those of G^F:
        [ 2, 67, 9, 3, 68, 28, 5, 69, 31, 13, 80, 11, 9, 78, 15, 15, 84, 13, 
  17, 74, 54, 20, 76, 60, 24, 94, 63, 34, 85, 29, 27, 81, 36, 35, 87, 33, 31, 
  82, 38, 47, 106, 49, 58, 102, 56, 67, 5, 78, 69, 7, 82, 72, 19, 96, 71, 20, 
  98, 78, 31, 84, 84, 38, 80, 88, 40, 86, 90, 43, 110, 94, 51, 112, 95, 59, 
  99 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]

i = 4: Pi = [ 1, 2, 3, 4, 5, 7, 8, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [4,1,1]
      Dynkin type is D_5(q) + A_3(q)
      Order of center |Z^F|: 1 times
        1, q congruent 0 modulo 4
        4, q congruent 1 modulo 4
        1, q congruent 2 modulo 4
        2, q congruent 3 modulo 4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   1
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1
        q congruent 41 modulo 60:   1
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1
        q congruent 53 modulo 60:   1
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 4, 8, 70, 4, 68, 3, 30, 72, 3, 69, 5, 27, 71, 66, 4, 68, 77, 
  19, 70, 19, 72, 97, 18, 68, 7, 69, 81, 20, 72, 20, 71, 95, 17, 4, 68, 7, 
  30, 76, 16, 73, 18, 53, 75, 19, 76, 20, 59, 74, 8, 77, 30, 14, 97, 28, 82, 
  31, 36, 98, 30, 81, 27, 37, 95, 77, 30, 81, 83, 59, 96, 60, 98, 99, 54, 70, 
  19, 76, 97, 22, 89, 43, 90, 109, 45, 23, 93, 50, 62, 107 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 9, 1, 1, 1 ] ]

    k = 2: F-action on Pi is (  2,  5)(  7,240)      [4,1,2]
      Dynkin type is ^2D_5(q) + ^2A_3(q)
      Order of center |Z^F|: 1 times
        1, q congruent 0 modulo 4
        2, q congruent 1 modulo 4
        1, q congruent 2 modulo 4
        4, q congruent 3 modulo 4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   1
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1
        q congruent 47 modulo 60:   1
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   1
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 68, 4, 28, 70, 5, 69, 3, 31, 72, 2, 67, 5, 9, 71, 72, 19, 70, 
  96, 16, 69, 7, 68, 82, 19, 71, 20, 72, 98, 18, 67, 5, 69, 78, 20, 20, 76, 
  19, 60, 73, 5, 69, 7, 31, 76, 17, 74, 18, 54, 75, 31, 82, 28, 38, 96, 27, 
  81, 30, 36, 97, 9, 78, 31, 15, 98, 78, 31, 82, 84, 60, 95, 59, 97, 99, 53, 
  90, 43, 89, 110, 44, 71, 20, 76, 98, 22, 24, 94, 51, 63, 108 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 9, 1, 1, 1 ] ]

i = 5: Pi = [ 1, 2, 3, 4, 6, 7, 8, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [5,1,1]
      Dynkin type is A_4(q) + A_4(q)
      Order of center |Z^F|: 1 times
        1, q congruent 0 modulo 5
        5, q congruent 1 modulo 5
        1, q congruent 2 modulo 5
        1, q congruent 3 modulo 5
        1, q congruent 4 modulo 5
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   1
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   1
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   1
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 4, 8, 77, 70, 23, 66, 4, 68, 77, 30, 19, 93, 4, 68, 7, 30, 
  81, 76, 50, 8, 77, 30, 14, 83, 97, 62, 77, 30, 81, 83, 37, 59, 111, 70, 19, 
  76, 97, 59, 22, 107, 23, 93, 50, 62, 111, 107, 25 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]

    k = 2: F-action on Pi is (  1,  2)(  3,  4)(  6,240)(  7,  8)      [5,1,2]
      Dynkin type is ^2A_4(q) + ^2A_4(q)
      Order of center |Z^F|: 1 times
        1, q congruent 0 modulo 5
        1, q congruent 1 modulo 5
        1, q congruent 2 modulo 5
        1, q congruent 3 modulo 5
        5, q congruent 4 modulo 5
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   1
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   1
      Fusion of maximal tori of C^F in those of G^F:
        [ 2, 67, 5, 9, 78, 71, 24, 67, 5, 69, 78, 31, 20, 94, 5, 69, 7, 31, 
  82, 76, 51, 9, 78, 31, 15, 84, 98, 63, 78, 31, 82, 84, 38, 60, 112, 71, 20, 
  76, 98, 60, 22, 108, 24, 94, 51, 63, 112, 108, 26 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]

    k = 3: F-action on Pi is (  1,  6,  2,240)(  3,  7,  4,  8)      [5,1,3]
      Dynkin type is ^2A_4(q^2)
      Order of center |Z^F|: 1 times
        1, q congruent 0 modulo 5
        1, q congruent 1 modulo 5
        5, q congruent 2 modulo 5
        1, q congruent 3 modulo 5
        1, q congruent 4 modulo 5
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   1
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   1
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   1
        q congruent 37 modulo 60:   1
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   1
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 6, 75, 22, 39, 100, 92, 52 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]

    k = 4: F-action on Pi is (  1,240,  2,  6)(  3,  8,  4,  7)      [5,1,4]
      Dynkin type is ^2A_4(q^2)
      Order of center |Z^F|: 1 times
        1, q congruent 0 modulo 5
        1, q congruent 1 modulo 5
        1, q congruent 2 modulo 5
        5, q congruent 3 modulo 5
        1, q congruent 4 modulo 5
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   1
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   1
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 6, 75, 22, 39, 100, 92, 52 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]

i = 6: Pi = [ 1, 2, 3, 5, 6, 7, 8, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [6,1,1]
      Dynkin type is A_5(q) + A_2(q) + A_1(q)
      Order of center |Z^F|: 1 times
        6, q congruent 1 modulo 6
        1, q congruent 2 modulo 6
        2, q congruent 3 modulo 6
        3, q congruent 4 modulo 6
        2, q congruent 5 modulo 6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 8, 77, 66, 4, 4, 68, 77, 30, 4, 68, 68, 7, 30, 81, 
  68, 3, 7, 69, 81, 27, 8, 77, 77, 30, 14, 83, 77, 30, 30, 81, 83, 37, 14, 
  83, 83, 37, 12, 79, 70, 19, 19, 76, 97, 59, 19, 72, 76, 20, 59, 95, 23, 93, 
  93, 50, 62, 111, 87, 35, 40, 88, 85, 34 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ] ]

    k = 2: F-action on Pi is (  1,  3)(  5,240)(  6,  8)      [6,1,2]
      Dynkin type is ^2A_5(q) + ^2A_2(q) + A_1(q)
      Order of center |Z^F|: 1 times
        2, q congruent 1 modulo 6
        3, q congruent 2 modulo 6
        2, q congruent 3 modulo 6
        1, q congruent 4 modulo 6
        6, q congruent 5 modulo 6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   1
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   1
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   1
        q congruent 59 modulo 60:   1
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 2, 5, 67, 78, 9, 5, 67, 69, 5, 31, 78, 69, 5, 7, 69, 82, 31, 3, 
  69, 68, 7, 28, 82, 78, 9, 31, 78, 84, 15, 31, 78, 82, 31, 38, 84, 84, 15, 
  38, 84, 80, 13, 20, 71, 76, 20, 60, 98, 72, 20, 19, 76, 96, 60, 94, 24, 51, 
  94, 112, 63, 35, 88, 87, 40, 33, 86 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ] ]

i = 7: Pi = [ 1, 2, 4, 5, 6, 7, 8, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [7,1,1]
      Dynkin type is A_7(q) + A_1(q)
      Order of center |Z^F|: 1 times
        1, q congruent 0 modulo 4
        4, q congruent 1 modulo 4
        1, q congruent 2 modulo 4
        2, q congruent 3 modulo 4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   1
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1
        q congruent 41 modulo 60:   1
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1
        q congruent 53 modulo 60:   1
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 4, 68, 68, 7, 3, 69, 8, 77, 77, 30, 30, 81, 14, 83, 
  83, 37, 70, 19, 19, 76, 72, 20, 97, 59, 18, 74, 23, 93, 93, 50, 62, 111, 
  87, 40, 35, 88, 41, 103, 91, 45 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ]

    k = 2: F-action on Pi is (  2,240)(  4,  8)(  5,  7)      [7,1,2]
      Dynkin type is ^2A_7(q) + A_1(q)
      Order of center |Z^F|: 1 times
        1, q congruent 0 modulo 4
        2, q congruent 1 modulo 4
        1, q congruent 2 modulo 4
        4, q congruent 3 modulo 4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   1
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1
        q congruent 47 modulo 60:   1
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   1
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 2, 5, 67, 69, 5, 7, 69, 68, 3, 78, 9, 31, 78, 82, 31, 84, 15, 
  38, 84, 20, 71, 76, 20, 19, 72, 60, 98, 73, 18, 94, 24, 51, 94, 112, 63, 
  40, 88, 87, 35, 104, 42, 44, 91 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ]

i = 8: Pi = [ 1, 3, 4, 5, 6, 7, 8, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [8,1,1]
      Dynkin type is A_8(q)
      Order of center |Z^F|: 1 times
        1, q congruent 0 modulo 3
        3, q congruent 1 modulo 3
        1, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   1
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1
        q congruent 16 modulo 60:   1
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 4, 68, 7, 8, 77, 30, 81, 14, 83, 12, 70, 19, 76, 97, 59, 22, 
  23, 93, 50, 62, 107, 87, 40, 85, 41, 103, 92, 48 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]

    k = 2: F-action on Pi is (  1,240)(  3,  8)(  4,  7)(  5,  6)      [8,1,2]
      Dynkin type is ^2A_8(q)
      Order of center |Z^F|: 1 times
        1, q congruent 0 modulo 3
        1, q congruent 1 modulo 3
        3, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   1
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   1
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   1
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   1
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   1
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   1
        q congruent 59 modulo 60:   1
      Fusion of maximal tori of C^F in those of G^F:
        [ 2, 67, 5, 69, 7, 9, 78, 31, 82, 15, 84, 13, 71, 20, 76, 98, 60, 22, 
  24, 94, 51, 63, 108, 88, 40, 86, 42, 104, 92, 49 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]

i = 9: Pi = [ 2, 3, 4, 5, 6, 7, 8, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [9,1,1]
      Dynkin type is D_8(q)
      Order of center |Z^F|: 1 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1
        q congruent 7 modulo 60:   1
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1
        q congruent 11 modulo 60:   1
        q congruent 13 modulo 60:   1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1
        q congruent 19 modulo 60:   1
        q congruent 21 modulo 60:   1
        q congruent 23 modulo 60:   1
        q congruent 25 modulo 60:   1
        q congruent 27 modulo 60:   1
        q congruent 29 modulo 60:   1
        q congruent 31 modulo 60:   1
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1
        q congruent 41 modulo 60:   1
        q congruent 43 modulo 60:   1
        q congruent 47 modulo 60:   1
        q congruent 49 modulo 60:   1
        q congruent 53 modulo 60:   1
        q congruent 59 modulo 60:   1
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 4, 3, 5, 2, 66, 70, 68, 72, 69, 71, 67, 4, 16, 19, 7, 18, 20, 5, 
  17, 68, 73, 76, 75, 69, 74, 3, 7, 18, 6, 8, 28, 30, 31, 27, 9, 77, 96, 82, 
  97, 81, 98, 78, 95, 30, 60, 53, 31, 59, 54, 14, 38, 36, 37, 15, 83, 84, 99, 
  70, 89, 76, 90, 71, 19, 44, 43, 22, 20, 45, 72, 76, 91, 75, 97, 110, 109, 
  98, 18, 22, 21, 23, 51, 50, 24, 93, 108, 94, 107, 62, 63, 87, 100, 88, 35, 
  40, 39, 41, 42, 91, 92 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]

i = 10: Pi = [ 1, 2, 3, 4, 5, 6, 7 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [10,1,1]
      Dynkin type is E_7(q) + T(phi1)
      Order of center |Z^F|: phi1
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 ( q-3 )
        q congruent 2 modulo 60:   1/2 ( q-2 )
        q congruent 3 modulo 60:   1/2 ( q-3 )
        q congruent 4 modulo 60:   1/2 ( q-2 )
        q congruent 5 modulo 60:   1/2 ( q-3 )
        q congruent 7 modulo 60:   1/2 ( q-3 )
        q congruent 8 modulo 60:   1/2 ( q-2 )
        q congruent 9 modulo 60:   1/2 ( q-3 )
        q congruent 11 modulo 60:   1/2 ( q-3 )
        q congruent 13 modulo 60:   1/2 ( q-3 )
        q congruent 16 modulo 60:   1/2 ( q-2 )
        q congruent 17 modulo 60:   1/2 ( q-3 )
        q congruent 19 modulo 60:   1/2 ( q-3 )
        q congruent 21 modulo 60:   1/2 ( q-3 )
        q congruent 23 modulo 60:   1/2 ( q-3 )
        q congruent 25 modulo 60:   1/2 ( q-3 )
        q congruent 27 modulo 60:   1/2 ( q-3 )
        q congruent 29 modulo 60:   1/2 ( q-3 )
        q congruent 31 modulo 60:   1/2 ( q-3 )
        q congruent 32 modulo 60:   1/2 ( q-2 )
        q congruent 37 modulo 60:   1/2 ( q-3 )
        q congruent 41 modulo 60:   1/2 ( q-3 )
        q congruent 43 modulo 60:   1/2 ( q-3 )
        q congruent 47 modulo 60:   1/2 ( q-3 )
        q congruent 49 modulo 60:   1/2 ( q-3 )
        q congruent 53 modulo 60:   1/2 ( q-3 )
        q congruent 59 modulo 60:   1/2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 5, 3, 4, 7, 8, 12, 14, 16, 19, 20, 18, 19, 23, 31, 28, 33, 30, 
  38, 35, 40, 41, 43, 44, 46, 51, 59, 60, 57, 62, 67, 66, 68, 69, 68, 78, 80, 
  84, 74, 72, 70, 73, 76, 94, 77, 81, 85, 82, 83, 87, 87, 104, 89, 91, 106, 
  93, 96, 97, 102, 112 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ]

    k = 2: F-action on Pi is ()      [10,1,2]
      Dynkin type is E_7(q) + T(phi2)
      Order of center |Z^F|: phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 phi1
        q congruent 2 modulo 60:   1/2 q
        q congruent 3 modulo 60:   1/2 phi1
        q congruent 4 modulo 60:   1/2 q
        q congruent 5 modulo 60:   1/2 phi1
        q congruent 7 modulo 60:   1/2 phi1
        q congruent 8 modulo 60:   1/2 q
        q congruent 9 modulo 60:   1/2 phi1
        q congruent 11 modulo 60:   1/2 phi1
        q congruent 13 modulo 60:   1/2 phi1
        q congruent 16 modulo 60:   1/2 q
        q congruent 17 modulo 60:   1/2 phi1
        q congruent 19 modulo 60:   1/2 phi1
        q congruent 21 modulo 60:   1/2 phi1
        q congruent 23 modulo 60:   1/2 phi1
        q congruent 25 modulo 60:   1/2 phi1
        q congruent 27 modulo 60:   1/2 phi1
        q congruent 29 modulo 60:   1/2 phi1
        q congruent 31 modulo 60:   1/2 phi1
        q congruent 32 modulo 60:   1/2 q
        q congruent 37 modulo 60:   1/2 phi1
        q congruent 41 modulo 60:   1/2 phi1
        q congruent 43 modulo 60:   1/2 phi1
        q congruent 47 modulo 60:   1/2 phi1
        q congruent 49 modulo 60:   1/2 phi1
        q congruent 53 modulo 60:   1/2 phi1
        q congruent 59 modulo 60:   1/2 phi1
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 67, 69, 68, 69, 77, 79, 83, 73, 72, 71, 74, 76, 93, 78, 82, 86, 
  81, 84, 88, 88, 103, 90, 91, 105, 94, 95, 98, 101, 111, 2, 4, 3, 5, 7, 9, 
  13, 15, 17, 20, 19, 18, 20, 24, 30, 27, 34, 31, 37, 35, 40, 42, 43, 45, 47, 
  50, 60, 59, 58, 63 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ] ]

i = 11: Pi = [ 1, 2, 3, 4, 5, 6, 8 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [11,1,1]
      Dynkin type is E_6(q) + A_1(q) + T(phi1)
      Order of center |Z^F|: phi1
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 ( q-5 )
        q congruent 2 modulo 60:   1/2 ( q-2 )
        q congruent 3 modulo 60:   1/2 ( q-3 )
        q congruent 4 modulo 60:   1/2 ( q-4 )
        q congruent 5 modulo 60:   1/2 ( q-3 )
        q congruent 7 modulo 60:   1/2 ( q-5 )
        q congruent 8 modulo 60:   1/2 ( q-2 )
        q congruent 9 modulo 60:   1/2 ( q-3 )
        q congruent 11 modulo 60:   1/2 ( q-3 )
        q congruent 13 modulo 60:   1/2 ( q-5 )
        q congruent 16 modulo 60:   1/2 ( q-4 )
        q congruent 17 modulo 60:   1/2 ( q-3 )
        q congruent 19 modulo 60:   1/2 ( q-5 )
        q congruent 21 modulo 60:   1/2 ( q-3 )
        q congruent 23 modulo 60:   1/2 ( q-3 )
        q congruent 25 modulo 60:   1/2 ( q-5 )
        q congruent 27 modulo 60:   1/2 ( q-3 )
        q congruent 29 modulo 60:   1/2 ( q-3 )
        q congruent 31 modulo 60:   1/2 ( q-5 )
        q congruent 32 modulo 60:   1/2 ( q-2 )
        q congruent 37 modulo 60:   1/2 ( q-5 )
        q congruent 41 modulo 60:   1/2 ( q-3 )
        q congruent 43 modulo 60:   1/2 ( q-5 )
        q congruent 47 modulo 60:   1/2 ( q-3 )
        q congruent 49 modulo 60:   1/2 ( q-5 )
        q congruent 53 modulo 60:   1/2 ( q-3 )
        q congruent 59 modulo 60:   1/2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 3, 69, 4, 68, 12, 79, 8, 77, 14, 83, 16, 73, 19, 76, 23, 93, 
  33, 86, 28, 82, 35, 88, 30, 81, 46, 105, 57, 101, 66, 4, 68, 7, 72, 20, 70, 
  19, 77, 30, 83, 37, 87, 40, 89, 43, 93, 50, 96, 60 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ] ]

    k = 2: F-action on Pi is (1,6)(3,5)      [11,1,2]
      Dynkin type is ^2E_6(q) + A_1(q) + T(phi2)
      Order of center |Z^F|: phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 phi1
        q congruent 2 modulo 60:   1/2 ( q-2 )
        q congruent 3 modulo 60:   1/2 phi1
        q congruent 4 modulo 60:   1/2 q
        q congruent 5 modulo 60:   1/2 ( q-3 )
        q congruent 7 modulo 60:   1/2 phi1
        q congruent 8 modulo 60:   1/2 ( q-2 )
        q congruent 9 modulo 60:   1/2 phi1
        q congruent 11 modulo 60:   1/2 ( q-3 )
        q congruent 13 modulo 60:   1/2 phi1
        q congruent 16 modulo 60:   1/2 q
        q congruent 17 modulo 60:   1/2 ( q-3 )
        q congruent 19 modulo 60:   1/2 phi1
        q congruent 21 modulo 60:   1/2 phi1
        q congruent 23 modulo 60:   1/2 ( q-3 )
        q congruent 25 modulo 60:   1/2 phi1
        q congruent 27 modulo 60:   1/2 phi1
        q congruent 29 modulo 60:   1/2 ( q-3 )
        q congruent 31 modulo 60:   1/2 phi1
        q congruent 32 modulo 60:   1/2 ( q-2 )
        q congruent 37 modulo 60:   1/2 phi1
        q congruent 41 modulo 60:   1/2 ( q-3 )
        q congruent 43 modulo 60:   1/2 phi1
        q congruent 47 modulo 60:   1/2 ( q-3 )
        q congruent 49 modulo 60:   1/2 phi1
        q congruent 53 modulo 60:   1/2 ( q-3 )
        q congruent 59 modulo 60:   1/2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 2, 68, 3, 69, 5, 80, 13, 78, 9, 84, 15, 74, 17, 76, 20, 94, 24, 
  85, 34, 81, 27, 87, 35, 82, 31, 106, 47, 102, 58, 5, 67, 7, 69, 19, 72, 20, 
  71, 31, 78, 38, 84, 40, 88, 43, 90, 51, 94, 59, 95 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ] ]

i = 12: Pi = [ 1, 2, 3, 4, 5, 7, 8 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [12,1,1]
      Dynkin type is D_5(q) + A_2(q) + T(phi1)
      Order of center |Z^F|: phi1
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 ( q-7 )
        q congruent 2 modulo 60:   1/2 ( q-2 )
        q congruent 3 modulo 60:   1/2 ( q-3 )
        q congruent 4 modulo 60:   1/2 ( q-4 )
        q congruent 5 modulo 60:   1/2 ( q-5 )
        q congruent 7 modulo 60:   1/2 ( q-5 )
        q congruent 8 modulo 60:   1/2 ( q-2 )
        q congruent 9 modulo 60:   1/2 ( q-5 )
        q congruent 11 modulo 60:   1/2 ( q-3 )
        q congruent 13 modulo 60:   1/2 ( q-7 )
        q congruent 16 modulo 60:   1/2 ( q-4 )
        q congruent 17 modulo 60:   1/2 ( q-5 )
        q congruent 19 modulo 60:   1/2 ( q-5 )
        q congruent 21 modulo 60:   1/2 ( q-5 )
        q congruent 23 modulo 60:   1/2 ( q-3 )
        q congruent 25 modulo 60:   1/2 ( q-7 )
        q congruent 27 modulo 60:   1/2 ( q-3 )
        q congruent 29 modulo 60:   1/2 ( q-5 )
        q congruent 31 modulo 60:   1/2 ( q-5 )
        q congruent 32 modulo 60:   1/2 ( q-2 )
        q congruent 37 modulo 60:   1/2 ( q-7 )
        q congruent 41 modulo 60:   1/2 ( q-5 )
        q congruent 43 modulo 60:   1/2 ( q-5 )
        q congruent 47 modulo 60:   1/2 ( q-3 )
        q congruent 49 modulo 60:   1/2 ( q-7 )
        q congruent 53 modulo 60:   1/2 ( q-5 )
        q congruent 59 modulo 60:   1/2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 8, 4, 68, 30, 3, 69, 27, 66, 4, 77, 70, 19, 97, 68, 7, 81, 
  72, 20, 95, 4, 68, 30, 16, 73, 53, 19, 76, 59, 8, 77, 14, 28, 82, 36, 30, 
  81, 37, 77, 30, 83, 96, 60, 99, 70, 19, 97, 89, 43, 109, 23, 93, 62 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ] ]

    k = 2: F-action on Pi is (2,5)(7,8)      [12,1,2]
      Dynkin type is ^2D_5(q) + ^2A_2(q) + T(phi2)
      Order of center |Z^F|: phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 phi1
        q congruent 2 modulo 60:   1/2 ( q-2 )
        q congruent 3 modulo 60:   1/2 ( q-3 )
        q congruent 4 modulo 60:   1/2 q
        q congruent 5 modulo 60:   1/2 ( q-3 )
        q congruent 7 modulo 60:   1/2 ( q-3 )
        q congruent 8 modulo 60:   1/2 ( q-2 )
        q congruent 9 modulo 60:   1/2 phi1
        q congruent 11 modulo 60:   1/2 ( q-5 )
        q congruent 13 modulo 60:   1/2 phi1
        q congruent 16 modulo 60:   1/2 q
        q congruent 17 modulo 60:   1/2 ( q-3 )
        q congruent 19 modulo 60:   1/2 ( q-3 )
        q congruent 21 modulo 60:   1/2 phi1
        q congruent 23 modulo 60:   1/2 ( q-5 )
        q congruent 25 modulo 60:   1/2 phi1
        q congruent 27 modulo 60:   1/2 ( q-3 )
        q congruent 29 modulo 60:   1/2 ( q-3 )
        q congruent 31 modulo 60:   1/2 ( q-3 )
        q congruent 32 modulo 60:   1/2 ( q-2 )
        q congruent 37 modulo 60:   1/2 phi1
        q congruent 41 modulo 60:   1/2 ( q-3 )
        q congruent 43 modulo 60:   1/2 ( q-3 )
        q congruent 47 modulo 60:   1/2 ( q-5 )
        q congruent 49 modulo 60:   1/2 phi1
        q congruent 53 modulo 60:   1/2 ( q-3 )
        q congruent 59 modulo 60:   1/2 ( q-5 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 68, 28, 5, 69, 31, 2, 67, 9, 72, 19, 96, 69, 7, 82, 71, 20, 98, 
  67, 5, 78, 20, 76, 60, 5, 69, 31, 17, 74, 54, 31, 82, 38, 27, 81, 36, 9, 
  78, 15, 78, 31, 84, 95, 59, 99, 90, 43, 110, 71, 20, 98, 24, 94, 63 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ] ]

i = 13: Pi = [ 1, 2, 3, 4, 5, 7, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [13,1,1]
      Dynkin type is D_5(q) + A_1(q) + A_1(q) + T(phi1)
      Order of center |Z^F|: phi1 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 ( q-5 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 ( q-5 )
        q congruent 7 modulo 60:   1/4 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4 ( q-5 )
        q congruent 11 modulo 60:   1/4 ( q-3 )
        q congruent 13 modulo 60:   1/4 ( q-5 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 ( q-5 )
        q congruent 19 modulo 60:   1/4 ( q-3 )
        q congruent 21 modulo 60:   1/4 ( q-5 )
        q congruent 23 modulo 60:   1/4 ( q-3 )
        q congruent 25 modulo 60:   1/4 ( q-5 )
        q congruent 27 modulo 60:   1/4 ( q-3 )
        q congruent 29 modulo 60:   1/4 ( q-5 )
        q congruent 31 modulo 60:   1/4 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 ( q-5 )
        q congruent 41 modulo 60:   1/4 ( q-5 )
        q congruent 43 modulo 60:   1/4 ( q-3 )
        q congruent 47 modulo 60:   1/4 ( q-3 )
        q congruent 49 modulo 60:   1/4 ( q-5 )
        q congruent 53 modulo 60:   1/4 ( q-5 )
        q congruent 59 modulo 60:   1/4 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 4, 68, 68, 3, 3, 69, 69, 5, 66, 4, 4, 68, 70, 19, 19, 
  72, 68, 7, 7, 69, 72, 20, 20, 71, 4, 68, 68, 7, 16, 73, 73, 18, 19, 76, 76, 
  20, 8, 77, 77, 30, 28, 82, 82, 31, 30, 81, 81, 27, 77, 30, 30, 81, 96, 60, 
  60, 98, 70, 19, 19, 76, 89, 43, 43, 90, 23, 93, 93, 50 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], 
  [ 23, 1, 1, 2 ] ]

    k = 2: F-action on Pi is (  7,240)      [13,1,2]
      Dynkin type is D_5(q) + A_1(q^2) + T(phi2)
      Order of center |Z^F|: phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 phi1
        q congruent 7 modulo 60:   1/4 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4 phi1
        q congruent 11 modulo 60:   1/4 phi2
        q congruent 13 modulo 60:   1/4 phi1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 phi1
        q congruent 19 modulo 60:   1/4 phi2
        q congruent 21 modulo 60:   1/4 phi1
        q congruent 23 modulo 60:   1/4 phi2
        q congruent 25 modulo 60:   1/4 phi1
        q congruent 27 modulo 60:   1/4 phi2
        q congruent 29 modulo 60:   1/4 phi1
        q congruent 31 modulo 60:   1/4 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 phi1
        q congruent 41 modulo 60:   1/4 phi1
        q congruent 43 modulo 60:   1/4 phi2
        q congruent 47 modulo 60:   1/4 phi2
        q congruent 49 modulo 60:   1/4 phi1
        q congruent 53 modulo 60:   1/4 phi1
        q congruent 59 modulo 60:   1/4 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 70, 3, 72, 5, 71, 68, 19, 72, 18, 69, 20, 71, 17, 7, 76, 18, 75, 
  20, 74, 30, 97, 31, 98, 27, 95, 81, 59, 98, 54, 76, 22, 90, 45, 50, 107 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 23, 1, 2, 2 ] ]

    k = 3: F-action on Pi is (  2,  5)(  7,240)      [13,1,3]
      Dynkin type is ^2D_5(q) + A_1(q^2) + T(phi1)
      Order of center |Z^F|: phi1 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 phi1
        q congruent 7 modulo 60:   1/4 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4 phi1
        q congruent 11 modulo 60:   1/4 ( q-3 )
        q congruent 13 modulo 60:   1/4 phi1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 phi1
        q congruent 19 modulo 60:   1/4 ( q-3 )
        q congruent 21 modulo 60:   1/4 phi1
        q congruent 23 modulo 60:   1/4 ( q-3 )
        q congruent 25 modulo 60:   1/4 phi1
        q congruent 27 modulo 60:   1/4 ( q-3 )
        q congruent 29 modulo 60:   1/4 phi1
        q congruent 31 modulo 60:   1/4 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 phi1
        q congruent 41 modulo 60:   1/4 phi1
        q congruent 43 modulo 60:   1/4 ( q-3 )
        q congruent 47 modulo 60:   1/4 ( q-3 )
        q congruent 49 modulo 60:   1/4 phi1
        q congruent 53 modulo 60:   1/4 phi1
        q congruent 59 modulo 60:   1/4 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 70, 3, 72, 5, 71, 70, 16, 68, 19, 72, 18, 69, 20, 19, 73, 7, 76, 
  18, 75, 28, 96, 30, 97, 31, 98, 82, 60, 97, 53, 89, 44, 76, 22, 51, 108 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 23, 1, 1, 2 ] ]

    k = 4: F-action on Pi is (2,5)      [13,1,4]
      Dynkin type is ^2D_5(q) + A_1(q) + A_1(q) + T(phi2)
      Order of center |Z^F|: phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 phi1
        q congruent 7 modulo 60:   1/4 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4 phi1
        q congruent 11 modulo 60:   1/4 ( q-3 )
        q congruent 13 modulo 60:   1/4 phi1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 phi1
        q congruent 19 modulo 60:   1/4 ( q-3 )
        q congruent 21 modulo 60:   1/4 phi1
        q congruent 23 modulo 60:   1/4 ( q-3 )
        q congruent 25 modulo 60:   1/4 phi1
        q congruent 27 modulo 60:   1/4 ( q-3 )
        q congruent 29 modulo 60:   1/4 phi1
        q congruent 31 modulo 60:   1/4 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 phi1
        q congruent 41 modulo 60:   1/4 phi1
        q congruent 43 modulo 60:   1/4 ( q-3 )
        q congruent 47 modulo 60:   1/4 ( q-3 )
        q congruent 49 modulo 60:   1/4 phi1
        q congruent 53 modulo 60:   1/4 phi1
        q congruent 59 modulo 60:   1/4 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 68, 68, 3, 3, 69, 69, 5, 5, 67, 67, 2, 70, 19, 19, 72, 68, 7, 7, 
  69, 72, 20, 20, 71, 69, 5, 5, 67, 19, 76, 76, 20, 7, 69, 69, 5, 18, 74, 74, 
  17, 28, 82, 82, 31, 30, 81, 81, 27, 31, 78, 78, 9, 82, 31, 31, 78, 97, 59, 
  59, 95, 89, 43, 43, 90, 76, 20, 20, 71, 51, 94, 94, 24 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], 
  [ 23, 1, 2, 2 ] ]

i = 14: Pi = [ 1, 2, 3, 4, 6, 7, 8 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [14,1,1]
      Dynkin type is A_4(q) + A_3(q) + T(phi1)
      Order of center |Z^F|: phi1
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 ( q-11 )
        q congruent 2 modulo 60:   1/2 ( q-2 )
        q congruent 3 modulo 60:   1/2 ( q-3 )
        q congruent 4 modulo 60:   1/2 ( q-4 )
        q congruent 5 modulo 60:   1/2 ( q-5 )
        q congruent 7 modulo 60:   1/2 ( q-5 )
        q congruent 8 modulo 60:   1/2 ( q-2 )
        q congruent 9 modulo 60:   1/2 ( q-5 )
        q congruent 11 modulo 60:   1/2 ( q-7 )
        q congruent 13 modulo 60:   1/2 ( q-7 )
        q congruent 16 modulo 60:   1/2 ( q-8 )
        q congruent 17 modulo 60:   1/2 ( q-5 )
        q congruent 19 modulo 60:   1/2 ( q-5 )
        q congruent 21 modulo 60:   1/2 ( q-9 )
        q congruent 23 modulo 60:   1/2 ( q-3 )
        q congruent 25 modulo 60:   1/2 ( q-7 )
        q congruent 27 modulo 60:   1/2 ( q-3 )
        q congruent 29 modulo 60:   1/2 ( q-5 )
        q congruent 31 modulo 60:   1/2 ( q-9 )
        q congruent 32 modulo 60:   1/2 ( q-2 )
        q congruent 37 modulo 60:   1/2 ( q-7 )
        q congruent 41 modulo 60:   1/2 ( q-9 )
        q congruent 43 modulo 60:   1/2 ( q-5 )
        q congruent 47 modulo 60:   1/2 ( q-3 )
        q congruent 49 modulo 60:   1/2 ( q-7 )
        q congruent 53 modulo 60:   1/2 ( q-5 )
        q congruent 59 modulo 60:   1/2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 4, 8, 70, 66, 4, 68, 77, 19, 4, 68, 7, 30, 76, 8, 77, 30, 
  14, 97, 77, 30, 81, 83, 59, 70, 19, 76, 97, 22, 23, 93, 50, 62, 107 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 8, 1, 1, 2 ], 
  [ 9, 1, 1, 1 ] ]

    k = 2: F-action on Pi is (1,2)(3,4)(6,8)      [14,1,2]
      Dynkin type is ^2A_4(q) + ^2A_3(q) + T(phi2)
      Order of center |Z^F|: phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 phi1
        q congruent 2 modulo 60:   1/2 ( q-2 )
        q congruent 3 modulo 60:   1/2 ( q-3 )
        q congruent 4 modulo 60:   1/2 ( q-4 )
        q congruent 5 modulo 60:   1/2 ( q-3 )
        q congruent 7 modulo 60:   1/2 ( q-3 )
        q congruent 8 modulo 60:   1/2 ( q-2 )
        q congruent 9 modulo 60:   1/2 ( q-5 )
        q congruent 11 modulo 60:   1/2 ( q-5 )
        q congruent 13 modulo 60:   1/2 phi1
        q congruent 16 modulo 60:   1/2 q
        q congruent 17 modulo 60:   1/2 ( q-3 )
        q congruent 19 modulo 60:   1/2 ( q-7 )
        q congruent 21 modulo 60:   1/2 phi1
        q congruent 23 modulo 60:   1/2 ( q-5 )
        q congruent 25 modulo 60:   1/2 phi1
        q congruent 27 modulo 60:   1/2 ( q-3 )
        q congruent 29 modulo 60:   1/2 ( q-7 )
        q congruent 31 modulo 60:   1/2 ( q-3 )
        q congruent 32 modulo 60:   1/2 ( q-2 )
        q congruent 37 modulo 60:   1/2 phi1
        q congruent 41 modulo 60:   1/2 ( q-3 )
        q congruent 43 modulo 60:   1/2 ( q-3 )
        q congruent 47 modulo 60:   1/2 ( q-5 )
        q congruent 49 modulo 60:   1/2 ( q-5 )
        q congruent 53 modulo 60:   1/2 ( q-3 )
        q congruent 59 modulo 60:   1/2 ( q-9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 2, 67, 5, 9, 71, 67, 5, 69, 78, 20, 5, 69, 7, 31, 76, 9, 78, 31, 
  15, 98, 78, 31, 82, 84, 60, 71, 20, 76, 98, 22, 24, 94, 51, 63, 108 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 8, 1, 2, 2 ], 
  [ 9, 1, 1, 1 ] ]

i = 15: Pi = [ 1, 2, 3, 5, 6, 7, 8 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [15,1,1]
      Dynkin type is A_4(q) + A_2(q) + A_1(q) + T(phi1)
      Order of center |Z^F|: phi1
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 ( q-13 )
        q congruent 2 modulo 60:   1/2 ( q-2 )
        q congruent 3 modulo 60:   1/2 ( q-3 )
        q congruent 4 modulo 60:   1/2 ( q-4 )
        q congruent 5 modulo 60:   1/2 ( q-5 )
        q congruent 7 modulo 60:   1/2 ( q-7 )
        q congruent 8 modulo 60:   1/2 ( q-2 )
        q congruent 9 modulo 60:   1/2 ( q-5 )
        q congruent 11 modulo 60:   1/2 ( q-7 )
        q congruent 13 modulo 60:   1/2 ( q-9 )
        q congruent 16 modulo 60:   1/2 ( q-8 )
        q congruent 17 modulo 60:   1/2 ( q-5 )
        q congruent 19 modulo 60:   1/2 ( q-7 )
        q congruent 21 modulo 60:   1/2 ( q-9 )
        q congruent 23 modulo 60:   1/2 ( q-3 )
        q congruent 25 modulo 60:   1/2 ( q-9 )
        q congruent 27 modulo 60:   1/2 ( q-3 )
        q congruent 29 modulo 60:   1/2 ( q-5 )
        q congruent 31 modulo 60:   1/2 ( q-11 )
        q congruent 32 modulo 60:   1/2 ( q-2 )
        q congruent 37 modulo 60:   1/2 ( q-9 )
        q congruent 41 modulo 60:   1/2 ( q-9 )
        q congruent 43 modulo 60:   1/2 ( q-7 )
        q congruent 47 modulo 60:   1/2 ( q-3 )
        q congruent 49 modulo 60:   1/2 ( q-9 )
        q congruent 53 modulo 60:   1/2 ( q-5 )
        q congruent 59 modulo 60:   1/2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 8, 77, 66, 4, 4, 68, 77, 30, 4, 68, 68, 7, 30, 81, 8, 
  77, 77, 30, 14, 83, 77, 30, 30, 81, 83, 37, 70, 19, 19, 76, 97, 59, 23, 93, 
  93, 50, 62, 111 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 4 ], 
  [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ] ]

    k = 2: F-action on Pi is (1,3)(5,8)(6,7)      [15,1,2]
      Dynkin type is ^2A_4(q) + ^2A_2(q) + A_1(q) + T(phi2)
      Order of center |Z^F|: phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 phi1
        q congruent 2 modulo 60:   1/2 ( q-2 )
        q congruent 3 modulo 60:   1/2 ( q-3 )
        q congruent 4 modulo 60:   1/2 ( q-4 )
        q congruent 5 modulo 60:   1/2 ( q-5 )
        q congruent 7 modulo 60:   1/2 ( q-3 )
        q congruent 8 modulo 60:   1/2 ( q-2 )
        q congruent 9 modulo 60:   1/2 ( q-5 )
        q congruent 11 modulo 60:   1/2 ( q-7 )
        q congruent 13 modulo 60:   1/2 phi1
        q congruent 16 modulo 60:   1/2 q
        q congruent 17 modulo 60:   1/2 ( q-5 )
        q congruent 19 modulo 60:   1/2 ( q-7 )
        q congruent 21 modulo 60:   1/2 phi1
        q congruent 23 modulo 60:   1/2 ( q-7 )
        q congruent 25 modulo 60:   1/2 phi1
        q congruent 27 modulo 60:   1/2 ( q-3 )
        q congruent 29 modulo 60:   1/2 ( q-9 )
        q congruent 31 modulo 60:   1/2 ( q-3 )
        q congruent 32 modulo 60:   1/2 ( q-2 )
        q congruent 37 modulo 60:   1/2 phi1
        q congruent 41 modulo 60:   1/2 ( q-5 )
        q congruent 43 modulo 60:   1/2 ( q-3 )
        q congruent 47 modulo 60:   1/2 ( q-7 )
        q congruent 49 modulo 60:   1/2 ( q-5 )
        q congruent 53 modulo 60:   1/2 ( q-5 )
        q congruent 59 modulo 60:   1/2 ( q-11 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 2, 5, 67, 78, 9, 5, 67, 69, 5, 31, 78, 69, 5, 7, 69, 82, 31, 
  78, 9, 31, 78, 84, 15, 31, 78, 82, 31, 38, 84, 20, 71, 76, 20, 60, 98, 94, 
  24, 51, 94, 112, 63 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 2, 4 ], 
  [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ] ]

i = 16: Pi = [ 1, 2, 3, 5, 6, 7, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [16,1,1]
      Dynkin type is A_3(q) + A_2(q) + A_1(q) + A_1(q) + T(phi1)
      Order of center |Z^F|: phi1 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 ( q-9 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 ( q-5 )
        q congruent 7 modulo 60:   1/4 ( q-7 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4 ( q-5 )
        q congruent 11 modulo 60:   1/4 ( q-3 )
        q congruent 13 modulo 60:   1/4 ( q-9 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 ( q-5 )
        q congruent 19 modulo 60:   1/4 ( q-7 )
        q congruent 21 modulo 60:   1/4 ( q-5 )
        q congruent 23 modulo 60:   1/4 ( q-3 )
        q congruent 25 modulo 60:   1/4 ( q-9 )
        q congruent 27 modulo 60:   1/4 ( q-3 )
        q congruent 29 modulo 60:   1/4 ( q-5 )
        q congruent 31 modulo 60:   1/4 ( q-7 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 ( q-9 )
        q congruent 41 modulo 60:   1/4 ( q-5 )
        q congruent 43 modulo 60:   1/4 ( q-7 )
        q congruent 47 modulo 60:   1/4 ( q-3 )
        q congruent 49 modulo 60:   1/4 ( q-9 )
        q congruent 53 modulo 60:   1/4 ( q-5 )
        q congruent 59 modulo 60:   1/4 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 66, 4, 4, 68, 8, 77, 77, 30, 66, 4, 4, 68, 4, 68, 68, 
  7, 77, 30, 30, 81, 4, 68, 68, 3, 68, 7, 7, 69, 30, 81, 81, 27, 8, 77, 77, 
  30, 77, 30, 30, 81, 14, 83, 83, 37, 70, 19, 19, 72, 19, 76, 76, 20, 97, 59, 
  59, 95 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], 
  [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ] ]

    k = 2: F-action on Pi is (  2,240)(  5,  7)      [16,1,2]
      Dynkin type is ^2A_3(q) + A_2(q) + A_1(q^2) + T(phi1)
      Order of center |Z^F|: phi1 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 phi1
        q congruent 7 modulo 60:   1/4 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4 phi1
        q congruent 11 modulo 60:   1/4 ( q-3 )
        q congruent 13 modulo 60:   1/4 phi1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 phi1
        q congruent 19 modulo 60:   1/4 ( q-3 )
        q congruent 21 modulo 60:   1/4 phi1
        q congruent 23 modulo 60:   1/4 ( q-3 )
        q congruent 25 modulo 60:   1/4 phi1
        q congruent 27 modulo 60:   1/4 ( q-3 )
        q congruent 29 modulo 60:   1/4 phi1
        q congruent 31 modulo 60:   1/4 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 phi1
        q congruent 41 modulo 60:   1/4 phi1
        q congruent 43 modulo 60:   1/4 ( q-3 )
        q congruent 47 modulo 60:   1/4 ( q-3 )
        q congruent 49 modulo 60:   1/4 phi1
        q congruent 53 modulo 60:   1/4 phi1
        q congruent 59 modulo 60:   1/4 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 72, 69, 20, 27, 95, 68, 19, 7, 76, 81, 59, 4, 70, 68, 19, 30, 
  97, 28, 96, 82, 60, 36, 99, 70, 16, 19, 73, 97, 53 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], 
  [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ] ]

    k = 3: F-action on Pi is (1,3)(5,7)      [16,1,3]
      Dynkin type is ^2A_3(q) + ^2A_2(q) + A_1(q) + A_1(q) + T(phi2)
      Order of center |Z^F|: phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 ( q-5 )
        q congruent 7 modulo 60:   1/4 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4 phi1
        q congruent 11 modulo 60:   1/4 ( q-7 )
        q congruent 13 modulo 60:   1/4 phi1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 ( q-5 )
        q congruent 19 modulo 60:   1/4 ( q-3 )
        q congruent 21 modulo 60:   1/4 phi1
        q congruent 23 modulo 60:   1/4 ( q-7 )
        q congruent 25 modulo 60:   1/4 phi1
        q congruent 27 modulo 60:   1/4 ( q-3 )
        q congruent 29 modulo 60:   1/4 ( q-5 )
        q congruent 31 modulo 60:   1/4 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 phi1
        q congruent 41 modulo 60:   1/4 ( q-5 )
        q congruent 43 modulo 60:   1/4 ( q-3 )
        q congruent 47 modulo 60:   1/4 ( q-7 )
        q congruent 49 modulo 60:   1/4 phi1
        q congruent 53 modulo 60:   1/4 ( q-5 )
        q congruent 59 modulo 60:   1/4 ( q-7 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 67, 67, 2, 69, 5, 5, 67, 31, 78, 78, 9, 69, 5, 5, 67, 7, 69, 69, 
  5, 82, 31, 31, 78, 3, 69, 69, 5, 68, 7, 7, 69, 28, 82, 82, 31, 31, 78, 78, 
  9, 82, 31, 31, 78, 38, 84, 84, 15, 72, 20, 20, 71, 19, 76, 76, 20, 96, 60, 
  60, 98 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], 
  [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ] ]

    k = 4: F-action on Pi is (  1,  3)(  2,240)      [16,1,4]
      Dynkin type is A_3(q) + ^2A_2(q) + A_1(q^2) + T(phi2)
      Order of center |Z^F|: phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 phi1
        q congruent 7 modulo 60:   1/4 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4 phi1
        q congruent 11 modulo 60:   1/4 phi2
        q congruent 13 modulo 60:   1/4 phi1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 phi1
        q congruent 19 modulo 60:   1/4 phi2
        q congruent 21 modulo 60:   1/4 phi1
        q congruent 23 modulo 60:   1/4 phi2
        q congruent 25 modulo 60:   1/4 phi1
        q congruent 27 modulo 60:   1/4 phi2
        q congruent 29 modulo 60:   1/4 phi1
        q congruent 31 modulo 60:   1/4 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 phi1
        q congruent 41 modulo 60:   1/4 phi1
        q congruent 43 modulo 60:   1/4 phi2
        q congruent 47 modulo 60:   1/4 phi2
        q congruent 49 modulo 60:   1/4 phi1
        q congruent 53 modulo 60:   1/4 phi1
        q congruent 59 modulo 60:   1/4 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 72, 68, 19, 28, 96, 69, 20, 7, 76, 82, 60, 5, 71, 69, 20, 31, 
  98, 27, 95, 81, 59, 36, 99, 71, 17, 20, 74, 98, 54 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], 
  [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ] ]

i = 17: Pi = [ 1, 2, 3, 5, 6, 8, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [17,1,1]
      Dynkin type is A_2(q) + A_2(q) + A_2(q) + A_1(q) + T(phi1)
      Order of center |Z^F|: phi1 times
        1, q congruent 0 modulo 3
        3, q congruent 1 modulo 3
        1, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/6 ( q-7 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   1/6 ( q-4 )
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1/6 ( q-7 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1/6 ( q-7 )
        q congruent 16 modulo 60:   1/6 ( q-4 )
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1/6 ( q-7 )
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1/6 ( q-7 )
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1/6 ( q-7 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/6 ( q-7 )
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1/6 ( q-7 )
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1/6 ( q-7 )
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 8, 77, 66, 4, 4, 68, 77, 30, 8, 77, 77, 30, 14, 83, 
  66, 4, 4, 68, 77, 30, 4, 68, 68, 7, 30, 81, 77, 30, 30, 81, 83, 37, 8, 77, 
  77, 30, 14, 83, 77, 30, 30, 81, 83, 37, 14, 83, 83, 37, 12, 79 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 6, 1, 1, 6 ], 
  [ 11, 1, 1, 2 ] ]

    k = 2: F-action on Pi is (  5,  8)(  6,240)      [17,1,2]
      Dynkin type is A_2(q) + A_2(q^2) + A_1(q) + T(phi2)
      Order of center |Z^F|: phi2 times
        1, q congruent 0 modulo 3
        3, q congruent 1 modulo 3
        1, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   1/2 q
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1/2 phi1
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1/2 phi1
        q congruent 16 modulo 60:   1/2 q
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1/2 phi1
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1/2 phi1
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1/2 phi1
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/2 phi1
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1/2 phi1
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1/2 phi1
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 3, 19, 72, 87, 35, 7, 69, 76, 20, 40, 88, 81, 27, 59, 95, 85, 
  34 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], 
  [ 6, 1, 1, 2 ], [ 11, 1, 2, 2 ] ]

    k = 3: F-action on Pi is (  1,  3)(  5,240)(  6,  8)      [17,1,3]
      Dynkin type is ^2A_2(q) + A_2(q^2) + A_1(q) + T(phi1)
      Order of center |Z^F|: phi1 times
        1, q congruent 0 modulo 3
        1, q congruent 1 modulo 3
        3, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   1/2 ( q-2 )
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/2 ( q-3 )
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   1/2 ( q-2 )
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1/2 ( q-3 )
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/2 ( q-3 )
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1/2 ( q-3 )
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1/2 ( q-3 )
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   1/2 ( q-2 )
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   1/2 ( q-3 )
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   1/2 ( q-3 )
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   1/2 ( q-3 )
        q congruent 59 modulo 60:   1/2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 69, 72, 20, 35, 88, 68, 7, 19, 76, 87, 40, 28, 82, 96, 60, 33, 
  86 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], 
  [ 6, 1, 2, 2 ], [ 11, 1, 1, 2 ] ]

    k = 4: F-action on Pi is (  1,  3)(  5,  6)(  8,240)      [17,1,4]
      Dynkin type is ^2A_2(q) + ^2A_2(q) + ^2A_2(q) + A_1(q) + T(phi2)
      Order of center |Z^F|: phi2 times
        1, q congruent 0 modulo 3
        1, q congruent 1 modulo 3
        3, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   1/6 ( q-2 )
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/6 ( q-5 )
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   1/6 ( q-2 )
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1/6 ( q-5 )
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/6 ( q-5 )
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1/6 ( q-5 )
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1/6 ( q-5 )
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   1/6 ( q-2 )
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   1/6 ( q-5 )
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   1/6 ( q-5 )
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   1/6 ( q-5 )
        q congruent 59 modulo 60:   1/6 ( q-5 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 2, 5, 67, 78, 9, 5, 67, 69, 5, 31, 78, 78, 9, 31, 78, 84, 15, 
  5, 67, 69, 5, 31, 78, 69, 5, 7, 69, 82, 31, 31, 78, 82, 31, 38, 84, 78, 9, 
  31, 78, 84, 15, 31, 78, 82, 31, 38, 84, 84, 15, 38, 84, 80, 13 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 6, 1, 2, 6 ], 
  [ 11, 1, 2, 2 ] ]

    k = 5: F-action on Pi is (  1,  5,  8)(  3,  6,240)      [17,1,5]
      Dynkin type is A_2(q^3) + A_1(q) + T(phi1)
      Order of center |Z^F|: phi1 times
        1, q congruent 0 modulo 3
        3, q congruent 1 modulo 3
        1, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/3 phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   1/3 phi1
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1/3 phi1
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1/3 phi1
        q congruent 16 modulo 60:   1/3 phi1
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1/3 phi1
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1/3 phi1
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1/3 phi1
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/3 phi1
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1/3 phi1
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1/3 phi1
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 14, 83, 87, 40, 46, 105 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 11, 1, 1, 2 ] ]

    k = 6: F-action on Pi is (  1,  6,  8,  3,  5,240)      [17,1,6]
      Dynkin type is ^2A_2(q^3) + A_1(q) + T(phi2)
      Order of center |Z^F|: phi2 times
        1, q congruent 0 modulo 3
        1, q congruent 1 modulo 3
        3, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   1/3 phi2
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/3 phi2
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   1/3 phi2
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1/3 phi2
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/3 phi2
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1/3 phi2
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1/3 phi2
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   1/3 phi2
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   1/3 phi2
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   1/3 phi2
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   1/3 phi2
        q congruent 59 modulo 60:   1/3 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 84, 15, 40, 88, 106, 47 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 11, 1, 2, 2 ] ]

i = 18: Pi = [ 1, 2, 4, 5, 6, 7, 8 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [18,1,1]
      Dynkin type is A_6(q) + A_1(q) + T(phi1)
      Order of center |Z^F|: phi1
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 ( q-7 )
        q congruent 2 modulo 60:   1/2 ( q-2 )
        q congruent 3 modulo 60:   1/2 ( q-3 )
        q congruent 4 modulo 60:   1/2 ( q-4 )
        q congruent 5 modulo 60:   1/2 ( q-5 )
        q congruent 7 modulo 60:   1/2 ( q-5 )
        q congruent 8 modulo 60:   1/2 ( q-2 )
        q congruent 9 modulo 60:   1/2 ( q-5 )
        q congruent 11 modulo 60:   1/2 ( q-3 )
        q congruent 13 modulo 60:   1/2 ( q-7 )
        q congruent 16 modulo 60:   1/2 ( q-4 )
        q congruent 17 modulo 60:   1/2 ( q-5 )
        q congruent 19 modulo 60:   1/2 ( q-5 )
        q congruent 21 modulo 60:   1/2 ( q-5 )
        q congruent 23 modulo 60:   1/2 ( q-3 )
        q congruent 25 modulo 60:   1/2 ( q-7 )
        q congruent 27 modulo 60:   1/2 ( q-3 )
        q congruent 29 modulo 60:   1/2 ( q-5 )
        q congruent 31 modulo 60:   1/2 ( q-5 )
        q congruent 32 modulo 60:   1/2 ( q-2 )
        q congruent 37 modulo 60:   1/2 ( q-7 )
        q congruent 41 modulo 60:   1/2 ( q-5 )
        q congruent 43 modulo 60:   1/2 ( q-5 )
        q congruent 47 modulo 60:   1/2 ( q-3 )
        q congruent 49 modulo 60:   1/2 ( q-7 )
        q congruent 53 modulo 60:   1/2 ( q-5 )
        q congruent 59 modulo 60:   1/2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 4, 68, 68, 7, 8, 77, 77, 30, 30, 81, 14, 83, 70, 19, 
  19, 76, 97, 59, 23, 93, 93, 50, 87, 40, 41, 103 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 2 ] ]

    k = 2: F-action on Pi is (2,8)(4,7)(5,6)      [18,1,2]
      Dynkin type is ^2A_6(q) + A_1(q) + T(phi2)
      Order of center |Z^F|: phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 phi1
        q congruent 2 modulo 60:   1/2 ( q-2 )
        q congruent 3 modulo 60:   1/2 ( q-3 )
        q congruent 4 modulo 60:   1/2 q
        q congruent 5 modulo 60:   1/2 ( q-3 )
        q congruent 7 modulo 60:   1/2 ( q-3 )
        q congruent 8 modulo 60:   1/2 ( q-2 )
        q congruent 9 modulo 60:   1/2 phi1
        q congruent 11 modulo 60:   1/2 ( q-5 )
        q congruent 13 modulo 60:   1/2 phi1
        q congruent 16 modulo 60:   1/2 q
        q congruent 17 modulo 60:   1/2 ( q-3 )
        q congruent 19 modulo 60:   1/2 ( q-3 )
        q congruent 21 modulo 60:   1/2 phi1
        q congruent 23 modulo 60:   1/2 ( q-5 )
        q congruent 25 modulo 60:   1/2 phi1
        q congruent 27 modulo 60:   1/2 ( q-3 )
        q congruent 29 modulo 60:   1/2 ( q-3 )
        q congruent 31 modulo 60:   1/2 ( q-3 )
        q congruent 32 modulo 60:   1/2 ( q-2 )
        q congruent 37 modulo 60:   1/2 phi1
        q congruent 41 modulo 60:   1/2 ( q-3 )
        q congruent 43 modulo 60:   1/2 ( q-3 )
        q congruent 47 modulo 60:   1/2 ( q-5 )
        q congruent 49 modulo 60:   1/2 phi1
        q congruent 53 modulo 60:   1/2 ( q-3 )
        q congruent 59 modulo 60:   1/2 ( q-5 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 2, 5, 67, 69, 5, 7, 69, 78, 9, 31, 78, 82, 31, 84, 15, 20, 71, 
  76, 20, 60, 98, 94, 24, 51, 94, 40, 88, 104, 42 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 2 ] ]

i = 19: Pi = [ 1, 2, 4, 5, 6, 7, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [19,1,1]
      Dynkin type is A_5(q) + A_1(q) + A_1(q) + T(phi1)
      Order of center |Z^F|: phi1 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 ( q-7 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/2 ( q-5 )
        q congruent 7 modulo 60:   1/2 ( q-5 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/2 ( q-5 )
        q congruent 11 modulo 60:   1/2 ( q-3 )
        q congruent 13 modulo 60:   1/2 ( q-7 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/2 ( q-5 )
        q congruent 19 modulo 60:   1/2 ( q-5 )
        q congruent 21 modulo 60:   1/2 ( q-5 )
        q congruent 23 modulo 60:   1/2 ( q-3 )
        q congruent 25 modulo 60:   1/2 ( q-7 )
        q congruent 27 modulo 60:   1/2 ( q-3 )
        q congruent 29 modulo 60:   1/2 ( q-5 )
        q congruent 31 modulo 60:   1/2 ( q-5 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/2 ( q-7 )
        q congruent 41 modulo 60:   1/2 ( q-5 )
        q congruent 43 modulo 60:   1/2 ( q-5 )
        q congruent 47 modulo 60:   1/2 ( q-3 )
        q congruent 49 modulo 60:   1/2 ( q-7 )
        q congruent 53 modulo 60:   1/2 ( q-5 )
        q congruent 59 modulo 60:   1/2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 66, 4, 4, 68, 4, 68, 68, 7, 68, 3, 7, 69, 8, 77, 77, 
  30, 77, 30, 30, 81, 14, 83, 83, 37, 70, 19, 19, 76, 19, 72, 76, 20, 23, 93, 
  93, 50, 87, 35, 40, 88 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], 
  [ 7, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 11, 1, 1, 2 ] ]

    k = 2: F-action on Pi is (2,7)(4,6)      [19,1,2]
      Dynkin type is ^2A_5(q) + A_1(q) + A_1(q) + T(phi2)
      Order of center |Z^F|: phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/2 ( q-3 )
        q congruent 7 modulo 60:   1/2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/2 phi1
        q congruent 11 modulo 60:   1/2 ( q-5 )
        q congruent 13 modulo 60:   1/2 phi1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/2 ( q-3 )
        q congruent 19 modulo 60:   1/2 ( q-3 )
        q congruent 21 modulo 60:   1/2 phi1
        q congruent 23 modulo 60:   1/2 ( q-5 )
        q congruent 25 modulo 60:   1/2 phi1
        q congruent 27 modulo 60:   1/2 ( q-3 )
        q congruent 29 modulo 60:   1/2 ( q-3 )
        q congruent 31 modulo 60:   1/2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/2 phi1
        q congruent 41 modulo 60:   1/2 ( q-3 )
        q congruent 43 modulo 60:   1/2 ( q-3 )
        q congruent 47 modulo 60:   1/2 ( q-5 )
        q congruent 49 modulo 60:   1/2 phi1
        q congruent 53 modulo 60:   1/2 ( q-3 )
        q congruent 59 modulo 60:   1/2 ( q-5 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 67, 67, 2, 69, 5, 5, 67, 7, 69, 69, 5, 68, 7, 3, 69, 31, 78, 78, 
  9, 82, 31, 31, 78, 38, 84, 84, 15, 76, 20, 20, 71, 19, 76, 72, 20, 51, 94, 
  94, 24, 87, 40, 35, 88 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], 
  [ 7, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 11, 1, 2, 2 ] ]

i = 20: Pi = [ 1, 2, 4, 5, 7, 8, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [20,1,1]
      Dynkin type is A_3(q) + A_3(q) + A_1(q) + T(phi1)
      Order of center |Z^F|: phi1 times
        1, q congruent 0 modulo 4
        4, q congruent 1 modulo 4
        1, q congruent 2 modulo 4
        2, q congruent 3 modulo 4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 ( q-5 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 ( q-5 )
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4 ( q-5 )
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1/4 ( q-5 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 ( q-5 )
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   1/4 ( q-5 )
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1/4 ( q-5 )
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1/4 ( q-5 )
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 ( q-5 )
        q congruent 41 modulo 60:   1/4 ( q-5 )
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1/4 ( q-5 )
        q congruent 53 modulo 60:   1/4 ( q-5 )
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 4, 68, 8, 77, 70, 19, 66, 4, 4, 68, 68, 7, 77, 30, 
  19, 76, 4, 68, 68, 7, 3, 69, 30, 81, 72, 20, 8, 77, 77, 30, 30, 81, 14, 83, 
  97, 59, 70, 19, 19, 76, 72, 20, 97, 59, 18, 74 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 7, 1, 1, 4 ], 
  [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 24, 1, 1, 2 ] ]

    k = 2: F-action on Pi is ()      [20,1,2]
      Dynkin type is A_3(q) + A_3(q) + A_1(q) + T(phi2)
      Order of center |Z^F|: phi2 times
        1, q congruent 0 modulo 4
        4, q congruent 1 modulo 4
        1, q congruent 2 modulo 4
        2, q congruent 3 modulo 4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 phi1
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4 phi1
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1/4 phi1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 phi1
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   1/4 phi1
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1/4 phi1
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1/4 phi1
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 phi1
        q congruent 41 modulo 60:   1/4 phi1
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1/4 phi1
        q congruent 53 modulo 60:   1/4 phi1
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 4, 68, 68, 3, 77, 30, 19, 72, 4, 68, 68, 7, 7, 69, 30, 81, 
  76, 20, 68, 3, 7, 69, 69, 5, 81, 27, 20, 71, 77, 30, 30, 81, 81, 27, 83, 
  37, 59, 95, 19, 72, 76, 20, 20, 71, 59, 95, 74, 17 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 2, 2 ], [ 24, 1, 2, 2 ] ]

    k = 3: F-action on Pi is (  2,  5)(  7,240)      [20,1,3]
      Dynkin type is ^2A_3(q) + ^2A_3(q) + A_1(q) + T(phi1)
      Order of center |Z^F|: phi1 times
        1, q congruent 0 modulo 4
        2, q congruent 1 modulo 4
        1, q congruent 2 modulo 4
        4, q congruent 3 modulo 4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1/4 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1/4 ( q-3 )
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1/4 ( q-3 )
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1/4 ( q-3 )
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   1/4 ( q-3 )
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1/4 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1/4 ( q-3 )
        q congruent 47 modulo 60:   1/4 ( q-3 )
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   1/4 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 67, 69, 5, 3, 69, 31, 78, 72, 20, 69, 5, 7, 69, 68, 7, 82, 31, 
  19, 76, 3, 69, 68, 7, 4, 68, 28, 82, 70, 19, 31, 78, 82, 31, 28, 82, 38, 
  84, 96, 60, 72, 20, 19, 76, 70, 19, 96, 60, 16, 73 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 1, 2 ], [ 24, 1, 1, 2 ] ]

    k = 4: F-action on Pi is (  2,  5)(  7,240)      [20,1,4]
      Dynkin type is ^2A_3(q) + ^2A_3(q) + A_1(q) + T(phi2)
      Order of center |Z^F|: phi2 times
        1, q congruent 0 modulo 4
        2, q congruent 1 modulo 4
        1, q congruent 2 modulo 4
        4, q congruent 3 modulo 4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1/4 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1/4 ( q-3 )
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1/4 ( q-3 )
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1/4 ( q-3 )
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   1/4 ( q-3 )
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1/4 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1/4 ( q-3 )
        q congruent 47 modulo 60:   1/4 ( q-3 )
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   1/4 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 2, 5, 67, 69, 5, 78, 9, 20, 71, 5, 67, 69, 5, 7, 69, 31, 78, 
  76, 20, 69, 5, 7, 69, 68, 3, 82, 31, 19, 72, 78, 9, 31, 78, 82, 31, 84, 15, 
  60, 98, 20, 71, 76, 20, 19, 72, 60, 98, 73, 18 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 4 ], 
  [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 24, 1, 2, 2 ] ]

    k = 5: F-action on Pi is (  2,  7)(  4,  8)(  5,240)      [20,1,5]
      Dynkin type is A_3(q^2) + A_1(q) + T(phi2)
      Order of center |Z^F|: phi2 times
        1, q congruent 0 modulo 4
        4, q congruent 1 modulo 4
        1, q congruent 2 modulo 4
        2, q congruent 3 modulo 4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 phi1
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4 phi1
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1/4 phi1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 phi1
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   1/4 phi1
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1/4 phi1
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1/4 phi1
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 phi1
        q congruent 41 modulo 60:   1/4 phi1
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1/4 phi1
        q congruent 53 modulo 60:   1/4 phi1
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 69, 72, 20, 18, 74, 35, 88, 91, 45 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 2, 2 ], [ 24, 1, 2, 2 ] ]

    k = 6: F-action on Pi is (  2,  7)(  4,  8)(  5,240)      [20,1,6]
      Dynkin type is A_3(q^2) + A_1(q) + T(phi1)
      Order of center |Z^F|: phi1 times
        1, q congruent 0 modulo 4
        4, q congruent 1 modulo 4
        1, q congruent 2 modulo 4
        2, q congruent 3 modulo 4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 phi1
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4 phi1
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1/4 phi1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 phi1
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   1/4 phi1
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1/4 phi1
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1/4 phi1
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 phi1
        q congruent 41 modulo 60:   1/4 phi1
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1/4 phi1
        q congruent 53 modulo 60:   1/4 phi1
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 7, 19, 76, 73, 18, 87, 40, 44, 91 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], 
  [ 24, 1, 1, 2 ] ]

    k = 7: F-action on Pi is (  2,240)(  4,  8)(  5,  7)      [20,1,7]
      Dynkin type is A_3(q^2) + A_1(q) + T(phi2)
      Order of center |Z^F|: phi2 times
        1, q congruent 0 modulo 4
        2, q congruent 1 modulo 4
        1, q congruent 2 modulo 4
        4, q congruent 3 modulo 4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1/4 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1/4 phi2
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1/4 phi2
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1/4 phi2
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   1/4 phi2
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1/4 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1/4 phi2
        q congruent 47 modulo 60:   1/4 phi2
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   1/4 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 7, 69, 76, 20, 18, 74, 40, 88, 91, 45 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], 
  [ 24, 1, 2, 2 ] ]

    k = 8: F-action on Pi is (  2,240)(  4,  8)(  5,  7)      [20,1,8]
      Dynkin type is A_3(q^2) + A_1(q) + T(phi1)
      Order of center |Z^F|: phi1 times
        1, q congruent 0 modulo 4
        2, q congruent 1 modulo 4
        1, q congruent 2 modulo 4
        4, q congruent 3 modulo 4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1/4 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1/4 ( q-3 )
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1/4 ( q-3 )
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1/4 ( q-3 )
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   1/4 ( q-3 )
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1/4 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1/4 ( q-3 )
        q congruent 47 modulo 60:   1/4 ( q-3 )
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   1/4 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 3, 19, 72, 73, 18, 87, 35, 44, 91 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 1, 2 ], [ 24, 1, 1, 2 ] ]

i = 21: Pi = [ 1, 3, 4, 5, 6, 7, 8 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [21,1,1]
      Dynkin type is A_7(q) + T(phi1)
      Order of center |Z^F|: phi1
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 ( q-5 )
        q congruent 2 modulo 60:   1/2 ( q-2 )
        q congruent 3 modulo 60:   1/2 ( q-3 )
        q congruent 4 modulo 60:   1/2 ( q-4 )
        q congruent 5 modulo 60:   1/2 ( q-3 )
        q congruent 7 modulo 60:   1/2 ( q-5 )
        q congruent 8 modulo 60:   1/2 ( q-2 )
        q congruent 9 modulo 60:   1/2 ( q-3 )
        q congruent 11 modulo 60:   1/2 ( q-3 )
        q congruent 13 modulo 60:   1/2 ( q-5 )
        q congruent 16 modulo 60:   1/2 ( q-4 )
        q congruent 17 modulo 60:   1/2 ( q-3 )
        q congruent 19 modulo 60:   1/2 ( q-5 )
        q congruent 21 modulo 60:   1/2 ( q-3 )
        q congruent 23 modulo 60:   1/2 ( q-3 )
        q congruent 25 modulo 60:   1/2 ( q-5 )
        q congruent 27 modulo 60:   1/2 ( q-3 )
        q congruent 29 modulo 60:   1/2 ( q-3 )
        q congruent 31 modulo 60:   1/2 ( q-5 )
        q congruent 32 modulo 60:   1/2 ( q-2 )
        q congruent 37 modulo 60:   1/2 ( q-5 )
        q congruent 41 modulo 60:   1/2 ( q-3 )
        q congruent 43 modulo 60:   1/2 ( q-5 )
        q congruent 47 modulo 60:   1/2 ( q-3 )
        q congruent 49 modulo 60:   1/2 ( q-5 )
        q congruent 53 modulo 60:   1/2 ( q-3 )
        q congruent 59 modulo 60:   1/2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 4, 68, 7, 8, 77, 30, 14, 83, 70, 19, 76, 97, 22, 23, 93, 62, 
  87, 40, 41, 92 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 8, 1, 1, 2 ], [ 9, 1, 1, 1 ] ]

    k = 2: F-action on Pi is (1,8)(3,7)(4,6)      [21,1,2]
      Dynkin type is ^2A_7(q) + T(phi2)
      Order of center |Z^F|: phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 phi1
        q congruent 2 modulo 60:   1/2 ( q-2 )
        q congruent 3 modulo 60:   1/2 phi1
        q congruent 4 modulo 60:   1/2 q
        q congruent 5 modulo 60:   1/2 ( q-3 )
        q congruent 7 modulo 60:   1/2 phi1
        q congruent 8 modulo 60:   1/2 ( q-2 )
        q congruent 9 modulo 60:   1/2 phi1
        q congruent 11 modulo 60:   1/2 ( q-3 )
        q congruent 13 modulo 60:   1/2 phi1
        q congruent 16 modulo 60:   1/2 q
        q congruent 17 modulo 60:   1/2 ( q-3 )
        q congruent 19 modulo 60:   1/2 phi1
        q congruent 21 modulo 60:   1/2 phi1
        q congruent 23 modulo 60:   1/2 ( q-3 )
        q congruent 25 modulo 60:   1/2 phi1
        q congruent 27 modulo 60:   1/2 phi1
        q congruent 29 modulo 60:   1/2 ( q-3 )
        q congruent 31 modulo 60:   1/2 phi1
        q congruent 32 modulo 60:   1/2 ( q-2 )
        q congruent 37 modulo 60:   1/2 phi1
        q congruent 41 modulo 60:   1/2 ( q-3 )
        q congruent 43 modulo 60:   1/2 phi1
        q congruent 47 modulo 60:   1/2 ( q-3 )
        q congruent 49 modulo 60:   1/2 phi1
        q congruent 53 modulo 60:   1/2 ( q-3 )
        q congruent 59 modulo 60:   1/2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 2, 67, 5, 69, 7, 9, 78, 31, 15, 84, 71, 20, 76, 98, 22, 24, 94, 63, 
  88, 40, 42, 92 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 1 ] ]

i = 22: Pi = [ 1, 3, 4, 5, 6, 8, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [22,1,1]
      Dynkin type is A_5(q) + A_2(q) + T(phi1)
      Order of center |Z^F|: phi1 times
        1, q congruent 0 modulo 3
        3, q congruent 1 modulo 3
        1, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 ( q-5 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   1/2 ( q-4 )
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1/2 ( q-5 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1/2 ( q-5 )
        q congruent 16 modulo 60:   1/2 ( q-4 )
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1/2 ( q-5 )
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1/2 ( q-5 )
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1/2 ( q-5 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/2 ( q-5 )
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1/2 ( q-5 )
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1/2 ( q-5 )
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 8, 66, 4, 77, 4, 68, 30, 68, 7, 81, 8, 77, 14, 77, 30, 83, 
  14, 83, 12, 70, 19, 97, 19, 76, 59, 23, 93, 62, 87, 40, 85 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], 
  [ 8, 1, 1, 4 ], [ 10, 1, 1, 2 ] ]

    k = 2: F-action on Pi is ()      [22,1,2]
      Dynkin type is A_5(q) + A_2(q) + T(phi2)
      Order of center |Z^F|: phi2 times
        1, q congruent 0 modulo 3
        3, q congruent 1 modulo 3
        1, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   1/2 q
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1/2 phi1
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1/2 phi1
        q congruent 16 modulo 60:   1/2 q
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1/2 phi1
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1/2 phi1
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1/2 phi1
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/2 phi1
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1/2 phi1
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1/2 phi1
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 77, 4, 68, 30, 68, 7, 81, 3, 69, 27, 77, 30, 83, 30, 81, 37, 
  83, 37, 79, 19, 76, 59, 72, 20, 95, 93, 50, 111, 35, 88, 34 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ] ]

    k = 3: F-action on Pi is (  1,  6)(  3,  5)(  8,240)      [22,1,3]
      Dynkin type is ^2A_5(q) + ^2A_2(q) + T(phi1)
      Order of center |Z^F|: phi1 times
        1, q congruent 0 modulo 3
        1, q congruent 1 modulo 3
        3, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   1/2 ( q-2 )
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/2 ( q-3 )
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   1/2 ( q-2 )
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1/2 ( q-3 )
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/2 ( q-3 )
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1/2 ( q-3 )
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1/2 ( q-3 )
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   1/2 ( q-2 )
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   1/2 ( q-3 )
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   1/2 ( q-3 )
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   1/2 ( q-3 )
        q congruent 59 modulo 60:   1/2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 5, 78, 5, 69, 31, 69, 7, 82, 3, 68, 28, 78, 31, 84, 31, 82, 38, 
  84, 38, 80, 20, 76, 60, 72, 19, 96, 94, 51, 112, 35, 87, 33 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], 
  [ 10, 1, 1, 2 ] ]

    k = 4: F-action on Pi is (  1,  6)(  3,  5)(  8,240)      [22,1,4]
      Dynkin type is ^2A_5(q) + ^2A_2(q) + T(phi2)
      Order of center |Z^F|: phi2 times
        1, q congruent 0 modulo 3
        1, q congruent 1 modulo 3
        3, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   1/2 ( q-2 )
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/2 ( q-3 )
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   1/2 ( q-2 )
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1/2 ( q-3 )
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/2 ( q-3 )
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1/2 ( q-3 )
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1/2 ( q-3 )
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   1/2 ( q-2 )
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   1/2 ( q-3 )
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   1/2 ( q-3 )
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   1/2 ( q-3 )
        q congruent 59 modulo 60:   1/2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 2, 67, 9, 67, 5, 78, 5, 69, 31, 69, 7, 82, 9, 78, 15, 78, 31, 84, 
  15, 84, 13, 71, 20, 98, 20, 76, 60, 24, 94, 63, 88, 40, 86 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], 
  [ 8, 1, 2, 4 ], [ 10, 1, 2, 2 ] ]

i = 23: Pi = [ 2, 3, 4, 5, 6, 7, 8 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [23,1,1]
      Dynkin type is D_7(q) + T(phi1)
      Order of center |Z^F|: phi1
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 ( q-3 )
        q congruent 2 modulo 60:   1/2 ( q-2 )
        q congruent 3 modulo 60:   1/2 ( q-3 )
        q congruent 4 modulo 60:   1/2 ( q-2 )
        q congruent 5 modulo 60:   1/2 ( q-3 )
        q congruent 7 modulo 60:   1/2 ( q-3 )
        q congruent 8 modulo 60:   1/2 ( q-2 )
        q congruent 9 modulo 60:   1/2 ( q-3 )
        q congruent 11 modulo 60:   1/2 ( q-3 )
        q congruent 13 modulo 60:   1/2 ( q-3 )
        q congruent 16 modulo 60:   1/2 ( q-2 )
        q congruent 17 modulo 60:   1/2 ( q-3 )
        q congruent 19 modulo 60:   1/2 ( q-3 )
        q congruent 21 modulo 60:   1/2 ( q-3 )
        q congruent 23 modulo 60:   1/2 ( q-3 )
        q congruent 25 modulo 60:   1/2 ( q-3 )
        q congruent 27 modulo 60:   1/2 ( q-3 )
        q congruent 29 modulo 60:   1/2 ( q-3 )
        q congruent 31 modulo 60:   1/2 ( q-3 )
        q congruent 32 modulo 60:   1/2 ( q-2 )
        q congruent 37 modulo 60:   1/2 ( q-3 )
        q congruent 41 modulo 60:   1/2 ( q-3 )
        q congruent 43 modulo 60:   1/2 ( q-3 )
        q congruent 47 modulo 60:   1/2 ( q-3 )
        q congruent 49 modulo 60:   1/2 ( q-3 )
        q congruent 53 modulo 60:   1/2 ( q-3 )
        q congruent 59 modulo 60:   1/2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 4, 3, 5, 66, 70, 68, 72, 69, 71, 4, 16, 19, 7, 18, 20, 68, 73, 
  76, 75, 8, 28, 30, 31, 27, 77, 96, 82, 97, 81, 98, 30, 60, 53, 14, 38, 36, 
  70, 89, 76, 90, 19, 44, 43, 22, 97, 110, 23, 51, 50, 93, 108, 87, 100, 41 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 9, 1, 1, 1 ] ]

    k = 2: F-action on Pi is (2,3)      [23,1,2]
      Dynkin type is ^2D_7(q) + T(phi2)
      Order of center |Z^F|: phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 phi1
        q congruent 2 modulo 60:   1/2 q
        q congruent 3 modulo 60:   1/2 phi1
        q congruent 4 modulo 60:   1/2 q
        q congruent 5 modulo 60:   1/2 phi1
        q congruent 7 modulo 60:   1/2 phi1
        q congruent 8 modulo 60:   1/2 q
        q congruent 9 modulo 60:   1/2 phi1
        q congruent 11 modulo 60:   1/2 phi1
        q congruent 13 modulo 60:   1/2 phi1
        q congruent 16 modulo 60:   1/2 q
        q congruent 17 modulo 60:   1/2 phi1
        q congruent 19 modulo 60:   1/2 phi1
        q congruent 21 modulo 60:   1/2 phi1
        q congruent 23 modulo 60:   1/2 phi1
        q congruent 25 modulo 60:   1/2 phi1
        q congruent 27 modulo 60:   1/2 phi1
        q congruent 29 modulo 60:   1/2 phi1
        q congruent 31 modulo 60:   1/2 phi1
        q congruent 32 modulo 60:   1/2 q
        q congruent 37 modulo 60:   1/2 phi1
        q congruent 41 modulo 60:   1/2 phi1
        q congruent 43 modulo 60:   1/2 phi1
        q congruent 47 modulo 60:   1/2 phi1
        q congruent 49 modulo 60:   1/2 phi1
        q congruent 53 modulo 60:   1/2 phi1
        q congruent 59 modulo 60:   1/2 phi1
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 3, 5, 2, 70, 68, 72, 69, 71, 67, 19, 7, 18, 20, 5, 17, 76, 75, 
  69, 74, 28, 30, 31, 27, 9, 82, 97, 81, 98, 78, 95, 31, 59, 54, 36, 37, 15, 
  89, 76, 90, 71, 43, 22, 20, 45, 109, 98, 51, 50, 24, 94, 107, 100, 88, 42 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 9, 1, 1, 1 ] ]

i = 24: Pi = [ 2, 3, 4, 5, 6, 7, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [24,1,1]
      Dynkin type is D_6(q) + A_1(q) + T(phi1)
      Order of center |Z^F|: phi1 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/2 ( q-3 )
        q congruent 7 modulo 60:   1/2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/2 ( q-3 )
        q congruent 11 modulo 60:   1/2 ( q-3 )
        q congruent 13 modulo 60:   1/2 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/2 ( q-3 )
        q congruent 19 modulo 60:   1/2 ( q-3 )
        q congruent 21 modulo 60:   1/2 ( q-3 )
        q congruent 23 modulo 60:   1/2 ( q-3 )
        q congruent 25 modulo 60:   1/2 ( q-3 )
        q congruent 27 modulo 60:   1/2 ( q-3 )
        q congruent 29 modulo 60:   1/2 ( q-3 )
        q congruent 31 modulo 60:   1/2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/2 ( q-3 )
        q congruent 41 modulo 60:   1/2 ( q-3 )
        q congruent 43 modulo 60:   1/2 ( q-3 )
        q congruent 47 modulo 60:   1/2 ( q-3 )
        q congruent 49 modulo 60:   1/2 ( q-3 )
        q congruent 53 modulo 60:   1/2 ( q-3 )
        q congruent 59 modulo 60:   1/2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 4, 68, 3, 69, 5, 67, 66, 4, 70, 19, 68, 7, 72, 20, 69, 5, 4, 
  68, 16, 73, 19, 76, 7, 69, 18, 74, 68, 3, 68, 7, 73, 18, 8, 77, 28, 82, 30, 
  81, 31, 78, 77, 30, 96, 60, 82, 31, 97, 59, 14, 83, 38, 84, 70, 19, 89, 43, 
  76, 20, 19, 72, 19, 76, 44, 91, 23, 93, 51, 94, 87, 35, 87, 40 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ] ]

    k = 2: F-action on Pi is ()      [24,1,2]
      Dynkin type is D_6(q) + A_1(q) + T(phi2)
      Order of center |Z^F|: phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/2 phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/2 phi1
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/2 phi1
        q congruent 7 modulo 60:   1/2 phi1
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/2 phi1
        q congruent 11 modulo 60:   1/2 phi1
        q congruent 13 modulo 60:   1/2 phi1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/2 phi1
        q congruent 19 modulo 60:   1/2 phi1
        q congruent 21 modulo 60:   1/2 phi1
        q congruent 23 modulo 60:   1/2 phi1
        q congruent 25 modulo 60:   1/2 phi1
        q congruent 27 modulo 60:   1/2 phi1
        q congruent 29 modulo 60:   1/2 phi1
        q congruent 31 modulo 60:   1/2 phi1
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/2 phi1
        q congruent 41 modulo 60:   1/2 phi1
        q congruent 43 modulo 60:   1/2 phi1
        q congruent 47 modulo 60:   1/2 phi1
        q congruent 49 modulo 60:   1/2 phi1
        q congruent 53 modulo 60:   1/2 phi1
        q congruent 59 modulo 60:   1/2 phi1
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 68, 3, 69, 5, 67, 2, 4, 68, 19, 72, 7, 69, 20, 71, 5, 67, 
  68, 7, 73, 18, 76, 20, 69, 5, 74, 17, 7, 69, 3, 69, 18, 74, 77, 30, 82, 31, 
  81, 27, 78, 9, 30, 81, 60, 98, 31, 78, 59, 95, 83, 37, 84, 15, 19, 76, 43, 
  90, 20, 71, 76, 20, 72, 20, 91, 45, 93, 50, 94, 24, 40, 88, 35, 88 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ] ]

i = 25: Pi = [ 2, 3, 4, 5, 7, 8, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [25,1,1]
      Dynkin type is D_4(q) + A_3(q) + T(phi1)
      Order of center |Z^F|: phi1 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 ( q-5 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 ( q-5 )
        q congruent 7 modulo 60:   1/4 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4 ( q-5 )
        q congruent 11 modulo 60:   1/4 ( q-3 )
        q congruent 13 modulo 60:   1/4 ( q-5 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 ( q-5 )
        q congruent 19 modulo 60:   1/4 ( q-3 )
        q congruent 21 modulo 60:   1/4 ( q-5 )
        q congruent 23 modulo 60:   1/4 ( q-3 )
        q congruent 25 modulo 60:   1/4 ( q-5 )
        q congruent 27 modulo 60:   1/4 ( q-3 )
        q congruent 29 modulo 60:   1/4 ( q-5 )
        q congruent 31 modulo 60:   1/4 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 ( q-5 )
        q congruent 41 modulo 60:   1/4 ( q-5 )
        q congruent 43 modulo 60:   1/4 ( q-3 )
        q congruent 47 modulo 60:   1/4 ( q-3 )
        q congruent 49 modulo 60:   1/4 ( q-5 )
        q congruent 53 modulo 60:   1/4 ( q-5 )
        q congruent 59 modulo 60:   1/4 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 4, 8, 70, 4, 68, 7, 30, 76, 3, 69, 5, 27, 71, 66, 4, 68, 77, 
  19, 70, 19, 76, 97, 22, 68, 7, 69, 81, 20, 4, 68, 3, 30, 72, 4, 68, 7, 30, 
  76, 16, 73, 18, 53, 75, 8, 77, 30, 14, 97, 28, 82, 31, 36, 98, 70, 19, 72, 
  97, 18, 70, 19, 76, 97, 22 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 3 ], [ 23, 1, 1, 2 ] ]

    k = 2: F-action on Pi is (  2,  5)(  7,240)      [25,1,2]
      Dynkin type is ^2D_4(q) + ^2A_3(q) + T(phi1)
      Order of center |Z^F|: phi1 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 phi1
        q congruent 7 modulo 60:   1/4 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4 phi1
        q congruent 11 modulo 60:   1/4 ( q-3 )
        q congruent 13 modulo 60:   1/4 phi1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 phi1
        q congruent 19 modulo 60:   1/4 ( q-3 )
        q congruent 21 modulo 60:   1/4 phi1
        q congruent 23 modulo 60:   1/4 ( q-3 )
        q congruent 25 modulo 60:   1/4 phi1
        q congruent 27 modulo 60:   1/4 ( q-3 )
        q congruent 29 modulo 60:   1/4 phi1
        q congruent 31 modulo 60:   1/4 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 phi1
        q congruent 41 modulo 60:   1/4 phi1
        q congruent 43 modulo 60:   1/4 ( q-3 )
        q congruent 47 modulo 60:   1/4 ( q-3 )
        q congruent 49 modulo 60:   1/4 phi1
        q congruent 53 modulo 60:   1/4 phi1
        q congruent 59 modulo 60:   1/4 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 68, 4, 28, 70, 5, 69, 3, 31, 72, 72, 19, 70, 96, 16, 69, 7, 68, 
  82, 19, 71, 20, 72, 98, 18, 20, 76, 19, 60, 73, 31, 82, 28, 38, 96, 27, 81, 
  30, 36, 97, 90, 43, 89, 110, 44 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 23, 1, 1, 2 ] ]

    k = 3: F-action on Pi is (  7,240)      [25,1,3]
      Dynkin type is D_4(q) + ^2A_3(q) + T(phi2)
      Order of center |Z^F|: phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 phi1
        q congruent 7 modulo 60:   1/4 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4 phi1
        q congruent 11 modulo 60:   1/4 ( q-3 )
        q congruent 13 modulo 60:   1/4 phi1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 phi1
        q congruent 19 modulo 60:   1/4 ( q-3 )
        q congruent 21 modulo 60:   1/4 phi1
        q congruent 23 modulo 60:   1/4 ( q-3 )
        q congruent 25 modulo 60:   1/4 phi1
        q congruent 27 modulo 60:   1/4 ( q-3 )
        q congruent 29 modulo 60:   1/4 phi1
        q congruent 31 modulo 60:   1/4 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 phi1
        q congruent 41 modulo 60:   1/4 phi1
        q congruent 43 modulo 60:   1/4 ( q-3 )
        q congruent 47 modulo 60:   1/4 ( q-3 )
        q congruent 49 modulo 60:   1/4 phi1
        q congruent 53 modulo 60:   1/4 phi1
        q congruent 59 modulo 60:   1/4 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 68, 4, 28, 70, 5, 69, 7, 31, 76, 2, 67, 5, 9, 71, 69, 7, 68, 82, 
  19, 71, 20, 76, 98, 22, 67, 5, 69, 78, 20, 5, 69, 3, 31, 72, 5, 69, 7, 31, 
  76, 17, 74, 18, 54, 75, 27, 81, 30, 36, 97, 9, 78, 31, 15, 98, 71, 20, 72, 
  98, 18, 71, 20, 76, 98, 22 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 3 ], [ 23, 1, 2, 2 ] ]

    k = 4: F-action on Pi is (2,5)      [25,1,4]
      Dynkin type is ^2D_4(q) + A_3(q) + T(phi2)
      Order of center |Z^F|: phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 phi1
        q congruent 7 modulo 60:   1/4 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4 phi1
        q congruent 11 modulo 60:   1/4 phi2
        q congruent 13 modulo 60:   1/4 phi1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 phi1
        q congruent 19 modulo 60:   1/4 phi2
        q congruent 21 modulo 60:   1/4 phi1
        q congruent 23 modulo 60:   1/4 phi2
        q congruent 25 modulo 60:   1/4 phi1
        q congruent 27 modulo 60:   1/4 phi2
        q congruent 29 modulo 60:   1/4 phi1
        q congruent 31 modulo 60:   1/4 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 phi1
        q congruent 41 modulo 60:   1/4 phi1
        q congruent 43 modulo 60:   1/4 phi2
        q congruent 47 modulo 60:   1/4 phi2
        q congruent 49 modulo 60:   1/4 phi1
        q congruent 53 modulo 60:   1/4 phi1
        q congruent 59 modulo 60:   1/4 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 68, 3, 30, 72, 3, 69, 5, 27, 71, 70, 19, 72, 97, 18, 68, 7, 69, 
  81, 20, 72, 20, 71, 95, 17, 19, 76, 20, 59, 74, 28, 82, 31, 36, 98, 30, 81, 
  27, 37, 95, 89, 43, 90, 109, 45 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 23, 1, 2, 2 ] ]

i = 26: Pi = [ 2, 4, 5, 6, 7, 8, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [26,1,1]
      Dynkin type is A_7(q) + T(phi1)
      Order of center |Z^F|: phi1 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 ( q-5 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 ( q-5 )
        q congruent 7 modulo 60:   1/4 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4 ( q-5 )
        q congruent 11 modulo 60:   1/4 ( q-3 )
        q congruent 13 modulo 60:   1/4 ( q-5 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 ( q-5 )
        q congruent 19 modulo 60:   1/4 ( q-3 )
        q congruent 21 modulo 60:   1/4 ( q-5 )
        q congruent 23 modulo 60:   1/4 ( q-3 )
        q congruent 25 modulo 60:   1/4 ( q-5 )
        q congruent 27 modulo 60:   1/4 ( q-3 )
        q congruent 29 modulo 60:   1/4 ( q-5 )
        q congruent 31 modulo 60:   1/4 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 ( q-5 )
        q congruent 41 modulo 60:   1/4 ( q-5 )
        q congruent 43 modulo 60:   1/4 ( q-3 )
        q congruent 47 modulo 60:   1/4 ( q-3 )
        q congruent 49 modulo 60:   1/4 ( q-5 )
        q congruent 53 modulo 60:   1/4 ( q-5 )
        q congruent 59 modulo 60:   1/4 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 4, 68, 3, 8, 77, 30, 14, 83, 70, 19, 72, 97, 18, 23, 93, 62, 
  87, 35, 41, 91 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 9, 1, 1, 2 ], 
  [ 10, 1, 1, 2 ] ]

    k = 2: F-action on Pi is (  2,240)(  4,  8)(  5,  7)      [26,1,2]
      Dynkin type is ^2A_7(q) + T(phi1)
      Order of center |Z^F|: phi1 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 phi1
        q congruent 7 modulo 60:   1/4 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4 phi1
        q congruent 11 modulo 60:   1/4 ( q-3 )
        q congruent 13 modulo 60:   1/4 phi1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 phi1
        q congruent 19 modulo 60:   1/4 ( q-3 )
        q congruent 21 modulo 60:   1/4 phi1
        q congruent 23 modulo 60:   1/4 ( q-3 )
        q congruent 25 modulo 60:   1/4 phi1
        q congruent 27 modulo 60:   1/4 ( q-3 )
        q congruent 29 modulo 60:   1/4 phi1
        q congruent 31 modulo 60:   1/4 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 phi1
        q congruent 41 modulo 60:   1/4 phi1
        q congruent 43 modulo 60:   1/4 ( q-3 )
        q congruent 47 modulo 60:   1/4 ( q-3 )
        q congruent 49 modulo 60:   1/4 phi1
        q congruent 53 modulo 60:   1/4 phi1
        q congruent 59 modulo 60:   1/4 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 5, 69, 7, 68, 78, 31, 82, 84, 38, 20, 76, 19, 60, 73, 94, 51, 
  112, 40, 87, 104, 44 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 2, 2 ], [ 10, 1, 1, 2 ] ]

    k = 3: F-action on Pi is ()      [26,1,3]
      Dynkin type is A_7(q) + T(phi2)
      Order of center |Z^F|: phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 phi1
        q congruent 7 modulo 60:   1/4 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4 phi1
        q congruent 11 modulo 60:   1/4 phi2
        q congruent 13 modulo 60:   1/4 phi1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 phi1
        q congruent 19 modulo 60:   1/4 phi2
        q congruent 21 modulo 60:   1/4 phi1
        q congruent 23 modulo 60:   1/4 phi2
        q congruent 25 modulo 60:   1/4 phi1
        q congruent 27 modulo 60:   1/4 phi2
        q congruent 29 modulo 60:   1/4 phi1
        q congruent 31 modulo 60:   1/4 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 phi1
        q congruent 41 modulo 60:   1/4 phi1
        q congruent 43 modulo 60:   1/4 phi2
        q congruent 47 modulo 60:   1/4 phi2
        q congruent 49 modulo 60:   1/4 phi1
        q congruent 53 modulo 60:   1/4 phi1
        q congruent 59 modulo 60:   1/4 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 68, 7, 69, 77, 30, 81, 83, 37, 19, 76, 20, 59, 74, 93, 50, 
  111, 40, 88, 103, 45 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 10, 1, 2, 2 ] ]

    k = 4: F-action on Pi is (  2,240)(  4,  8)(  5,  7)      [26,1,4]
      Dynkin type is ^2A_7(q) + T(phi2)
      Order of center |Z^F|: phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 phi1
        q congruent 7 modulo 60:   1/4 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4 phi1
        q congruent 11 modulo 60:   1/4 ( q-3 )
        q congruent 13 modulo 60:   1/4 phi1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 phi1
        q congruent 19 modulo 60:   1/4 ( q-3 )
        q congruent 21 modulo 60:   1/4 phi1
        q congruent 23 modulo 60:   1/4 ( q-3 )
        q congruent 25 modulo 60:   1/4 phi1
        q congruent 27 modulo 60:   1/4 ( q-3 )
        q congruent 29 modulo 60:   1/4 phi1
        q congruent 31 modulo 60:   1/4 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 phi1
        q congruent 41 modulo 60:   1/4 phi1
        q congruent 43 modulo 60:   1/4 ( q-3 )
        q congruent 47 modulo 60:   1/4 ( q-3 )
        q congruent 49 modulo 60:   1/4 phi1
        q congruent 53 modulo 60:   1/4 phi1
        q congruent 59 modulo 60:   1/4 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 2, 67, 5, 69, 3, 9, 78, 31, 15, 84, 71, 20, 72, 98, 18, 24, 94, 63, 
  88, 35, 42, 91 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 2, 2 ], [ 9, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ] ]

i = 27: Pi = [ 1, 2, 3, 4, 5, 6 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [27,1,1]
      Dynkin type is E_6(q) + T(phi1^2)
      Order of center |Z^F|: phi1^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 ( q^2-8*q+19 )
        q congruent 2 modulo 60:   1/12 ( q^2-8*q+12 )
        q congruent 3 modulo 60:   1/12 ( q^2-8*q+15 )
        q congruent 4 modulo 60:   1/12 ( q^2-8*q+16 )
        q congruent 5 modulo 60:   1/12 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/12 ( q^2-8*q+19 )
        q congruent 8 modulo 60:   1/12 ( q^2-8*q+12 )
        q congruent 9 modulo 60:   1/12 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/12 ( q^2-8*q+15 )
        q congruent 13 modulo 60:   1/12 ( q^2-8*q+19 )
        q congruent 16 modulo 60:   1/12 ( q^2-8*q+16 )
        q congruent 17 modulo 60:   1/12 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/12 ( q^2-8*q+19 )
        q congruent 21 modulo 60:   1/12 ( q^2-8*q+15 )
        q congruent 23 modulo 60:   1/12 ( q^2-8*q+15 )
        q congruent 25 modulo 60:   1/12 ( q^2-8*q+19 )
        q congruent 27 modulo 60:   1/12 ( q^2-8*q+15 )
        q congruent 29 modulo 60:   1/12 ( q^2-8*q+15 )
        q congruent 31 modulo 60:   1/12 ( q^2-8*q+19 )
        q congruent 32 modulo 60:   1/12 ( q^2-8*q+12 )
        q congruent 37 modulo 60:   1/12 ( q^2-8*q+19 )
        q congruent 41 modulo 60:   1/12 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/12 ( q^2-8*q+19 )
        q congruent 47 modulo 60:   1/12 ( q^2-8*q+15 )
        q congruent 49 modulo 60:   1/12 ( q^2-8*q+19 )
        q congruent 53 modulo 60:   1/12 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/12 ( q^2-8*q+15 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 3, 4, 12, 8, 14, 16, 19, 23, 33, 28, 35, 30, 46, 57, 66, 68, 72, 
  70, 77, 83, 87, 89, 93, 96 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 10, 1, 1, 6 ], 
  [ 11, 1, 1, 6 ] ]

    k = 2: F-action on Pi is ()      [27,1,2]
      Dynkin type is E_6(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1^2
        q congruent 2 modulo 60:   1/4 q ( q-2 )
        q congruent 3 modulo 60:   1/4 phi1^2
        q congruent 4 modulo 60:   1/4 q ( q-2 )
        q congruent 5 modulo 60:   1/4 phi1^2
        q congruent 7 modulo 60:   1/4 phi1^2
        q congruent 8 modulo 60:   1/4 q ( q-2 )
        q congruent 9 modulo 60:   1/4 phi1^2
        q congruent 11 modulo 60:   1/4 phi1^2
        q congruent 13 modulo 60:   1/4 phi1^2
        q congruent 16 modulo 60:   1/4 q ( q-2 )
        q congruent 17 modulo 60:   1/4 phi1^2
        q congruent 19 modulo 60:   1/4 phi1^2
        q congruent 21 modulo 60:   1/4 phi1^2
        q congruent 23 modulo 60:   1/4 phi1^2
        q congruent 25 modulo 60:   1/4 phi1^2
        q congruent 27 modulo 60:   1/4 phi1^2
        q congruent 29 modulo 60:   1/4 phi1^2
        q congruent 31 modulo 60:   1/4 phi1^2
        q congruent 32 modulo 60:   1/4 q ( q-2 )
        q congruent 37 modulo 60:   1/4 phi1^2
        q congruent 41 modulo 60:   1/4 phi1^2
        q congruent 43 modulo 60:   1/4 phi1^2
        q congruent 47 modulo 60:   1/4 phi1^2
        q congruent 49 modulo 60:   1/4 phi1^2
        q congruent 53 modulo 60:   1/4 phi1^2
        q congruent 59 modulo 60:   1/4 phi1^2
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 69, 68, 79, 77, 83, 73, 76, 93, 86, 82, 88, 81, 105, 101, 4, 7, 
  20, 19, 30, 37, 40, 43, 50, 60 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 10, 1, 2, 2 ], 
  [ 11, 1, 1, 2 ] ]

    k = 3: F-action on Pi is (1,6)(3,5)      [27,1,3]
      Dynkin type is ^2E_6(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1^2
        q congruent 2 modulo 60:   1/4 q ( q-2 )
        q congruent 3 modulo 60:   1/4 phi1^2
        q congruent 4 modulo 60:   1/4 q ( q-2 )
        q congruent 5 modulo 60:   1/4 phi1^2
        q congruent 7 modulo 60:   1/4 phi1^2
        q congruent 8 modulo 60:   1/4 q ( q-2 )
        q congruent 9 modulo 60:   1/4 phi1^2
        q congruent 11 modulo 60:   1/4 phi1^2
        q congruent 13 modulo 60:   1/4 phi1^2
        q congruent 16 modulo 60:   1/4 q ( q-2 )
        q congruent 17 modulo 60:   1/4 phi1^2
        q congruent 19 modulo 60:   1/4 phi1^2
        q congruent 21 modulo 60:   1/4 phi1^2
        q congruent 23 modulo 60:   1/4 phi1^2
        q congruent 25 modulo 60:   1/4 phi1^2
        q congruent 27 modulo 60:   1/4 phi1^2
        q congruent 29 modulo 60:   1/4 phi1^2
        q congruent 31 modulo 60:   1/4 phi1^2
        q congruent 32 modulo 60:   1/4 q ( q-2 )
        q congruent 37 modulo 60:   1/4 phi1^2
        q congruent 41 modulo 60:   1/4 phi1^2
        q congruent 43 modulo 60:   1/4 phi1^2
        q congruent 47 modulo 60:   1/4 phi1^2
        q congruent 49 modulo 60:   1/4 phi1^2
        q congruent 53 modulo 60:   1/4 phi1^2
        q congruent 59 modulo 60:   1/4 phi1^2
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 68, 69, 80, 78, 84, 74, 76, 94, 85, 81, 87, 82, 106, 102, 5, 7, 
  19, 20, 31, 38, 40, 43, 51, 59 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 10, 1, 1, 2 ], 
  [ 11, 1, 2, 2 ] ]

    k = 4: F-action on Pi is (1,6)(3,5)      [27,1,4]
      Dynkin type is ^2E_6(q) + T(phi6)
      Order of center |Z^F|: phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/6 q phi1
        q congruent 2 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 3 modulo 60:   1/6 q phi1
        q congruent 4 modulo 60:   1/6 q phi1
        q congruent 5 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 7 modulo 60:   1/6 q phi1
        q congruent 8 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 9 modulo 60:   1/6 q phi1
        q congruent 11 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 13 modulo 60:   1/6 q phi1
        q congruent 16 modulo 60:   1/6 q phi1
        q congruent 17 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 19 modulo 60:   1/6 q phi1
        q congruent 21 modulo 60:   1/6 q phi1
        q congruent 23 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 25 modulo 60:   1/6 q phi1
        q congruent 27 modulo 60:   1/6 q phi1
        q congruent 29 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 31 modulo 60:   1/6 q phi1
        q congruent 32 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 37 modulo 60:   1/6 q phi1
        q congruent 41 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 43 modulo 60:   1/6 q phi1
        q congruent 47 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 49 modulo 60:   1/6 q phi1
        q congruent 53 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 59 modulo 60:   1/6 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 9, 28, 31, 11, 15, 13, 54, 60, 63, 29, 36, 33, 38, 49, 56, 78, 82, 
  96, 98, 84, 80, 86, 110, 112, 99 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ] ]

    k = 5: F-action on Pi is ()      [27,1,5]
      Dynkin type is E_6(q) + T(phi3)
      Order of center |Z^F|: phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 2 modulo 60:   1/6 q phi2
        q congruent 3 modulo 60:   1/6 q phi2
        q congruent 4 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 5 modulo 60:   1/6 q phi2
        q congruent 7 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 8 modulo 60:   1/6 q phi2
        q congruent 9 modulo 60:   1/6 q phi2
        q congruent 11 modulo 60:   1/6 q phi2
        q congruent 13 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 16 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 17 modulo 60:   1/6 q phi2
        q congruent 19 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 21 modulo 60:   1/6 q phi2
        q congruent 23 modulo 60:   1/6 q phi2
        q congruent 25 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 27 modulo 60:   1/6 q phi2
        q congruent 29 modulo 60:   1/6 q phi2
        q congruent 31 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 32 modulo 60:   1/6 q phi2
        q congruent 37 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 41 modulo 60:   1/6 q phi2
        q congruent 43 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 47 modulo 60:   1/6 q phi2
        q congruent 49 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 53 modulo 60:   1/6 q phi2
        q congruent 59 modulo 60:   1/6 q phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 8, 27, 30, 10, 14, 12, 53, 59, 62, 29, 36, 34, 37, 48, 55, 77, 81, 
  95, 97, 83, 79, 85, 109, 111, 99 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ] ]

    k = 6: F-action on Pi is (1,6)(3,5)      [27,1,6]
      Dynkin type is ^2E_6(q) + T(phi2^2)
      Order of center |Z^F|: phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 2 modulo 60:   1/12 ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 4 modulo 60:   1/12 q ( q-4 )
        q congruent 5 modulo 60:   1/12 ( q^2-4*q+7 )
        q congruent 7 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 8 modulo 60:   1/12 ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 11 modulo 60:   1/12 ( q^2-4*q+7 )
        q congruent 13 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 16 modulo 60:   1/12 q ( q-4 )
        q congruent 17 modulo 60:   1/12 ( q^2-4*q+7 )
        q congruent 19 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 21 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 23 modulo 60:   1/12 ( q^2-4*q+7 )
        q congruent 25 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 27 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 29 modulo 60:   1/12 ( q^2-4*q+7 )
        q congruent 31 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 32 modulo 60:   1/12 ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 41 modulo 60:   1/12 ( q^2-4*q+7 )
        q congruent 43 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 47 modulo 60:   1/12 ( q^2-4*q+7 )
        q congruent 49 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 53 modulo 60:   1/12 ( q^2-4*q+7 )
        q congruent 59 modulo 60:   1/12 ( q^2-4*q+7 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 2, 3, 5, 13, 9, 15, 17, 20, 24, 34, 27, 35, 31, 47, 58, 67, 69, 72, 
  71, 78, 84, 88, 90, 94, 95 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 10, 1, 2, 6 ], 
  [ 11, 1, 2, 6 ] ]

i = 28: Pi = [ 1, 2, 3, 4, 5, 7 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [28,1,1]
      Dynkin type is D_5(q) + A_1(q) + T(phi1^2)
      Order of center |Z^F|: phi1^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 ( q^2-10*q+29 )
        q congruent 2 modulo 60:   1/4 ( q^2-8*q+12 )
        q congruent 3 modulo 60:   1/4 ( q^2-10*q+21 )
        q congruent 4 modulo 60:   1/4 ( q^2-8*q+16 )
        q congruent 5 modulo 60:   1/4 ( q^2-10*q+25 )
        q congruent 7 modulo 60:   1/4 ( q^2-10*q+25 )
        q congruent 8 modulo 60:   1/4 ( q^2-8*q+12 )
        q congruent 9 modulo 60:   1/4 ( q^2-10*q+25 )
        q congruent 11 modulo 60:   1/4 ( q^2-10*q+21 )
        q congruent 13 modulo 60:   1/4 ( q^2-10*q+29 )
        q congruent 16 modulo 60:   1/4 ( q^2-8*q+16 )
        q congruent 17 modulo 60:   1/4 ( q^2-10*q+25 )
        q congruent 19 modulo 60:   1/4 ( q^2-10*q+25 )
        q congruent 21 modulo 60:   1/4 ( q^2-10*q+25 )
        q congruent 23 modulo 60:   1/4 ( q^2-10*q+21 )
        q congruent 25 modulo 60:   1/4 ( q^2-10*q+29 )
        q congruent 27 modulo 60:   1/4 ( q^2-10*q+21 )
        q congruent 29 modulo 60:   1/4 ( q^2-10*q+25 )
        q congruent 31 modulo 60:   1/4 ( q^2-10*q+25 )
        q congruent 32 modulo 60:   1/4 ( q^2-8*q+12 )
        q congruent 37 modulo 60:   1/4 ( q^2-10*q+29 )
        q congruent 41 modulo 60:   1/4 ( q^2-10*q+25 )
        q congruent 43 modulo 60:   1/4 ( q^2-10*q+25 )
        q congruent 47 modulo 60:   1/4 ( q^2-10*q+21 )
        q congruent 49 modulo 60:   1/4 ( q^2-10*q+29 )
        q congruent 53 modulo 60:   1/4 ( q^2-10*q+25 )
        q congruent 59 modulo 60:   1/4 ( q^2-10*q+21 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 4, 68, 3, 69, 66, 4, 70, 19, 68, 7, 72, 20, 4, 68, 16, 73, 
  19, 76, 8, 77, 28, 82, 30, 81, 77, 30, 96, 60, 70, 19, 89, 43, 23, 93 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], 
  [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], 
  [ 13, 1, 1, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 2 ] ]

    k = 2: F-action on Pi is ()      [28,1,2]
      Dynkin type is D_5(q) + A_1(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 2 modulo 60:   1/4 q ( q-2 )
        q congruent 3 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 4 modulo 60:   1/4 q ( q-2 )
        q congruent 5 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 7 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 8 modulo 60:   1/4 q ( q-2 )
        q congruent 9 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 11 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 16 modulo 60:   1/4 q ( q-2 )
        q congruent 17 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 19 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 23 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 27 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 29 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 31 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 32 modulo 60:   1/4 q ( q-2 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 41 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 43 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 47 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 53 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 59 modulo 60:   1/4 phi1 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 68, 3, 69, 5, 4, 68, 19, 72, 7, 69, 20, 71, 68, 7, 73, 18, 
  76, 20, 77, 30, 82, 31, 81, 27, 30, 81, 60, 98, 19, 76, 43, 90, 93, 50 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 2, 2 ], [ 13, 1, 1, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 2, 2 ] ]

    k = 3: F-action on Pi is (2,5)      [28,1,3]
      Dynkin type is ^2D_5(q) + A_1(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 2 modulo 60:   1/4 q ( q-2 )
        q congruent 3 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 4 modulo 60:   1/4 q ( q-2 )
        q congruent 5 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 7 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 8 modulo 60:   1/4 q ( q-2 )
        q congruent 9 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 11 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 16 modulo 60:   1/4 q ( q-2 )
        q congruent 17 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 19 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 23 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 27 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 29 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 31 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 32 modulo 60:   1/4 q ( q-2 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 41 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 43 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 47 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 53 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 59 modulo 60:   1/4 phi1 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 68, 3, 69, 5, 67, 70, 19, 68, 7, 72, 20, 69, 5, 19, 76, 7, 69, 
  18, 74, 28, 82, 30, 81, 31, 78, 82, 31, 97, 59, 89, 43, 76, 20, 51, 94 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 1, 2 ], [ 13, 1, 4, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ] ]

    k = 4: F-action on Pi is (2,5)      [28,1,4]
      Dynkin type is ^2D_5(q) + A_1(q) + T(phi2^2)
      Order of center |Z^F|: phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 2 modulo 60:   1/4 ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 4 modulo 60:   1/4 q ( q-4 )
        q congruent 5 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 7 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 8 modulo 60:   1/4 ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 11 modulo 60:   1/4 ( q^2-6*q+13 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 16 modulo 60:   1/4 q ( q-4 )
        q congruent 17 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 19 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 23 modulo 60:   1/4 ( q^2-6*q+13 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 27 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 31 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 32 modulo 60:   1/4 ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 41 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 43 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 47 modulo 60:   1/4 ( q^2-6*q+13 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 53 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 59 modulo 60:   1/4 ( q^2-6*q+13 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 3, 69, 5, 67, 2, 19, 72, 7, 69, 20, 71, 5, 67, 76, 20, 69, 5, 
  74, 17, 82, 31, 81, 27, 78, 9, 31, 78, 59, 95, 43, 90, 20, 71, 94, 24 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 2 ], 
  [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], 
  [ 13, 1, 4, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 2, 2 ] ]

i = 29: Pi = [ 1, 2, 3, 4, 6, 7 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [29,1,1]
      Dynkin type is A_4(q) + A_2(q) + T(phi1^2)
      Order of center |Z^F|: phi1^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 ( q^2-13*q+56 )
        q congruent 2 modulo 60:   1/4 ( q^2-10*q+16 )
        q congruent 3 modulo 60:   1/4 ( q^2-11*q+24 )
        q congruent 4 modulo 60:   1/4 ( q^2-12*q+32 )
        q congruent 5 modulo 60:   1/4 ( q^2-11*q+30 )
        q congruent 7 modulo 60:   1/4 ( q^2-13*q+42 )
        q congruent 8 modulo 60:   1/4 ( q^2-10*q+16 )
        q congruent 9 modulo 60:   1/4 ( q^2-11*q+30 )
        q congruent 11 modulo 60:   1/4 ( q^2-11*q+32 )
        q congruent 13 modulo 60:   1/4 ( q^2-13*q+48 )
        q congruent 16 modulo 60:   1/4 ( q^2-12*q+40 )
        q congruent 17 modulo 60:   1/4 ( q^2-11*q+30 )
        q congruent 19 modulo 60:   1/4 ( q^2-13*q+42 )
        q congruent 21 modulo 60:   1/4 ( q^2-11*q+38 )
        q congruent 23 modulo 60:   1/4 ( q^2-11*q+24 )
        q congruent 25 modulo 60:   1/4 ( q^2-13*q+48 )
        q congruent 27 modulo 60:   1/4 ( q^2-11*q+24 )
        q congruent 29 modulo 60:   1/4 ( q^2-11*q+30 )
        q congruent 31 modulo 60:   1/4 ( q^2-13*q+50 )
        q congruent 32 modulo 60:   1/4 ( q^2-10*q+16 )
        q congruent 37 modulo 60:   1/4 ( q^2-13*q+48 )
        q congruent 41 modulo 60:   1/4 ( q^2-11*q+38 )
        q congruent 43 modulo 60:   1/4 ( q^2-13*q+42 )
        q congruent 47 modulo 60:   1/4 ( q^2-11*q+24 )
        q congruent 49 modulo 60:   1/4 ( q^2-13*q+48 )
        q congruent 53 modulo 60:   1/4 ( q^2-11*q+30 )
        q congruent 59 modulo 60:   1/4 ( q^2-11*q+24 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 8, 66, 4, 77, 4, 68, 30, 8, 77, 14, 77, 30, 83, 70, 19, 97, 
  23, 93, 62 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], 
  [ 5, 1, 1, 4 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 4 ], 
  [ 9, 1, 1, 2 ], [ 10, 1, 1, 2 ], [ 12, 1, 1, 4 ], [ 14, 1, 1, 4 ], 
  [ 15, 1, 1, 2 ], [ 21, 1, 1, 4 ], [ 22, 1, 1, 4 ], [ 26, 1, 1, 4 ] ]

    k = 2: F-action on Pi is ()      [29,1,2]
      Dynkin type is A_4(q) + A_2(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-4 )
        q congruent 2 modulo 60:   1/4 q ( q-2 )
        q congruent 3 modulo 60:   1/4 q ( q-3 )
        q congruent 4 modulo 60:   1/4 q ( q-4 )
        q congruent 5 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 7 modulo 60:   1/4 ( q^2-5*q+2 )
        q congruent 8 modulo 60:   1/4 q ( q-2 )
        q congruent 9 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 11 modulo 60:   1/4 q ( q-3 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-4 )
        q congruent 16 modulo 60:   1/4 q ( q-4 )
        q congruent 17 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 19 modulo 60:   1/4 ( q^2-5*q+2 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 23 modulo 60:   1/4 q ( q-3 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-4 )
        q congruent 27 modulo 60:   1/4 q ( q-3 )
        q congruent 29 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 31 modulo 60:   1/4 ( q^2-5*q+2 )
        q congruent 32 modulo 60:   1/4 q ( q-2 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-4 )
        q congruent 41 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 43 modulo 60:   1/4 ( q^2-5*q+2 )
        q congruent 47 modulo 60:   1/4 q ( q-3 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-4 )
        q congruent 53 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 59 modulo 60:   1/4 q ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 77, 4, 68, 30, 68, 7, 81, 77, 30, 83, 30, 81, 37, 19, 76, 
  59, 93, 50, 111 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 4 ], 
  [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 15, 1, 1, 2 ], 
  [ 22, 1, 2, 4 ], [ 26, 1, 3, 4 ] ]

    k = 3: F-action on Pi is (1,2)(3,4)(6,7)      [29,1,3]
      Dynkin type is ^2A_4(q) + ^2A_2(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 2 modulo 60:   1/4 ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 4 modulo 60:   1/4 q ( q-2 )
        q congruent 5 modulo 60:   1/4 ( q^2-5*q+8 )
        q congruent 7 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 8 modulo 60:   1/4 ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 11 modulo 60:   1/4 ( q^2-5*q+10 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 16 modulo 60:   1/4 q ( q-2 )
        q congruent 17 modulo 60:   1/4 ( q^2-5*q+8 )
        q congruent 19 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 23 modulo 60:   1/4 ( q^2-5*q+10 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 27 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 29 modulo 60:   1/4 ( q^2-5*q+8 )
        q congruent 31 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 32 modulo 60:   1/4 ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 41 modulo 60:   1/4 ( q^2-5*q+8 )
        q congruent 43 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 47 modulo 60:   1/4 ( q^2-5*q+10 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 53 modulo 60:   1/4 ( q^2-5*q+8 )
        q congruent 59 modulo 60:   1/4 ( q^2-5*q+10 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 5, 78, 5, 69, 31, 69, 7, 82, 78, 31, 84, 31, 82, 38, 20, 76, 
  60, 94, 51, 112 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 2, 4 ], 
  [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 1, 2 ], [ 15, 1, 2, 2 ], 
  [ 22, 1, 3, 4 ], [ 26, 1, 2, 4 ] ]

    k = 4: F-action on Pi is (1,2)(3,4)(6,7)      [29,1,4]
      Dynkin type is ^2A_4(q) + ^2A_2(q) + T(phi2^2)
      Order of center |Z^F|: phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-6 )
        q congruent 2 modulo 60:   1/4 ( q^2-8*q+12 )
        q congruent 3 modulo 60:   1/4 ( q^2-7*q+12 )
        q congruent 4 modulo 60:   1/4 ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/4 ( q^2-9*q+20 )
        q congruent 7 modulo 60:   1/4 ( q^2-7*q+12 )
        q congruent 8 modulo 60:   1/4 ( q^2-8*q+12 )
        q congruent 9 modulo 60:   1/4 ( q^2-7*q+14 )
        q congruent 11 modulo 60:   1/4 ( q^2-9*q+26 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-6 )
        q congruent 16 modulo 60:   1/4 q ( q-6 )
        q congruent 17 modulo 60:   1/4 ( q^2-9*q+20 )
        q congruent 19 modulo 60:   1/4 ( q^2-7*q+20 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-6 )
        q congruent 23 modulo 60:   1/4 ( q^2-9*q+26 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-6 )
        q congruent 27 modulo 60:   1/4 ( q^2-7*q+12 )
        q congruent 29 modulo 60:   1/4 ( q^2-9*q+28 )
        q congruent 31 modulo 60:   1/4 ( q^2-7*q+12 )
        q congruent 32 modulo 60:   1/4 ( q^2-8*q+12 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-6 )
        q congruent 41 modulo 60:   1/4 ( q^2-9*q+20 )
        q congruent 43 modulo 60:   1/4 ( q^2-7*q+12 )
        q congruent 47 modulo 60:   1/4 ( q^2-9*q+26 )
        q congruent 49 modulo 60:   1/4 ( q^2-7*q+14 )
        q congruent 53 modulo 60:   1/4 ( q^2-9*q+20 )
        q congruent 59 modulo 60:   1/4 ( q^2-9*q+34 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 2, 67, 9, 67, 5, 78, 5, 69, 31, 9, 78, 15, 78, 31, 84, 71, 20, 98, 
  24, 94, 63 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], 
  [ 5, 1, 2, 4 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 4 ], 
  [ 9, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 12, 1, 2, 4 ], [ 14, 1, 2, 4 ], 
  [ 15, 1, 2, 2 ], [ 21, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 26, 1, 4, 4 ] ]

i = 30: Pi = [ 1, 2, 3, 4, 6, 8 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [30,1,1]
      Dynkin type is A_4(q) + A_1(q) + A_1(q) + T(phi1^2)
      Order of center |Z^F|: phi1^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 ( q^2-13*q+60 )
        q congruent 2 modulo 60:   1/4 ( q^2-10*q+16 )
        q congruent 3 modulo 60:   1/4 ( q^2-13*q+30 )
        q congruent 4 modulo 60:   1/4 ( q^2-10*q+24 )
        q congruent 5 modulo 60:   1/4 ( q^2-13*q+40 )
        q congruent 7 modulo 60:   1/4 ( q^2-13*q+42 )
        q congruent 8 modulo 60:   1/4 ( q^2-10*q+16 )
        q congruent 9 modulo 60:   1/4 ( q^2-13*q+40 )
        q congruent 11 modulo 60:   1/4 ( q^2-13*q+38 )
        q congruent 13 modulo 60:   1/4 ( q^2-13*q+52 )
        q congruent 16 modulo 60:   1/4 ( q^2-10*q+32 )
        q congruent 17 modulo 60:   1/4 ( q^2-13*q+40 )
        q congruent 19 modulo 60:   1/4 ( q^2-13*q+42 )
        q congruent 21 modulo 60:   1/4 ( q^2-13*q+48 )
        q congruent 23 modulo 60:   1/4 ( q^2-13*q+30 )
        q congruent 25 modulo 60:   1/4 ( q^2-13*q+52 )
        q congruent 27 modulo 60:   1/4 ( q^2-13*q+30 )
        q congruent 29 modulo 60:   1/4 ( q^2-13*q+40 )
        q congruent 31 modulo 60:   1/4 ( q^2-13*q+50 )
        q congruent 32 modulo 60:   1/4 ( q^2-10*q+16 )
        q congruent 37 modulo 60:   1/4 ( q^2-13*q+52 )
        q congruent 41 modulo 60:   1/4 ( q^2-13*q+48 )
        q congruent 43 modulo 60:   1/4 ( q^2-13*q+42 )
        q congruent 47 modulo 60:   1/4 ( q^2-13*q+30 )
        q congruent 49 modulo 60:   1/4 ( q^2-13*q+52 )
        q congruent 53 modulo 60:   1/4 ( q^2-13*q+40 )
        q congruent 59 modulo 60:   1/4 ( q^2-13*q+30 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 66, 4, 4, 68, 4, 68, 68, 7, 8, 77, 77, 30, 77, 30, 
  30, 81, 70, 19, 19, 76, 23, 93, 93, 50 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], 
  [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 2 ], 
  [ 9, 1, 1, 1 ], [ 11, 1, 1, 4 ], [ 13, 1, 1, 4 ], [ 14, 1, 1, 2 ], 
  [ 15, 1, 1, 4 ], [ 18, 1, 1, 4 ], [ 19, 1, 1, 4 ], [ 23, 1, 1, 2 ] ]

    k = 2: F-action on Pi is (6,8)      [30,1,2]
      Dynkin type is A_4(q) + A_1(q^2) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 2 modulo 60:   1/4 q ( q-2 )
        q congruent 3 modulo 60:   1/4 q ( q-3 )
        q congruent 4 modulo 60:   1/4 q ( q-2 )
        q congruent 5 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 7 modulo 60:   1/4 q ( q-3 )
        q congruent 8 modulo 60:   1/4 q ( q-2 )
        q congruent 9 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 11 modulo 60:   1/4 q ( q-3 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 16 modulo 60:   1/4 q ( q-2 )
        q congruent 17 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 19 modulo 60:   1/4 q ( q-3 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 23 modulo 60:   1/4 q ( q-3 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 27 modulo 60:   1/4 q ( q-3 )
        q congruent 29 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 31 modulo 60:   1/4 q ( q-3 )
        q congruent 32 modulo 60:   1/4 q ( q-2 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 41 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 43 modulo 60:   1/4 q ( q-3 )
        q congruent 47 modulo 60:   1/4 q ( q-3 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 53 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 59 modulo 60:   1/4 q ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 70, 68, 19, 7, 76, 30, 97, 81, 59, 76, 22, 50, 107 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 8, 1, 1, 2 ], 
  [ 9, 1, 1, 1 ], [ 13, 1, 2, 4 ], [ 14, 1, 1, 2 ], [ 23, 1, 2, 2 ] ]

    k = 3: F-action on Pi is (1,2)(3,4)      [30,1,3]
      Dynkin type is ^2A_4(q) + A_1(q) + A_1(q) + T(phi2^2)
      Order of center |Z^F|: phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-8 )
        q congruent 2 modulo 60:   1/4 ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/4 ( q^2-9*q+18 )
        q congruent 4 modulo 60:   1/4 ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/4 ( q^2-9*q+20 )
        q congruent 7 modulo 60:   1/4 ( q^2-9*q+18 )
        q congruent 8 modulo 60:   1/4 ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/4 ( q^2-9*q+16 )
        q congruent 11 modulo 60:   1/4 ( q^2-9*q+30 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-8 )
        q congruent 16 modulo 60:   1/4 q ( q-6 )
        q congruent 17 modulo 60:   1/4 ( q^2-9*q+20 )
        q congruent 19 modulo 60:   1/4 ( q^2-9*q+26 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-8 )
        q congruent 23 modulo 60:   1/4 ( q^2-9*q+30 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-8 )
        q congruent 27 modulo 60:   1/4 ( q^2-9*q+18 )
        q congruent 29 modulo 60:   1/4 ( q^2-9*q+28 )
        q congruent 31 modulo 60:   1/4 ( q^2-9*q+18 )
        q congruent 32 modulo 60:   1/4 ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-8 )
        q congruent 41 modulo 60:   1/4 ( q^2-9*q+20 )
        q congruent 43 modulo 60:   1/4 ( q^2-9*q+18 )
        q congruent 47 modulo 60:   1/4 ( q^2-9*q+30 )
        q congruent 49 modulo 60:   1/4 ( q^2-9*q+16 )
        q congruent 53 modulo 60:   1/4 ( q^2-9*q+20 )
        q congruent 59 modulo 60:   1/4 ( q^2-9*q+38 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 67, 67, 2, 69, 5, 5, 67, 7, 69, 69, 5, 31, 78, 78, 9, 82, 31, 
  31, 78, 76, 20, 20, 71, 51, 94, 94, 24 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 2 ], 
  [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 2 ], 
  [ 9, 1, 1, 1 ], [ 11, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 14, 1, 2, 2 ], 
  [ 15, 1, 2, 4 ], [ 18, 1, 2, 4 ], [ 19, 1, 2, 4 ], [ 23, 1, 2, 2 ] ]

    k = 4: F-action on Pi is (1,2)(3,4)(6,8)      [30,1,4]
      Dynkin type is ^2A_4(q) + A_1(q^2) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 2 modulo 60:   1/4 q ( q-2 )
        q congruent 3 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 4 modulo 60:   1/4 q ( q-2 )
        q congruent 5 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 7 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 8 modulo 60:   1/4 q ( q-2 )
        q congruent 9 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 11 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 16 modulo 60:   1/4 q ( q-2 )
        q congruent 17 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 19 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 23 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 27 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 29 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 31 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 32 modulo 60:   1/4 q ( q-2 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 41 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 43 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 47 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 53 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 59 modulo 60:   1/4 ( q^2-3*q+4 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 71, 69, 20, 7, 76, 31, 98, 82, 60, 76, 22, 51, 108 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 8, 1, 2, 2 ], 
  [ 9, 1, 1, 1 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 2 ], [ 23, 1, 1, 2 ] ]

i = 31: Pi = [ 1, 2, 3, 5, 6, 7 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [31,1,1]
      Dynkin type is A_3(q) + A_2(q) + A_1(q) + T(phi1^2)
      Order of center |Z^F|: phi1^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 ( q^2-16*q+75 )
        q congruent 2 modulo 60:   1/4 ( q^2-10*q+16 )
        q congruent 3 modulo 60:   1/4 ( q^2-12*q+27 )
        q congruent 4 modulo 60:   1/4 ( q^2-12*q+32 )
        q congruent 5 modulo 60:   1/4 ( q^2-14*q+45 )
        q congruent 7 modulo 60:   1/4 ( q^2-14*q+49 )
        q congruent 8 modulo 60:   1/4 ( q^2-10*q+16 )
        q congruent 9 modulo 60:   1/4 ( q^2-14*q+45 )
        q congruent 11 modulo 60:   1/4 ( q^2-12*q+35 )
        q congruent 13 modulo 60:   1/4 ( q^2-16*q+67 )
        q congruent 16 modulo 60:   1/4 ( q^2-12*q+40 )
        q congruent 17 modulo 60:   1/4 ( q^2-14*q+45 )
        q congruent 19 modulo 60:   1/4 ( q^2-14*q+49 )
        q congruent 21 modulo 60:   1/4 ( q^2-14*q+53 )
        q congruent 23 modulo 60:   1/4 ( q^2-12*q+27 )
        q congruent 25 modulo 60:   1/4 ( q^2-16*q+67 )
        q congruent 27 modulo 60:   1/4 ( q^2-12*q+27 )
        q congruent 29 modulo 60:   1/4 ( q^2-14*q+45 )
        q congruent 31 modulo 60:   1/4 ( q^2-14*q+57 )
        q congruent 32 modulo 60:   1/4 ( q^2-10*q+16 )
        q congruent 37 modulo 60:   1/4 ( q^2-16*q+67 )
        q congruent 41 modulo 60:   1/4 ( q^2-14*q+53 )
        q congruent 43 modulo 60:   1/4 ( q^2-14*q+49 )
        q congruent 47 modulo 60:   1/4 ( q^2-12*q+27 )
        q congruent 49 modulo 60:   1/4 ( q^2-16*q+67 )
        q congruent 53 modulo 60:   1/4 ( q^2-14*q+45 )
        q congruent 59 modulo 60:   1/4 ( q^2-12*q+27 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 8, 77, 66, 4, 4, 68, 77, 30, 4, 68, 68, 7, 30, 81, 8, 
  77, 77, 30, 14, 83, 70, 19, 19, 76, 97, 59 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], 
  [ 5, 1, 1, 8 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 4 ], 
  [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 12, 1, 1, 2 ], [ 14, 1, 1, 4 ], 
  [ 15, 1, 1, 4 ], [ 16, 1, 1, 4 ], [ 18, 1, 1, 4 ], [ 20, 1, 1, 8 ], 
  [ 22, 1, 1, 4 ], [ 24, 1, 1, 2 ] ]

    k = 2: F-action on Pi is ()      [31,1,2]
      Dynkin type is A_3(q) + A_2(q) + A_1(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-7 )
        q congruent 2 modulo 60:   1/4 q ( q-2 )
        q congruent 3 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 4 modulo 60:   1/4 q ( q-4 )
        q congruent 5 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 7 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 8 modulo 60:   1/4 q ( q-2 )
        q congruent 9 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 11 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-7 )
        q congruent 16 modulo 60:   1/4 q ( q-4 )
        q congruent 17 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 19 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 23 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-7 )
        q congruent 27 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 29 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 31 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 32 modulo 60:   1/4 q ( q-2 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-7 )
        q congruent 41 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 43 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 47 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-7 )
        q congruent 53 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 59 modulo 60:   1/4 phi1 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 4, 68, 77, 30, 4, 68, 68, 7, 30, 81, 68, 3, 7, 69, 81, 27, 
  77, 30, 30, 81, 83, 37, 19, 72, 76, 20, 59, 95 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], 
  [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 12, 1, 1, 2 ], 
  [ 16, 1, 1, 4 ], [ 20, 1, 2, 8 ], [ 22, 1, 2, 4 ], [ 24, 1, 2, 2 ] ]

    k = 3: F-action on Pi is (1,3)(5,7)      [31,1,3]
      Dynkin type is ^2A_3(q) + ^2A_2(q) + A_1(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 2 modulo 60:   1/4 ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 4 modulo 60:   1/4 q ( q-2 )
        q congruent 5 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 7 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 8 modulo 60:   1/4 ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 11 modulo 60:   1/4 ( q^2-8*q+15 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 16 modulo 60:   1/4 q ( q-2 )
        q congruent 17 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 19 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 23 modulo 60:   1/4 ( q^2-8*q+15 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 27 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 31 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 32 modulo 60:   1/4 ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 41 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 43 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 47 modulo 60:   1/4 ( q^2-8*q+15 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 53 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 59 modulo 60:   1/4 ( q^2-8*q+15 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 67, 69, 5, 31, 78, 69, 5, 7, 69, 82, 31, 3, 69, 68, 7, 28, 82, 
  31, 78, 82, 31, 38, 84, 72, 20, 19, 76, 96, 60 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], 
  [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 12, 1, 2, 2 ], 
  [ 16, 1, 3, 4 ], [ 20, 1, 3, 8 ], [ 22, 1, 3, 4 ], [ 24, 1, 1, 2 ] ]

    k = 4: F-action on Pi is (1,3)(5,7)      [31,1,4]
      Dynkin type is ^2A_3(q) + ^2A_2(q) + A_1(q) + T(phi2^2)
      Order of center |Z^F|: phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-7 )
        q congruent 2 modulo 60:   1/4 ( q^2-8*q+12 )
        q congruent 3 modulo 60:   1/4 ( q^2-10*q+21 )
        q congruent 4 modulo 60:   1/4 ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/4 ( q^2-10*q+25 )
        q congruent 7 modulo 60:   1/4 ( q^2-10*q+21 )
        q congruent 8 modulo 60:   1/4 ( q^2-8*q+12 )
        q congruent 9 modulo 60:   1/4 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/4 ( q^2-12*q+39 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-7 )
        q congruent 16 modulo 60:   1/4 q ( q-6 )
        q congruent 17 modulo 60:   1/4 ( q^2-10*q+25 )
        q congruent 19 modulo 60:   1/4 ( q^2-10*q+29 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-7 )
        q congruent 23 modulo 60:   1/4 ( q^2-12*q+39 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-7 )
        q congruent 27 modulo 60:   1/4 ( q^2-10*q+21 )
        q congruent 29 modulo 60:   1/4 ( q^2-10*q+33 )
        q congruent 31 modulo 60:   1/4 ( q^2-10*q+21 )
        q congruent 32 modulo 60:   1/4 ( q^2-8*q+12 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-7 )
        q congruent 41 modulo 60:   1/4 ( q^2-10*q+25 )
        q congruent 43 modulo 60:   1/4 ( q^2-10*q+21 )
        q congruent 47 modulo 60:   1/4 ( q^2-12*q+39 )
        q congruent 49 modulo 60:   1/4 ( q^2-8*q+15 )
        q congruent 53 modulo 60:   1/4 ( q^2-10*q+25 )
        q congruent 59 modulo 60:   1/4 ( q^2-12*q+47 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 2, 5, 67, 78, 9, 5, 67, 69, 5, 31, 78, 69, 5, 7, 69, 82, 31, 
  78, 9, 31, 78, 84, 15, 20, 71, 76, 20, 60, 98 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], 
  [ 5, 1, 2, 8 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 4 ], 
  [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 12, 1, 2, 2 ], [ 14, 1, 2, 4 ], 
  [ 15, 1, 2, 4 ], [ 16, 1, 3, 4 ], [ 18, 1, 2, 4 ], [ 20, 1, 4, 8 ], 
  [ 22, 1, 4, 4 ], [ 24, 1, 2, 2 ] ]

i = 32: Pi = [ 1, 2, 3, 5, 6, 8 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [32,1,1]
      Dynkin type is A_2(q) + A_2(q) + A_1(q) + A_1(q) + T(phi1^2)
      Order of center |Z^F|: phi1^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 ( q^2-18*q+97 )
        q congruent 2 modulo 60:   1/8 ( q^2-10*q+16 )
        q congruent 3 modulo 60:   1/8 ( q^2-14*q+33 )
        q congruent 4 modulo 60:   1/8 ( q^2-14*q+40 )
        q congruent 5 modulo 60:   1/8 ( q^2-14*q+45 )
        q congruent 7 modulo 60:   1/8 ( q^2-18*q+77 )
        q congruent 8 modulo 60:   1/8 ( q^2-10*q+16 )
        q congruent 9 modulo 60:   1/8 ( q^2-14*q+45 )
        q congruent 11 modulo 60:   1/8 ( q^2-14*q+41 )
        q congruent 13 modulo 60:   1/8 ( q^2-18*q+89 )
        q congruent 16 modulo 60:   1/8 ( q^2-14*q+48 )
        q congruent 17 modulo 60:   1/8 ( q^2-14*q+45 )
        q congruent 19 modulo 60:   1/8 ( q^2-18*q+77 )
        q congruent 21 modulo 60:   1/8 ( q^2-14*q+53 )
        q congruent 23 modulo 60:   1/8 ( q^2-14*q+33 )
        q congruent 25 modulo 60:   1/8 ( q^2-18*q+89 )
        q congruent 27 modulo 60:   1/8 ( q^2-14*q+33 )
        q congruent 29 modulo 60:   1/8 ( q^2-14*q+45 )
        q congruent 31 modulo 60:   1/8 ( q^2-18*q+85 )
        q congruent 32 modulo 60:   1/8 ( q^2-10*q+16 )
        q congruent 37 modulo 60:   1/8 ( q^2-18*q+89 )
        q congruent 41 modulo 60:   1/8 ( q^2-14*q+53 )
        q congruent 43 modulo 60:   1/8 ( q^2-18*q+77 )
        q congruent 47 modulo 60:   1/8 ( q^2-14*q+33 )
        q congruent 49 modulo 60:   1/8 ( q^2-18*q+89 )
        q congruent 53 modulo 60:   1/8 ( q^2-14*q+45 )
        q congruent 59 modulo 60:   1/8 ( q^2-14*q+33 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 66, 4, 4, 68, 8, 77, 77, 30, 66, 4, 4, 68, 4, 68, 68, 
  7, 77, 30, 30, 81, 8, 77, 77, 30, 77, 30, 30, 81, 14, 83, 83, 37 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], 
  [ 5, 1, 1, 8 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], 
  [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 8 ], 
  [ 17, 1, 1, 24 ], [ 19, 1, 1, 4 ] ]

    k = 2: F-action on Pi is (2,8)(5,6)      [32,1,2]
      Dynkin type is A_2(q) + ^2A_2(q) + A_1(q^2) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 2 modulo 60:   1/4 q ( q-2 )
        q congruent 3 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 4 modulo 60:   1/4 q ( q-2 )
        q congruent 5 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 7 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 8 modulo 60:   1/4 q ( q-2 )
        q congruent 9 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 11 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 16 modulo 60:   1/4 q ( q-2 )
        q congruent 17 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 19 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 23 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 27 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 29 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 31 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 32 modulo 60:   1/4 q ( q-2 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 41 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 43 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 47 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 53 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 59 modulo 60:   1/4 phi1 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 72, 68, 19, 28, 96, 69, 20, 7, 76, 82, 60, 27, 95, 81, 59, 36, 
  99 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], 
  [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 2 ], 
  [ 16, 1, 2, 4 ], [ 16, 1, 4, 4 ] ]

    k = 3: F-action on Pi is (1,3)(5,6)      [32,1,3]
      Dynkin type is ^2A_2(q) + ^2A_2(q) + A_1(q) + A_1(q) + T(phi2^2)
      Order of center |Z^F|: phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q-9 )
        q congruent 2 modulo 60:   1/8 ( q^2-10*q+16 )
        q congruent 3 modulo 60:   1/8 ( q^2-10*q+21 )
        q congruent 4 modulo 60:   1/8 ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/8 ( q^2-14*q+45 )
        q congruent 7 modulo 60:   1/8 ( q^2-10*q+21 )
        q congruent 8 modulo 60:   1/8 ( q^2-10*q+16 )
        q congruent 9 modulo 60:   1/8 ( q^2-10*q+17 )
        q congruent 11 modulo 60:   1/8 ( q^2-14*q+57 )
        q congruent 13 modulo 60:   1/8 phi1 ( q-9 )
        q congruent 16 modulo 60:   1/8 q ( q-6 )
        q congruent 17 modulo 60:   1/8 ( q^2-14*q+45 )
        q congruent 19 modulo 60:   1/8 ( q^2-10*q+29 )
        q congruent 21 modulo 60:   1/8 phi1 ( q-9 )
        q congruent 23 modulo 60:   1/8 ( q^2-14*q+57 )
        q congruent 25 modulo 60:   1/8 phi1 ( q-9 )
        q congruent 27 modulo 60:   1/8 ( q^2-10*q+21 )
        q congruent 29 modulo 60:   1/8 ( q^2-14*q+53 )
        q congruent 31 modulo 60:   1/8 ( q^2-10*q+21 )
        q congruent 32 modulo 60:   1/8 ( q^2-10*q+16 )
        q congruent 37 modulo 60:   1/8 phi1 ( q-9 )
        q congruent 41 modulo 60:   1/8 ( q^2-14*q+45 )
        q congruent 43 modulo 60:   1/8 ( q^2-10*q+21 )
        q congruent 47 modulo 60:   1/8 ( q^2-14*q+57 )
        q congruent 49 modulo 60:   1/8 ( q^2-10*q+17 )
        q congruent 53 modulo 60:   1/8 ( q^2-14*q+45 )
        q congruent 59 modulo 60:   1/8 ( q^2-14*q+65 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 67, 67, 2, 69, 5, 5, 67, 31, 78, 78, 9, 69, 5, 5, 67, 7, 69, 69, 
  5, 82, 31, 31, 78, 31, 78, 78, 9, 82, 31, 31, 78, 38, 84, 84, 15 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 4 ], 
  [ 5, 1, 2, 8 ], [ 6, 1, 2, 12 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], 
  [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 15, 1, 2, 8 ], [ 16, 1, 3, 8 ], 
  [ 17, 1, 4, 24 ], [ 19, 1, 2, 4 ] ]

    k = 4: F-action on Pi is (1,5)(3,6)      [32,1,4]
      Dynkin type is A_2(q^2) + A_1(q) + A_1(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 2 modulo 60:   1/4 ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 4 modulo 60:   1/4 q ( q-4 )
        q congruent 5 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 7 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 8 modulo 60:   1/4 ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 11 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 16 modulo 60:   1/4 q ( q-4 )
        q congruent 17 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 19 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 23 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 27 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 29 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 31 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 32 modulo 60:   1/4 ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 41 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 43 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 47 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 53 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 59 modulo 60:   1/4 ( q^2-6*q+9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 7, 3, 69, 19, 76, 72, 20, 87, 40, 35, 88 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], 
  [ 6, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], 
  [ 9, 1, 1, 1 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], 
  [ 17, 1, 3, 4 ], [ 19, 1, 1, 2 ], [ 19, 1, 2, 2 ] ]

    k = 5: F-action on Pi is (1,5,3,6)(2,8)      [32,1,5]
      Dynkin type is ^2A_2(q^2) + A_1(q^2) + T(phi4)
      Order of center |Z^F|: phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 phi2
        q congruent 2 modulo 60:   1/4 ( q^2-4 )
        q congruent 3 modulo 60:   1/4 ( q^2-5 )
        q congruent 4 modulo 60:   1/4 q^2
        q congruent 5 modulo 60:   1/4 phi1 phi2
        q congruent 7 modulo 60:   1/4 ( q^2-5 )
        q congruent 8 modulo 60:   1/4 ( q^2-4 )
        q congruent 9 modulo 60:   1/4 phi1 phi2
        q congruent 11 modulo 60:   1/4 phi1 phi2
        q congruent 13 modulo 60:   1/4 ( q^2-5 )
        q congruent 16 modulo 60:   1/4 q^2
        q congruent 17 modulo 60:   1/4 ( q^2-5 )
        q congruent 19 modulo 60:   1/4 phi1 phi2
        q congruent 21 modulo 60:   1/4 phi1 phi2
        q congruent 23 modulo 60:   1/4 ( q^2-5 )
        q congruent 25 modulo 60:   1/4 phi1 phi2
        q congruent 27 modulo 60:   1/4 ( q^2-5 )
        q congruent 29 modulo 60:   1/4 phi1 phi2
        q congruent 31 modulo 60:   1/4 phi1 phi2
        q congruent 32 modulo 60:   1/4 ( q^2-4 )
        q congruent 37 modulo 60:   1/4 ( q^2-5 )
        q congruent 41 modulo 60:   1/4 phi1 phi2
        q congruent 43 modulo 60:   1/4 ( q^2-5 )
        q congruent 47 modulo 60:   1/4 ( q^2-5 )
        q congruent 49 modulo 60:   1/4 phi1 phi2
        q congruent 53 modulo 60:   1/4 ( q^2-5 )
        q congruent 59 modulo 60:   1/4 phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 75, 6, 22, 75, 100, 39 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 5, 1, 3, 4 ], [ 5, 1, 4, 4 ], [ 9, 1, 1, 1 ] ]

i = 33: Pi = [ 1, 2, 3, 5, 7, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [33,1,1]
      Dynkin type is A_2(q) + A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^2)
      Order of center |Z^F|: phi1^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/48 ( q^2-14*q+61 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/48 ( q^2-14*q+33 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/48 ( q^2-14*q+45 )
        q congruent 7 modulo 60:   1/48 ( q^2-14*q+49 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/48 ( q^2-14*q+45 )
        q congruent 11 modulo 60:   1/48 ( q^2-14*q+33 )
        q congruent 13 modulo 60:   1/48 ( q^2-14*q+61 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/48 ( q^2-14*q+45 )
        q congruent 19 modulo 60:   1/48 ( q^2-14*q+49 )
        q congruent 21 modulo 60:   1/48 ( q^2-14*q+45 )
        q congruent 23 modulo 60:   1/48 ( q^2-14*q+33 )
        q congruent 25 modulo 60:   1/48 ( q^2-14*q+61 )
        q congruent 27 modulo 60:   1/48 ( q^2-14*q+33 )
        q congruent 29 modulo 60:   1/48 ( q^2-14*q+45 )
        q congruent 31 modulo 60:   1/48 ( q^2-14*q+49 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/48 ( q^2-14*q+61 )
        q congruent 41 modulo 60:   1/48 ( q^2-14*q+45 )
        q congruent 43 modulo 60:   1/48 ( q^2-14*q+49 )
        q congruent 47 modulo 60:   1/48 ( q^2-14*q+33 )
        q congruent 49 modulo 60:   1/48 ( q^2-14*q+61 )
        q congruent 53 modulo 60:   1/48 ( q^2-14*q+45 )
        q congruent 59 modulo 60:   1/48 ( q^2-14*q+33 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 66, 4, 4, 68, 66, 4, 4, 68, 4, 68, 68, 3, 66, 4, 4, 
  68, 4, 68, 68, 7, 4, 68, 68, 7, 68, 7, 7, 69, 8, 77, 77, 30, 77, 30, 30, 
  81, 77, 30, 30, 81, 30, 81, 81, 27 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 18 ], 
  [ 6, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 13, 1, 1, 24 ], 
  [ 16, 1, 1, 24 ], [ 23, 1, 1, 6 ], [ 25, 1, 1, 12 ], [ 40, 1, 1, 12 ] ]

    k = 2: F-action on Pi is (  7,240)      [33,1,2]
      Dynkin type is A_2(q) + A_1(q) + A_1(q) + A_1(q^2) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 7 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 11 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 13 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 19 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 21 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 23 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 25 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 27 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 29 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 31 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 41 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 43 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 47 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 49 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 53 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 59 modulo 60:   1/8 phi1 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 70, 68, 19, 68, 19, 3, 72, 68, 19, 7, 76, 7, 76, 69, 20, 30, 97, 
  81, 59, 81, 59, 27, 95 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], 
  [ 4, 1, 2, 2 ], [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], 
  [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], 
  [ 23, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 40, 1, 3, 4 ] ]

    k = 3: F-action on Pi is (  5,  7,240)      [33,1,3]
      Dynkin type is A_2(q) + A_1(q) + A_1(q^3) + T(phi3)
      Order of center |Z^F|: phi3 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/6 q phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/6 q phi2
        q congruent 7 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/6 q phi2
        q congruent 11 modulo 60:   1/6 q phi2
        q congruent 13 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/6 q phi2
        q congruent 19 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 21 modulo 60:   1/6 q phi2
        q congruent 23 modulo 60:   1/6 q phi2
        q congruent 25 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 27 modulo 60:   1/6 q phi2
        q congruent 29 modulo 60:   1/6 q phi2
        q congruent 31 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 41 modulo 60:   1/6 q phi2
        q congruent 43 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 47 modulo 60:   1/6 q phi2
        q congruent 49 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 53 modulo 60:   1/6 q phi2
        q congruent 59 modulo 60:   1/6 q phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 14, 87, 83, 35, 83, 40, 37, 88, 12, 85, 79, 34 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], 
  [ 40, 1, 5, 6 ] ]

    k = 4: F-action on Pi is (  2,  5)(  7,240)      [33,1,4]
      Dynkin type is A_2(q) + A_1(q^2) + A_1(q^2) + T(phi1^2)
      Order of center |Z^F|: phi1^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 7 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 11 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 13 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 19 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 21 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 23 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 25 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 27 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 31 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 41 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 43 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 47 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 49 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 53 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 59 modulo 60:   1/16 ( q^2-6*q+9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 70, 70, 16, 68, 19, 19, 73, 30, 97, 97, 53 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 4 ], 
  [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 13, 1, 3, 8 ], [ 16, 1, 2, 8 ], 
  [ 23, 1, 1, 6 ], [ 25, 1, 1, 12 ], [ 40, 1, 1, 12 ] ]

    k = 5: F-action on Pi is (  2,  5,240,  7)      [33,1,5]
      Dynkin type is A_2(q) + A_1(q^4) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 phi2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/8 phi1 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/8 phi1 phi2
        q congruent 7 modulo 60:   1/8 phi1 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/8 phi1 phi2
        q congruent 11 modulo 60:   1/8 phi1 phi2
        q congruent 13 modulo 60:   1/8 phi1 phi2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/8 phi1 phi2
        q congruent 19 modulo 60:   1/8 phi1 phi2
        q congruent 21 modulo 60:   1/8 phi1 phi2
        q congruent 23 modulo 60:   1/8 phi1 phi2
        q congruent 25 modulo 60:   1/8 phi1 phi2
        q congruent 27 modulo 60:   1/8 phi1 phi2
        q congruent 29 modulo 60:   1/8 phi1 phi2
        q congruent 31 modulo 60:   1/8 phi1 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/8 phi1 phi2
        q congruent 41 modulo 60:   1/8 phi1 phi2
        q congruent 43 modulo 60:   1/8 phi1 phi2
        q congruent 47 modulo 60:   1/8 phi1 phi2
        q congruent 49 modulo 60:   1/8 phi1 phi2
        q congruent 53 modulo 60:   1/8 phi1 phi2
        q congruent 59 modulo 60:   1/8 phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 19, 89, 76, 43, 59, 109 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], 
  [ 12, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 40, 1, 3, 4 ] ]

    k = 6: F-action on Pi is (  1,  3)(  5,240)      [33,1,6]
      Dynkin type is ^2A_2(q) + A_1(q) + A_1(q^2) + A_1(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 7 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 11 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 13 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 19 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 21 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 23 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 25 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 27 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 29 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 31 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 41 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 43 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 47 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 49 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 53 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 59 modulo 60:   1/8 phi1 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 69, 72, 20, 69, 5, 20, 71, 68, 7, 19, 76, 7, 69, 76, 20, 28, 82, 
  96, 60, 82, 31, 60, 98 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], 
  [ 4, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ], 
  [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], 
  [ 23, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 40, 1, 2, 4 ] ]

    k = 7: F-action on Pi is (  1,  3)(  5,240,  7)      [33,1,7]
      Dynkin type is ^2A_2(q) + A_1(q) + A_1(q^3) + T(phi6)
      Order of center |Z^F|: phi6 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/6 q phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/6 q phi1
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 7 modulo 60:   1/6 q phi1
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/6 q phi1
        q congruent 11 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 13 modulo 60:   1/6 q phi1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 19 modulo 60:   1/6 q phi1
        q congruent 21 modulo 60:   1/6 q phi1
        q congruent 23 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 25 modulo 60:   1/6 q phi1
        q congruent 27 modulo 60:   1/6 q phi1
        q congruent 29 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 31 modulo 60:   1/6 q phi1
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/6 q phi1
        q congruent 41 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 43 modulo 60:   1/6 q phi1
        q congruent 47 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 49 modulo 60:   1/6 q phi1
        q congruent 53 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 59 modulo 60:   1/6 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 35, 84, 88, 15, 87, 38, 40, 84, 33, 80, 86, 13 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], 
  [ 40, 1, 4, 6 ] ]

    k = 8: F-action on Pi is (1,3)      [33,1,8]
      Dynkin type is ^2A_2(q) + A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi2^2)
      Order of center |Z^F|: phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/48 phi1 ( q-9 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/48 ( q^2-10*q+21 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/48 ( q^2-10*q+25 )
        q congruent 7 modulo 60:   1/48 ( q^2-10*q+21 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/48 phi1 ( q-9 )
        q congruent 11 modulo 60:   1/48 ( q^2-10*q+37 )
        q congruent 13 modulo 60:   1/48 phi1 ( q-9 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/48 ( q^2-10*q+25 )
        q congruent 19 modulo 60:   1/48 ( q^2-10*q+21 )
        q congruent 21 modulo 60:   1/48 phi1 ( q-9 )
        q congruent 23 modulo 60:   1/48 ( q^2-10*q+37 )
        q congruent 25 modulo 60:   1/48 phi1 ( q-9 )
        q congruent 27 modulo 60:   1/48 ( q^2-10*q+21 )
        q congruent 29 modulo 60:   1/48 ( q^2-10*q+25 )
        q congruent 31 modulo 60:   1/48 ( q^2-10*q+21 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/48 phi1 ( q-9 )
        q congruent 41 modulo 60:   1/48 ( q^2-10*q+25 )
        q congruent 43 modulo 60:   1/48 ( q^2-10*q+21 )
        q congruent 47 modulo 60:   1/48 ( q^2-10*q+37 )
        q congruent 49 modulo 60:   1/48 phi1 ( q-9 )
        q congruent 53 modulo 60:   1/48 ( q^2-10*q+25 )
        q congruent 59 modulo 60:   1/48 ( q^2-10*q+37 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 69, 69, 5, 69, 5, 5, 67, 69, 5, 5, 67, 5, 67, 67, 2, 68, 7, 7, 
  69, 7, 69, 69, 5, 7, 69, 69, 5, 69, 5, 5, 67, 28, 82, 82, 31, 82, 31, 31, 
  78, 82, 31, 31, 78, 31, 78, 78, 9 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 18 ], 
  [ 6, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 12, 1, 2, 6 ], [ 13, 1, 4, 24 ], 
  [ 16, 1, 3, 24 ], [ 23, 1, 2, 6 ], [ 25, 1, 3, 12 ], [ 40, 1, 6, 12 ] ]

    k = 9: F-action on Pi is (  1,  3)(  2,  5,  7,240)      [33,1,9]
      Dynkin type is ^2A_2(q) + A_1(q^4) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 phi2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/8 phi1 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/8 phi1 phi2
        q congruent 7 modulo 60:   1/8 phi1 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/8 phi1 phi2
        q congruent 11 modulo 60:   1/8 phi1 phi2
        q congruent 13 modulo 60:   1/8 phi1 phi2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/8 phi1 phi2
        q congruent 19 modulo 60:   1/8 phi1 phi2
        q congruent 21 modulo 60:   1/8 phi1 phi2
        q congruent 23 modulo 60:   1/8 phi1 phi2
        q congruent 25 modulo 60:   1/8 phi1 phi2
        q congruent 27 modulo 60:   1/8 phi1 phi2
        q congruent 29 modulo 60:   1/8 phi1 phi2
        q congruent 31 modulo 60:   1/8 phi1 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/8 phi1 phi2
        q congruent 41 modulo 60:   1/8 phi1 phi2
        q congruent 43 modulo 60:   1/8 phi1 phi2
        q congruent 47 modulo 60:   1/8 phi1 phi2
        q congruent 49 modulo 60:   1/8 phi1 phi2
        q congruent 53 modulo 60:   1/8 phi1 phi2
        q congruent 59 modulo 60:   1/8 phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 20, 90, 76, 43, 60, 110 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], 
  [ 12, 1, 2, 2 ], [ 23, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 40, 1, 2, 4 ] ]

    k = 10: F-action on Pi is (  1,  3)(  2,  5)(  7,240)      [33,1,10]
      Dynkin type is ^2A_2(q) + A_1(q^2) + A_1(q^2) + T(phi2^2)
      Order of center |Z^F|: phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1^2
        q congruent 7 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1^2
        q congruent 11 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/16 phi1^2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1^2
        q congruent 19 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/16 phi1^2
        q congruent 23 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/16 phi1^2
        q congruent 27 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/16 phi1^2
        q congruent 31 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1^2
        q congruent 41 modulo 60:   1/16 phi1^2
        q congruent 43 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/16 phi1^2
        q congruent 53 modulo 60:   1/16 phi1^2
        q congruent 59 modulo 60:   1/16 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 71, 71, 17, 69, 20, 20, 74, 31, 98, 98, 54 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 6 ], 
  [ 9, 1, 1, 3 ], [ 12, 1, 2, 6 ], [ 13, 1, 2, 8 ], [ 16, 1, 4, 8 ], 
  [ 23, 1, 2, 6 ], [ 25, 1, 3, 12 ], [ 40, 1, 6, 12 ] ]

i = 34: Pi = [ 1, 2, 4, 5, 6, 7 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [34,1,1]
      Dynkin type is A_5(q) + A_1(q) + T(phi1^2)
      Order of center |Z^F|: phi1^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 ( q^2-12*q+39 )
        q congruent 2 modulo 60:   1/4 ( q^2-8*q+12 )
        q congruent 3 modulo 60:   1/4 ( q^2-10*q+21 )
        q congruent 4 modulo 60:   1/4 ( q^2-10*q+24 )
        q congruent 5 modulo 60:   1/4 ( q^2-10*q+25 )
        q congruent 7 modulo 60:   1/4 ( q^2-12*q+35 )
        q congruent 8 modulo 60:   1/4 ( q^2-8*q+12 )
        q congruent 9 modulo 60:   1/4 ( q^2-10*q+25 )
        q congruent 11 modulo 60:   1/4 ( q^2-10*q+21 )
        q congruent 13 modulo 60:   1/4 ( q^2-12*q+39 )
        q congruent 16 modulo 60:   1/4 ( q^2-10*q+24 )
        q congruent 17 modulo 60:   1/4 ( q^2-10*q+25 )
        q congruent 19 modulo 60:   1/4 ( q^2-12*q+35 )
        q congruent 21 modulo 60:   1/4 ( q^2-10*q+25 )
        q congruent 23 modulo 60:   1/4 ( q^2-10*q+21 )
        q congruent 25 modulo 60:   1/4 ( q^2-12*q+39 )
        q congruent 27 modulo 60:   1/4 ( q^2-10*q+21 )
        q congruent 29 modulo 60:   1/4 ( q^2-10*q+25 )
        q congruent 31 modulo 60:   1/4 ( q^2-12*q+35 )
        q congruent 32 modulo 60:   1/4 ( q^2-8*q+12 )
        q congruent 37 modulo 60:   1/4 ( q^2-12*q+39 )
        q congruent 41 modulo 60:   1/4 ( q^2-10*q+25 )
        q congruent 43 modulo 60:   1/4 ( q^2-12*q+35 )
        q congruent 47 modulo 60:   1/4 ( q^2-10*q+21 )
        q congruent 49 modulo 60:   1/4 ( q^2-12*q+39 )
        q congruent 53 modulo 60:   1/4 ( q^2-10*q+25 )
        q congruent 59 modulo 60:   1/4 ( q^2-10*q+21 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 4, 68, 68, 7, 8, 77, 77, 30, 14, 83, 70, 19, 19, 76, 
  23, 93, 87, 40 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], 
  [ 7, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], 
  [ 11, 1, 1, 2 ], [ 18, 1, 1, 4 ], [ 19, 1, 1, 2 ], [ 21, 1, 1, 4 ], 
  [ 22, 1, 1, 4 ], [ 24, 1, 1, 2 ] ]

    k = 2: F-action on Pi is ()      [34,1,2]
      Dynkin type is A_5(q) + A_1(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 2 modulo 60:   1/4 q ( q-2 )
        q congruent 3 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 4 modulo 60:   1/4 q ( q-4 )
        q congruent 5 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 7 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 8 modulo 60:   1/4 q ( q-2 )
        q congruent 9 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 11 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 16 modulo 60:   1/4 q ( q-4 )
        q congruent 17 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 19 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 23 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 27 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 29 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 31 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 32 modulo 60:   1/4 q ( q-2 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 41 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 43 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 47 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 53 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 59 modulo 60:   1/4 phi1 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 4, 68, 68, 7, 3, 69, 77, 30, 30, 81, 83, 37, 19, 76, 72, 20, 
  93, 50, 35, 88 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], 
  [ 7, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], 
  [ 19, 1, 1, 2 ], [ 22, 1, 2, 4 ], [ 24, 1, 2, 2 ] ]

    k = 3: F-action on Pi is (2,7)(4,6)      [34,1,3]
      Dynkin type is ^2A_5(q) + A_1(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 2 modulo 60:   1/4 ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 4 modulo 60:   1/4 q ( q-2 )
        q congruent 5 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 7 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 8 modulo 60:   1/4 ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 11 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 16 modulo 60:   1/4 q ( q-2 )
        q congruent 17 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 19 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 23 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 27 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 29 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 31 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 32 modulo 60:   1/4 ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 41 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 43 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 47 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 53 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 59 modulo 60:   1/4 ( q^2-6*q+9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 67, 69, 5, 7, 69, 68, 3, 31, 78, 82, 31, 38, 84, 76, 20, 19, 72, 
  51, 94, 87, 35 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], 
  [ 7, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], 
  [ 19, 1, 2, 2 ], [ 22, 1, 3, 4 ], [ 24, 1, 1, 2 ] ]

    k = 4: F-action on Pi is (2,7)(4,6)      [34,1,4]
      Dynkin type is ^2A_5(q) + A_1(q) + T(phi2^2)
      Order of center |Z^F|: phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 2 modulo 60:   1/4 ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 4 modulo 60:   1/4 q ( q-4 )
        q congruent 5 modulo 60:   1/4 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 8 modulo 60:   1/4 ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 11 modulo 60:   1/4 ( q^2-8*q+19 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 16 modulo 60:   1/4 q ( q-4 )
        q congruent 17 modulo 60:   1/4 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 23 modulo 60:   1/4 ( q^2-8*q+19 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 27 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/4 ( q^2-8*q+15 )
        q congruent 31 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 32 modulo 60:   1/4 ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 41 modulo 60:   1/4 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/4 ( q^2-6*q+9 )
        q congruent 47 modulo 60:   1/4 ( q^2-8*q+19 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-5 )
        q congruent 53 modulo 60:   1/4 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/4 ( q^2-8*q+19 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 2, 5, 67, 69, 5, 7, 69, 78, 9, 31, 78, 84, 15, 20, 71, 76, 20, 
  94, 24, 40, 88 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], 
  [ 7, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], 
  [ 11, 1, 2, 2 ], [ 18, 1, 2, 4 ], [ 19, 1, 2, 2 ], [ 21, 1, 2, 4 ], 
  [ 22, 1, 4, 4 ], [ 24, 1, 2, 2 ] ]

i = 35: Pi = [ 1, 2, 4, 5, 7, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [35,1,1]
      Dynkin type is A_3(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^2)
      Order of center |Z^F|: phi1^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 ( q^2-14*q+53 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/8 ( q^2-12*q+27 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/8 ( q^2-14*q+45 )
        q congruent 7 modulo 60:   1/8 ( q^2-12*q+35 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/8 ( q^2-14*q+45 )
        q congruent 11 modulo 60:   1/8 ( q^2-12*q+27 )
        q congruent 13 modulo 60:   1/8 ( q^2-14*q+53 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/8 ( q^2-14*q+45 )
        q congruent 19 modulo 60:   1/8 ( q^2-12*q+35 )
        q congruent 21 modulo 60:   1/8 ( q^2-14*q+45 )
        q congruent 23 modulo 60:   1/8 ( q^2-12*q+27 )
        q congruent 25 modulo 60:   1/8 ( q^2-14*q+53 )
        q congruent 27 modulo 60:   1/8 ( q^2-12*q+27 )
        q congruent 29 modulo 60:   1/8 ( q^2-14*q+45 )
        q congruent 31 modulo 60:   1/8 ( q^2-12*q+35 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/8 ( q^2-14*q+53 )
        q congruent 41 modulo 60:   1/8 ( q^2-14*q+45 )
        q congruent 43 modulo 60:   1/8 ( q^2-12*q+35 )
        q congruent 47 modulo 60:   1/8 ( q^2-12*q+27 )
        q congruent 49 modulo 60:   1/8 ( q^2-14*q+53 )
        q congruent 53 modulo 60:   1/8 ( q^2-14*q+45 )
        q congruent 59 modulo 60:   1/8 ( q^2-12*q+27 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 66, 4, 4, 68, 66, 4, 4, 68, 4, 68, 68, 7, 4, 68, 68, 
  3, 68, 7, 7, 69, 8, 77, 77, 30, 77, 30, 30, 81, 70, 19, 19, 72, 19, 76, 76, 
  20 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 6 ], 
  [ 6, 1, 1, 8 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], 
  [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 16, 1, 1, 8 ], 
  [ 19, 1, 1, 8 ], [ 20, 1, 1, 8 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 6 ], 
  [ 25, 1, 1, 4 ], [ 28, 1, 1, 4 ] ]

    k = 2: F-action on Pi is (  7,240)      [35,1,2]
      Dynkin type is A_3(q) + A_1(q) + A_1(q^2) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/8 phi2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 7 modulo 60:   1/8 phi2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 11 modulo 60:   1/8 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 19 modulo 60:   1/8 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 23 modulo 60:   1/8 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 27 modulo 60:   1/8 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 31 modulo 60:   1/8 phi2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 41 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 43 modulo 60:   1/8 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/8 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 53 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 59 modulo 60:   1/8 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 70, 68, 19, 68, 19, 7, 76, 3, 72, 69, 20, 30, 97, 81, 59, 72, 
  18, 20, 74 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], 
  [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 13, 1, 2, 4 ], 
  [ 13, 1, 4, 4 ], [ 20, 1, 1, 8 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], 
  [ 25, 1, 4, 4 ], [ 28, 1, 3, 4 ] ]

    k = 3: F-action on Pi is ()      [35,1,3]
      Dynkin type is A_3(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 7 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 11 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 13 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 19 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 21 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 23 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 25 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 27 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 29 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 31 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 41 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 43 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 47 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 49 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 53 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 59 modulo 60:   1/8 phi1 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 4, 68, 4, 68, 68, 3, 4, 68, 68, 7, 68, 7, 7, 69, 68, 7, 7, 
  69, 3, 69, 69, 5, 77, 30, 30, 81, 30, 81, 81, 27, 19, 76, 76, 20, 72, 20, 
  20, 71 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 6 ], [ 9, 1, 1, 3 ], 
  [ 10, 1, 2, 2 ], [ 13, 1, 1, 8 ], [ 20, 1, 2, 8 ], [ 23, 1, 1, 2 ], 
  [ 24, 1, 2, 6 ], [ 25, 1, 1, 4 ], [ 28, 1, 2, 4 ] ]

    k = 4: F-action on Pi is (  7,240)      [35,1,4]
      Dynkin type is A_3(q) + A_1(q) + A_1(q^2) + T(phi2^2)
      Order of center |Z^F|: phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/8 phi2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 7 modulo 60:   1/8 phi2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 11 modulo 60:   1/8 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 19 modulo 60:   1/8 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 23 modulo 60:   1/8 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 27 modulo 60:   1/8 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 31 modulo 60:   1/8 phi2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 41 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 43 modulo 60:   1/8 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/8 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 53 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 59 modulo 60:   1/8 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 19, 3, 72, 7, 76, 69, 20, 69, 20, 5, 71, 81, 59, 27, 95, 20, 
  74, 71, 17 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], 
  [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], 
  [ 12, 1, 2, 4 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 16, 1, 4, 8 ], 
  [ 20, 1, 2, 8 ], [ 23, 1, 2, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 4, 4 ], 
  [ 28, 1, 4, 4 ] ]

    k = 5: F-action on Pi is (  2,  5)(  7,240)      [35,1,5]
      Dynkin type is ^2A_3(q) + A_1(q) + A_1(q^2) + T(phi1^2)
      Order of center |Z^F|: phi1^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 7 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 11 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 13 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 19 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 21 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 23 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 25 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 27 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 29 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 31 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 41 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 43 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 47 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 49 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 53 modulo 60:   1/8 phi1 ( q-5 )
        q congruent 59 modulo 60:   1/8 ( q^2-8*q+15 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 72, 69, 20, 68, 19, 7, 76, 4, 70, 68, 19, 28, 96, 82, 60, 70, 
  16, 19, 73 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], 
  [ 4, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 4 ], 
  [ 12, 1, 1, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 16, 1, 2, 8 ], 
  [ 20, 1, 3, 8 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 2 ], [ 25, 1, 2, 4 ], 
  [ 28, 1, 1, 4 ] ]

    k = 6: F-action on Pi is (2,5)      [35,1,6]
      Dynkin type is ^2A_3(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/8 ( q^2-6*q+9 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 7 modulo 60:   1/8 ( q^2-6*q+9 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 11 modulo 60:   1/8 ( q^2-6*q+9 )
        q congruent 13 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 19 modulo 60:   1/8 ( q^2-6*q+9 )
        q congruent 21 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 23 modulo 60:   1/8 ( q^2-6*q+9 )
        q congruent 25 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 27 modulo 60:   1/8 ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 31 modulo 60:   1/8 ( q^2-6*q+9 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 41 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 43 modulo 60:   1/8 ( q^2-6*q+9 )
        q congruent 47 modulo 60:   1/8 ( q^2-6*q+9 )
        q congruent 49 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 53 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 59 modulo 60:   1/8 ( q^2-6*q+9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 69, 69, 5, 69, 5, 5, 67, 68, 7, 7, 69, 7, 69, 69, 5, 4, 68, 68, 
  3, 68, 7, 7, 69, 28, 82, 82, 31, 82, 31, 31, 78, 70, 19, 19, 72, 19, 76, 
  76, 20 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], 
  [ 10, 1, 1, 2 ], [ 13, 1, 4, 8 ], [ 20, 1, 3, 8 ], [ 23, 1, 2, 2 ], 
  [ 24, 1, 1, 6 ], [ 25, 1, 3, 4 ], [ 28, 1, 3, 4 ] ]

    k = 7: F-action on Pi is (  2,  5)(  7,240)      [35,1,7]
      Dynkin type is ^2A_3(q) + A_1(q) + A_1(q^2) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1^2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/8 phi1^2
        q congruent 7 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/8 phi1^2
        q congruent 11 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 13 modulo 60:   1/8 phi1^2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/8 phi1^2
        q congruent 19 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 21 modulo 60:   1/8 phi1^2
        q congruent 23 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 25 modulo 60:   1/8 phi1^2
        q congruent 27 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 29 modulo 60:   1/8 phi1^2
        q congruent 31 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/8 phi1^2
        q congruent 41 modulo 60:   1/8 phi1^2
        q congruent 43 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 47 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 49 modulo 60:   1/8 phi1^2
        q congruent 53 modulo 60:   1/8 phi1^2
        q congruent 59 modulo 60:   1/8 phi1 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 69, 20, 5, 71, 7, 76, 69, 20, 68, 19, 3, 72, 82, 60, 31, 98, 19, 
  73, 72, 18 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], 
  [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 13, 1, 1, 4 ], 
  [ 13, 1, 3, 4 ], [ 20, 1, 4, 8 ], [ 23, 1, 1, 2 ], [ 24, 1, 2, 2 ], 
  [ 25, 1, 2, 4 ], [ 28, 1, 2, 4 ] ]

    k = 8: F-action on Pi is (2,5)      [35,1,8]
      Dynkin type is ^2A_3(q) + A_1(q) + A_1(q) + A_1(q) + T(phi2^2)
      Order of center |Z^F|: phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q-7 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/8 ( q^2-10*q+21 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/8 ( q^2-10*q+21 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/8 phi1 ( q-7 )
        q congruent 11 modulo 60:   1/8 ( q^2-10*q+29 )
        q congruent 13 modulo 60:   1/8 phi1 ( q-7 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/8 ( q^2-10*q+21 )
        q congruent 21 modulo 60:   1/8 phi1 ( q-7 )
        q congruent 23 modulo 60:   1/8 ( q^2-10*q+29 )
        q congruent 25 modulo 60:   1/8 phi1 ( q-7 )
        q congruent 27 modulo 60:   1/8 ( q^2-10*q+21 )
        q congruent 29 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 31 modulo 60:   1/8 ( q^2-10*q+21 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/8 phi1 ( q-7 )
        q congruent 41 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/8 ( q^2-10*q+21 )
        q congruent 47 modulo 60:   1/8 ( q^2-10*q+29 )
        q congruent 49 modulo 60:   1/8 phi1 ( q-7 )
        q congruent 53 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/8 ( q^2-10*q+29 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 69, 5, 5, 67, 5, 67, 67, 2, 7, 69, 69, 5, 69, 5, 5, 67, 68, 7, 7, 
  69, 3, 69, 69, 5, 82, 31, 31, 78, 31, 78, 78, 9, 19, 76, 76, 20, 72, 20, 
  20, 71 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 6 ], 
  [ 6, 1, 2, 8 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 2 ], 
  [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 4, 8 ], [ 16, 1, 3, 8 ], 
  [ 19, 1, 2, 8 ], [ 20, 1, 4, 8 ], [ 23, 1, 2, 2 ], [ 24, 1, 2, 6 ], 
  [ 25, 1, 3, 4 ], [ 28, 1, 4, 4 ] ]

i = 36: Pi = [ 1, 3, 4, 5, 6, 7 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [36,1,1]
      Dynkin type is A_6(q) + T(phi1^2)
      Order of center |Z^F|: phi1^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 ( q^2-9*q+24 )
        q congruent 2 modulo 60:   1/4 ( q^2-8*q+12 )
        q congruent 3 modulo 60:   1/4 ( q^2-9*q+18 )
        q congruent 4 modulo 60:   1/4 ( q^2-8*q+16 )
        q congruent 5 modulo 60:   1/4 ( q^2-9*q+20 )
        q congruent 7 modulo 60:   1/4 ( q^2-9*q+22 )
        q congruent 8 modulo 60:   1/4 ( q^2-8*q+12 )
        q congruent 9 modulo 60:   1/4 ( q^2-9*q+20 )
        q congruent 11 modulo 60:   1/4 ( q^2-9*q+18 )
        q congruent 13 modulo 60:   1/4 ( q^2-9*q+24 )
        q congruent 16 modulo 60:   1/4 ( q^2-8*q+16 )
        q congruent 17 modulo 60:   1/4 ( q^2-9*q+20 )
        q congruent 19 modulo 60:   1/4 ( q^2-9*q+22 )
        q congruent 21 modulo 60:   1/4 ( q^2-9*q+20 )
        q congruent 23 modulo 60:   1/4 ( q^2-9*q+18 )
        q congruent 25 modulo 60:   1/4 ( q^2-9*q+24 )
        q congruent 27 modulo 60:   1/4 ( q^2-9*q+18 )
        q congruent 29 modulo 60:   1/4 ( q^2-9*q+20 )
        q congruent 31 modulo 60:   1/4 ( q^2-9*q+22 )
        q congruent 32 modulo 60:   1/4 ( q^2-8*q+12 )
        q congruent 37 modulo 60:   1/4 ( q^2-9*q+24 )
        q congruent 41 modulo 60:   1/4 ( q^2-9*q+20 )
        q congruent 43 modulo 60:   1/4 ( q^2-9*q+22 )
        q congruent 47 modulo 60:   1/4 ( q^2-9*q+18 )
        q congruent 49 modulo 60:   1/4 ( q^2-9*q+24 )
        q congruent 53 modulo 60:   1/4 ( q^2-9*q+20 )
        q congruent 59 modulo 60:   1/4 ( q^2-9*q+18 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 4, 68, 8, 77, 30, 14, 70, 19, 97, 23, 93, 87, 41 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 2 ], 
  [ 9, 1, 1, 2 ], [ 10, 1, 1, 2 ], [ 18, 1, 1, 2 ], [ 21, 1, 1, 4 ], 
  [ 23, 1, 1, 4 ], [ 26, 1, 1, 4 ] ]

    k = 2: F-action on Pi is ()      [36,1,2]
      Dynkin type is A_6(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 2 modulo 60:   1/4 q ( q-2 )
        q congruent 3 modulo 60:   1/4 q ( q-3 )
        q congruent 4 modulo 60:   1/4 q ( q-2 )
        q congruent 5 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 7 modulo 60:   1/4 q ( q-3 )
        q congruent 8 modulo 60:   1/4 q ( q-2 )
        q congruent 9 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 11 modulo 60:   1/4 q ( q-3 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 16 modulo 60:   1/4 q ( q-2 )
        q congruent 17 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 19 modulo 60:   1/4 q ( q-3 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 23 modulo 60:   1/4 q ( q-3 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 27 modulo 60:   1/4 q ( q-3 )
        q congruent 29 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 31 modulo 60:   1/4 q ( q-3 )
        q congruent 32 modulo 60:   1/4 q ( q-2 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 41 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 43 modulo 60:   1/4 q ( q-3 )
        q congruent 47 modulo 60:   1/4 q ( q-3 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 53 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 59 modulo 60:   1/4 q ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 68, 7, 77, 30, 81, 83, 19, 76, 59, 93, 50, 40, 103 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 18, 1, 1, 2 ], [ 26, 1, 3, 4 ] ]

    k = 3: F-action on Pi is (1,7)(3,6)(4,5)      [36,1,3]
      Dynkin type is ^2A_6(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 2 modulo 60:   1/4 q ( q-2 )
        q congruent 3 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 4 modulo 60:   1/4 q ( q-2 )
        q congruent 5 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 7 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 8 modulo 60:   1/4 q ( q-2 )
        q congruent 9 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 11 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 16 modulo 60:   1/4 q ( q-2 )
        q congruent 17 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 19 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 23 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 27 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 29 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 31 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 32 modulo 60:   1/4 q ( q-2 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 41 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 43 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 47 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 53 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 59 modulo 60:   1/4 ( q^2-3*q+4 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 5, 69, 7, 78, 31, 82, 84, 20, 76, 60, 94, 51, 40, 104 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 2 ], 
  [ 10, 1, 1, 2 ], [ 18, 1, 2, 2 ], [ 26, 1, 2, 4 ] ]

    k = 4: F-action on Pi is (1,7)(3,6)(4,5)      [36,1,4]
      Dynkin type is ^2A_6(q) + T(phi2^2)
      Order of center |Z^F|: phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-4 )
        q congruent 2 modulo 60:   1/4 ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/4 ( q^2-5*q+6 )
        q congruent 4 modulo 60:   1/4 q ( q-4 )
        q congruent 5 modulo 60:   1/4 ( q^2-5*q+8 )
        q congruent 7 modulo 60:   1/4 ( q^2-5*q+6 )
        q congruent 8 modulo 60:   1/4 ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/4 phi1 ( q-4 )
        q congruent 11 modulo 60:   1/4 ( q^2-5*q+10 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-4 )
        q congruent 16 modulo 60:   1/4 q ( q-4 )
        q congruent 17 modulo 60:   1/4 ( q^2-5*q+8 )
        q congruent 19 modulo 60:   1/4 ( q^2-5*q+6 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-4 )
        q congruent 23 modulo 60:   1/4 ( q^2-5*q+10 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-4 )
        q congruent 27 modulo 60:   1/4 ( q^2-5*q+6 )
        q congruent 29 modulo 60:   1/4 ( q^2-5*q+8 )
        q congruent 31 modulo 60:   1/4 ( q^2-5*q+6 )
        q congruent 32 modulo 60:   1/4 ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-4 )
        q congruent 41 modulo 60:   1/4 ( q^2-5*q+8 )
        q congruent 43 modulo 60:   1/4 ( q^2-5*q+6 )
        q congruent 47 modulo 60:   1/4 ( q^2-5*q+10 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-4 )
        q congruent 53 modulo 60:   1/4 ( q^2-5*q+8 )
        q congruent 59 modulo 60:   1/4 ( q^2-5*q+10 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 2, 67, 5, 69, 9, 78, 31, 15, 71, 20, 98, 24, 94, 88, 42 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 2 ], 
  [ 9, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 18, 1, 2, 2 ], [ 21, 1, 2, 4 ], 
  [ 23, 1, 2, 4 ], [ 26, 1, 4, 4 ] ]

i = 37: Pi = [ 1, 3, 4, 6, 7, 8 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [37,1,1]
      Dynkin type is A_3(q) + A_3(q) + T(phi1^2)
      Order of center |Z^F|: phi1^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 ( q^2-12*q+51 )
        q congruent 2 modulo 60:   1/8 ( q^2-10*q+16 )
        q congruent 3 modulo 60:   1/8 ( q^2-12*q+27 )
        q congruent 4 modulo 60:   1/8 ( q^2-10*q+24 )
        q congruent 5 modulo 60:   1/8 ( q^2-12*q+35 )
        q congruent 7 modulo 60:   1/8 ( q^2-12*q+35 )
        q congruent 8 modulo 60:   1/8 ( q^2-10*q+16 )
        q congruent 9 modulo 60:   1/8 ( q^2-12*q+35 )
        q congruent 11 modulo 60:   1/8 ( q^2-12*q+35 )
        q congruent 13 modulo 60:   1/8 ( q^2-12*q+43 )
        q congruent 16 modulo 60:   1/8 ( q^2-10*q+32 )
        q congruent 17 modulo 60:   1/8 ( q^2-12*q+35 )
        q congruent 19 modulo 60:   1/8 ( q^2-12*q+35 )
        q congruent 21 modulo 60:   1/8 ( q^2-12*q+43 )
        q congruent 23 modulo 60:   1/8 ( q^2-12*q+27 )
        q congruent 25 modulo 60:   1/8 ( q^2-12*q+43 )
        q congruent 27 modulo 60:   1/8 ( q^2-12*q+27 )
        q congruent 29 modulo 60:   1/8 ( q^2-12*q+35 )
        q congruent 31 modulo 60:   1/8 ( q^2-12*q+43 )
        q congruent 32 modulo 60:   1/8 ( q^2-10*q+16 )
        q congruent 37 modulo 60:   1/8 ( q^2-12*q+43 )
        q congruent 41 modulo 60:   1/8 ( q^2-12*q+43 )
        q congruent 43 modulo 60:   1/8 ( q^2-12*q+35 )
        q congruent 47 modulo 60:   1/8 ( q^2-12*q+27 )
        q congruent 49 modulo 60:   1/8 ( q^2-12*q+43 )
        q congruent 53 modulo 60:   1/8 ( q^2-12*q+35 )
        q congruent 59 modulo 60:   1/8 ( q^2-12*q+27 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 4, 8, 70, 66, 4, 68, 77, 19, 4, 68, 7, 30, 76, 8, 77, 30, 
  14, 97, 70, 19, 76, 97, 22 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 5, 1, 1, 8 ], [ 8, 1, 1, 4 ], 
  [ 9, 1, 1, 3 ], [ 14, 1, 1, 8 ], [ 21, 1, 1, 4 ], [ 23, 1, 1, 4 ], 
  [ 25, 1, 1, 8 ] ]

    k = 2: F-action on Pi is (6,8)      [37,1,2]
      Dynkin type is A_3(q) + ^2A_3(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 2 modulo 60:   1/4 q ( q-2 )
        q congruent 3 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 4 modulo 60:   1/4 q ( q-2 )
        q congruent 5 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 7 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 8 modulo 60:   1/4 q ( q-2 )
        q congruent 9 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 11 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 16 modulo 60:   1/4 q ( q-2 )
        q congruent 17 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 19 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 23 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 27 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 29 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 31 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 32 modulo 60:   1/4 q ( q-2 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 41 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 43 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 47 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 53 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 59 modulo 60:   1/4 phi1 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 68, 4, 28, 70, 69, 7, 68, 82, 19, 5, 69, 7, 31, 76, 27, 81, 30, 
  36, 97, 71, 20, 76, 98, 22 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 3 ], 
  [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 1, 4 ], [ 25, 1, 3, 4 ] ]

    k = 3: F-action on Pi is (1,4)(6,8)      [37,1,3]
      Dynkin type is ^2A_3(q) + ^2A_3(q) + T(phi2^2)
      Order of center |Z^F|: phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q-7 )
        q congruent 2 modulo 60:   1/8 ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 4 modulo 60:   1/8 ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 8 modulo 60:   1/8 ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/8 ( q^2-8*q+23 )
        q congruent 13 modulo 60:   1/8 phi1 ( q-7 )
        q congruent 16 modulo 60:   1/8 q ( q-6 )
        q congruent 17 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/8 ( q^2-8*q+23 )
        q congruent 21 modulo 60:   1/8 phi1 ( q-7 )
        q congruent 23 modulo 60:   1/8 ( q^2-8*q+23 )
        q congruent 25 modulo 60:   1/8 phi1 ( q-7 )
        q congruent 27 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 29 modulo 60:   1/8 ( q^2-8*q+23 )
        q congruent 31 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 32 modulo 60:   1/8 ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/8 phi1 ( q-7 )
        q congruent 41 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 47 modulo 60:   1/8 ( q^2-8*q+23 )
        q congruent 49 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 53 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/8 ( q^2-8*q+31 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 2, 67, 5, 9, 71, 67, 5, 69, 78, 20, 5, 69, 7, 31, 76, 9, 78, 31, 
  15, 98, 71, 20, 76, 98, 22 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 8, 1, 2, 4 ], 
  [ 9, 1, 1, 3 ], [ 14, 1, 2, 8 ], [ 21, 1, 2, 4 ], [ 23, 1, 2, 4 ], 
  [ 25, 1, 3, 8 ] ]

    k = 4: F-action on Pi is (1,6)(3,7)(4,8)      [37,1,4]
      Dynkin type is A_3(q^2) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1^2
        q congruent 2 modulo 60:   1/4 q ( q-2 )
        q congruent 3 modulo 60:   1/4 phi1^2
        q congruent 4 modulo 60:   1/4 q ( q-2 )
        q congruent 5 modulo 60:   1/4 phi1^2
        q congruent 7 modulo 60:   1/4 phi1^2
        q congruent 8 modulo 60:   1/4 q ( q-2 )
        q congruent 9 modulo 60:   1/4 phi1^2
        q congruent 11 modulo 60:   1/4 phi1^2
        q congruent 13 modulo 60:   1/4 phi1^2
        q congruent 16 modulo 60:   1/4 q ( q-2 )
        q congruent 17 modulo 60:   1/4 phi1^2
        q congruent 19 modulo 60:   1/4 phi1^2
        q congruent 21 modulo 60:   1/4 phi1^2
        q congruent 23 modulo 60:   1/4 phi1^2
        q congruent 25 modulo 60:   1/4 phi1^2
        q congruent 27 modulo 60:   1/4 phi1^2
        q congruent 29 modulo 60:   1/4 phi1^2
        q congruent 31 modulo 60:   1/4 phi1^2
        q congruent 32 modulo 60:   1/4 q ( q-2 )
        q congruent 37 modulo 60:   1/4 phi1^2
        q congruent 41 modulo 60:   1/4 phi1^2
        q congruent 43 modulo 60:   1/4 phi1^2
        q congruent 47 modulo 60:   1/4 phi1^2
        q congruent 49 modulo 60:   1/4 phi1^2
        q congruent 53 modulo 60:   1/4 phi1^2
        q congruent 59 modulo 60:   1/4 phi1^2
      Fusion of maximal tori of C^F in those of G^F:
        [ 7, 76, 22, 40, 92 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 8, 1, 1, 2 ], [ 8, 1, 2, 2 ], [ 9, 1, 1, 1 ], 
  [ 21, 1, 1, 2 ], [ 21, 1, 2, 2 ] ]

    k = 5: F-action on Pi is (1,6,4,8)(3,7)      [37,1,5]
      Dynkin type is ^2A_3(q^2) + T(phi4)
      Order of center |Z^F|: phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 phi2
        q congruent 2 modulo 60:   1/4 ( q^2-4 )
        q congruent 3 modulo 60:   1/4 ( q^2-5 )
        q congruent 4 modulo 60:   1/4 q^2
        q congruent 5 modulo 60:   1/4 phi1 phi2
        q congruent 7 modulo 60:   1/4 ( q^2-5 )
        q congruent 8 modulo 60:   1/4 ( q^2-4 )
        q congruent 9 modulo 60:   1/4 phi1 phi2
        q congruent 11 modulo 60:   1/4 phi1 phi2
        q congruent 13 modulo 60:   1/4 ( q^2-5 )
        q congruent 16 modulo 60:   1/4 q^2
        q congruent 17 modulo 60:   1/4 ( q^2-5 )
        q congruent 19 modulo 60:   1/4 phi1 phi2
        q congruent 21 modulo 60:   1/4 phi1 phi2
        q congruent 23 modulo 60:   1/4 ( q^2-5 )
        q congruent 25 modulo 60:   1/4 phi1 phi2
        q congruent 27 modulo 60:   1/4 ( q^2-5 )
        q congruent 29 modulo 60:   1/4 phi1 phi2
        q congruent 31 modulo 60:   1/4 phi1 phi2
        q congruent 32 modulo 60:   1/4 ( q^2-4 )
        q congruent 37 modulo 60:   1/4 ( q^2-5 )
        q congruent 41 modulo 60:   1/4 phi1 phi2
        q congruent 43 modulo 60:   1/4 ( q^2-5 )
        q congruent 47 modulo 60:   1/4 ( q^2-5 )
        q congruent 49 modulo 60:   1/4 phi1 phi2
        q congruent 53 modulo 60:   1/4 ( q^2-5 )
        q congruent 59 modulo 60:   1/4 phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 6, 75, 22, 39, 92 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 5, 1, 3, 4 ], [ 5, 1, 4, 4 ], [ 9, 1, 1, 1 ] ]

i = 38: Pi = [ 1, 3, 5, 6, 8, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [38,1,1]
      Dynkin type is A_2(q) + A_2(q) + A_2(q) + T(phi1^2)
      Order of center |Z^F|: phi1^2 times
        1, q congruent 0 modulo 3
        3, q congruent 1 modulo 3
        1, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/36 ( q^2-14*q+49 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   1/36 ( q^2-14*q+40 )
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1/36 ( q^2-14*q+49 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1/36 ( q^2-14*q+49 )
        q congruent 16 modulo 60:   1/36 ( q^2-14*q+40 )
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1/36 ( q^2-14*q+49 )
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1/36 ( q^2-14*q+49 )
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1/36 ( q^2-14*q+49 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/36 ( q^2-14*q+49 )
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1/36 ( q^2-14*q+49 )
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1/36 ( q^2-14*q+49 )
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 8, 66, 4, 77, 8, 77, 14, 66, 4, 77, 4, 68, 30, 77, 30, 83, 
  8, 77, 14, 77, 30, 83, 14, 83, 12 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 8 ], [ 6, 1, 1, 18 ], 
  [ 8, 1, 1, 12 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 17, 1, 1, 36 ], 
  [ 22, 1, 1, 36 ], [ 27, 1, 1, 12 ] ]

    k = 2: F-action on Pi is (  5,  8)(  6,240)      [38,1,2]
      Dynkin type is A_2(q) + A_2(q^2) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 3
        3, q congruent 1 modulo 3
        1, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1^2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   1/4 q ( q-2 )
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1/4 phi1^2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1/4 phi1^2
        q congruent 16 modulo 60:   1/4 q ( q-2 )
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1/4 phi1^2
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1/4 phi1^2
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1/4 phi1^2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 phi1^2
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1/4 phi1^2
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1/4 phi1^2
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 19, 87, 7, 76, 40, 81, 59, 85 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], 
  [ 6, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], 
  [ 17, 1, 2, 4 ], [ 22, 1, 1, 4 ], [ 27, 1, 3, 4 ] ]

    k = 3: F-action on Pi is ()      [38,1,3]
      Dynkin type is A_2(q) + A_2(q) + A_2(q) + T(phi3)
      Order of center |Z^F|: phi3 times
        1, q congruent 0 modulo 3
        3, q congruent 1 modulo 3
        1, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/18 phi1 ( q+2 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   1/18 phi1 ( q+2 )
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1/18 phi1 ( q+2 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1/18 phi1 ( q+2 )
        q congruent 16 modulo 60:   1/18 phi1 ( q+2 )
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1/18 phi1 ( q+2 )
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1/18 phi1 ( q+2 )
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1/18 phi1 ( q+2 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/18 phi1 ( q+2 )
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1/18 phi1 ( q+2 )
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1/18 phi1 ( q+2 )
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 8, 77, 14, 77, 30, 83, 14, 83, 12, 77, 30, 83, 30, 81, 37, 83, 37, 
  79, 14, 83, 12, 83, 37, 79, 12, 79, 10 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 27, 1, 5, 6 ] ]

    k = 4: F-action on Pi is (  5,  8)(  6,240)      [38,1,4]
      Dynkin type is A_2(q) + A_2(q^2) + T(phi6)
      Order of center |Z^F|: phi6 times
        1, q congruent 0 modulo 3
        3, q congruent 1 modulo 3
        1, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/6 q phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   1/6 q phi1
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1/6 q phi1
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1/6 q phi1
        q congruent 16 modulo 60:   1/6 q phi1
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1/6 q phi1
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1/6 q phi1
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1/6 q phi1
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/6 q phi1
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1/6 q phi1
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1/6 q phi1
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 28, 96, 33, 82, 60, 86, 36, 99, 29 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 27, 1, 4, 6 ] ]

    k = 5: F-action on Pi is ()      [38,1,5]
      Dynkin type is A_2(q) + A_2(q) + A_2(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 3
        3, q congruent 1 modulo 3
        1, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   1/12 q ( q-4 )
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 16 modulo 60:   1/12 q ( q-4 )
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 77, 4, 68, 30, 77, 30, 83, 4, 68, 30, 68, 7, 81, 30, 81, 37, 
  77, 30, 83, 30, 81, 37, 83, 37, 79 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 6, 1, 1, 6 ], 
  [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 17, 1, 1, 12 ], [ 22, 1, 2, 12 ], 
  [ 27, 1, 2, 4 ] ]

    k = 6: F-action on Pi is (  5,  8)(  6,240)      [38,1,6]
      Dynkin type is A_2(q) + A_2(q^2) + T(phi2^2)
      Order of center |Z^F|: phi2^2 times
        1, q congruent 0 modulo 3
        3, q congruent 1 modulo 3
        1, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   1/12 q ( q-4 )
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 16 modulo 60:   1/12 q ( q-4 )
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1/12 phi1 ( q-3 )
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 72, 35, 69, 20, 88, 27, 95, 34 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], 
  [ 6, 1, 1, 6 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ], [ 17, 1, 2, 12 ], 
  [ 22, 1, 2, 12 ], [ 27, 1, 6, 12 ] ]

    k = 7: F-action on Pi is (  1,  3)(  5,240)(  6,  8)      [38,1,7]
      Dynkin type is ^2A_2(q) + A_2(q^2) + T(phi1^2)
      Order of center |Z^F|: phi1^2 times
        1, q congruent 0 modulo 3
        1, q congruent 1 modulo 3
        3, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   1/12 ( q^2-8*q+12 )
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/12 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   1/12 ( q^2-8*q+12 )
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1/12 ( q^2-8*q+15 )
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/12 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1/12 ( q^2-8*q+15 )
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1/12 ( q^2-8*q+15 )
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   1/12 ( q^2-8*q+12 )
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   1/12 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   1/12 ( q^2-8*q+15 )
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   1/12 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/12 ( q^2-8*q+15 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 72, 35, 68, 19, 87, 28, 96, 33 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], 
  [ 6, 1, 2, 6 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 17, 1, 3, 12 ], 
  [ 22, 1, 3, 12 ], [ 27, 1, 1, 12 ] ]

    k = 8: F-action on Pi is (  1,  3)(  5,  6)(  8,240)      [38,1,8]
      Dynkin type is ^2A_2(q) + ^2A_2(q) + ^2A_2(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 3
        1, q congruent 1 modulo 3
        3, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   1/12 ( q^2-4*q+4 )
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/12 ( q^2-4*q+7 )
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   1/12 ( q^2-4*q+4 )
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1/12 ( q^2-4*q+7 )
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/12 ( q^2-4*q+7 )
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1/12 ( q^2-4*q+7 )
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1/12 ( q^2-4*q+7 )
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   1/12 ( q^2-4*q+4 )
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   1/12 ( q^2-4*q+7 )
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   1/12 ( q^2-4*q+7 )
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   1/12 ( q^2-4*q+7 )
        q congruent 59 modulo 60:   1/12 ( q^2-4*q+7 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 5, 78, 5, 69, 31, 78, 31, 84, 5, 69, 31, 69, 7, 82, 31, 82, 38, 
  78, 31, 84, 31, 82, 38, 84, 38, 80 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 6, 1, 2, 6 ], 
  [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 4, 12 ], [ 22, 1, 3, 12 ], 
  [ 27, 1, 3, 4 ] ]

    k = 9: F-action on Pi is (  1,  3)(  5,240)(  6,  8)      [38,1,9]
      Dynkin type is ^2A_2(q) + A_2(q^2) + T(phi3)
      Order of center |Z^F|: phi3 times
        1, q congruent 0 modulo 3
        1, q congruent 1 modulo 3
        3, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   1/6 q phi2
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/6 q phi2
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   1/6 q phi2
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1/6 q phi2
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/6 q phi2
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1/6 q phi2
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1/6 q phi2
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   1/6 q phi2
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   1/6 q phi2
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   1/6 q phi2
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   1/6 q phi2
        q congruent 59 modulo 60:   1/6 q phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 27, 95, 34, 81, 59, 85, 36, 99, 29 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 27, 1, 5, 6 ] ]

    k = 10: F-action on Pi is (  1,  3)(  5,240)(  6,  8)      [38,1,10]
      Dynkin type is ^2A_2(q) + A_2(q^2) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 3
        1, q congruent 1 modulo 3
        3, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   1/4 q ( q-2 )
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 phi1^2
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   1/4 q ( q-2 )
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1/4 phi1^2
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 phi1^2
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1/4 phi1^2
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1/4 phi1^2
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   1/4 q ( q-2 )
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   1/4 phi1^2
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   1/4 phi1^2
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   1/4 phi1^2
        q congruent 59 modulo 60:   1/4 phi1^2
      Fusion of maximal tori of C^F in those of G^F:
        [ 69, 20, 88, 7, 76, 40, 82, 60, 86 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], 
  [ 6, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], 
  [ 17, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 27, 1, 2, 4 ] ]

    k = 11: F-action on Pi is (  1,  3)(  5,  6)(  8,240)      [38,1,11]
      Dynkin type is ^2A_2(q) + ^2A_2(q) + ^2A_2(q) + T(phi6)
      Order of center |Z^F|: phi6 times
        1, q congruent 0 modulo 3
        1, q congruent 1 modulo 3
        3, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   1/18 phi2 ( q-2 )
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/18 phi2 ( q-2 )
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   1/18 phi2 ( q-2 )
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1/18 phi2 ( q-2 )
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/18 phi2 ( q-2 )
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1/18 phi2 ( q-2 )
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1/18 phi2 ( q-2 )
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   1/18 phi2 ( q-2 )
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   1/18 phi2 ( q-2 )
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   1/18 phi2 ( q-2 )
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   1/18 phi2 ( q-2 )
        q congruent 59 modulo 60:   1/18 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 9, 78, 15, 78, 31, 84, 15, 84, 13, 78, 31, 84, 31, 82, 38, 84, 38, 
  80, 15, 84, 13, 84, 38, 80, 13, 80, 11 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 27, 1, 4, 6 ] ]

    k = 12: F-action on Pi is (  1,  3)(  5,  6)(  8,240)      [38,1,12]
      Dynkin type is ^2A_2(q) + ^2A_2(q) + ^2A_2(q) + T(phi2^2)
      Order of center |Z^F|: phi2^2 times
        1, q congruent 0 modulo 3
        1, q congruent 1 modulo 3
        3, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   1/36 ( q^2-10*q+16 )
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/36 ( q^2-10*q+25 )
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   1/36 ( q^2-10*q+16 )
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1/36 ( q^2-10*q+25 )
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/36 ( q^2-10*q+25 )
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1/36 ( q^2-10*q+25 )
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1/36 ( q^2-10*q+25 )
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   1/36 ( q^2-10*q+16 )
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   1/36 ( q^2-10*q+25 )
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   1/36 ( q^2-10*q+25 )
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   1/36 ( q^2-10*q+25 )
        q congruent 59 modulo 60:   1/36 ( q^2-10*q+25 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 2, 67, 9, 67, 5, 78, 9, 78, 15, 67, 5, 78, 5, 69, 31, 78, 31, 84, 
  9, 78, 15, 78, 31, 84, 15, 84, 13 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 8 ], [ 6, 1, 2, 18 ], 
  [ 8, 1, 2, 12 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ], [ 17, 1, 4, 36 ], 
  [ 22, 1, 4, 36 ], [ 27, 1, 6, 12 ] ]

    k = 13: F-action on Pi is (  1,  5,  8)(  3,  6,240)      [38,1,13]
      Dynkin type is A_2(q^3) + T(phi1^2)
      Order of center |Z^F|: phi1^2 times
        1, q congruent 0 modulo 3
        3, q congruent 1 modulo 3
        1, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/18 phi1 ( q-4 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   1/18 phi1 ( q-4 )
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1/18 phi1 ( q-4 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1/18 phi1 ( q-4 )
        q congruent 16 modulo 60:   1/18 phi1 ( q-4 )
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1/18 phi1 ( q-4 )
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1/18 phi1 ( q-4 )
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1/18 phi1 ( q-4 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/18 phi1 ( q-4 )
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1/18 phi1 ( q-4 )
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1/18 phi1 ( q-4 )
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 14, 87, 46 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 10, 1, 1, 6 ], 
  [ 11, 1, 1, 6 ], [ 17, 1, 5, 18 ], [ 27, 1, 1, 12 ] ]

    k = 14: F-action on Pi is (  1,  5,  8)(  3,  6,240)      [38,1,14]
      Dynkin type is A_2(q^3) + T(phi3)
      Order of center |Z^F|: phi3 times
        1, q congruent 0 modulo 3
        3, q congruent 1 modulo 3
        1, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/9 phi1 ( q+2 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   1/9 phi1 ( q+2 )
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1/9 phi1 ( q+2 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1/9 phi1 ( q+2 )
        q congruent 16 modulo 60:   1/9 phi1 ( q+2 )
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1/9 phi1 ( q+2 )
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1/9 phi1 ( q+2 )
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1/9 phi1 ( q+2 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/9 phi1 ( q+2 )
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1/9 phi1 ( q+2 )
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1/9 phi1 ( q+2 )
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 12, 85, 48 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 8, 1, 1, 6 ], [ 27, 1, 5, 6 ] ]

    k = 15: F-action on Pi is (  1,  5,  8)(  3,  6,240)      [38,1,15]
      Dynkin type is A_2(q^3) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 3
        3, q congruent 1 modulo 3
        1, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/6 q phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   1/6 q phi1
        q congruent 5 modulo 60:   0
        q congruent 7 modulo 60:   1/6 q phi1
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   0
        q congruent 13 modulo 60:   1/6 q phi1
        q congruent 16 modulo 60:   1/6 q phi1
        q congruent 17 modulo 60:   0
        q congruent 19 modulo 60:   1/6 q phi1
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   0
        q congruent 25 modulo 60:   1/6 q phi1
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   0
        q congruent 31 modulo 60:   1/6 q phi1
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/6 q phi1
        q congruent 41 modulo 60:   0
        q congruent 43 modulo 60:   1/6 q phi1
        q congruent 47 modulo 60:   0
        q congruent 49 modulo 60:   1/6 q phi1
        q congruent 53 modulo 60:   0
        q congruent 59 modulo 60:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 83, 40, 105 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 10, 1, 2, 2 ], 
  [ 11, 1, 1, 2 ], [ 17, 1, 5, 6 ], [ 27, 1, 2, 4 ] ]

    k = 16: F-action on Pi is (  1,  6,  8,  3,  5,240)      [38,1,16]
      Dynkin type is ^2A_2(q^3) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 3
        1, q congruent 1 modulo 3
        3, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 59 modulo 60:   1/6 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 84, 40, 106 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 10, 1, 1, 2 ], 
  [ 11, 1, 2, 2 ], [ 17, 1, 6, 6 ], [ 27, 1, 3, 4 ] ]

    k = 17: F-action on Pi is (  1,  6,  8,  3,  5,240)      [38,1,17]
      Dynkin type is ^2A_2(q^3) + T(phi6)
      Order of center |Z^F|: phi6 times
        1, q congruent 0 modulo 3
        1, q congruent 1 modulo 3
        3, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   1/9 phi2 ( q-2 )
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/9 phi2 ( q-2 )
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   1/9 phi2 ( q-2 )
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1/9 phi2 ( q-2 )
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/9 phi2 ( q-2 )
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1/9 phi2 ( q-2 )
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1/9 phi2 ( q-2 )
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   1/9 phi2 ( q-2 )
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   1/9 phi2 ( q-2 )
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   1/9 phi2 ( q-2 )
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   1/9 phi2 ( q-2 )
        q congruent 59 modulo 60:   1/9 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 13, 86, 49 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 8, 1, 2, 6 ], [ 27, 1, 4, 6 ] ]

    k = 18: F-action on Pi is (  1,  6,  8,  3,  5,240)      [38,1,18]
      Dynkin type is ^2A_2(q^3) + T(phi2^2)
      Order of center |Z^F|: phi2^2 times
        1, q congruent 0 modulo 3
        1, q congruent 1 modulo 3
        3, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   0
        q congruent 2 modulo 60:   1/18 phi2 ( q-2 )
        q congruent 3 modulo 60:   0
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/18 phi2 ( q-2 )
        q congruent 7 modulo 60:   0
        q congruent 8 modulo 60:   1/18 phi2 ( q-2 )
        q congruent 9 modulo 60:   0
        q congruent 11 modulo 60:   1/18 phi2 ( q-2 )
        q congruent 13 modulo 60:   0
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/18 phi2 ( q-2 )
        q congruent 19 modulo 60:   0
        q congruent 21 modulo 60:   0
        q congruent 23 modulo 60:   1/18 phi2 ( q-2 )
        q congruent 25 modulo 60:   0
        q congruent 27 modulo 60:   0
        q congruent 29 modulo 60:   1/18 phi2 ( q-2 )
        q congruent 31 modulo 60:   0
        q congruent 32 modulo 60:   1/18 phi2 ( q-2 )
        q congruent 37 modulo 60:   0
        q congruent 41 modulo 60:   1/18 phi2 ( q-2 )
        q congruent 43 modulo 60:   0
        q congruent 47 modulo 60:   1/18 phi2 ( q-2 )
        q congruent 49 modulo 60:   0
        q congruent 53 modulo 60:   1/18 phi2 ( q-2 )
        q congruent 59 modulo 60:   1/18 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 15, 88, 47 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 10, 1, 2, 6 ], 
  [ 11, 1, 2, 6 ], [ 17, 1, 6, 18 ], [ 27, 1, 6, 12 ] ]

i = 39: Pi = [ 2, 3, 4, 5, 6, 7 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [39,1,1]
      Dynkin type is D_6(q) + T(phi1^2)
      Order of center |Z^F|: phi1^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 2 modulo 60:   1/8 ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 4 modulo 60:   1/8 ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 8 modulo 60:   1/8 ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 13 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 16 modulo 60:   1/8 ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 21 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 23 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 25 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 27 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 29 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 31 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 32 modulo 60:   1/8 ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 41 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 47 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 49 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 53 modulo 60:   1/8 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/8 ( q^2-8*q+15 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 4, 3, 5, 66, 70, 68, 72, 69, 4, 16, 19, 7, 18, 68, 68, 73, 8, 
  28, 30, 31, 77, 96, 82, 97, 14, 38, 70, 89, 76, 19, 19, 44, 23, 51, 87, 87 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], 
  [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ] ]

    k = 2: F-action on Pi is (2,3)      [39,1,2]
      Dynkin type is ^2D_6(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1^2
        q congruent 2 modulo 60:   1/4 q ( q-2 )
        q congruent 3 modulo 60:   1/4 phi1^2
        q congruent 4 modulo 60:   1/4 q ( q-2 )
        q congruent 5 modulo 60:   1/4 phi1^2
        q congruent 7 modulo 60:   1/4 phi1^2
        q congruent 8 modulo 60:   1/4 q ( q-2 )
        q congruent 9 modulo 60:   1/4 phi1^2
        q congruent 11 modulo 60:   1/4 phi1^2
        q congruent 13 modulo 60:   1/4 phi1^2
        q congruent 16 modulo 60:   1/4 q ( q-2 )
        q congruent 17 modulo 60:   1/4 phi1^2
        q congruent 19 modulo 60:   1/4 phi1^2
        q congruent 21 modulo 60:   1/4 phi1^2
        q congruent 23 modulo 60:   1/4 phi1^2
        q congruent 25 modulo 60:   1/4 phi1^2
        q congruent 27 modulo 60:   1/4 phi1^2
        q congruent 29 modulo 60:   1/4 phi1^2
        q congruent 31 modulo 60:   1/4 phi1^2
        q congruent 32 modulo 60:   1/4 q ( q-2 )
        q congruent 37 modulo 60:   1/4 phi1^2
        q congruent 41 modulo 60:   1/4 phi1^2
        q congruent 43 modulo 60:   1/4 phi1^2
        q congruent 47 modulo 60:   1/4 phi1^2
        q congruent 49 modulo 60:   1/4 phi1^2
        q congruent 53 modulo 60:   1/4 phi1^2
        q congruent 59 modulo 60:   1/4 phi1^2
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 3, 5, 70, 68, 72, 69, 71, 19, 7, 18, 20, 76, 75, 28, 30, 31, 27, 
  82, 97, 81, 98, 36, 89, 76, 90, 43, 22, 51, 50, 100 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 9, 1, 1, 1 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ] ]

    k = 3: F-action on Pi is ()      [39,1,3]
      Dynkin type is D_6(q) + T(phi2^2)
      Order of center |Z^F|: phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 2 modulo 60:   1/8 q ( q-2 )
        q congruent 3 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 4 modulo 60:   1/8 q ( q-2 )
        q congruent 5 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 7 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 8 modulo 60:   1/8 q ( q-2 )
        q congruent 9 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 11 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 13 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 16 modulo 60:   1/8 q ( q-2 )
        q congruent 17 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 19 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 21 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 23 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 25 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 27 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 29 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 31 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 32 modulo 60:   1/8 q ( q-2 )
        q congruent 37 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 41 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 43 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 47 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 49 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 53 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 59 modulo 60:   1/8 phi1 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 3, 5, 2, 68, 72, 69, 71, 67, 7, 18, 20, 5, 17, 69, 69, 74, 30, 
  31, 27, 9, 81, 98, 78, 95, 37, 15, 76, 90, 71, 20, 20, 45, 50, 24, 88, 88 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], 
  [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ] ]

    k = 4: F-action on Pi is ()      [39,1,4]
      Dynkin type is D_6(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 2 modulo 60:   1/4 q ( q-2 )
        q congruent 3 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 4 modulo 60:   1/4 q ( q-2 )
        q congruent 5 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 7 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 8 modulo 60:   1/4 q ( q-2 )
        q congruent 9 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 11 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 16 modulo 60:   1/4 q ( q-2 )
        q congruent 17 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 19 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 23 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 27 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 29 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 31 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 32 modulo 60:   1/4 q ( q-2 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 41 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 43 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 47 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 53 modulo 60:   1/4 phi1 ( q-3 )
        q congruent 59 modulo 60:   1/4 phi1 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 68, 69, 67, 4, 19, 7, 20, 5, 68, 73, 76, 69, 74, 7, 3, 18, 77, 
  82, 81, 78, 30, 60, 31, 59, 83, 84, 19, 43, 20, 76, 72, 91, 93, 94, 40, 35 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ] ]

    k = 5: F-action on Pi is (2,3)      [39,1,5]
      Dynkin type is ^2D_6(q) + T(phi4)
      Order of center |Z^F|: phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 phi2
        q congruent 2 modulo 60:   1/4 q^2
        q congruent 3 modulo 60:   1/4 phi1 phi2
        q congruent 4 modulo 60:   1/4 q^2
        q congruent 5 modulo 60:   1/4 phi1 phi2
        q congruent 7 modulo 60:   1/4 phi1 phi2
        q congruent 8 modulo 60:   1/4 q^2
        q congruent 9 modulo 60:   1/4 phi1 phi2
        q congruent 11 modulo 60:   1/4 phi1 phi2
        q congruent 13 modulo 60:   1/4 phi1 phi2
        q congruent 16 modulo 60:   1/4 q^2
        q congruent 17 modulo 60:   1/4 phi1 phi2
        q congruent 19 modulo 60:   1/4 phi1 phi2
        q congruent 21 modulo 60:   1/4 phi1 phi2
        q congruent 23 modulo 60:   1/4 phi1 phi2
        q congruent 25 modulo 60:   1/4 phi1 phi2
        q congruent 27 modulo 60:   1/4 phi1 phi2
        q congruent 29 modulo 60:   1/4 phi1 phi2
        q congruent 31 modulo 60:   1/4 phi1 phi2
        q congruent 32 modulo 60:   1/4 q^2
        q congruent 37 modulo 60:   1/4 phi1 phi2
        q congruent 41 modulo 60:   1/4 phi1 phi2
        q congruent 43 modulo 60:   1/4 phi1 phi2
        q congruent 47 modulo 60:   1/4 phi1 phi2
        q congruent 49 modulo 60:   1/4 phi1 phi2
        q congruent 53 modulo 60:   1/4 phi1 phi2
        q congruent 59 modulo 60:   1/4 phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 70, 72, 71, 16, 19, 18, 20, 17, 73, 76, 75, 74, 18, 6, 96, 97, 98, 
  95, 60, 53, 59, 54, 99, 44, 22, 45, 91, 75, 108, 107, 39 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 9, 1, 1, 1 ] ]

i = 40: Pi = [ 2, 3, 4, 5, 7, 8 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [40,1,1]
      Dynkin type is D_4(q) + A_2(q) + T(phi1^2)
      Order of center |Z^F|: phi1^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 ( q^2-11*q+34 )
        q congruent 2 modulo 60:   1/12 ( q^2-8*q+12 )
        q congruent 3 modulo 60:   1/12 ( q^2-11*q+24 )
        q congruent 4 modulo 60:   1/12 ( q^2-8*q+16 )
        q congruent 5 modulo 60:   1/12 ( q^2-11*q+30 )
        q congruent 7 modulo 60:   1/12 ( q^2-11*q+28 )
        q congruent 8 modulo 60:   1/12 ( q^2-8*q+12 )
        q congruent 9 modulo 60:   1/12 ( q^2-11*q+30 )
        q congruent 11 modulo 60:   1/12 ( q^2-11*q+24 )
        q congruent 13 modulo 60:   1/12 ( q^2-11*q+34 )
        q congruent 16 modulo 60:   1/12 ( q^2-8*q+16 )
        q congruent 17 modulo 60:   1/12 ( q^2-11*q+30 )
        q congruent 19 modulo 60:   1/12 ( q^2-11*q+28 )
        q congruent 21 modulo 60:   1/12 ( q^2-11*q+30 )
        q congruent 23 modulo 60:   1/12 ( q^2-11*q+24 )
        q congruent 25 modulo 60:   1/12 ( q^2-11*q+34 )
        q congruent 27 modulo 60:   1/12 ( q^2-11*q+24 )
        q congruent 29 modulo 60:   1/12 ( q^2-11*q+30 )
        q congruent 31 modulo 60:   1/12 ( q^2-11*q+28 )
        q congruent 32 modulo 60:   1/12 ( q^2-8*q+12 )
        q congruent 37 modulo 60:   1/12 ( q^2-11*q+34 )
        q congruent 41 modulo 60:   1/12 ( q^2-11*q+30 )
        q congruent 43 modulo 60:   1/12 ( q^2-11*q+28 )
        q congruent 47 modulo 60:   1/12 ( q^2-11*q+24 )
        q congruent 49 modulo 60:   1/12 ( q^2-11*q+34 )
        q congruent 53 modulo 60:   1/12 ( q^2-11*q+30 )
        q congruent 59 modulo 60:   1/12 ( q^2-11*q+24 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 8, 4, 68, 30, 3, 69, 27, 66, 4, 77, 70, 19, 97, 68, 7, 81, 
  4, 68, 30, 4, 68, 30, 16, 73, 53, 8, 77, 14, 28, 82, 36, 70, 19, 97, 70, 
  19, 97 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 6 ], [ 9, 1, 1, 3 ], 
  [ 12, 1, 1, 6 ], [ 23, 1, 1, 6 ], [ 25, 1, 1, 12 ] ]

    k = 2: F-action on Pi is (2,3)(7,8)      [40,1,2]
      Dynkin type is ^2D_4(q) + ^2A_2(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 2 modulo 60:   1/4 q ( q-2 )
        q congruent 3 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 4 modulo 60:   1/4 q ( q-2 )
        q congruent 5 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 7 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 8 modulo 60:   1/4 q ( q-2 )
        q congruent 9 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 11 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 16 modulo 60:   1/4 q ( q-2 )
        q congruent 17 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 19 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 23 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 27 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 29 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 31 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 32 modulo 60:   1/4 q ( q-2 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 41 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 43 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 47 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 53 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 59 modulo 60:   1/4 ( q^2-3*q+4 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 68, 28, 5, 69, 31, 72, 19, 96, 69, 7, 82, 71, 20, 98, 20, 76, 
  60, 31, 82, 38, 27, 81, 36, 90, 43, 110 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], 
  [ 12, 1, 2, 2 ], [ 23, 1, 1, 2 ], [ 25, 1, 2, 4 ] ]

    k = 3: F-action on Pi is (2,5)      [40,1,3]
      Dynkin type is ^2D_4(q) + A_2(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 2 modulo 60:   1/4 q ( q-2 )
        q congruent 3 modulo 60:   1/4 q ( q-3 )
        q congruent 4 modulo 60:   1/4 q ( q-2 )
        q congruent 5 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 7 modulo 60:   1/4 q ( q-3 )
        q congruent 8 modulo 60:   1/4 q ( q-2 )
        q congruent 9 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 11 modulo 60:   1/4 q ( q-3 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 16 modulo 60:   1/4 q ( q-2 )
        q congruent 17 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 19 modulo 60:   1/4 q ( q-3 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 23 modulo 60:   1/4 q ( q-3 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 27 modulo 60:   1/4 q ( q-3 )
        q congruent 29 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 31 modulo 60:   1/4 q ( q-3 )
        q congruent 32 modulo 60:   1/4 q ( q-2 )
        q congruent 37 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 41 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 43 modulo 60:   1/4 q ( q-3 )
        q congruent 47 modulo 60:   1/4 q ( q-3 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 53 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 59 modulo 60:   1/4 q ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 68, 30, 3, 69, 27, 70, 19, 97, 68, 7, 81, 72, 20, 95, 19, 76, 
  59, 28, 82, 36, 30, 81, 37, 89, 43, 109 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], 
  [ 12, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 4, 4 ] ]

    k = 4: F-action on Pi is (2,3,5)(7,8)      [40,1,4]
      Dynkin type is ^3D_4(q) + ^2A_2(q) + T(phi6)
      Order of center |Z^F|: phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/6 q phi1
        q congruent 2 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 3 modulo 60:   1/6 q phi1
        q congruent 4 modulo 60:   1/6 q phi1
        q congruent 5 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 7 modulo 60:   1/6 q phi1
        q congruent 8 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 9 modulo 60:   1/6 q phi1
        q congruent 11 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 13 modulo 60:   1/6 q phi1
        q congruent 16 modulo 60:   1/6 q phi1
        q congruent 17 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 19 modulo 60:   1/6 q phi1
        q congruent 21 modulo 60:   1/6 q phi1
        q congruent 23 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 25 modulo 60:   1/6 q phi1
        q congruent 27 modulo 60:   1/6 q phi1
        q congruent 29 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 31 modulo 60:   1/6 q phi1
        q congruent 32 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 37 modulo 60:   1/6 q phi1
        q congruent 41 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 43 modulo 60:   1/6 q phi1
        q congruent 47 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 49 modulo 60:   1/6 q phi1
        q congruent 53 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 59 modulo 60:   1/6 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 35, 87, 33, 84, 38, 80, 88, 40, 86, 15, 84, 13, 34, 85, 29, 58, 
  102, 56, 13, 80, 11 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ] ]

    k = 5: F-action on Pi is (2,5,3)      [40,1,5]
      Dynkin type is ^3D_4(q) + A_2(q) + T(phi3)
      Order of center |Z^F|: phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 2 modulo 60:   1/6 q phi2
        q congruent 3 modulo 60:   1/6 q phi2
        q congruent 4 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 5 modulo 60:   1/6 q phi2
        q congruent 7 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 8 modulo 60:   1/6 q phi2
        q congruent 9 modulo 60:   1/6 q phi2
        q congruent 11 modulo 60:   1/6 q phi2
        q congruent 13 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 16 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 17 modulo 60:   1/6 q phi2
        q congruent 19 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 21 modulo 60:   1/6 q phi2
        q congruent 23 modulo 60:   1/6 q phi2
        q congruent 25 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 27 modulo 60:   1/6 q phi2
        q congruent 29 modulo 60:   1/6 q phi2
        q congruent 31 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 32 modulo 60:   1/6 q phi2
        q congruent 37 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 41 modulo 60:   1/6 q phi2
        q congruent 43 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 47 modulo 60:   1/6 q phi2
        q congruent 49 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 53 modulo 60:   1/6 q phi2
        q congruent 59 modulo 60:   1/6 q phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 14, 83, 12, 87, 40, 85, 83, 37, 79, 35, 88, 34, 12, 79, 10, 57, 
  101, 55, 33, 86, 29 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ] ]

    k = 6: F-action on Pi is (7,8)      [40,1,6]
      Dynkin type is D_4(q) + ^2A_2(q) + T(phi2^2)
      Order of center |Z^F|: phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 phi1 ( q-6 )
        q congruent 2 modulo 60:   1/12 ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/12 ( q^2-7*q+12 )
        q congruent 4 modulo 60:   1/12 q ( q-4 )
        q congruent 5 modulo 60:   1/12 ( q^2-7*q+10 )
        q congruent 7 modulo 60:   1/12 ( q^2-7*q+12 )
        q congruent 8 modulo 60:   1/12 ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/12 phi1 ( q-6 )
        q congruent 11 modulo 60:   1/12 ( q^2-7*q+16 )
        q congruent 13 modulo 60:   1/12 phi1 ( q-6 )
        q congruent 16 modulo 60:   1/12 q ( q-4 )
        q congruent 17 modulo 60:   1/12 ( q^2-7*q+10 )
        q congruent 19 modulo 60:   1/12 ( q^2-7*q+12 )
        q congruent 21 modulo 60:   1/12 phi1 ( q-6 )
        q congruent 23 modulo 60:   1/12 ( q^2-7*q+16 )
        q congruent 25 modulo 60:   1/12 phi1 ( q-6 )
        q congruent 27 modulo 60:   1/12 ( q^2-7*q+12 )
        q congruent 29 modulo 60:   1/12 ( q^2-7*q+10 )
        q congruent 31 modulo 60:   1/12 ( q^2-7*q+12 )
        q congruent 32 modulo 60:   1/12 ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/12 phi1 ( q-6 )
        q congruent 41 modulo 60:   1/12 ( q^2-7*q+10 )
        q congruent 43 modulo 60:   1/12 ( q^2-7*q+12 )
        q congruent 47 modulo 60:   1/12 ( q^2-7*q+16 )
        q congruent 49 modulo 60:   1/12 phi1 ( q-6 )
        q congruent 53 modulo 60:   1/12 ( q^2-7*q+10 )
        q congruent 59 modulo 60:   1/12 ( q^2-7*q+16 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 68, 28, 5, 69, 31, 2, 67, 9, 69, 7, 82, 71, 20, 98, 67, 5, 78, 
  5, 69, 31, 5, 69, 31, 17, 74, 54, 27, 81, 36, 9, 78, 15, 71, 20, 98, 71, 
  20, 98 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], 
  [ 12, 1, 2, 6 ], [ 23, 1, 2, 6 ], [ 25, 1, 3, 12 ] ]

i = 41: Pi = [ 2, 3, 4, 5, 7, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [41,1,1]
      Dynkin type is D_4(q) + A_1(q) + A_1(q) + T(phi1^2)
      Order of center |Z^F|: phi1^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 ( q^2-10*q+25 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 ( q^2-10*q+21 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 ( q^2-10*q+25 )
        q congruent 7 modulo 60:   1/16 ( q^2-10*q+21 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 ( q^2-10*q+25 )
        q congruent 11 modulo 60:   1/16 ( q^2-10*q+21 )
        q congruent 13 modulo 60:   1/16 ( q^2-10*q+25 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 ( q^2-10*q+25 )
        q congruent 19 modulo 60:   1/16 ( q^2-10*q+21 )
        q congruent 21 modulo 60:   1/16 ( q^2-10*q+25 )
        q congruent 23 modulo 60:   1/16 ( q^2-10*q+21 )
        q congruent 25 modulo 60:   1/16 ( q^2-10*q+25 )
        q congruent 27 modulo 60:   1/16 ( q^2-10*q+21 )
        q congruent 29 modulo 60:   1/16 ( q^2-10*q+25 )
        q congruent 31 modulo 60:   1/16 ( q^2-10*q+21 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 ( q^2-10*q+25 )
        q congruent 41 modulo 60:   1/16 ( q^2-10*q+25 )
        q congruent 43 modulo 60:   1/16 ( q^2-10*q+21 )
        q congruent 47 modulo 60:   1/16 ( q^2-10*q+21 )
        q congruent 49 modulo 60:   1/16 ( q^2-10*q+25 )
        q congruent 53 modulo 60:   1/16 ( q^2-10*q+25 )
        q congruent 59 modulo 60:   1/16 ( q^2-10*q+21 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 4, 68, 68, 7, 3, 69, 69, 5, 66, 4, 4, 68, 70, 19, 19, 
  76, 68, 7, 7, 69, 4, 68, 68, 3, 4, 68, 68, 7, 16, 73, 73, 18, 8, 77, 77, 
  30, 28, 82, 82, 31, 70, 19, 19, 72, 70, 19, 19, 76 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 9, 1, 1, 3 ], 
  [ 10, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 12 ], 
  [ 25, 1, 1, 8 ], [ 39, 1, 1, 8 ] ]

    k = 2: F-action on Pi is (  7,240)      [41,1,2]
      Dynkin type is D_4(q) + A_1(q^2) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 7 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 11 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 13 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 19 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 21 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 23 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 25 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 27 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 29 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 31 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 41 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 43 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 47 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 49 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 53 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 59 modulo 60:   1/8 phi1 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 70, 7, 76, 5, 71, 68, 19, 76, 22, 69, 20, 3, 72, 7, 76, 18, 75, 
  30, 97, 31, 98, 72, 18, 76, 22 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 3 ], 
  [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], 
  [ 25, 1, 1, 4 ], [ 25, 1, 3, 4 ], [ 39, 1, 2, 4 ] ]

    k = 3: F-action on Pi is (  2,  5)(  7,240)      [41,1,3]
      Dynkin type is ^2D_4(q) + A_1(q^2) + T(phi1^2)
      Order of center |Z^F|: phi1^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 7 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 11 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 13 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 19 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 21 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 23 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 25 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 27 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 31 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 41 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 43 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 47 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 49 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 53 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 59 modulo 60:   1/16 ( q^2-6*q+9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 70, 3, 72, 70, 16, 68, 19, 72, 18, 19, 73, 28, 96, 30, 97, 89, 
  44 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 1, 4 ], [ 13, 1, 3, 8 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ], 
  [ 25, 1, 2, 8 ], [ 39, 1, 1, 8 ] ]

    k = 4: F-action on Pi is (2,5)      [41,1,4]
      Dynkin type is ^2D_4(q) + A_1(q) + A_1(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 7 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 11 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 13 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 19 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 21 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 23 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 25 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 27 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 29 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 31 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 41 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 43 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 47 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 49 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 53 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 59 modulo 60:   1/8 phi1 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 68, 68, 3, 3, 69, 69, 5, 70, 19, 19, 72, 68, 7, 7, 69, 72, 20, 
  20, 71, 19, 76, 76, 20, 28, 82, 82, 31, 30, 81, 81, 27, 89, 43, 43, 90 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], 
  [ 9, 1, 1, 1 ], [ 13, 1, 1, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 1, 2 ], 
  [ 23, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 25, 1, 4, 4 ], [ 39, 1, 2, 4 ] ]

    k = 5: F-action on Pi is (  7,240)      [41,1,5]
      Dynkin type is D_4(q) + A_1(q^2) + T(phi4)
      Order of center |Z^F|: phi4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 phi2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/8 phi1 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/8 phi1 phi2
        q congruent 7 modulo 60:   1/8 phi1 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/8 phi1 phi2
        q congruent 11 modulo 60:   1/8 phi1 phi2
        q congruent 13 modulo 60:   1/8 phi1 phi2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/8 phi1 phi2
        q congruent 19 modulo 60:   1/8 phi1 phi2
        q congruent 21 modulo 60:   1/8 phi1 phi2
        q congruent 23 modulo 60:   1/8 phi1 phi2
        q congruent 25 modulo 60:   1/8 phi1 phi2
        q congruent 27 modulo 60:   1/8 phi1 phi2
        q congruent 29 modulo 60:   1/8 phi1 phi2
        q congruent 31 modulo 60:   1/8 phi1 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/8 phi1 phi2
        q congruent 41 modulo 60:   1/8 phi1 phi2
        q congruent 43 modulo 60:   1/8 phi1 phi2
        q congruent 47 modulo 60:   1/8 phi1 phi2
        q congruent 49 modulo 60:   1/8 phi1 phi2
        q congruent 53 modulo 60:   1/8 phi1 phi2
        q congruent 59 modulo 60:   1/8 phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 70, 16, 76, 18, 71, 17, 19, 73, 22, 75, 20, 74, 72, 18, 76, 18, 75, 
  6, 97, 53, 98, 54, 18, 75, 22, 75 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 9, 1, 1, 3 ], [ 39, 1, 5, 4 ] ]

    k = 6: F-action on Pi is ()      [41,1,6]
      Dynkin type is D_4(q) + A_1(q) + A_1(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 7 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 11 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 13 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 19 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 21 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 23 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 25 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 27 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 29 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 31 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 41 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 43 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 47 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 49 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 53 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 59 modulo 60:   1/8 phi1 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 4, 68, 68, 7, 3, 69, 69, 5, 5, 67, 4, 68, 68, 7, 19, 76, 72, 
  20, 7, 69, 69, 5, 68, 7, 7, 69, 68, 3, 7, 69, 73, 18, 18, 74, 77, 30, 30, 
  81, 82, 31, 31, 78, 19, 76, 76, 20, 19, 72, 76, 20 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 39, 1, 4, 4 ] ]

    k = 7: F-action on Pi is (  2,  5)(  7,240)      [41,1,7]
      Dynkin type is ^2D_4(q) + A_1(q^2) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 phi2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/8 phi1 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/8 phi1 phi2
        q congruent 7 modulo 60:   1/8 phi1 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/8 phi1 phi2
        q congruent 11 modulo 60:   1/8 phi1 phi2
        q congruent 13 modulo 60:   1/8 phi1 phi2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/8 phi1 phi2
        q congruent 19 modulo 60:   1/8 phi1 phi2
        q congruent 21 modulo 60:   1/8 phi1 phi2
        q congruent 23 modulo 60:   1/8 phi1 phi2
        q congruent 25 modulo 60:   1/8 phi1 phi2
        q congruent 27 modulo 60:   1/8 phi1 phi2
        q congruent 29 modulo 60:   1/8 phi1 phi2
        q congruent 31 modulo 60:   1/8 phi1 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/8 phi1 phi2
        q congruent 41 modulo 60:   1/8 phi1 phi2
        q congruent 43 modulo 60:   1/8 phi1 phi2
        q congruent 47 modulo 60:   1/8 phi1 phi2
        q congruent 49 modulo 60:   1/8 phi1 phi2
        q congruent 53 modulo 60:   1/8 phi1 phi2
        q congruent 59 modulo 60:   1/8 phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 19, 69, 20, 19, 73, 7, 76, 20, 74, 76, 18, 82, 60, 81, 59, 43, 
  91 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 39, 1, 4, 4 ] ]

    k = 8: F-action on Pi is (2,5)      [41,1,8]
      Dynkin type is ^2D_4(q) + A_1(q) + A_1(q) + T(phi4)
      Order of center |Z^F|: phi4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 phi2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/8 phi1 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/8 phi1 phi2
        q congruent 7 modulo 60:   1/8 phi1 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/8 phi1 phi2
        q congruent 11 modulo 60:   1/8 phi1 phi2
        q congruent 13 modulo 60:   1/8 phi1 phi2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/8 phi1 phi2
        q congruent 19 modulo 60:   1/8 phi1 phi2
        q congruent 21 modulo 60:   1/8 phi1 phi2
        q congruent 23 modulo 60:   1/8 phi1 phi2
        q congruent 25 modulo 60:   1/8 phi1 phi2
        q congruent 27 modulo 60:   1/8 phi1 phi2
        q congruent 29 modulo 60:   1/8 phi1 phi2
        q congruent 31 modulo 60:   1/8 phi1 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/8 phi1 phi2
        q congruent 41 modulo 60:   1/8 phi1 phi2
        q congruent 43 modulo 60:   1/8 phi1 phi2
        q congruent 47 modulo 60:   1/8 phi1 phi2
        q congruent 49 modulo 60:   1/8 phi1 phi2
        q congruent 53 modulo 60:   1/8 phi1 phi2
        q congruent 59 modulo 60:   1/8 phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 70, 19, 19, 72, 72, 20, 20, 71, 16, 73, 73, 18, 19, 76, 76, 20, 18, 
  74, 74, 17, 73, 18, 18, 74, 96, 60, 60, 98, 97, 59, 59, 95, 44, 91, 91, 45 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 39, 1, 5, 4 ] ]

    k = 9: F-action on Pi is ()      [41,1,9]
      Dynkin type is D_4(q) + A_1(q) + A_1(q) + T(phi2^2)
      Order of center |Z^F|: phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 7 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 11 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 13 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 19 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 21 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 23 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 25 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 27 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 31 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 41 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 43 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 47 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 49 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 53 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 59 modulo 60:   1/16 ( q^2-6*q+9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 68, 68, 3, 7, 69, 69, 5, 5, 67, 67, 2, 68, 7, 7, 69, 76, 20, 20, 
  71, 69, 5, 5, 67, 3, 69, 69, 5, 7, 69, 69, 5, 18, 74, 74, 17, 30, 81, 81, 
  27, 31, 78, 78, 9, 72, 20, 20, 71, 76, 20, 20, 71 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], 
  [ 10, 1, 2, 4 ], [ 13, 1, 4, 8 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 12 ], 
  [ 25, 1, 3, 8 ], [ 39, 1, 3, 8 ] ]

    k = 10: F-action on Pi is (  2,  5)(  7,240)      [41,1,10]
      Dynkin type is ^2D_4(q) + A_1(q^2) + T(phi2^2)
      Order of center |Z^F|: phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1^2
        q congruent 7 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1^2
        q congruent 11 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/16 phi1^2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1^2
        q congruent 19 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/16 phi1^2
        q congruent 23 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/16 phi1^2
        q congruent 27 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/16 phi1^2
        q congruent 31 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1^2
        q congruent 41 modulo 60:   1/16 phi1^2
        q congruent 43 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/16 phi1^2
        q congruent 53 modulo 60:   1/16 phi1^2
        q congruent 59 modulo 60:   1/16 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 72, 5, 71, 72, 18, 69, 20, 71, 17, 20, 74, 31, 98, 27, 95, 90, 
  45 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 2, 4 ], [ 13, 1, 2, 8 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], 
  [ 25, 1, 4, 8 ], [ 39, 1, 3, 8 ] ]

i = 42: Pi = [ 2, 4, 5, 6, 7, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [42,1,1]
      Dynkin type is A_5(q) + A_1(q) + T(phi1^2)
      Order of center |Z^F|: phi1^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 ( q^2-11*q+34 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/12 ( q^2-11*q+24 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/12 ( q^2-11*q+30 )
        q congruent 7 modulo 60:   1/12 ( q^2-11*q+28 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/12 ( q^2-11*q+30 )
        q congruent 11 modulo 60:   1/12 ( q^2-11*q+24 )
        q congruent 13 modulo 60:   1/12 ( q^2-11*q+34 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/12 ( q^2-11*q+30 )
        q congruent 19 modulo 60:   1/12 ( q^2-11*q+28 )
        q congruent 21 modulo 60:   1/12 ( q^2-11*q+30 )
        q congruent 23 modulo 60:   1/12 ( q^2-11*q+24 )
        q congruent 25 modulo 60:   1/12 ( q^2-11*q+34 )
        q congruent 27 modulo 60:   1/12 ( q^2-11*q+24 )
        q congruent 29 modulo 60:   1/12 ( q^2-11*q+30 )
        q congruent 31 modulo 60:   1/12 ( q^2-11*q+28 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/12 ( q^2-11*q+34 )
        q congruent 41 modulo 60:   1/12 ( q^2-11*q+30 )
        q congruent 43 modulo 60:   1/12 ( q^2-11*q+28 )
        q congruent 47 modulo 60:   1/12 ( q^2-11*q+24 )
        q congruent 49 modulo 60:   1/12 ( q^2-11*q+34 )
        q congruent 53 modulo 60:   1/12 ( q^2-11*q+30 )
        q congruent 59 modulo 60:   1/12 ( q^2-11*q+24 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 4, 68, 68, 3, 8, 77, 77, 30, 14, 83, 70, 19, 19, 72, 
  23, 93, 87, 35 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], 
  [ 7, 1, 1, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], 
  [ 19, 1, 1, 6 ], [ 24, 1, 1, 6 ], [ 26, 1, 1, 12 ], [ 27, 1, 1, 12 ] ]

    k = 2: F-action on Pi is (2,7)(4,6)      [42,1,2]
      Dynkin type is ^2A_5(q) + A_1(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 7 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 11 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 19 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 23 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 27 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 29 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 31 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 41 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 43 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 47 modulo 60:   1/4 ( q^2-3*q+4 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 53 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 59 modulo 60:   1/4 ( q^2-3*q+4 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 67, 69, 5, 7, 69, 68, 7, 31, 78, 82, 31, 38, 84, 76, 20, 19, 76, 
  51, 94, 87, 40 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], 
  [ 7, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], 
  [ 19, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 26, 1, 2, 4 ], [ 27, 1, 3, 4 ] ]

    k = 3: F-action on Pi is ()      [42,1,3]
      Dynkin type is A_5(q) + A_1(q) + T(phi3)
      Order of center |Z^F|: phi3 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/6 q phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/6 q phi2
        q congruent 7 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/6 q phi2
        q congruent 11 modulo 60:   1/6 q phi2
        q congruent 13 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/6 q phi2
        q congruent 19 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 21 modulo 60:   1/6 q phi2
        q congruent 23 modulo 60:   1/6 q phi2
        q congruent 25 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 27 modulo 60:   1/6 q phi2
        q congruent 29 modulo 60:   1/6 q phi2
        q congruent 31 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 41 modulo 60:   1/6 q phi2
        q congruent 43 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 47 modulo 60:   1/6 q phi2
        q congruent 49 modulo 60:   1/6 phi1 ( q+2 )
        q congruent 53 modulo 60:   1/6 q phi2
        q congruent 59 modulo 60:   1/6 q phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 8, 77, 77, 30, 30, 81, 81, 27, 14, 83, 83, 37, 12, 79, 97, 59, 59, 
  95, 62, 111, 85, 34 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], 
  [ 27, 1, 5, 6 ] ]

    k = 4: F-action on Pi is ()      [42,1,4]
      Dynkin type is A_5(q) + A_1(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4 q ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 7 modulo 60:   1/4 q ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 11 modulo 60:   1/4 q ( q-3 )
        q congruent 13 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 19 modulo 60:   1/4 q ( q-3 )
        q congruent 21 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 23 modulo 60:   1/4 q ( q-3 )
        q congruent 25 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 27 modulo 60:   1/4 q ( q-3 )
        q congruent 29 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 31 modulo 60:   1/4 q ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 41 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 43 modulo 60:   1/4 q ( q-3 )
        q congruent 47 modulo 60:   1/4 q ( q-3 )
        q congruent 49 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 53 modulo 60:   1/4 phi1 ( q-2 )
        q congruent 59 modulo 60:   1/4 q ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 4, 68, 68, 7, 7, 69, 77, 30, 30, 81, 83, 37, 19, 76, 76, 20, 
  93, 50, 40, 88 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], 
  [ 7, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], 
  [ 19, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 3, 4 ], [ 27, 1, 2, 4 ] ]

    k = 5: F-action on Pi is (2,7)(4,6)      [42,1,5]
      Dynkin type is ^2A_5(q) + A_1(q) + T(phi6)
      Order of center |Z^F|: phi6 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/6 q phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/6 q phi1
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 7 modulo 60:   1/6 q phi1
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/6 q phi1
        q congruent 11 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 13 modulo 60:   1/6 q phi1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 19 modulo 60:   1/6 q phi1
        q congruent 21 modulo 60:   1/6 q phi1
        q congruent 23 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 25 modulo 60:   1/6 q phi1
        q congruent 27 modulo 60:   1/6 q phi1
        q congruent 29 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 31 modulo 60:   1/6 q phi1
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/6 q phi1
        q congruent 41 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 43 modulo 60:   1/6 q phi1
        q congruent 47 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 49 modulo 60:   1/6 q phi1
        q congruent 53 modulo 60:   1/6 phi2 ( q-2 )
        q congruent 59 modulo 60:   1/6 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 78, 9, 31, 78, 82, 31, 28, 82, 84, 15, 38, 84, 80, 13, 60, 98, 96, 
  60, 112, 63, 33, 86 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], 
  [ 27, 1, 4, 6 ] ]

    k = 6: F-action on Pi is (2,7)(4,6)      [42,1,6]
      Dynkin type is ^2A_5(q) + A_1(q) + T(phi2^2)
      Order of center |Z^F|: phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 phi1 ( q-6 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/12 ( q^2-7*q+12 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/12 ( q^2-7*q+10 )
        q congruent 7 modulo 60:   1/12 ( q^2-7*q+12 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/12 phi1 ( q-6 )
        q congruent 11 modulo 60:   1/12 ( q^2-7*q+16 )
        q congruent 13 modulo 60:   1/12 phi1 ( q-6 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/12 ( q^2-7*q+10 )
        q congruent 19 modulo 60:   1/12 ( q^2-7*q+12 )
        q congruent 21 modulo 60:   1/12 phi1 ( q-6 )
        q congruent 23 modulo 60:   1/12 ( q^2-7*q+16 )
        q congruent 25 modulo 60:   1/12 phi1 ( q-6 )
        q congruent 27 modulo 60:   1/12 ( q^2-7*q+12 )
        q congruent 29 modulo 60:   1/12 ( q^2-7*q+10 )
        q congruent 31 modulo 60:   1/12 ( q^2-7*q+12 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/12 phi1 ( q-6 )
        q congruent 41 modulo 60:   1/12 ( q^2-7*q+10 )
        q congruent 43 modulo 60:   1/12 ( q^2-7*q+12 )
        q congruent 47 modulo 60:   1/12 ( q^2-7*q+16 )
        q congruent 49 modulo 60:   1/12 phi1 ( q-6 )
        q congruent 53 modulo 60:   1/12 ( q^2-7*q+10 )
        q congruent 59 modulo 60:   1/12 ( q^2-7*q+16 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 2, 5, 67, 69, 5, 3, 69, 78, 9, 31, 78, 84, 15, 20, 71, 72, 20, 
  94, 24, 35, 88 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], 
  [ 7, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ], 
  [ 19, 1, 2, 6 ], [ 24, 1, 2, 6 ], [ 26, 1, 4, 12 ], [ 27, 1, 6, 12 ] ]

i = 43: Pi = [ 2, 4, 5, 7, 8, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [43,1,1]
      Dynkin type is A_3(q) + A_3(q) + T(phi1^2)
      Order of center |Z^F|: phi1^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 ( q^2-14*q+45 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/32 ( q^2-14*q+45 )
        q congruent 7 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/32 ( q^2-14*q+45 )
        q congruent 11 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 13 modulo 60:   1/32 ( q^2-14*q+45 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/32 ( q^2-14*q+45 )
        q congruent 19 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 21 modulo 60:   1/32 ( q^2-14*q+45 )
        q congruent 23 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 25 modulo 60:   1/32 ( q^2-14*q+45 )
        q congruent 27 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 29 modulo 60:   1/32 ( q^2-14*q+45 )
        q congruent 31 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/32 ( q^2-14*q+45 )
        q congruent 41 modulo 60:   1/32 ( q^2-14*q+45 )
        q congruent 43 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 47 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 49 modulo 60:   1/32 ( q^2-14*q+45 )
        q congruent 53 modulo 60:   1/32 ( q^2-14*q+45 )
        q congruent 59 modulo 60:   1/32 ( q^2-10*q+21 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 4, 8, 70, 66, 4, 68, 77, 19, 4, 68, 3, 30, 72, 8, 77, 30, 
  14, 97, 70, 19, 72, 97, 18 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 7, 1, 1, 8 ], 
  [ 9, 1, 1, 5 ], [ 10, 1, 1, 4 ], [ 20, 1, 1, 16 ], [ 23, 1, 1, 4 ], 
  [ 24, 1, 1, 4 ], [ 25, 1, 1, 16 ], [ 26, 1, 1, 16 ], [ 39, 1, 1, 8 ] ]

    k = 2: F-action on Pi is ()      [43,1,2]
      Dynkin type is A_3(q) + A_3(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 7 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 11 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 19 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 23 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 27 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 31 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 41 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 43 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 53 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 59 modulo 60:   1/16 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 68, 77, 19, 4, 68, 7, 30, 76, 68, 7, 69, 81, 20, 77, 30, 81, 
  83, 59, 19, 76, 20, 59, 74 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 7, 1, 1, 4 ], 
  [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 20, 1, 1, 8 ], 
  [ 20, 1, 2, 8 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 3, 8 ], 
  [ 39, 1, 4, 4 ] ]

    k = 3: F-action on Pi is (  2,  5)(  7,240)      [43,1,3]
      Dynkin type is ^2A_3(q) + ^2A_3(q) + T(phi1^2)
      Order of center |Z^F|: phi1^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 7 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 11 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 13 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 19 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 21 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 23 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 25 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 27 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 29 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 31 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 41 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 43 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 47 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 49 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 53 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 59 modulo 60:   1/32 ( q^2-10*q+21 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 69, 3, 31, 72, 69, 7, 68, 82, 19, 3, 68, 4, 28, 70, 31, 82, 28, 
  38, 96, 72, 19, 70, 96, 16 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 1, 4 ], [ 20, 1, 3, 16 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ], 
  [ 25, 1, 2, 16 ], [ 39, 1, 1, 8 ] ]

    k = 4: F-action on Pi is (  2,  5)(  7,240)      [43,1,4]
      Dynkin type is ^2A_3(q) + ^2A_3(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1^2
        q congruent 7 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1^2
        q congruent 11 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 13 modulo 60:   1/16 phi1^2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1^2
        q congruent 19 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 21 modulo 60:   1/16 phi1^2
        q congruent 23 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 25 modulo 60:   1/16 phi1^2
        q congruent 27 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/16 phi1^2
        q congruent 31 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1^2
        q congruent 41 modulo 60:   1/16 phi1^2
        q congruent 43 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 47 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 49 modulo 60:   1/16 phi1^2
        q congruent 53 modulo 60:   1/16 phi1^2
        q congruent 59 modulo 60:   1/16 ( q^2-6*q+9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 5, 69, 78, 20, 5, 69, 7, 31, 76, 69, 7, 68, 82, 19, 78, 31, 82, 
  84, 60, 20, 76, 19, 60, 73 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 4 ], 
  [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 20, 1, 3, 8 ], 
  [ 20, 1, 4, 8 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 2, 8 ], 
  [ 39, 1, 4, 4 ] ]

    k = 5: F-action on Pi is (  2,  7)(  4,  8)(  5,240)      [43,1,5]
      Dynkin type is A_3(q^2) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 7 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 11 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 13 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 19 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 21 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 23 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 25 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 27 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 31 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 41 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 43 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 47 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 49 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 53 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 59 modulo 60:   1/16 ( q^2-6*q+9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 72, 18, 35, 91 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], 
  [ 9, 1, 1, 5 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 20, 1, 5, 8 ], 
  [ 20, 1, 8, 8 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 1, 8 ], 
  [ 26, 1, 4, 8 ], [ 39, 1, 4, 4 ] ]

    k = 6: F-action on Pi is (  2,  7)(  4,  8)(  5,240)      [43,1,6]
      Dynkin type is A_3(q^2) + T(phi1^2)
      Order of center |Z^F|: phi1^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 7 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 11 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 13 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 19 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 21 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 23 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 25 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 27 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 31 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 41 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 43 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 47 modulo 60:   1/16 ( q^2-6*q+9 )
        q congruent 49 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 53 modulo 60:   1/16 phi1 ( q-5 )
        q congruent 59 modulo 60:   1/16 ( q^2-6*q+9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 19, 73, 87, 44 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 1, 4 ], [ 20, 1, 6, 8 ], [ 20, 1, 8, 8 ], [ 23, 1, 1, 4 ], 
  [ 24, 1, 1, 4 ], [ 26, 1, 2, 8 ], [ 39, 1, 1, 8 ] ]

    k = 7: F-action on Pi is (  2,240)(  4,  8)(  5,  7)      [43,1,7]
      Dynkin type is A_3(q^2) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1^2
        q congruent 7 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1^2
        q congruent 11 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/16 phi1^2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1^2
        q congruent 19 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/16 phi1^2
        q congruent 23 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/16 phi1^2
        q congruent 27 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/16 phi1^2
        q congruent 31 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1^2
        q congruent 41 modulo 60:   1/16 phi1^2
        q congruent 43 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/16 phi1^2
        q congruent 53 modulo 60:   1/16 phi1^2
        q congruent 59 modulo 60:   1/16 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 7, 76, 18, 40, 91 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 20, 1, 6, 8 ], [ 20, 1, 7, 8 ], [ 24, 1, 1, 2 ], 
  [ 24, 1, 2, 2 ], [ 39, 1, 4, 4 ] ]

    k = 8: F-action on Pi is (  7,240)      [43,1,8]
      Dynkin type is A_3(q) + ^2A_3(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 7 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 11 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 13 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 19 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 21 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 23 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 25 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 27 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 29 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 31 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 41 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 43 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 47 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 49 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 53 modulo 60:   1/8 phi1 ( q-3 )
        q congruent 59 modulo 60:   1/8 phi1 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 68, 4, 28, 70, 69, 7, 68, 82, 19, 5, 69, 3, 31, 72, 27, 81, 30, 
  36, 97, 71, 20, 72, 98, 18 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 3 ], 
  [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 4 ], 
  [ 25, 1, 3, 4 ], [ 25, 1, 4, 4 ], [ 39, 1, 2, 4 ] ]

    k = 9: F-action on Pi is (  7,240)      [43,1,9]
      Dynkin type is A_3(q) + ^2A_3(q) + T(phi4)
      Order of center |Z^F|: phi4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 phi2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/8 phi1 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/8 phi1 phi2
        q congruent 7 modulo 60:   1/8 phi1 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/8 phi1 phi2
        q congruent 11 modulo 60:   1/8 phi1 phi2
        q congruent 13 modulo 60:   1/8 phi1 phi2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/8 phi1 phi2
        q congruent 19 modulo 60:   1/8 phi1 phi2
        q congruent 21 modulo 60:   1/8 phi1 phi2
        q congruent 23 modulo 60:   1/8 phi1 phi2
        q congruent 25 modulo 60:   1/8 phi1 phi2
        q congruent 27 modulo 60:   1/8 phi1 phi2
        q congruent 29 modulo 60:   1/8 phi1 phi2
        q congruent 31 modulo 60:   1/8 phi1 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/8 phi1 phi2
        q congruent 41 modulo 60:   1/8 phi1 phi2
        q congruent 43 modulo 60:   1/8 phi1 phi2
        q congruent 47 modulo 60:   1/8 phi1 phi2
        q congruent 49 modulo 60:   1/8 phi1 phi2
        q congruent 53 modulo 60:   1/8 phi1 phi2
        q congruent 59 modulo 60:   1/8 phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 72, 19, 70, 96, 16, 20, 76, 19, 60, 73, 71, 20, 72, 98, 18, 95, 59, 
  97, 99, 53, 17, 74, 18, 54, 75 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], 
  [ 39, 1, 5, 4 ] ]

    k = 10: F-action on Pi is (  2,  7,  5,240)(  4,  8)      [43,1,10]
      Dynkin type is ^2A_3(q^2) + T(phi4)
      Order of center |Z^F|: phi4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 phi2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/8 phi1 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/8 phi1 phi2
        q congruent 7 modulo 60:   1/8 phi1 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/8 phi1 phi2
        q congruent 11 modulo 60:   1/8 phi1 phi2
        q congruent 13 modulo 60:   1/8 phi1 phi2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/8 phi1 phi2
        q congruent 19 modulo 60:   1/8 phi1 phi2
        q congruent 21 modulo 60:   1/8 phi1 phi2
        q congruent 23 modulo 60:   1/8 phi1 phi2
        q congruent 25 modulo 60:   1/8 phi1 phi2
        q congruent 27 modulo 60:   1/8 phi1 phi2
        q congruent 29 modulo 60:   1/8 phi1 phi2
        q congruent 31 modulo 60:   1/8 phi1 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/8 phi1 phi2
        q congruent 41 modulo 60:   1/8 phi1 phi2
        q congruent 43 modulo 60:   1/8 phi1 phi2
        q congruent 47 modulo 60:   1/8 phi1 phi2
        q congruent 49 modulo 60:   1/8 phi1 phi2
        q congruent 53 modulo 60:   1/8 phi1 phi2
        q congruent 59 modulo 60:   1/8 phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 6, 75, 18, 39, 91 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 9, 1, 1, 3 ], [ 39, 1, 5, 4 ] ]

    k = 11: F-action on Pi is (  2,  7,  5,240)(  4,  8)      [43,1,11]
      Dynkin type is ^2A_3(q^2) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 phi2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/8 phi1 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/8 phi1 phi2
        q congruent 7 modulo 60:   1/8 phi1 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/8 phi1 phi2
        q congruent 11 modulo 60:   1/8 phi1 phi2
        q congruent 13 modulo 60:   1/8 phi1 phi2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/8 phi1 phi2
        q congruent 19 modulo 60:   1/8 phi1 phi2
        q congruent 21 modulo 60:   1/8 phi1 phi2
        q congruent 23 modulo 60:   1/8 phi1 phi2
        q congruent 25 modulo 60:   1/8 phi1 phi2
        q congruent 27 modulo 60:   1/8 phi1 phi2
        q congruent 29 modulo 60:   1/8 phi1 phi2
        q congruent 31 modulo 60:   1/8 phi1 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/8 phi1 phi2
        q congruent 41 modulo 60:   1/8 phi1 phi2
        q congruent 43 modulo 60:   1/8 phi1 phi2
        q congruent 47 modulo 60:   1/8 phi1 phi2
        q congruent 49 modulo 60:   1/8 phi1 phi2
        q congruent 53 modulo 60:   1/8 phi1 phi2
        q congruent 59 modulo 60:   1/8 phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 75, 22, 76, 100, 43 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 9, 1, 1, 1 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], 
  [ 39, 1, 2, 4 ] ]

    k = 12: F-action on Pi is ()      [43,1,12]
      Dynkin type is A_3(q) + A_3(q) + T(phi2^2)
      Order of center |Z^F|: phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/32 phi2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 7 modulo 60:   1/32 phi2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 11 modulo 60:   1/32 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 19 modulo 60:   1/32 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 23 modulo 60:   1/32 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 27 modulo 60:   1/32 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 31 modulo 60:   1/32 phi2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 41 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 43 modulo 60:   1/32 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/32 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 53 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 59 modulo 60:   1/32 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 68, 3, 30, 72, 68, 7, 69, 81, 20, 3, 69, 5, 27, 71, 30, 81, 27, 
  37, 95, 72, 20, 71, 95, 17 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 2, 4 ], [ 20, 1, 2, 16 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], 
  [ 25, 1, 4, 16 ], [ 39, 1, 3, 8 ] ]

    k = 13: F-action on Pi is (  2,  5)(  7,240)      [43,1,13]
      Dynkin type is ^2A_3(q) + ^2A_3(q) + T(phi2^2)
      Order of center |Z^F|: phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 7 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 11 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 13 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 19 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 21 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 23 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 25 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 27 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 29 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 31 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 41 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 43 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 47 modulo 60:   1/32 ( q^2-10*q+21 )
        q congruent 49 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 53 modulo 60:   1/32 phi1 ( q-5 )
        q congruent 59 modulo 60:   1/32 ( q^2-10*q+21 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 2, 67, 5, 9, 71, 67, 5, 69, 78, 20, 5, 69, 3, 31, 72, 9, 78, 31, 
  15, 98, 71, 20, 72, 98, 18 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 8 ], 
  [ 9, 1, 1, 5 ], [ 10, 1, 2, 4 ], [ 20, 1, 4, 16 ], [ 23, 1, 2, 4 ], 
  [ 24, 1, 2, 4 ], [ 25, 1, 3, 16 ], [ 26, 1, 4, 16 ], [ 39, 1, 3, 8 ] ]

    k = 14: F-action on Pi is (  2,  7)(  4,  8)(  5,240)      [43,1,14]
      Dynkin type is A_3(q^2) + T(phi2^2)
      Order of center |Z^F|: phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1^2
        q congruent 7 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1^2
        q congruent 11 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/16 phi1^2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1^2
        q congruent 19 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/16 phi1^2
        q congruent 23 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/16 phi1^2
        q congruent 27 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/16 phi1^2
        q congruent 31 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1^2
        q congruent 41 modulo 60:   1/16 phi1^2
        q congruent 43 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/16 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/16 phi1^2
        q congruent 53 modulo 60:   1/16 phi1^2
        q congruent 59 modulo 60:   1/16 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 69, 20, 74, 88, 45 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 2, 4 ], [ 20, 1, 5, 8 ], [ 20, 1, 7, 8 ], [ 23, 1, 2, 4 ], 
  [ 24, 1, 2, 4 ], [ 26, 1, 3, 8 ], [ 39, 1, 3, 8 ] ]

i = 44: Pi = [ 1, 2, 3, 4, 5 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [44,1,1]
      Dynkin type is D_5(q) + T(phi1^3)
      Order of center |Z^F|: phi1^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/48 ( q^3-16*q^2+85*q-166 )
        q congruent 2 modulo 60:   1/48 ( q^3-16*q^2+76*q-96 )
        q congruent 3 modulo 60:   1/48 ( q^3-16*q^2+85*q-138 )
        q congruent 4 modulo 60:   1/48 ( q^3-16*q^2+76*q-112 )
        q congruent 5 modulo 60:   1/48 ( q^3-16*q^2+85*q-150 )
        q congruent 7 modulo 60:   1/48 ( q^3-16*q^2+85*q-154 )
        q congruent 8 modulo 60:   1/48 ( q^3-16*q^2+76*q-96 )
        q congruent 9 modulo 60:   1/48 ( q^3-16*q^2+85*q-150 )
        q congruent 11 modulo 60:   1/48 ( q^3-16*q^2+85*q-138 )
        q congruent 13 modulo 60:   1/48 ( q^3-16*q^2+85*q-166 )
        q congruent 16 modulo 60:   1/48 ( q^3-16*q^2+76*q-112 )
        q congruent 17 modulo 60:   1/48 ( q^3-16*q^2+85*q-150 )
        q congruent 19 modulo 60:   1/48 ( q^3-16*q^2+85*q-154 )
        q congruent 21 modulo 60:   1/48 ( q^3-16*q^2+85*q-150 )
        q congruent 23 modulo 60:   1/48 ( q^3-16*q^2+85*q-138 )
        q congruent 25 modulo 60:   1/48 ( q^3-16*q^2+85*q-166 )
        q congruent 27 modulo 60:   1/48 ( q^3-16*q^2+85*q-138 )
        q congruent 29 modulo 60:   1/48 ( q^3-16*q^2+85*q-150 )
        q congruent 31 modulo 60:   1/48 ( q^3-16*q^2+85*q-154 )
        q congruent 32 modulo 60:   1/48 ( q^3-16*q^2+76*q-96 )
        q congruent 37 modulo 60:   1/48 ( q^3-16*q^2+85*q-166 )
        q congruent 41 modulo 60:   1/48 ( q^3-16*q^2+85*q-150 )
        q congruent 43 modulo 60:   1/48 ( q^3-16*q^2+85*q-154 )
        q congruent 47 modulo 60:   1/48 ( q^3-16*q^2+85*q-138 )
        q congruent 49 modulo 60:   1/48 ( q^3-16*q^2+85*q-166 )
        q congruent 53 modulo 60:   1/48 ( q^3-16*q^2+85*q-150 )
        q congruent 59 modulo 60:   1/48 ( q^3-16*q^2+85*q-138 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 4, 3, 66, 70, 68, 72, 4, 16, 19, 8, 28, 30, 77, 96, 70, 89, 23 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 2 ], 
  [ 9, 1, 1, 1 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 8 ], 
  [ 13, 1, 1, 12 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 12 ], [ 27, 1, 1, 48 ], 
  [ 28, 1, 1, 24 ], [ 39, 1, 1, 24 ] ]

    k = 2: F-action on Pi is ()      [44,1,2]
      Dynkin type is D_5(q) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 2 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 4 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 7 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 8 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 11 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 13 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 16 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 19 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 21 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 23 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 25 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 27 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 29 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 31 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 32 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 41 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 43 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 47 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 49 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 53 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 59 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 68, 69, 4, 19, 7, 20, 68, 73, 76, 77, 82, 81, 30, 60, 19, 43, 
  93 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], 
  [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], 
  [ 12, 1, 1, 4 ], [ 13, 1, 1, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 2 ], 
  [ 24, 1, 2, 2 ], [ 27, 1, 2, 8 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 4 ], 
  [ 39, 1, 4, 4 ] ]

    k = 3: F-action on Pi is ()      [44,1,3]
      Dynkin type is D_5(q) + T(phi1 phi3)
      Order of center |Z^F|: phi1 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 2 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 3 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 4 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 5 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 7 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 8 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 9 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 11 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 13 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 16 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 17 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 19 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 21 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 23 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 25 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 27 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 29 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 31 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 32 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 37 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 41 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 43 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 47 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 49 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 53 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 59 modulo 60:   1/6 q phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 8, 30, 27, 77, 97, 81, 95, 30, 53, 59, 14, 36, 37, 83, 99, 97, 109, 
  62 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], 
  [ 12, 1, 1, 2 ], [ 27, 1, 5, 6 ] ]

    k = 4: F-action on Pi is ()      [44,1,4]
      Dynkin type is D_5(q) + T(phi2 phi4)
      Order of center |Z^F|: phi2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 q phi1 phi2
        q congruent 2 modulo 60:   1/8 q^3
        q congruent 3 modulo 60:   1/8 q phi1 phi2
        q congruent 4 modulo 60:   1/8 q^3
        q congruent 5 modulo 60:   1/8 q phi1 phi2
        q congruent 7 modulo 60:   1/8 q phi1 phi2
        q congruent 8 modulo 60:   1/8 q^3
        q congruent 9 modulo 60:   1/8 q phi1 phi2
        q congruent 11 modulo 60:   1/8 q phi1 phi2
        q congruent 13 modulo 60:   1/8 q phi1 phi2
        q congruent 16 modulo 60:   1/8 q^3
        q congruent 17 modulo 60:   1/8 q phi1 phi2
        q congruent 19 modulo 60:   1/8 q phi1 phi2
        q congruent 21 modulo 60:   1/8 q phi1 phi2
        q congruent 23 modulo 60:   1/8 q phi1 phi2
        q congruent 25 modulo 60:   1/8 q phi1 phi2
        q congruent 27 modulo 60:   1/8 q phi1 phi2
        q congruent 29 modulo 60:   1/8 q phi1 phi2
        q congruent 31 modulo 60:   1/8 q phi1 phi2
        q congruent 32 modulo 60:   1/8 q^3
        q congruent 37 modulo 60:   1/8 q phi1 phi2
        q congruent 41 modulo 60:   1/8 q phi1 phi2
        q congruent 43 modulo 60:   1/8 q phi1 phi2
        q congruent 47 modulo 60:   1/8 q phi1 phi2
        q congruent 49 modulo 60:   1/8 q phi1 phi2
        q congruent 53 modulo 60:   1/8 q phi1 phi2
        q congruent 59 modulo 60:   1/8 q phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 70, 72, 71, 19, 18, 20, 17, 76, 75, 74, 97, 98, 95, 59, 54, 22, 45, 
  107 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 13, 1, 2, 4 ], 
  [ 23, 1, 2, 2 ], [ 39, 1, 5, 4 ] ]

    k = 5: F-action on Pi is ()      [44,1,5]
      Dynkin type is D_5(q) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^2 ( q-2 )
        q congruent 2 modulo 60:   1/16 q ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/16 ( q^3-4*q^2+5*q-6 )
        q congruent 4 modulo 60:   1/16 q ( q^2-4*q+4 )
        q congruent 5 modulo 60:   1/16 phi1^2 ( q-2 )
        q congruent 7 modulo 60:   1/16 ( q^3-4*q^2+5*q-6 )
        q congruent 8 modulo 60:   1/16 q ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/16 phi1^2 ( q-2 )
        q congruent 11 modulo 60:   1/16 ( q^3-4*q^2+5*q-6 )
        q congruent 13 modulo 60:   1/16 phi1^2 ( q-2 )
        q congruent 16 modulo 60:   1/16 q ( q^2-4*q+4 )
        q congruent 17 modulo 60:   1/16 phi1^2 ( q-2 )
        q congruent 19 modulo 60:   1/16 ( q^3-4*q^2+5*q-6 )
        q congruent 21 modulo 60:   1/16 phi1^2 ( q-2 )
        q congruent 23 modulo 60:   1/16 ( q^3-4*q^2+5*q-6 )
        q congruent 25 modulo 60:   1/16 phi1^2 ( q-2 )
        q congruent 27 modulo 60:   1/16 ( q^3-4*q^2+5*q-6 )
        q congruent 29 modulo 60:   1/16 phi1^2 ( q-2 )
        q congruent 31 modulo 60:   1/16 ( q^3-4*q^2+5*q-6 )
        q congruent 32 modulo 60:   1/16 q ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/16 phi1^2 ( q-2 )
        q congruent 41 modulo 60:   1/16 phi1^2 ( q-2 )
        q congruent 43 modulo 60:   1/16 ( q^3-4*q^2+5*q-6 )
        q congruent 47 modulo 60:   1/16 ( q^3-4*q^2+5*q-6 )
        q congruent 49 modulo 60:   1/16 phi1^2 ( q-2 )
        q congruent 53 modulo 60:   1/16 phi1^2 ( q-2 )
        q congruent 59 modulo 60:   1/16 ( q^3-4*q^2+5*q-6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 3, 5, 68, 72, 69, 71, 7, 18, 20, 30, 31, 27, 81, 98, 76, 90, 50 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 2, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 2, 8 ], [ 23, 1, 1, 2 ], 
  [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 28, 1, 2, 8 ], [ 39, 1, 2, 8 ], 
  [ 39, 1, 3, 8 ] ]

    k = 6: F-action on Pi is (2,5)      [44,1,6]
      Dynkin type is ^2D_5(q) + T(phi1 phi4)
      Order of center |Z^F|: phi1 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 phi2 ( q-2 )
        q congruent 2 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 3 modulo 60:   1/8 phi1 phi2 ( q-2 )
        q congruent 4 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 5 modulo 60:   1/8 phi1 phi2 ( q-2 )
        q congruent 7 modulo 60:   1/8 phi1 phi2 ( q-2 )
        q congruent 8 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 9 modulo 60:   1/8 phi1 phi2 ( q-2 )
        q congruent 11 modulo 60:   1/8 phi1 phi2 ( q-2 )
        q congruent 13 modulo 60:   1/8 phi1 phi2 ( q-2 )
        q congruent 16 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 17 modulo 60:   1/8 phi1 phi2 ( q-2 )
        q congruent 19 modulo 60:   1/8 phi1 phi2 ( q-2 )
        q congruent 21 modulo 60:   1/8 phi1 phi2 ( q-2 )
        q congruent 23 modulo 60:   1/8 phi1 phi2 ( q-2 )
        q congruent 25 modulo 60:   1/8 phi1 phi2 ( q-2 )
        q congruent 27 modulo 60:   1/8 phi1 phi2 ( q-2 )
        q congruent 29 modulo 60:   1/8 phi1 phi2 ( q-2 )
        q congruent 31 modulo 60:   1/8 phi1 phi2 ( q-2 )
        q congruent 32 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 37 modulo 60:   1/8 phi1 phi2 ( q-2 )
        q congruent 41 modulo 60:   1/8 phi1 phi2 ( q-2 )
        q congruent 43 modulo 60:   1/8 phi1 phi2 ( q-2 )
        q congruent 47 modulo 60:   1/8 phi1 phi2 ( q-2 )
        q congruent 49 modulo 60:   1/8 phi1 phi2 ( q-2 )
        q congruent 53 modulo 60:   1/8 phi1 phi2 ( q-2 )
        q congruent 59 modulo 60:   1/8 phi1 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 70, 72, 71, 16, 19, 18, 20, 73, 76, 75, 96, 97, 98, 60, 53, 44, 22, 
  108 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 13, 1, 3, 4 ], 
  [ 23, 1, 1, 2 ], [ 39, 1, 5, 4 ] ]

    k = 7: F-action on Pi is (2,5)      [44,1,7]
      Dynkin type is ^2D_5(q) + T(phi2 phi6)
      Order of center |Z^F|: phi2 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/6 q^2 phi1
        q congruent 2 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 3 modulo 60:   1/6 q^2 phi1
        q congruent 4 modulo 60:   1/6 q^2 phi1
        q congruent 5 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 7 modulo 60:   1/6 q^2 phi1
        q congruent 8 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 9 modulo 60:   1/6 q^2 phi1
        q congruent 11 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 13 modulo 60:   1/6 q^2 phi1
        q congruent 16 modulo 60:   1/6 q^2 phi1
        q congruent 17 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 19 modulo 60:   1/6 q^2 phi1
        q congruent 21 modulo 60:   1/6 q^2 phi1
        q congruent 23 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 25 modulo 60:   1/6 q^2 phi1
        q congruent 27 modulo 60:   1/6 q^2 phi1
        q congruent 29 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 31 modulo 60:   1/6 q^2 phi1
        q congruent 32 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 37 modulo 60:   1/6 q^2 phi1
        q congruent 41 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 43 modulo 60:   1/6 q^2 phi1
        q congruent 47 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 49 modulo 60:   1/6 q^2 phi1
        q congruent 53 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 59 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 28, 31, 9, 96, 82, 98, 78, 60, 31, 54, 38, 36, 15, 84, 99, 110, 98, 
  63 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], 
  [ 12, 1, 2, 2 ], [ 27, 1, 4, 6 ] ]

    k = 8: F-action on Pi is (2,5)      [44,1,8]
      Dynkin type is ^2D_5(q) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q^2-3*q+4 )
        q congruent 2 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/8 phi1 ( q^2-3*q+4 )
        q congruent 4 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 5 modulo 60:   1/8 phi1 ( q^2-3*q+4 )
        q congruent 7 modulo 60:   1/8 phi1 ( q^2-3*q+4 )
        q congruent 8 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/8 phi1 ( q^2-3*q+4 )
        q congruent 11 modulo 60:   1/8 phi1 ( q^2-3*q+4 )
        q congruent 13 modulo 60:   1/8 phi1 ( q^2-3*q+4 )
        q congruent 16 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 17 modulo 60:   1/8 phi1 ( q^2-3*q+4 )
        q congruent 19 modulo 60:   1/8 phi1 ( q^2-3*q+4 )
        q congruent 21 modulo 60:   1/8 phi1 ( q^2-3*q+4 )
        q congruent 23 modulo 60:   1/8 phi1 ( q^2-3*q+4 )
        q congruent 25 modulo 60:   1/8 phi1 ( q^2-3*q+4 )
        q congruent 27 modulo 60:   1/8 phi1 ( q^2-3*q+4 )
        q congruent 29 modulo 60:   1/8 phi1 ( q^2-3*q+4 )
        q congruent 31 modulo 60:   1/8 phi1 ( q^2-3*q+4 )
        q congruent 32 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/8 phi1 ( q^2-3*q+4 )
        q congruent 41 modulo 60:   1/8 phi1 ( q^2-3*q+4 )
        q congruent 43 modulo 60:   1/8 phi1 ( q^2-3*q+4 )
        q congruent 47 modulo 60:   1/8 phi1 ( q^2-3*q+4 )
        q congruent 49 modulo 60:   1/8 phi1 ( q^2-3*q+4 )
        q congruent 53 modulo 60:   1/8 phi1 ( q^2-3*q+4 )
        q congruent 59 modulo 60:   1/8 phi1 ( q^2-3*q+4 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 69, 67, 19, 7, 20, 5, 76, 69, 74, 82, 81, 78, 31, 59, 43, 20, 
  94 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 2 ], 
  [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], 
  [ 12, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], 
  [ 24, 1, 2, 2 ], [ 27, 1, 3, 8 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], 
  [ 39, 1, 4, 4 ] ]

    k = 9: F-action on Pi is (2,5)      [44,1,9]
      Dynkin type is ^2D_5(q) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^2 ( q-4 )
        q congruent 2 modulo 60:   1/16 q ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/16 q ( q^2-6*q+9 )
        q congruent 4 modulo 60:   1/16 q ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/16 phi1^2 ( q-4 )
        q congruent 7 modulo 60:   1/16 q ( q^2-6*q+9 )
        q congruent 8 modulo 60:   1/16 q ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/16 phi1^2 ( q-4 )
        q congruent 11 modulo 60:   1/16 q ( q^2-6*q+9 )
        q congruent 13 modulo 60:   1/16 phi1^2 ( q-4 )
        q congruent 16 modulo 60:   1/16 q ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/16 phi1^2 ( q-4 )
        q congruent 19 modulo 60:   1/16 q ( q^2-6*q+9 )
        q congruent 21 modulo 60:   1/16 phi1^2 ( q-4 )
        q congruent 23 modulo 60:   1/16 q ( q^2-6*q+9 )
        q congruent 25 modulo 60:   1/16 phi1^2 ( q-4 )
        q congruent 27 modulo 60:   1/16 q ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/16 phi1^2 ( q-4 )
        q congruent 31 modulo 60:   1/16 q ( q^2-6*q+9 )
        q congruent 32 modulo 60:   1/16 q ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/16 phi1^2 ( q-4 )
        q congruent 41 modulo 60:   1/16 phi1^2 ( q-4 )
        q congruent 43 modulo 60:   1/16 q ( q^2-6*q+9 )
        q congruent 47 modulo 60:   1/16 q ( q^2-6*q+9 )
        q congruent 49 modulo 60:   1/16 phi1^2 ( q-4 )
        q congruent 53 modulo 60:   1/16 phi1^2 ( q-4 )
        q congruent 59 modulo 60:   1/16 q ( q^2-6*q+9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 3, 5, 70, 68, 72, 69, 19, 7, 18, 28, 30, 31, 82, 97, 89, 76, 51 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 1, 4 ], [ 13, 1, 3, 8 ], [ 13, 1, 4, 4 ], [ 23, 1, 1, 4 ], 
  [ 23, 1, 2, 2 ], [ 24, 1, 1, 4 ], [ 28, 1, 3, 8 ], [ 39, 1, 1, 8 ], 
  [ 39, 1, 2, 8 ] ]

    k = 10: F-action on Pi is (2,5)      [44,1,10]
      Dynkin type is ^2D_5(q) + T(phi2^3)
      Order of center |Z^F|: phi2^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/48 phi1 ( q^2-9*q+24 )
        q congruent 2 modulo 60:   1/48 ( q^3-10*q^2+24*q-16 )
        q congruent 3 modulo 60:   1/48 ( q^3-10*q^2+33*q-36 )
        q congruent 4 modulo 60:   1/48 q ( q^2-10*q+24 )
        q congruent 5 modulo 60:   1/48 ( q^3-10*q^2+33*q-40 )
        q congruent 7 modulo 60:   1/48 ( q^3-10*q^2+33*q-36 )
        q congruent 8 modulo 60:   1/48 ( q^3-10*q^2+24*q-16 )
        q congruent 9 modulo 60:   1/48 phi1 ( q^2-9*q+24 )
        q congruent 11 modulo 60:   1/48 ( q^3-10*q^2+33*q-52 )
        q congruent 13 modulo 60:   1/48 phi1 ( q^2-9*q+24 )
        q congruent 16 modulo 60:   1/48 q ( q^2-10*q+24 )
        q congruent 17 modulo 60:   1/48 ( q^3-10*q^2+33*q-40 )
        q congruent 19 modulo 60:   1/48 ( q^3-10*q^2+33*q-36 )
        q congruent 21 modulo 60:   1/48 phi1 ( q^2-9*q+24 )
        q congruent 23 modulo 60:   1/48 ( q^3-10*q^2+33*q-52 )
        q congruent 25 modulo 60:   1/48 phi1 ( q^2-9*q+24 )
        q congruent 27 modulo 60:   1/48 ( q^3-10*q^2+33*q-36 )
        q congruent 29 modulo 60:   1/48 ( q^3-10*q^2+33*q-40 )
        q congruent 31 modulo 60:   1/48 ( q^3-10*q^2+33*q-36 )
        q congruent 32 modulo 60:   1/48 ( q^3-10*q^2+24*q-16 )
        q congruent 37 modulo 60:   1/48 phi1 ( q^2-9*q+24 )
        q congruent 41 modulo 60:   1/48 ( q^3-10*q^2+33*q-40 )
        q congruent 43 modulo 60:   1/48 ( q^3-10*q^2+33*q-36 )
        q congruent 47 modulo 60:   1/48 ( q^3-10*q^2+33*q-52 )
        q congruent 49 modulo 60:   1/48 phi1 ( q^2-9*q+24 )
        q congruent 53 modulo 60:   1/48 ( q^3-10*q^2+33*q-40 )
        q congruent 59 modulo 60:   1/48 ( q^3-10*q^2+33*q-52 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 5, 2, 72, 69, 71, 67, 20, 5, 17, 31, 27, 9, 78, 95, 90, 71, 24 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 2 ], 
  [ 9, 1, 1, 1 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 24 ], [ 12, 1, 2, 8 ], 
  [ 13, 1, 4, 12 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 12 ], [ 27, 1, 6, 48 ], 
  [ 28, 1, 4, 24 ], [ 39, 1, 3, 24 ] ]

i = 45: Pi = [ 1, 2, 3, 4, 6 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [45,1,1]
      Dynkin type is A_4(q) + A_1(q) + T(phi1^3)
      Order of center |Z^F|: phi1^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 ( q^3-20*q^2+135*q-368 )
        q congruent 2 modulo 60:   1/12 ( q^3-19*q^2+106*q-144 )
        q congruent 3 modulo 60:   1/12 ( q^3-20*q^2+129*q-234 )
        q congruent 4 modulo 60:   1/12 ( q^3-19*q^2+112*q-208 )
        q congruent 5 modulo 60:   1/12 ( q^3-20*q^2+129*q-270 )
        q congruent 7 modulo 60:   1/12 ( q^3-20*q^2+135*q-308 )
        q congruent 8 modulo 60:   1/12 ( q^3-19*q^2+106*q-144 )
        q congruent 9 modulo 60:   1/12 ( q^3-20*q^2+129*q-270 )
        q congruent 11 modulo 60:   1/12 ( q^3-20*q^2+129*q-258 )
        q congruent 13 modulo 60:   1/12 ( q^3-20*q^2+135*q-344 )
        q congruent 16 modulo 60:   1/12 ( q^3-19*q^2+112*q-232 )
        q congruent 17 modulo 60:   1/12 ( q^3-20*q^2+129*q-270 )
        q congruent 19 modulo 60:   1/12 ( q^3-20*q^2+135*q-308 )
        q congruent 21 modulo 60:   1/12 ( q^3-20*q^2+129*q-294 )
        q congruent 23 modulo 60:   1/12 ( q^3-20*q^2+129*q-234 )
        q congruent 25 modulo 60:   1/12 ( q^3-20*q^2+135*q-344 )
        q congruent 27 modulo 60:   1/12 ( q^3-20*q^2+129*q-234 )
        q congruent 29 modulo 60:   1/12 ( q^3-20*q^2+129*q-270 )
        q congruent 31 modulo 60:   1/12 ( q^3-20*q^2+135*q-332 )
        q congruent 32 modulo 60:   1/12 ( q^3-19*q^2+106*q-144 )
        q congruent 37 modulo 60:   1/12 ( q^3-20*q^2+135*q-344 )
        q congruent 41 modulo 60:   1/12 ( q^3-20*q^2+129*q-294 )
        q congruent 43 modulo 60:   1/12 ( q^3-20*q^2+135*q-308 )
        q congruent 47 modulo 60:   1/12 ( q^3-20*q^2+129*q-234 )
        q congruent 49 modulo 60:   1/12 ( q^3-20*q^2+135*q-344 )
        q congruent 53 modulo 60:   1/12 ( q^3-20*q^2+129*q-270 )
        q congruent 59 modulo 60:   1/12 ( q^3-20*q^2+129*q-234 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 4, 68, 8, 77, 77, 30, 70, 19, 23, 93 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 6 ], 
  [ 5, 1, 1, 4 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 8 ], [ 8, 1, 1, 6 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 12 ], [ 12, 1, 1, 12 ], 
  [ 13, 1, 1, 12 ], [ 14, 1, 1, 6 ], [ 15, 1, 1, 8 ], [ 18, 1, 1, 12 ], 
  [ 19, 1, 1, 12 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 12 ], [ 23, 1, 1, 6 ], 
  [ 24, 1, 1, 6 ], [ 26, 1, 1, 12 ], [ 27, 1, 1, 12 ], [ 28, 1, 1, 12 ], 
  [ 29, 1, 1, 12 ], [ 30, 1, 1, 12 ], [ 34, 1, 1, 12 ], [ 36, 1, 1, 12 ], 
  [ 42, 1, 1, 12 ] ]

    k = 2: F-action on Pi is ()      [45,1,2]
      Dynkin type is A_4(q) + A_1(q) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q^2-7*q+12 )
        q congruent 2 modulo 60:   1/4 q ( q^2-7*q+10 )
        q congruent 3 modulo 60:   1/4 ( q^3-8*q^2+17*q-6 )
        q congruent 4 modulo 60:   1/4 q ( q^2-7*q+12 )
        q congruent 5 modulo 60:   1/4 phi1 ( q^2-7*q+10 )
        q congruent 7 modulo 60:   1/4 ( q^3-8*q^2+19*q-8 )
        q congruent 8 modulo 60:   1/4 q ( q^2-7*q+10 )
        q congruent 9 modulo 60:   1/4 phi1 ( q^2-7*q+10 )
        q congruent 11 modulo 60:   1/4 ( q^3-8*q^2+17*q-6 )
        q congruent 13 modulo 60:   1/4 phi1 ( q^2-7*q+12 )
        q congruent 16 modulo 60:   1/4 q ( q^2-7*q+12 )
        q congruent 17 modulo 60:   1/4 phi1 ( q^2-7*q+10 )
        q congruent 19 modulo 60:   1/4 ( q^3-8*q^2+19*q-8 )
        q congruent 21 modulo 60:   1/4 phi1 ( q^2-7*q+10 )
        q congruent 23 modulo 60:   1/4 ( q^3-8*q^2+17*q-6 )
        q congruent 25 modulo 60:   1/4 phi1 ( q^2-7*q+12 )
        q congruent 27 modulo 60:   1/4 ( q^3-8*q^2+17*q-6 )
        q congruent 29 modulo 60:   1/4 phi1 ( q^2-7*q+10 )
        q congruent 31 modulo 60:   1/4 ( q^3-8*q^2+19*q-8 )
        q congruent 32 modulo 60:   1/4 q ( q^2-7*q+10 )
        q congruent 37 modulo 60:   1/4 phi1 ( q^2-7*q+12 )
        q congruent 41 modulo 60:   1/4 phi1 ( q^2-7*q+10 )
        q congruent 43 modulo 60:   1/4 ( q^3-8*q^2+19*q-8 )
        q congruent 47 modulo 60:   1/4 ( q^3-8*q^2+17*q-6 )
        q congruent 49 modulo 60:   1/4 phi1 ( q^2-7*q+12 )
        q congruent 53 modulo 60:   1/4 phi1 ( q^2-7*q+10 )
        q congruent 59 modulo 60:   1/4 ( q^3-8*q^2+17*q-6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 4, 68, 68, 7, 77, 30, 30, 81, 19, 76, 93, 50 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], 
  [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 2 ], 
  [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 13, 1, 1, 4 ], 
  [ 14, 1, 1, 2 ], [ 15, 1, 1, 4 ], [ 18, 1, 1, 4 ], [ 19, 1, 1, 4 ], 
  [ 22, 1, 2, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 3, 4 ], 
  [ 27, 1, 2, 4 ], [ 28, 1, 2, 4 ], [ 29, 1, 2, 4 ], [ 30, 1, 1, 4 ], 
  [ 34, 1, 2, 4 ], [ 36, 1, 2, 4 ], [ 42, 1, 4, 4 ] ]

    k = 3: F-action on Pi is ()      [45,1,3]
      Dynkin type is A_4(q) + A_1(q) + T(phi1 phi3)
      Order of center |Z^F|: phi1 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/6 phi1 ( q^2-q-4 )
        q congruent 2 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 3 modulo 60:   1/6 q phi2 ( q-3 )
        q congruent 4 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 5 modulo 60:   1/6 q phi2 ( q-3 )
        q congruent 7 modulo 60:   1/6 phi1 ( q^2-q-4 )
        q congruent 8 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 9 modulo 60:   1/6 q phi2 ( q-3 )
        q congruent 11 modulo 60:   1/6 q phi2 ( q-3 )
        q congruent 13 modulo 60:   1/6 phi1 ( q^2-q-4 )
        q congruent 16 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 17 modulo 60:   1/6 q phi2 ( q-3 )
        q congruent 19 modulo 60:   1/6 phi1 ( q^2-q-4 )
        q congruent 21 modulo 60:   1/6 q phi2 ( q-3 )
        q congruent 23 modulo 60:   1/6 q phi2 ( q-3 )
        q congruent 25 modulo 60:   1/6 phi1 ( q^2-q-4 )
        q congruent 27 modulo 60:   1/6 q phi2 ( q-3 )
        q congruent 29 modulo 60:   1/6 q phi2 ( q-3 )
        q congruent 31 modulo 60:   1/6 phi1 ( q^2-q-4 )
        q congruent 32 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 37 modulo 60:   1/6 phi1 ( q^2-q-4 )
        q congruent 41 modulo 60:   1/6 q phi2 ( q-3 )
        q congruent 43 modulo 60:   1/6 phi1 ( q^2-q-4 )
        q congruent 47 modulo 60:   1/6 q phi2 ( q-3 )
        q congruent 49 modulo 60:   1/6 phi1 ( q^2-q-4 )
        q congruent 53 modulo 60:   1/6 q phi2 ( q-3 )
        q congruent 59 modulo 60:   1/6 q phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 8, 77, 77, 30, 30, 81, 14, 83, 83, 37, 97, 59, 62, 111 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 4 ], 
  [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 15, 1, 1, 2 ], [ 27, 1, 5, 6 ], 
  [ 42, 1, 3, 6 ] ]

    k = 4: F-action on Pi is (1,2)(3,4)      [45,1,4]
      Dynkin type is ^2A_4(q) + A_1(q) + T(phi2 phi6)
      Order of center |Z^F|: phi2 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/6 q phi1^2
        q congruent 2 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 3 modulo 60:   1/6 q phi1^2
        q congruent 4 modulo 60:   1/6 q^2 phi1
        q congruent 5 modulo 60:   1/6 phi2 ( q^2-3*q+4 )
        q congruent 7 modulo 60:   1/6 q phi1^2
        q congruent 8 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 9 modulo 60:   1/6 q phi1^2
        q congruent 11 modulo 60:   1/6 phi2 ( q^2-3*q+4 )
        q congruent 13 modulo 60:   1/6 q phi1^2
        q congruent 16 modulo 60:   1/6 q^2 phi1
        q congruent 17 modulo 60:   1/6 phi2 ( q^2-3*q+4 )
        q congruent 19 modulo 60:   1/6 q phi1^2
        q congruent 21 modulo 60:   1/6 q phi1^2
        q congruent 23 modulo 60:   1/6 phi2 ( q^2-3*q+4 )
        q congruent 25 modulo 60:   1/6 q phi1^2
        q congruent 27 modulo 60:   1/6 q phi1^2
        q congruent 29 modulo 60:   1/6 phi2 ( q^2-3*q+4 )
        q congruent 31 modulo 60:   1/6 q phi1^2
        q congruent 32 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 37 modulo 60:   1/6 q phi1^2
        q congruent 41 modulo 60:   1/6 phi2 ( q^2-3*q+4 )
        q congruent 43 modulo 60:   1/6 q phi1^2
        q congruent 47 modulo 60:   1/6 phi2 ( q^2-3*q+4 )
        q congruent 49 modulo 60:   1/6 q phi1^2
        q congruent 53 modulo 60:   1/6 phi2 ( q^2-3*q+4 )
        q congruent 59 modulo 60:   1/6 phi2 ( q^2-3*q+4 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 78, 9, 31, 78, 82, 31, 84, 15, 38, 84, 60, 98, 112, 63 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 2, 4 ], 
  [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 15, 1, 2, 2 ], [ 27, 1, 4, 6 ], 
  [ 42, 1, 5, 6 ] ]

    k = 5: F-action on Pi is (1,2)(3,4)      [45,1,5]
      Dynkin type is ^2A_4(q) + A_1(q) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4 phi1 ( q^2-5*q+8 )
        q congruent 2 modulo 60:   1/4 phi1 ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/4 ( q^3-6*q^2+13*q-12 )
        q congruent 4 modulo 60:   1/4 q ( q^2-5*q+6 )
        q congruent 5 modulo 60:   1/4 ( q^3-6*q^2+15*q-14 )
        q congruent 7 modulo 60:   1/4 ( q^3-6*q^2+13*q-12 )
        q congruent 8 modulo 60:   1/4 phi1 ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/4 phi1 ( q^2-5*q+8 )
        q congruent 11 modulo 60:   1/4 ( q^3-6*q^2+15*q-18 )
        q congruent 13 modulo 60:   1/4 phi1 ( q^2-5*q+8 )
        q congruent 16 modulo 60:   1/4 q ( q^2-5*q+6 )
        q congruent 17 modulo 60:   1/4 ( q^3-6*q^2+15*q-14 )
        q congruent 19 modulo 60:   1/4 ( q^3-6*q^2+13*q-12 )
        q congruent 21 modulo 60:   1/4 phi1 ( q^2-5*q+8 )
        q congruent 23 modulo 60:   1/4 ( q^3-6*q^2+15*q-18 )
        q congruent 25 modulo 60:   1/4 phi1 ( q^2-5*q+8 )
        q congruent 27 modulo 60:   1/4 ( q^3-6*q^2+13*q-12 )
        q congruent 29 modulo 60:   1/4 ( q^3-6*q^2+15*q-14 )
        q congruent 31 modulo 60:   1/4 ( q^3-6*q^2+13*q-12 )
        q congruent 32 modulo 60:   1/4 phi1 ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/4 phi1 ( q^2-5*q+8 )
        q congruent 41 modulo 60:   1/4 ( q^3-6*q^2+15*q-14 )
        q congruent 43 modulo 60:   1/4 ( q^3-6*q^2+13*q-12 )
        q congruent 47 modulo 60:   1/4 ( q^3-6*q^2+15*q-18 )
        q congruent 49 modulo 60:   1/4 phi1 ( q^2-5*q+8 )
        q congruent 53 modulo 60:   1/4 ( q^3-6*q^2+15*q-14 )
        q congruent 59 modulo 60:   1/4 ( q^3-6*q^2+15*q-18 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 67, 69, 5, 7, 69, 31, 78, 82, 31, 76, 20, 51, 94 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 2 ], 
  [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 2 ], 
  [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 4 ], [ 13, 1, 4, 4 ], 
  [ 14, 1, 2, 2 ], [ 15, 1, 2, 4 ], [ 18, 1, 2, 4 ], [ 19, 1, 2, 4 ], 
  [ 22, 1, 3, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 26, 1, 2, 4 ], 
  [ 27, 1, 3, 4 ], [ 28, 1, 3, 4 ], [ 29, 1, 3, 4 ], [ 30, 1, 3, 4 ], 
  [ 34, 1, 3, 4 ], [ 36, 1, 3, 4 ], [ 42, 1, 2, 4 ] ]

    k = 6: F-action on Pi is (1,2)(3,4)      [45,1,6]
      Dynkin type is ^2A_4(q) + A_1(q) + T(phi2^3)
      Order of center |Z^F|: phi2^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 phi1 ( q^2-13*q+48 )
        q congruent 2 modulo 60:   1/12 ( q^3-13*q^2+48*q-52 )
        q congruent 3 modulo 60:   1/12 ( q^3-14*q^2+61*q-84 )
        q congruent 4 modulo 60:   1/12 ( q^3-13*q^2+42*q-24 )
        q congruent 5 modulo 60:   1/12 ( q^3-14*q^2+67*q-110 )
        q congruent 7 modulo 60:   1/12 ( q^3-14*q^2+61*q-84 )
        q congruent 8 modulo 60:   1/12 ( q^3-13*q^2+48*q-52 )
        q congruent 9 modulo 60:   1/12 ( q^3-14*q^2+61*q-72 )
        q congruent 11 modulo 60:   1/12 ( q^3-14*q^2+67*q-146 )
        q congruent 13 modulo 60:   1/12 phi1 ( q^2-13*q+48 )
        q congruent 16 modulo 60:   1/12 q ( q^2-13*q+42 )
        q congruent 17 modulo 60:   1/12 ( q^3-14*q^2+67*q-110 )
        q congruent 19 modulo 60:   1/12 ( q^3-14*q^2+61*q-108 )
        q congruent 21 modulo 60:   1/12 phi1 ( q^2-13*q+48 )
        q congruent 23 modulo 60:   1/12 ( q^3-14*q^2+67*q-146 )
        q congruent 25 modulo 60:   1/12 phi1 ( q^2-13*q+48 )
        q congruent 27 modulo 60:   1/12 ( q^3-14*q^2+61*q-84 )
        q congruent 29 modulo 60:   1/12 ( q^3-14*q^2+67*q-134 )
        q congruent 31 modulo 60:   1/12 ( q^3-14*q^2+61*q-84 )
        q congruent 32 modulo 60:   1/12 ( q^3-13*q^2+48*q-52 )
        q congruent 37 modulo 60:   1/12 phi1 ( q^2-13*q+48 )
        q congruent 41 modulo 60:   1/12 ( q^3-14*q^2+67*q-110 )
        q congruent 43 modulo 60:   1/12 ( q^3-14*q^2+61*q-84 )
        q congruent 47 modulo 60:   1/12 ( q^3-14*q^2+67*q-146 )
        q congruent 49 modulo 60:   1/12 ( q^3-14*q^2+61*q-72 )
        q congruent 53 modulo 60:   1/12 ( q^3-14*q^2+67*q-110 )
        q congruent 59 modulo 60:   1/12 ( q^3-14*q^2+67*q-170 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 2, 5, 67, 69, 5, 78, 9, 31, 78, 20, 71, 94, 24 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 6 ], 
  [ 5, 1, 2, 4 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 6 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 12 ], [ 12, 1, 2, 12 ], 
  [ 13, 1, 4, 12 ], [ 14, 1, 2, 6 ], [ 15, 1, 2, 8 ], [ 18, 1, 2, 12 ], 
  [ 19, 1, 2, 12 ], [ 21, 1, 2, 12 ], [ 22, 1, 4, 12 ], [ 23, 1, 2, 6 ], 
  [ 24, 1, 2, 6 ], [ 26, 1, 4, 12 ], [ 27, 1, 6, 12 ], [ 28, 1, 4, 12 ], 
  [ 29, 1, 4, 12 ], [ 30, 1, 3, 12 ], [ 34, 1, 4, 12 ], [ 36, 1, 4, 12 ], 
  [ 42, 1, 6, 12 ] ]

i = 46: Pi = [ 1, 2, 3, 5, 6 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [46,1,1]
      Dynkin type is A_2(q) + A_2(q) + A_1(q) + T(phi1^3)
      Order of center |Z^F|: phi1^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 ( q^3-25*q^2+215*q-719 )
        q congruent 2 modulo 60:   1/24 ( q^3-22*q^2+136*q-192 )
        q congruent 3 modulo 60:   1/24 ( q^3-23*q^2+165*q-315 )
        q congruent 4 modulo 60:   1/24 ( q^3-24*q^2+180*q-400 )
        q congruent 5 modulo 60:   1/24 ( q^3-23*q^2+171*q-405 )
        q congruent 7 modulo 60:   1/24 ( q^3-25*q^2+209*q-581 )
        q congruent 8 modulo 60:   1/24 ( q^3-22*q^2+136*q-192 )
        q congruent 9 modulo 60:   1/24 ( q^3-23*q^2+171*q-405 )
        q congruent 11 modulo 60:   1/24 ( q^3-23*q^2+165*q-363 )
        q congruent 13 modulo 60:   1/24 ( q^3-25*q^2+215*q-671 )
        q congruent 16 modulo 60:   1/24 ( q^3-24*q^2+180*q-448 )
        q congruent 17 modulo 60:   1/24 ( q^3-23*q^2+171*q-405 )
        q congruent 19 modulo 60:   1/24 ( q^3-25*q^2+209*q-581 )
        q congruent 21 modulo 60:   1/24 ( q^3-23*q^2+171*q-453 )
        q congruent 23 modulo 60:   1/24 ( q^3-23*q^2+165*q-315 )
        q congruent 25 modulo 60:   1/24 ( q^3-25*q^2+215*q-671 )
        q congruent 27 modulo 60:   1/24 ( q^3-23*q^2+165*q-315 )
        q congruent 29 modulo 60:   1/24 ( q^3-23*q^2+171*q-405 )
        q congruent 31 modulo 60:   1/24 ( q^3-25*q^2+209*q-629 )
        q congruent 32 modulo 60:   1/24 ( q^3-22*q^2+136*q-192 )
        q congruent 37 modulo 60:   1/24 ( q^3-25*q^2+215*q-671 )
        q congruent 41 modulo 60:   1/24 ( q^3-23*q^2+171*q-453 )
        q congruent 43 modulo 60:   1/24 ( q^3-25*q^2+209*q-581 )
        q congruent 47 modulo 60:   1/24 ( q^3-23*q^2+165*q-315 )
        q congruent 49 modulo 60:   1/24 ( q^3-25*q^2+215*q-671 )
        q congruent 53 modulo 60:   1/24 ( q^3-23*q^2+171*q-405 )
        q congruent 59 modulo 60:   1/24 ( q^3-23*q^2+165*q-315 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 8, 77, 66, 4, 4, 68, 77, 30, 8, 77, 77, 30, 14, 83 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 12 ], 
  [ 5, 1, 1, 24 ], [ 6, 1, 1, 24 ], [ 7, 1, 1, 12 ], [ 8, 1, 1, 12 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 12 ], 
  [ 14, 1, 1, 24 ], [ 15, 1, 1, 24 ], [ 16, 1, 1, 24 ], [ 17, 1, 1, 48 ], 
  [ 18, 1, 1, 12 ], [ 19, 1, 1, 12 ], [ 20, 1, 1, 24 ], [ 21, 1, 1, 12 ], 
  [ 22, 1, 1, 36 ], [ 24, 1, 1, 6 ], [ 26, 1, 1, 12 ], [ 27, 1, 1, 12 ], 
  [ 29, 1, 1, 24 ], [ 31, 1, 1, 24 ], [ 32, 1, 1, 24 ], [ 34, 1, 1, 12 ], 
  [ 38, 1, 1, 72 ], [ 42, 1, 1, 12 ] ]

    k = 2: F-action on Pi is ()      [46,1,2]
      Dynkin type is A_2(q) + A_2(q) + A_1(q) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q^2-10*q+25 )
        q congruent 2 modulo 60:   1/8 q ( q^2-8*q+12 )
        q congruent 3 modulo 60:   1/8 ( q^3-9*q^2+21*q-9 )
        q congruent 4 modulo 60:   1/8 q ( q^2-10*q+24 )
        q congruent 5 modulo 60:   1/8 phi1 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/8 ( q^3-11*q^2+33*q-19 )
        q congruent 8 modulo 60:   1/8 q ( q^2-8*q+12 )
        q congruent 9 modulo 60:   1/8 phi1 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/8 ( q^3-9*q^2+21*q-9 )
        q congruent 13 modulo 60:   1/8 phi1 ( q^2-10*q+25 )
        q congruent 16 modulo 60:   1/8 q ( q^2-10*q+24 )
        q congruent 17 modulo 60:   1/8 phi1 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/8 ( q^3-11*q^2+33*q-19 )
        q congruent 21 modulo 60:   1/8 phi1 ( q^2-8*q+15 )
        q congruent 23 modulo 60:   1/8 ( q^3-9*q^2+21*q-9 )
        q congruent 25 modulo 60:   1/8 phi1 ( q^2-10*q+25 )
        q congruent 27 modulo 60:   1/8 ( q^3-9*q^2+21*q-9 )
        q congruent 29 modulo 60:   1/8 phi1 ( q^2-8*q+15 )
        q congruent 31 modulo 60:   1/8 ( q^3-11*q^2+33*q-19 )
        q congruent 32 modulo 60:   1/8 q ( q^2-8*q+12 )
        q congruent 37 modulo 60:   1/8 phi1 ( q^2-10*q+25 )
        q congruent 41 modulo 60:   1/8 phi1 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/8 ( q^3-11*q^2+33*q-19 )
        q congruent 47 modulo 60:   1/8 ( q^3-9*q^2+21*q-9 )
        q congruent 49 modulo 60:   1/8 phi1 ( q^2-10*q+25 )
        q congruent 53 modulo 60:   1/8 phi1 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/8 ( q^3-9*q^2+21*q-9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 4, 68, 77, 30, 4, 68, 68, 7, 30, 81, 77, 30, 30, 81, 83, 37 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], 
  [ 5, 1, 1, 8 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 15, 1, 1, 8 ], 
  [ 16, 1, 1, 8 ], [ 17, 1, 1, 24 ], [ 19, 1, 1, 4 ], [ 20, 1, 2, 8 ], 
  [ 22, 1, 2, 12 ], [ 24, 1, 2, 2 ], [ 26, 1, 3, 4 ], [ 27, 1, 2, 4 ], 
  [ 29, 1, 2, 8 ], [ 31, 1, 2, 8 ], [ 32, 1, 1, 8 ], [ 34, 1, 2, 4 ], 
  [ 38, 1, 5, 24 ], [ 42, 1, 4, 4 ] ]

    k = 3: F-action on Pi is ()      [46,1,3]
      Dynkin type is A_2(q) + A_2(q) + A_1(q) + T(phi1 phi3)
      Order of center |Z^F|: phi1 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 phi1 ( q^2-3*q-10 )
        q congruent 2 modulo 60:   1/12 q phi2 ( q-2 )
        q congruent 3 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 4 modulo 60:   1/12 phi1 ( q^2-2*q-8 )
        q congruent 5 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 7 modulo 60:   1/12 phi1 ( q^2-3*q-10 )
        q congruent 8 modulo 60:   1/12 q phi2 ( q-2 )
        q congruent 9 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 11 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 13 modulo 60:   1/12 phi1 ( q^2-3*q-10 )
        q congruent 16 modulo 60:   1/12 phi1 ( q^2-2*q-8 )
        q congruent 17 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 19 modulo 60:   1/12 phi1 ( q^2-3*q-10 )
        q congruent 21 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 23 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 25 modulo 60:   1/12 phi1 ( q^2-3*q-10 )
        q congruent 27 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 29 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 31 modulo 60:   1/12 phi1 ( q^2-3*q-10 )
        q congruent 32 modulo 60:   1/12 q phi2 ( q-2 )
        q congruent 37 modulo 60:   1/12 phi1 ( q^2-3*q-10 )
        q congruent 41 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 43 modulo 60:   1/12 phi1 ( q^2-3*q-10 )
        q congruent 47 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 49 modulo 60:   1/12 phi1 ( q^2-3*q-10 )
        q congruent 53 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 59 modulo 60:   1/12 q phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 8, 77, 77, 30, 14, 83, 77, 30, 30, 81, 83, 37, 14, 83, 83, 37, 12, 
  79 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 6, 1, 1, 6 ], 
  [ 11, 1, 1, 2 ], [ 17, 1, 1, 12 ], [ 27, 1, 5, 6 ], [ 38, 1, 3, 36 ], 
  [ 42, 1, 3, 6 ] ]

    k = 4: F-action on Pi is (1,3)(5,6)      [46,1,4]
      Dynkin type is ^2A_2(q) + ^2A_2(q) + A_1(q) + T(phi2 phi6)
      Order of center |Z^F|: phi2 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q phi1^2
        q congruent 2 modulo 60:   1/12 phi2 ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/12 q phi1^2
        q congruent 4 modulo 60:   1/12 q^2 phi1
        q congruent 5 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 7 modulo 60:   1/12 q phi1^2
        q congruent 8 modulo 60:   1/12 phi2 ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/12 q phi1^2
        q congruent 11 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 13 modulo 60:   1/12 q phi1^2
        q congruent 16 modulo 60:   1/12 q^2 phi1
        q congruent 17 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 19 modulo 60:   1/12 q phi1^2
        q congruent 21 modulo 60:   1/12 q phi1^2
        q congruent 23 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 25 modulo 60:   1/12 q phi1^2
        q congruent 27 modulo 60:   1/12 q phi1^2
        q congruent 29 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 31 modulo 60:   1/12 q phi1^2
        q congruent 32 modulo 60:   1/12 phi2 ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/12 q phi1^2
        q congruent 41 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 43 modulo 60:   1/12 q phi1^2
        q congruent 47 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 49 modulo 60:   1/12 q phi1^2
        q congruent 53 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 59 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 78, 9, 31, 78, 84, 15, 31, 78, 82, 31, 38, 84, 84, 15, 38, 84, 80, 
  13 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 6, 1, 2, 6 ], 
  [ 11, 1, 2, 2 ], [ 17, 1, 4, 12 ], [ 27, 1, 4, 6 ], [ 38, 1, 11, 36 ], 
  [ 42, 1, 5, 6 ] ]

    k = 5: F-action on Pi is (1,3)(5,6)      [46,1,5]
      Dynkin type is ^2A_2(q) + ^2A_2(q) + A_1(q) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q^2-6*q+11 )
        q congruent 2 modulo 60:   1/8 ( q^3-8*q^2+20*q-16 )
        q congruent 3 modulo 60:   1/8 ( q^3-7*q^2+19*q-21 )
        q congruent 4 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/8 ( q^3-9*q^2+29*q-37 )
        q congruent 7 modulo 60:   1/8 ( q^3-7*q^2+19*q-21 )
        q congruent 8 modulo 60:   1/8 ( q^3-8*q^2+20*q-16 )
        q congruent 9 modulo 60:   1/8 phi1 ( q^2-6*q+11 )
        q congruent 11 modulo 60:   1/8 ( q^3-9*q^2+31*q-47 )
        q congruent 13 modulo 60:   1/8 phi1 ( q^2-6*q+11 )
        q congruent 16 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/8 ( q^3-9*q^2+29*q-37 )
        q congruent 19 modulo 60:   1/8 ( q^3-7*q^2+19*q-21 )
        q congruent 21 modulo 60:   1/8 phi1 ( q^2-6*q+11 )
        q congruent 23 modulo 60:   1/8 ( q^3-9*q^2+31*q-47 )
        q congruent 25 modulo 60:   1/8 phi1 ( q^2-6*q+11 )
        q congruent 27 modulo 60:   1/8 ( q^3-7*q^2+19*q-21 )
        q congruent 29 modulo 60:   1/8 ( q^3-9*q^2+29*q-37 )
        q congruent 31 modulo 60:   1/8 ( q^3-7*q^2+19*q-21 )
        q congruent 32 modulo 60:   1/8 ( q^3-8*q^2+20*q-16 )
        q congruent 37 modulo 60:   1/8 phi1 ( q^2-6*q+11 )
        q congruent 41 modulo 60:   1/8 ( q^3-9*q^2+29*q-37 )
        q congruent 43 modulo 60:   1/8 ( q^3-7*q^2+19*q-21 )
        q congruent 47 modulo 60:   1/8 ( q^3-9*q^2+31*q-47 )
        q congruent 49 modulo 60:   1/8 phi1 ( q^2-6*q+11 )
        q congruent 53 modulo 60:   1/8 ( q^3-9*q^2+29*q-37 )
        q congruent 59 modulo 60:   1/8 ( q^3-9*q^2+31*q-47 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 67, 69, 5, 31, 78, 69, 5, 7, 69, 82, 31, 31, 78, 82, 31, 38, 84 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 4 ], 
  [ 5, 1, 2, 8 ], [ 6, 1, 2, 12 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 1, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 15, 1, 2, 8 ], 
  [ 16, 1, 3, 8 ], [ 17, 1, 4, 24 ], [ 19, 1, 2, 4 ], [ 20, 1, 3, 8 ], 
  [ 22, 1, 3, 12 ], [ 24, 1, 1, 2 ], [ 26, 1, 2, 4 ], [ 27, 1, 3, 4 ], 
  [ 29, 1, 3, 8 ], [ 31, 1, 3, 8 ], [ 32, 1, 3, 8 ], [ 34, 1, 3, 4 ], 
  [ 38, 1, 8, 24 ], [ 42, 1, 2, 4 ] ]

    k = 6: F-action on Pi is (1,3)(5,6)      [46,1,6]
      Dynkin type is ^2A_2(q) + ^2A_2(q) + A_1(q) + T(phi2^3)
      Order of center |Z^F|: phi2^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 phi1 ( q^2-16*q+69 )
        q congruent 2 modulo 60:   1/24 ( q^3-18*q^2+96*q-128 )
        q congruent 3 modulo 60:   1/24 ( q^3-17*q^2+91*q-147 )
        q congruent 4 modulo 60:   1/24 ( q^3-16*q^2+60*q-48 )
        q congruent 5 modulo 60:   1/24 ( q^3-19*q^2+121*q-255 )
        q congruent 7 modulo 60:   1/24 ( q^3-17*q^2+91*q-147 )
        q congruent 8 modulo 60:   1/24 ( q^3-18*q^2+96*q-128 )
        q congruent 9 modulo 60:   1/24 ( q^3-17*q^2+85*q-117 )
        q congruent 11 modulo 60:   1/24 ( q^3-19*q^2+127*q-333 )
        q congruent 13 modulo 60:   1/24 phi1 ( q^2-16*q+69 )
        q congruent 16 modulo 60:   1/24 q ( q^2-16*q+60 )
        q congruent 17 modulo 60:   1/24 ( q^3-19*q^2+121*q-255 )
        q congruent 19 modulo 60:   1/24 ( q^3-17*q^2+91*q-195 )
        q congruent 21 modulo 60:   1/24 phi1 ( q^2-16*q+69 )
        q congruent 23 modulo 60:   1/24 ( q^3-19*q^2+127*q-333 )
        q congruent 25 modulo 60:   1/24 phi1 ( q^2-16*q+69 )
        q congruent 27 modulo 60:   1/24 ( q^3-17*q^2+91*q-147 )
        q congruent 29 modulo 60:   1/24 ( q^3-19*q^2+121*q-303 )
        q congruent 31 modulo 60:   1/24 ( q^3-17*q^2+91*q-147 )
        q congruent 32 modulo 60:   1/24 ( q^3-18*q^2+96*q-128 )
        q congruent 37 modulo 60:   1/24 phi1 ( q^2-16*q+69 )
        q congruent 41 modulo 60:   1/24 ( q^3-19*q^2+121*q-255 )
        q congruent 43 modulo 60:   1/24 ( q^3-17*q^2+91*q-147 )
        q congruent 47 modulo 60:   1/24 ( q^3-19*q^2+127*q-333 )
        q congruent 49 modulo 60:   1/24 ( q^3-17*q^2+85*q-117 )
        q congruent 53 modulo 60:   1/24 ( q^3-19*q^2+121*q-255 )
        q congruent 59 modulo 60:   1/24 ( q^3-19*q^2+127*q-381 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 2, 5, 67, 78, 9, 5, 67, 69, 5, 31, 78, 78, 9, 31, 78, 84, 15 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 12 ], 
  [ 5, 1, 2, 24 ], [ 6, 1, 2, 24 ], [ 7, 1, 2, 12 ], [ 8, 1, 2, 12 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 12 ], 
  [ 14, 1, 2, 24 ], [ 15, 1, 2, 24 ], [ 16, 1, 3, 24 ], [ 17, 1, 4, 48 ], 
  [ 18, 1, 2, 12 ], [ 19, 1, 2, 12 ], [ 20, 1, 4, 24 ], [ 21, 1, 2, 12 ], 
  [ 22, 1, 4, 36 ], [ 24, 1, 2, 6 ], [ 26, 1, 4, 12 ], [ 27, 1, 6, 12 ], 
  [ 29, 1, 4, 24 ], [ 31, 1, 4, 24 ], [ 32, 1, 3, 24 ], [ 34, 1, 4, 12 ], 
  [ 38, 1, 12, 72 ], [ 42, 1, 6, 12 ] ]

    k = 7: F-action on Pi is (1,5)(3,6)      [46,1,7]
      Dynkin type is A_2(q^2) + A_1(q) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 phi1 ( q^2-8*q+19 )
        q congruent 2 modulo 60:   1/24 ( q^3-10*q^2+28*q-24 )
        q congruent 3 modulo 60:   1/24 ( q^3-9*q^2+17*q+3 )
        q congruent 4 modulo 60:   1/24 q ( q^2-8*q+16 )
        q congruent 5 modulo 60:   1/24 ( q^3-11*q^2+39*q-45 )
        q congruent 7 modulo 60:   1/24 ( q^3-9*q^2+21*q-1 )
        q congruent 8 modulo 60:   1/24 ( q^3-10*q^2+28*q-24 )
        q congruent 9 modulo 60:   1/24 phi1 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/24 ( q^3-11*q^2+33*q-27 )
        q congruent 13 modulo 60:   1/24 phi1 ( q^2-8*q+19 )
        q congruent 16 modulo 60:   1/24 q ( q^2-8*q+16 )
        q congruent 17 modulo 60:   1/24 ( q^3-11*q^2+39*q-45 )
        q congruent 19 modulo 60:   1/24 ( q^3-9*q^2+21*q-1 )
        q congruent 21 modulo 60:   1/24 phi1 ( q^2-8*q+15 )
        q congruent 23 modulo 60:   1/24 ( q^3-11*q^2+33*q-27 )
        q congruent 25 modulo 60:   1/24 phi1 ( q^2-8*q+19 )
        q congruent 27 modulo 60:   1/24 ( q^3-9*q^2+17*q+3 )
        q congruent 29 modulo 60:   1/24 ( q^3-11*q^2+39*q-45 )
        q congruent 31 modulo 60:   1/24 ( q^3-9*q^2+21*q-1 )
        q congruent 32 modulo 60:   1/24 ( q^3-10*q^2+28*q-24 )
        q congruent 37 modulo 60:   1/24 phi1 ( q^2-8*q+19 )
        q congruent 41 modulo 60:   1/24 ( q^3-11*q^2+39*q-45 )
        q congruent 43 modulo 60:   1/24 ( q^3-9*q^2+21*q-1 )
        q congruent 47 modulo 60:   1/24 ( q^3-11*q^2+33*q-27 )
        q congruent 49 modulo 60:   1/24 phi1 ( q^2-8*q+19 )
        q congruent 53 modulo 60:   1/24 ( q^3-11*q^2+39*q-45 )
        q congruent 59 modulo 60:   1/24 ( q^3-11*q^2+33*q-27 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 3, 19, 72, 87, 35 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], 
  [ 6, 1, 1, 2 ], [ 6, 1, 2, 6 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 6 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 11, 1, 2, 2 ], 
  [ 17, 1, 2, 4 ], [ 17, 1, 3, 12 ], [ 19, 1, 1, 6 ], [ 19, 1, 2, 6 ], 
  [ 20, 1, 8, 24 ], [ 22, 1, 3, 12 ], [ 24, 1, 1, 6 ], [ 26, 1, 1, 12 ], 
  [ 27, 1, 1, 12 ], [ 32, 1, 4, 12 ], [ 34, 1, 3, 12 ], [ 38, 1, 7, 24 ], 
  [ 42, 1, 1, 12 ] ]

    k = 8: F-action on Pi is (1,5)(3,6)      [46,1,8]
      Dynkin type is A_2(q^2) + A_1(q) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1^3
        q congruent 2 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/8 phi4 ( q-3 )
        q congruent 4 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 5 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 7 modulo 60:   1/8 phi4 ( q-3 )
        q congruent 8 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/8 phi1^3
        q congruent 11 modulo 60:   1/8 ( q^3-5*q^2+5*q-5 )
        q congruent 13 modulo 60:   1/8 phi1^3
        q congruent 16 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 17 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 19 modulo 60:   1/8 phi4 ( q-3 )
        q congruent 21 modulo 60:   1/8 phi1^3
        q congruent 23 modulo 60:   1/8 ( q^3-5*q^2+5*q-5 )
        q congruent 25 modulo 60:   1/8 phi1^3
        q congruent 27 modulo 60:   1/8 phi4 ( q-3 )
        q congruent 29 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 31 modulo 60:   1/8 phi4 ( q-3 )
        q congruent 32 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/8 phi1^3
        q congruent 41 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 43 modulo 60:   1/8 phi4 ( q-3 )
        q congruent 47 modulo 60:   1/8 ( q^3-5*q^2+5*q-5 )
        q congruent 49 modulo 60:   1/8 phi1^3
        q congruent 53 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 59 modulo 60:   1/8 ( q^3-5*q^2+5*q-5 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 7, 69, 76, 20, 40, 88 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], 
  [ 6, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], 
  [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], 
  [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 1, 3, 4 ], [ 18, 1, 2, 4 ], 
  [ 19, 1, 1, 2 ], [ 19, 1, 2, 2 ], [ 20, 1, 7, 8 ], [ 21, 1, 2, 4 ], 
  [ 22, 1, 4, 4 ], [ 24, 1, 2, 2 ], [ 26, 1, 3, 4 ], [ 27, 1, 2, 4 ], 
  [ 32, 1, 4, 4 ], [ 34, 1, 4, 4 ], [ 38, 1, 10, 8 ], [ 42, 1, 4, 4 ] ]

    k = 9: F-action on Pi is (1,5)(3,6)      [46,1,9]
      Dynkin type is A_2(q^2) + A_1(q) + T(phi2 phi3)
      Order of center |Z^F|: phi2 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 2 modulo 60:   1/12 q phi2 ( q-2 )
        q congruent 3 modulo 60:   1/12 q phi1 phi2
        q congruent 4 modulo 60:   1/12 q phi1 ( q+2 )
        q congruent 5 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 7 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 8 modulo 60:   1/12 q phi2 ( q-2 )
        q congruent 9 modulo 60:   1/12 q phi1 phi2
        q congruent 11 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 13 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 16 modulo 60:   1/12 q phi1 ( q+2 )
        q congruent 17 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 19 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 21 modulo 60:   1/12 q phi1 phi2
        q congruent 23 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 25 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 27 modulo 60:   1/12 q phi1 phi2
        q congruent 29 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 31 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 32 modulo 60:   1/12 q phi2 ( q-2 )
        q congruent 37 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 41 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 43 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 47 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 49 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 53 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 59 modulo 60:   1/12 q phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 81, 27, 59, 95, 85, 34 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], 
  [ 6, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 27, 1, 5, 6 ], 
  [ 38, 1, 9, 12 ], [ 42, 1, 3, 6 ] ]

    k = 10: F-action on Pi is (1,6)(3,5)      [46,1,10]
      Dynkin type is A_2(q^2) + A_1(q) + T(phi1 phi6)
      Order of center |Z^F|: phi1 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q phi1 ( q-5 )
        q congruent 2 modulo 60:   1/12 phi2 ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 4 modulo 60:   1/12 q phi1 ( q-4 )
        q congruent 5 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 7 modulo 60:   1/12 q phi1 ( q-5 )
        q congruent 8 modulo 60:   1/12 phi2 ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 11 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 13 modulo 60:   1/12 q phi1 ( q-5 )
        q congruent 16 modulo 60:   1/12 q phi1 ( q-4 )
        q congruent 17 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 19 modulo 60:   1/12 q phi1 ( q-5 )
        q congruent 21 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 23 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 25 modulo 60:   1/12 q phi1 ( q-5 )
        q congruent 27 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 29 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 31 modulo 60:   1/12 q phi1 ( q-5 )
        q congruent 32 modulo 60:   1/12 phi2 ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/12 q phi1 ( q-5 )
        q congruent 41 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 43 modulo 60:   1/12 q phi1 ( q-5 )
        q congruent 47 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 49 modulo 60:   1/12 q phi1 ( q-5 )
        q congruent 53 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 59 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 28, 82, 96, 60, 33, 86 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], 
  [ 6, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 17, 1, 3, 4 ], [ 27, 1, 4, 6 ], 
  [ 38, 1, 4, 12 ], [ 42, 1, 5, 6 ] ]

    k = 11: F-action on Pi is (1,6)(3,5)      [46,1,11]
      Dynkin type is A_2(q^2) + A_1(q) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q^2-6*q+3 )
        q congruent 2 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 4 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/8 phi1 ( q^2-4*q+1 )
        q congruent 7 modulo 60:   1/8 phi1^2 ( q-5 )
        q congruent 8 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/8 phi1 ( q^2-4*q+1 )
        q congruent 11 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 13 modulo 60:   1/8 phi1 ( q^2-6*q+3 )
        q congruent 16 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/8 phi1 ( q^2-4*q+1 )
        q congruent 19 modulo 60:   1/8 phi1^2 ( q-5 )
        q congruent 21 modulo 60:   1/8 phi1 ( q^2-4*q+1 )
        q congruent 23 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 25 modulo 60:   1/8 phi1 ( q^2-6*q+3 )
        q congruent 27 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 29 modulo 60:   1/8 phi1 ( q^2-4*q+1 )
        q congruent 31 modulo 60:   1/8 phi1^2 ( q-5 )
        q congruent 32 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/8 phi1 ( q^2-6*q+3 )
        q congruent 41 modulo 60:   1/8 phi1 ( q^2-4*q+1 )
        q congruent 43 modulo 60:   1/8 phi1^2 ( q-5 )
        q congruent 47 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 49 modulo 60:   1/8 phi1 ( q^2-6*q+3 )
        q congruent 53 modulo 60:   1/8 phi1 ( q^2-4*q+1 )
        q congruent 59 modulo 60:   1/8 phi1^2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 7, 19, 76, 87, 40 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], 
  [ 6, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], 
  [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 2 ], 
  [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 1, 3, 4 ], [ 18, 1, 1, 4 ], 
  [ 19, 1, 1, 2 ], [ 19, 1, 2, 2 ], [ 20, 1, 6, 8 ], [ 21, 1, 1, 4 ], 
  [ 22, 1, 1, 4 ], [ 24, 1, 1, 2 ], [ 26, 1, 2, 4 ], [ 27, 1, 3, 4 ], 
  [ 32, 1, 4, 4 ], [ 34, 1, 1, 4 ], [ 38, 1, 2, 8 ], [ 42, 1, 2, 4 ] ]

    k = 12: F-action on Pi is (1,6)(3,5)      [46,1,12]
      Dynkin type is A_2(q^2) + A_1(q) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 phi1 ( q^2-8*q+9 )
        q congruent 2 modulo 60:   1/24 ( q^3-6*q^2+12*q-8 )
        q congruent 3 modulo 60:   1/24 phi1 ( q^2-6*q+9 )
        q congruent 4 modulo 60:   1/24 q ( q^2-8*q+16 )
        q congruent 5 modulo 60:   1/24 ( q^3-7*q^2+13*q-15 )
        q congruent 7 modulo 60:   1/24 phi1 ( q^2-8*q+15 )
        q congruent 8 modulo 60:   1/24 ( q^3-6*q^2+12*q-8 )
        q congruent 9 modulo 60:   1/24 phi1 ( q^2-6*q+3 )
        q congruent 11 modulo 60:   1/24 ( q^3-7*q^2+19*q-21 )
        q congruent 13 modulo 60:   1/24 phi1 ( q^2-8*q+9 )
        q congruent 16 modulo 60:   1/24 q ( q^2-8*q+16 )
        q congruent 17 modulo 60:   1/24 ( q^3-7*q^2+13*q-15 )
        q congruent 19 modulo 60:   1/24 phi1 ( q^2-8*q+15 )
        q congruent 21 modulo 60:   1/24 phi1 ( q^2-6*q+3 )
        q congruent 23 modulo 60:   1/24 ( q^3-7*q^2+19*q-21 )
        q congruent 25 modulo 60:   1/24 phi1 ( q^2-8*q+9 )
        q congruent 27 modulo 60:   1/24 phi1 ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/24 ( q^3-7*q^2+13*q-15 )
        q congruent 31 modulo 60:   1/24 phi1 ( q^2-8*q+15 )
        q congruent 32 modulo 60:   1/24 ( q^3-6*q^2+12*q-8 )
        q congruent 37 modulo 60:   1/24 phi1 ( q^2-8*q+9 )
        q congruent 41 modulo 60:   1/24 ( q^3-7*q^2+13*q-15 )
        q congruent 43 modulo 60:   1/24 phi1 ( q^2-8*q+15 )
        q congruent 47 modulo 60:   1/24 ( q^3-7*q^2+19*q-21 )
        q congruent 49 modulo 60:   1/24 phi1 ( q^2-8*q+9 )
        q congruent 53 modulo 60:   1/24 ( q^3-7*q^2+13*q-15 )
        q congruent 59 modulo 60:   1/24 ( q^3-7*q^2+19*q-21 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 69, 72, 20, 35, 88 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], 
  [ 6, 1, 1, 6 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 6 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 6 ], 
  [ 17, 1, 2, 12 ], [ 17, 1, 3, 4 ], [ 19, 1, 1, 6 ], [ 19, 1, 2, 6 ], 
  [ 20, 1, 5, 24 ], [ 22, 1, 2, 12 ], [ 24, 1, 2, 6 ], [ 26, 1, 4, 12 ], 
  [ 27, 1, 6, 12 ], [ 32, 1, 4, 12 ], [ 34, 1, 2, 12 ], [ 38, 1, 6, 24 ], 
  [ 42, 1, 6, 12 ] ]

i = 47: Pi = [ 1, 2, 3, 5, 7 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [47,1,1]
      Dynkin type is A_2(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^3)
      Order of center |Z^F|: phi1^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 ( q^3-26*q^2+229*q-804 )
        q congruent 2 modulo 60:   1/24 ( q^3-22*q^2+136*q-192 )
        q congruent 3 modulo 60:   1/24 ( q^3-26*q^2+207*q-414 )
        q congruent 4 modulo 60:   1/24 ( q^3-22*q^2+152*q-320 )
        q congruent 5 modulo 60:   1/24 ( q^3-26*q^2+213*q-540 )
        q congruent 7 modulo 60:   1/24 ( q^3-26*q^2+223*q-630 )
        q congruent 8 modulo 60:   1/24 ( q^3-22*q^2+136*q-192 )
        q congruent 9 modulo 60:   1/24 ( q^3-26*q^2+213*q-540 )
        q congruent 11 modulo 60:   1/24 ( q^3-26*q^2+207*q-462 )
        q congruent 13 modulo 60:   1/24 ( q^3-26*q^2+229*q-756 )
        q congruent 16 modulo 60:   1/24 ( q^3-22*q^2+152*q-368 )
        q congruent 17 modulo 60:   1/24 ( q^3-26*q^2+213*q-540 )
        q congruent 19 modulo 60:   1/24 ( q^3-26*q^2+223*q-630 )
        q congruent 21 modulo 60:   1/24 ( q^3-26*q^2+213*q-588 )
        q congruent 23 modulo 60:   1/24 ( q^3-26*q^2+207*q-414 )
        q congruent 25 modulo 60:   1/24 ( q^3-26*q^2+229*q-756 )
        q congruent 27 modulo 60:   1/24 ( q^3-26*q^2+207*q-414 )
        q congruent 29 modulo 60:   1/24 ( q^3-26*q^2+213*q-540 )
        q congruent 31 modulo 60:   1/24 ( q^3-26*q^2+223*q-678 )
        q congruent 32 modulo 60:   1/24 ( q^3-22*q^2+136*q-192 )
        q congruent 37 modulo 60:   1/24 ( q^3-26*q^2+229*q-756 )
        q congruent 41 modulo 60:   1/24 ( q^3-26*q^2+213*q-588 )
        q congruent 43 modulo 60:   1/24 ( q^3-26*q^2+223*q-630 )
        q congruent 47 modulo 60:   1/24 ( q^3-26*q^2+207*q-414 )
        q congruent 49 modulo 60:   1/24 ( q^3-26*q^2+229*q-756 )
        q congruent 53 modulo 60:   1/24 ( q^3-26*q^2+213*q-540 )
        q congruent 59 modulo 60:   1/24 ( q^3-26*q^2+207*q-414 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 66, 4, 4, 68, 66, 4, 4, 68, 4, 68, 68, 7, 8, 77, 77, 
  30, 77, 30, 30, 81 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 14 ], [ 4, 1, 1, 18 ], 
  [ 5, 1, 1, 24 ], [ 6, 1, 1, 32 ], [ 7, 1, 1, 12 ], [ 8, 1, 1, 4 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 12 ], [ 12, 1, 1, 18 ], 
  [ 13, 1, 1, 24 ], [ 14, 1, 1, 12 ], [ 15, 1, 1, 36 ], [ 16, 1, 1, 48 ], 
  [ 17, 1, 1, 72 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 24 ], [ 20, 1, 1, 24 ], 
  [ 22, 1, 1, 4 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 6 ], [ 25, 1, 1, 12 ], 
  [ 28, 1, 1, 12 ], [ 30, 1, 1, 24 ], [ 31, 1, 1, 12 ], [ 32, 1, 1, 48 ], 
  [ 33, 1, 1, 48 ], [ 35, 1, 1, 24 ], [ 40, 1, 1, 12 ] ]

    k = 2: F-action on Pi is ()      [47,1,2]
      Dynkin type is A_2(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 phi1 ( q^2-11*q+34 )
        q congruent 2 modulo 60:   1/24 q ( q^2-8*q+12 )
        q congruent 3 modulo 60:   1/24 phi1 ( q^2-11*q+24 )
        q congruent 4 modulo 60:   1/24 q ( q^2-8*q+16 )
        q congruent 5 modulo 60:   1/24 phi1 ( q^2-11*q+30 )
        q congruent 7 modulo 60:   1/24 phi1 ( q^2-11*q+28 )
        q congruent 8 modulo 60:   1/24 q ( q^2-8*q+12 )
        q congruent 9 modulo 60:   1/24 phi1 ( q^2-11*q+30 )
        q congruent 11 modulo 60:   1/24 phi1 ( q^2-11*q+24 )
        q congruent 13 modulo 60:   1/24 phi1 ( q^2-11*q+34 )
        q congruent 16 modulo 60:   1/24 q ( q^2-8*q+16 )
        q congruent 17 modulo 60:   1/24 phi1 ( q^2-11*q+30 )
        q congruent 19 modulo 60:   1/24 phi1 ( q^2-11*q+28 )
        q congruent 21 modulo 60:   1/24 phi1 ( q^2-11*q+30 )
        q congruent 23 modulo 60:   1/24 phi1 ( q^2-11*q+24 )
        q congruent 25 modulo 60:   1/24 phi1 ( q^2-11*q+34 )
        q congruent 27 modulo 60:   1/24 phi1 ( q^2-11*q+24 )
        q congruent 29 modulo 60:   1/24 phi1 ( q^2-11*q+30 )
        q congruent 31 modulo 60:   1/24 phi1 ( q^2-11*q+28 )
        q congruent 32 modulo 60:   1/24 q ( q^2-8*q+12 )
        q congruent 37 modulo 60:   1/24 phi1 ( q^2-11*q+34 )
        q congruent 41 modulo 60:   1/24 phi1 ( q^2-11*q+30 )
        q congruent 43 modulo 60:   1/24 phi1 ( q^2-11*q+28 )
        q congruent 47 modulo 60:   1/24 phi1 ( q^2-11*q+24 )
        q congruent 49 modulo 60:   1/24 phi1 ( q^2-11*q+34 )
        q congruent 53 modulo 60:   1/24 phi1 ( q^2-11*q+30 )
        q congruent 59 modulo 60:   1/24 phi1 ( q^2-11*q+24 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 4, 68, 4, 68, 68, 3, 4, 68, 68, 7, 68, 7, 7, 69, 77, 30, 30, 
  81, 30, 81, 81, 27 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 18 ], 
  [ 6, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 2 ], [ 12, 1, 1, 6 ], 
  [ 13, 1, 1, 24 ], [ 16, 1, 1, 24 ], [ 20, 1, 2, 24 ], [ 22, 1, 2, 4 ], 
  [ 23, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 12 ], [ 28, 1, 2, 12 ], 
  [ 31, 1, 2, 12 ], [ 33, 1, 1, 48 ], [ 35, 1, 3, 24 ], [ 40, 1, 1, 12 ] ]

    k = 3: F-action on Pi is (5,7)      [47,1,3]
      Dynkin type is A_2(q) + A_1(q) + A_1(q^2) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q^2-7*q+10 )
        q congruent 2 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/8 q ( q^2-8*q+15 )
        q congruent 4 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/8 phi1 ( q^2-7*q+10 )
        q congruent 7 modulo 60:   1/8 q ( q^2-8*q+15 )
        q congruent 8 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/8 phi1 ( q^2-7*q+10 )
        q congruent 11 modulo 60:   1/8 q ( q^2-8*q+15 )
        q congruent 13 modulo 60:   1/8 phi1 ( q^2-7*q+10 )
        q congruent 16 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/8 phi1 ( q^2-7*q+10 )
        q congruent 19 modulo 60:   1/8 q ( q^2-8*q+15 )
        q congruent 21 modulo 60:   1/8 phi1 ( q^2-7*q+10 )
        q congruent 23 modulo 60:   1/8 q ( q^2-8*q+15 )
        q congruent 25 modulo 60:   1/8 phi1 ( q^2-7*q+10 )
        q congruent 27 modulo 60:   1/8 q ( q^2-8*q+15 )
        q congruent 29 modulo 60:   1/8 phi1 ( q^2-7*q+10 )
        q congruent 31 modulo 60:   1/8 q ( q^2-8*q+15 )
        q congruent 32 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/8 phi1 ( q^2-7*q+10 )
        q congruent 41 modulo 60:   1/8 phi1 ( q^2-7*q+10 )
        q congruent 43 modulo 60:   1/8 q ( q^2-8*q+15 )
        q congruent 47 modulo 60:   1/8 q ( q^2-8*q+15 )
        q congruent 49 modulo 60:   1/8 phi1 ( q^2-7*q+10 )
        q congruent 53 modulo 60:   1/8 phi1 ( q^2-7*q+10 )
        q congruent 59 modulo 60:   1/8 q ( q^2-8*q+15 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 70, 68, 19, 68, 19, 7, 76, 30, 97, 81, 59 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], 
  [ 4, 1, 2, 2 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], 
  [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 12, 1, 1, 2 ], 
  [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 14, 1, 1, 4 ], [ 15, 1, 1, 4 ], 
  [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 18, 1, 1, 4 ], [ 20, 1, 1, 8 ], 
  [ 22, 1, 1, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 25, 1, 4, 4 ], 
  [ 28, 1, 3, 4 ], [ 30, 1, 2, 8 ], [ 31, 1, 1, 4 ], [ 33, 1, 2, 8 ], 
  [ 35, 1, 2, 8 ], [ 40, 1, 3, 4 ] ]

    k = 4: F-action on Pi is (5,7)      [47,1,4]
      Dynkin type is A_2(q) + A_1(q) + A_1(q^2) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1^2 ( q-4 )
        q congruent 2 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 4 modulo 60:   1/8 q^2 ( q-4 )
        q congruent 5 modulo 60:   1/8 phi1 ( q^2-5*q+8 )
        q congruent 7 modulo 60:   1/8 phi1 ( q^2-5*q+2 )
        q congruent 8 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/8 phi1 ( q^2-5*q+8 )
        q congruent 11 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 13 modulo 60:   1/8 phi1^2 ( q-4 )
        q congruent 16 modulo 60:   1/8 q^2 ( q-4 )
        q congruent 17 modulo 60:   1/8 phi1 ( q^2-5*q+8 )
        q congruent 19 modulo 60:   1/8 phi1 ( q^2-5*q+2 )
        q congruent 21 modulo 60:   1/8 phi1 ( q^2-5*q+8 )
        q congruent 23 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 25 modulo 60:   1/8 phi1^2 ( q-4 )
        q congruent 27 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 29 modulo 60:   1/8 phi1 ( q^2-5*q+8 )
        q congruent 31 modulo 60:   1/8 phi1 ( q^2-5*q+2 )
        q congruent 32 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/8 phi1^2 ( q-4 )
        q congruent 41 modulo 60:   1/8 phi1 ( q^2-5*q+8 )
        q congruent 43 modulo 60:   1/8 phi1 ( q^2-5*q+2 )
        q congruent 47 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 49 modulo 60:   1/8 phi1^2 ( q-4 )
        q congruent 53 modulo 60:   1/8 phi1 ( q^2-5*q+8 )
        q congruent 59 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 19, 3, 72, 7, 76, 69, 20, 81, 59, 27, 95 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 4 ], 
  [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 4 ], 
  [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], 
  [ 16, 1, 4, 8 ], [ 17, 1, 2, 8 ], [ 20, 1, 2, 8 ], [ 22, 1, 2, 4 ], 
  [ 23, 1, 2, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 28, 1, 4, 4 ], 
  [ 31, 1, 2, 4 ], [ 32, 1, 2, 8 ], [ 33, 1, 2, 8 ], [ 35, 1, 4, 8 ], 
  [ 40, 1, 3, 4 ] ]

    k = 5: F-action on Pi is (2,5,7)      [47,1,5]
      Dynkin type is A_2(q) + A_1(q^3) + T(phi1 phi3)
      Order of center |Z^F|: phi1 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 phi1 ( q^2-q-6 )
        q congruent 2 modulo 60:   1/12 q phi2 ( q-2 )
        q congruent 3 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 4 modulo 60:   1/12 phi1 ( q^2-4 )
        q congruent 5 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 7 modulo 60:   1/12 phi1 ( q^2-q-6 )
        q congruent 8 modulo 60:   1/12 q phi2 ( q-2 )
        q congruent 9 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 11 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 13 modulo 60:   1/12 phi1 ( q^2-q-6 )
        q congruent 16 modulo 60:   1/12 phi1 ( q^2-4 )
        q congruent 17 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 19 modulo 60:   1/12 phi1 ( q^2-q-6 )
        q congruent 21 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 23 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 25 modulo 60:   1/12 phi1 ( q^2-q-6 )
        q congruent 27 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 29 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 31 modulo 60:   1/12 phi1 ( q^2-q-6 )
        q congruent 32 modulo 60:   1/12 q phi2 ( q-2 )
        q congruent 37 modulo 60:   1/12 phi1 ( q^2-q-6 )
        q congruent 41 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 43 modulo 60:   1/12 phi1 ( q^2-q-6 )
        q congruent 47 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 49 modulo 60:   1/12 phi1 ( q^2-q-6 )
        q congruent 53 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 59 modulo 60:   1/12 q phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 14, 87, 83, 40, 12, 85 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], 
  [ 8, 1, 1, 4 ], [ 10, 1, 1, 2 ], [ 22, 1, 1, 4 ], [ 33, 1, 3, 6 ], 
  [ 40, 1, 5, 6 ] ]

    k = 6: F-action on Pi is (2,5,7)      [47,1,6]
      Dynkin type is A_2(q) + A_1(q^3) + T(phi2 phi3)
      Order of center |Z^F|: phi2 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 2 modulo 60:   1/12 q^2 phi2
        q congruent 3 modulo 60:   1/12 q phi1 phi2
        q congruent 4 modulo 60:   1/12 q phi1 ( q+2 )
        q congruent 5 modulo 60:   1/12 q phi1 phi2
        q congruent 7 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 8 modulo 60:   1/12 q^2 phi2
        q congruent 9 modulo 60:   1/12 q phi1 phi2
        q congruent 11 modulo 60:   1/12 q phi1 phi2
        q congruent 13 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 16 modulo 60:   1/12 q phi1 ( q+2 )
        q congruent 17 modulo 60:   1/12 q phi1 phi2
        q congruent 19 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 21 modulo 60:   1/12 q phi1 phi2
        q congruent 23 modulo 60:   1/12 q phi1 phi2
        q congruent 25 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 27 modulo 60:   1/12 q phi1 phi2
        q congruent 29 modulo 60:   1/12 q phi1 phi2
        q congruent 31 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 32 modulo 60:   1/12 q^2 phi2
        q congruent 37 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 41 modulo 60:   1/12 q phi1 phi2
        q congruent 43 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 47 modulo 60:   1/12 q phi1 phi2
        q congruent 49 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 53 modulo 60:   1/12 q phi1 phi2
        q congruent 59 modulo 60:   1/12 q phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 83, 35, 37, 88, 79, 34 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 22, 1, 2, 4 ], [ 33, 1, 3, 6 ], [ 40, 1, 5, 6 ] ]

    k = 7: F-action on Pi is (1,3)      [47,1,7]
      Dynkin type is ^2A_2(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 phi1 ( q^2-9*q+18 )
        q congruent 2 modulo 60:   1/24 ( q^3-6*q^2+12*q-8 )
        q congruent 3 modulo 60:   1/24 ( q^3-10*q^2+33*q-36 )
        q congruent 4 modulo 60:   1/24 q ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/24 ( q^3-10*q^2+31*q-30 )
        q congruent 7 modulo 60:   1/24 ( q^3-10*q^2+33*q-36 )
        q congruent 8 modulo 60:   1/24 ( q^3-6*q^2+12*q-8 )
        q congruent 9 modulo 60:   1/24 phi1 ( q^2-9*q+18 )
        q congruent 11 modulo 60:   1/24 ( q^3-10*q^2+37*q-48 )
        q congruent 13 modulo 60:   1/24 phi1 ( q^2-9*q+18 )
        q congruent 16 modulo 60:   1/24 q ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/24 ( q^3-10*q^2+31*q-30 )
        q congruent 19 modulo 60:   1/24 ( q^3-10*q^2+33*q-36 )
        q congruent 21 modulo 60:   1/24 phi1 ( q^2-9*q+18 )
        q congruent 23 modulo 60:   1/24 ( q^3-10*q^2+37*q-48 )
        q congruent 25 modulo 60:   1/24 phi1 ( q^2-9*q+18 )
        q congruent 27 modulo 60:   1/24 ( q^3-10*q^2+33*q-36 )
        q congruent 29 modulo 60:   1/24 ( q^3-10*q^2+31*q-30 )
        q congruent 31 modulo 60:   1/24 ( q^3-10*q^2+33*q-36 )
        q congruent 32 modulo 60:   1/24 ( q^3-6*q^2+12*q-8 )
        q congruent 37 modulo 60:   1/24 phi1 ( q^2-9*q+18 )
        q congruent 41 modulo 60:   1/24 ( q^3-10*q^2+31*q-30 )
        q congruent 43 modulo 60:   1/24 ( q^3-10*q^2+33*q-36 )
        q congruent 47 modulo 60:   1/24 ( q^3-10*q^2+37*q-48 )
        q congruent 49 modulo 60:   1/24 phi1 ( q^2-9*q+18 )
        q congruent 53 modulo 60:   1/24 ( q^3-10*q^2+31*q-30 )
        q congruent 59 modulo 60:   1/24 ( q^3-10*q^2+37*q-48 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 69, 69, 5, 69, 5, 5, 67, 68, 7, 7, 69, 7, 69, 69, 5, 28, 82, 82, 
  31, 82, 31, 31, 78 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 18 ], 
  [ 6, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 12, 1, 2, 6 ], 
  [ 13, 1, 4, 24 ], [ 16, 1, 3, 24 ], [ 20, 1, 3, 24 ], [ 22, 1, 3, 4 ], 
  [ 23, 1, 2, 6 ], [ 24, 1, 1, 6 ], [ 25, 1, 3, 12 ], [ 28, 1, 3, 12 ], 
  [ 31, 1, 3, 12 ], [ 33, 1, 8, 48 ], [ 35, 1, 6, 24 ], [ 40, 1, 6, 12 ] ]

    k = 8: F-action on Pi is (1,3)      [47,1,8]
      Dynkin type is ^2A_2(q) + A_1(q) + A_1(q) + A_1(q) + T(phi2^3)
      Order of center |Z^F|: phi2^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 phi1 ( q^2-19*q+96 )
        q congruent 2 modulo 60:   1/24 ( q^3-16*q^2+76*q-96 )
        q congruent 3 modulo 60:   1/24 ( q^3-20*q^2+121*q-210 )
        q congruent 4 modulo 60:   1/24 ( q^3-16*q^2+60*q-48 )
        q congruent 5 modulo 60:   1/24 ( q^3-20*q^2+131*q-280 )
        q congruent 7 modulo 60:   1/24 ( q^3-20*q^2+121*q-210 )
        q congruent 8 modulo 60:   1/24 ( q^3-16*q^2+76*q-96 )
        q congruent 9 modulo 60:   1/24 ( q^3-20*q^2+115*q-144 )
        q congruent 11 modulo 60:   1/24 ( q^3-20*q^2+137*q-394 )
        q congruent 13 modulo 60:   1/24 phi1 ( q^2-19*q+96 )
        q congruent 16 modulo 60:   1/24 q ( q^2-16*q+60 )
        q congruent 17 modulo 60:   1/24 ( q^3-20*q^2+131*q-280 )
        q congruent 19 modulo 60:   1/24 ( q^3-20*q^2+121*q-258 )
        q congruent 21 modulo 60:   1/24 phi1 ( q^2-19*q+96 )
        q congruent 23 modulo 60:   1/24 ( q^3-20*q^2+137*q-394 )
        q congruent 25 modulo 60:   1/24 phi1 ( q^2-19*q+96 )
        q congruent 27 modulo 60:   1/24 ( q^3-20*q^2+121*q-210 )
        q congruent 29 modulo 60:   1/24 ( q^3-20*q^2+131*q-328 )
        q congruent 31 modulo 60:   1/24 ( q^3-20*q^2+121*q-210 )
        q congruent 32 modulo 60:   1/24 ( q^3-16*q^2+76*q-96 )
        q congruent 37 modulo 60:   1/24 phi1 ( q^2-19*q+96 )
        q congruent 41 modulo 60:   1/24 ( q^3-20*q^2+131*q-280 )
        q congruent 43 modulo 60:   1/24 ( q^3-20*q^2+121*q-210 )
        q congruent 47 modulo 60:   1/24 ( q^3-20*q^2+137*q-394 )
        q congruent 49 modulo 60:   1/24 ( q^3-20*q^2+115*q-144 )
        q congruent 53 modulo 60:   1/24 ( q^3-20*q^2+131*q-280 )
        q congruent 59 modulo 60:   1/24 ( q^3-20*q^2+137*q-442 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 69, 5, 5, 67, 5, 67, 67, 2, 7, 69, 69, 5, 69, 5, 5, 67, 82, 31, 31, 
  78, 31, 78, 78, 9 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 14 ], [ 4, 1, 2, 18 ], 
  [ 5, 1, 2, 24 ], [ 6, 1, 2, 32 ], [ 7, 1, 2, 12 ], [ 8, 1, 2, 4 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 12 ], [ 12, 1, 2, 18 ], 
  [ 13, 1, 4, 24 ], [ 14, 1, 2, 12 ], [ 15, 1, 2, 36 ], [ 16, 1, 3, 48 ], 
  [ 17, 1, 4, 72 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 24 ], [ 20, 1, 4, 24 ], 
  [ 22, 1, 4, 4 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 3, 12 ], 
  [ 28, 1, 4, 12 ], [ 30, 1, 3, 24 ], [ 31, 1, 4, 12 ], [ 32, 1, 3, 48 ], 
  [ 33, 1, 8, 48 ], [ 35, 1, 8, 24 ], [ 40, 1, 6, 12 ] ]

    k = 9: F-action on Pi is (1,3)(5,7)      [47,1,9]
      Dynkin type is ^2A_2(q) + A_1(q) + A_1(q^2) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q^2-7*q+12 )
        q congruent 2 modulo 60:   1/8 ( q^3-6*q^2+4*q+8 )
        q congruent 3 modulo 60:   1/8 ( q^3-8*q^2+21*q-18 )
        q congruent 4 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/8 q ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/8 ( q^3-8*q^2+21*q-18 )
        q congruent 8 modulo 60:   1/8 ( q^3-6*q^2+4*q+8 )
        q congruent 9 modulo 60:   1/8 phi1 ( q^2-7*q+12 )
        q congruent 11 modulo 60:   1/8 ( q^3-8*q^2+17*q-6 )
        q congruent 13 modulo 60:   1/8 phi1 ( q^2-7*q+12 )
        q congruent 16 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/8 q ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/8 ( q^3-8*q^2+21*q-18 )
        q congruent 21 modulo 60:   1/8 phi1 ( q^2-7*q+12 )
        q congruent 23 modulo 60:   1/8 ( q^3-8*q^2+17*q-6 )
        q congruent 25 modulo 60:   1/8 phi1 ( q^2-7*q+12 )
        q congruent 27 modulo 60:   1/8 ( q^3-8*q^2+21*q-18 )
        q congruent 29 modulo 60:   1/8 q ( q^2-8*q+15 )
        q congruent 31 modulo 60:   1/8 ( q^3-8*q^2+21*q-18 )
        q congruent 32 modulo 60:   1/8 ( q^3-6*q^2+4*q+8 )
        q congruent 37 modulo 60:   1/8 phi1 ( q^2-7*q+12 )
        q congruent 41 modulo 60:   1/8 q ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/8 ( q^3-8*q^2+21*q-18 )
        q congruent 47 modulo 60:   1/8 ( q^3-8*q^2+17*q-6 )
        q congruent 49 modulo 60:   1/8 phi1 ( q^2-7*q+12 )
        q congruent 53 modulo 60:   1/8 q ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/8 ( q^3-8*q^2+17*q-6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 72, 69, 20, 68, 19, 7, 76, 28, 96, 82, 60 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 2 ], 
  [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 1, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 2 ], 
  [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 16, 1, 2, 8 ], [ 16, 1, 3, 4 ], 
  [ 16, 1, 4, 4 ], [ 17, 1, 3, 8 ], [ 20, 1, 3, 8 ], [ 22, 1, 3, 4 ], 
  [ 23, 1, 1, 2 ], [ 24, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 28, 1, 1, 4 ], 
  [ 31, 1, 3, 4 ], [ 32, 1, 2, 8 ], [ 33, 1, 6, 8 ], [ 35, 1, 5, 8 ], 
  [ 40, 1, 2, 4 ] ]

    k = 10: F-action on Pi is (1,3)(5,7)      [47,1,10]
      Dynkin type is ^2A_2(q) + A_1(q) + A_1(q^2) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 2 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/8 ( q^3-6*q^2+13*q-12 )
        q congruent 4 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 5 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 7 modulo 60:   1/8 ( q^3-6*q^2+13*q-12 )
        q congruent 8 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 11 modulo 60:   1/8 ( q^3-6*q^2+13*q-12 )
        q congruent 13 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 16 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 17 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 19 modulo 60:   1/8 ( q^3-6*q^2+13*q-12 )
        q congruent 21 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 23 modulo 60:   1/8 ( q^3-6*q^2+13*q-12 )
        q congruent 25 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 27 modulo 60:   1/8 ( q^3-6*q^2+13*q-12 )
        q congruent 29 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 31 modulo 60:   1/8 ( q^3-6*q^2+13*q-12 )
        q congruent 32 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 41 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 43 modulo 60:   1/8 ( q^3-6*q^2+13*q-12 )
        q congruent 47 modulo 60:   1/8 ( q^3-6*q^2+13*q-12 )
        q congruent 49 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 53 modulo 60:   1/8 phi1 ( q^2-5*q+6 )
        q congruent 59 modulo 60:   1/8 ( q^3-6*q^2+13*q-12 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 69, 20, 5, 71, 7, 76, 69, 20, 82, 60, 31, 98 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], 
  [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], 
  [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 12, 1, 2, 2 ], 
  [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 4 ], [ 15, 1, 2, 4 ], 
  [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], [ 18, 1, 2, 4 ], [ 20, 1, 4, 8 ], 
  [ 22, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], 
  [ 28, 1, 2, 4 ], [ 30, 1, 4, 8 ], [ 31, 1, 4, 4 ], [ 33, 1, 6, 8 ], 
  [ 35, 1, 7, 8 ], [ 40, 1, 2, 4 ] ]

    k = 11: F-action on Pi is (1,3)(2,5,7)      [47,1,11]
      Dynkin type is ^2A_2(q) + A_1(q^3) + T(phi1 phi6)
      Order of center |Z^F|: phi1 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 2 modulo 60:   1/12 phi2 ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 4 modulo 60:   1/12 q phi1 ( q-2 )
        q congruent 5 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 7 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 8 modulo 60:   1/12 phi2 ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 11 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 13 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 16 modulo 60:   1/12 q phi1 ( q-2 )
        q congruent 17 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 19 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 21 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 23 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 25 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 27 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 29 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 31 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 32 modulo 60:   1/12 phi2 ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 41 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 43 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 47 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 49 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 53 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 59 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 35, 84, 87, 38, 33, 80 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], 
  [ 10, 1, 1, 2 ], [ 22, 1, 3, 4 ], [ 33, 1, 7, 6 ], [ 40, 1, 4, 6 ] ]

    k = 12: F-action on Pi is (1,3)(2,5,7)      [47,1,12]
      Dynkin type is ^2A_2(q) + A_1(q^3) + T(phi2 phi6)
      Order of center |Z^F|: phi2 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q phi1^2
        q congruent 2 modulo 60:   1/12 q phi2 ( q-2 )
        q congruent 3 modulo 60:   1/12 q phi1^2
        q congruent 4 modulo 60:   1/12 q^2 phi1
        q congruent 5 modulo 60:   1/12 phi1 phi2 ( q-2 )
        q congruent 7 modulo 60:   1/12 q phi1^2
        q congruent 8 modulo 60:   1/12 q phi2 ( q-2 )
        q congruent 9 modulo 60:   1/12 q phi1^2
        q congruent 11 modulo 60:   1/12 phi1 phi2 ( q-2 )
        q congruent 13 modulo 60:   1/12 q phi1^2
        q congruent 16 modulo 60:   1/12 q^2 phi1
        q congruent 17 modulo 60:   1/12 phi1 phi2 ( q-2 )
        q congruent 19 modulo 60:   1/12 q phi1^2
        q congruent 21 modulo 60:   1/12 q phi1^2
        q congruent 23 modulo 60:   1/12 phi1 phi2 ( q-2 )
        q congruent 25 modulo 60:   1/12 q phi1^2
        q congruent 27 modulo 60:   1/12 q phi1^2
        q congruent 29 modulo 60:   1/12 phi1 phi2 ( q-2 )
        q congruent 31 modulo 60:   1/12 q phi1^2
        q congruent 32 modulo 60:   1/12 q phi2 ( q-2 )
        q congruent 37 modulo 60:   1/12 q phi1^2
        q congruent 41 modulo 60:   1/12 phi1 phi2 ( q-2 )
        q congruent 43 modulo 60:   1/12 q phi1^2
        q congruent 47 modulo 60:   1/12 phi1 phi2 ( q-2 )
        q congruent 49 modulo 60:   1/12 q phi1^2
        q congruent 53 modulo 60:   1/12 phi1 phi2 ( q-2 )
        q congruent 59 modulo 60:   1/12 phi1 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 88, 15, 40, 84, 86, 13 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], 
  [ 8, 1, 2, 4 ], [ 10, 1, 2, 2 ], [ 22, 1, 4, 4 ], [ 33, 1, 7, 6 ], 
  [ 40, 1, 4, 6 ] ]

i = 48: Pi = [ 1, 2, 4, 5, 7 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [48,1,1]
      Dynkin type is A_3(q) + A_1(q) + A_1(q) + T(phi1^3)
      Order of center |Z^F|: phi1^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 ( q^3-23*q^2+179*q-541 )
        q congruent 2 modulo 60:   1/16 ( q^3-20*q^2+116*q-160 )
        q congruent 3 modulo 60:   1/16 ( q^3-23*q^2+163*q-309 )
        q congruent 4 modulo 60:   1/16 ( q^3-20*q^2+124*q-240 )
        q congruent 5 modulo 60:   1/16 ( q^3-23*q^2+171*q-405 )
        q congruent 7 modulo 60:   1/16 ( q^3-23*q^2+171*q-413 )
        q congruent 8 modulo 60:   1/16 ( q^3-20*q^2+116*q-160 )
        q congruent 9 modulo 60:   1/16 ( q^3-23*q^2+171*q-405 )
        q congruent 11 modulo 60:   1/16 ( q^3-23*q^2+163*q-341 )
        q congruent 13 modulo 60:   1/16 ( q^3-23*q^2+179*q-509 )
        q congruent 16 modulo 60:   1/16 ( q^3-20*q^2+124*q-272 )
        q congruent 17 modulo 60:   1/16 ( q^3-23*q^2+171*q-405 )
        q congruent 19 modulo 60:   1/16 ( q^3-23*q^2+171*q-413 )
        q congruent 21 modulo 60:   1/16 ( q^3-23*q^2+171*q-437 )
        q congruent 23 modulo 60:   1/16 ( q^3-23*q^2+163*q-309 )
        q congruent 25 modulo 60:   1/16 ( q^3-23*q^2+179*q-509 )
        q congruent 27 modulo 60:   1/16 ( q^3-23*q^2+163*q-309 )
        q congruent 29 modulo 60:   1/16 ( q^3-23*q^2+171*q-405 )
        q congruent 31 modulo 60:   1/16 ( q^3-23*q^2+171*q-445 )
        q congruent 32 modulo 60:   1/16 ( q^3-20*q^2+116*q-160 )
        q congruent 37 modulo 60:   1/16 ( q^3-23*q^2+179*q-509 )
        q congruent 41 modulo 60:   1/16 ( q^3-23*q^2+171*q-437 )
        q congruent 43 modulo 60:   1/16 ( q^3-23*q^2+171*q-413 )
        q congruent 47 modulo 60:   1/16 ( q^3-23*q^2+163*q-309 )
        q congruent 49 modulo 60:   1/16 ( q^3-23*q^2+179*q-509 )
        q congruent 53 modulo 60:   1/16 ( q^3-23*q^2+171*q-405 )
        q congruent 59 modulo 60:   1/16 ( q^3-23*q^2+163*q-309 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 66, 4, 4, 68, 4, 68, 68, 7, 8, 77, 77, 30, 70, 19, 
  19, 76 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 10 ], 
  [ 5, 1, 1, 16 ], [ 6, 1, 1, 16 ], [ 7, 1, 1, 8 ], [ 8, 1, 1, 8 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 8 ], 
  [ 13, 1, 1, 16 ], [ 14, 1, 1, 16 ], [ 15, 1, 1, 16 ], [ 16, 1, 1, 16 ], 
  [ 18, 1, 1, 16 ], [ 19, 1, 1, 16 ], [ 20, 1, 1, 16 ], [ 21, 1, 1, 8 ], 
  [ 22, 1, 1, 16 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 12 ], [ 25, 1, 1, 12 ], 
  [ 28, 1, 1, 8 ], [ 30, 1, 1, 16 ], [ 31, 1, 1, 16 ], [ 34, 1, 1, 16 ], 
  [ 35, 1, 1, 16 ], [ 37, 1, 1, 16 ], [ 39, 1, 1, 8 ], [ 41, 1, 1, 16 ] ]

    k = 2: F-action on Pi is ()      [48,1,2]
      Dynkin type is A_3(q) + A_1(q) + A_1(q) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q^2-10*q+29 )
        q congruent 2 modulo 60:   1/8 q ( q^2-8*q+12 )
        q congruent 3 modulo 60:   1/8 phi1 ( q^2-10*q+21 )
        q congruent 4 modulo 60:   1/8 q ( q^2-8*q+16 )
        q congruent 5 modulo 60:   1/8 phi1 ( q^2-10*q+25 )
        q congruent 7 modulo 60:   1/8 phi1 ( q^2-10*q+25 )
        q congruent 8 modulo 60:   1/8 q ( q^2-8*q+12 )
        q congruent 9 modulo 60:   1/8 phi1 ( q^2-10*q+25 )
        q congruent 11 modulo 60:   1/8 phi1 ( q^2-10*q+21 )
        q congruent 13 modulo 60:   1/8 phi1 ( q^2-10*q+29 )
        q congruent 16 modulo 60:   1/8 q ( q^2-8*q+16 )
        q congruent 17 modulo 60:   1/8 phi1 ( q^2-10*q+25 )
        q congruent 19 modulo 60:   1/8 phi1 ( q^2-10*q+25 )
        q congruent 21 modulo 60:   1/8 phi1 ( q^2-10*q+25 )
        q congruent 23 modulo 60:   1/8 phi1 ( q^2-10*q+21 )
        q congruent 25 modulo 60:   1/8 phi1 ( q^2-10*q+29 )
        q congruent 27 modulo 60:   1/8 phi1 ( q^2-10*q+21 )
        q congruent 29 modulo 60:   1/8 phi1 ( q^2-10*q+25 )
        q congruent 31 modulo 60:   1/8 phi1 ( q^2-10*q+25 )
        q congruent 32 modulo 60:   1/8 q ( q^2-8*q+12 )
        q congruent 37 modulo 60:   1/8 phi1 ( q^2-10*q+29 )
        q congruent 41 modulo 60:   1/8 phi1 ( q^2-10*q+25 )
        q congruent 43 modulo 60:   1/8 phi1 ( q^2-10*q+25 )
        q congruent 47 modulo 60:   1/8 phi1 ( q^2-10*q+21 )
        q congruent 49 modulo 60:   1/8 phi1 ( q^2-10*q+29 )
        q congruent 53 modulo 60:   1/8 phi1 ( q^2-10*q+25 )
        q congruent 59 modulo 60:   1/8 phi1 ( q^2-10*q+21 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 4, 68, 4, 68, 68, 7, 68, 3, 7, 69, 77, 30, 30, 81, 19, 72, 
  76, 20 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 6 ], 
  [ 6, 1, 1, 8 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 13, 1, 1, 8 ], 
  [ 16, 1, 1, 8 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 8 ], 
  [ 22, 1, 2, 8 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], 
  [ 25, 1, 1, 4 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 4 ], [ 31, 1, 2, 8 ], 
  [ 34, 1, 2, 8 ], [ 35, 1, 1, 8 ], [ 35, 1, 3, 8 ], [ 39, 1, 4, 4 ], 
  [ 41, 1, 6, 8 ] ]

    k = 3: F-action on Pi is ()      [48,1,3]
      Dynkin type is A_3(q) + A_1(q) + A_1(q) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 2 modulo 60:   1/16 q ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 4 modulo 60:   1/16 q ( q^2-4*q+4 )
        q congruent 5 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 7 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 8 modulo 60:   1/16 q ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 11 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 13 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 16 modulo 60:   1/16 q ( q^2-4*q+4 )
        q congruent 17 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 19 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 21 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 23 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 25 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 27 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 31 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 32 modulo 60:   1/16 q ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 41 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 43 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 47 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 49 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 53 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 59 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 68, 68, 3, 68, 7, 7, 69, 7, 69, 69, 5, 30, 81, 81, 27, 76, 20, 
  20, 71 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 4 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 4, 8 ], 
  [ 20, 1, 2, 16 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 12 ], 
  [ 25, 1, 1, 4 ], [ 25, 1, 3, 8 ], [ 28, 1, 2, 8 ], [ 35, 1, 3, 16 ], 
  [ 37, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 41, 1, 9, 16 ] ]

    k = 4: F-action on Pi is (2,5)      [48,1,4]
      Dynkin type is ^2A_3(q) + A_1(q) + A_1(q) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 2 modulo 60:   1/16 q ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 4 modulo 60:   1/16 q ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 8 modulo 60:   1/16 q ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 13 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 16 modulo 60:   1/16 q ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 21 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 23 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 25 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 27 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 29 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 31 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 32 modulo 60:   1/16 q ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 41 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 47 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 49 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 53 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 69, 69, 5, 68, 7, 7, 69, 4, 68, 68, 7, 28, 82, 82, 31, 70, 19, 
  19, 76 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 6 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 4, 8 ], 
  [ 20, 1, 3, 16 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 12 ], 
  [ 25, 1, 1, 8 ], [ 25, 1, 3, 4 ], [ 28, 1, 3, 8 ], [ 35, 1, 6, 16 ], 
  [ 37, 1, 2, 8 ], [ 39, 1, 1, 8 ], [ 41, 1, 1, 16 ] ]

    k = 5: F-action on Pi is (2,5)      [48,1,5]
      Dynkin type is ^2A_3(q) + A_1(q) + A_1(q) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q^2-8*q+15 )
        q congruent 2 modulo 60:   1/8 ( q^3-6*q^2+12*q-8 )
        q congruent 3 modulo 60:   1/8 ( q^3-9*q^2+27*q-27 )
        q congruent 4 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/8 ( q^3-9*q^2+27*q-27 )
        q congruent 7 modulo 60:   1/8 ( q^3-9*q^2+27*q-27 )
        q congruent 8 modulo 60:   1/8 ( q^3-6*q^2+12*q-8 )
        q congruent 9 modulo 60:   1/8 phi1 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/8 ( q^3-9*q^2+31*q-39 )
        q congruent 13 modulo 60:   1/8 phi1 ( q^2-8*q+15 )
        q congruent 16 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/8 ( q^3-9*q^2+27*q-27 )
        q congruent 19 modulo 60:   1/8 ( q^3-9*q^2+27*q-27 )
        q congruent 21 modulo 60:   1/8 phi1 ( q^2-8*q+15 )
        q congruent 23 modulo 60:   1/8 ( q^3-9*q^2+31*q-39 )
        q congruent 25 modulo 60:   1/8 phi1 ( q^2-8*q+15 )
        q congruent 27 modulo 60:   1/8 ( q^3-9*q^2+27*q-27 )
        q congruent 29 modulo 60:   1/8 ( q^3-9*q^2+27*q-27 )
        q congruent 31 modulo 60:   1/8 ( q^3-9*q^2+27*q-27 )
        q congruent 32 modulo 60:   1/8 ( q^3-6*q^2+12*q-8 )
        q congruent 37 modulo 60:   1/8 phi1 ( q^2-8*q+15 )
        q congruent 41 modulo 60:   1/8 ( q^3-9*q^2+27*q-27 )
        q congruent 43 modulo 60:   1/8 ( q^3-9*q^2+27*q-27 )
        q congruent 47 modulo 60:   1/8 ( q^3-9*q^2+31*q-39 )
        q congruent 49 modulo 60:   1/8 phi1 ( q^2-8*q+15 )
        q congruent 53 modulo 60:   1/8 ( q^3-9*q^2+27*q-27 )
        q congruent 59 modulo 60:   1/8 ( q^3-9*q^2+31*q-39 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 69, 5, 5, 67, 7, 69, 69, 5, 68, 3, 7, 69, 82, 31, 31, 78, 19, 72, 
  76, 20 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 6 ], 
  [ 6, 1, 2, 8 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 4, 8 ], 
  [ 16, 1, 3, 8 ], [ 19, 1, 2, 8 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 8 ], 
  [ 22, 1, 3, 8 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], 
  [ 25, 1, 3, 4 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], [ 31, 1, 3, 8 ], 
  [ 34, 1, 3, 8 ], [ 35, 1, 6, 8 ], [ 35, 1, 8, 8 ], [ 39, 1, 4, 4 ], 
  [ 41, 1, 6, 8 ] ]

    k = 6: F-action on Pi is (2,5)      [48,1,6]
      Dynkin type is ^2A_3(q) + A_1(q) + A_1(q) + T(phi2^3)
      Order of center |Z^F|: phi2^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q^2-16*q+67 )
        q congruent 2 modulo 60:   1/16 ( q^3-14*q^2+56*q-64 )
        q congruent 3 modulo 60:   1/16 ( q^3-17*q^2+91*q-147 )
        q congruent 4 modulo 60:   1/16 ( q^3-14*q^2+48*q-32 )
        q congruent 5 modulo 60:   1/16 ( q^3-17*q^2+91*q-155 )
        q congruent 7 modulo 60:   1/16 ( q^3-17*q^2+91*q-147 )
        q congruent 8 modulo 60:   1/16 ( q^3-14*q^2+56*q-64 )
        q congruent 9 modulo 60:   1/16 ( q^3-17*q^2+83*q-99 )
        q congruent 11 modulo 60:   1/16 ( q^3-17*q^2+99*q-235 )
        q congruent 13 modulo 60:   1/16 phi1 ( q^2-16*q+67 )
        q congruent 16 modulo 60:   1/16 q ( q^2-14*q+48 )
        q congruent 17 modulo 60:   1/16 ( q^3-17*q^2+91*q-155 )
        q congruent 19 modulo 60:   1/16 ( q^3-17*q^2+91*q-179 )
        q congruent 21 modulo 60:   1/16 phi1 ( q^2-16*q+67 )
        q congruent 23 modulo 60:   1/16 ( q^3-17*q^2+99*q-235 )
        q congruent 25 modulo 60:   1/16 phi1 ( q^2-16*q+67 )
        q congruent 27 modulo 60:   1/16 ( q^3-17*q^2+91*q-147 )
        q congruent 29 modulo 60:   1/16 ( q^3-17*q^2+91*q-187 )
        q congruent 31 modulo 60:   1/16 ( q^3-17*q^2+91*q-147 )
        q congruent 32 modulo 60:   1/16 ( q^3-14*q^2+56*q-64 )
        q congruent 37 modulo 60:   1/16 phi1 ( q^2-16*q+67 )
        q congruent 41 modulo 60:   1/16 ( q^3-17*q^2+91*q-155 )
        q congruent 43 modulo 60:   1/16 ( q^3-17*q^2+91*q-147 )
        q congruent 47 modulo 60:   1/16 ( q^3-17*q^2+99*q-235 )
        q congruent 49 modulo 60:   1/16 ( q^3-17*q^2+83*q-99 )
        q congruent 53 modulo 60:   1/16 ( q^3-17*q^2+91*q-155 )
        q congruent 59 modulo 60:   1/16 ( q^3-17*q^2+99*q-267 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 67, 67, 2, 69, 5, 5, 67, 7, 69, 69, 5, 31, 78, 78, 9, 76, 20, 
  20, 71 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 10 ], 
  [ 5, 1, 2, 16 ], [ 6, 1, 2, 16 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 8 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 2, 4 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 8 ], 
  [ 13, 1, 4, 16 ], [ 14, 1, 2, 16 ], [ 15, 1, 2, 16 ], [ 16, 1, 3, 16 ], 
  [ 18, 1, 2, 16 ], [ 19, 1, 2, 16 ], [ 20, 1, 4, 16 ], [ 21, 1, 2, 8 ], 
  [ 22, 1, 4, 16 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 3, 12 ], 
  [ 28, 1, 4, 8 ], [ 30, 1, 3, 16 ], [ 31, 1, 4, 16 ], [ 34, 1, 4, 16 ], 
  [ 35, 1, 8, 16 ], [ 37, 1, 3, 16 ], [ 39, 1, 3, 8 ], [ 41, 1, 9, 16 ] ]

    k = 7: F-action on Pi is (1,7)      [48,1,7]
      Dynkin type is A_3(q) + A_1(q^2) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 2 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 4 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 7 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 8 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 11 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 13 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 16 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 19 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 21 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 23 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 25 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 27 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 29 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 31 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 32 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 41 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 43 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 47 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 49 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 53 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 59 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 70, 68, 19, 7, 76, 30, 97, 76, 22 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 5, 1, 1, 8 ], 
  [ 8, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], 
  [ 14, 1, 1, 8 ], [ 21, 1, 1, 4 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 2 ], 
  [ 25, 1, 1, 8 ], [ 25, 1, 3, 4 ], [ 30, 1, 2, 8 ], [ 37, 1, 1, 8 ], 
  [ 37, 1, 2, 4 ], [ 39, 1, 2, 4 ], [ 41, 1, 2, 8 ] ]

    k = 8: F-action on Pi is (1,7)      [48,1,8]
      Dynkin type is A_3(q) + A_1(q^2) + T(phi1 phi4)
      Order of center |Z^F|: phi1 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 2 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 3 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 4 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 5 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 7 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 8 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 9 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 11 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 16 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 17 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 19 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 23 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 27 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 31 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 32 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 37 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 41 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 43 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 53 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 59 modulo 60:   1/8 phi1 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 70, 16, 19, 73, 76, 18, 97, 53, 22, 75 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 3 ], [ 23, 1, 1, 2 ], 
  [ 25, 1, 1, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 5, 8 ] ]

    k = 9: F-action on Pi is (1,7)(2,5)      [48,1,9]
      Dynkin type is ^2A_3(q) + A_1(q^2) + T(phi2 phi4)
      Order of center |Z^F|: phi2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1^2 phi2
        q congruent 2 modulo 60:   1/8 q^3
        q congruent 3 modulo 60:   1/8 phi1^2 phi2
        q congruent 4 modulo 60:   1/8 q^3
        q congruent 5 modulo 60:   1/8 phi1^2 phi2
        q congruent 7 modulo 60:   1/8 phi1^2 phi2
        q congruent 8 modulo 60:   1/8 q^3
        q congruent 9 modulo 60:   1/8 phi1^2 phi2
        q congruent 11 modulo 60:   1/8 phi1^2 phi2
        q congruent 13 modulo 60:   1/8 phi1^2 phi2
        q congruent 16 modulo 60:   1/8 q^3
        q congruent 17 modulo 60:   1/8 phi1^2 phi2
        q congruent 19 modulo 60:   1/8 phi1^2 phi2
        q congruent 21 modulo 60:   1/8 phi1^2 phi2
        q congruent 23 modulo 60:   1/8 phi1^2 phi2
        q congruent 25 modulo 60:   1/8 phi1^2 phi2
        q congruent 27 modulo 60:   1/8 phi1^2 phi2
        q congruent 29 modulo 60:   1/8 phi1^2 phi2
        q congruent 31 modulo 60:   1/8 phi1^2 phi2
        q congruent 32 modulo 60:   1/8 q^3
        q congruent 37 modulo 60:   1/8 phi1^2 phi2
        q congruent 41 modulo 60:   1/8 phi1^2 phi2
        q congruent 43 modulo 60:   1/8 phi1^2 phi2
        q congruent 47 modulo 60:   1/8 phi1^2 phi2
        q congruent 49 modulo 60:   1/8 phi1^2 phi2
        q congruent 53 modulo 60:   1/8 phi1^2 phi2
        q congruent 59 modulo 60:   1/8 phi1^2 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 71, 17, 20, 74, 76, 18, 98, 54, 22, 75 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 3 ], [ 23, 1, 2, 2 ], 
  [ 25, 1, 3, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 5, 8 ] ]

    k = 10: F-action on Pi is (1,7)(2,5)      [48,1,10]
      Dynkin type is ^2A_3(q) + A_1(q^2) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 2 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 4 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 5 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 7 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 8 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 11 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 13 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 16 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 17 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 19 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 21 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 23 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 25 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 27 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 29 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 31 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 32 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 41 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 43 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 47 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 49 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 53 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 59 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 71, 69, 20, 7, 76, 31, 98, 76, 22 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], 
  [ 8, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], 
  [ 14, 1, 2, 8 ], [ 21, 1, 2, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 4 ], 
  [ 25, 1, 1, 4 ], [ 25, 1, 3, 8 ], [ 30, 1, 4, 8 ], [ 37, 1, 2, 4 ], 
  [ 37, 1, 3, 8 ], [ 39, 1, 2, 4 ], [ 41, 1, 2, 8 ] ]

i = 49: Pi = [ 1, 2, 5, 7, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [49,1,1]
      Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^3)
      Order of center |Z^F|: phi1^3 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/192 ( q^3-25*q^2+199*q-559 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/192 ( q^3-25*q^2+187*q-363 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/192 ( q^3-25*q^2+199*q-495 )
        q congruent 7 modulo 60:   1/192 ( q^3-25*q^2+187*q-427 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/192 ( q^3-25*q^2+199*q-495 )
        q congruent 11 modulo 60:   1/192 ( q^3-25*q^2+187*q-363 )
        q congruent 13 modulo 60:   1/192 ( q^3-25*q^2+199*q-559 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/192 ( q^3-25*q^2+199*q-495 )
        q congruent 19 modulo 60:   1/192 ( q^3-25*q^2+187*q-427 )
        q congruent 21 modulo 60:   1/192 ( q^3-25*q^2+199*q-495 )
        q congruent 23 modulo 60:   1/192 ( q^3-25*q^2+187*q-363 )
        q congruent 25 modulo 60:   1/192 ( q^3-25*q^2+199*q-559 )
        q congruent 27 modulo 60:   1/192 ( q^3-25*q^2+187*q-363 )
        q congruent 29 modulo 60:   1/192 ( q^3-25*q^2+199*q-495 )
        q congruent 31 modulo 60:   1/192 ( q^3-25*q^2+187*q-427 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/192 ( q^3-25*q^2+199*q-559 )
        q congruent 41 modulo 60:   1/192 ( q^3-25*q^2+199*q-495 )
        q congruent 43 modulo 60:   1/192 ( q^3-25*q^2+187*q-427 )
        q congruent 47 modulo 60:   1/192 ( q^3-25*q^2+187*q-363 )
        q congruent 49 modulo 60:   1/192 ( q^3-25*q^2+199*q-559 )
        q congruent 53 modulo 60:   1/192 ( q^3-25*q^2+199*q-495 )
        q congruent 59 modulo 60:   1/192 ( q^3-25*q^2+187*q-363 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 66, 4, 4, 68, 66, 4, 4, 68, 4, 68, 68, 3, 66, 4, 4, 
  68, 4, 68, 68, 7, 4, 68, 68, 7, 68, 7, 7, 69 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 36 ], 
  [ 6, 1, 1, 32 ], [ 7, 1, 1, 8 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 6 ], 
  [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 72 ], [ 16, 1, 1, 96 ], 
  [ 19, 1, 1, 32 ], [ 20, 1, 1, 48 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 42 ], 
  [ 25, 1, 1, 72 ], [ 28, 1, 1, 24 ], [ 33, 1, 1, 192 ], [ 35, 1, 1, 96 ], 
  [ 39, 1, 1, 24 ], [ 40, 1, 1, 48 ], [ 41, 1, 1, 144 ], [ 52, 1, 1, 48 ] ]

    k = 2: F-action on Pi is (  7,240)      [49,1,2]
      Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q^2) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 13 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 21 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 23 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 25 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 27 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 29 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 31 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 41 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 47 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 49 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 53 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 70, 68, 19, 68, 19, 3, 72, 68, 19, 7, 76, 7, 76, 69, 20 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 6 ], 
  [ 4, 1, 2, 6 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 3 ], 
  [ 10, 1, 1, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 13, 1, 1, 8 ], 
  [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 8 ], [ 16, 1, 1, 8 ], 
  [ 16, 1, 2, 8 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 8 ], [ 20, 1, 3, 8 ], 
  [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 6 ], [ 25, 1, 1, 4 ], 
  [ 25, 1, 2, 8 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 28, 1, 1, 4 ], 
  [ 28, 1, 3, 4 ], [ 33, 1, 2, 16 ], [ 35, 1, 1, 8 ], [ 35, 1, 2, 8 ], 
  [ 35, 1, 5, 8 ], [ 35, 1, 6, 8 ], [ 39, 1, 2, 4 ], [ 40, 1, 3, 8 ], 
  [ 41, 1, 2, 8 ], [ 41, 1, 4, 16 ], [ 52, 1, 3, 8 ] ]

    k = 3: F-action on Pi is (  5,  7,240)      [49,1,3]
      Dynkin type is A_1(q) + A_1(q) + A_1(q^3) + T(phi1 phi3)
      Order of center |Z^F|: phi1 phi3 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 7 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 11 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 13 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 19 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 21 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 23 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 25 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 27 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 29 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 31 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 41 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 43 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 47 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 49 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 53 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 59 modulo 60:   1/6 q phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 14, 87, 83, 35, 83, 40, 37, 88 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], 
  [ 7, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 11, 1, 1, 2 ], [ 19, 1, 1, 2 ], 
  [ 33, 1, 3, 6 ], [ 40, 1, 5, 6 ], [ 52, 1, 6, 6 ] ]

    k = 4: F-action on Pi is (  5,240)      [49,1,4]
      Dynkin type is A_1(q) + A_1(q) + A_1(q^2) + A_1(q) + T(phi2 phi4)
      Order of center |Z^F|: phi2 phi4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^2 phi2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 phi1^2 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1^2 phi2
        q congruent 7 modulo 60:   1/16 phi1^2 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1^2 phi2
        q congruent 11 modulo 60:   1/16 phi1^2 phi2
        q congruent 13 modulo 60:   1/16 phi1^2 phi2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1^2 phi2
        q congruent 19 modulo 60:   1/16 phi1^2 phi2
        q congruent 21 modulo 60:   1/16 phi1^2 phi2
        q congruent 23 modulo 60:   1/16 phi1^2 phi2
        q congruent 25 modulo 60:   1/16 phi1^2 phi2
        q congruent 27 modulo 60:   1/16 phi1^2 phi2
        q congruent 29 modulo 60:   1/16 phi1^2 phi2
        q congruent 31 modulo 60:   1/16 phi1^2 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1^2 phi2
        q congruent 41 modulo 60:   1/16 phi1^2 phi2
        q congruent 43 modulo 60:   1/16 phi1^2 phi2
        q congruent 47 modulo 60:   1/16 phi1^2 phi2
        q congruent 49 modulo 60:   1/16 phi1^2 phi2
        q congruent 53 modulo 60:   1/16 phi1^2 phi2
        q congruent 59 modulo 60:   1/16 phi1^2 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 19, 76, 73, 18, 76, 20, 18, 74, 72, 20, 18, 74, 20, 71, 74, 17 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 2 ], 
  [ 24, 1, 2, 6 ], [ 39, 1, 5, 4 ], [ 41, 1, 5, 8 ], [ 41, 1, 8, 16 ], 
  [ 52, 1, 5, 8 ] ]

    k = 5: F-action on Pi is ()      [49,1,5]
      Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/64 phi1 ( q^2-8*q+15 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/64 ( q^3-9*q^2+27*q-27 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/64 phi1 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/64 ( q^3-9*q^2+27*q-27 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/64 phi1 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/64 ( q^3-9*q^2+27*q-27 )
        q congruent 13 modulo 60:   1/64 phi1 ( q^2-8*q+15 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/64 phi1 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/64 ( q^3-9*q^2+27*q-27 )
        q congruent 21 modulo 60:   1/64 phi1 ( q^2-8*q+15 )
        q congruent 23 modulo 60:   1/64 ( q^3-9*q^2+27*q-27 )
        q congruent 25 modulo 60:   1/64 phi1 ( q^2-8*q+15 )
        q congruent 27 modulo 60:   1/64 ( q^3-9*q^2+27*q-27 )
        q congruent 29 modulo 60:   1/64 phi1 ( q^2-8*q+15 )
        q congruent 31 modulo 60:   1/64 ( q^3-9*q^2+27*q-27 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/64 phi1 ( q^2-8*q+15 )
        q congruent 41 modulo 60:   1/64 phi1 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/64 ( q^3-9*q^2+27*q-27 )
        q congruent 47 modulo 60:   1/64 ( q^3-9*q^2+27*q-27 )
        q congruent 49 modulo 60:   1/64 phi1 ( q^2-8*q+15 )
        q congruent 53 modulo 60:   1/64 phi1 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/64 ( q^3-9*q^2+27*q-27 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 68, 68, 3, 68, 7, 7, 69, 68, 7, 7, 69, 3, 69, 69, 5, 68, 7, 7, 
  69, 7, 69, 69, 5, 7, 69, 69, 5, 69, 5, 5, 67 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 4, 1, 2, 12 ], [ 9, 1, 1, 7 ], 
  [ 10, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 13, 1, 4, 24 ], [ 20, 1, 3, 16 ], 
  [ 23, 1, 2, 4 ], [ 24, 1, 1, 14 ], [ 24, 1, 2, 28 ], [ 25, 1, 3, 24 ], 
  [ 28, 1, 3, 8 ], [ 35, 1, 6, 32 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 8 ], 
  [ 41, 1, 6, 48 ], [ 41, 1, 9, 48 ], [ 52, 1, 9, 16 ] ]

    k = 6: F-action on Pi is (  5,240,  7)      [49,1,6]
      Dynkin type is A_1(q) + A_1(q) + A_1(q^3) + T(phi2 phi6)
      Order of center |Z^F|: phi2 phi6 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/6 q^2 phi1
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/6 q^2 phi1
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 7 modulo 60:   1/6 q^2 phi1
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/6 q^2 phi1
        q congruent 11 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 13 modulo 60:   1/6 q^2 phi1
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 19 modulo 60:   1/6 q^2 phi1
        q congruent 21 modulo 60:   1/6 q^2 phi1
        q congruent 23 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 25 modulo 60:   1/6 q^2 phi1
        q congruent 27 modulo 60:   1/6 q^2 phi1
        q congruent 29 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 31 modulo 60:   1/6 q^2 phi1
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/6 q^2 phi1
        q congruent 41 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 43 modulo 60:   1/6 q^2 phi1
        q congruent 47 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 49 modulo 60:   1/6 q^2 phi1
        q congruent 53 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 59 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 87, 38, 40, 84, 35, 84, 88, 15 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], 
  [ 7, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 11, 1, 2, 2 ], [ 19, 1, 2, 2 ], 
  [ 33, 1, 7, 6 ], [ 40, 1, 4, 6 ], [ 52, 1, 7, 6 ] ]

    k = 7: F-action on Pi is (  5,240)      [49,1,7]
      Dynkin type is A_1(q) + A_1(q) + A_1(q^2) + A_1(q) + T(phi1 phi4)
      Order of center |Z^F|: phi1 phi4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 7 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 11 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 19 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 23 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 27 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 31 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 41 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 43 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 53 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 59 modulo 60:   1/16 phi1 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 70, 19, 16, 73, 19, 72, 73, 18, 19, 76, 73, 18, 76, 20, 18, 74 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], 
  [ 24, 1, 1, 6 ], [ 39, 1, 5, 4 ], [ 41, 1, 5, 8 ], [ 41, 1, 8, 16 ], 
  [ 52, 1, 8, 8 ] ]

    k = 8: F-action on Pi is (5,7)      [49,1,8]
      Dynkin type is A_1(q) + A_1(q) + A_1(q^2) + A_1(q) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 7 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 11 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 13 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 19 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 21 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 23 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 25 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 27 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 31 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 41 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 43 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 47 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 49 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 53 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 59 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 7, 19, 76, 7, 69, 76, 20, 3, 69, 72, 20, 69, 5, 20, 71 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 6 ], 
  [ 4, 1, 2, 6 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 3 ], 
  [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 1, 8 ], 
  [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 13, 1, 4, 8 ], [ 16, 1, 3, 8 ], 
  [ 16, 1, 4, 8 ], [ 19, 1, 2, 8 ], [ 20, 1, 2, 8 ], [ 20, 1, 4, 8 ], 
  [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 4 ], 
  [ 25, 1, 2, 8 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 28, 1, 2, 4 ], 
  [ 28, 1, 4, 4 ], [ 33, 1, 6, 16 ], [ 35, 1, 3, 8 ], [ 35, 1, 4, 8 ], 
  [ 35, 1, 7, 8 ], [ 35, 1, 8, 8 ], [ 39, 1, 2, 4 ], [ 40, 1, 2, 8 ], 
  [ 41, 1, 2, 8 ], [ 41, 1, 4, 16 ], [ 52, 1, 4, 8 ] ]

    k = 9: F-action on Pi is ()      [49,1,9]
      Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/64 phi1 ( q^2-10*q+25 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/64 phi1 ( q^2-10*q+21 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/64 phi1 ( q^2-10*q+25 )
        q congruent 7 modulo 60:   1/64 phi1 ( q^2-10*q+21 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/64 phi1 ( q^2-10*q+25 )
        q congruent 11 modulo 60:   1/64 phi1 ( q^2-10*q+21 )
        q congruent 13 modulo 60:   1/64 phi1 ( q^2-10*q+25 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/64 phi1 ( q^2-10*q+25 )
        q congruent 19 modulo 60:   1/64 phi1 ( q^2-10*q+21 )
        q congruent 21 modulo 60:   1/64 phi1 ( q^2-10*q+25 )
        q congruent 23 modulo 60:   1/64 phi1 ( q^2-10*q+21 )
        q congruent 25 modulo 60:   1/64 phi1 ( q^2-10*q+25 )
        q congruent 27 modulo 60:   1/64 phi1 ( q^2-10*q+21 )
        q congruent 29 modulo 60:   1/64 phi1 ( q^2-10*q+25 )
        q congruent 31 modulo 60:   1/64 phi1 ( q^2-10*q+21 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/64 phi1 ( q^2-10*q+25 )
        q congruent 41 modulo 60:   1/64 phi1 ( q^2-10*q+25 )
        q congruent 43 modulo 60:   1/64 phi1 ( q^2-10*q+21 )
        q congruent 47 modulo 60:   1/64 phi1 ( q^2-10*q+21 )
        q congruent 49 modulo 60:   1/64 phi1 ( q^2-10*q+25 )
        q congruent 53 modulo 60:   1/64 phi1 ( q^2-10*q+25 )
        q congruent 59 modulo 60:   1/64 phi1 ( q^2-10*q+21 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 4, 68, 4, 68, 68, 7, 4, 68, 68, 7, 68, 7, 7, 69, 4, 68, 68, 
  7, 68, 7, 3, 69, 68, 3, 7, 69, 7, 69, 69, 5 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 4, 1, 1, 12 ], [ 9, 1, 1, 7 ], 
  [ 10, 1, 1, 4 ], [ 10, 1, 2, 2 ], [ 13, 1, 1, 24 ], [ 20, 1, 2, 16 ], 
  [ 23, 1, 1, 4 ], [ 24, 1, 1, 28 ], [ 24, 1, 2, 14 ], [ 25, 1, 1, 24 ], 
  [ 28, 1, 2, 8 ], [ 35, 1, 3, 32 ], [ 39, 1, 1, 8 ], [ 39, 1, 4, 8 ], 
  [ 41, 1, 1, 48 ], [ 41, 1, 6, 48 ], [ 52, 1, 2, 16 ] ]

    k = 10: F-action on Pi is ()      [49,1,10]
      Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi2^3)
      Order of center |Z^F|: phi2^3 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/192 phi1 ( q^2-18*q+81 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/192 ( q^3-19*q^2+111*q-189 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/192 ( q^3-19*q^2+99*q-145 )
        q congruent 7 modulo 60:   1/192 ( q^3-19*q^2+111*q-189 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/192 phi1 ( q^2-18*q+81 )
        q congruent 11 modulo 60:   1/192 ( q^3-19*q^2+111*q-253 )
        q congruent 13 modulo 60:   1/192 phi1 ( q^2-18*q+81 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/192 ( q^3-19*q^2+99*q-145 )
        q congruent 19 modulo 60:   1/192 ( q^3-19*q^2+111*q-189 )
        q congruent 21 modulo 60:   1/192 phi1 ( q^2-18*q+81 )
        q congruent 23 modulo 60:   1/192 ( q^3-19*q^2+111*q-253 )
        q congruent 25 modulo 60:   1/192 phi1 ( q^2-18*q+81 )
        q congruent 27 modulo 60:   1/192 ( q^3-19*q^2+111*q-189 )
        q congruent 29 modulo 60:   1/192 ( q^3-19*q^2+99*q-145 )
        q congruent 31 modulo 60:   1/192 ( q^3-19*q^2+111*q-189 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/192 phi1 ( q^2-18*q+81 )
        q congruent 41 modulo 60:   1/192 ( q^3-19*q^2+99*q-145 )
        q congruent 43 modulo 60:   1/192 ( q^3-19*q^2+111*q-189 )
        q congruent 47 modulo 60:   1/192 ( q^3-19*q^2+111*q-253 )
        q congruent 49 modulo 60:   1/192 phi1 ( q^2-18*q+81 )
        q congruent 53 modulo 60:   1/192 ( q^3-19*q^2+99*q-145 )
        q congruent 59 modulo 60:   1/192 ( q^3-19*q^2+111*q-253 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 7, 7, 69, 7, 69, 69, 5, 7, 69, 69, 5, 69, 5, 5, 67, 3, 69, 69, 
  5, 69, 5, 5, 67, 69, 5, 5, 67, 5, 67, 67, 2 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 36 ], 
  [ 6, 1, 2, 32 ], [ 7, 1, 2, 8 ], [ 9, 1, 1, 7 ], [ 10, 1, 2, 6 ], 
  [ 11, 1, 2, 8 ], [ 12, 1, 2, 24 ], [ 13, 1, 4, 72 ], [ 16, 1, 3, 96 ], 
  [ 19, 1, 2, 32 ], [ 20, 1, 4, 48 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 42 ], 
  [ 25, 1, 3, 72 ], [ 28, 1, 4, 24 ], [ 33, 1, 8, 192 ], [ 35, 1, 8, 96 ], 
  [ 39, 1, 3, 24 ], [ 40, 1, 6, 48 ], [ 41, 1, 9, 144 ], [ 52, 1, 10, 48 ] ]

    k = 11: F-action on Pi is (  2,  5)(  7,240)      [49,1,11]
      Dynkin type is A_1(q) + A_1(q^2) + A_1(q^2) + T(phi1^3)
      Order of center |Z^F|: phi1^3 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/64 phi1 ( q^2-12*q+35 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/64 ( q^3-13*q^2+51*q-63 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/64 phi1 ( q^2-12*q+35 )
        q congruent 7 modulo 60:   1/64 ( q^3-13*q^2+51*q-63 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/64 phi1 ( q^2-12*q+35 )
        q congruent 11 modulo 60:   1/64 ( q^3-13*q^2+51*q-63 )
        q congruent 13 modulo 60:   1/64 phi1 ( q^2-12*q+35 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/64 phi1 ( q^2-12*q+35 )
        q congruent 19 modulo 60:   1/64 ( q^3-13*q^2+51*q-63 )
        q congruent 21 modulo 60:   1/64 phi1 ( q^2-12*q+35 )
        q congruent 23 modulo 60:   1/64 ( q^3-13*q^2+51*q-63 )
        q congruent 25 modulo 60:   1/64 phi1 ( q^2-12*q+35 )
        q congruent 27 modulo 60:   1/64 ( q^3-13*q^2+51*q-63 )
        q congruent 29 modulo 60:   1/64 phi1 ( q^2-12*q+35 )
        q congruent 31 modulo 60:   1/64 ( q^3-13*q^2+51*q-63 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/64 phi1 ( q^2-12*q+35 )
        q congruent 41 modulo 60:   1/64 phi1 ( q^2-12*q+35 )
        q congruent 43 modulo 60:   1/64 ( q^3-13*q^2+51*q-63 )
        q congruent 47 modulo 60:   1/64 ( q^3-13*q^2+51*q-63 )
        q congruent 49 modulo 60:   1/64 phi1 ( q^2-12*q+35 )
        q congruent 53 modulo 60:   1/64 phi1 ( q^2-12*q+35 )
        q congruent 59 modulo 60:   1/64 ( q^3-13*q^2+51*q-63 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 70, 70, 16, 68, 19, 19, 73 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 12 ], 
  [ 4, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 8 ], 
  [ 12, 1, 1, 24 ], [ 13, 1, 1, 24 ], [ 13, 1, 3, 16 ], [ 16, 1, 2, 32 ], 
  [ 20, 1, 3, 16 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 18 ], [ 25, 1, 1, 24 ], 
  [ 25, 1, 2, 16 ], [ 28, 1, 1, 24 ], [ 33, 1, 4, 64 ], [ 35, 1, 5, 32 ], 
  [ 39, 1, 1, 24 ], [ 40, 1, 1, 48 ], [ 41, 1, 1, 48 ], [ 41, 1, 3, 32 ], 
  [ 52, 1, 1, 48 ] ]

    k = 12: F-action on Pi is (  2,  5,240,  7)      [49,1,12]
      Dynkin type is A_1(q) + A_1(q^4) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 7 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 11 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 19 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 23 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 27 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 31 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 41 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 43 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 53 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 59 modulo 60:   1/16 phi1 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 19, 89, 76, 43 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], 
  [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 4 ], 
  [ 12, 1, 1, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 1, 2 ], 
  [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 25, 1, 4, 4 ], 
  [ 28, 1, 1, 4 ], [ 28, 1, 3, 4 ], [ 33, 1, 5, 16 ], [ 39, 1, 2, 4 ], 
  [ 40, 1, 3, 8 ], [ 41, 1, 4, 8 ], [ 52, 1, 3, 8 ] ]

    k = 13: F-action on Pi is (  2,  5,  7,240)      [49,1,13]
      Dynkin type is A_1(q) + A_1(q^4) + T(phi2 phi4)
      Order of center |Z^F|: phi2 phi4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 phi2^2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 phi1 phi2^2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1 phi2^2
        q congruent 7 modulo 60:   1/16 phi1 phi2^2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1 phi2^2
        q congruent 11 modulo 60:   1/16 phi1 phi2^2
        q congruent 13 modulo 60:   1/16 phi1 phi2^2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1 phi2^2
        q congruent 19 modulo 60:   1/16 phi1 phi2^2
        q congruent 21 modulo 60:   1/16 phi1 phi2^2
        q congruent 23 modulo 60:   1/16 phi1 phi2^2
        q congruent 25 modulo 60:   1/16 phi1 phi2^2
        q congruent 27 modulo 60:   1/16 phi1 phi2^2
        q congruent 29 modulo 60:   1/16 phi1 phi2^2
        q congruent 31 modulo 60:   1/16 phi1 phi2^2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1 phi2^2
        q congruent 41 modulo 60:   1/16 phi1 phi2^2
        q congruent 43 modulo 60:   1/16 phi1 phi2^2
        q congruent 47 modulo 60:   1/16 phi1 phi2^2
        q congruent 49 modulo 60:   1/16 phi1 phi2^2
        q congruent 53 modulo 60:   1/16 phi1 phi2^2
        q congruent 59 modulo 60:   1/16 phi1 phi2^2
      Fusion of maximal tori of C^F in those of G^F:
        [ 18, 91, 74, 45 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 2, 2 ], [ 20, 1, 5, 8 ], [ 20, 1, 7, 8 ], [ 24, 1, 2, 2 ], 
  [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ], [ 52, 1, 5, 8 ] ]

    k = 14: F-action on Pi is (  2,  5)(  7,240)      [49,1,14]
      Dynkin type is A_1(q) + A_1(q^2) + A_1(q^2) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/64 phi1 phi2 ( q-5 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/64 phi2 ( q^2-6*q+9 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/64 phi1 phi2 ( q-5 )
        q congruent 7 modulo 60:   1/64 phi2 ( q^2-6*q+9 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/64 phi1 phi2 ( q-5 )
        q congruent 11 modulo 60:   1/64 phi2 ( q^2-6*q+9 )
        q congruent 13 modulo 60:   1/64 phi1 phi2 ( q-5 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/64 phi1 phi2 ( q-5 )
        q congruent 19 modulo 60:   1/64 phi2 ( q^2-6*q+9 )
        q congruent 21 modulo 60:   1/64 phi1 phi2 ( q-5 )
        q congruent 23 modulo 60:   1/64 phi2 ( q^2-6*q+9 )
        q congruent 25 modulo 60:   1/64 phi1 phi2 ( q-5 )
        q congruent 27 modulo 60:   1/64 phi2 ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/64 phi1 phi2 ( q-5 )
        q congruent 31 modulo 60:   1/64 phi2 ( q^2-6*q+9 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/64 phi1 phi2 ( q-5 )
        q congruent 41 modulo 60:   1/64 phi1 phi2 ( q-5 )
        q congruent 43 modulo 60:   1/64 phi2 ( q^2-6*q+9 )
        q congruent 47 modulo 60:   1/64 phi2 ( q^2-6*q+9 )
        q congruent 49 modulo 60:   1/64 phi1 phi2 ( q-5 )
        q congruent 53 modulo 60:   1/64 phi1 phi2 ( q-5 )
        q congruent 59 modulo 60:   1/64 phi2 ( q^2-6*q+9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 72, 72, 18, 69, 20, 20, 74 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 4 ], 
  [ 7, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 4 ], 
  [ 13, 1, 2, 16 ], [ 13, 1, 4, 8 ], [ 20, 1, 1, 16 ], [ 20, 1, 5, 32 ], 
  [ 23, 1, 2, 4 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 3, 8 ], 
  [ 25, 1, 4, 16 ], [ 28, 1, 3, 8 ], [ 35, 1, 2, 32 ], [ 39, 1, 3, 8 ], 
  [ 39, 1, 4, 8 ], [ 41, 1, 6, 16 ], [ 41, 1, 9, 16 ], [ 41, 1, 10, 32 ], 
  [ 52, 1, 9, 16 ] ]

    k = 15: F-action on Pi is (  2,  5)(  7,240)      [49,1,15]
      Dynkin type is A_1(q) + A_1(q^2) + A_1(q^2) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1^2 phi2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/32 phi2^2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/32 phi1^2 phi2
        q congruent 7 modulo 60:   1/32 phi2^2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/32 phi1^2 phi2
        q congruent 11 modulo 60:   1/32 phi2^2 ( q-3 )
        q congruent 13 modulo 60:   1/32 phi1^2 phi2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/32 phi1^2 phi2
        q congruent 19 modulo 60:   1/32 phi2^2 ( q-3 )
        q congruent 21 modulo 60:   1/32 phi1^2 phi2
        q congruent 23 modulo 60:   1/32 phi2^2 ( q-3 )
        q congruent 25 modulo 60:   1/32 phi1^2 phi2
        q congruent 27 modulo 60:   1/32 phi2^2 ( q-3 )
        q congruent 29 modulo 60:   1/32 phi1^2 phi2
        q congruent 31 modulo 60:   1/32 phi2^2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/32 phi1^2 phi2
        q congruent 41 modulo 60:   1/32 phi1^2 phi2
        q congruent 43 modulo 60:   1/32 phi2^2 ( q-3 )
        q congruent 47 modulo 60:   1/32 phi2^2 ( q-3 )
        q congruent 49 modulo 60:   1/32 phi1^2 phi2
        q congruent 53 modulo 60:   1/32 phi1^2 phi2
        q congruent 59 modulo 60:   1/32 phi2^2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 7, 76, 76, 18, 69, 20, 20, 74 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], 
  [ 10, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 13, 1, 4, 8 ], [ 20, 1, 7, 16 ], 
  [ 23, 1, 2, 4 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 3, 8 ], 
  [ 28, 1, 3, 8 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 8 ], [ 41, 1, 6, 16 ], 
  [ 41, 1, 7, 16 ], [ 41, 1, 9, 16 ], [ 52, 1, 9, 16 ] ]

    k = 16: F-action on Pi is (  2,  5,240,  7)      [49,1,16]
      Dynkin type is A_1(q) + A_1(q^4) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^2 phi2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 phi1^2 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1^2 phi2
        q congruent 7 modulo 60:   1/16 phi1^2 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1^2 phi2
        q congruent 11 modulo 60:   1/16 phi1^2 phi2
        q congruent 13 modulo 60:   1/16 phi1^2 phi2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1^2 phi2
        q congruent 19 modulo 60:   1/16 phi1^2 phi2
        q congruent 21 modulo 60:   1/16 phi1^2 phi2
        q congruent 23 modulo 60:   1/16 phi1^2 phi2
        q congruent 25 modulo 60:   1/16 phi1^2 phi2
        q congruent 27 modulo 60:   1/16 phi1^2 phi2
        q congruent 29 modulo 60:   1/16 phi1^2 phi2
        q congruent 31 modulo 60:   1/16 phi1^2 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1^2 phi2
        q congruent 41 modulo 60:   1/16 phi1^2 phi2
        q congruent 43 modulo 60:   1/16 phi1^2 phi2
        q congruent 47 modulo 60:   1/16 phi1^2 phi2
        q congruent 49 modulo 60:   1/16 phi1^2 phi2
        q congruent 53 modulo 60:   1/16 phi1^2 phi2
        q congruent 59 modulo 60:   1/16 phi1^2 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 76, 43, 20, 90 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 2 ], 
  [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], 
  [ 12, 1, 2, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 1, 2 ], 
  [ 23, 1, 2, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 25, 1, 4, 4 ], 
  [ 28, 1, 2, 4 ], [ 28, 1, 4, 4 ], [ 33, 1, 9, 16 ], [ 39, 1, 2, 4 ], 
  [ 40, 1, 2, 8 ], [ 41, 1, 4, 8 ], [ 52, 1, 4, 8 ] ]

    k = 17: F-action on Pi is (  2,  5,  7,240)      [49,1,17]
      Dynkin type is A_1(q) + A_1(q^4) + T(phi1 phi4)
      Order of center |Z^F|: phi1 phi4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^2 phi2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 phi1^2 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1^2 phi2
        q congruent 7 modulo 60:   1/16 phi1^2 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1^2 phi2
        q congruent 11 modulo 60:   1/16 phi1^2 phi2
        q congruent 13 modulo 60:   1/16 phi1^2 phi2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1^2 phi2
        q congruent 19 modulo 60:   1/16 phi1^2 phi2
        q congruent 21 modulo 60:   1/16 phi1^2 phi2
        q congruent 23 modulo 60:   1/16 phi1^2 phi2
        q congruent 25 modulo 60:   1/16 phi1^2 phi2
        q congruent 27 modulo 60:   1/16 phi1^2 phi2
        q congruent 29 modulo 60:   1/16 phi1^2 phi2
        q congruent 31 modulo 60:   1/16 phi1^2 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1^2 phi2
        q congruent 41 modulo 60:   1/16 phi1^2 phi2
        q congruent 43 modulo 60:   1/16 phi1^2 phi2
        q congruent 47 modulo 60:   1/16 phi1^2 phi2
        q congruent 49 modulo 60:   1/16 phi1^2 phi2
        q congruent 53 modulo 60:   1/16 phi1^2 phi2
        q congruent 59 modulo 60:   1/16 phi1^2 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 73, 44, 18, 91 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 1, 2 ], [ 20, 1, 6, 8 ], [ 20, 1, 8, 8 ], [ 24, 1, 1, 2 ], 
  [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ], [ 52, 1, 8, 8 ] ]

    k = 18: F-action on Pi is (  2,  5)(  7,240)      [49,1,18]
      Dynkin type is A_1(q) + A_1(q^2) + A_1(q^2) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 ( q^2-2*q-7 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/32 phi1 phi2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/32 phi1 ( q^2-2*q-7 )
        q congruent 7 modulo 60:   1/32 phi1 phi2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/32 phi1 ( q^2-2*q-7 )
        q congruent 11 modulo 60:   1/32 phi1 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/32 phi1 ( q^2-2*q-7 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/32 phi1 ( q^2-2*q-7 )
        q congruent 19 modulo 60:   1/32 phi1 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/32 phi1 ( q^2-2*q-7 )
        q congruent 23 modulo 60:   1/32 phi1 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/32 phi1 ( q^2-2*q-7 )
        q congruent 27 modulo 60:   1/32 phi1 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/32 phi1 ( q^2-2*q-7 )
        q congruent 31 modulo 60:   1/32 phi1 phi2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/32 phi1 ( q^2-2*q-7 )
        q congruent 41 modulo 60:   1/32 phi1 ( q^2-2*q-7 )
        q congruent 43 modulo 60:   1/32 phi1 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/32 phi1 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/32 phi1 ( q^2-2*q-7 )
        q congruent 53 modulo 60:   1/32 phi1 ( q^2-2*q-7 )
        q congruent 59 modulo 60:   1/32 phi1 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 19, 19, 73, 7, 76, 76, 18 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 9, 1, 1, 3 ], 
  [ 10, 1, 1, 4 ], [ 10, 1, 2, 2 ], [ 13, 1, 1, 8 ], [ 20, 1, 6, 16 ], 
  [ 23, 1, 1, 4 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 8 ], 
  [ 28, 1, 2, 8 ], [ 39, 1, 1, 8 ], [ 39, 1, 4, 8 ], [ 41, 1, 1, 16 ], 
  [ 41, 1, 6, 16 ], [ 41, 1, 7, 16 ], [ 52, 1, 2, 16 ] ]

    k = 19: F-action on Pi is (  2,  5)(  7,240)      [49,1,19]
      Dynkin type is A_1(q) + A_1(q^2) + A_1(q^2) + T(phi2^3)
      Order of center |Z^F|: phi2^3 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/64 phi2 ( q^2-8*q+15 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 7 modulo 60:   1/64 phi2 ( q^2-8*q+15 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 11 modulo 60:   1/64 phi2 ( q^2-8*q+15 )
        q congruent 13 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 19 modulo 60:   1/64 phi2 ( q^2-8*q+15 )
        q congruent 21 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 23 modulo 60:   1/64 phi2 ( q^2-8*q+15 )
        q congruent 25 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 27 modulo 60:   1/64 phi2 ( q^2-8*q+15 )
        q congruent 29 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 31 modulo 60:   1/64 phi2 ( q^2-8*q+15 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 41 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 43 modulo 60:   1/64 phi2 ( q^2-8*q+15 )
        q congruent 47 modulo 60:   1/64 phi2 ( q^2-8*q+15 )
        q congruent 49 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 53 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 59 modulo 60:   1/64 phi2 ( q^2-8*q+15 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 69, 20, 20, 74, 5, 71, 71, 17 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 8 ], 
  [ 4, 1, 2, 12 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], 
  [ 12, 1, 2, 24 ], [ 13, 1, 2, 16 ], [ 13, 1, 4, 24 ], [ 16, 1, 4, 32 ], 
  [ 20, 1, 2, 16 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 18 ], [ 25, 1, 3, 24 ], 
  [ 25, 1, 4, 16 ], [ 28, 1, 4, 24 ], [ 33, 1, 10, 64 ], [ 35, 1, 4, 32 ], 
  [ 39, 1, 3, 24 ], [ 40, 1, 6, 48 ], [ 41, 1, 9, 48 ], [ 41, 1, 10, 32 ], 
  [ 52, 1, 10, 48 ] ]

    k = 20: F-action on Pi is (  2,  5)(  7,240)      [49,1,20]
      Dynkin type is A_1(q) + A_1(q^2) + A_1(q^2) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/64 phi2 ( q^2-8*q+15 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 7 modulo 60:   1/64 phi2 ( q^2-8*q+15 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 11 modulo 60:   1/64 phi2 ( q^2-8*q+15 )
        q congruent 13 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 19 modulo 60:   1/64 phi2 ( q^2-8*q+15 )
        q congruent 21 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 23 modulo 60:   1/64 phi2 ( q^2-8*q+15 )
        q congruent 25 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 27 modulo 60:   1/64 phi2 ( q^2-8*q+15 )
        q congruent 29 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 31 modulo 60:   1/64 phi2 ( q^2-8*q+15 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 41 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 43 modulo 60:   1/64 phi2 ( q^2-8*q+15 )
        q congruent 47 modulo 60:   1/64 phi2 ( q^2-8*q+15 )
        q congruent 49 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 53 modulo 60:   1/64 phi1^2 ( q-5 )
        q congruent 59 modulo 60:   1/64 phi2 ( q^2-8*q+15 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 19, 19, 73, 3, 72, 72, 18 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 8 ], 
  [ 7, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 2 ], 
  [ 13, 1, 1, 8 ], [ 13, 1, 3, 16 ], [ 20, 1, 4, 16 ], [ 20, 1, 8, 32 ], 
  [ 23, 1, 1, 4 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 8 ], 
  [ 25, 1, 2, 16 ], [ 28, 1, 2, 8 ], [ 35, 1, 7, 32 ], [ 39, 1, 1, 8 ], 
  [ 39, 1, 4, 8 ], [ 41, 1, 1, 16 ], [ 41, 1, 3, 32 ], [ 41, 1, 6, 16 ], 
  [ 52, 1, 2, 16 ] ]

i = 50: Pi = [ 1, 3, 4, 5, 6 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [50,1,1]
      Dynkin type is A_5(q) + T(phi1^3)
      Order of center |Z^F|: phi1^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 ( q^3-17*q^2+97*q-201 )
        q congruent 2 modulo 60:   1/24 ( q^3-16*q^2+76*q-96 )
        q congruent 3 modulo 60:   1/24 ( q^3-17*q^2+93*q-153 )
        q congruent 4 modulo 60:   1/24 ( q^3-16*q^2+80*q-128 )
        q congruent 5 modulo 60:   1/24 ( q^3-17*q^2+93*q-165 )
        q congruent 7 modulo 60:   1/24 ( q^3-17*q^2+97*q-189 )
        q congruent 8 modulo 60:   1/24 ( q^3-16*q^2+76*q-96 )
        q congruent 9 modulo 60:   1/24 ( q^3-17*q^2+93*q-165 )
        q congruent 11 modulo 60:   1/24 ( q^3-17*q^2+93*q-153 )
        q congruent 13 modulo 60:   1/24 ( q^3-17*q^2+97*q-201 )
        q congruent 16 modulo 60:   1/24 ( q^3-16*q^2+80*q-128 )
        q congruent 17 modulo 60:   1/24 ( q^3-17*q^2+93*q-165 )
        q congruent 19 modulo 60:   1/24 ( q^3-17*q^2+97*q-189 )
        q congruent 21 modulo 60:   1/24 ( q^3-17*q^2+93*q-165 )
        q congruent 23 modulo 60:   1/24 ( q^3-17*q^2+93*q-153 )
        q congruent 25 modulo 60:   1/24 ( q^3-17*q^2+97*q-201 )
        q congruent 27 modulo 60:   1/24 ( q^3-17*q^2+93*q-153 )
        q congruent 29 modulo 60:   1/24 ( q^3-17*q^2+93*q-165 )
        q congruent 31 modulo 60:   1/24 ( q^3-17*q^2+97*q-189 )
        q congruent 32 modulo 60:   1/24 ( q^3-16*q^2+76*q-96 )
        q congruent 37 modulo 60:   1/24 ( q^3-17*q^2+97*q-201 )
        q congruent 41 modulo 60:   1/24 ( q^3-17*q^2+93*q-165 )
        q congruent 43 modulo 60:   1/24 ( q^3-17*q^2+97*q-189 )
        q congruent 47 modulo 60:   1/24 ( q^3-17*q^2+93*q-153 )
        q congruent 49 modulo 60:   1/24 ( q^3-17*q^2+97*q-201 )
        q congruent 53 modulo 60:   1/24 ( q^3-17*q^2+93*q-165 )
        q congruent 59 modulo 60:   1/24 ( q^3-17*q^2+93*q-153 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 4, 68, 8, 77, 14, 70, 19, 23, 87 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], 
  [ 7, 1, 1, 6 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 8 ], 
  [ 11, 1, 1, 6 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 6 ], [ 21, 1, 1, 12 ], 
  [ 22, 1, 1, 4 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 12 ], [ 26, 1, 1, 12 ], 
  [ 27, 1, 1, 12 ], [ 34, 1, 1, 12 ], [ 36, 1, 1, 24 ], [ 39, 1, 1, 24 ], 
  [ 42, 1, 1, 12 ] ]

    k = 2: F-action on Pi is ()      [50,1,2]
      Dynkin type is A_5(q) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 2 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 4 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 7 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 8 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 11 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 13 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 16 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 19 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 21 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 23 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 25 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 27 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 29 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 31 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 32 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 41 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 43 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 47 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 49 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 53 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 59 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 68, 7, 77, 30, 83, 19, 76, 93, 40 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], 
  [ 7, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 18, 1, 1, 4 ], [ 19, 1, 1, 2 ], 
  [ 21, 1, 1, 4 ], [ 22, 1, 1, 4 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], 
  [ 26, 1, 3, 4 ], [ 27, 1, 2, 4 ], [ 34, 1, 1, 4 ], [ 36, 1, 2, 8 ], 
  [ 39, 1, 4, 4 ], [ 42, 1, 4, 4 ] ]

    k = 3: F-action on Pi is ()      [50,1,3]
      Dynkin type is A_5(q) + T(phi1 phi3)
      Order of center |Z^F|: phi1 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 phi1 ( q^2-q-6 )
        q congruent 2 modulo 60:   1/12 q phi2 ( q-2 )
        q congruent 3 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 4 modulo 60:   1/12 phi1 ( q^2-4 )
        q congruent 5 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 7 modulo 60:   1/12 phi1 ( q^2-q-6 )
        q congruent 8 modulo 60:   1/12 q phi2 ( q-2 )
        q congruent 9 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 11 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 13 modulo 60:   1/12 phi1 ( q^2-q-6 )
        q congruent 16 modulo 60:   1/12 phi1 ( q^2-4 )
        q congruent 17 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 19 modulo 60:   1/12 phi1 ( q^2-q-6 )
        q congruent 21 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 23 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 25 modulo 60:   1/12 phi1 ( q^2-q-6 )
        q congruent 27 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 29 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 31 modulo 60:   1/12 phi1 ( q^2-q-6 )
        q congruent 32 modulo 60:   1/12 q phi2 ( q-2 )
        q congruent 37 modulo 60:   1/12 phi1 ( q^2-q-6 )
        q congruent 41 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 43 modulo 60:   1/12 phi1 ( q^2-q-6 )
        q congruent 47 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 49 modulo 60:   1/12 phi1 ( q^2-q-6 )
        q congruent 53 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 59 modulo 60:   1/12 q phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 8, 77, 30, 81, 14, 83, 12, 97, 59, 62, 85 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], 
  [ 8, 1, 1, 4 ], [ 10, 1, 1, 2 ], [ 22, 1, 1, 4 ], [ 27, 1, 5, 6 ], 
  [ 42, 1, 3, 6 ] ]

    k = 4: F-action on Pi is ()      [50,1,4]
      Dynkin type is A_5(q) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 phi1 ( q^2-8*q+19 )
        q congruent 2 modulo 60:   1/24 q ( q^2-8*q+12 )
        q congruent 3 modulo 60:   1/24 phi1 ( q^2-8*q+15 )
        q congruent 4 modulo 60:   1/24 q ( q^2-8*q+16 )
        q congruent 5 modulo 60:   1/24 phi1 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/24 phi1 ( q^2-8*q+19 )
        q congruent 8 modulo 60:   1/24 q ( q^2-8*q+12 )
        q congruent 9 modulo 60:   1/24 phi1 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/24 phi1 ( q^2-8*q+15 )
        q congruent 13 modulo 60:   1/24 phi1 ( q^2-8*q+19 )
        q congruent 16 modulo 60:   1/24 q ( q^2-8*q+16 )
        q congruent 17 modulo 60:   1/24 phi1 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/24 phi1 ( q^2-8*q+19 )
        q congruent 21 modulo 60:   1/24 phi1 ( q^2-8*q+15 )
        q congruent 23 modulo 60:   1/24 phi1 ( q^2-8*q+15 )
        q congruent 25 modulo 60:   1/24 phi1 ( q^2-8*q+19 )
        q congruent 27 modulo 60:   1/24 phi1 ( q^2-8*q+15 )
        q congruent 29 modulo 60:   1/24 phi1 ( q^2-8*q+15 )
        q congruent 31 modulo 60:   1/24 phi1 ( q^2-8*q+19 )
        q congruent 32 modulo 60:   1/24 q ( q^2-8*q+12 )
        q congruent 37 modulo 60:   1/24 phi1 ( q^2-8*q+19 )
        q congruent 41 modulo 60:   1/24 phi1 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/24 phi1 ( q^2-8*q+19 )
        q congruent 47 modulo 60:   1/24 phi1 ( q^2-8*q+15 )
        q congruent 49 modulo 60:   1/24 phi1 ( q^2-8*q+19 )
        q congruent 53 modulo 60:   1/24 phi1 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/24 phi1 ( q^2-8*q+15 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 68, 3, 77, 30, 83, 19, 72, 93, 35 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], 
  [ 7, 1, 1, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 2 ], 
  [ 11, 1, 1, 6 ], [ 19, 1, 1, 6 ], [ 22, 1, 2, 4 ], [ 24, 1, 1, 6 ], 
  [ 24, 1, 2, 6 ], [ 26, 1, 1, 12 ], [ 27, 1, 1, 12 ], [ 34, 1, 2, 12 ], 
  [ 39, 1, 4, 12 ], [ 42, 1, 1, 12 ] ]

    k = 5: F-action on Pi is ()      [50,1,5]
      Dynkin type is A_5(q) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1^3
        q congruent 2 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 3 modulo 60:   1/8 phi1^3
        q congruent 4 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 5 modulo 60:   1/8 phi1^3
        q congruent 7 modulo 60:   1/8 phi1^3
        q congruent 8 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 9 modulo 60:   1/8 phi1^3
        q congruent 11 modulo 60:   1/8 phi1^3
        q congruent 13 modulo 60:   1/8 phi1^3
        q congruent 16 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 17 modulo 60:   1/8 phi1^3
        q congruent 19 modulo 60:   1/8 phi1^3
        q congruent 21 modulo 60:   1/8 phi1^3
        q congruent 23 modulo 60:   1/8 phi1^3
        q congruent 25 modulo 60:   1/8 phi1^3
        q congruent 27 modulo 60:   1/8 phi1^3
        q congruent 29 modulo 60:   1/8 phi1^3
        q congruent 31 modulo 60:   1/8 phi1^3
        q congruent 32 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 37 modulo 60:   1/8 phi1^3
        q congruent 41 modulo 60:   1/8 phi1^3
        q congruent 43 modulo 60:   1/8 phi1^3
        q congruent 47 modulo 60:   1/8 phi1^3
        q congruent 49 modulo 60:   1/8 phi1^3
        q congruent 53 modulo 60:   1/8 phi1^3
        q congruent 59 modulo 60:   1/8 phi1^3
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 68, 7, 69, 30, 81, 37, 76, 20, 50, 88 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], 
  [ 7, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 2 ], 
  [ 19, 1, 1, 2 ], [ 22, 1, 2, 4 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], 
  [ 26, 1, 3, 4 ], [ 27, 1, 2, 4 ], [ 34, 1, 2, 4 ], [ 39, 1, 3, 8 ], 
  [ 42, 1, 4, 4 ] ]

    k = 6: F-action on Pi is ()      [50,1,6]
      Dynkin type is A_5(q) + T(phi2 phi3)
      Order of center |Z^F|: phi2 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 2 modulo 60:   1/12 q^2 phi2
        q congruent 3 modulo 60:   1/12 q phi1 phi2
        q congruent 4 modulo 60:   1/12 q phi1 ( q+2 )
        q congruent 5 modulo 60:   1/12 q phi1 phi2
        q congruent 7 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 8 modulo 60:   1/12 q^2 phi2
        q congruent 9 modulo 60:   1/12 q phi1 phi2
        q congruent 11 modulo 60:   1/12 q phi1 phi2
        q congruent 13 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 16 modulo 60:   1/12 q phi1 ( q+2 )
        q congruent 17 modulo 60:   1/12 q phi1 phi2
        q congruent 19 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 21 modulo 60:   1/12 q phi1 phi2
        q congruent 23 modulo 60:   1/12 q phi1 phi2
        q congruent 25 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 27 modulo 60:   1/12 q phi1 phi2
        q congruent 29 modulo 60:   1/12 q phi1 phi2
        q congruent 31 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 32 modulo 60:   1/12 q^2 phi2
        q congruent 37 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 41 modulo 60:   1/12 q phi1 phi2
        q congruent 43 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 47 modulo 60:   1/12 q phi1 phi2
        q congruent 49 modulo 60:   1/12 phi1^2 ( q+2 )
        q congruent 53 modulo 60:   1/12 q phi1 phi2
        q congruent 59 modulo 60:   1/12 q phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 77, 30, 81, 27, 83, 37, 79, 59, 95, 111, 34 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 22, 1, 2, 4 ], [ 27, 1, 5, 6 ], [ 42, 1, 3, 6 ] ]

    k = 7: F-action on Pi is (1,6)(3,5)      [50,1,7]
      Dynkin type is ^2A_5(q) + T(phi1 phi6)
      Order of center |Z^F|: phi1 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 2 modulo 60:   1/12 phi2 ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 4 modulo 60:   1/12 q phi1 ( q-2 )
        q congruent 5 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 7 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 8 modulo 60:   1/12 phi2 ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 11 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 13 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 16 modulo 60:   1/12 q phi1 ( q-2 )
        q congruent 17 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 19 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 21 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 23 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 25 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 27 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 29 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 31 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 32 modulo 60:   1/12 phi2 ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 41 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 43 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 47 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 49 modulo 60:   1/12 q phi1 ( q-3 )
        q congruent 53 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
        q congruent 59 modulo 60:   1/12 phi2 ( q^2-5*q+6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 78, 31, 82, 28, 84, 38, 80, 60, 96, 112, 33 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], 
  [ 10, 1, 1, 2 ], [ 22, 1, 3, 4 ], [ 27, 1, 4, 6 ], [ 42, 1, 5, 6 ] ]

    k = 8: F-action on Pi is (1,6)(3,5)      [50,1,8]
      Dynkin type is ^2A_5(q) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 2 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 4 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 5 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 7 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 8 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 11 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 13 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 16 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 17 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 19 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 21 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 23 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 25 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 27 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 29 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 31 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 32 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 41 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 43 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 47 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 49 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 53 modulo 60:   1/8 phi1^2 ( q-3 )
        q congruent 59 modulo 60:   1/8 phi1^2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 69, 7, 68, 31, 82, 38, 76, 19, 51, 87 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], 
  [ 7, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], [ 11, 1, 2, 2 ], 
  [ 19, 1, 2, 2 ], [ 22, 1, 3, 4 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ], 
  [ 26, 1, 2, 4 ], [ 27, 1, 3, 4 ], [ 34, 1, 3, 4 ], [ 39, 1, 1, 8 ], 
  [ 42, 1, 2, 4 ] ]

    k = 9: F-action on Pi is (1,6)(3,5)      [50,1,9]
      Dynkin type is ^2A_5(q) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 phi1 ( q^2-6*q+9 )
        q congruent 2 modulo 60:   1/24 ( q^3-6*q^2+12*q-8 )
        q congruent 3 modulo 60:   1/24 phi1 ( q^2-6*q+9 )
        q congruent 4 modulo 60:   1/24 q ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/24 ( q^3-7*q^2+19*q-21 )
        q congruent 7 modulo 60:   1/24 phi1 ( q^2-6*q+9 )
        q congruent 8 modulo 60:   1/24 ( q^3-6*q^2+12*q-8 )
        q congruent 9 modulo 60:   1/24 phi1 ( q^2-6*q+9 )
        q congruent 11 modulo 60:   1/24 ( q^3-7*q^2+19*q-21 )
        q congruent 13 modulo 60:   1/24 phi1 ( q^2-6*q+9 )
        q congruent 16 modulo 60:   1/24 q ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/24 ( q^3-7*q^2+19*q-21 )
        q congruent 19 modulo 60:   1/24 phi1 ( q^2-6*q+9 )
        q congruent 21 modulo 60:   1/24 phi1 ( q^2-6*q+9 )
        q congruent 23 modulo 60:   1/24 ( q^3-7*q^2+19*q-21 )
        q congruent 25 modulo 60:   1/24 phi1 ( q^2-6*q+9 )
        q congruent 27 modulo 60:   1/24 phi1 ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/24 ( q^3-7*q^2+19*q-21 )
        q congruent 31 modulo 60:   1/24 phi1 ( q^2-6*q+9 )
        q congruent 32 modulo 60:   1/24 ( q^3-6*q^2+12*q-8 )
        q congruent 37 modulo 60:   1/24 phi1 ( q^2-6*q+9 )
        q congruent 41 modulo 60:   1/24 ( q^3-7*q^2+19*q-21 )
        q congruent 43 modulo 60:   1/24 phi1 ( q^2-6*q+9 )
        q congruent 47 modulo 60:   1/24 ( q^3-7*q^2+19*q-21 )
        q congruent 49 modulo 60:   1/24 phi1 ( q^2-6*q+9 )
        q congruent 53 modulo 60:   1/24 ( q^3-7*q^2+19*q-21 )
        q congruent 59 modulo 60:   1/24 ( q^3-7*q^2+19*q-21 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 5, 69, 3, 78, 31, 84, 20, 72, 94, 35 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], 
  [ 7, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 6 ], 
  [ 11, 1, 2, 6 ], [ 19, 1, 2, 6 ], [ 22, 1, 3, 4 ], [ 24, 1, 1, 6 ], 
  [ 24, 1, 2, 6 ], [ 26, 1, 4, 12 ], [ 27, 1, 6, 12 ], [ 34, 1, 3, 12 ], 
  [ 39, 1, 4, 12 ], [ 42, 1, 6, 12 ] ]

    k = 10: F-action on Pi is (1,6)(3,5)      [50,1,10]
      Dynkin type is ^2A_5(q) + T(phi2 phi6)
      Order of center |Z^F|: phi2 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q phi1^2
        q congruent 2 modulo 60:   1/12 q phi2 ( q-2 )
        q congruent 3 modulo 60:   1/12 q phi1^2
        q congruent 4 modulo 60:   1/12 q^2 phi1
        q congruent 5 modulo 60:   1/12 phi1 phi2 ( q-2 )
        q congruent 7 modulo 60:   1/12 q phi1^2
        q congruent 8 modulo 60:   1/12 q phi2 ( q-2 )
        q congruent 9 modulo 60:   1/12 q phi1^2
        q congruent 11 modulo 60:   1/12 phi1 phi2 ( q-2 )
        q congruent 13 modulo 60:   1/12 q phi1^2
        q congruent 16 modulo 60:   1/12 q^2 phi1
        q congruent 17 modulo 60:   1/12 phi1 phi2 ( q-2 )
        q congruent 19 modulo 60:   1/12 q phi1^2
        q congruent 21 modulo 60:   1/12 q phi1^2
        q congruent 23 modulo 60:   1/12 phi1 phi2 ( q-2 )
        q congruent 25 modulo 60:   1/12 q phi1^2
        q congruent 27 modulo 60:   1/12 q phi1^2
        q congruent 29 modulo 60:   1/12 phi1 phi2 ( q-2 )
        q congruent 31 modulo 60:   1/12 q phi1^2
        q congruent 32 modulo 60:   1/12 q phi2 ( q-2 )
        q congruent 37 modulo 60:   1/12 q phi1^2
        q congruent 41 modulo 60:   1/12 phi1 phi2 ( q-2 )
        q congruent 43 modulo 60:   1/12 q phi1^2
        q congruent 47 modulo 60:   1/12 phi1 phi2 ( q-2 )
        q congruent 49 modulo 60:   1/12 q phi1^2
        q congruent 53 modulo 60:   1/12 phi1 phi2 ( q-2 )
        q congruent 59 modulo 60:   1/12 phi1 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 9, 78, 31, 82, 15, 84, 13, 98, 60, 63, 86 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], 
  [ 8, 1, 2, 4 ], [ 10, 1, 2, 2 ], [ 22, 1, 4, 4 ], [ 27, 1, 4, 6 ], 
  [ 42, 1, 5, 6 ] ]

    k = 11: F-action on Pi is (1,6)(3,5)      [50,1,11]
      Dynkin type is ^2A_5(q) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 2 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 4 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 5 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 7 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 8 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 11 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 13 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 16 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 17 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 19 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 21 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 23 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 25 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 27 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 29 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 31 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 32 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 41 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 43 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 47 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 49 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 53 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 59 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 5, 69, 7, 78, 31, 84, 20, 76, 94, 40 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], 
  [ 7, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 11, 1, 2, 2 ], [ 18, 1, 2, 4 ], [ 19, 1, 2, 2 ], 
  [ 21, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], 
  [ 26, 1, 2, 4 ], [ 27, 1, 3, 4 ], [ 34, 1, 4, 4 ], [ 36, 1, 3, 8 ], 
  [ 39, 1, 4, 4 ], [ 42, 1, 2, 4 ] ]

    k = 12: F-action on Pi is (1,6)(3,5)      [50,1,12]
      Dynkin type is ^2A_5(q) + T(phi2^3)
      Order of center |Z^F|: phi2^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 phi1 ( q^2-10*q+27 )
        q congruent 2 modulo 60:   1/24 ( q^3-10*q^2+28*q-24 )
        q congruent 3 modulo 60:   1/24 ( q^3-11*q^2+37*q-39 )
        q congruent 4 modulo 60:   1/24 q ( q^2-10*q+24 )
        q congruent 5 modulo 60:   1/24 ( q^3-11*q^2+41*q-55 )
        q congruent 7 modulo 60:   1/24 ( q^3-11*q^2+37*q-39 )
        q congruent 8 modulo 60:   1/24 ( q^3-10*q^2+28*q-24 )
        q congruent 9 modulo 60:   1/24 phi1 ( q^2-10*q+27 )
        q congruent 11 modulo 60:   1/24 ( q^3-11*q^2+41*q-67 )
        q congruent 13 modulo 60:   1/24 phi1 ( q^2-10*q+27 )
        q congruent 16 modulo 60:   1/24 q ( q^2-10*q+24 )
        q congruent 17 modulo 60:   1/24 ( q^3-11*q^2+41*q-55 )
        q congruent 19 modulo 60:   1/24 ( q^3-11*q^2+37*q-39 )
        q congruent 21 modulo 60:   1/24 phi1 ( q^2-10*q+27 )
        q congruent 23 modulo 60:   1/24 ( q^3-11*q^2+41*q-67 )
        q congruent 25 modulo 60:   1/24 phi1 ( q^2-10*q+27 )
        q congruent 27 modulo 60:   1/24 ( q^3-11*q^2+37*q-39 )
        q congruent 29 modulo 60:   1/24 ( q^3-11*q^2+41*q-55 )
        q congruent 31 modulo 60:   1/24 ( q^3-11*q^2+37*q-39 )
        q congruent 32 modulo 60:   1/24 ( q^3-10*q^2+28*q-24 )
        q congruent 37 modulo 60:   1/24 phi1 ( q^2-10*q+27 )
        q congruent 41 modulo 60:   1/24 ( q^3-11*q^2+41*q-55 )
        q congruent 43 modulo 60:   1/24 ( q^3-11*q^2+37*q-39 )
        q congruent 47 modulo 60:   1/24 ( q^3-11*q^2+41*q-67 )
        q congruent 49 modulo 60:   1/24 phi1 ( q^2-10*q+27 )
        q congruent 53 modulo 60:   1/24 ( q^3-11*q^2+41*q-55 )
        q congruent 59 modulo 60:   1/24 ( q^3-11*q^2+41*q-67 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 2, 67, 5, 69, 9, 78, 15, 71, 20, 24, 88 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], 
  [ 7, 1, 2, 6 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 8 ], 
  [ 11, 1, 2, 6 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 6 ], [ 21, 1, 2, 12 ], 
  [ 22, 1, 4, 4 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 12 ], [ 26, 1, 4, 12 ], 
  [ 27, 1, 6, 12 ], [ 34, 1, 4, 12 ], [ 36, 1, 4, 24 ], [ 39, 1, 3, 24 ], 
  [ 42, 1, 6, 12 ] ]

i = 51: Pi = [ 1, 3, 4, 6, 7 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [51,1,1]
      Dynkin type is A_3(q) + A_2(q) + T(phi1^3)
      Order of center |Z^F|: phi1^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 ( q^3-21*q^2+151*q-435 )
        q congruent 2 modulo 60:   1/16 ( q^3-20*q^2+116*q-160 )
        q congruent 3 modulo 60:   1/16 ( q^3-21*q^2+139*q-255 )
        q congruent 4 modulo 60:   1/16 ( q^3-20*q^2+124*q-240 )
        q congruent 5 modulo 60:   1/16 ( q^3-21*q^2+143*q-315 )
        q congruent 7 modulo 60:   1/16 ( q^3-21*q^2+147*q-343 )
        q congruent 8 modulo 60:   1/16 ( q^3-20*q^2+116*q-160 )
        q congruent 9 modulo 60:   1/16 ( q^3-21*q^2+143*q-315 )
        q congruent 11 modulo 60:   1/16 ( q^3-21*q^2+139*q-287 )
        q congruent 13 modulo 60:   1/16 ( q^3-21*q^2+151*q-403 )
        q congruent 16 modulo 60:   1/16 ( q^3-20*q^2+124*q-272 )
        q congruent 17 modulo 60:   1/16 ( q^3-21*q^2+143*q-315 )
        q congruent 19 modulo 60:   1/16 ( q^3-21*q^2+147*q-343 )
        q congruent 21 modulo 60:   1/16 ( q^3-21*q^2+143*q-347 )
        q congruent 23 modulo 60:   1/16 ( q^3-21*q^2+139*q-255 )
        q congruent 25 modulo 60:   1/16 ( q^3-21*q^2+151*q-403 )
        q congruent 27 modulo 60:   1/16 ( q^3-21*q^2+139*q-255 )
        q congruent 29 modulo 60:   1/16 ( q^3-21*q^2+143*q-315 )
        q congruent 31 modulo 60:   1/16 ( q^3-21*q^2+147*q-375 )
        q congruent 32 modulo 60:   1/16 ( q^3-20*q^2+116*q-160 )
        q congruent 37 modulo 60:   1/16 ( q^3-21*q^2+151*q-403 )
        q congruent 41 modulo 60:   1/16 ( q^3-21*q^2+143*q-347 )
        q congruent 43 modulo 60:   1/16 ( q^3-21*q^2+147*q-343 )
        q congruent 47 modulo 60:   1/16 ( q^3-21*q^2+139*q-255 )
        q congruent 49 modulo 60:   1/16 ( q^3-21*q^2+151*q-403 )
        q congruent 53 modulo 60:   1/16 ( q^3-21*q^2+143*q-315 )
        q congruent 59 modulo 60:   1/16 ( q^3-21*q^2+139*q-255 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 8, 66, 4, 77, 4, 68, 30, 8, 77, 14, 70, 19, 97 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 12 ], 
  [ 5, 1, 1, 16 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 8 ], [ 8, 1, 1, 8 ], 
  [ 9, 1, 1, 5 ], [ 10, 1, 1, 4 ], [ 12, 1, 1, 10 ], [ 14, 1, 1, 24 ], 
  [ 15, 1, 1, 8 ], [ 16, 1, 1, 4 ], [ 18, 1, 1, 8 ], [ 20, 1, 1, 16 ], 
  [ 21, 1, 1, 16 ], [ 22, 1, 1, 8 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 4 ], 
  [ 25, 1, 1, 32 ], [ 26, 1, 1, 16 ], [ 29, 1, 1, 16 ], [ 31, 1, 1, 8 ], 
  [ 36, 1, 1, 16 ], [ 37, 1, 1, 32 ], [ 39, 1, 1, 8 ], [ 40, 1, 1, 24 ], 
  [ 43, 1, 1, 32 ] ]

    k = 2: F-action on Pi is ()      [51,1,2]
      Dynkin type is A_3(q) + A_2(q) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q^2-8*q+19 )
        q congruent 2 modulo 60:   1/8 q ( q^2-8*q+12 )
        q congruent 3 modulo 60:   1/8 ( q^3-9*q^2+19*q-3 )
        q congruent 4 modulo 60:   1/8 q ( q^2-8*q+16 )
        q congruent 5 modulo 60:   1/8 phi1 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/8 ( q^3-9*q^2+23*q-7 )
        q congruent 8 modulo 60:   1/8 q ( q^2-8*q+12 )
        q congruent 9 modulo 60:   1/8 phi1 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/8 ( q^3-9*q^2+19*q-3 )
        q congruent 13 modulo 60:   1/8 phi1 ( q^2-8*q+19 )
        q congruent 16 modulo 60:   1/8 q ( q^2-8*q+16 )
        q congruent 17 modulo 60:   1/8 phi1 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/8 ( q^3-9*q^2+23*q-7 )
        q congruent 21 modulo 60:   1/8 phi1 ( q^2-8*q+15 )
        q congruent 23 modulo 60:   1/8 ( q^3-9*q^2+19*q-3 )
        q congruent 25 modulo 60:   1/8 phi1 ( q^2-8*q+19 )
        q congruent 27 modulo 60:   1/8 ( q^3-9*q^2+19*q-3 )
        q congruent 29 modulo 60:   1/8 phi1 ( q^2-8*q+15 )
        q congruent 31 modulo 60:   1/8 ( q^3-9*q^2+23*q-7 )
        q congruent 32 modulo 60:   1/8 q ( q^2-8*q+12 )
        q congruent 37 modulo 60:   1/8 phi1 ( q^2-8*q+19 )
        q congruent 41 modulo 60:   1/8 phi1 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/8 ( q^3-9*q^2+23*q-7 )
        q congruent 47 modulo 60:   1/8 ( q^3-9*q^2+19*q-3 )
        q congruent 49 modulo 60:   1/8 phi1 ( q^2-8*q+19 )
        q congruent 53 modulo 60:   1/8 phi1 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/8 ( q^3-9*q^2+19*q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 77, 4, 68, 30, 68, 7, 81, 77, 30, 83, 19, 76, 59 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], 
  [ 5, 1, 1, 8 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 4 ], 
  [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 12, 1, 1, 2 ], 
  [ 14, 1, 1, 4 ], [ 15, 1, 1, 4 ], [ 16, 1, 1, 4 ], [ 18, 1, 1, 4 ], 
  [ 20, 1, 1, 8 ], [ 20, 1, 2, 8 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 4 ], 
  [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 3, 8 ], [ 29, 1, 2, 8 ], 
  [ 31, 1, 1, 4 ], [ 31, 1, 2, 4 ], [ 36, 1, 2, 8 ], [ 39, 1, 4, 4 ], 
  [ 43, 1, 2, 16 ] ]

    k = 3: F-action on Pi is (6,7)      [51,1,3]
      Dynkin type is A_3(q) + ^2A_2(q) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 2 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 4 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 5 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 7 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 8 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 11 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 13 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 16 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 17 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 19 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 21 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 23 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 25 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 27 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 29 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 31 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 32 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 41 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 43 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 47 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 49 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 53 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 59 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 68, 28, 69, 7, 82, 5, 69, 31, 27, 81, 36, 71, 20, 98 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 6 ], 
  [ 9, 1, 1, 3 ], [ 12, 1, 2, 6 ], [ 16, 1, 4, 4 ], [ 23, 1, 1, 2 ], 
  [ 23, 1, 2, 6 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 4 ], [ 25, 1, 3, 12 ], 
  [ 25, 1, 4, 4 ], [ 37, 1, 2, 8 ], [ 39, 1, 2, 4 ], [ 40, 1, 2, 4 ], 
  [ 40, 1, 6, 12 ], [ 43, 1, 8, 8 ] ]

    k = 4: F-action on Pi is (6,7)      [51,1,4]
      Dynkin type is A_3(q) + ^2A_2(q) + T(phi2 phi4)
      Order of center |Z^F|: phi2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1^2 phi2
        q congruent 2 modulo 60:   1/8 q^3
        q congruent 3 modulo 60:   1/8 phi1^2 phi2
        q congruent 4 modulo 60:   1/8 q^3
        q congruent 5 modulo 60:   1/8 phi1^2 phi2
        q congruent 7 modulo 60:   1/8 phi1^2 phi2
        q congruent 8 modulo 60:   1/8 q^3
        q congruent 9 modulo 60:   1/8 phi1^2 phi2
        q congruent 11 modulo 60:   1/8 phi1^2 phi2
        q congruent 13 modulo 60:   1/8 phi1^2 phi2
        q congruent 16 modulo 60:   1/8 q^3
        q congruent 17 modulo 60:   1/8 phi1^2 phi2
        q congruent 19 modulo 60:   1/8 phi1^2 phi2
        q congruent 21 modulo 60:   1/8 phi1^2 phi2
        q congruent 23 modulo 60:   1/8 phi1^2 phi2
        q congruent 25 modulo 60:   1/8 phi1^2 phi2
        q congruent 27 modulo 60:   1/8 phi1^2 phi2
        q congruent 29 modulo 60:   1/8 phi1^2 phi2
        q congruent 31 modulo 60:   1/8 phi1^2 phi2
        q congruent 32 modulo 60:   1/8 q^3
        q congruent 37 modulo 60:   1/8 phi1^2 phi2
        q congruent 41 modulo 60:   1/8 phi1^2 phi2
        q congruent 43 modulo 60:   1/8 phi1^2 phi2
        q congruent 47 modulo 60:   1/8 phi1^2 phi2
        q congruent 49 modulo 60:   1/8 phi1^2 phi2
        q congruent 53 modulo 60:   1/8 phi1^2 phi2
        q congruent 59 modulo 60:   1/8 phi1^2 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 72, 19, 96, 20, 76, 60, 71, 20, 98, 95, 59, 99, 17, 74, 54 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], 
  [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ], [ 16, 1, 4, 4 ], [ 39, 1, 5, 4 ], 
  [ 43, 1, 9, 8 ] ]

    k = 5: F-action on Pi is ()      [51,1,5]
      Dynkin type is A_3(q) + A_2(q) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q^2-4*q+7 )
        q congruent 2 modulo 60:   1/16 q ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/16 phi1^2 ( q-3 )
        q congruent 4 modulo 60:   1/16 q ( q^2-4*q+4 )
        q congruent 5 modulo 60:   1/16 phi1 ( q^2-4*q+7 )
        q congruent 7 modulo 60:   1/16 phi1^2 ( q-3 )
        q congruent 8 modulo 60:   1/16 q ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/16 phi1 ( q^2-4*q+7 )
        q congruent 11 modulo 60:   1/16 phi1^2 ( q-3 )
        q congruent 13 modulo 60:   1/16 phi1 ( q^2-4*q+7 )
        q congruent 16 modulo 60:   1/16 q ( q^2-4*q+4 )
        q congruent 17 modulo 60:   1/16 phi1 ( q^2-4*q+7 )
        q congruent 19 modulo 60:   1/16 phi1^2 ( q-3 )
        q congruent 21 modulo 60:   1/16 phi1 ( q^2-4*q+7 )
        q congruent 23 modulo 60:   1/16 phi1^2 ( q-3 )
        q congruent 25 modulo 60:   1/16 phi1 ( q^2-4*q+7 )
        q congruent 27 modulo 60:   1/16 phi1^2 ( q-3 )
        q congruent 29 modulo 60:   1/16 phi1 ( q^2-4*q+7 )
        q congruent 31 modulo 60:   1/16 phi1^2 ( q-3 )
        q congruent 32 modulo 60:   1/16 q ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/16 phi1 ( q^2-4*q+7 )
        q congruent 41 modulo 60:   1/16 phi1 ( q^2-4*q+7 )
        q congruent 43 modulo 60:   1/16 phi1^2 ( q-3 )
        q congruent 47 modulo 60:   1/16 phi1^2 ( q-3 )
        q congruent 49 modulo 60:   1/16 phi1 ( q^2-4*q+7 )
        q congruent 53 modulo 60:   1/16 phi1 ( q^2-4*q+7 )
        q congruent 59 modulo 60:   1/16 phi1^2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 68, 30, 68, 7, 81, 3, 69, 27, 30, 81, 37, 72, 20, 95 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], 
  [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], [ 12, 1, 1, 2 ], 
  [ 16, 1, 1, 4 ], [ 20, 1, 2, 16 ], [ 22, 1, 2, 8 ], [ 23, 1, 2, 4 ], 
  [ 24, 1, 2, 4 ], [ 25, 1, 4, 16 ], [ 31, 1, 2, 8 ], [ 39, 1, 3, 8 ], 
  [ 40, 1, 3, 8 ], [ 43, 1, 12, 32 ] ]

    k = 6: F-action on Pi is (1,4)      [51,1,6]
      Dynkin type is ^2A_3(q) + A_2(q) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 2 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 4 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 7 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 8 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 11 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 13 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 16 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 19 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 21 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 23 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 25 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 27 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 29 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 31 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 32 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 41 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 43 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 47 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 49 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 53 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 59 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 69, 27, 68, 7, 81, 4, 68, 30, 28, 82, 36, 70, 19, 97 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 2 ], 
  [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 16, 1, 2, 4 ], [ 23, 1, 1, 6 ], 
  [ 23, 1, 2, 2 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 4 ], [ 25, 1, 3, 4 ], 
  [ 25, 1, 4, 4 ], [ 37, 1, 2, 8 ], [ 39, 1, 2, 4 ], [ 40, 1, 1, 12 ], 
  [ 40, 1, 3, 4 ], [ 43, 1, 8, 8 ] ]

    k = 7: F-action on Pi is (1,4)      [51,1,7]
      Dynkin type is ^2A_3(q) + A_2(q) + T(phi1 phi4)
      Order of center |Z^F|: phi1 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 2 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 3 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 4 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 5 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 7 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 8 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 9 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 11 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 16 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 17 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 19 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 23 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 27 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 31 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 32 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 37 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 41 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 43 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 53 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 59 modulo 60:   1/8 phi1 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 72, 20, 95, 19, 76, 59, 70, 19, 97, 96, 60, 99, 16, 73, 53 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], 
  [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 39, 1, 5, 4 ], 
  [ 43, 1, 9, 8 ] ]

    k = 8: F-action on Pi is (1,4)(6,7)      [51,1,8]
      Dynkin type is ^2A_3(q) + ^2A_2(q) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q^2-6*q+9 )
        q congruent 2 modulo 60:   1/8 ( q^3-6*q^2+12*q-8 )
        q congruent 3 modulo 60:   1/8 ( q^3-7*q^2+19*q-21 )
        q congruent 4 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/8 ( q^3-7*q^2+19*q-21 )
        q congruent 7 modulo 60:   1/8 ( q^3-7*q^2+19*q-21 )
        q congruent 8 modulo 60:   1/8 ( q^3-6*q^2+12*q-8 )
        q congruent 9 modulo 60:   1/8 phi1 ( q^2-6*q+9 )
        q congruent 11 modulo 60:   1/8 ( q^3-7*q^2+23*q-33 )
        q congruent 13 modulo 60:   1/8 phi1 ( q^2-6*q+9 )
        q congruent 16 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/8 ( q^3-7*q^2+19*q-21 )
        q congruent 19 modulo 60:   1/8 ( q^3-7*q^2+19*q-21 )
        q congruent 21 modulo 60:   1/8 phi1 ( q^2-6*q+9 )
        q congruent 23 modulo 60:   1/8 ( q^3-7*q^2+23*q-33 )
        q congruent 25 modulo 60:   1/8 phi1 ( q^2-6*q+9 )
        q congruent 27 modulo 60:   1/8 ( q^3-7*q^2+19*q-21 )
        q congruent 29 modulo 60:   1/8 ( q^3-7*q^2+19*q-21 )
        q congruent 31 modulo 60:   1/8 ( q^3-7*q^2+19*q-21 )
        q congruent 32 modulo 60:   1/8 ( q^3-6*q^2+12*q-8 )
        q congruent 37 modulo 60:   1/8 phi1 ( q^2-6*q+9 )
        q congruent 41 modulo 60:   1/8 ( q^3-7*q^2+19*q-21 )
        q congruent 43 modulo 60:   1/8 ( q^3-7*q^2+19*q-21 )
        q congruent 47 modulo 60:   1/8 ( q^3-7*q^2+23*q-33 )
        q congruent 49 modulo 60:   1/8 phi1 ( q^2-6*q+9 )
        q congruent 53 modulo 60:   1/8 ( q^3-7*q^2+19*q-21 )
        q congruent 59 modulo 60:   1/8 ( q^3-7*q^2+23*q-33 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 5, 78, 5, 69, 31, 69, 7, 82, 78, 31, 84, 20, 76, 60 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], 
  [ 5, 1, 2, 8 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 4 ], 
  [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 12, 1, 2, 2 ], 
  [ 14, 1, 2, 4 ], [ 15, 1, 2, 4 ], [ 16, 1, 3, 4 ], [ 18, 1, 2, 4 ], 
  [ 20, 1, 3, 8 ], [ 20, 1, 4, 8 ], [ 22, 1, 3, 4 ], [ 22, 1, 4, 4 ], 
  [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 2, 8 ], [ 29, 1, 3, 8 ], 
  [ 31, 1, 3, 4 ], [ 31, 1, 4, 4 ], [ 36, 1, 3, 8 ], [ 39, 1, 4, 4 ], 
  [ 43, 1, 4, 16 ] ]

    k = 9: F-action on Pi is (1,4)(6,7)      [51,1,9]
      Dynkin type is ^2A_3(q) + ^2A_2(q) + T(phi2^3)
      Order of center |Z^F|: phi2^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q^2-14*q+53 )
        q congruent 2 modulo 60:   1/16 ( q^3-14*q^2+56*q-64 )
        q congruent 3 modulo 60:   1/16 ( q^3-15*q^2+71*q-105 )
        q congruent 4 modulo 60:   1/16 ( q^3-14*q^2+48*q-32 )
        q congruent 5 modulo 60:   1/16 ( q^3-15*q^2+75*q-125 )
        q congruent 7 modulo 60:   1/16 ( q^3-15*q^2+71*q-105 )
        q congruent 8 modulo 60:   1/16 ( q^3-14*q^2+56*q-64 )
        q congruent 9 modulo 60:   1/16 ( q^3-15*q^2+67*q-85 )
        q congruent 11 modulo 60:   1/16 ( q^3-15*q^2+79*q-177 )
        q congruent 13 modulo 60:   1/16 phi1 ( q^2-14*q+53 )
        q congruent 16 modulo 60:   1/16 q ( q^2-14*q+48 )
        q congruent 17 modulo 60:   1/16 ( q^3-15*q^2+75*q-125 )
        q congruent 19 modulo 60:   1/16 ( q^3-15*q^2+71*q-137 )
        q congruent 21 modulo 60:   1/16 phi1 ( q^2-14*q+53 )
        q congruent 23 modulo 60:   1/16 ( q^3-15*q^2+79*q-177 )
        q congruent 25 modulo 60:   1/16 phi1 ( q^2-14*q+53 )
        q congruent 27 modulo 60:   1/16 ( q^3-15*q^2+71*q-105 )
        q congruent 29 modulo 60:   1/16 ( q^3-15*q^2+75*q-157 )
        q congruent 31 modulo 60:   1/16 ( q^3-15*q^2+71*q-105 )
        q congruent 32 modulo 60:   1/16 ( q^3-14*q^2+56*q-64 )
        q congruent 37 modulo 60:   1/16 phi1 ( q^2-14*q+53 )
        q congruent 41 modulo 60:   1/16 ( q^3-15*q^2+75*q-125 )
        q congruent 43 modulo 60:   1/16 ( q^3-15*q^2+71*q-105 )
        q congruent 47 modulo 60:   1/16 ( q^3-15*q^2+79*q-177 )
        q congruent 49 modulo 60:   1/16 ( q^3-15*q^2+67*q-85 )
        q congruent 53 modulo 60:   1/16 ( q^3-15*q^2+75*q-125 )
        q congruent 59 modulo 60:   1/16 ( q^3-15*q^2+79*q-209 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 2, 67, 9, 67, 5, 78, 5, 69, 31, 9, 78, 15, 71, 20, 98 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 12 ], 
  [ 5, 1, 2, 16 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 8 ], 
  [ 9, 1, 1, 5 ], [ 10, 1, 2, 4 ], [ 12, 1, 2, 10 ], [ 14, 1, 2, 24 ], 
  [ 15, 1, 2, 8 ], [ 16, 1, 3, 4 ], [ 18, 1, 2, 8 ], [ 20, 1, 4, 16 ], 
  [ 21, 1, 2, 16 ], [ 22, 1, 4, 8 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 4 ], 
  [ 25, 1, 3, 32 ], [ 26, 1, 4, 16 ], [ 29, 1, 4, 16 ], [ 31, 1, 4, 8 ], 
  [ 36, 1, 4, 16 ], [ 37, 1, 3, 32 ], [ 39, 1, 3, 8 ], [ 40, 1, 6, 24 ], 
  [ 43, 1, 13, 32 ] ]

    k = 10: F-action on Pi is (1,4)(6,7)      [51,1,10]
      Dynkin type is ^2A_3(q) + ^2A_2(q) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 2 modulo 60:   1/16 q ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/16 ( q^3-7*q^2+19*q-21 )
        q congruent 4 modulo 60:   1/16 q ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 7 modulo 60:   1/16 ( q^3-7*q^2+19*q-21 )
        q congruent 8 modulo 60:   1/16 q ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 11 modulo 60:   1/16 ( q^3-7*q^2+19*q-21 )
        q congruent 13 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 16 modulo 60:   1/16 q ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 19 modulo 60:   1/16 ( q^3-7*q^2+19*q-21 )
        q congruent 21 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 23 modulo 60:   1/16 ( q^3-7*q^2+19*q-21 )
        q congruent 25 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 27 modulo 60:   1/16 ( q^3-7*q^2+19*q-21 )
        q congruent 29 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 31 modulo 60:   1/16 ( q^3-7*q^2+19*q-21 )
        q congruent 32 modulo 60:   1/16 q ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 41 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 43 modulo 60:   1/16 ( q^3-7*q^2+19*q-21 )
        q congruent 47 modulo 60:   1/16 ( q^3-7*q^2+19*q-21 )
        q congruent 49 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 53 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 59 modulo 60:   1/16 ( q^3-7*q^2+19*q-21 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 69, 31, 69, 7, 82, 3, 68, 28, 31, 82, 38, 72, 19, 96 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], 
  [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], [ 12, 1, 2, 2 ], 
  [ 16, 1, 3, 4 ], [ 20, 1, 3, 16 ], [ 22, 1, 3, 8 ], [ 23, 1, 1, 4 ], 
  [ 24, 1, 1, 4 ], [ 25, 1, 2, 16 ], [ 31, 1, 3, 8 ], [ 39, 1, 1, 8 ], 
  [ 40, 1, 2, 8 ], [ 43, 1, 3, 32 ] ]

i = 52: Pi = [ 2, 3, 4, 5, 7 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [52,1,1]
      Dynkin type is D_4(q) + A_1(q) + T(phi1^3)
      Order of center |Z^F|: phi1^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/48 ( q^3-19*q^2+115*q-241 )
        q congruent 2 modulo 60:   1/48 ( q^3-16*q^2+76*q-96 )
        q congruent 3 modulo 60:   1/48 ( q^3-19*q^2+115*q-201 )
        q congruent 4 modulo 60:   1/48 ( q^3-16*q^2+76*q-112 )
        q congruent 5 modulo 60:   1/48 ( q^3-19*q^2+115*q-225 )
        q congruent 7 modulo 60:   1/48 ( q^3-19*q^2+115*q-217 )
        q congruent 8 modulo 60:   1/48 ( q^3-16*q^2+76*q-96 )
        q congruent 9 modulo 60:   1/48 ( q^3-19*q^2+115*q-225 )
        q congruent 11 modulo 60:   1/48 ( q^3-19*q^2+115*q-201 )
        q congruent 13 modulo 60:   1/48 ( q^3-19*q^2+115*q-241 )
        q congruent 16 modulo 60:   1/48 ( q^3-16*q^2+76*q-112 )
        q congruent 17 modulo 60:   1/48 ( q^3-19*q^2+115*q-225 )
        q congruent 19 modulo 60:   1/48 ( q^3-19*q^2+115*q-217 )
        q congruent 21 modulo 60:   1/48 ( q^3-19*q^2+115*q-225 )
        q congruent 23 modulo 60:   1/48 ( q^3-19*q^2+115*q-201 )
        q congruent 25 modulo 60:   1/48 ( q^3-19*q^2+115*q-241 )
        q congruent 27 modulo 60:   1/48 ( q^3-19*q^2+115*q-201 )
        q congruent 29 modulo 60:   1/48 ( q^3-19*q^2+115*q-225 )
        q congruent 31 modulo 60:   1/48 ( q^3-19*q^2+115*q-217 )
        q congruent 32 modulo 60:   1/48 ( q^3-16*q^2+76*q-96 )
        q congruent 37 modulo 60:   1/48 ( q^3-19*q^2+115*q-241 )
        q congruent 41 modulo 60:   1/48 ( q^3-19*q^2+115*q-225 )
        q congruent 43 modulo 60:   1/48 ( q^3-19*q^2+115*q-217 )
        q congruent 47 modulo 60:   1/48 ( q^3-19*q^2+115*q-201 )
        q congruent 49 modulo 60:   1/48 ( q^3-19*q^2+115*q-241 )
        q congruent 53 modulo 60:   1/48 ( q^3-19*q^2+115*q-225 )
        q congruent 59 modulo 60:   1/48 ( q^3-19*q^2+115*q-201 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 4, 68, 3, 69, 66, 4, 70, 19, 68, 7, 4, 68, 4, 68, 16, 73, 8, 
  77, 28, 82, 70, 19, 70, 19 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 12 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], 
  [ 13, 1, 1, 24 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 18 ], [ 25, 1, 1, 24 ], 
  [ 28, 1, 1, 24 ], [ 39, 1, 1, 24 ], [ 40, 1, 1, 48 ], [ 41, 1, 1, 48 ] ]

    k = 2: F-action on Pi is ()      [52,1,2]
      Dynkin type is D_4(q) + A_1(q) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 2 modulo 60:   1/16 q ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 4 modulo 60:   1/16 q ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 8 modulo 60:   1/16 q ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 13 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 16 modulo 60:   1/16 q ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 21 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 23 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 25 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 27 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 29 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 31 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 32 modulo 60:   1/16 q ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 41 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 47 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 49 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 53 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 68, 7, 69, 5, 4, 68, 19, 76, 7, 69, 68, 3, 68, 7, 73, 18, 
  77, 30, 82, 31, 19, 72, 19, 76 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 9, 1, 1, 3 ], 
  [ 10, 1, 1, 4 ], [ 10, 1, 2, 2 ], [ 13, 1, 1, 8 ], [ 23, 1, 1, 4 ], 
  [ 24, 1, 1, 12 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 8 ], [ 28, 1, 2, 8 ], 
  [ 39, 1, 1, 8 ], [ 39, 1, 4, 8 ], [ 41, 1, 1, 16 ], [ 41, 1, 6, 16 ] ]

    k = 3: F-action on Pi is (2,5)      [52,1,3]
      Dynkin type is ^2D_4(q) + A_1(q) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 2 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 4 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 7 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 8 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 11 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 13 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 16 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 19 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 21 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 23 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 25 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 27 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 29 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 31 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 32 modulo 60:   1/8 q ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 41 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 43 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 47 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
        q congruent 49 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 53 modulo 60:   1/8 phi1 ( q^2-6*q+7 )
        q congruent 59 modulo 60:   1/8 ( q^3-7*q^2+13*q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 68, 3, 69, 70, 19, 68, 7, 72, 20, 19, 76, 28, 82, 30, 81, 89, 43 
 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], 
  [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 4 ], 
  [ 12, 1, 1, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 1, 2 ], 
  [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 25, 1, 4, 4 ], 
  [ 28, 1, 1, 4 ], [ 28, 1, 3, 4 ], [ 39, 1, 2, 4 ], [ 40, 1, 3, 8 ], 
  [ 41, 1, 4, 8 ] ]

    k = 4: F-action on Pi is (2,5)      [52,1,4]
      Dynkin type is ^2D_4(q) + A_1(q) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 2 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 4 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 5 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 7 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 8 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 11 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 13 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 16 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 17 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 19 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 21 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 23 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 25 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 27 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 29 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 31 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 32 modulo 60:   1/8 q ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 41 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 43 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 47 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
        q congruent 49 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 53 modulo 60:   1/8 phi1 ( q^2-4*q+5 )
        q congruent 59 modulo 60:   1/8 ( q^3-5*q^2+9*q-9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 3, 69, 5, 19, 72, 7, 69, 20, 71, 76, 20, 82, 31, 81, 27, 43, 90 
 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 2 ], 
  [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], 
  [ 12, 1, 2, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 1, 2 ], 
  [ 23, 1, 2, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], [ 25, 1, 4, 4 ], 
  [ 28, 1, 2, 4 ], [ 28, 1, 4, 4 ], [ 39, 1, 2, 4 ], [ 40, 1, 2, 8 ], 
  [ 41, 1, 4, 8 ] ]

    k = 5: F-action on Pi is (3,5)      [52,1,5]
      Dynkin type is ^2D_4(q) + A_1(q) + T(phi2 phi4)
      Order of center |Z^F|: phi2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1^2 phi2
        q congruent 2 modulo 60:   1/8 q^3
        q congruent 3 modulo 60:   1/8 phi1^2 phi2
        q congruent 4 modulo 60:   1/8 q^3
        q congruent 5 modulo 60:   1/8 phi1^2 phi2
        q congruent 7 modulo 60:   1/8 phi1^2 phi2
        q congruent 8 modulo 60:   1/8 q^3
        q congruent 9 modulo 60:   1/8 phi1^2 phi2
        q congruent 11 modulo 60:   1/8 phi1^2 phi2
        q congruent 13 modulo 60:   1/8 phi1^2 phi2
        q congruent 16 modulo 60:   1/8 q^3
        q congruent 17 modulo 60:   1/8 phi1^2 phi2
        q congruent 19 modulo 60:   1/8 phi1^2 phi2
        q congruent 21 modulo 60:   1/8 phi1^2 phi2
        q congruent 23 modulo 60:   1/8 phi1^2 phi2
        q congruent 25 modulo 60:   1/8 phi1^2 phi2
        q congruent 27 modulo 60:   1/8 phi1^2 phi2
        q congruent 29 modulo 60:   1/8 phi1^2 phi2
        q congruent 31 modulo 60:   1/8 phi1^2 phi2
        q congruent 32 modulo 60:   1/8 q^3
        q congruent 37 modulo 60:   1/8 phi1^2 phi2
        q congruent 41 modulo 60:   1/8 phi1^2 phi2
        q congruent 43 modulo 60:   1/8 phi1^2 phi2
        q congruent 47 modulo 60:   1/8 phi1^2 phi2
        q congruent 49 modulo 60:   1/8 phi1^2 phi2
        q congruent 53 modulo 60:   1/8 phi1^2 phi2
        q congruent 59 modulo 60:   1/8 phi1^2 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 19, 72, 20, 71, 73, 18, 76, 20, 74, 17, 18, 74, 60, 98, 59, 95, 91, 
  45 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], 
  [ 24, 1, 2, 2 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ] ]

    k = 6: F-action on Pi is (2,3,5)      [52,1,6]
      Dynkin type is ^3D_4(q) + A_1(q) + T(phi1 phi3)
      Order of center |Z^F|: phi1 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 2 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 3 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 4 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 5 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 7 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 8 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 9 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 11 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 13 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 16 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 17 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 19 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 21 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 23 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 25 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 27 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 29 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 31 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 32 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 37 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 41 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 43 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 47 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 49 modulo 60:   1/6 phi1 ( q^2-2 )
        q congruent 53 modulo 60:   1/6 q phi2 ( q-2 )
        q congruent 59 modulo 60:   1/6 q phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 14, 83, 87, 40, 83, 37, 35, 88, 12, 79, 57, 101, 33, 86 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 11, 1, 1, 2 ], 
  [ 40, 1, 5, 6 ] ]

    k = 7: F-action on Pi is (2,3,5)      [52,1,7]
      Dynkin type is ^3D_4(q) + A_1(q) + T(phi2 phi6)
      Order of center |Z^F|: phi2 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/6 q^2 phi1
        q congruent 2 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 3 modulo 60:   1/6 q^2 phi1
        q congruent 4 modulo 60:   1/6 q^2 phi1
        q congruent 5 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 7 modulo 60:   1/6 q^2 phi1
        q congruent 8 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 9 modulo 60:   1/6 q^2 phi1
        q congruent 11 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 13 modulo 60:   1/6 q^2 phi1
        q congruent 16 modulo 60:   1/6 q^2 phi1
        q congruent 17 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 19 modulo 60:   1/6 q^2 phi1
        q congruent 21 modulo 60:   1/6 q^2 phi1
        q congruent 23 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 25 modulo 60:   1/6 q^2 phi1
        q congruent 27 modulo 60:   1/6 q^2 phi1
        q congruent 29 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 31 modulo 60:   1/6 q^2 phi1
        q congruent 32 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 37 modulo 60:   1/6 q^2 phi1
        q congruent 41 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 43 modulo 60:   1/6 q^2 phi1
        q congruent 47 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 49 modulo 60:   1/6 q^2 phi1
        q congruent 53 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
        q congruent 59 modulo 60:   1/6 phi2 ( q^2-2*q+2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 87, 35, 38, 84, 40, 88, 84, 15, 85, 34, 102, 58, 80, 13 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 11, 1, 2, 2 ], 
  [ 40, 1, 4, 6 ] ]

    k = 8: F-action on Pi is (2,3)      [52,1,8]
      Dynkin type is ^2D_4(q) + A_1(q) + T(phi1 phi4)
      Order of center |Z^F|: phi1 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 2 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 3 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 4 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 5 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 7 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 8 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 9 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 11 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 16 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 17 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 19 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 23 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 27 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 31 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 32 modulo 60:   1/8 q^2 ( q-2 )
        q congruent 37 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 41 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 43 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 53 modulo 60:   1/8 phi1 phi2 ( q-3 )
        q congruent 59 modulo 60:   1/8 phi1 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 70, 19, 72, 20, 16, 73, 19, 76, 18, 74, 73, 18, 96, 60, 97, 59, 44, 
  91 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], 
  [ 24, 1, 1, 2 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ] ]

    k = 9: F-action on Pi is ()      [52,1,9]
      Dynkin type is D_4(q) + A_1(q) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 2 modulo 60:   1/16 q ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 4 modulo 60:   1/16 q ( q^2-4*q+4 )
        q congruent 5 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 7 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 8 modulo 60:   1/16 q ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 11 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 13 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 16 modulo 60:   1/16 q ( q^2-4*q+4 )
        q congruent 17 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 19 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 21 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 23 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 25 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 27 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 31 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 32 modulo 60:   1/16 q ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 41 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 43 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 47 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 49 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 53 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 59 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 68, 7, 69, 5, 67, 68, 7, 76, 20, 69, 5, 7, 69, 3, 69, 18, 74, 
  30, 81, 31, 78, 76, 20, 72, 20 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], 
  [ 10, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 13, 1, 4, 8 ], [ 23, 1, 2, 4 ], 
  [ 24, 1, 1, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 3, 8 ], [ 28, 1, 3, 8 ], 
  [ 39, 1, 3, 8 ], [ 39, 1, 4, 8 ], [ 41, 1, 6, 16 ], [ 41, 1, 9, 16 ] ]

    k = 10: F-action on Pi is ()      [52,1,10]
      Dynkin type is D_4(q) + A_1(q) + T(phi2^3)
      Order of center |Z^F|: phi2^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/48 phi1 ( q^2-12*q+39 )
        q congruent 2 modulo 60:   1/48 ( q^3-10*q^2+24*q-16 )
        q congruent 3 modulo 60:   1/48 ( q^3-13*q^2+51*q-63 )
        q congruent 4 modulo 60:   1/48 q ( q^2-10*q+24 )
        q congruent 5 modulo 60:   1/48 ( q^3-13*q^2+51*q-55 )
        q congruent 7 modulo 60:   1/48 ( q^3-13*q^2+51*q-63 )
        q congruent 8 modulo 60:   1/48 ( q^3-10*q^2+24*q-16 )
        q congruent 9 modulo 60:   1/48 phi1 ( q^2-12*q+39 )
        q congruent 11 modulo 60:   1/48 ( q^3-13*q^2+51*q-79 )
        q congruent 13 modulo 60:   1/48 phi1 ( q^2-12*q+39 )
        q congruent 16 modulo 60:   1/48 q ( q^2-10*q+24 )
        q congruent 17 modulo 60:   1/48 ( q^3-13*q^2+51*q-55 )
        q congruent 19 modulo 60:   1/48 ( q^3-13*q^2+51*q-63 )
        q congruent 21 modulo 60:   1/48 phi1 ( q^2-12*q+39 )
        q congruent 23 modulo 60:   1/48 ( q^3-13*q^2+51*q-79 )
        q congruent 25 modulo 60:   1/48 phi1 ( q^2-12*q+39 )
        q congruent 27 modulo 60:   1/48 ( q^3-13*q^2+51*q-63 )
        q congruent 29 modulo 60:   1/48 ( q^3-13*q^2+51*q-55 )
        q congruent 31 modulo 60:   1/48 ( q^3-13*q^2+51*q-63 )
        q congruent 32 modulo 60:   1/48 ( q^3-10*q^2+24*q-16 )
        q congruent 37 modulo 60:   1/48 phi1 ( q^2-12*q+39 )
        q congruent 41 modulo 60:   1/48 ( q^3-13*q^2+51*q-55 )
        q congruent 43 modulo 60:   1/48 ( q^3-13*q^2+51*q-63 )
        q congruent 47 modulo 60:   1/48 ( q^3-13*q^2+51*q-79 )
        q congruent 49 modulo 60:   1/48 phi1 ( q^2-12*q+39 )
        q congruent 53 modulo 60:   1/48 ( q^3-13*q^2+51*q-55 )
        q congruent 59 modulo 60:   1/48 ( q^3-13*q^2+51*q-79 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 3, 69, 5, 67, 2, 7, 69, 20, 71, 5, 67, 69, 5, 69, 5, 74, 17, 
  81, 27, 78, 9, 20, 71, 20, 71 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 12 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 24 ], 
  [ 13, 1, 4, 24 ], [ 23, 1, 2, 12 ], [ 24, 1, 2, 18 ], [ 25, 1, 3, 24 ], 
  [ 28, 1, 4, 24 ], [ 39, 1, 3, 24 ], [ 40, 1, 6, 48 ], [ 41, 1, 9, 48 ] ]

i = 53: Pi = [ 2, 4, 5, 7, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [53,1,1]
      Dynkin type is A_3(q) + A_1(q) + A_1(q) + T(phi1^3)
      Order of center |Z^F|: phi1^3 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/96 ( q^3-23*q^2+171*q-437 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/96 ( q^3-23*q^2+159*q-297 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/96 ( q^3-23*q^2+171*q-405 )
        q congruent 7 modulo 60:   1/96 ( q^3-23*q^2+159*q-329 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/96 ( q^3-23*q^2+171*q-405 )
        q congruent 11 modulo 60:   1/96 ( q^3-23*q^2+159*q-297 )
        q congruent 13 modulo 60:   1/96 ( q^3-23*q^2+171*q-437 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/96 ( q^3-23*q^2+171*q-405 )
        q congruent 19 modulo 60:   1/96 ( q^3-23*q^2+159*q-329 )
        q congruent 21 modulo 60:   1/96 ( q^3-23*q^2+171*q-405 )
        q congruent 23 modulo 60:   1/96 ( q^3-23*q^2+159*q-297 )
        q congruent 25 modulo 60:   1/96 ( q^3-23*q^2+171*q-437 )
        q congruent 27 modulo 60:   1/96 ( q^3-23*q^2+159*q-297 )
        q congruent 29 modulo 60:   1/96 ( q^3-23*q^2+171*q-405 )
        q congruent 31 modulo 60:   1/96 ( q^3-23*q^2+159*q-329 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/96 ( q^3-23*q^2+171*q-437 )
        q congruent 41 modulo 60:   1/96 ( q^3-23*q^2+171*q-405 )
        q congruent 43 modulo 60:   1/96 ( q^3-23*q^2+159*q-329 )
        q congruent 47 modulo 60:   1/96 ( q^3-23*q^2+159*q-297 )
        q congruent 49 modulo 60:   1/96 ( q^3-23*q^2+171*q-437 )
        q congruent 53 modulo 60:   1/96 ( q^3-23*q^2+171*q-405 )
        q congruent 59 modulo 60:   1/96 ( q^3-23*q^2+159*q-297 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 66, 4, 4, 68, 4, 68, 68, 3, 8, 77, 77, 30, 70, 19, 
  19, 72 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 10 ], 
  [ 6, 1, 1, 16 ], [ 7, 1, 1, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 12 ], 
  [ 11, 1, 1, 24 ], [ 12, 1, 1, 8 ], [ 13, 1, 1, 24 ], [ 16, 1, 1, 16 ], 
  [ 19, 1, 1, 48 ], [ 20, 1, 1, 48 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 36 ], 
  [ 25, 1, 1, 36 ], [ 26, 1, 1, 48 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 24 ], 
  [ 35, 1, 1, 48 ], [ 39, 1, 1, 24 ], [ 41, 1, 1, 48 ], [ 42, 1, 1, 96 ], 
  [ 43, 1, 1, 96 ], [ 44, 1, 1, 48 ] ]

    k = 2: F-action on Pi is (  7,240)      [53,1,2]
      Dynkin type is A_3(q) + A_1(q^2) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/32 ( q^3-9*q^2+19*q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/32 ( q^3-9*q^2+19*q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/32 ( q^3-9*q^2+19*q-3 )
        q congruent 13 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/32 ( q^3-9*q^2+19*q-3 )
        q congruent 21 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 23 modulo 60:   1/32 ( q^3-9*q^2+19*q-3 )
        q congruent 25 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 27 modulo 60:   1/32 ( q^3-9*q^2+19*q-3 )
        q congruent 29 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 31 modulo 60:   1/32 ( q^3-9*q^2+19*q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 41 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/32 ( q^3-9*q^2+19*q-3 )
        q congruent 47 modulo 60:   1/32 ( q^3-9*q^2+19*q-3 )
        q congruent 49 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 53 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/32 ( q^3-9*q^2+19*q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 70, 68, 19, 3, 72, 30, 97, 72, 18 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 6 ], 
  [ 7, 1, 1, 8 ], [ 9, 1, 1, 5 ], [ 10, 1, 1, 4 ], [ 13, 1, 2, 4 ], 
  [ 13, 1, 3, 16 ], [ 13, 1, 4, 4 ], [ 20, 1, 1, 16 ], [ 23, 1, 1, 4 ], 
  [ 23, 1, 2, 2 ], [ 24, 1, 1, 4 ], [ 25, 1, 1, 16 ], [ 25, 1, 2, 8 ], 
  [ 25, 1, 3, 8 ], [ 25, 1, 4, 4 ], [ 26, 1, 1, 16 ], [ 28, 1, 3, 8 ], 
  [ 35, 1, 2, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 8 ], [ 41, 1, 2, 16 ], 
  [ 41, 1, 3, 16 ], [ 43, 1, 1, 32 ], [ 43, 1, 8, 16 ], [ 44, 1, 9, 16 ] ]

    k = 3: F-action on Pi is ()      [53,1,3]
      Dynkin type is A_3(q) + A_1(q) + A_1(q) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 ( q^3-9*q^2+19*q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/16 ( q^3-9*q^2+19*q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/16 ( q^3-9*q^2+19*q-3 )
        q congruent 13 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/16 ( q^3-9*q^2+19*q-3 )
        q congruent 21 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 23 modulo 60:   1/16 ( q^3-9*q^2+19*q-3 )
        q congruent 25 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 27 modulo 60:   1/16 ( q^3-9*q^2+19*q-3 )
        q congruent 29 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 31 modulo 60:   1/16 ( q^3-9*q^2+19*q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 41 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/16 ( q^3-9*q^2+19*q-3 )
        q congruent 47 modulo 60:   1/16 ( q^3-9*q^2+19*q-3 )
        q congruent 49 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 53 modulo 60:   1/16 phi1 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/16 ( q^3-9*q^2+19*q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 4, 68, 4, 68, 68, 7, 68, 7, 7, 69, 77, 30, 30, 81, 19, 76, 
  76, 20 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 6 ], 
  [ 6, 1, 1, 8 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 13, 1, 1, 8 ], 
  [ 16, 1, 1, 8 ], [ 19, 1, 1, 8 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 8 ], 
  [ 23, 1, 1, 2 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 4 ], 
  [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 4 ], 
  [ 35, 1, 1, 8 ], [ 35, 1, 3, 8 ], [ 39, 1, 4, 4 ], [ 41, 1, 6, 8 ], 
  [ 42, 1, 4, 16 ], [ 43, 1, 2, 16 ], [ 44, 1, 2, 8 ] ]

    k = 4: F-action on Pi is (  7,240)      [53,1,4]
      Dynkin type is A_3(q) + A_1(q^2) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^3
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1^3
        q congruent 7 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1^3
        q congruent 11 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/16 phi1^3
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1^3
        q congruent 19 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/16 phi1^3
        q congruent 23 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/16 phi1^3
        q congruent 27 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/16 phi1^3
        q congruent 31 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1^3
        q congruent 41 modulo 60:   1/16 phi1^3
        q congruent 43 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/16 phi1^3
        q congruent 53 modulo 60:   1/16 phi1^3
        q congruent 59 modulo 60:   1/16 phi1 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 19, 7, 76, 69, 20, 81, 59, 20, 74 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], 
  [ 4, 1, 2, 2 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 2, 4 ], 
  [ 13, 1, 4, 4 ], [ 16, 1, 4, 8 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 8 ], 
  [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 4, 4 ], 
  [ 26, 1, 3, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], 
  [ 35, 1, 2, 8 ], [ 35, 1, 4, 8 ], [ 39, 1, 4, 4 ], [ 41, 1, 7, 8 ], 
  [ 43, 1, 2, 16 ], [ 44, 1, 8, 8 ] ]

    k = 5: F-action on Pi is (  2,  5)(  7,240)      [53,1,5]
      Dynkin type is ^2A_3(q) + A_1(q^2) + T(phi1^3)
      Order of center |Z^F|: phi1^3 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/96 phi1 ( q^2-14*q+45 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/96 ( q^3-15*q^2+71*q-105 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/96 phi1 ( q^2-14*q+45 )
        q congruent 7 modulo 60:   1/96 ( q^3-15*q^2+71*q-105 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/96 phi1 ( q^2-14*q+45 )
        q congruent 11 modulo 60:   1/96 ( q^3-15*q^2+71*q-105 )
        q congruent 13 modulo 60:   1/96 phi1 ( q^2-14*q+45 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/96 phi1 ( q^2-14*q+45 )
        q congruent 19 modulo 60:   1/96 ( q^3-15*q^2+71*q-105 )
        q congruent 21 modulo 60:   1/96 phi1 ( q^2-14*q+45 )
        q congruent 23 modulo 60:   1/96 ( q^3-15*q^2+71*q-105 )
        q congruent 25 modulo 60:   1/96 phi1 ( q^2-14*q+45 )
        q congruent 27 modulo 60:   1/96 ( q^3-15*q^2+71*q-105 )
        q congruent 29 modulo 60:   1/96 phi1 ( q^2-14*q+45 )
        q congruent 31 modulo 60:   1/96 ( q^3-15*q^2+71*q-105 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/96 phi1 ( q^2-14*q+45 )
        q congruent 41 modulo 60:   1/96 phi1 ( q^2-14*q+45 )
        q congruent 43 modulo 60:   1/96 ( q^3-15*q^2+71*q-105 )
        q congruent 47 modulo 60:   1/96 ( q^3-15*q^2+71*q-105 )
        q congruent 49 modulo 60:   1/96 phi1 ( q^2-14*q+45 )
        q congruent 53 modulo 60:   1/96 phi1 ( q^2-14*q+45 )
        q congruent 59 modulo 60:   1/96 ( q^3-15*q^2+71*q-105 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 72, 68, 19, 4, 70, 28, 96, 70, 16 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 2 ], 
  [ 4, 1, 2, 8 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], 
  [ 12, 1, 1, 8 ], [ 13, 1, 1, 12 ], [ 13, 1, 3, 12 ], [ 16, 1, 2, 16 ], 
  [ 20, 1, 3, 48 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 12 ], [ 25, 1, 2, 36 ], 
  [ 27, 1, 1, 48 ], [ 28, 1, 1, 24 ], [ 35, 1, 5, 48 ], [ 39, 1, 1, 24 ], 
  [ 41, 1, 3, 48 ], [ 43, 1, 3, 96 ], [ 44, 1, 1, 48 ] ]

    k = 6: F-action on Pi is (2,5)      [53,1,6]
      Dynkin type is ^2A_3(q) + A_1(q) + A_1(q) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/32 ( q^3-9*q^2+27*q-27 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/32 ( q^3-9*q^2+27*q-27 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/32 ( q^3-9*q^2+27*q-27 )
        q congruent 13 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/32 ( q^3-9*q^2+27*q-27 )
        q congruent 21 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 23 modulo 60:   1/32 ( q^3-9*q^2+27*q-27 )
        q congruent 25 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 27 modulo 60:   1/32 ( q^3-9*q^2+27*q-27 )
        q congruent 29 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 31 modulo 60:   1/32 ( q^3-9*q^2+27*q-27 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 41 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/32 ( q^3-9*q^2+27*q-27 )
        q congruent 47 modulo 60:   1/32 ( q^3-9*q^2+27*q-27 )
        q congruent 49 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 53 modulo 60:   1/32 phi1 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/32 ( q^3-9*q^2+27*q-27 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 69, 69, 5, 68, 7, 7, 69, 4, 68, 68, 3, 28, 82, 82, 31, 70, 19, 
  19, 72 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 6 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 3, 8 ], 
  [ 13, 1, 4, 8 ], [ 20, 1, 3, 16 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 2 ], 
  [ 24, 1, 1, 12 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 4 ], 
  [ 25, 1, 4, 8 ], [ 28, 1, 3, 8 ], [ 35, 1, 6, 16 ], [ 39, 1, 1, 8 ], 
  [ 39, 1, 2, 8 ], [ 41, 1, 1, 16 ], [ 41, 1, 4, 16 ], [ 43, 1, 3, 32 ], 
  [ 43, 1, 8, 16 ], [ 44, 1, 9, 16 ] ]

    k = 7: F-action on Pi is (  2,  5)(  7,240)      [53,1,7]
      Dynkin type is ^2A_3(q) + A_1(q^2) + T(phi1^2 phi2)
      Order of center |Z^F|: phi1^2 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q^2-4*q-1 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 phi1^2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1 ( q^2-4*q-1 )
        q congruent 7 modulo 60:   1/16 phi1^2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1 ( q^2-4*q-1 )
        q congruent 11 modulo 60:   1/16 phi1^2 ( q-3 )
        q congruent 13 modulo 60:   1/16 phi1 ( q^2-4*q-1 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1 ( q^2-4*q-1 )
        q congruent 19 modulo 60:   1/16 phi1^2 ( q-3 )
        q congruent 21 modulo 60:   1/16 phi1 ( q^2-4*q-1 )
        q congruent 23 modulo 60:   1/16 phi1^2 ( q-3 )
        q congruent 25 modulo 60:   1/16 phi1 ( q^2-4*q-1 )
        q congruent 27 modulo 60:   1/16 phi1^2 ( q-3 )
        q congruent 29 modulo 60:   1/16 phi1 ( q^2-4*q-1 )
        q congruent 31 modulo 60:   1/16 phi1^2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1 ( q^2-4*q-1 )
        q congruent 41 modulo 60:   1/16 phi1 ( q^2-4*q-1 )
        q congruent 43 modulo 60:   1/16 phi1^2 ( q-3 )
        q congruent 47 modulo 60:   1/16 phi1^2 ( q-3 )
        q congruent 49 modulo 60:   1/16 phi1 ( q^2-4*q-1 )
        q congruent 53 modulo 60:   1/16 phi1 ( q^2-4*q-1 )
        q congruent 59 modulo 60:   1/16 phi1^2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 69, 20, 7, 76, 68, 19, 82, 60, 19, 73 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], 
  [ 4, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 13, 1, 1, 4 ], 
  [ 13, 1, 3, 4 ], [ 16, 1, 2, 8 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 8 ], 
  [ 23, 1, 1, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], 
  [ 26, 1, 2, 8 ], [ 27, 1, 2, 8 ], [ 28, 1, 1, 4 ], [ 28, 1, 2, 4 ], 
  [ 35, 1, 5, 8 ], [ 35, 1, 7, 8 ], [ 39, 1, 4, 4 ], [ 41, 1, 7, 8 ], 
  [ 43, 1, 4, 16 ], [ 44, 1, 2, 8 ] ]

    k = 8: F-action on Pi is (2,5)      [53,1,8]
      Dynkin type is ^2A_3(q) + A_1(q) + A_1(q) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 ( q^3-7*q^2+19*q-21 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 7 modulo 60:   1/16 ( q^3-7*q^2+19*q-21 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 11 modulo 60:   1/16 ( q^3-7*q^2+19*q-21 )
        q congruent 13 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 19 modulo 60:   1/16 ( q^3-7*q^2+19*q-21 )
        q congruent 21 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 23 modulo 60:   1/16 ( q^3-7*q^2+19*q-21 )
        q congruent 25 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 27 modulo 60:   1/16 ( q^3-7*q^2+19*q-21 )
        q congruent 29 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 31 modulo 60:   1/16 ( q^3-7*q^2+19*q-21 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 41 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 43 modulo 60:   1/16 ( q^3-7*q^2+19*q-21 )
        q congruent 47 modulo 60:   1/16 ( q^3-7*q^2+19*q-21 )
        q congruent 49 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 53 modulo 60:   1/16 phi1 ( q^2-6*q+9 )
        q congruent 59 modulo 60:   1/16 ( q^3-7*q^2+19*q-21 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 69, 5, 5, 67, 7, 69, 69, 5, 68, 7, 7, 69, 82, 31, 31, 78, 19, 76, 
  76, 20 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 6 ], 
  [ 6, 1, 2, 8 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 13, 1, 4, 8 ], 
  [ 16, 1, 3, 8 ], [ 19, 1, 2, 8 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 8 ], 
  [ 23, 1, 2, 2 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 3, 4 ], 
  [ 26, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], 
  [ 35, 1, 6, 8 ], [ 35, 1, 8, 8 ], [ 39, 1, 4, 4 ], [ 41, 1, 6, 8 ], 
  [ 42, 1, 2, 16 ], [ 43, 1, 4, 16 ], [ 44, 1, 8, 8 ] ]

    k = 9: F-action on Pi is ()      [53,1,9]
      Dynkin type is A_3(q) + A_1(q) + A_1(q) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 ( q^2-6*q+13 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/32 phi1 ( q^2-6*q+9 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/32 phi1 ( q^2-6*q+13 )
        q congruent 7 modulo 60:   1/32 phi1 ( q^2-6*q+9 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/32 phi1 ( q^2-6*q+13 )
        q congruent 11 modulo 60:   1/32 phi1 ( q^2-6*q+9 )
        q congruent 13 modulo 60:   1/32 phi1 ( q^2-6*q+13 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/32 phi1 ( q^2-6*q+13 )
        q congruent 19 modulo 60:   1/32 phi1 ( q^2-6*q+9 )
        q congruent 21 modulo 60:   1/32 phi1 ( q^2-6*q+13 )
        q congruent 23 modulo 60:   1/32 phi1 ( q^2-6*q+9 )
        q congruent 25 modulo 60:   1/32 phi1 ( q^2-6*q+13 )
        q congruent 27 modulo 60:   1/32 phi1 ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/32 phi1 ( q^2-6*q+13 )
        q congruent 31 modulo 60:   1/32 phi1 ( q^2-6*q+9 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/32 phi1 ( q^2-6*q+13 )
        q congruent 41 modulo 60:   1/32 phi1 ( q^2-6*q+13 )
        q congruent 43 modulo 60:   1/32 phi1 ( q^2-6*q+9 )
        q congruent 47 modulo 60:   1/32 phi1 ( q^2-6*q+9 )
        q congruent 49 modulo 60:   1/32 phi1 ( q^2-6*q+13 )
        q congruent 53 modulo 60:   1/32 phi1 ( q^2-6*q+13 )
        q congruent 59 modulo 60:   1/32 phi1 ( q^2-6*q+9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 68, 68, 3, 68, 7, 7, 69, 3, 69, 69, 5, 30, 81, 81, 27, 72, 20, 
  20, 71 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 4 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 8 ], 
  [ 13, 1, 4, 8 ], [ 20, 1, 2, 16 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 4 ], 
  [ 24, 1, 2, 12 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], 
  [ 25, 1, 4, 16 ], [ 28, 1, 2, 8 ], [ 35, 1, 3, 16 ], [ 39, 1, 2, 8 ], 
  [ 39, 1, 3, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 9, 16 ], [ 43, 1, 8, 16 ], 
  [ 43, 1, 12, 32 ], [ 44, 1, 5, 16 ] ]

    k = 10: F-action on Pi is (  7,240)      [53,1,10]
      Dynkin type is A_3(q) + A_1(q^2) + T(phi1 phi4)
      Order of center |Z^F|: phi1 phi4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 7 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 11 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 19 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 23 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 27 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 31 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 41 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 43 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 53 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 59 modulo 60:   1/16 phi1 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 70, 16, 19, 73, 72, 18, 97, 53, 18, 75 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], 
  [ 13, 1, 3, 8 ], [ 23, 1, 1, 2 ], [ 25, 1, 1, 4 ], [ 39, 1, 5, 4 ], 
  [ 41, 1, 5, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 6, 8 ] ]

    k = 11: F-action on Pi is ()      [53,1,11]
      Dynkin type is A_3(q) + A_1(q) + A_1(q) + T(phi2 phi4)
      Order of center |Z^F|: phi2 phi4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^2 phi2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 phi1^2 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1^2 phi2
        q congruent 7 modulo 60:   1/16 phi1^2 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1^2 phi2
        q congruent 11 modulo 60:   1/16 phi1^2 phi2
        q congruent 13 modulo 60:   1/16 phi1^2 phi2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1^2 phi2
        q congruent 19 modulo 60:   1/16 phi1^2 phi2
        q congruent 21 modulo 60:   1/16 phi1^2 phi2
        q congruent 23 modulo 60:   1/16 phi1^2 phi2
        q congruent 25 modulo 60:   1/16 phi1^2 phi2
        q congruent 27 modulo 60:   1/16 phi1^2 phi2
        q congruent 29 modulo 60:   1/16 phi1^2 phi2
        q congruent 31 modulo 60:   1/16 phi1^2 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1^2 phi2
        q congruent 41 modulo 60:   1/16 phi1^2 phi2
        q congruent 43 modulo 60:   1/16 phi1^2 phi2
        q congruent 47 modulo 60:   1/16 phi1^2 phi2
        q congruent 49 modulo 60:   1/16 phi1^2 phi2
        q congruent 53 modulo 60:   1/16 phi1^2 phi2
        q congruent 59 modulo 60:   1/16 phi1^2 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 70, 19, 19, 72, 19, 76, 76, 20, 72, 20, 20, 71, 97, 59, 59, 95, 18, 
  74, 74, 17 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], 
  [ 9, 1, 1, 1 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 2, 2 ], 
  [ 25, 1, 4, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ], [ 43, 1, 9, 8 ], 
  [ 44, 1, 4, 8 ] ]

    k = 12: F-action on Pi is (  2,  5)(  7,240)      [53,1,12]
      Dynkin type is ^2A_3(q) + A_1(q^2) + T(phi1 phi2^2)
      Order of center |Z^F|: phi1 phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1^2 ( q-5 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/32 phi1 ( q^2-6*q+9 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/32 phi1^2 ( q-5 )
        q congruent 7 modulo 60:   1/32 phi1 ( q^2-6*q+9 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/32 phi1^2 ( q-5 )
        q congruent 11 modulo 60:   1/32 phi1 ( q^2-6*q+9 )
        q congruent 13 modulo 60:   1/32 phi1^2 ( q-5 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/32 phi1^2 ( q-5 )
        q congruent 19 modulo 60:   1/32 phi1 ( q^2-6*q+9 )
        q congruent 21 modulo 60:   1/32 phi1^2 ( q-5 )
        q congruent 23 modulo 60:   1/32 phi1 ( q^2-6*q+9 )
        q congruent 25 modulo 60:   1/32 phi1^2 ( q-5 )
        q congruent 27 modulo 60:   1/32 phi1 ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/32 phi1^2 ( q-5 )
        q congruent 31 modulo 60:   1/32 phi1 ( q^2-6*q+9 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/32 phi1^2 ( q-5 )
        q congruent 41 modulo 60:   1/32 phi1^2 ( q-5 )
        q congruent 43 modulo 60:   1/32 phi1 ( q^2-6*q+9 )
        q congruent 47 modulo 60:   1/32 phi1 ( q^2-6*q+9 )
        q congruent 49 modulo 60:   1/32 phi1^2 ( q-5 )
        q congruent 53 modulo 60:   1/32 phi1^2 ( q-5 )
        q congruent 59 modulo 60:   1/32 phi1 ( q^2-6*q+9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 71, 69, 20, 3, 72, 31, 98, 72, 18 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 4 ], 
  [ 7, 1, 2, 8 ], [ 9, 1, 1, 5 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 4 ], 
  [ 13, 1, 2, 16 ], [ 13, 1, 3, 4 ], [ 20, 1, 4, 16 ], [ 23, 1, 1, 2 ], 
  [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 4 ], 
  [ 25, 1, 3, 16 ], [ 25, 1, 4, 8 ], [ 26, 1, 4, 16 ], [ 28, 1, 2, 8 ], 
  [ 35, 1, 7, 16 ], [ 39, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 41, 1, 2, 16 ], 
  [ 41, 1, 10, 16 ], [ 43, 1, 8, 16 ], [ 43, 1, 13, 32 ], [ 44, 1, 5, 16 ] ]

    k = 13: F-action on Pi is (2,5)      [53,1,13]
      Dynkin type is ^2A_3(q) + A_1(q) + A_1(q) + T(phi1 phi4)
      Order of center |Z^F|: phi1 phi4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 7 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 11 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 19 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 23 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 27 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 31 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 41 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 43 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 53 modulo 60:   1/16 phi1 phi2 ( q-3 )
        q congruent 59 modulo 60:   1/16 phi1 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 72, 20, 20, 71, 19, 76, 76, 20, 70, 19, 19, 72, 96, 60, 60, 98, 16, 
  73, 73, 18 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], 
  [ 9, 1, 1, 1 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 23, 1, 1, 2 ], 
  [ 25, 1, 2, 4 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ], [ 43, 1, 9, 8 ], 
  [ 44, 1, 6, 8 ] ]

    k = 14: F-action on Pi is (  2,  5)(  7,240)      [53,1,14]
      Dynkin type is ^2A_3(q) + A_1(q^2) + T(phi2 phi4)
      Order of center |Z^F|: phi2 phi4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^2 phi2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 phi1^2 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1^2 phi2
        q congruent 7 modulo 60:   1/16 phi1^2 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1^2 phi2
        q congruent 11 modulo 60:   1/16 phi1^2 phi2
        q congruent 13 modulo 60:   1/16 phi1^2 phi2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1^2 phi2
        q congruent 19 modulo 60:   1/16 phi1^2 phi2
        q congruent 21 modulo 60:   1/16 phi1^2 phi2
        q congruent 23 modulo 60:   1/16 phi1^2 phi2
        q congruent 25 modulo 60:   1/16 phi1^2 phi2
        q congruent 27 modulo 60:   1/16 phi1^2 phi2
        q congruent 29 modulo 60:   1/16 phi1^2 phi2
        q congruent 31 modulo 60:   1/16 phi1^2 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1^2 phi2
        q congruent 41 modulo 60:   1/16 phi1^2 phi2
        q congruent 43 modulo 60:   1/16 phi1^2 phi2
        q congruent 47 modulo 60:   1/16 phi1^2 phi2
        q congruent 49 modulo 60:   1/16 phi1^2 phi2
        q congruent 53 modulo 60:   1/16 phi1^2 phi2
        q congruent 59 modulo 60:   1/16 phi1^2 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 71, 17, 20, 74, 72, 18, 98, 54, 18, 75 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 3 ], 
  [ 13, 1, 2, 8 ], [ 23, 1, 2, 2 ], [ 25, 1, 3, 4 ], [ 39, 1, 5, 4 ], 
  [ 41, 1, 5, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 4, 8 ] ]

    k = 15: F-action on Pi is (  7,240)      [53,1,15]
      Dynkin type is A_3(q) + A_1(q^2) + T(phi2 phi6)
      Order of center |Z^F|: phi2 phi6 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q phi1 phi2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/12 q phi1 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/12 q phi1 phi2
        q congruent 7 modulo 60:   1/12 q phi1 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/12 q phi1 phi2
        q congruent 11 modulo 60:   1/12 q phi1 phi2
        q congruent 13 modulo 60:   1/12 q phi1 phi2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/12 q phi1 phi2
        q congruent 19 modulo 60:   1/12 q phi1 phi2
        q congruent 21 modulo 60:   1/12 q phi1 phi2
        q congruent 23 modulo 60:   1/12 q phi1 phi2
        q congruent 25 modulo 60:   1/12 q phi1 phi2
        q congruent 27 modulo 60:   1/12 q phi1 phi2
        q congruent 29 modulo 60:   1/12 q phi1 phi2
        q congruent 31 modulo 60:   1/12 q phi1 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/12 q phi1 phi2
        q congruent 41 modulo 60:   1/12 q phi1 phi2
        q congruent 43 modulo 60:   1/12 q phi1 phi2
        q congruent 47 modulo 60:   1/12 q phi1 phi2
        q congruent 49 modulo 60:   1/12 q phi1 phi2
        q congruent 53 modulo 60:   1/12 q phi1 phi2
        q congruent 59 modulo 60:   1/12 q phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 28, 96, 82, 60, 31, 98, 36, 99, 98, 54 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], 
  [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ], [ 16, 1, 4, 4 ], [ 27, 1, 4, 6 ], 
  [ 44, 1, 7, 6 ] ]

    k = 16: F-action on Pi is ()      [53,1,16]
      Dynkin type is A_3(q) + A_1(q) + A_1(q) + T(phi1 phi3)
      Order of center |Z^F|: phi1 phi3 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 phi1 ( q^2-q-4 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 7 modulo 60:   1/12 phi1 ( q^2-q-4 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 11 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 13 modulo 60:   1/12 phi1 ( q^2-q-4 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 19 modulo 60:   1/12 phi1 ( q^2-q-4 )
        q congruent 21 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 23 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 25 modulo 60:   1/12 phi1 ( q^2-q-4 )
        q congruent 27 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 29 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 31 modulo 60:   1/12 phi1 ( q^2-q-4 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/12 phi1 ( q^2-q-4 )
        q congruent 41 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 43 modulo 60:   1/12 phi1 ( q^2-q-4 )
        q congruent 47 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 49 modulo 60:   1/12 phi1 ( q^2-q-4 )
        q congruent 53 modulo 60:   1/12 q phi2 ( q-3 )
        q congruent 59 modulo 60:   1/12 q phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 8, 77, 77, 30, 77, 30, 30, 81, 30, 81, 81, 27, 14, 83, 83, 37, 97, 
  59, 59, 95 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], 
  [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 16, 1, 1, 4 ], 
  [ 27, 1, 5, 6 ], [ 42, 1, 3, 12 ], [ 44, 1, 3, 6 ] ]

    k = 17: F-action on Pi is (  2,  5)(  7,240)      [53,1,17]
      Dynkin type is ^2A_3(q) + A_1(q^2) + T(phi1 phi3)
      Order of center |Z^F|: phi1 phi3 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q phi1 phi2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/12 q phi1 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/12 q phi1 phi2
        q congruent 7 modulo 60:   1/12 q phi1 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/12 q phi1 phi2
        q congruent 11 modulo 60:   1/12 q phi1 phi2
        q congruent 13 modulo 60:   1/12 q phi1 phi2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/12 q phi1 phi2
        q congruent 19 modulo 60:   1/12 q phi1 phi2
        q congruent 21 modulo 60:   1/12 q phi1 phi2
        q congruent 23 modulo 60:   1/12 q phi1 phi2
        q congruent 25 modulo 60:   1/12 q phi1 phi2
        q congruent 27 modulo 60:   1/12 q phi1 phi2
        q congruent 29 modulo 60:   1/12 q phi1 phi2
        q congruent 31 modulo 60:   1/12 q phi1 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/12 q phi1 phi2
        q congruent 41 modulo 60:   1/12 q phi1 phi2
        q congruent 43 modulo 60:   1/12 q phi1 phi2
        q congruent 47 modulo 60:   1/12 q phi1 phi2
        q congruent 49 modulo 60:   1/12 q phi1 phi2
        q congruent 53 modulo 60:   1/12 q phi1 phi2
        q congruent 59 modulo 60:   1/12 q phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 27, 95, 81, 59, 30, 97, 36, 99, 97, 53 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], 
  [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 16, 1, 2, 4 ], [ 27, 1, 5, 6 ], 
  [ 44, 1, 3, 6 ] ]

    k = 18: F-action on Pi is (2,5)      [53,1,18]
      Dynkin type is ^2A_3(q) + A_1(q) + A_1(q) + T(phi2 phi6)
      Order of center |Z^F|: phi2 phi6 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q phi1^2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/12 q phi1^2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/12 phi2 ( q^2-3*q+4 )
        q congruent 7 modulo 60:   1/12 q phi1^2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/12 q phi1^2
        q congruent 11 modulo 60:   1/12 phi2 ( q^2-3*q+4 )
        q congruent 13 modulo 60:   1/12 q phi1^2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/12 phi2 ( q^2-3*q+4 )
        q congruent 19 modulo 60:   1/12 q phi1^2
        q congruent 21 modulo 60:   1/12 q phi1^2
        q congruent 23 modulo 60:   1/12 phi2 ( q^2-3*q+4 )
        q congruent 25 modulo 60:   1/12 q phi1^2
        q congruent 27 modulo 60:   1/12 q phi1^2
        q congruent 29 modulo 60:   1/12 phi2 ( q^2-3*q+4 )
        q congruent 31 modulo 60:   1/12 q phi1^2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/12 q phi1^2
        q congruent 41 modulo 60:   1/12 phi2 ( q^2-3*q+4 )
        q congruent 43 modulo 60:   1/12 q phi1^2
        q congruent 47 modulo 60:   1/12 phi2 ( q^2-3*q+4 )
        q congruent 49 modulo 60:   1/12 q phi1^2
        q congruent 53 modulo 60:   1/12 phi2 ( q^2-3*q+4 )
        q congruent 59 modulo 60:   1/12 phi2 ( q^2-3*q+4 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 31, 78, 78, 9, 82, 31, 31, 78, 28, 82, 82, 31, 38, 84, 84, 15, 96, 
  60, 60, 98 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], 
  [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ], [ 16, 1, 3, 4 ], 
  [ 27, 1, 4, 6 ], [ 42, 1, 5, 12 ], [ 44, 1, 7, 6 ] ]

    k = 19: F-action on Pi is (  7,240)      [53,1,19]
      Dynkin type is A_3(q) + A_1(q^2) + T(phi2^3)
      Order of center |Z^F|: phi2^3 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/96 phi1 ( q^2-8*q+15 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/96 phi2 ( q^2-10*q+21 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/96 phi1 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/96 phi2 ( q^2-10*q+21 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/96 phi1 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/96 phi2 ( q^2-10*q+21 )
        q congruent 13 modulo 60:   1/96 phi1 ( q^2-8*q+15 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/96 phi1 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/96 phi2 ( q^2-10*q+21 )
        q congruent 21 modulo 60:   1/96 phi1 ( q^2-8*q+15 )
        q congruent 23 modulo 60:   1/96 phi2 ( q^2-10*q+21 )
        q congruent 25 modulo 60:   1/96 phi1 ( q^2-8*q+15 )
        q congruent 27 modulo 60:   1/96 phi2 ( q^2-10*q+21 )
        q congruent 29 modulo 60:   1/96 phi1 ( q^2-8*q+15 )
        q congruent 31 modulo 60:   1/96 phi2 ( q^2-10*q+21 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/96 phi1 ( q^2-8*q+15 )
        q congruent 41 modulo 60:   1/96 phi1 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/96 phi2 ( q^2-10*q+21 )
        q congruent 47 modulo 60:   1/96 phi2 ( q^2-10*q+21 )
        q congruent 49 modulo 60:   1/96 phi1 ( q^2-8*q+15 )
        q congruent 53 modulo 60:   1/96 phi1 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/96 phi2 ( q^2-10*q+21 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 72, 69, 20, 5, 71, 27, 95, 71, 17 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 8 ], 
  [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 24 ], 
  [ 12, 1, 2, 8 ], [ 13, 1, 2, 12 ], [ 13, 1, 4, 12 ], [ 16, 1, 4, 16 ], 
  [ 20, 1, 2, 48 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 4, 36 ], 
  [ 27, 1, 6, 48 ], [ 28, 1, 4, 24 ], [ 35, 1, 4, 48 ], [ 39, 1, 3, 24 ], 
  [ 41, 1, 10, 48 ], [ 43, 1, 12, 96 ], [ 44, 1, 10, 48 ] ]

    k = 20: F-action on Pi is (2,5)      [53,1,20]
      Dynkin type is ^2A_3(q) + A_1(q) + A_1(q) + T(phi2^3)
      Order of center |Z^F|: phi2^3 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/96 phi1 ( q^2-16*q+63 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/96 ( q^3-17*q^2+91*q-147 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/96 ( q^3-17*q^2+79*q-95 )
        q congruent 7 modulo 60:   1/96 ( q^3-17*q^2+91*q-147 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/96 phi1 ( q^2-16*q+63 )
        q congruent 11 modulo 60:   1/96 ( q^3-17*q^2+91*q-179 )
        q congruent 13 modulo 60:   1/96 phi1 ( q^2-16*q+63 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/96 ( q^3-17*q^2+79*q-95 )
        q congruent 19 modulo 60:   1/96 ( q^3-17*q^2+91*q-147 )
        q congruent 21 modulo 60:   1/96 phi1 ( q^2-16*q+63 )
        q congruent 23 modulo 60:   1/96 ( q^3-17*q^2+91*q-179 )
        q congruent 25 modulo 60:   1/96 phi1 ( q^2-16*q+63 )
        q congruent 27 modulo 60:   1/96 ( q^3-17*q^2+91*q-147 )
        q congruent 29 modulo 60:   1/96 ( q^3-17*q^2+79*q-95 )
        q congruent 31 modulo 60:   1/96 ( q^3-17*q^2+91*q-147 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/96 phi1 ( q^2-16*q+63 )
        q congruent 41 modulo 60:   1/96 ( q^3-17*q^2+79*q-95 )
        q congruent 43 modulo 60:   1/96 ( q^3-17*q^2+91*q-147 )
        q congruent 47 modulo 60:   1/96 ( q^3-17*q^2+91*q-179 )
        q congruent 49 modulo 60:   1/96 phi1 ( q^2-16*q+63 )
        q congruent 53 modulo 60:   1/96 ( q^3-17*q^2+79*q-95 )
        q congruent 59 modulo 60:   1/96 ( q^3-17*q^2+91*q-179 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 67, 67, 2, 69, 5, 5, 67, 3, 69, 69, 5, 31, 78, 78, 9, 72, 20, 
  20, 71 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 10 ], 
  [ 6, 1, 2, 16 ], [ 7, 1, 2, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 2, 12 ], 
  [ 11, 1, 2, 24 ], [ 12, 1, 2, 8 ], [ 13, 1, 4, 24 ], [ 16, 1, 3, 16 ], 
  [ 19, 1, 2, 48 ], [ 20, 1, 4, 48 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 36 ], 
  [ 25, 1, 3, 36 ], [ 26, 1, 4, 48 ], [ 27, 1, 6, 48 ], [ 28, 1, 4, 24 ], 
  [ 35, 1, 8, 48 ], [ 39, 1, 3, 24 ], [ 41, 1, 9, 48 ], [ 42, 1, 6, 96 ], 
  [ 43, 1, 13, 96 ], [ 44, 1, 10, 48 ] ]

i = 54: Pi = [ 1, 2, 3, 4 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [54,1,1]
      Dynkin type is A_4(q) + T(phi1^4)
      Order of center |Z^F|: phi1^4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/240 ( q^4-29*q^3+306*q^2-1429*q+2831 )
        q congruent 2 modulo 60:   1/240 ( q^4-29*q^3+296*q^2-1204*q+1440 )
        q congruent 3 modulo 60:   1/240 ( q^4-29*q^3+306*q^2-1389*q+2115 )
        q congruent 4 modulo 60:   1/240 ( q^4-29*q^3+296*q^2-1244*q+1840 )
        q congruent 5 modulo 60:   1/240 ( q^4-29*q^3+306*q^2-1389*q+2295 )
        q congruent 7 modulo 60:   1/240 ( q^4-29*q^3+306*q^2-1429*q+2555 )
        q congruent 8 modulo 60:   1/240 ( q^4-29*q^3+296*q^2-1204*q+1440 )
        q congruent 9 modulo 60:   1/240 ( q^4-29*q^3+306*q^2-1389*q+2295 )
        q congruent 11 modulo 60:   1/240 ( q^4-29*q^3+306*q^2-1389*q+2211 )
        q congruent 13 modulo 60:   1/240 ( q^4-29*q^3+306*q^2-1429*q+2735 )
        q congruent 16 modulo 60:   1/240 ( q^4-29*q^3+296*q^2-1244*q+1936 )
        q congruent 17 modulo 60:   1/240 ( q^4-29*q^3+306*q^2-1389*q+2295 )
        q congruent 19 modulo 60:   1/240 ( q^4-29*q^3+306*q^2-1429*q+2555 )
        q congruent 21 modulo 60:   1/240 ( q^4-29*q^3+306*q^2-1389*q+2391 )
        q congruent 23 modulo 60:   1/240 ( q^4-29*q^3+306*q^2-1389*q+2115 )
        q congruent 25 modulo 60:   1/240 ( q^4-29*q^3+306*q^2-1429*q+2735 )
        q congruent 27 modulo 60:   1/240 ( q^4-29*q^3+306*q^2-1389*q+2115 )
        q congruent 29 modulo 60:   1/240 ( q^4-29*q^3+306*q^2-1389*q+2295 )
        q congruent 31 modulo 60:   1/240 ( q^4-29*q^3+306*q^2-1429*q+2651 )
        q congruent 32 modulo 60:   1/240 ( q^4-29*q^3+296*q^2-1204*q+1440 )
        q congruent 37 modulo 60:   1/240 ( q^4-29*q^3+306*q^2-1429*q+2735 )
        q congruent 41 modulo 60:   1/240 ( q^4-29*q^3+306*q^2-1389*q+2391 )
        q congruent 43 modulo 60:   1/240 ( q^4-29*q^3+306*q^2-1429*q+2555 )
        q congruent 47 modulo 60:   1/240 ( q^4-29*q^3+306*q^2-1389*q+2115 )
        q congruent 49 modulo 60:   1/240 ( q^4-29*q^3+306*q^2-1429*q+2735 )
        q congruent 53 modulo 60:   1/240 ( q^4-29*q^3+306*q^2-1389*q+2295 )
        q congruent 59 modulo 60:   1/240 ( q^4-29*q^3+306*q^2-1389*q+2115 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 4, 8, 77, 70, 23 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 10 ], [ 3, 1, 1, 20 ], [ 4, 1, 1, 10 ], 
  [ 5, 1, 1, 4 ], [ 6, 1, 1, 20 ], [ 7, 1, 1, 20 ], [ 8, 1, 1, 10 ], 
  [ 9, 1, 1, 5 ], [ 10, 1, 1, 20 ], [ 11, 1, 1, 60 ], [ 12, 1, 1, 40 ], 
  [ 13, 1, 1, 60 ], [ 14, 1, 1, 10 ], [ 15, 1, 1, 20 ], [ 18, 1, 1, 60 ], 
  [ 19, 1, 1, 60 ], [ 21, 1, 1, 40 ], [ 22, 1, 1, 40 ], [ 23, 1, 1, 30 ], 
  [ 24, 1, 1, 60 ], [ 26, 1, 1, 40 ], [ 27, 1, 1, 120 ], [ 28, 1, 1, 120 ], 
  [ 29, 1, 1, 40 ], [ 30, 1, 1, 60 ], [ 34, 1, 1, 120 ], [ 36, 1, 1, 120 ], 
  [ 39, 1, 1, 120 ], [ 42, 1, 1, 120 ], [ 44, 1, 1, 240 ], [ 45, 1, 1, 120 ], 
  [ 50, 1, 1, 240 ] ]

    k = 2: F-action on Pi is ()      [54,1,2]
      Dynkin type is A_4(q) + T(phi1^3 phi2)
      Order of center |Z^F|: phi1^3 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 phi1 ( q^3-12*q^2+44*q-49 )
        q congruent 2 modulo 60:   1/24 q ( q^3-13*q^2+52*q-60 )
        q congruent 3 modulo 60:   1/24 ( q^4-13*q^3+56*q^2-89*q+33 )
        q congruent 4 modulo 60:   1/24 q ( q^3-13*q^2+52*q-64 )
        q congruent 5 modulo 60:   1/24 phi1 ( q^3-12*q^2+44*q-45 )
        q congruent 7 modulo 60:   1/24 ( q^4-13*q^3+56*q^2-93*q+37 )
        q congruent 8 modulo 60:   1/24 q ( q^3-13*q^2+52*q-60 )
        q congruent 9 modulo 60:   1/24 phi1 ( q^3-12*q^2+44*q-45 )
        q congruent 11 modulo 60:   1/24 ( q^4-13*q^3+56*q^2-89*q+33 )
        q congruent 13 modulo 60:   1/24 phi1 ( q^3-12*q^2+44*q-49 )
        q congruent 16 modulo 60:   1/24 q ( q^3-13*q^2+52*q-64 )
        q congruent 17 modulo 60:   1/24 phi1 ( q^3-12*q^2+44*q-45 )
        q congruent 19 modulo 60:   1/24 ( q^4-13*q^3+56*q^2-93*q+37 )
        q congruent 21 modulo 60:   1/24 phi1 ( q^3-12*q^2+44*q-45 )
        q congruent 23 modulo 60:   1/24 ( q^4-13*q^3+56*q^2-89*q+33 )
        q congruent 25 modulo 60:   1/24 phi1 ( q^3-12*q^2+44*q-49 )
        q congruent 27 modulo 60:   1/24 ( q^4-13*q^3+56*q^2-89*q+33 )
        q congruent 29 modulo 60:   1/24 phi1 ( q^3-12*q^2+44*q-45 )
        q congruent 31 modulo 60:   1/24 ( q^4-13*q^3+56*q^2-93*q+37 )
        q congruent 32 modulo 60:   1/24 q ( q^3-13*q^2+52*q-60 )
        q congruent 37 modulo 60:   1/24 phi1 ( q^3-12*q^2+44*q-49 )
        q congruent 41 modulo 60:   1/24 phi1 ( q^3-12*q^2+44*q-45 )
        q congruent 43 modulo 60:   1/24 ( q^4-13*q^3+56*q^2-93*q+37 )
        q congruent 47 modulo 60:   1/24 ( q^4-13*q^3+56*q^2-89*q+33 )
        q congruent 49 modulo 60:   1/24 phi1 ( q^3-12*q^2+44*q-49 )
        q congruent 53 modulo 60:   1/24 phi1 ( q^3-12*q^2+44*q-45 )
        q congruent 59 modulo 60:   1/24 ( q^4-13*q^3+56*q^2-89*q+33 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 68, 77, 30, 19, 93 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 6 ], 
  [ 5, 1, 1, 4 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 8 ], [ 8, 1, 1, 6 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 12 ], 
  [ 12, 1, 1, 12 ], [ 13, 1, 1, 12 ], [ 14, 1, 1, 6 ], [ 15, 1, 1, 8 ], 
  [ 18, 1, 1, 12 ], [ 19, 1, 1, 12 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 12 ], 
  [ 22, 1, 2, 4 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], 
  [ 26, 1, 1, 12 ], [ 26, 1, 3, 4 ], [ 27, 1, 1, 12 ], [ 27, 1, 2, 12 ], 
  [ 28, 1, 1, 12 ], [ 28, 1, 2, 12 ], [ 29, 1, 1, 12 ], [ 29, 1, 2, 4 ], 
  [ 30, 1, 1, 12 ], [ 34, 1, 1, 12 ], [ 34, 1, 2, 12 ], [ 36, 1, 1, 12 ], 
  [ 36, 1, 2, 12 ], [ 39, 1, 4, 12 ], [ 42, 1, 1, 12 ], [ 42, 1, 4, 12 ], 
  [ 44, 1, 2, 24 ], [ 45, 1, 1, 12 ], [ 45, 1, 2, 12 ], [ 50, 1, 2, 24 ], 
  [ 50, 1, 4, 24 ] ]

    k = 3: F-action on Pi is ()      [54,1,3]
      Dynkin type is A_4(q) + T(phi1^2 phi3)
      Order of center |Z^F|: phi1^2 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 phi1 ( q^3-4*q^2-q+10 )
        q congruent 2 modulo 60:   1/12 q phi2 ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/12 q phi2 ( q^2-6*q+9 )
        q congruent 4 modulo 60:   1/12 phi1 ( q^3-4*q^2-2*q+8 )
        q congruent 5 modulo 60:   1/12 q phi2 ( q^2-6*q+9 )
        q congruent 7 modulo 60:   1/12 phi1 ( q^3-4*q^2-q+10 )
        q congruent 8 modulo 60:   1/12 q phi2 ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/12 q phi2 ( q^2-6*q+9 )
        q congruent 11 modulo 60:   1/12 q phi2 ( q^2-6*q+9 )
        q congruent 13 modulo 60:   1/12 phi1 ( q^3-4*q^2-q+10 )
        q congruent 16 modulo 60:   1/12 phi1 ( q^3-4*q^2-2*q+8 )
        q congruent 17 modulo 60:   1/12 q phi2 ( q^2-6*q+9 )
        q congruent 19 modulo 60:   1/12 phi1 ( q^3-4*q^2-q+10 )
        q congruent 21 modulo 60:   1/12 q phi2 ( q^2-6*q+9 )
        q congruent 23 modulo 60:   1/12 q phi2 ( q^2-6*q+9 )
        q congruent 25 modulo 60:   1/12 phi1 ( q^3-4*q^2-q+10 )
        q congruent 27 modulo 60:   1/12 q phi2 ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/12 q phi2 ( q^2-6*q+9 )
        q congruent 31 modulo 60:   1/12 phi1 ( q^3-4*q^2-q+10 )
        q congruent 32 modulo 60:   1/12 q phi2 ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/12 phi1 ( q^3-4*q^2-q+10 )
        q congruent 41 modulo 60:   1/12 q phi2 ( q^2-6*q+9 )
        q congruent 43 modulo 60:   1/12 phi1 ( q^3-4*q^2-q+10 )
        q congruent 47 modulo 60:   1/12 q phi2 ( q^2-6*q+9 )
        q congruent 49 modulo 60:   1/12 phi1 ( q^3-4*q^2-q+10 )
        q congruent 53 modulo 60:   1/12 q phi2 ( q^2-6*q+9 )
        q congruent 59 modulo 60:   1/12 q phi2 ( q^2-6*q+9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 8, 77, 30, 14, 83, 97, 62 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], 
  [ 5, 1, 1, 4 ], [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 8, 1, 1, 4 ], 
  [ 9, 1, 1, 2 ], [ 10, 1, 1, 2 ], [ 12, 1, 1, 4 ], [ 14, 1, 1, 4 ], 
  [ 15, 1, 1, 2 ], [ 21, 1, 1, 4 ], [ 22, 1, 1, 4 ], [ 26, 1, 1, 4 ], 
  [ 27, 1, 5, 6 ], [ 29, 1, 1, 4 ], [ 42, 1, 3, 6 ], [ 44, 1, 3, 12 ], 
  [ 45, 1, 3, 6 ], [ 50, 1, 3, 12 ] ]

    k = 4: F-action on Pi is ()      [54,1,4]
      Dynkin type is A_4(q) + T(phi1 phi2 phi4)
      Order of center |Z^F|: phi1 phi2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 phi2 ( q^2-q-1 )
        q congruent 2 modulo 60:   1/8 q^2 phi2 ( q-2 )
        q congruent 3 modulo 60:   1/8 phi1 phi2 ( q^2-q-1 )
        q congruent 4 modulo 60:   1/8 q^2 phi2 ( q-2 )
        q congruent 5 modulo 60:   1/8 phi1 phi2 ( q^2-q-1 )
        q congruent 7 modulo 60:   1/8 phi1 phi2 ( q^2-q-1 )
        q congruent 8 modulo 60:   1/8 q^2 phi2 ( q-2 )
        q congruent 9 modulo 60:   1/8 phi1 phi2 ( q^2-q-1 )
        q congruent 11 modulo 60:   1/8 phi1 phi2 ( q^2-q-1 )
        q congruent 13 modulo 60:   1/8 phi1 phi2 ( q^2-q-1 )
        q congruent 16 modulo 60:   1/8 q^2 phi2 ( q-2 )
        q congruent 17 modulo 60:   1/8 phi1 phi2 ( q^2-q-1 )
        q congruent 19 modulo 60:   1/8 phi1 phi2 ( q^2-q-1 )
        q congruent 21 modulo 60:   1/8 phi1 phi2 ( q^2-q-1 )
        q congruent 23 modulo 60:   1/8 phi1 phi2 ( q^2-q-1 )
        q congruent 25 modulo 60:   1/8 phi1 phi2 ( q^2-q-1 )
        q congruent 27 modulo 60:   1/8 phi1 phi2 ( q^2-q-1 )
        q congruent 29 modulo 60:   1/8 phi1 phi2 ( q^2-q-1 )
        q congruent 31 modulo 60:   1/8 phi1 phi2 ( q^2-q-1 )
        q congruent 32 modulo 60:   1/8 q^2 phi2 ( q-2 )
        q congruent 37 modulo 60:   1/8 phi1 phi2 ( q^2-q-1 )
        q congruent 41 modulo 60:   1/8 phi1 phi2 ( q^2-q-1 )
        q congruent 43 modulo 60:   1/8 phi1 phi2 ( q^2-q-1 )
        q congruent 47 modulo 60:   1/8 phi1 phi2 ( q^2-q-1 )
        q congruent 49 modulo 60:   1/8 phi1 phi2 ( q^2-q-1 )
        q congruent 53 modulo 60:   1/8 phi1 phi2 ( q^2-q-1 )
        q congruent 59 modulo 60:   1/8 phi1 phi2 ( q^2-q-1 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 70, 19, 76, 97, 59, 22, 107 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 5, 1, 1, 4 ], [ 8, 1, 1, 2 ], 
  [ 9, 1, 1, 1 ], [ 13, 1, 2, 4 ], [ 14, 1, 1, 2 ], [ 23, 1, 2, 2 ], 
  [ 30, 1, 2, 4 ], [ 39, 1, 5, 4 ], [ 44, 1, 4, 8 ] ]

    k = 5: F-action on Pi is ()      [54,1,5]
      Dynkin type is A_4(q) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^2 ( q^2-3*q-1 )
        q congruent 2 modulo 60:   1/16 q ( q^3-5*q^2+4*q+4 )
        q congruent 3 modulo 60:   1/16 ( q^4-5*q^3+6*q^2-q+3 )
        q congruent 4 modulo 60:   1/16 q ( q^3-5*q^2+4*q+4 )
        q congruent 5 modulo 60:   1/16 phi1^2 ( q^2-3*q-1 )
        q congruent 7 modulo 60:   1/16 ( q^4-5*q^3+6*q^2-q+3 )
        q congruent 8 modulo 60:   1/16 q ( q^3-5*q^2+4*q+4 )
        q congruent 9 modulo 60:   1/16 phi1^2 ( q^2-3*q-1 )
        q congruent 11 modulo 60:   1/16 ( q^4-5*q^3+6*q^2-q+3 )
        q congruent 13 modulo 60:   1/16 phi1^2 ( q^2-3*q-1 )
        q congruent 16 modulo 60:   1/16 q ( q^3-5*q^2+4*q+4 )
        q congruent 17 modulo 60:   1/16 phi1^2 ( q^2-3*q-1 )
        q congruent 19 modulo 60:   1/16 ( q^4-5*q^3+6*q^2-q+3 )
        q congruent 21 modulo 60:   1/16 phi1^2 ( q^2-3*q-1 )
        q congruent 23 modulo 60:   1/16 ( q^4-5*q^3+6*q^2-q+3 )
        q congruent 25 modulo 60:   1/16 phi1^2 ( q^2-3*q-1 )
        q congruent 27 modulo 60:   1/16 ( q^4-5*q^3+6*q^2-q+3 )
        q congruent 29 modulo 60:   1/16 phi1^2 ( q^2-3*q-1 )
        q congruent 31 modulo 60:   1/16 ( q^4-5*q^3+6*q^2-q+3 )
        q congruent 32 modulo 60:   1/16 q ( q^3-5*q^2+4*q+4 )
        q congruent 37 modulo 60:   1/16 phi1^2 ( q^2-3*q-1 )
        q congruent 41 modulo 60:   1/16 phi1^2 ( q^2-3*q-1 )
        q congruent 43 modulo 60:   1/16 ( q^4-5*q^3+6*q^2-q+3 )
        q congruent 47 modulo 60:   1/16 ( q^4-5*q^3+6*q^2-q+3 )
        q congruent 49 modulo 60:   1/16 phi1^2 ( q^2-3*q-1 )
        q congruent 53 modulo 60:   1/16 phi1^2 ( q^2-3*q-1 )
        q congruent 59 modulo 60:   1/16 ( q^4-5*q^3+6*q^2-q+3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 68, 7, 30, 81, 76, 50 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], 
  [ 5, 1, 1, 4 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 2 ], 
  [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 4 ], [ 13, 1, 1, 4 ], 
  [ 13, 1, 2, 8 ], [ 14, 1, 1, 2 ], [ 15, 1, 1, 4 ], [ 18, 1, 1, 4 ], 
  [ 19, 1, 1, 4 ], [ 22, 1, 2, 8 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 4 ], 
  [ 24, 1, 2, 4 ], [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 28, 1, 2, 8 ], 
  [ 29, 1, 2, 8 ], [ 30, 1, 1, 4 ], [ 30, 1, 2, 8 ], [ 34, 1, 2, 8 ], 
  [ 36, 1, 2, 8 ], [ 39, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 42, 1, 4, 8 ], 
  [ 44, 1, 5, 16 ], [ 45, 1, 2, 8 ], [ 50, 1, 5, 16 ] ]

    k = 6: F-action on Pi is ()      [54,1,6]
      Dynkin type is A_4(q) + T(phi5)
      Order of center |Z^F|: phi5
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/10 phi1 ( q^3+2*q^2+3*q+4 )
        q congruent 2 modulo 60:   1/10 q phi2 phi4
        q congruent 3 modulo 60:   1/10 q phi2 phi4
        q congruent 4 modulo 60:   1/10 q phi2 phi4
        q congruent 5 modulo 60:   1/10 q phi2 phi4
        q congruent 7 modulo 60:   1/10 q phi2 phi4
        q congruent 8 modulo 60:   1/10 q phi2 phi4
        q congruent 9 modulo 60:   1/10 q phi2 phi4
        q congruent 11 modulo 60:   1/10 phi1 ( q^3+2*q^2+3*q+4 )
        q congruent 13 modulo 60:   1/10 q phi2 phi4
        q congruent 16 modulo 60:   1/10 phi1 ( q^3+2*q^2+3*q+4 )
        q congruent 17 modulo 60:   1/10 q phi2 phi4
        q congruent 19 modulo 60:   1/10 q phi2 phi4
        q congruent 21 modulo 60:   1/10 phi1 ( q^3+2*q^2+3*q+4 )
        q congruent 23 modulo 60:   1/10 q phi2 phi4
        q congruent 25 modulo 60:   1/10 q phi2 phi4
        q congruent 27 modulo 60:   1/10 q phi2 phi4
        q congruent 29 modulo 60:   1/10 q phi2 phi4
        q congruent 31 modulo 60:   1/10 phi1 ( q^3+2*q^2+3*q+4 )
        q congruent 32 modulo 60:   1/10 q phi2 phi4
        q congruent 37 modulo 60:   1/10 q phi2 phi4
        q congruent 41 modulo 60:   1/10 phi1 ( q^3+2*q^2+3*q+4 )
        q congruent 43 modulo 60:   1/10 q phi2 phi4
        q congruent 47 modulo 60:   1/10 q phi2 phi4
        q congruent 49 modulo 60:   1/10 q phi2 phi4
        q congruent 53 modulo 60:   1/10 q phi2 phi4
        q congruent 59 modulo 60:   1/10 q phi2 phi4
      Fusion of maximal tori of C^F in those of G^F:
        [ 23, 93, 50, 62, 111, 107, 25 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 5, 1, 1, 4 ] ]

    k = 7: F-action on Pi is ()      [54,1,7]
      Dynkin type is A_4(q) + T(phi1 phi2 phi3)
      Order of center |Z^F|: phi1 phi2 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 phi1 ( q^3-q+2 )
        q congruent 2 modulo 60:   1/12 q^2 phi2 ( q-2 )
        q congruent 3 modulo 60:   1/12 q phi1^2 phi2
        q congruent 4 modulo 60:   1/12 q phi1 ( q^2-2 )
        q congruent 5 modulo 60:   1/12 q phi1^2 phi2
        q congruent 7 modulo 60:   1/12 phi1 ( q^3-q+2 )
        q congruent 8 modulo 60:   1/12 q^2 phi2 ( q-2 )
        q congruent 9 modulo 60:   1/12 q phi1^2 phi2
        q congruent 11 modulo 60:   1/12 q phi1^2 phi2
        q congruent 13 modulo 60:   1/12 phi1 ( q^3-q+2 )
        q congruent 16 modulo 60:   1/12 q phi1 ( q^2-2 )
        q congruent 17 modulo 60:   1/12 q phi1^2 phi2
        q congruent 19 modulo 60:   1/12 phi1 ( q^3-q+2 )
        q congruent 21 modulo 60:   1/12 q phi1^2 phi2
        q congruent 23 modulo 60:   1/12 q phi1^2 phi2
        q congruent 25 modulo 60:   1/12 phi1 ( q^3-q+2 )
        q congruent 27 modulo 60:   1/12 q phi1^2 phi2
        q congruent 29 modulo 60:   1/12 q phi1^2 phi2
        q congruent 31 modulo 60:   1/12 phi1 ( q^3-q+2 )
        q congruent 32 modulo 60:   1/12 q^2 phi2 ( q-2 )
        q congruent 37 modulo 60:   1/12 phi1 ( q^3-q+2 )
        q congruent 41 modulo 60:   1/12 q phi1^2 phi2
        q congruent 43 modulo 60:   1/12 phi1 ( q^3-q+2 )
        q congruent 47 modulo 60:   1/12 q phi1^2 phi2
        q congruent 49 modulo 60:   1/12 phi1 ( q^3-q+2 )
        q congruent 53 modulo 60:   1/12 q phi1^2 phi2
        q congruent 59 modulo 60:   1/12 q phi1^2 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 77, 30, 81, 83, 37, 59, 111 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 5, 1, 1, 4 ], 
  [ 6, 1, 1, 2 ], [ 7, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 15, 1, 1, 2 ], 
  [ 22, 1, 2, 4 ], [ 26, 1, 3, 4 ], [ 27, 1, 5, 6 ], [ 29, 1, 2, 4 ], 
  [ 42, 1, 3, 6 ], [ 45, 1, 3, 6 ], [ 50, 1, 6, 12 ] ]

    k = 8: F-action on Pi is (1,2)(3,4)      [54,1,8]
      Dynkin type is ^2A_4(q) + T(phi10)
      Order of center |Z^F|: phi10
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/10 q phi1 phi4
        q congruent 2 modulo 60:   1/10 q phi1 phi4
        q congruent 3 modulo 60:   1/10 q phi1 phi4
        q congruent 4 modulo 60:   1/10 phi2 ( q^3-2*q^2+3*q-4 )
        q congruent 5 modulo 60:   1/10 q phi1 phi4
        q congruent 7 modulo 60:   1/10 q phi1 phi4
        q congruent 8 modulo 60:   1/10 q phi1 phi4
        q congruent 9 modulo 60:   1/10 phi2 ( q^3-2*q^2+3*q-4 )
        q congruent 11 modulo 60:   1/10 q phi1 phi4
        q congruent 13 modulo 60:   1/10 q phi1 phi4
        q congruent 16 modulo 60:   1/10 q phi1 phi4
        q congruent 17 modulo 60:   1/10 q phi1 phi4
        q congruent 19 modulo 60:   1/10 phi2 ( q^3-2*q^2+3*q-4 )
        q congruent 21 modulo 60:   1/10 q phi1 phi4
        q congruent 23 modulo 60:   1/10 q phi1 phi4
        q congruent 25 modulo 60:   1/10 q phi1 phi4
        q congruent 27 modulo 60:   1/10 q phi1 phi4
        q congruent 29 modulo 60:   1/10 phi2 ( q^3-2*q^2+3*q-4 )
        q congruent 31 modulo 60:   1/10 q phi1 phi4
        q congruent 32 modulo 60:   1/10 q phi1 phi4
        q congruent 37 modulo 60:   1/10 q phi1 phi4
        q congruent 41 modulo 60:   1/10 q phi1 phi4
        q congruent 43 modulo 60:   1/10 q phi1 phi4
        q congruent 47 modulo 60:   1/10 q phi1 phi4
        q congruent 49 modulo 60:   1/10 phi2 ( q^3-2*q^2+3*q-4 )
        q congruent 53 modulo 60:   1/10 q phi1 phi4
        q congruent 59 modulo 60:   1/10 phi2 ( q^3-2*q^2+3*q-4 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 24, 94, 51, 63, 112, 108, 26 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 5, 1, 2, 4 ] ]

    k = 9: F-action on Pi is (1,2)(3,4)      [54,1,9]
      Dynkin type is ^2A_4(q) + T(phi1 phi2 phi4)
      Order of center |Z^F|: phi1 phi2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 phi2 phi6
        q congruent 2 modulo 60:   1/8 q^3 phi1
        q congruent 3 modulo 60:   1/8 phi1 phi2 phi6
        q congruent 4 modulo 60:   1/8 q^3 phi1
        q congruent 5 modulo 60:   1/8 phi1 phi2 phi6
        q congruent 7 modulo 60:   1/8 phi1 phi2 phi6
        q congruent 8 modulo 60:   1/8 q^3 phi1
        q congruent 9 modulo 60:   1/8 phi1 phi2 phi6
        q congruent 11 modulo 60:   1/8 phi1 phi2 phi6
        q congruent 13 modulo 60:   1/8 phi1 phi2 phi6
        q congruent 16 modulo 60:   1/8 q^3 phi1
        q congruent 17 modulo 60:   1/8 phi1 phi2 phi6
        q congruent 19 modulo 60:   1/8 phi1 phi2 phi6
        q congruent 21 modulo 60:   1/8 phi1 phi2 phi6
        q congruent 23 modulo 60:   1/8 phi1 phi2 phi6
        q congruent 25 modulo 60:   1/8 phi1 phi2 phi6
        q congruent 27 modulo 60:   1/8 phi1 phi2 phi6
        q congruent 29 modulo 60:   1/8 phi1 phi2 phi6
        q congruent 31 modulo 60:   1/8 phi1 phi2 phi6
        q congruent 32 modulo 60:   1/8 q^3 phi1
        q congruent 37 modulo 60:   1/8 phi1 phi2 phi6
        q congruent 41 modulo 60:   1/8 phi1 phi2 phi6
        q congruent 43 modulo 60:   1/8 phi1 phi2 phi6
        q congruent 47 modulo 60:   1/8 phi1 phi2 phi6
        q congruent 49 modulo 60:   1/8 phi1 phi2 phi6
        q congruent 53 modulo 60:   1/8 phi1 phi2 phi6
        q congruent 59 modulo 60:   1/8 phi1 phi2 phi6
      Fusion of maximal tori of C^F in those of G^F:
        [ 71, 20, 76, 98, 60, 22, 108 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 2, 2 ], [ 5, 1, 2, 4 ], [ 8, 1, 2, 2 ], 
  [ 9, 1, 1, 1 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 2 ], [ 23, 1, 1, 2 ], 
  [ 30, 1, 4, 4 ], [ 39, 1, 5, 4 ], [ 44, 1, 6, 8 ] ]

    k = 10: F-action on Pi is (1,2)(3,4)      [54,1,10]
      Dynkin type is ^2A_4(q) + T(phi2^2 phi6)
      Order of center |Z^F|: phi2^2 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q phi1^3
        q congruent 2 modulo 60:   1/12 phi2 ( q^3-4*q^2+6*q-4 )
        q congruent 3 modulo 60:   1/12 q phi1^3
        q congruent 4 modulo 60:   1/12 q^2 phi1 ( q-2 )
        q congruent 5 modulo 60:   1/12 phi2 ( q^3-4*q^2+7*q-6 )
        q congruent 7 modulo 60:   1/12 q phi1^3
        q congruent 8 modulo 60:   1/12 phi2 ( q^3-4*q^2+6*q-4 )
        q congruent 9 modulo 60:   1/12 q phi1^3
        q congruent 11 modulo 60:   1/12 phi2 ( q^3-4*q^2+7*q-6 )
        q congruent 13 modulo 60:   1/12 q phi1^3
        q congruent 16 modulo 60:   1/12 q^2 phi1 ( q-2 )
        q congruent 17 modulo 60:   1/12 phi2 ( q^3-4*q^2+7*q-6 )
        q congruent 19 modulo 60:   1/12 q phi1^3
        q congruent 21 modulo 60:   1/12 q phi1^3
        q congruent 23 modulo 60:   1/12 phi2 ( q^3-4*q^2+7*q-6 )
        q congruent 25 modulo 60:   1/12 q phi1^3
        q congruent 27 modulo 60:   1/12 q phi1^3
        q congruent 29 modulo 60:   1/12 phi2 ( q^3-4*q^2+7*q-6 )
        q congruent 31 modulo 60:   1/12 q phi1^3
        q congruent 32 modulo 60:   1/12 phi2 ( q^3-4*q^2+6*q-4 )
        q congruent 37 modulo 60:   1/12 q phi1^3
        q congruent 41 modulo 60:   1/12 phi2 ( q^3-4*q^2+7*q-6 )
        q congruent 43 modulo 60:   1/12 q phi1^3
        q congruent 47 modulo 60:   1/12 phi2 ( q^3-4*q^2+7*q-6 )
        q congruent 49 modulo 60:   1/12 q phi1^3
        q congruent 53 modulo 60:   1/12 phi2 ( q^3-4*q^2+7*q-6 )
        q congruent 59 modulo 60:   1/12 phi2 ( q^3-4*q^2+7*q-6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 9, 78, 31, 15, 84, 98, 63 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], 
  [ 5, 1, 2, 4 ], [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 8, 1, 2, 4 ], 
  [ 9, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 12, 1, 2, 4 ], [ 14, 1, 2, 4 ], 
  [ 15, 1, 2, 2 ], [ 21, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 26, 1, 4, 4 ], 
  [ 27, 1, 4, 6 ], [ 29, 1, 4, 4 ], [ 42, 1, 5, 6 ], [ 44, 1, 7, 12 ], 
  [ 45, 1, 4, 6 ], [ 50, 1, 10, 12 ] ]

    k = 11: F-action on Pi is (1,2)(3,4)      [54,1,11]
      Dynkin type is ^2A_4(q) + T(phi1 phi2 phi6)
      Order of center |Z^F|: phi1 phi2 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q phi1^3
        q congruent 2 modulo 60:   1/12 phi2 ( q^3-4*q^2+6*q-4 )
        q congruent 3 modulo 60:   1/12 q phi1^3
        q congruent 4 modulo 60:   1/12 q^2 phi1 ( q-2 )
        q congruent 5 modulo 60:   1/12 phi2 ( q^3-4*q^2+7*q-6 )
        q congruent 7 modulo 60:   1/12 q phi1^3
        q congruent 8 modulo 60:   1/12 phi2 ( q^3-4*q^2+6*q-4 )
        q congruent 9 modulo 60:   1/12 q phi1^3
        q congruent 11 modulo 60:   1/12 phi2 ( q^3-4*q^2+7*q-6 )
        q congruent 13 modulo 60:   1/12 q phi1^3
        q congruent 16 modulo 60:   1/12 q^2 phi1 ( q-2 )
        q congruent 17 modulo 60:   1/12 phi2 ( q^3-4*q^2+7*q-6 )
        q congruent 19 modulo 60:   1/12 q phi1^3
        q congruent 21 modulo 60:   1/12 q phi1^3
        q congruent 23 modulo 60:   1/12 phi2 ( q^3-4*q^2+7*q-6 )
        q congruent 25 modulo 60:   1/12 q phi1^3
        q congruent 27 modulo 60:   1/12 q phi1^3
        q congruent 29 modulo 60:   1/12 phi2 ( q^3-4*q^2+7*q-6 )
        q congruent 31 modulo 60:   1/12 q phi1^3
        q congruent 32 modulo 60:   1/12 phi2 ( q^3-4*q^2+6*q-4 )
        q congruent 37 modulo 60:   1/12 q phi1^3
        q congruent 41 modulo 60:   1/12 phi2 ( q^3-4*q^2+7*q-6 )
        q congruent 43 modulo 60:   1/12 q phi1^3
        q congruent 47 modulo 60:   1/12 phi2 ( q^3-4*q^2+7*q-6 )
        q congruent 49 modulo 60:   1/12 q phi1^3
        q congruent 53 modulo 60:   1/12 phi2 ( q^3-4*q^2+7*q-6 )
        q congruent 59 modulo 60:   1/12 phi2 ( q^3-4*q^2+7*q-6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 78, 31, 82, 84, 38, 60, 112 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 5, 1, 2, 4 ], 
  [ 6, 1, 2, 2 ], [ 7, 1, 2, 2 ], [ 10, 1, 1, 2 ], [ 15, 1, 2, 2 ], 
  [ 22, 1, 3, 4 ], [ 26, 1, 2, 4 ], [ 27, 1, 4, 6 ], [ 29, 1, 3, 4 ], 
  [ 42, 1, 5, 6 ], [ 45, 1, 4, 6 ], [ 50, 1, 7, 12 ] ]

    k = 12: F-action on Pi is (1,2)(3,4)      [54,1,12]
      Dynkin type is ^2A_4(q) + T(phi1 phi2^3)
      Order of center |Z^F|: phi1 phi2^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 phi1 ( q^3-8*q^2+22*q-27 )
        q congruent 2 modulo 60:   1/24 ( q^4-9*q^3+26*q^2-28*q+8 )
        q congruent 3 modulo 60:   1/24 ( q^4-9*q^3+30*q^2-49*q+39 )
        q congruent 4 modulo 60:   1/24 q ( q^3-9*q^2+26*q-24 )
        q congruent 5 modulo 60:   1/24 ( q^4-9*q^3+30*q^2-53*q+39 )
        q congruent 7 modulo 60:   1/24 ( q^4-9*q^3+30*q^2-49*q+39 )
        q congruent 8 modulo 60:   1/24 ( q^4-9*q^3+26*q^2-28*q+8 )
        q congruent 9 modulo 60:   1/24 phi1 ( q^3-8*q^2+22*q-27 )
        q congruent 11 modulo 60:   1/24 ( q^4-9*q^3+30*q^2-53*q+51 )
        q congruent 13 modulo 60:   1/24 phi1 ( q^3-8*q^2+22*q-27 )
        q congruent 16 modulo 60:   1/24 q ( q^3-9*q^2+26*q-24 )
        q congruent 17 modulo 60:   1/24 ( q^4-9*q^3+30*q^2-53*q+39 )
        q congruent 19 modulo 60:   1/24 ( q^4-9*q^3+30*q^2-49*q+39 )
        q congruent 21 modulo 60:   1/24 phi1 ( q^3-8*q^2+22*q-27 )
        q congruent 23 modulo 60:   1/24 ( q^4-9*q^3+30*q^2-53*q+51 )
        q congruent 25 modulo 60:   1/24 phi1 ( q^3-8*q^2+22*q-27 )
        q congruent 27 modulo 60:   1/24 ( q^4-9*q^3+30*q^2-49*q+39 )
        q congruent 29 modulo 60:   1/24 ( q^4-9*q^3+30*q^2-53*q+39 )
        q congruent 31 modulo 60:   1/24 ( q^4-9*q^3+30*q^2-49*q+39 )
        q congruent 32 modulo 60:   1/24 ( q^4-9*q^3+26*q^2-28*q+8 )
        q congruent 37 modulo 60:   1/24 phi1 ( q^3-8*q^2+22*q-27 )
        q congruent 41 modulo 60:   1/24 ( q^4-9*q^3+30*q^2-53*q+39 )
        q congruent 43 modulo 60:   1/24 ( q^4-9*q^3+30*q^2-49*q+39 )
        q congruent 47 modulo 60:   1/24 ( q^4-9*q^3+30*q^2-53*q+51 )
        q congruent 49 modulo 60:   1/24 phi1 ( q^3-8*q^2+22*q-27 )
        q congruent 53 modulo 60:   1/24 ( q^4-9*q^3+30*q^2-53*q+39 )
        q congruent 59 modulo 60:   1/24 ( q^4-9*q^3+30*q^2-53*q+51 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 5, 69, 78, 31, 20, 94 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 6 ], 
  [ 5, 1, 2, 4 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 6 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 12 ], 
  [ 12, 1, 2, 12 ], [ 13, 1, 4, 12 ], [ 14, 1, 2, 6 ], [ 15, 1, 2, 8 ], 
  [ 18, 1, 2, 12 ], [ 19, 1, 2, 12 ], [ 21, 1, 2, 12 ], [ 22, 1, 3, 4 ], 
  [ 22, 1, 4, 12 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], 
  [ 26, 1, 2, 4 ], [ 26, 1, 4, 12 ], [ 27, 1, 3, 12 ], [ 27, 1, 6, 12 ], 
  [ 28, 1, 3, 12 ], [ 28, 1, 4, 12 ], [ 29, 1, 3, 4 ], [ 29, 1, 4, 12 ], 
  [ 30, 1, 3, 12 ], [ 34, 1, 3, 12 ], [ 34, 1, 4, 12 ], [ 36, 1, 3, 12 ], 
  [ 36, 1, 4, 12 ], [ 39, 1, 4, 12 ], [ 42, 1, 2, 12 ], [ 42, 1, 6, 12 ], 
  [ 44, 1, 8, 24 ], [ 45, 1, 5, 12 ], [ 45, 1, 6, 12 ], [ 50, 1, 9, 24 ], 
  [ 50, 1, 11, 24 ] ]

    k = 13: F-action on Pi is (1,2)(3,4)      [54,1,13]
      Dynkin type is ^2A_4(q) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^2 ( q^2-3*q+1 )
        q congruent 2 modulo 60:   1/16 q^2 ( q^2-5*q+6 )
        q congruent 3 modulo 60:   1/16 ( q^4-5*q^3+8*q^2-5*q-3 )
        q congruent 4 modulo 60:   1/16 q^2 ( q^2-5*q+6 )
        q congruent 5 modulo 60:   1/16 phi1^2 ( q^2-3*q+1 )
        q congruent 7 modulo 60:   1/16 ( q^4-5*q^3+8*q^2-5*q-3 )
        q congruent 8 modulo 60:   1/16 q^2 ( q^2-5*q+6 )
        q congruent 9 modulo 60:   1/16 phi1^2 ( q^2-3*q+1 )
        q congruent 11 modulo 60:   1/16 ( q^4-5*q^3+8*q^2-5*q-3 )
        q congruent 13 modulo 60:   1/16 phi1^2 ( q^2-3*q+1 )
        q congruent 16 modulo 60:   1/16 q^2 ( q^2-5*q+6 )
        q congruent 17 modulo 60:   1/16 phi1^2 ( q^2-3*q+1 )
        q congruent 19 modulo 60:   1/16 ( q^4-5*q^3+8*q^2-5*q-3 )
        q congruent 21 modulo 60:   1/16 phi1^2 ( q^2-3*q+1 )
        q congruent 23 modulo 60:   1/16 ( q^4-5*q^3+8*q^2-5*q-3 )
        q congruent 25 modulo 60:   1/16 phi1^2 ( q^2-3*q+1 )
        q congruent 27 modulo 60:   1/16 ( q^4-5*q^3+8*q^2-5*q-3 )
        q congruent 29 modulo 60:   1/16 phi1^2 ( q^2-3*q+1 )
        q congruent 31 modulo 60:   1/16 ( q^4-5*q^3+8*q^2-5*q-3 )
        q congruent 32 modulo 60:   1/16 q^2 ( q^2-5*q+6 )
        q congruent 37 modulo 60:   1/16 phi1^2 ( q^2-3*q+1 )
        q congruent 41 modulo 60:   1/16 phi1^2 ( q^2-3*q+1 )
        q congruent 43 modulo 60:   1/16 ( q^4-5*q^3+8*q^2-5*q-3 )
        q congruent 47 modulo 60:   1/16 ( q^4-5*q^3+8*q^2-5*q-3 )
        q congruent 49 modulo 60:   1/16 phi1^2 ( q^2-3*q+1 )
        q congruent 53 modulo 60:   1/16 phi1^2 ( q^2-3*q+1 )
        q congruent 59 modulo 60:   1/16 ( q^4-5*q^3+8*q^2-5*q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 69, 7, 31, 82, 76, 51 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 2, 2 ], 
  [ 5, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 2 ], 
  [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 13, 1, 3, 8 ], 
  [ 13, 1, 4, 4 ], [ 14, 1, 2, 2 ], [ 15, 1, 2, 4 ], [ 18, 1, 2, 4 ], 
  [ 19, 1, 2, 4 ], [ 22, 1, 3, 8 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 2 ], 
  [ 24, 1, 1, 4 ], [ 26, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 3, 8 ], 
  [ 29, 1, 3, 8 ], [ 30, 1, 3, 4 ], [ 30, 1, 4, 8 ], [ 34, 1, 3, 8 ], 
  [ 36, 1, 3, 8 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 8 ], [ 42, 1, 2, 8 ], 
  [ 44, 1, 9, 16 ], [ 45, 1, 5, 8 ], [ 50, 1, 8, 16 ] ]

    k = 14: F-action on Pi is (1,2)(3,4)      [54,1,14]
      Dynkin type is ^2A_4(q) + T(phi2^4)
      Order of center |Z^F|: phi2^4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/240 phi1 ( q^3-20*q^2+136*q-345 )
        q congruent 2 modulo 60:   1/240 ( q^4-21*q^3+146*q^2-376*q+320 )
        q congruent 3 modulo 60:   1/240 ( q^4-21*q^3+156*q^2-481*q+525 )
        q congruent 4 modulo 60:   1/240 ( q^4-21*q^3+146*q^2-336*q+96 )
        q congruent 5 modulo 60:   1/240 ( q^4-21*q^3+156*q^2-521*q+705 )
        q congruent 7 modulo 60:   1/240 ( q^4-21*q^3+156*q^2-481*q+525 )
        q congruent 8 modulo 60:   1/240 ( q^4-21*q^3+146*q^2-376*q+320 )
        q congruent 9 modulo 60:   1/240 ( q^4-21*q^3+156*q^2-481*q+441 )
        q congruent 11 modulo 60:   1/240 ( q^4-21*q^3+156*q^2-521*q+885 )
        q congruent 13 modulo 60:   1/240 phi1 ( q^3-20*q^2+136*q-345 )
        q congruent 16 modulo 60:   1/240 q ( q^3-21*q^2+146*q-336 )
        q congruent 17 modulo 60:   1/240 ( q^4-21*q^3+156*q^2-521*q+705 )
        q congruent 19 modulo 60:   1/240 ( q^4-21*q^3+156*q^2-481*q+621 )
        q congruent 21 modulo 60:   1/240 phi1 ( q^3-20*q^2+136*q-345 )
        q congruent 23 modulo 60:   1/240 ( q^4-21*q^3+156*q^2-521*q+885 )
        q congruent 25 modulo 60:   1/240 phi1 ( q^3-20*q^2+136*q-345 )
        q congruent 27 modulo 60:   1/240 ( q^4-21*q^3+156*q^2-481*q+525 )
        q congruent 29 modulo 60:   1/240 ( q^4-21*q^3+156*q^2-521*q+801 )
        q congruent 31 modulo 60:   1/240 ( q^4-21*q^3+156*q^2-481*q+525 )
        q congruent 32 modulo 60:   1/240 ( q^4-21*q^3+146*q^2-376*q+320 )
        q congruent 37 modulo 60:   1/240 phi1 ( q^3-20*q^2+136*q-345 )
        q congruent 41 modulo 60:   1/240 ( q^4-21*q^3+156*q^2-521*q+705 )
        q congruent 43 modulo 60:   1/240 ( q^4-21*q^3+156*q^2-481*q+525 )
        q congruent 47 modulo 60:   1/240 ( q^4-21*q^3+156*q^2-521*q+885 )
        q congruent 49 modulo 60:   1/240 ( q^4-21*q^3+156*q^2-481*q+441 )
        q congruent 53 modulo 60:   1/240 ( q^4-21*q^3+156*q^2-521*q+705 )
        q congruent 59 modulo 60:   1/240 ( q^4-21*q^3+156*q^2-521*q+981 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 2, 67, 5, 9, 78, 71, 24 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 10 ], [ 3, 1, 2, 20 ], [ 4, 1, 2, 10 ], 
  [ 5, 1, 2, 4 ], [ 6, 1, 2, 20 ], [ 7, 1, 2, 20 ], [ 8, 1, 2, 10 ], 
  [ 9, 1, 1, 5 ], [ 10, 1, 2, 20 ], [ 11, 1, 2, 60 ], [ 12, 1, 2, 40 ], 
  [ 13, 1, 4, 60 ], [ 14, 1, 2, 10 ], [ 15, 1, 2, 20 ], [ 18, 1, 2, 60 ], 
  [ 19, 1, 2, 60 ], [ 21, 1, 2, 40 ], [ 22, 1, 4, 40 ], [ 23, 1, 2, 30 ], 
  [ 24, 1, 2, 60 ], [ 26, 1, 4, 40 ], [ 27, 1, 6, 120 ], [ 28, 1, 4, 120 ], 
  [ 29, 1, 4, 40 ], [ 30, 1, 3, 60 ], [ 34, 1, 4, 120 ], [ 36, 1, 4, 120 ], 
  [ 39, 1, 3, 120 ], [ 42, 1, 6, 120 ], [ 44, 1, 10, 240 ], [ 45, 1, 6, 120 ],
  [ 50, 1, 12, 240 ] ]

i = 55: Pi = [ 1, 2, 3, 5 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [55,1,1]
      Dynkin type is A_2(q) + A_1(q) + A_1(q) + T(phi1^4)
      Order of center |Z^F|: phi1^4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/96 ( q^4-37*q^3+501*q^2-3039*q+7950 )
        q congruent 2 modulo 60:   1/96 ( q^4-36*q^3+444*q^2-2096*q+2688 )
        q congruent 3 modulo 60:   1/96 ( q^4-37*q^3+493*q^2-2739*q+4698 )
        q congruent 4 modulo 60:   1/96 ( q^4-36*q^3+452*q^2-2336*q+4160 )
        q congruent 5 modulo 60:   1/96 ( q^4-37*q^3+493*q^2-2799*q+5670 )
        q congruent 7 modulo 60:   1/96 ( q^4-37*q^3+501*q^2-2979*q+6594 )
        q congruent 8 modulo 60:   1/96 ( q^4-36*q^3+444*q^2-2096*q+2688 )
        q congruent 9 modulo 60:   1/96 ( q^4-37*q^3+493*q^2-2799*q+5670 )
        q congruent 11 modulo 60:   1/96 ( q^4-37*q^3+493*q^2-2739*q+5082 )
        q congruent 13 modulo 60:   1/96 ( q^4-37*q^3+501*q^2-3039*q+7566 )
        q congruent 16 modulo 60:   1/96 ( q^4-36*q^3+452*q^2-2336*q+4544 )
        q congruent 17 modulo 60:   1/96 ( q^4-37*q^3+493*q^2-2799*q+5670 )
        q congruent 19 modulo 60:   1/96 ( q^4-37*q^3+501*q^2-2979*q+6594 )
        q congruent 21 modulo 60:   1/96 ( q^4-37*q^3+493*q^2-2799*q+6054 )
        q congruent 23 modulo 60:   1/96 ( q^4-37*q^3+493*q^2-2739*q+4698 )
        q congruent 25 modulo 60:   1/96 ( q^4-37*q^3+501*q^2-3039*q+7566 )
        q congruent 27 modulo 60:   1/96 ( q^4-37*q^3+493*q^2-2739*q+4698 )
        q congruent 29 modulo 60:   1/96 ( q^4-37*q^3+493*q^2-2799*q+5670 )
        q congruent 31 modulo 60:   1/96 ( q^4-37*q^3+501*q^2-2979*q+6978 )
        q congruent 32 modulo 60:   1/96 ( q^4-36*q^3+444*q^2-2096*q+2688 )
        q congruent 37 modulo 60:   1/96 ( q^4-37*q^3+501*q^2-3039*q+7566 )
        q congruent 41 modulo 60:   1/96 ( q^4-37*q^3+493*q^2-2799*q+6054 )
        q congruent 43 modulo 60:   1/96 ( q^4-37*q^3+501*q^2-2979*q+6594 )
        q congruent 47 modulo 60:   1/96 ( q^4-37*q^3+493*q^2-2739*q+4698 )
        q congruent 49 modulo 60:   1/96 ( q^4-37*q^3+501*q^2-3039*q+7566 )
        q congruent 53 modulo 60:   1/96 ( q^4-37*q^3+493*q^2-2799*q+5670 )
        q congruent 59 modulo 60:   1/96 ( q^4-37*q^3+493*q^2-2739*q+4698 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 66, 4, 4, 68, 8, 77, 77, 30 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 26 ], [ 4, 1, 1, 46 ], 
  [ 5, 1, 1, 80 ], [ 6, 1, 1, 96 ], [ 7, 1, 1, 40 ], [ 8, 1, 1, 24 ], 
  [ 9, 1, 1, 7 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 40 ], [ 12, 1, 1, 70 ], 
  [ 13, 1, 1, 72 ], [ 14, 1, 1, 120 ], [ 15, 1, 1, 152 ], [ 16, 1, 1, 176 ], 
  [ 17, 1, 1, 240 ], [ 18, 1, 1, 72 ], [ 19, 1, 1, 112 ], [ 20, 1, 1, 144 ], 
  [ 21, 1, 1, 48 ], [ 22, 1, 1, 120 ], [ 23, 1, 1, 18 ], [ 24, 1, 1, 36 ], 
  [ 25, 1, 1, 60 ], [ 26, 1, 1, 48 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 72 ], 
  [ 29, 1, 1, 144 ], [ 30, 1, 1, 144 ], [ 31, 1, 1, 168 ], [ 32, 1, 1, 224 ], 
  [ 33, 1, 1, 144 ], [ 34, 1, 1, 96 ], [ 35, 1, 1, 144 ], [ 36, 1, 1, 48 ], 
  [ 37, 1, 1, 96 ], [ 38, 1, 1, 288 ], [ 39, 1, 1, 24 ], [ 40, 1, 1, 36 ], 
  [ 41, 1, 1, 48 ], [ 42, 1, 1, 96 ], [ 43, 1, 1, 96 ], [ 44, 1, 1, 48 ], 
  [ 45, 1, 1, 96 ], [ 46, 1, 1, 192 ], [ 47, 1, 1, 144 ], [ 48, 1, 1, 96 ], 
  [ 51, 1, 1, 48 ], [ 53, 1, 1, 96 ] ]

    k = 2: F-action on Pi is ()      [55,1,2]
      Dynkin type is A_2(q) + A_1(q) + A_1(q) + T(phi1^3 phi2)
      Order of center |Z^F|: phi1^3 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q^3-16*q^2+83*q-148 )
        q congruent 2 modulo 60:   1/16 q ( q^3-16*q^2+76*q-96 )
        q congruent 3 modulo 60:   1/16 ( q^4-17*q^3+95*q^2-187*q+84 )
        q congruent 4 modulo 60:   1/16 q ( q^3-16*q^2+80*q-128 )
        q congruent 5 modulo 60:   1/16 phi1 ( q^3-16*q^2+79*q-120 )
        q congruent 7 modulo 60:   1/16 ( q^4-17*q^3+99*q^2-219*q+112 )
        q congruent 8 modulo 60:   1/16 q ( q^3-16*q^2+76*q-96 )
        q congruent 9 modulo 60:   1/16 phi1 ( q^3-16*q^2+79*q-120 )
        q congruent 11 modulo 60:   1/16 ( q^4-17*q^3+95*q^2-187*q+84 )
        q congruent 13 modulo 60:   1/16 phi1 ( q^3-16*q^2+83*q-148 )
        q congruent 16 modulo 60:   1/16 q ( q^3-16*q^2+80*q-128 )
        q congruent 17 modulo 60:   1/16 phi1 ( q^3-16*q^2+79*q-120 )
        q congruent 19 modulo 60:   1/16 ( q^4-17*q^3+99*q^2-219*q+112 )
        q congruent 21 modulo 60:   1/16 phi1 ( q^3-16*q^2+79*q-120 )
        q congruent 23 modulo 60:   1/16 ( q^4-17*q^3+95*q^2-187*q+84 )
        q congruent 25 modulo 60:   1/16 phi1 ( q^3-16*q^2+83*q-148 )
        q congruent 27 modulo 60:   1/16 ( q^4-17*q^3+95*q^2-187*q+84 )
        q congruent 29 modulo 60:   1/16 phi1 ( q^3-16*q^2+79*q-120 )
        q congruent 31 modulo 60:   1/16 ( q^4-17*q^3+99*q^2-219*q+112 )
        q congruent 32 modulo 60:   1/16 q ( q^3-16*q^2+76*q-96 )
        q congruent 37 modulo 60:   1/16 phi1 ( q^3-16*q^2+83*q-148 )
        q congruent 41 modulo 60:   1/16 phi1 ( q^3-16*q^2+79*q-120 )
        q congruent 43 modulo 60:   1/16 ( q^4-17*q^3+99*q^2-219*q+112 )
        q congruent 47 modulo 60:   1/16 ( q^4-17*q^3+95*q^2-187*q+84 )
        q congruent 49 modulo 60:   1/16 phi1 ( q^3-16*q^2+83*q-148 )
        q congruent 53 modulo 60:   1/16 phi1 ( q^3-16*q^2+79*q-120 )
        q congruent 59 modulo 60:   1/16 ( q^4-17*q^3+95*q^2-187*q+84 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 4, 68, 4, 68, 68, 7, 77, 30, 30, 81 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 14 ], [ 4, 1, 1, 18 ], 
  [ 5, 1, 1, 24 ], [ 6, 1, 1, 32 ], [ 7, 1, 1, 12 ], [ 8, 1, 1, 4 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 12 ], 
  [ 12, 1, 1, 18 ], [ 13, 1, 1, 24 ], [ 14, 1, 1, 12 ], [ 15, 1, 1, 36 ], 
  [ 16, 1, 1, 48 ], [ 17, 1, 1, 72 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 24 ], 
  [ 20, 1, 1, 24 ], [ 20, 1, 2, 24 ], [ 22, 1, 1, 4 ], [ 22, 1, 2, 20 ], 
  [ 23, 1, 1, 6 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 12 ], 
  [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 28, 1, 1, 12 ], [ 28, 1, 2, 12 ], 
  [ 29, 1, 2, 24 ], [ 30, 1, 1, 24 ], [ 31, 1, 1, 12 ], [ 31, 1, 2, 28 ], 
  [ 32, 1, 1, 48 ], [ 33, 1, 1, 48 ], [ 34, 1, 2, 16 ], [ 35, 1, 1, 24 ], 
  [ 35, 1, 3, 24 ], [ 36, 1, 2, 8 ], [ 38, 1, 5, 48 ], [ 39, 1, 4, 4 ], 
  [ 40, 1, 1, 12 ], [ 41, 1, 6, 8 ], [ 42, 1, 4, 16 ], [ 43, 1, 2, 16 ], 
  [ 44, 1, 2, 8 ], [ 45, 1, 2, 16 ], [ 46, 1, 2, 32 ], [ 47, 1, 1, 24 ], 
  [ 47, 1, 2, 24 ], [ 48, 1, 2, 16 ], [ 51, 1, 2, 8 ], [ 53, 1, 3, 16 ] ]

    k = 3: F-action on Pi is ()      [55,1,3]
      Dynkin type is A_2(q) + A_1(q) + A_1(q) + T(phi1^2 phi3)
      Order of center |Z^F|: phi1^2 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 phi1 ( q^3-6*q^2+3*q+24 )
        q congruent 2 modulo 60:   1/12 q phi2 ( q^2-7*q+10 )
        q congruent 3 modulo 60:   1/12 q phi2 ( q^2-8*q+15 )
        q congruent 4 modulo 60:   1/12 phi1 ( q^3-5*q^2+16 )
        q congruent 5 modulo 60:   1/12 q phi2 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/12 phi1 ( q^3-6*q^2+3*q+24 )
        q congruent 8 modulo 60:   1/12 q phi2 ( q^2-7*q+10 )
        q congruent 9 modulo 60:   1/12 q phi2 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/12 q phi2 ( q^2-8*q+15 )
        q congruent 13 modulo 60:   1/12 phi1 ( q^3-6*q^2+3*q+24 )
        q congruent 16 modulo 60:   1/12 phi1 ( q^3-5*q^2+16 )
        q congruent 17 modulo 60:   1/12 q phi2 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/12 phi1 ( q^3-6*q^2+3*q+24 )
        q congruent 21 modulo 60:   1/12 q phi2 ( q^2-8*q+15 )
        q congruent 23 modulo 60:   1/12 q phi2 ( q^2-8*q+15 )
        q congruent 25 modulo 60:   1/12 phi1 ( q^3-6*q^2+3*q+24 )
        q congruent 27 modulo 60:   1/12 q phi2 ( q^2-8*q+15 )
        q congruent 29 modulo 60:   1/12 q phi2 ( q^2-8*q+15 )
        q congruent 31 modulo 60:   1/12 phi1 ( q^3-6*q^2+3*q+24 )
        q congruent 32 modulo 60:   1/12 q phi2 ( q^2-7*q+10 )
        q congruent 37 modulo 60:   1/12 phi1 ( q^3-6*q^2+3*q+24 )
        q congruent 41 modulo 60:   1/12 q phi2 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/12 phi1 ( q^3-6*q^2+3*q+24 )
        q congruent 47 modulo 60:   1/12 q phi2 ( q^2-8*q+15 )
        q congruent 49 modulo 60:   1/12 phi1 ( q^3-6*q^2+3*q+24 )
        q congruent 53 modulo 60:   1/12 q phi2 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/12 q phi2 ( q^2-8*q+15 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 8, 77, 77, 30, 77, 30, 30, 81, 14, 83, 83, 37 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], 
  [ 5, 1, 1, 8 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], 
  [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 15, 1, 1, 8 ], [ 16, 1, 1, 8 ], 
  [ 17, 1, 1, 24 ], [ 19, 1, 1, 4 ], [ 27, 1, 5, 6 ], [ 32, 1, 1, 8 ], 
  [ 38, 1, 3, 36 ], [ 42, 1, 3, 12 ], [ 44, 1, 3, 6 ], [ 45, 1, 3, 12 ], 
  [ 46, 1, 3, 24 ], [ 53, 1, 16, 12 ] ]

    k = 4: F-action on Pi is ()      [55,1,4]
      Dynkin type is A_2(q) + A_1(q) + A_1(q) + T(phi1 phi2 phi4)
      Order of center |Z^F|: phi1 phi2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 2 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 3 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 4 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 5 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 7 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 8 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 9 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 11 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 16 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 17 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 19 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 23 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 27 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 31 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 32 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 37 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 41 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 43 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 53 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 59 modulo 60:   1/16 q phi1 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 70, 19, 19, 72, 19, 76, 76, 20, 97, 59, 59, 95 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], 
  [ 4, 1, 2, 2 ], [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], 
  [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], 
  [ 23, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 33, 1, 2, 8 ], [ 39, 1, 5, 4 ], 
  [ 40, 1, 3, 4 ], [ 41, 1, 8, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 4, 8 ], 
  [ 51, 1, 7, 8 ], [ 53, 1, 11, 16 ] ]

    k = 5: F-action on Pi is ()      [55,1,5]
      Dynkin type is A_2(q) + A_1(q) + A_1(q) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 2 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 3 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-18 )
        q congruent 4 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 5 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 7 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-18 )
        q congruent 8 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 9 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 11 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-18 )
        q congruent 13 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 16 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 17 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 19 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-18 )
        q congruent 21 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 23 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-18 )
        q congruent 25 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 27 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-18 )
        q congruent 29 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 31 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-18 )
        q congruent 32 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 37 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 41 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 43 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-18 )
        q congruent 47 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-18 )
        q congruent 49 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 53 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 59 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-18 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 68, 68, 3, 68, 7, 7, 69, 30, 81, 81, 27 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 18 ], 
  [ 4, 1, 2, 4 ], [ 6, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 4 ], 
  [ 12, 1, 1, 6 ], [ 13, 1, 1, 24 ], [ 13, 1, 2, 8 ], [ 13, 1, 4, 8 ], 
  [ 16, 1, 1, 24 ], [ 16, 1, 2, 8 ], [ 20, 1, 2, 48 ], [ 22, 1, 2, 8 ], 
  [ 23, 1, 1, 6 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 12 ], 
  [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 16 ], [ 28, 1, 2, 24 ], 
  [ 31, 1, 2, 24 ], [ 33, 1, 1, 48 ], [ 33, 1, 2, 16 ], [ 35, 1, 3, 48 ], 
  [ 37, 1, 2, 16 ], [ 39, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 40, 1, 1, 12 ], 
  [ 40, 1, 3, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 9, 16 ], [ 43, 1, 8, 16 ], 
  [ 43, 1, 12, 32 ], [ 44, 1, 5, 16 ], [ 47, 1, 2, 48 ], [ 48, 1, 3, 32 ], 
  [ 51, 1, 5, 16 ], [ 51, 1, 6, 16 ], [ 53, 1, 9, 32 ] ]

    k = 6: F-action on Pi is (2,5)      [55,1,6]
      Dynkin type is A_2(q) + A_1(q^2) + T(phi1^2 phi4)
      Order of center |Z^F|: phi1^2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 2 modulo 60:   1/16 q^2 ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 4 modulo 60:   1/16 q^2 ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 7 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 8 modulo 60:   1/16 q^2 ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 11 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 13 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 16 modulo 60:   1/16 q^2 ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 19 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 21 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 23 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 25 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 27 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 29 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 31 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 32 modulo 60:   1/16 q^2 ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 41 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 43 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 47 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 49 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 53 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 59 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 70, 16, 19, 73, 97, 53 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 4 ], 
  [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 13, 1, 3, 8 ], [ 16, 1, 2, 8 ], 
  [ 23, 1, 1, 6 ], [ 25, 1, 1, 12 ], [ 33, 1, 4, 16 ], [ 39, 1, 5, 4 ], 
  [ 40, 1, 1, 12 ], [ 41, 1, 5, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 6, 8 ], 
  [ 48, 1, 8, 16 ], [ 51, 1, 7, 8 ], [ 53, 1, 10, 16 ] ]

    k = 7: F-action on Pi is (2,5)      [55,1,7]
      Dynkin type is A_2(q) + A_1(q^2) + T(phi1 phi2 phi6)
      Order of center |Z^F|: phi1 phi2 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q phi1 ( q^2-2*q-5 )
        q congruent 2 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 3 modulo 60:   1/12 q phi1 phi2 ( q-3 )
        q congruent 4 modulo 60:   1/12 q phi1 ( q^2-q-4 )
        q congruent 5 modulo 60:   1/12 q phi1 phi2 ( q-3 )
        q congruent 7 modulo 60:   1/12 q phi1 ( q^2-2*q-5 )
        q congruent 8 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 9 modulo 60:   1/12 q phi1 phi2 ( q-3 )
        q congruent 11 modulo 60:   1/12 q phi1 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/12 q phi1 ( q^2-2*q-5 )
        q congruent 16 modulo 60:   1/12 q phi1 ( q^2-q-4 )
        q congruent 17 modulo 60:   1/12 q phi1 phi2 ( q-3 )
        q congruent 19 modulo 60:   1/12 q phi1 ( q^2-2*q-5 )
        q congruent 21 modulo 60:   1/12 q phi1 phi2 ( q-3 )
        q congruent 23 modulo 60:   1/12 q phi1 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/12 q phi1 ( q^2-2*q-5 )
        q congruent 27 modulo 60:   1/12 q phi1 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/12 q phi1 phi2 ( q-3 )
        q congruent 31 modulo 60:   1/12 q phi1 ( q^2-2*q-5 )
        q congruent 32 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 37 modulo 60:   1/12 q phi1 ( q^2-2*q-5 )
        q congruent 41 modulo 60:   1/12 q phi1 phi2 ( q-3 )
        q congruent 43 modulo 60:   1/12 q phi1 ( q^2-2*q-5 )
        q congruent 47 modulo 60:   1/12 q phi1 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/12 q phi1 ( q^2-2*q-5 )
        q congruent 53 modulo 60:   1/12 q phi1 phi2 ( q-3 )
        q congruent 59 modulo 60:   1/12 q phi1 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 28, 96, 82, 60, 36, 99 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], 
  [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 2 ], 
  [ 16, 1, 2, 4 ], [ 16, 1, 4, 4 ], [ 27, 1, 4, 6 ], [ 32, 1, 2, 4 ], 
  [ 38, 1, 4, 12 ], [ 44, 1, 7, 6 ], [ 53, 1, 15, 12 ] ]

    k = 8: F-action on Pi is (2,5)      [55,1,8]
      Dynkin type is A_2(q) + A_1(q^2) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 q phi1 ( q^2-4*q-1 )
        q congruent 2 modulo 60:   1/16 q^2 ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/16 q phi1^2 ( q-3 )
        q congruent 4 modulo 60:   1/16 q ( q^3-4*q^2+8 )
        q congruent 5 modulo 60:   1/16 phi1 ( q^3-4*q^2+3*q-4 )
        q congruent 7 modulo 60:   1/16 phi1^2 phi2 ( q-4 )
        q congruent 8 modulo 60:   1/16 q^2 ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/16 phi1 ( q^3-4*q^2+3*q-4 )
        q congruent 11 modulo 60:   1/16 q phi1^2 ( q-3 )
        q congruent 13 modulo 60:   1/16 q phi1 ( q^2-4*q-1 )
        q congruent 16 modulo 60:   1/16 q ( q^3-4*q^2+8 )
        q congruent 17 modulo 60:   1/16 phi1 ( q^3-4*q^2+3*q-4 )
        q congruent 19 modulo 60:   1/16 phi1^2 phi2 ( q-4 )
        q congruent 21 modulo 60:   1/16 phi1 ( q^3-4*q^2+3*q-4 )
        q congruent 23 modulo 60:   1/16 q phi1^2 ( q-3 )
        q congruent 25 modulo 60:   1/16 q phi1 ( q^2-4*q-1 )
        q congruent 27 modulo 60:   1/16 q phi1^2 ( q-3 )
        q congruent 29 modulo 60:   1/16 phi1 ( q^3-4*q^2+3*q-4 )
        q congruent 31 modulo 60:   1/16 phi1^2 phi2 ( q-4 )
        q congruent 32 modulo 60:   1/16 q^2 ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/16 q phi1 ( q^2-4*q-1 )
        q congruent 41 modulo 60:   1/16 phi1 ( q^3-4*q^2+3*q-4 )
        q congruent 43 modulo 60:   1/16 phi1^2 phi2 ( q-4 )
        q congruent 47 modulo 60:   1/16 q phi1^2 ( q-3 )
        q congruent 49 modulo 60:   1/16 q phi1 ( q^2-4*q-1 )
        q congruent 53 modulo 60:   1/16 phi1 ( q^3-4*q^2+3*q-4 )
        q congruent 59 modulo 60:   1/16 q phi1^2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 19, 7, 76, 81, 59 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 4 ], 
  [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], [ 5, 1, 1, 8 ], [ 6, 1, 1, 4 ], 
  [ 7, 1, 1, 4 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 4 ], 
  [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 14, 1, 1, 4 ], [ 15, 1, 1, 4 ], 
  [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], [ 16, 1, 4, 8 ], [ 17, 1, 2, 8 ], 
  [ 18, 1, 1, 4 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 8 ], [ 22, 1, 1, 4 ], 
  [ 22, 1, 2, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], 
  [ 25, 1, 4, 4 ], [ 26, 1, 3, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 3, 4 ], 
  [ 28, 1, 4, 4 ], [ 29, 1, 2, 8 ], [ 30, 1, 2, 8 ], [ 31, 1, 1, 4 ], 
  [ 31, 1, 2, 4 ], [ 32, 1, 2, 8 ], [ 33, 1, 2, 8 ], [ 35, 1, 2, 8 ], 
  [ 35, 1, 4, 8 ], [ 36, 1, 2, 8 ], [ 38, 1, 2, 16 ], [ 39, 1, 4, 4 ], 
  [ 40, 1, 3, 4 ], [ 41, 1, 7, 8 ], [ 43, 1, 2, 16 ], [ 44, 1, 8, 8 ], 
  [ 47, 1, 3, 8 ], [ 47, 1, 4, 8 ], [ 51, 1, 2, 8 ], [ 53, 1, 4, 16 ] ]

    k = 9: F-action on Pi is (2,5)      [55,1,9]
      Dynkin type is A_2(q) + A_1(q^2) + T(phi1^3 phi2)
      Order of center |Z^F|: phi1^3 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1^2 ( q^2-11*q+30 )
        q congruent 2 modulo 60:   1/32 q ( q^3-12*q^2+44*q-48 )
        q congruent 3 modulo 60:   1/32 ( q^4-13*q^3+53*q^2-67*q-6 )
        q congruent 4 modulo 60:   1/32 q ( q^3-12*q^2+44*q-48 )
        q congruent 5 modulo 60:   1/32 phi1^2 ( q^2-11*q+30 )
        q congruent 7 modulo 60:   1/32 ( q^4-13*q^3+53*q^2-67*q-6 )
        q congruent 8 modulo 60:   1/32 q ( q^3-12*q^2+44*q-48 )
        q congruent 9 modulo 60:   1/32 phi1^2 ( q^2-11*q+30 )
        q congruent 11 modulo 60:   1/32 ( q^4-13*q^3+53*q^2-67*q-6 )
        q congruent 13 modulo 60:   1/32 phi1^2 ( q^2-11*q+30 )
        q congruent 16 modulo 60:   1/32 q ( q^3-12*q^2+44*q-48 )
        q congruent 17 modulo 60:   1/32 phi1^2 ( q^2-11*q+30 )
        q congruent 19 modulo 60:   1/32 ( q^4-13*q^3+53*q^2-67*q-6 )
        q congruent 21 modulo 60:   1/32 phi1^2 ( q^2-11*q+30 )
        q congruent 23 modulo 60:   1/32 ( q^4-13*q^3+53*q^2-67*q-6 )
        q congruent 25 modulo 60:   1/32 phi1^2 ( q^2-11*q+30 )
        q congruent 27 modulo 60:   1/32 ( q^4-13*q^3+53*q^2-67*q-6 )
        q congruent 29 modulo 60:   1/32 phi1^2 ( q^2-11*q+30 )
        q congruent 31 modulo 60:   1/32 ( q^4-13*q^3+53*q^2-67*q-6 )
        q congruent 32 modulo 60:   1/32 q ( q^3-12*q^2+44*q-48 )
        q congruent 37 modulo 60:   1/32 phi1^2 ( q^2-11*q+30 )
        q congruent 41 modulo 60:   1/32 phi1^2 ( q^2-11*q+30 )
        q congruent 43 modulo 60:   1/32 ( q^4-13*q^3+53*q^2-67*q-6 )
        q congruent 47 modulo 60:   1/32 ( q^4-13*q^3+53*q^2-67*q-6 )
        q congruent 49 modulo 60:   1/32 phi1^2 ( q^2-11*q+30 )
        q congruent 53 modulo 60:   1/32 phi1^2 ( q^2-11*q+30 )
        q congruent 59 modulo 60:   1/32 ( q^4-13*q^3+53*q^2-67*q-6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 70, 68, 19, 30, 97 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 12 ], 
  [ 4, 1, 2, 6 ], [ 5, 1, 1, 16 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 8 ], 
  [ 8, 1, 1, 8 ], [ 9, 1, 1, 5 ], [ 10, 1, 1, 4 ], [ 12, 1, 1, 10 ], 
  [ 13, 1, 2, 4 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 4 ], [ 14, 1, 1, 24 ], 
  [ 15, 1, 1, 8 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 12 ], [ 18, 1, 1, 8 ], 
  [ 20, 1, 1, 16 ], [ 21, 1, 1, 16 ], [ 22, 1, 1, 8 ], [ 23, 1, 1, 12 ], 
  [ 23, 1, 2, 2 ], [ 24, 1, 1, 4 ], [ 25, 1, 1, 32 ], [ 25, 1, 2, 8 ], 
  [ 25, 1, 3, 8 ], [ 25, 1, 4, 4 ], [ 26, 1, 1, 16 ], [ 28, 1, 3, 8 ], 
  [ 29, 1, 1, 16 ], [ 30, 1, 2, 16 ], [ 31, 1, 1, 8 ], [ 33, 1, 2, 8 ], 
  [ 33, 1, 4, 32 ], [ 35, 1, 2, 16 ], [ 36, 1, 1, 16 ], [ 37, 1, 1, 32 ], 
  [ 37, 1, 2, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 8 ], [ 40, 1, 1, 24 ], 
  [ 40, 1, 3, 4 ], [ 41, 1, 2, 16 ], [ 41, 1, 3, 16 ], [ 43, 1, 1, 32 ], 
  [ 43, 1, 8, 16 ], [ 44, 1, 9, 16 ], [ 47, 1, 3, 16 ], [ 48, 1, 7, 32 ], 
  [ 51, 1, 1, 16 ], [ 51, 1, 6, 16 ], [ 53, 1, 2, 32 ] ]

    k = 10: F-action on Pi is (2,5)      [55,1,10]
      Dynkin type is A_2(q) + A_1(q^2) + T(phi1 phi2^3)
      Order of center |Z^F|: phi1 phi2^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/96 phi1^3 ( q-6 )
        q congruent 2 modulo 60:   1/96 q ( q^3-8*q^2+20*q-16 )
        q congruent 3 modulo 60:   1/96 phi1 ( q^3-8*q^2+21*q-18 )
        q congruent 4 modulo 60:   1/96 q ( q^3-8*q^2+12*q+16 )
        q congruent 5 modulo 60:   1/96 phi1 ( q^3-8*q^2+21*q-30 )
        q congruent 7 modulo 60:   1/96 phi1 ( q^3-8*q^2+13*q+6 )
        q congruent 8 modulo 60:   1/96 q ( q^3-8*q^2+20*q-16 )
        q congruent 9 modulo 60:   1/96 phi1 ( q^3-8*q^2+21*q-30 )
        q congruent 11 modulo 60:   1/96 phi1 ( q^3-8*q^2+21*q-18 )
        q congruent 13 modulo 60:   1/96 phi1^3 ( q-6 )
        q congruent 16 modulo 60:   1/96 q ( q^3-8*q^2+12*q+16 )
        q congruent 17 modulo 60:   1/96 phi1 ( q^3-8*q^2+21*q-30 )
        q congruent 19 modulo 60:   1/96 phi1 ( q^3-8*q^2+13*q+6 )
        q congruent 21 modulo 60:   1/96 phi1 ( q^3-8*q^2+21*q-30 )
        q congruent 23 modulo 60:   1/96 phi1 ( q^3-8*q^2+21*q-18 )
        q congruent 25 modulo 60:   1/96 phi1^3 ( q-6 )
        q congruent 27 modulo 60:   1/96 phi1 ( q^3-8*q^2+21*q-18 )
        q congruent 29 modulo 60:   1/96 phi1 ( q^3-8*q^2+21*q-30 )
        q congruent 31 modulo 60:   1/96 phi1 ( q^3-8*q^2+13*q+6 )
        q congruent 32 modulo 60:   1/96 q ( q^3-8*q^2+20*q-16 )
        q congruent 37 modulo 60:   1/96 phi1^3 ( q-6 )
        q congruent 41 modulo 60:   1/96 phi1 ( q^3-8*q^2+21*q-30 )
        q congruent 43 modulo 60:   1/96 phi1 ( q^3-8*q^2+13*q+6 )
        q congruent 47 modulo 60:   1/96 phi1 ( q^3-8*q^2+21*q-18 )
        q congruent 49 modulo 60:   1/96 phi1^3 ( q-6 )
        q congruent 53 modulo 60:   1/96 phi1 ( q^3-8*q^2+21*q-30 )
        q congruent 59 modulo 60:   1/96 phi1 ( q^3-8*q^2+21*q-18 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 72, 69, 20, 27, 95 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 8 ], 
  [ 4, 1, 1, 8 ], [ 4, 1, 2, 2 ], [ 6, 1, 1, 12 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 2, 12 ], [ 11, 1, 2, 24 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 8 ], 
  [ 13, 1, 2, 12 ], [ 13, 1, 4, 12 ], [ 16, 1, 1, 12 ], [ 16, 1, 2, 4 ], 
  [ 16, 1, 4, 16 ], [ 17, 1, 2, 48 ], [ 20, 1, 2, 48 ], [ 22, 1, 2, 24 ], 
  [ 23, 1, 2, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 4, 36 ], [ 27, 1, 6, 48 ], 
  [ 28, 1, 4, 24 ], [ 31, 1, 2, 24 ], [ 32, 1, 2, 16 ], [ 33, 1, 2, 24 ], 
  [ 35, 1, 4, 48 ], [ 38, 1, 6, 96 ], [ 39, 1, 3, 24 ], [ 40, 1, 3, 12 ], 
  [ 41, 1, 10, 48 ], [ 43, 1, 12, 96 ], [ 44, 1, 10, 48 ], [ 47, 1, 4, 48 ], 
  [ 51, 1, 5, 48 ], [ 53, 1, 19, 96 ] ]

    k = 11: F-action on Pi is (1,3)      [55,1,11]
      Dynkin type is ^2A_2(q) + A_1(q) + A_1(q) + T(phi1 phi2 phi4)
      Order of center |Z^F|: phi1 phi2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 2 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 3 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 4 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 5 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 7 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 8 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 9 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 11 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 13 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 16 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 17 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 19 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 21 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 23 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 25 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 27 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 29 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 31 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 32 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 37 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 41 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 43 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 47 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 49 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 53 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 59 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 72, 20, 20, 71, 19, 76, 76, 20, 96, 60, 60, 98 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], 
  [ 4, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ], 
  [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], 
  [ 23, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 33, 1, 6, 8 ], [ 39, 1, 5, 4 ], 
  [ 40, 1, 2, 4 ], [ 41, 1, 8, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 6, 8 ], 
  [ 51, 1, 4, 8 ], [ 53, 1, 13, 16 ] ]

    k = 12: F-action on Pi is (1,3)      [55,1,12]
      Dynkin type is ^2A_2(q) + A_1(q) + A_1(q) + T(phi2^2 phi6)
      Order of center |Z^F|: phi2^2 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q phi1^2 ( q-3 )
        q congruent 2 modulo 60:   1/12 phi2 ( q^3-5*q^2+10*q-8 )
        q congruent 3 modulo 60:   1/12 q phi1^2 ( q-3 )
        q congruent 4 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 5 modulo 60:   1/12 phi2 ( q^3-6*q^2+15*q-16 )
        q congruent 7 modulo 60:   1/12 q phi1^2 ( q-3 )
        q congruent 8 modulo 60:   1/12 phi2 ( q^3-5*q^2+10*q-8 )
        q congruent 9 modulo 60:   1/12 q phi1^2 ( q-3 )
        q congruent 11 modulo 60:   1/12 phi2 ( q^3-6*q^2+15*q-16 )
        q congruent 13 modulo 60:   1/12 q phi1^2 ( q-3 )
        q congruent 16 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 17 modulo 60:   1/12 phi2 ( q^3-6*q^2+15*q-16 )
        q congruent 19 modulo 60:   1/12 q phi1^2 ( q-3 )
        q congruent 21 modulo 60:   1/12 q phi1^2 ( q-3 )
        q congruent 23 modulo 60:   1/12 phi2 ( q^3-6*q^2+15*q-16 )
        q congruent 25 modulo 60:   1/12 q phi1^2 ( q-3 )
        q congruent 27 modulo 60:   1/12 q phi1^2 ( q-3 )
        q congruent 29 modulo 60:   1/12 phi2 ( q^3-6*q^2+15*q-16 )
        q congruent 31 modulo 60:   1/12 q phi1^2 ( q-3 )
        q congruent 32 modulo 60:   1/12 phi2 ( q^3-5*q^2+10*q-8 )
        q congruent 37 modulo 60:   1/12 q phi1^2 ( q-3 )
        q congruent 41 modulo 60:   1/12 phi2 ( q^3-6*q^2+15*q-16 )
        q congruent 43 modulo 60:   1/12 q phi1^2 ( q-3 )
        q congruent 47 modulo 60:   1/12 phi2 ( q^3-6*q^2+15*q-16 )
        q congruent 49 modulo 60:   1/12 q phi1^2 ( q-3 )
        q congruent 53 modulo 60:   1/12 phi2 ( q^3-6*q^2+15*q-16 )
        q congruent 59 modulo 60:   1/12 phi2 ( q^3-6*q^2+15*q-16 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 31, 78, 78, 9, 82, 31, 31, 78, 38, 84, 84, 15 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 4 ], 
  [ 5, 1, 2, 8 ], [ 6, 1, 2, 12 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], 
  [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 15, 1, 2, 8 ], [ 16, 1, 3, 8 ], 
  [ 17, 1, 4, 24 ], [ 19, 1, 2, 4 ], [ 27, 1, 4, 6 ], [ 32, 1, 3, 8 ], 
  [ 38, 1, 11, 36 ], [ 42, 1, 5, 12 ], [ 44, 1, 7, 6 ], [ 45, 1, 4, 12 ], 
  [ 46, 1, 4, 24 ], [ 53, 1, 18, 12 ] ]

    k = 13: F-action on Pi is (1,3)      [55,1,13]
      Dynkin type is ^2A_2(q) + A_1(q) + A_1(q) + T(phi1 phi2^3)
      Order of center |Z^F|: phi1 phi2^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q^3-12*q^2+49*q-74 )
        q congruent 2 modulo 60:   1/16 ( q^4-12*q^3+48*q^2-80*q+48 )
        q congruent 3 modulo 60:   1/16 ( q^4-13*q^3+61*q^2-135*q+126 )
        q congruent 4 modulo 60:   1/16 q ( q^3-12*q^2+44*q-48 )
        q congruent 5 modulo 60:   1/16 ( q^4-13*q^3+65*q^2-155*q+150 )
        q congruent 7 modulo 60:   1/16 ( q^4-13*q^3+61*q^2-135*q+126 )
        q congruent 8 modulo 60:   1/16 ( q^4-12*q^3+48*q^2-80*q+48 )
        q congruent 9 modulo 60:   1/16 phi1 ( q^3-12*q^2+49*q-74 )
        q congruent 11 modulo 60:   1/16 ( q^4-13*q^3+65*q^2-167*q+202 )
        q congruent 13 modulo 60:   1/16 phi1 ( q^3-12*q^2+49*q-74 )
        q congruent 16 modulo 60:   1/16 q ( q^3-12*q^2+44*q-48 )
        q congruent 17 modulo 60:   1/16 ( q^4-13*q^3+65*q^2-155*q+150 )
        q congruent 19 modulo 60:   1/16 ( q^4-13*q^3+61*q^2-135*q+126 )
        q congruent 21 modulo 60:   1/16 phi1 ( q^3-12*q^2+49*q-74 )
        q congruent 23 modulo 60:   1/16 ( q^4-13*q^3+65*q^2-167*q+202 )
        q congruent 25 modulo 60:   1/16 phi1 ( q^3-12*q^2+49*q-74 )
        q congruent 27 modulo 60:   1/16 ( q^4-13*q^3+61*q^2-135*q+126 )
        q congruent 29 modulo 60:   1/16 ( q^4-13*q^3+65*q^2-155*q+150 )
        q congruent 31 modulo 60:   1/16 ( q^4-13*q^3+61*q^2-135*q+126 )
        q congruent 32 modulo 60:   1/16 ( q^4-12*q^3+48*q^2-80*q+48 )
        q congruent 37 modulo 60:   1/16 phi1 ( q^3-12*q^2+49*q-74 )
        q congruent 41 modulo 60:   1/16 ( q^4-13*q^3+65*q^2-155*q+150 )
        q congruent 43 modulo 60:   1/16 ( q^4-13*q^3+61*q^2-135*q+126 )
        q congruent 47 modulo 60:   1/16 ( q^4-13*q^3+65*q^2-167*q+202 )
        q congruent 49 modulo 60:   1/16 phi1 ( q^3-12*q^2+49*q-74 )
        q congruent 53 modulo 60:   1/16 ( q^4-13*q^3+65*q^2-155*q+150 )
        q congruent 59 modulo 60:   1/16 ( q^4-13*q^3+65*q^2-167*q+202 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 69, 5, 5, 67, 7, 69, 69, 5, 82, 31, 31, 78 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 14 ], [ 4, 1, 2, 18 ], 
  [ 5, 1, 2, 24 ], [ 6, 1, 2, 32 ], [ 7, 1, 2, 12 ], [ 8, 1, 2, 4 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 12 ], 
  [ 12, 1, 2, 18 ], [ 13, 1, 4, 24 ], [ 14, 1, 2, 12 ], [ 15, 1, 2, 36 ], 
  [ 16, 1, 3, 48 ], [ 17, 1, 4, 72 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 24 ], 
  [ 20, 1, 3, 24 ], [ 20, 1, 4, 24 ], [ 22, 1, 3, 20 ], [ 22, 1, 4, 4 ], 
  [ 23, 1, 2, 6 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 3, 12 ], 
  [ 26, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 3, 12 ], [ 28, 1, 4, 12 ], 
  [ 29, 1, 3, 24 ], [ 30, 1, 3, 24 ], [ 31, 1, 3, 28 ], [ 31, 1, 4, 12 ], 
  [ 32, 1, 3, 48 ], [ 33, 1, 8, 48 ], [ 34, 1, 3, 16 ], [ 35, 1, 6, 24 ], 
  [ 35, 1, 8, 24 ], [ 36, 1, 3, 8 ], [ 38, 1, 8, 48 ], [ 39, 1, 4, 4 ], 
  [ 40, 1, 6, 12 ], [ 41, 1, 6, 8 ], [ 42, 1, 2, 16 ], [ 43, 1, 4, 16 ], 
  [ 44, 1, 8, 8 ], [ 45, 1, 5, 16 ], [ 46, 1, 5, 32 ], [ 47, 1, 7, 24 ], 
  [ 47, 1, 8, 24 ], [ 48, 1, 5, 16 ], [ 51, 1, 8, 8 ], [ 53, 1, 8, 16 ] ]

    k = 14: F-action on Pi is (1,3)      [55,1,14]
      Dynkin type is ^2A_2(q) + A_1(q) + A_1(q) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 ( q^3-8*q^2+23*q-24 )
        q congruent 2 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 3 modulo 60:   1/32 ( q^4-9*q^3+31*q^2-51*q+36 )
        q congruent 4 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 5 modulo 60:   1/32 phi1 ( q^3-8*q^2+23*q-24 )
        q congruent 7 modulo 60:   1/32 ( q^4-9*q^3+31*q^2-51*q+36 )
        q congruent 8 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 9 modulo 60:   1/32 phi1 ( q^3-8*q^2+23*q-24 )
        q congruent 11 modulo 60:   1/32 ( q^4-9*q^3+31*q^2-51*q+36 )
        q congruent 13 modulo 60:   1/32 phi1 ( q^3-8*q^2+23*q-24 )
        q congruent 16 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 17 modulo 60:   1/32 phi1 ( q^3-8*q^2+23*q-24 )
        q congruent 19 modulo 60:   1/32 ( q^4-9*q^3+31*q^2-51*q+36 )
        q congruent 21 modulo 60:   1/32 phi1 ( q^3-8*q^2+23*q-24 )
        q congruent 23 modulo 60:   1/32 ( q^4-9*q^3+31*q^2-51*q+36 )
        q congruent 25 modulo 60:   1/32 phi1 ( q^3-8*q^2+23*q-24 )
        q congruent 27 modulo 60:   1/32 ( q^4-9*q^3+31*q^2-51*q+36 )
        q congruent 29 modulo 60:   1/32 phi1 ( q^3-8*q^2+23*q-24 )
        q congruent 31 modulo 60:   1/32 ( q^4-9*q^3+31*q^2-51*q+36 )
        q congruent 32 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 37 modulo 60:   1/32 phi1 ( q^3-8*q^2+23*q-24 )
        q congruent 41 modulo 60:   1/32 phi1 ( q^3-8*q^2+23*q-24 )
        q congruent 43 modulo 60:   1/32 ( q^4-9*q^3+31*q^2-51*q+36 )
        q congruent 47 modulo 60:   1/32 ( q^4-9*q^3+31*q^2-51*q+36 )
        q congruent 49 modulo 60:   1/32 phi1 ( q^3-8*q^2+23*q-24 )
        q congruent 53 modulo 60:   1/32 phi1 ( q^3-8*q^2+23*q-24 )
        q congruent 59 modulo 60:   1/32 ( q^4-9*q^3+31*q^2-51*q+36 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 69, 69, 5, 68, 7, 7, 69, 28, 82, 82, 31 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 4 ], 
  [ 4, 1, 2, 18 ], [ 6, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], 
  [ 12, 1, 2, 6 ], [ 13, 1, 1, 8 ], [ 13, 1, 3, 8 ], [ 13, 1, 4, 24 ], 
  [ 16, 1, 3, 24 ], [ 16, 1, 4, 8 ], [ 20, 1, 3, 48 ], [ 22, 1, 3, 8 ], 
  [ 23, 1, 1, 4 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 12 ], [ 25, 1, 1, 8 ], 
  [ 25, 1, 2, 16 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 8 ], [ 28, 1, 3, 24 ], 
  [ 31, 1, 3, 24 ], [ 33, 1, 6, 16 ], [ 33, 1, 8, 48 ], [ 35, 1, 6, 48 ], 
  [ 37, 1, 2, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 8 ], [ 40, 1, 2, 8 ], 
  [ 40, 1, 6, 12 ], [ 41, 1, 1, 16 ], [ 41, 1, 4, 16 ], [ 43, 1, 3, 32 ], 
  [ 43, 1, 8, 16 ], [ 44, 1, 9, 16 ], [ 47, 1, 7, 48 ], [ 48, 1, 4, 32 ], 
  [ 51, 1, 3, 16 ], [ 51, 1, 10, 16 ], [ 53, 1, 6, 32 ] ]

    k = 15: F-action on Pi is (1,3)      [55,1,15]
      Dynkin type is ^2A_2(q) + A_1(q) + A_1(q) + T(phi2^4)
      Order of center |Z^F|: phi2^4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/96 phi1 ( q^3-28*q^2+267*q-912 )
        q congruent 2 modulo 60:   1/96 ( q^4-28*q^3+260*q^2-928*q+1024 )
        q congruent 3 modulo 60:   1/96 ( q^4-29*q^3+295*q^2-1239*q+1764 )
        q congruent 4 modulo 60:   1/96 ( q^4-28*q^3+252*q^2-720*q+384 )
        q congruent 5 modulo 60:   1/96 ( q^4-29*q^3+303*q^2-1387*q+2360 )
        q congruent 7 modulo 60:   1/96 ( q^4-29*q^3+295*q^2-1239*q+1764 )
        q congruent 8 modulo 60:   1/96 ( q^4-28*q^3+260*q^2-928*q+1024 )
        q congruent 9 modulo 60:   1/96 ( q^4-29*q^3+295*q^2-1179*q+1296 )
        q congruent 11 modulo 60:   1/96 ( q^4-29*q^3+303*q^2-1447*q+3212 )
        q congruent 13 modulo 60:   1/96 phi1 ( q^3-28*q^2+267*q-912 )
        q congruent 16 modulo 60:   1/96 q ( q^3-28*q^2+252*q-720 )
        q congruent 17 modulo 60:   1/96 ( q^4-29*q^3+303*q^2-1387*q+2360 )
        q congruent 19 modulo 60:   1/96 ( q^4-29*q^3+295*q^2-1239*q+2148 )
        q congruent 21 modulo 60:   1/96 phi1 ( q^3-28*q^2+267*q-912 )
        q congruent 23 modulo 60:   1/96 ( q^4-29*q^3+303*q^2-1447*q+3212 )
        q congruent 25 modulo 60:   1/96 phi1 ( q^3-28*q^2+267*q-912 )
        q congruent 27 modulo 60:   1/96 ( q^4-29*q^3+295*q^2-1239*q+1764 )
        q congruent 29 modulo 60:   1/96 ( q^4-29*q^3+303*q^2-1387*q+2744 )
        q congruent 31 modulo 60:   1/96 ( q^4-29*q^3+295*q^2-1239*q+1764 )
        q congruent 32 modulo 60:   1/96 ( q^4-28*q^3+260*q^2-928*q+1024 )
        q congruent 37 modulo 60:   1/96 phi1 ( q^3-28*q^2+267*q-912 )
        q congruent 41 modulo 60:   1/96 ( q^4-29*q^3+303*q^2-1387*q+2360 )
        q congruent 43 modulo 60:   1/96 ( q^4-29*q^3+295*q^2-1239*q+1764 )
        q congruent 47 modulo 60:   1/96 ( q^4-29*q^3+303*q^2-1447*q+3212 )
        q congruent 49 modulo 60:   1/96 ( q^4-29*q^3+295*q^2-1179*q+1296 )
        q congruent 53 modulo 60:   1/96 ( q^4-29*q^3+303*q^2-1387*q+2360 )
        q congruent 59 modulo 60:   1/96 ( q^4-29*q^3+303*q^2-1447*q+3596 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 67, 67, 2, 69, 5, 5, 67, 31, 78, 78, 9 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 26 ], [ 4, 1, 2, 46 ], 
  [ 5, 1, 2, 80 ], [ 6, 1, 2, 96 ], [ 7, 1, 2, 40 ], [ 8, 1, 2, 24 ], 
  [ 9, 1, 1, 7 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 40 ], [ 12, 1, 2, 70 ], 
  [ 13, 1, 4, 72 ], [ 14, 1, 2, 120 ], [ 15, 1, 2, 152 ], [ 16, 1, 3, 176 ], 
  [ 17, 1, 4, 240 ], [ 18, 1, 2, 72 ], [ 19, 1, 2, 112 ], [ 20, 1, 4, 144 ], 
  [ 21, 1, 2, 48 ], [ 22, 1, 4, 120 ], [ 23, 1, 2, 18 ], [ 24, 1, 2, 36 ], 
  [ 25, 1, 3, 60 ], [ 26, 1, 4, 48 ], [ 27, 1, 6, 48 ], [ 28, 1, 4, 72 ], 
  [ 29, 1, 4, 144 ], [ 30, 1, 3, 144 ], [ 31, 1, 4, 168 ], [ 32, 1, 3, 224 ], 
  [ 33, 1, 8, 144 ], [ 34, 1, 4, 96 ], [ 35, 1, 8, 144 ], [ 36, 1, 4, 48 ], 
  [ 37, 1, 3, 96 ], [ 38, 1, 12, 288 ], [ 39, 1, 3, 24 ], [ 40, 1, 6, 36 ], 
  [ 41, 1, 9, 48 ], [ 42, 1, 6, 96 ], [ 43, 1, 13, 96 ], [ 44, 1, 10, 48 ], 
  [ 45, 1, 6, 96 ], [ 46, 1, 6, 192 ], [ 47, 1, 8, 144 ], [ 48, 1, 6, 96 ], 
  [ 51, 1, 9, 48 ], [ 53, 1, 20, 96 ] ]

    k = 16: F-action on Pi is (1,3)(2,5)      [55,1,16]
      Dynkin type is ^2A_2(q) + A_1(q^2) + T(phi1^3 phi2)
      Order of center |Z^F|: phi1^3 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/96 phi1 ( q^3-12*q^2+47*q-60 )
        q congruent 2 modulo 60:   1/96 ( q^4-12*q^3+36*q^2+16*q-96 )
        q congruent 3 modulo 60:   1/96 ( q^4-13*q^3+59*q^2-119*q+96 )
        q congruent 4 modulo 60:   1/96 q ( q^3-12*q^2+44*q-48 )
        q congruent 5 modulo 60:   1/96 ( q^4-13*q^3+51*q^2-43*q-60 )
        q congruent 7 modulo 60:   1/96 ( q^4-13*q^3+59*q^2-119*q+96 )
        q congruent 8 modulo 60:   1/96 ( q^4-12*q^3+36*q^2+16*q-96 )
        q congruent 9 modulo 60:   1/96 phi1 ( q^3-12*q^2+47*q-60 )
        q congruent 11 modulo 60:   1/96 ( q^4-13*q^3+51*q^2-55*q-24 )
        q congruent 13 modulo 60:   1/96 phi1 ( q^3-12*q^2+47*q-60 )
        q congruent 16 modulo 60:   1/96 q ( q^3-12*q^2+44*q-48 )
        q congruent 17 modulo 60:   1/96 ( q^4-13*q^3+51*q^2-43*q-60 )
        q congruent 19 modulo 60:   1/96 ( q^4-13*q^3+59*q^2-119*q+96 )
        q congruent 21 modulo 60:   1/96 phi1 ( q^3-12*q^2+47*q-60 )
        q congruent 23 modulo 60:   1/96 ( q^4-13*q^3+51*q^2-55*q-24 )
        q congruent 25 modulo 60:   1/96 phi1 ( q^3-12*q^2+47*q-60 )
        q congruent 27 modulo 60:   1/96 ( q^4-13*q^3+59*q^2-119*q+96 )
        q congruent 29 modulo 60:   1/96 ( q^4-13*q^3+51*q^2-43*q-60 )
        q congruent 31 modulo 60:   1/96 ( q^4-13*q^3+59*q^2-119*q+96 )
        q congruent 32 modulo 60:   1/96 ( q^4-12*q^3+36*q^2+16*q-96 )
        q congruent 37 modulo 60:   1/96 phi1 ( q^3-12*q^2+47*q-60 )
        q congruent 41 modulo 60:   1/96 ( q^4-13*q^3+51*q^2-43*q-60 )
        q congruent 43 modulo 60:   1/96 ( q^4-13*q^3+59*q^2-119*q+96 )
        q congruent 47 modulo 60:   1/96 ( q^4-13*q^3+51*q^2-55*q-24 )
        q congruent 49 modulo 60:   1/96 phi1 ( q^3-12*q^2+47*q-60 )
        q congruent 53 modulo 60:   1/96 ( q^4-13*q^3+51*q^2-43*q-60 )
        q congruent 59 modulo 60:   1/96 ( q^4-13*q^3+51*q^2-55*q-24 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 72, 68, 19, 28, 96 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 8 ], [ 3, 1, 2, 2 ], 
  [ 4, 1, 1, 2 ], [ 4, 1, 2, 8 ], [ 6, 1, 2, 12 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 8 ], [ 12, 1, 2, 2 ], 
  [ 13, 1, 1, 12 ], [ 13, 1, 3, 12 ], [ 16, 1, 2, 16 ], [ 16, 1, 3, 12 ], 
  [ 16, 1, 4, 4 ], [ 17, 1, 3, 48 ], [ 20, 1, 3, 48 ], [ 22, 1, 3, 24 ], 
  [ 23, 1, 1, 6 ], [ 24, 1, 1, 12 ], [ 25, 1, 2, 36 ], [ 27, 1, 1, 48 ], 
  [ 28, 1, 1, 24 ], [ 31, 1, 3, 24 ], [ 32, 1, 2, 16 ], [ 33, 1, 6, 24 ], 
  [ 35, 1, 5, 48 ], [ 38, 1, 7, 96 ], [ 39, 1, 1, 24 ], [ 40, 1, 2, 12 ], 
  [ 41, 1, 3, 48 ], [ 43, 1, 3, 96 ], [ 44, 1, 1, 48 ], [ 47, 1, 9, 48 ], 
  [ 51, 1, 10, 48 ], [ 53, 1, 5, 96 ] ]

    k = 17: F-action on Pi is (1,3)(2,5)      [55,1,17]
      Dynkin type is ^2A_2(q) + A_1(q^2) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^3 ( q-2 )
        q congruent 2 modulo 60:   1/16 q ( q^3-4*q^2+8 )
        q congruent 3 modulo 60:   1/16 phi1 ( q^3-4*q^2+5*q-6 )
        q congruent 4 modulo 60:   1/16 q^2 ( q^2-4*q+4 )
        q congruent 5 modulo 60:   1/16 phi1^2 ( q^2-3*q-2 )
        q congruent 7 modulo 60:   1/16 phi1 ( q^3-4*q^2+5*q-6 )
        q congruent 8 modulo 60:   1/16 q ( q^3-4*q^2+8 )
        q congruent 9 modulo 60:   1/16 phi1^3 ( q-2 )
        q congruent 11 modulo 60:   1/16 phi1 ( q^3-4*q^2+q-2 )
        q congruent 13 modulo 60:   1/16 phi1^3 ( q-2 )
        q congruent 16 modulo 60:   1/16 q^2 ( q^2-4*q+4 )
        q congruent 17 modulo 60:   1/16 phi1^2 ( q^2-3*q-2 )
        q congruent 19 modulo 60:   1/16 phi1 ( q^3-4*q^2+5*q-6 )
        q congruent 21 modulo 60:   1/16 phi1^3 ( q-2 )
        q congruent 23 modulo 60:   1/16 phi1 ( q^3-4*q^2+q-2 )
        q congruent 25 modulo 60:   1/16 phi1^3 ( q-2 )
        q congruent 27 modulo 60:   1/16 phi1 ( q^3-4*q^2+5*q-6 )
        q congruent 29 modulo 60:   1/16 phi1^2 ( q^2-3*q-2 )
        q congruent 31 modulo 60:   1/16 phi1 ( q^3-4*q^2+5*q-6 )
        q congruent 32 modulo 60:   1/16 q ( q^3-4*q^2+8 )
        q congruent 37 modulo 60:   1/16 phi1^3 ( q-2 )
        q congruent 41 modulo 60:   1/16 phi1^2 ( q^2-3*q-2 )
        q congruent 43 modulo 60:   1/16 phi1 ( q^3-4*q^2+5*q-6 )
        q congruent 47 modulo 60:   1/16 phi1 ( q^3-4*q^2+q-2 )
        q congruent 49 modulo 60:   1/16 phi1^3 ( q-2 )
        q congruent 53 modulo 60:   1/16 phi1^2 ( q^2-3*q-2 )
        q congruent 59 modulo 60:   1/16 phi1 ( q^3-4*q^2+q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 69, 20, 7, 76, 82, 60 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 2 ], 
  [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 5, 1, 2, 8 ], [ 6, 1, 2, 4 ], 
  [ 7, 1, 2, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 12, 1, 2, 2 ], 
  [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 4 ], [ 15, 1, 2, 4 ], 
  [ 16, 1, 2, 8 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], [ 17, 1, 3, 8 ], 
  [ 18, 1, 2, 4 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 8 ], [ 22, 1, 3, 4 ], 
  [ 22, 1, 4, 4 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], 
  [ 25, 1, 2, 4 ], [ 26, 1, 2, 8 ], [ 27, 1, 2, 8 ], [ 28, 1, 1, 4 ], 
  [ 28, 1, 2, 4 ], [ 29, 1, 3, 8 ], [ 30, 1, 4, 8 ], [ 31, 1, 3, 4 ], 
  [ 31, 1, 4, 4 ], [ 32, 1, 2, 8 ], [ 33, 1, 6, 8 ], [ 35, 1, 5, 8 ], 
  [ 35, 1, 7, 8 ], [ 36, 1, 3, 8 ], [ 38, 1, 10, 16 ], [ 39, 1, 4, 4 ], 
  [ 40, 1, 2, 4 ], [ 41, 1, 7, 8 ], [ 43, 1, 4, 16 ], [ 44, 1, 2, 8 ], 
  [ 47, 1, 9, 8 ], [ 47, 1, 10, 8 ], [ 51, 1, 8, 8 ], [ 53, 1, 7, 16 ] ]

    k = 18: F-action on Pi is (1,3)(2,5)      [55,1,18]
      Dynkin type is ^2A_2(q) + A_1(q^2) + T(phi1 phi2 phi3)
      Order of center |Z^F|: phi1 phi2 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q phi1^2 phi2
        q congruent 2 modulo 60:   1/12 q phi2^2 ( q-2 )
        q congruent 3 modulo 60:   1/12 q phi1^2 phi2
        q congruent 4 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 5 modulo 60:   1/12 q phi2 ( q^2-2*q-1 )
        q congruent 7 modulo 60:   1/12 q phi1^2 phi2
        q congruent 8 modulo 60:   1/12 q phi2^2 ( q-2 )
        q congruent 9 modulo 60:   1/12 q phi1^2 phi2
        q congruent 11 modulo 60:   1/12 q phi2 ( q^2-2*q-1 )
        q congruent 13 modulo 60:   1/12 q phi1^2 phi2
        q congruent 16 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 17 modulo 60:   1/12 q phi2 ( q^2-2*q-1 )
        q congruent 19 modulo 60:   1/12 q phi1^2 phi2
        q congruent 21 modulo 60:   1/12 q phi1^2 phi2
        q congruent 23 modulo 60:   1/12 q phi2 ( q^2-2*q-1 )
        q congruent 25 modulo 60:   1/12 q phi1^2 phi2
        q congruent 27 modulo 60:   1/12 q phi1^2 phi2
        q congruent 29 modulo 60:   1/12 q phi2 ( q^2-2*q-1 )
        q congruent 31 modulo 60:   1/12 q phi1^2 phi2
        q congruent 32 modulo 60:   1/12 q phi2^2 ( q-2 )
        q congruent 37 modulo 60:   1/12 q phi1^2 phi2
        q congruent 41 modulo 60:   1/12 q phi2 ( q^2-2*q-1 )
        q congruent 43 modulo 60:   1/12 q phi1^2 phi2
        q congruent 47 modulo 60:   1/12 q phi2 ( q^2-2*q-1 )
        q congruent 49 modulo 60:   1/12 q phi1^2 phi2
        q congruent 53 modulo 60:   1/12 q phi2 ( q^2-2*q-1 )
        q congruent 59 modulo 60:   1/12 q phi2 ( q^2-2*q-1 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 27, 95, 81, 59, 36, 99 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], 
  [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 2 ], 
  [ 16, 1, 2, 4 ], [ 16, 1, 4, 4 ], [ 27, 1, 5, 6 ], [ 32, 1, 2, 4 ], 
  [ 38, 1, 9, 12 ], [ 44, 1, 3, 6 ], [ 53, 1, 17, 12 ] ]

    k = 19: F-action on Pi is (1,3)(2,5)      [55,1,19]
      Dynkin type is ^2A_2(q) + A_1(q^2) + T(phi2^2 phi4)
      Order of center |Z^F|: phi2^2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 2 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 3 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 4 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 5 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 7 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 8 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 9 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 11 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 13 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 16 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 17 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 19 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 21 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 23 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 25 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 27 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 29 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 31 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 32 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 37 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 41 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 43 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 47 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 49 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 53 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 59 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 71, 17, 20, 74, 98, 54 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 6 ], 
  [ 9, 1, 1, 3 ], [ 12, 1, 2, 6 ], [ 13, 1, 2, 8 ], [ 16, 1, 4, 8 ], 
  [ 23, 1, 2, 6 ], [ 25, 1, 3, 12 ], [ 33, 1, 10, 16 ], [ 39, 1, 5, 4 ], 
  [ 40, 1, 6, 12 ], [ 41, 1, 5, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 4, 8 ], 
  [ 48, 1, 9, 16 ], [ 51, 1, 4, 8 ], [ 53, 1, 14, 16 ] ]

    k = 20: F-action on Pi is (1,3)(2,5)      [55,1,20]
      Dynkin type is ^2A_2(q) + A_1(q^2) + T(phi1 phi2^3)
      Order of center |Z^F|: phi1 phi2^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 2 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 3 modulo 60:   1/32 ( q^4-9*q^3+27*q^2-43*q+48 )
        q congruent 4 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 5 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 7 modulo 60:   1/32 ( q^4-9*q^3+27*q^2-43*q+48 )
        q congruent 8 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 9 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 11 modulo 60:   1/32 ( q^4-9*q^3+27*q^2-43*q+48 )
        q congruent 13 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 16 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 17 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 19 modulo 60:   1/32 ( q^4-9*q^3+27*q^2-43*q+48 )
        q congruent 21 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 23 modulo 60:   1/32 ( q^4-9*q^3+27*q^2-43*q+48 )
        q congruent 25 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 27 modulo 60:   1/32 ( q^4-9*q^3+27*q^2-43*q+48 )
        q congruent 29 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 31 modulo 60:   1/32 ( q^4-9*q^3+27*q^2-43*q+48 )
        q congruent 32 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 37 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 41 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 43 modulo 60:   1/32 ( q^4-9*q^3+27*q^2-43*q+48 )
        q congruent 47 modulo 60:   1/32 ( q^4-9*q^3+27*q^2-43*q+48 )
        q congruent 49 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 53 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 59 modulo 60:   1/32 ( q^4-9*q^3+27*q^2-43*q+48 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 71, 69, 20, 31, 98 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 6 ], 
  [ 4, 1, 2, 12 ], [ 5, 1, 2, 16 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 8 ], 
  [ 8, 1, 2, 8 ], [ 9, 1, 1, 5 ], [ 10, 1, 2, 4 ], [ 12, 1, 2, 10 ], 
  [ 13, 1, 1, 4 ], [ 13, 1, 2, 16 ], [ 13, 1, 3, 4 ], [ 14, 1, 2, 24 ], 
  [ 15, 1, 2, 8 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 12 ], [ 18, 1, 2, 8 ], 
  [ 20, 1, 4, 16 ], [ 21, 1, 2, 16 ], [ 22, 1, 4, 8 ], [ 23, 1, 1, 2 ], 
  [ 23, 1, 2, 12 ], [ 24, 1, 2, 4 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 4 ], 
  [ 25, 1, 3, 32 ], [ 25, 1, 4, 8 ], [ 26, 1, 4, 16 ], [ 28, 1, 2, 8 ], 
  [ 29, 1, 4, 16 ], [ 30, 1, 4, 16 ], [ 31, 1, 4, 8 ], [ 33, 1, 6, 8 ], 
  [ 33, 1, 10, 32 ], [ 35, 1, 7, 16 ], [ 36, 1, 4, 16 ], [ 37, 1, 2, 16 ], 
  [ 37, 1, 3, 32 ], [ 39, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 40, 1, 2, 4 ], 
  [ 40, 1, 6, 24 ], [ 41, 1, 2, 16 ], [ 41, 1, 10, 16 ], [ 43, 1, 8, 16 ], 
  [ 43, 1, 13, 32 ], [ 44, 1, 5, 16 ], [ 47, 1, 10, 16 ], [ 48, 1, 10, 32 ], 
  [ 51, 1, 3, 16 ], [ 51, 1, 9, 16 ], [ 53, 1, 12, 32 ] ]

i = 56: Pi = [ 1, 2, 4, 5 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [56,1,1]
      Dynkin type is A_3(q) + A_1(q) + T(phi1^4)
      Order of center |Z^F|: phi1^4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/96 ( q^4-33*q^3+395*q^2-2095*q+4708 )
        q congruent 2 modulo 60:   1/96 ( q^4-32*q^3+356*q^2-1552*q+1920 )
        q congruent 3 modulo 60:   1/96 ( q^4-33*q^3+395*q^2-1995*q+3240 )
        q congruent 4 modulo 60:   1/96 ( q^4-32*q^3+356*q^2-1616*q+2560 )
        q congruent 5 modulo 60:   1/96 ( q^4-33*q^3+395*q^2-2031*q+3780 )
        q congruent 7 modulo 60:   1/96 ( q^4-33*q^3+395*q^2-2059*q+3976 )
        q congruent 8 modulo 60:   1/96 ( q^4-32*q^3+356*q^2-1552*q+1920 )
        q congruent 9 modulo 60:   1/96 ( q^4-33*q^3+395*q^2-2031*q+3780 )
        q congruent 11 modulo 60:   1/96 ( q^4-33*q^3+395*q^2-1995*q+3432 )
        q congruent 13 modulo 60:   1/96 ( q^4-33*q^3+395*q^2-2095*q+4516 )
        q congruent 16 modulo 60:   1/96 ( q^4-32*q^3+356*q^2-1616*q+2752 )
        q congruent 17 modulo 60:   1/96 ( q^4-33*q^3+395*q^2-2031*q+3780 )
        q congruent 19 modulo 60:   1/96 ( q^4-33*q^3+395*q^2-2059*q+3976 )
        q congruent 21 modulo 60:   1/96 ( q^4-33*q^3+395*q^2-2031*q+3972 )
        q congruent 23 modulo 60:   1/96 ( q^4-33*q^3+395*q^2-1995*q+3240 )
        q congruent 25 modulo 60:   1/96 ( q^4-33*q^3+395*q^2-2095*q+4516 )
        q congruent 27 modulo 60:   1/96 ( q^4-33*q^3+395*q^2-1995*q+3240 )
        q congruent 29 modulo 60:   1/96 ( q^4-33*q^3+395*q^2-2031*q+3780 )
        q congruent 31 modulo 60:   1/96 ( q^4-33*q^3+395*q^2-2059*q+4168 )
        q congruent 32 modulo 60:   1/96 ( q^4-32*q^3+356*q^2-1552*q+1920 )
        q congruent 37 modulo 60:   1/96 ( q^4-33*q^3+395*q^2-2095*q+4516 )
        q congruent 41 modulo 60:   1/96 ( q^4-33*q^3+395*q^2-2031*q+3972 )
        q congruent 43 modulo 60:   1/96 ( q^4-33*q^3+395*q^2-2059*q+3976 )
        q congruent 47 modulo 60:   1/96 ( q^4-33*q^3+395*q^2-1995*q+3240 )
        q congruent 49 modulo 60:   1/96 ( q^4-33*q^3+395*q^2-2095*q+4516 )
        q congruent 53 modulo 60:   1/96 ( q^4-33*q^3+395*q^2-2031*q+3780 )
        q congruent 59 modulo 60:   1/96 ( q^4-33*q^3+395*q^2-1995*q+3240 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 4, 68, 8, 77, 70, 19 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 20 ], [ 4, 1, 1, 34 ], 
  [ 5, 1, 1, 32 ], [ 6, 1, 1, 40 ], [ 7, 1, 1, 28 ], [ 8, 1, 1, 16 ], 
  [ 9, 1, 1, 7 ], [ 10, 1, 1, 14 ], [ 11, 1, 1, 36 ], [ 12, 1, 1, 68 ], 
  [ 13, 1, 1, 72 ], [ 14, 1, 1, 64 ], [ 15, 1, 1, 64 ], [ 16, 1, 1, 40 ], 
  [ 18, 1, 1, 64 ], [ 19, 1, 1, 72 ], [ 20, 1, 1, 56 ], [ 21, 1, 1, 48 ], 
  [ 22, 1, 1, 64 ], [ 23, 1, 1, 30 ], [ 24, 1, 1, 50 ], [ 25, 1, 1, 84 ], 
  [ 26, 1, 1, 48 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 84 ], [ 29, 1, 1, 96 ], 
  [ 30, 1, 1, 96 ], [ 31, 1, 1, 64 ], [ 34, 1, 1, 96 ], [ 35, 1, 1, 72 ], 
  [ 36, 1, 1, 96 ], [ 37, 1, 1, 96 ], [ 39, 1, 1, 72 ], [ 40, 1, 1, 144 ], 
  [ 41, 1, 1, 144 ], [ 42, 1, 1, 96 ], [ 43, 1, 1, 96 ], [ 44, 1, 1, 48 ], 
  [ 45, 1, 1, 96 ], [ 48, 1, 1, 96 ], [ 50, 1, 1, 96 ], [ 51, 1, 1, 96 ], 
  [ 52, 1, 1, 144 ], [ 53, 1, 1, 96 ] ]

    k = 2: F-action on Pi is ()      [56,1,2]
      Dynkin type is A_3(q) + A_1(q) + T(phi1^3 phi2)
      Order of center |Z^F|: phi1^3 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q^3-14*q^2+61*q-88 )
        q congruent 2 modulo 60:   1/16 q ( q^3-14*q^2+60*q-72 )
        q congruent 3 modulo 60:   1/16 ( q^4-15*q^3+75*q^2-133*q+48 )
        q congruent 4 modulo 60:   1/16 q ( q^3-14*q^2+60*q-80 )
        q congruent 5 modulo 60:   1/16 phi1 ( q^3-14*q^2+61*q-80 )
        q congruent 7 modulo 60:   1/16 ( q^4-15*q^3+75*q^2-141*q+56 )
        q congruent 8 modulo 60:   1/16 q ( q^3-14*q^2+60*q-72 )
        q congruent 9 modulo 60:   1/16 phi1 ( q^3-14*q^2+61*q-80 )
        q congruent 11 modulo 60:   1/16 ( q^4-15*q^3+75*q^2-133*q+48 )
        q congruent 13 modulo 60:   1/16 phi1 ( q^3-14*q^2+61*q-88 )
        q congruent 16 modulo 60:   1/16 q ( q^3-14*q^2+60*q-80 )
        q congruent 17 modulo 60:   1/16 phi1 ( q^3-14*q^2+61*q-80 )
        q congruent 19 modulo 60:   1/16 ( q^4-15*q^3+75*q^2-141*q+56 )
        q congruent 21 modulo 60:   1/16 phi1 ( q^3-14*q^2+61*q-80 )
        q congruent 23 modulo 60:   1/16 ( q^4-15*q^3+75*q^2-133*q+48 )
        q congruent 25 modulo 60:   1/16 phi1 ( q^3-14*q^2+61*q-88 )
        q congruent 27 modulo 60:   1/16 ( q^4-15*q^3+75*q^2-133*q+48 )
        q congruent 29 modulo 60:   1/16 phi1 ( q^3-14*q^2+61*q-80 )
        q congruent 31 modulo 60:   1/16 ( q^4-15*q^3+75*q^2-141*q+56 )
        q congruent 32 modulo 60:   1/16 q ( q^3-14*q^2+60*q-72 )
        q congruent 37 modulo 60:   1/16 phi1 ( q^3-14*q^2+61*q-88 )
        q congruent 41 modulo 60:   1/16 phi1 ( q^3-14*q^2+61*q-80 )
        q congruent 43 modulo 60:   1/16 ( q^4-15*q^3+75*q^2-141*q+56 )
        q congruent 47 modulo 60:   1/16 ( q^4-15*q^3+75*q^2-133*q+48 )
        q congruent 49 modulo 60:   1/16 phi1 ( q^3-14*q^2+61*q-88 )
        q congruent 53 modulo 60:   1/16 phi1 ( q^3-14*q^2+61*q-80 )
        q congruent 59 modulo 60:   1/16 ( q^4-15*q^3+75*q^2-133*q+48 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 4, 68, 68, 7, 77, 30, 19, 76 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 10 ], 
  [ 5, 1, 1, 16 ], [ 6, 1, 1, 16 ], [ 7, 1, 1, 8 ], [ 8, 1, 1, 8 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 8 ], 
  [ 12, 1, 1, 8 ], [ 13, 1, 1, 16 ], [ 14, 1, 1, 16 ], [ 15, 1, 1, 16 ], 
  [ 16, 1, 1, 16 ], [ 18, 1, 1, 16 ], [ 19, 1, 1, 16 ], [ 20, 1, 1, 16 ], 
  [ 20, 1, 2, 8 ], [ 21, 1, 1, 8 ], [ 22, 1, 1, 16 ], [ 22, 1, 2, 8 ], 
  [ 23, 1, 1, 6 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 12 ], 
  [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 28, 1, 1, 8 ], [ 28, 1, 2, 12 ], 
  [ 29, 1, 2, 16 ], [ 30, 1, 1, 16 ], [ 31, 1, 1, 16 ], [ 31, 1, 2, 8 ], 
  [ 34, 1, 1, 16 ], [ 34, 1, 2, 8 ], [ 35, 1, 1, 16 ], [ 35, 1, 3, 8 ], 
  [ 36, 1, 2, 16 ], [ 37, 1, 1, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 4, 8 ], 
  [ 41, 1, 1, 16 ], [ 41, 1, 6, 16 ], [ 42, 1, 4, 16 ], [ 43, 1, 2, 16 ], 
  [ 44, 1, 2, 8 ], [ 45, 1, 2, 16 ], [ 48, 1, 1, 16 ], [ 48, 1, 2, 8 ], 
  [ 50, 1, 2, 16 ], [ 51, 1, 2, 16 ], [ 52, 1, 2, 16 ], [ 53, 1, 3, 16 ] ]

    k = 3: F-action on Pi is ()      [56,1,3]
      Dynkin type is A_3(q) + A_1(q) + T(phi1^2 phi3)
      Order of center |Z^F|: phi1^2 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 phi1 ( q^3-5*q^2+14 )
        q congruent 2 modulo 60:   1/12 q phi2 ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/12 q phi2 ( q^2-7*q+12 )
        q congruent 4 modulo 60:   1/12 phi1 ( q^3-4*q^2-2*q+8 )
        q congruent 5 modulo 60:   1/12 q phi2 ( q^2-7*q+12 )
        q congruent 7 modulo 60:   1/12 phi1 ( q^3-5*q^2+14 )
        q congruent 8 modulo 60:   1/12 q phi2 ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/12 q phi2 ( q^2-7*q+12 )
        q congruent 11 modulo 60:   1/12 q phi2 ( q^2-7*q+12 )
        q congruent 13 modulo 60:   1/12 phi1 ( q^3-5*q^2+14 )
        q congruent 16 modulo 60:   1/12 phi1 ( q^3-4*q^2-2*q+8 )
        q congruent 17 modulo 60:   1/12 q phi2 ( q^2-7*q+12 )
        q congruent 19 modulo 60:   1/12 phi1 ( q^3-5*q^2+14 )
        q congruent 21 modulo 60:   1/12 q phi2 ( q^2-7*q+12 )
        q congruent 23 modulo 60:   1/12 q phi2 ( q^2-7*q+12 )
        q congruent 25 modulo 60:   1/12 phi1 ( q^3-5*q^2+14 )
        q congruent 27 modulo 60:   1/12 q phi2 ( q^2-7*q+12 )
        q congruent 29 modulo 60:   1/12 q phi2 ( q^2-7*q+12 )
        q congruent 31 modulo 60:   1/12 phi1 ( q^3-5*q^2+14 )
        q congruent 32 modulo 60:   1/12 q phi2 ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/12 phi1 ( q^3-5*q^2+14 )
        q congruent 41 modulo 60:   1/12 q phi2 ( q^2-7*q+12 )
        q congruent 43 modulo 60:   1/12 phi1 ( q^3-5*q^2+14 )
        q congruent 47 modulo 60:   1/12 q phi2 ( q^2-7*q+12 )
        q congruent 49 modulo 60:   1/12 phi1 ( q^3-5*q^2+14 )
        q congruent 53 modulo 60:   1/12 q phi2 ( q^2-7*q+12 )
        q congruent 59 modulo 60:   1/12 q phi2 ( q^2-7*q+12 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 8, 77, 77, 30, 30, 81, 14, 83, 97, 59 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], 
  [ 5, 1, 1, 8 ], [ 6, 1, 1, 4 ], [ 7, 1, 1, 4 ], [ 8, 1, 1, 4 ], 
  [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 12, 1, 1, 2 ], [ 14, 1, 1, 4 ], 
  [ 15, 1, 1, 4 ], [ 16, 1, 1, 4 ], [ 18, 1, 1, 4 ], [ 20, 1, 1, 8 ], 
  [ 22, 1, 1, 4 ], [ 24, 1, 1, 2 ], [ 27, 1, 5, 6 ], [ 31, 1, 1, 4 ], 
  [ 42, 1, 3, 12 ], [ 44, 1, 3, 6 ], [ 45, 1, 3, 12 ], [ 50, 1, 3, 12 ], 
  [ 53, 1, 16, 12 ] ]

    k = 4: F-action on Pi is ()      [56,1,4]
      Dynkin type is A_3(q) + A_1(q) + T(phi1 phi2 phi4)
      Order of center |Z^F|: phi1 phi2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 2 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 3 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 4 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 5 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 7 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 8 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 9 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 11 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 16 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 17 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 19 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 23 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 27 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 31 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 32 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 37 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 41 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 43 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 53 modulo 60:   1/16 q phi1 phi2 ( q-3 )
        q congruent 59 modulo 60:   1/16 q phi1 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 70, 19, 19, 76, 72, 20, 97, 59, 18, 74 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 2 ], 
  [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 13, 1, 2, 4 ], 
  [ 13, 1, 4, 4 ], [ 20, 1, 1, 8 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], 
  [ 25, 1, 4, 4 ], [ 28, 1, 3, 4 ], [ 35, 1, 2, 8 ], [ 39, 1, 5, 4 ], 
  [ 41, 1, 8, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 4, 8 ], [ 52, 1, 8, 8 ], 
  [ 53, 1, 11, 16 ] ]

    k = 5: F-action on Pi is ()      [56,1,5]
      Dynkin type is A_3(q) + A_1(q) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 2 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 3 modulo 60:   1/32 ( q^4-9*q^3+27*q^2-35*q+24 )
        q congruent 4 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 5 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 7 modulo 60:   1/32 ( q^4-9*q^3+27*q^2-35*q+24 )
        q congruent 8 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 9 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 11 modulo 60:   1/32 ( q^4-9*q^3+27*q^2-35*q+24 )
        q congruent 13 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 16 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 17 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 19 modulo 60:   1/32 ( q^4-9*q^3+27*q^2-35*q+24 )
        q congruent 21 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 23 modulo 60:   1/32 ( q^4-9*q^3+27*q^2-35*q+24 )
        q congruent 25 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 27 modulo 60:   1/32 ( q^4-9*q^3+27*q^2-35*q+24 )
        q congruent 29 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 31 modulo 60:   1/32 ( q^4-9*q^3+27*q^2-35*q+24 )
        q congruent 32 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 37 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 41 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 43 modulo 60:   1/32 ( q^4-9*q^3+27*q^2-35*q+24 )
        q congruent 47 modulo 60:   1/32 ( q^4-9*q^3+27*q^2-35*q+24 )
        q congruent 49 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 53 modulo 60:   1/32 phi1 ( q^3-8*q^2+19*q-20 )
        q congruent 59 modulo 60:   1/32 ( q^4-9*q^3+27*q^2-35*q+24 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 68, 68, 7, 3, 69, 30, 81, 72, 20 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 6 ], 
  [ 4, 1, 2, 4 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 3 ], 
  [ 10, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], 
  [ 13, 1, 1, 8 ], [ 13, 1, 2, 8 ], [ 13, 1, 4, 8 ], [ 16, 1, 1, 8 ], 
  [ 19, 1, 1, 8 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 16 ], [ 22, 1, 2, 16 ], 
  [ 23, 1, 1, 2 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 12 ], 
  [ 25, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 16 ], 
  [ 28, 1, 1, 4 ], [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 31, 1, 2, 16 ], 
  [ 34, 1, 2, 16 ], [ 35, 1, 1, 8 ], [ 35, 1, 2, 16 ], [ 35, 1, 3, 16 ], 
  [ 39, 1, 2, 8 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 8 ], [ 40, 1, 3, 16 ], 
  [ 41, 1, 4, 16 ], [ 41, 1, 6, 16 ], [ 41, 1, 9, 16 ], [ 43, 1, 8, 16 ], 
  [ 43, 1, 12, 32 ], [ 44, 1, 5, 16 ], [ 48, 1, 2, 16 ], [ 51, 1, 5, 32 ], 
  [ 52, 1, 3, 16 ], [ 52, 1, 9, 16 ], [ 53, 1, 9, 32 ] ]

    k = 6: F-action on Pi is ()      [56,1,6]
      Dynkin type is A_3(q) + A_1(q) + T(phi1^3 phi2)
      Order of center |Z^F|: phi1^3 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/96 phi1 ( q^3-16*q^2+85*q-166 )
        q congruent 2 modulo 60:   1/96 q ( q^3-16*q^2+76*q-96 )
        q congruent 3 modulo 60:   1/96 phi1 ( q^3-16*q^2+85*q-138 )
        q congruent 4 modulo 60:   1/96 q ( q^3-16*q^2+76*q-112 )
        q congruent 5 modulo 60:   1/96 phi1 ( q^3-16*q^2+85*q-150 )
        q congruent 7 modulo 60:   1/96 phi1 ( q^3-16*q^2+85*q-154 )
        q congruent 8 modulo 60:   1/96 q ( q^3-16*q^2+76*q-96 )
        q congruent 9 modulo 60:   1/96 phi1 ( q^3-16*q^2+85*q-150 )
        q congruent 11 modulo 60:   1/96 phi1 ( q^3-16*q^2+85*q-138 )
        q congruent 13 modulo 60:   1/96 phi1 ( q^3-16*q^2+85*q-166 )
        q congruent 16 modulo 60:   1/96 q ( q^3-16*q^2+76*q-112 )
        q congruent 17 modulo 60:   1/96 phi1 ( q^3-16*q^2+85*q-150 )
        q congruent 19 modulo 60:   1/96 phi1 ( q^3-16*q^2+85*q-154 )
        q congruent 21 modulo 60:   1/96 phi1 ( q^3-16*q^2+85*q-150 )
        q congruent 23 modulo 60:   1/96 phi1 ( q^3-16*q^2+85*q-138 )
        q congruent 25 modulo 60:   1/96 phi1 ( q^3-16*q^2+85*q-166 )
        q congruent 27 modulo 60:   1/96 phi1 ( q^3-16*q^2+85*q-138 )
        q congruent 29 modulo 60:   1/96 phi1 ( q^3-16*q^2+85*q-150 )
        q congruent 31 modulo 60:   1/96 phi1 ( q^3-16*q^2+85*q-154 )
        q congruent 32 modulo 60:   1/96 q ( q^3-16*q^2+76*q-96 )
        q congruent 37 modulo 60:   1/96 phi1 ( q^3-16*q^2+85*q-166 )
        q congruent 41 modulo 60:   1/96 phi1 ( q^3-16*q^2+85*q-150 )
        q congruent 43 modulo 60:   1/96 phi1 ( q^3-16*q^2+85*q-154 )
        q congruent 47 modulo 60:   1/96 phi1 ( q^3-16*q^2+85*q-138 )
        q congruent 49 modulo 60:   1/96 phi1 ( q^3-16*q^2+85*q-166 )
        q congruent 53 modulo 60:   1/96 phi1 ( q^3-16*q^2+85*q-150 )
        q congruent 59 modulo 60:   1/96 phi1 ( q^3-16*q^2+85*q-138 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 4, 68, 68, 3, 77, 30, 19, 72 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 10 ], 
  [ 6, 1, 1, 16 ], [ 7, 1, 1, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 12 ], 
  [ 10, 1, 2, 2 ], [ 11, 1, 1, 24 ], [ 12, 1, 1, 8 ], [ 13, 1, 1, 24 ], 
  [ 16, 1, 1, 16 ], [ 19, 1, 1, 48 ], [ 20, 1, 1, 48 ], [ 20, 1, 2, 8 ], 
  [ 22, 1, 2, 16 ], [ 23, 1, 1, 6 ], [ 24, 1, 1, 36 ], [ 24, 1, 2, 14 ], 
  [ 25, 1, 1, 36 ], [ 26, 1, 1, 48 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 24 ], 
  [ 28, 1, 2, 12 ], [ 31, 1, 2, 16 ], [ 34, 1, 2, 48 ], [ 35, 1, 1, 48 ], 
  [ 35, 1, 3, 24 ], [ 39, 1, 1, 24 ], [ 39, 1, 4, 24 ], [ 41, 1, 1, 48 ], 
  [ 41, 1, 6, 48 ], [ 42, 1, 1, 96 ], [ 43, 1, 1, 96 ], [ 44, 1, 1, 48 ], 
  [ 48, 1, 2, 48 ], [ 50, 1, 4, 96 ], [ 52, 1, 2, 48 ], [ 53, 1, 1, 96 ] ]

    k = 7: F-action on Pi is ()      [56,1,7]
      Dynkin type is A_3(q) + A_1(q) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^2 ( q^2-5*q+6 )
        q congruent 2 modulo 60:   1/16 q^2 ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/16 phi1^2 ( q^2-5*q+6 )
        q congruent 4 modulo 60:   1/16 q^2 ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/16 phi1^2 ( q^2-5*q+6 )
        q congruent 7 modulo 60:   1/16 phi1^2 ( q^2-5*q+6 )
        q congruent 8 modulo 60:   1/16 q^2 ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/16 phi1^2 ( q^2-5*q+6 )
        q congruent 11 modulo 60:   1/16 phi1^2 ( q^2-5*q+6 )
        q congruent 13 modulo 60:   1/16 phi1^2 ( q^2-5*q+6 )
        q congruent 16 modulo 60:   1/16 q^2 ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/16 phi1^2 ( q^2-5*q+6 )
        q congruent 19 modulo 60:   1/16 phi1^2 ( q^2-5*q+6 )
        q congruent 21 modulo 60:   1/16 phi1^2 ( q^2-5*q+6 )
        q congruent 23 modulo 60:   1/16 phi1^2 ( q^2-5*q+6 )
        q congruent 25 modulo 60:   1/16 phi1^2 ( q^2-5*q+6 )
        q congruent 27 modulo 60:   1/16 phi1^2 ( q^2-5*q+6 )
        q congruent 29 modulo 60:   1/16 phi1^2 ( q^2-5*q+6 )
        q congruent 31 modulo 60:   1/16 phi1^2 ( q^2-5*q+6 )
        q congruent 32 modulo 60:   1/16 q^2 ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/16 phi1^2 ( q^2-5*q+6 )
        q congruent 41 modulo 60:   1/16 phi1^2 ( q^2-5*q+6 )
        q congruent 43 modulo 60:   1/16 phi1^2 ( q^2-5*q+6 )
        q congruent 47 modulo 60:   1/16 phi1^2 ( q^2-5*q+6 )
        q congruent 49 modulo 60:   1/16 phi1^2 ( q^2-5*q+6 )
        q congruent 53 modulo 60:   1/16 phi1^2 ( q^2-5*q+6 )
        q congruent 59 modulo 60:   1/16 phi1^2 ( q^2-5*q+6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 68, 68, 7, 7, 69, 30, 81, 76, 20 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 6 ], 
  [ 4, 1, 2, 4 ], [ 6, 1, 1, 8 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 3 ], 
  [ 10, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], 
  [ 13, 1, 1, 8 ], [ 13, 1, 4, 8 ], [ 16, 1, 1, 8 ], [ 19, 1, 1, 8 ], 
  [ 20, 1, 1, 8 ], [ 20, 1, 2, 16 ], [ 22, 1, 2, 8 ], [ 23, 1, 1, 2 ], 
  [ 23, 1, 2, 4 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 4 ], 
  [ 25, 1, 3, 8 ], [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 28, 1, 1, 4 ], 
  [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 31, 1, 2, 8 ], [ 34, 1, 2, 8 ], 
  [ 35, 1, 1, 8 ], [ 35, 1, 3, 16 ], [ 37, 1, 2, 8 ], [ 39, 1, 3, 8 ], 
  [ 39, 1, 4, 8 ], [ 41, 1, 6, 16 ], [ 41, 1, 9, 16 ], [ 42, 1, 4, 16 ], 
  [ 43, 1, 2, 16 ], [ 44, 1, 2, 8 ], [ 48, 1, 2, 8 ], [ 48, 1, 3, 16 ], 
  [ 50, 1, 5, 16 ], [ 52, 1, 9, 16 ], [ 53, 1, 3, 16 ] ]

    k = 8: F-action on Pi is ()      [56,1,8]
      Dynkin type is A_3(q) + A_1(q) + T(phi1 phi2 phi3)
      Order of center |Z^F|: phi1 phi2 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 phi1^2 ( q^2-2 )
        q congruent 2 modulo 60:   1/12 q^2 phi2 ( q-2 )
        q congruent 3 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 4 modulo 60:   1/12 q phi1 ( q^2-2 )
        q congruent 5 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 7 modulo 60:   1/12 phi1^2 ( q^2-2 )
        q congruent 8 modulo 60:   1/12 q^2 phi2 ( q-2 )
        q congruent 9 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 11 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 13 modulo 60:   1/12 phi1^2 ( q^2-2 )
        q congruent 16 modulo 60:   1/12 q phi1 ( q^2-2 )
        q congruent 17 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 19 modulo 60:   1/12 phi1^2 ( q^2-2 )
        q congruent 21 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 23 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 25 modulo 60:   1/12 phi1^2 ( q^2-2 )
        q congruent 27 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 29 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 31 modulo 60:   1/12 phi1^2 ( q^2-2 )
        q congruent 32 modulo 60:   1/12 q^2 phi2 ( q-2 )
        q congruent 37 modulo 60:   1/12 phi1^2 ( q^2-2 )
        q congruent 41 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 43 modulo 60:   1/12 phi1^2 ( q^2-2 )
        q congruent 47 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 49 modulo 60:   1/12 phi1^2 ( q^2-2 )
        q congruent 53 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 59 modulo 60:   1/12 q phi1 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 77, 30, 30, 81, 81, 27, 83, 37, 59, 95 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], 
  [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 12, 1, 1, 2 ], 
  [ 16, 1, 1, 4 ], [ 20, 1, 2, 8 ], [ 22, 1, 2, 4 ], [ 24, 1, 2, 2 ], 
  [ 27, 1, 5, 6 ], [ 31, 1, 2, 4 ], [ 42, 1, 3, 12 ], [ 44, 1, 3, 6 ], 
  [ 50, 1, 6, 12 ], [ 53, 1, 16, 12 ] ]

    k = 9: F-action on Pi is ()      [56,1,9]
      Dynkin type is A_3(q) + A_1(q) + T(phi2^2 phi4)
      Order of center |Z^F|: phi2^2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 2 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 3 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 4 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 5 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 7 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 8 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 9 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 11 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 13 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 16 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 17 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 19 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 21 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 23 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 25 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 27 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 29 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 31 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 32 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 37 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 41 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 43 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 47 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 49 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 53 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 59 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 19, 72, 76, 20, 20, 71, 59, 95, 74, 17 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], 
  [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], 
  [ 12, 1, 2, 4 ], [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 16, 1, 4, 8 ], 
  [ 20, 1, 2, 8 ], [ 23, 1, 2, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 4, 4 ], 
  [ 28, 1, 4, 4 ], [ 35, 1, 4, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ], 
  [ 43, 1, 9, 8 ], [ 44, 1, 4, 8 ], [ 51, 1, 4, 16 ], [ 52, 1, 5, 8 ], 
  [ 53, 1, 11, 16 ] ]

    k = 10: F-action on Pi is ()      [56,1,10]
      Dynkin type is A_3(q) + A_1(q) + T(phi1 phi2^3)
      Order of center |Z^F|: phi1 phi2^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 2 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 3 modulo 60:   1/32 ( q^4-9*q^3+29*q^2-47*q+42 )
        q congruent 4 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 5 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 7 modulo 60:   1/32 ( q^4-9*q^3+29*q^2-47*q+42 )
        q congruent 8 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 9 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 11 modulo 60:   1/32 ( q^4-9*q^3+29*q^2-47*q+42 )
        q congruent 13 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 16 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 17 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 19 modulo 60:   1/32 ( q^4-9*q^3+29*q^2-47*q+42 )
        q congruent 21 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 23 modulo 60:   1/32 ( q^4-9*q^3+29*q^2-47*q+42 )
        q congruent 25 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 27 modulo 60:   1/32 ( q^4-9*q^3+29*q^2-47*q+42 )
        q congruent 29 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 31 modulo 60:   1/32 ( q^4-9*q^3+29*q^2-47*q+42 )
        q congruent 32 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 37 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 41 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 43 modulo 60:   1/32 ( q^4-9*q^3+29*q^2-47*q+42 )
        q congruent 47 modulo 60:   1/32 ( q^4-9*q^3+29*q^2-47*q+42 )
        q congruent 49 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 53 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 59 modulo 60:   1/32 ( q^4-9*q^3+29*q^2-47*q+42 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 3, 7, 69, 69, 5, 81, 27, 20, 71 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 6 ], 
  [ 4, 1, 2, 12 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], 
  [ 12, 1, 2, 24 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 8 ], [ 13, 1, 4, 24 ], 
  [ 16, 1, 4, 16 ], [ 20, 1, 2, 24 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 12 ], 
  [ 24, 1, 2, 18 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 8 ], [ 25, 1, 3, 24 ], 
  [ 25, 1, 4, 16 ], [ 28, 1, 2, 12 ], [ 28, 1, 4, 24 ], [ 35, 1, 3, 24 ], 
  [ 35, 1, 4, 16 ], [ 37, 1, 2, 16 ], [ 39, 1, 2, 8 ], [ 39, 1, 3, 24 ], 
  [ 40, 1, 2, 16 ], [ 40, 1, 6, 48 ], [ 41, 1, 4, 16 ], [ 41, 1, 9, 48 ], 
  [ 43, 1, 8, 16 ], [ 43, 1, 12, 32 ], [ 44, 1, 5, 16 ], [ 48, 1, 3, 32 ], 
  [ 51, 1, 3, 32 ], [ 52, 1, 4, 16 ], [ 52, 1, 10, 48 ], [ 53, 1, 9, 32 ] ]

    k = 11: F-action on Pi is (2,5)      [56,1,11]
      Dynkin type is ^2A_3(q) + A_1(q) + T(phi1^2 phi4)
      Order of center |Z^F|: phi1^2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 2 modulo 60:   1/16 q^2 ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 4 modulo 60:   1/16 q^2 ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 7 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 8 modulo 60:   1/16 q^2 ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 11 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 13 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 16 modulo 60:   1/16 q^2 ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 19 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 21 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 23 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 25 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 27 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 29 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 31 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 32 modulo 60:   1/16 q^2 ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 41 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 43 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 47 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 49 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 53 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
        q congruent 59 modulo 60:   1/16 phi1 phi2 ( q^2-7*q+12 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 72, 20, 19, 76, 70, 19, 96, 60, 16, 73 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 4, 1, 1, 2 ], 
  [ 4, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 1, 4 ], 
  [ 12, 1, 1, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 16, 1, 2, 8 ], 
  [ 20, 1, 3, 8 ], [ 23, 1, 1, 2 ], [ 24, 1, 1, 2 ], [ 25, 1, 2, 4 ], 
  [ 28, 1, 1, 4 ], [ 35, 1, 5, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ], 
  [ 43, 1, 9, 8 ], [ 44, 1, 6, 8 ], [ 51, 1, 7, 16 ], [ 52, 1, 8, 8 ], 
  [ 53, 1, 13, 16 ] ]

    k = 12: F-action on Pi is (2,5)      [56,1,12]
      Dynkin type is ^2A_3(q) + A_1(q) + T(phi1 phi2 phi6)
      Order of center |Z^F|: phi1 phi2 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 2 modulo 60:   1/12 phi2 ( q^3-4*q^2+6*q-4 )
        q congruent 3 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 4 modulo 60:   1/12 q^2 phi1 ( q-2 )
        q congruent 5 modulo 60:   1/12 phi2 ( q^3-5*q^2+8*q-6 )
        q congruent 7 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 8 modulo 60:   1/12 phi2 ( q^3-4*q^2+6*q-4 )
        q congruent 9 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 11 modulo 60:   1/12 phi2 ( q^3-5*q^2+8*q-6 )
        q congruent 13 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 16 modulo 60:   1/12 q^2 phi1 ( q-2 )
        q congruent 17 modulo 60:   1/12 phi2 ( q^3-5*q^2+8*q-6 )
        q congruent 19 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 21 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 23 modulo 60:   1/12 phi2 ( q^3-5*q^2+8*q-6 )
        q congruent 25 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 27 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 29 modulo 60:   1/12 phi2 ( q^3-5*q^2+8*q-6 )
        q congruent 31 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 32 modulo 60:   1/12 phi2 ( q^3-4*q^2+6*q-4 )
        q congruent 37 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 41 modulo 60:   1/12 phi2 ( q^3-5*q^2+8*q-6 )
        q congruent 43 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 47 modulo 60:   1/12 phi2 ( q^3-5*q^2+8*q-6 )
        q congruent 49 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 53 modulo 60:   1/12 phi2 ( q^3-5*q^2+8*q-6 )
        q congruent 59 modulo 60:   1/12 phi2 ( q^3-5*q^2+8*q-6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 31, 78, 82, 31, 28, 82, 38, 84, 96, 60 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], 
  [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 12, 1, 2, 2 ], 
  [ 16, 1, 3, 4 ], [ 20, 1, 3, 8 ], [ 22, 1, 3, 4 ], [ 24, 1, 1, 2 ], 
  [ 27, 1, 4, 6 ], [ 31, 1, 3, 4 ], [ 42, 1, 5, 12 ], [ 44, 1, 7, 6 ], 
  [ 50, 1, 7, 12 ], [ 53, 1, 18, 12 ] ]

    k = 13: F-action on Pi is (2,5)      [56,1,13]
      Dynkin type is ^2A_3(q) + A_1(q) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q^3-6*q^2+13*q-12 )
        q congruent 2 modulo 60:   1/16 q ( q^3-6*q^2+12*q-8 )
        q congruent 3 modulo 60:   1/16 phi1 ( q^3-6*q^2+13*q-12 )
        q congruent 4 modulo 60:   1/16 q ( q^3-6*q^2+12*q-8 )
        q congruent 5 modulo 60:   1/16 phi1 ( q^3-6*q^2+13*q-12 )
        q congruent 7 modulo 60:   1/16 phi1 ( q^3-6*q^2+13*q-12 )
        q congruent 8 modulo 60:   1/16 q ( q^3-6*q^2+12*q-8 )
        q congruent 9 modulo 60:   1/16 phi1 ( q^3-6*q^2+13*q-12 )
        q congruent 11 modulo 60:   1/16 phi1 ( q^3-6*q^2+13*q-12 )
        q congruent 13 modulo 60:   1/16 phi1 ( q^3-6*q^2+13*q-12 )
        q congruent 16 modulo 60:   1/16 q ( q^3-6*q^2+12*q-8 )
        q congruent 17 modulo 60:   1/16 phi1 ( q^3-6*q^2+13*q-12 )
        q congruent 19 modulo 60:   1/16 phi1 ( q^3-6*q^2+13*q-12 )
        q congruent 21 modulo 60:   1/16 phi1 ( q^3-6*q^2+13*q-12 )
        q congruent 23 modulo 60:   1/16 phi1 ( q^3-6*q^2+13*q-12 )
        q congruent 25 modulo 60:   1/16 phi1 ( q^3-6*q^2+13*q-12 )
        q congruent 27 modulo 60:   1/16 phi1 ( q^3-6*q^2+13*q-12 )
        q congruent 29 modulo 60:   1/16 phi1 ( q^3-6*q^2+13*q-12 )
        q congruent 31 modulo 60:   1/16 phi1 ( q^3-6*q^2+13*q-12 )
        q congruent 32 modulo 60:   1/16 q ( q^3-6*q^2+12*q-8 )
        q congruent 37 modulo 60:   1/16 phi1 ( q^3-6*q^2+13*q-12 )
        q congruent 41 modulo 60:   1/16 phi1 ( q^3-6*q^2+13*q-12 )
        q congruent 43 modulo 60:   1/16 phi1 ( q^3-6*q^2+13*q-12 )
        q congruent 47 modulo 60:   1/16 phi1 ( q^3-6*q^2+13*q-12 )
        q congruent 49 modulo 60:   1/16 phi1 ( q^3-6*q^2+13*q-12 )
        q congruent 53 modulo 60:   1/16 phi1 ( q^3-6*q^2+13*q-12 )
        q congruent 59 modulo 60:   1/16 phi1 ( q^3-6*q^2+13*q-12 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 69, 5, 7, 69, 68, 7, 82, 31, 19, 76 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], 
  [ 4, 1, 2, 6 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 3 ], 
  [ 10, 1, 1, 4 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], 
  [ 13, 1, 1, 8 ], [ 13, 1, 4, 8 ], [ 16, 1, 3, 8 ], [ 19, 1, 2, 8 ], 
  [ 20, 1, 3, 16 ], [ 20, 1, 4, 8 ], [ 22, 1, 3, 8 ], [ 23, 1, 1, 4 ], 
  [ 23, 1, 2, 2 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 8 ], 
  [ 25, 1, 3, 4 ], [ 26, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 2, 8 ], 
  [ 28, 1, 3, 8 ], [ 28, 1, 4, 4 ], [ 31, 1, 3, 8 ], [ 34, 1, 3, 8 ], 
  [ 35, 1, 6, 16 ], [ 35, 1, 8, 8 ], [ 37, 1, 2, 8 ], [ 39, 1, 1, 8 ], 
  [ 39, 1, 4, 8 ], [ 41, 1, 1, 16 ], [ 41, 1, 6, 16 ], [ 42, 1, 2, 16 ], 
  [ 43, 1, 4, 16 ], [ 44, 1, 8, 8 ], [ 48, 1, 4, 16 ], [ 48, 1, 5, 8 ], 
  [ 50, 1, 8, 16 ], [ 52, 1, 2, 16 ], [ 53, 1, 8, 16 ] ]

    k = 14: F-action on Pi is (2,5)      [56,1,14]
      Dynkin type is ^2A_3(q) + A_1(q) + T(phi1^3 phi2)
      Order of center |Z^F|: phi1^3 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 ( q^3-12*q^2+43*q-40 )
        q congruent 2 modulo 60:   1/32 q ( q^3-12*q^2+44*q-48 )
        q congruent 3 modulo 60:   1/32 ( q^4-13*q^3+55*q^2-79*q+12 )
        q congruent 4 modulo 60:   1/32 q ( q^3-12*q^2+44*q-48 )
        q congruent 5 modulo 60:   1/32 phi1 ( q^3-12*q^2+43*q-40 )
        q congruent 7 modulo 60:   1/32 ( q^4-13*q^3+55*q^2-79*q+12 )
        q congruent 8 modulo 60:   1/32 q ( q^3-12*q^2+44*q-48 )
        q congruent 9 modulo 60:   1/32 phi1 ( q^3-12*q^2+43*q-40 )
        q congruent 11 modulo 60:   1/32 ( q^4-13*q^3+55*q^2-79*q+12 )
        q congruent 13 modulo 60:   1/32 phi1 ( q^3-12*q^2+43*q-40 )
        q congruent 16 modulo 60:   1/32 q ( q^3-12*q^2+44*q-48 )
        q congruent 17 modulo 60:   1/32 phi1 ( q^3-12*q^2+43*q-40 )
        q congruent 19 modulo 60:   1/32 ( q^4-13*q^3+55*q^2-79*q+12 )
        q congruent 21 modulo 60:   1/32 phi1 ( q^3-12*q^2+43*q-40 )
        q congruent 23 modulo 60:   1/32 ( q^4-13*q^3+55*q^2-79*q+12 )
        q congruent 25 modulo 60:   1/32 phi1 ( q^3-12*q^2+43*q-40 )
        q congruent 27 modulo 60:   1/32 ( q^4-13*q^3+55*q^2-79*q+12 )
        q congruent 29 modulo 60:   1/32 phi1 ( q^3-12*q^2+43*q-40 )
        q congruent 31 modulo 60:   1/32 ( q^4-13*q^3+55*q^2-79*q+12 )
        q congruent 32 modulo 60:   1/32 q ( q^3-12*q^2+44*q-48 )
        q congruent 37 modulo 60:   1/32 phi1 ( q^3-12*q^2+43*q-40 )
        q congruent 41 modulo 60:   1/32 phi1 ( q^3-12*q^2+43*q-40 )
        q congruent 43 modulo 60:   1/32 ( q^4-13*q^3+55*q^2-79*q+12 )
        q congruent 47 modulo 60:   1/32 ( q^4-13*q^3+55*q^2-79*q+12 )
        q congruent 49 modulo 60:   1/32 phi1 ( q^3-12*q^2+43*q-40 )
        q congruent 53 modulo 60:   1/32 phi1 ( q^3-12*q^2+43*q-40 )
        q congruent 59 modulo 60:   1/32 ( q^4-13*q^3+55*q^2-79*q+12 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 69, 68, 7, 4, 68, 28, 82, 70, 19 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 12 ], 
  [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 8 ], 
  [ 12, 1, 1, 24 ], [ 13, 1, 1, 24 ], [ 13, 1, 3, 8 ], [ 13, 1, 4, 8 ], 
  [ 16, 1, 2, 16 ], [ 20, 1, 3, 24 ], [ 23, 1, 1, 12 ], [ 23, 1, 2, 2 ], 
  [ 24, 1, 1, 18 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 4 ], 
  [ 25, 1, 4, 8 ], [ 28, 1, 1, 24 ], [ 28, 1, 3, 12 ], [ 35, 1, 5, 16 ], 
  [ 35, 1, 6, 24 ], [ 37, 1, 2, 16 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 8 ], 
  [ 40, 1, 1, 48 ], [ 40, 1, 3, 16 ], [ 41, 1, 1, 48 ], [ 41, 1, 4, 16 ], 
  [ 43, 1, 3, 32 ], [ 43, 1, 8, 16 ], [ 44, 1, 9, 16 ], [ 48, 1, 4, 32 ], 
  [ 51, 1, 6, 32 ], [ 52, 1, 1, 48 ], [ 52, 1, 3, 16 ], [ 53, 1, 6, 32 ] ]

    k = 15: F-action on Pi is (2,5)      [56,1,15]
      Dynkin type is ^2A_3(q) + A_1(q) + T(phi1 phi2^3)
      Order of center |Z^F|: phi1 phi2^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/96 phi1 ( q^3-12*q^2+51*q-72 )
        q congruent 2 modulo 60:   1/96 ( q^4-12*q^3+44*q^2-64*q+32 )
        q congruent 3 modulo 60:   1/96 ( q^4-13*q^3+63*q^2-135*q+108 )
        q congruent 4 modulo 60:   1/96 q ( q^3-12*q^2+44*q-48 )
        q congruent 5 modulo 60:   1/96 ( q^4-13*q^3+63*q^2-139*q+120 )
        q congruent 7 modulo 60:   1/96 ( q^4-13*q^3+63*q^2-135*q+108 )
        q congruent 8 modulo 60:   1/96 ( q^4-12*q^3+44*q^2-64*q+32 )
        q congruent 9 modulo 60:   1/96 phi1 ( q^3-12*q^2+51*q-72 )
        q congruent 11 modulo 60:   1/96 ( q^4-13*q^3+63*q^2-151*q+156 )
        q congruent 13 modulo 60:   1/96 phi1 ( q^3-12*q^2+51*q-72 )
        q congruent 16 modulo 60:   1/96 q ( q^3-12*q^2+44*q-48 )
        q congruent 17 modulo 60:   1/96 ( q^4-13*q^3+63*q^2-139*q+120 )
        q congruent 19 modulo 60:   1/96 ( q^4-13*q^3+63*q^2-135*q+108 )
        q congruent 21 modulo 60:   1/96 phi1 ( q^3-12*q^2+51*q-72 )
        q congruent 23 modulo 60:   1/96 ( q^4-13*q^3+63*q^2-151*q+156 )
        q congruent 25 modulo 60:   1/96 phi1 ( q^3-12*q^2+51*q-72 )
        q congruent 27 modulo 60:   1/96 ( q^4-13*q^3+63*q^2-135*q+108 )
        q congruent 29 modulo 60:   1/96 ( q^4-13*q^3+63*q^2-139*q+120 )
        q congruent 31 modulo 60:   1/96 ( q^4-13*q^3+63*q^2-135*q+108 )
        q congruent 32 modulo 60:   1/96 ( q^4-12*q^3+44*q^2-64*q+32 )
        q congruent 37 modulo 60:   1/96 phi1 ( q^3-12*q^2+51*q-72 )
        q congruent 41 modulo 60:   1/96 ( q^4-13*q^3+63*q^2-139*q+120 )
        q congruent 43 modulo 60:   1/96 ( q^4-13*q^3+63*q^2-135*q+108 )
        q congruent 47 modulo 60:   1/96 ( q^4-13*q^3+63*q^2-151*q+156 )
        q congruent 49 modulo 60:   1/96 phi1 ( q^3-12*q^2+51*q-72 )
        q congruent 53 modulo 60:   1/96 ( q^4-13*q^3+63*q^2-139*q+120 )
        q congruent 59 modulo 60:   1/96 ( q^4-13*q^3+63*q^2-151*q+156 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 67, 69, 5, 3, 69, 31, 78, 72, 20 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 10 ], 
  [ 6, 1, 2, 16 ], [ 7, 1, 2, 24 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 12 ], [ 11, 1, 2, 24 ], [ 12, 1, 2, 8 ], [ 13, 1, 4, 24 ], 
  [ 16, 1, 3, 16 ], [ 19, 1, 2, 48 ], [ 20, 1, 3, 8 ], [ 20, 1, 4, 48 ], 
  [ 22, 1, 3, 16 ], [ 23, 1, 2, 6 ], [ 24, 1, 1, 14 ], [ 24, 1, 2, 36 ], 
  [ 25, 1, 3, 36 ], [ 26, 1, 4, 48 ], [ 27, 1, 6, 48 ], [ 28, 1, 3, 12 ], 
  [ 28, 1, 4, 24 ], [ 31, 1, 3, 16 ], [ 34, 1, 3, 48 ], [ 35, 1, 6, 24 ], 
  [ 35, 1, 8, 48 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 24 ], [ 41, 1, 6, 48 ], 
  [ 41, 1, 9, 48 ], [ 42, 1, 6, 96 ], [ 43, 1, 13, 96 ], [ 44, 1, 10, 48 ], 
  [ 48, 1, 5, 48 ], [ 50, 1, 9, 96 ], [ 52, 1, 9, 48 ], [ 53, 1, 20, 96 ] ]

    k = 16: F-action on Pi is (2,5)      [56,1,16]
      Dynkin type is ^2A_3(q) + A_1(q) + T(phi1 phi2 phi4)
      Order of center |Z^F|: phi1 phi2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 2 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 3 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 4 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 5 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 7 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 8 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 9 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 11 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 13 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 16 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 17 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 19 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 21 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 23 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 25 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 27 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 29 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 31 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 32 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 37 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 41 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 43 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 47 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 49 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 53 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
        q congruent 59 modulo 60:   1/16 phi1^2 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 20, 71, 76, 20, 19, 72, 60, 98, 73, 18 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 4 ], 
  [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 13, 1, 1, 4 ], 
  [ 13, 1, 3, 4 ], [ 20, 1, 4, 8 ], [ 23, 1, 1, 2 ], [ 24, 1, 2, 2 ], 
  [ 25, 1, 2, 4 ], [ 28, 1, 2, 4 ], [ 35, 1, 7, 8 ], [ 39, 1, 5, 4 ], 
  [ 41, 1, 8, 8 ], [ 43, 1, 9, 8 ], [ 44, 1, 6, 8 ], [ 52, 1, 5, 8 ], 
  [ 53, 1, 13, 16 ] ]

    k = 17: F-action on Pi is (2,5)      [56,1,17]
      Dynkin type is ^2A_3(q) + A_1(q) + T(phi2^2 phi6)
      Order of center |Z^F|: phi2^2 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q phi1^2 ( q-2 )
        q congruent 2 modulo 60:   1/12 phi2 ( q^3-4*q^2+6*q-4 )
        q congruent 3 modulo 60:   1/12 q phi1^2 ( q-2 )
        q congruent 4 modulo 60:   1/12 q^2 phi1 ( q-2 )
        q congruent 5 modulo 60:   1/12 phi2 ( q^3-5*q^2+10*q-10 )
        q congruent 7 modulo 60:   1/12 q phi1^2 ( q-2 )
        q congruent 8 modulo 60:   1/12 phi2 ( q^3-4*q^2+6*q-4 )
        q congruent 9 modulo 60:   1/12 q phi1^2 ( q-2 )
        q congruent 11 modulo 60:   1/12 phi2 ( q^3-5*q^2+10*q-10 )
        q congruent 13 modulo 60:   1/12 q phi1^2 ( q-2 )
        q congruent 16 modulo 60:   1/12 q^2 phi1 ( q-2 )
        q congruent 17 modulo 60:   1/12 phi2 ( q^3-5*q^2+10*q-10 )
        q congruent 19 modulo 60:   1/12 q phi1^2 ( q-2 )
        q congruent 21 modulo 60:   1/12 q phi1^2 ( q-2 )
        q congruent 23 modulo 60:   1/12 phi2 ( q^3-5*q^2+10*q-10 )
        q congruent 25 modulo 60:   1/12 q phi1^2 ( q-2 )
        q congruent 27 modulo 60:   1/12 q phi1^2 ( q-2 )
        q congruent 29 modulo 60:   1/12 phi2 ( q^3-5*q^2+10*q-10 )
        q congruent 31 modulo 60:   1/12 q phi1^2 ( q-2 )
        q congruent 32 modulo 60:   1/12 phi2 ( q^3-4*q^2+6*q-4 )
        q congruent 37 modulo 60:   1/12 q phi1^2 ( q-2 )
        q congruent 41 modulo 60:   1/12 phi2 ( q^3-5*q^2+10*q-10 )
        q congruent 43 modulo 60:   1/12 q phi1^2 ( q-2 )
        q congruent 47 modulo 60:   1/12 phi2 ( q^3-5*q^2+10*q-10 )
        q congruent 49 modulo 60:   1/12 q phi1^2 ( q-2 )
        q congruent 53 modulo 60:   1/12 phi2 ( q^3-5*q^2+10*q-10 )
        q congruent 59 modulo 60:   1/12 phi2 ( q^3-5*q^2+10*q-10 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 78, 9, 31, 78, 82, 31, 84, 15, 60, 98 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 4 ], 
  [ 5, 1, 2, 8 ], [ 6, 1, 2, 4 ], [ 7, 1, 2, 4 ], [ 8, 1, 2, 4 ], 
  [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 12, 1, 2, 2 ], [ 14, 1, 2, 4 ], 
  [ 15, 1, 2, 4 ], [ 16, 1, 3, 4 ], [ 18, 1, 2, 4 ], [ 20, 1, 4, 8 ], 
  [ 22, 1, 4, 4 ], [ 24, 1, 2, 2 ], [ 27, 1, 4, 6 ], [ 31, 1, 4, 4 ], 
  [ 42, 1, 5, 12 ], [ 44, 1, 7, 6 ], [ 45, 1, 4, 12 ], [ 50, 1, 10, 12 ], 
  [ 53, 1, 18, 12 ] ]

    k = 18: F-action on Pi is (2,5)      [56,1,18]
      Dynkin type is ^2A_3(q) + A_1(q) + T(phi1 phi2^3)
      Order of center |Z^F|: phi1 phi2^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q^3-10*q^2+35*q-46 )
        q congruent 2 modulo 60:   1/16 ( q^4-10*q^3+32*q^2-40*q+16 )
        q congruent 3 modulo 60:   1/16 ( q^4-11*q^3+45*q^2-89*q+78 )
        q congruent 4 modulo 60:   1/16 q ( q^3-10*q^2+32*q-32 )
        q congruent 5 modulo 60:   1/16 ( q^4-11*q^3+45*q^2-89*q+70 )
        q congruent 7 modulo 60:   1/16 ( q^4-11*q^3+45*q^2-89*q+78 )
        q congruent 8 modulo 60:   1/16 ( q^4-10*q^3+32*q^2-40*q+16 )
        q congruent 9 modulo 60:   1/16 phi1 ( q^3-10*q^2+35*q-46 )
        q congruent 11 modulo 60:   1/16 ( q^4-11*q^3+45*q^2-97*q+102 )
        q congruent 13 modulo 60:   1/16 phi1 ( q^3-10*q^2+35*q-46 )
        q congruent 16 modulo 60:   1/16 q ( q^3-10*q^2+32*q-32 )
        q congruent 17 modulo 60:   1/16 ( q^4-11*q^3+45*q^2-89*q+70 )
        q congruent 19 modulo 60:   1/16 ( q^4-11*q^3+45*q^2-89*q+78 )
        q congruent 21 modulo 60:   1/16 phi1 ( q^3-10*q^2+35*q-46 )
        q congruent 23 modulo 60:   1/16 ( q^4-11*q^3+45*q^2-97*q+102 )
        q congruent 25 modulo 60:   1/16 phi1 ( q^3-10*q^2+35*q-46 )
        q congruent 27 modulo 60:   1/16 ( q^4-11*q^3+45*q^2-89*q+78 )
        q congruent 29 modulo 60:   1/16 ( q^4-11*q^3+45*q^2-89*q+70 )
        q congruent 31 modulo 60:   1/16 ( q^4-11*q^3+45*q^2-89*q+78 )
        q congruent 32 modulo 60:   1/16 ( q^4-10*q^3+32*q^2-40*q+16 )
        q congruent 37 modulo 60:   1/16 phi1 ( q^3-10*q^2+35*q-46 )
        q congruent 41 modulo 60:   1/16 ( q^4-11*q^3+45*q^2-89*q+70 )
        q congruent 43 modulo 60:   1/16 ( q^4-11*q^3+45*q^2-89*q+78 )
        q congruent 47 modulo 60:   1/16 ( q^4-11*q^3+45*q^2-97*q+102 )
        q congruent 49 modulo 60:   1/16 phi1 ( q^3-10*q^2+35*q-46 )
        q congruent 53 modulo 60:   1/16 ( q^4-11*q^3+45*q^2-89*q+70 )
        q congruent 59 modulo 60:   1/16 ( q^4-11*q^3+45*q^2-97*q+102 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 67, 69, 5, 7, 69, 31, 78, 76, 20 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 10 ], 
  [ 5, 1, 2, 16 ], [ 6, 1, 2, 16 ], [ 7, 1, 2, 8 ], [ 8, 1, 2, 8 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 4 ], [ 11, 1, 2, 8 ], 
  [ 12, 1, 2, 8 ], [ 13, 1, 4, 16 ], [ 14, 1, 2, 16 ], [ 15, 1, 2, 16 ], 
  [ 16, 1, 3, 16 ], [ 18, 1, 2, 16 ], [ 19, 1, 2, 16 ], [ 20, 1, 3, 8 ], 
  [ 20, 1, 4, 16 ], [ 21, 1, 2, 8 ], [ 22, 1, 3, 8 ], [ 22, 1, 4, 16 ], 
  [ 23, 1, 2, 6 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 3, 12 ], 
  [ 26, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 3, 12 ], [ 28, 1, 4, 8 ], 
  [ 29, 1, 3, 16 ], [ 30, 1, 3, 16 ], [ 31, 1, 3, 8 ], [ 31, 1, 4, 16 ], 
  [ 34, 1, 3, 8 ], [ 34, 1, 4, 16 ], [ 35, 1, 6, 8 ], [ 35, 1, 8, 16 ], 
  [ 36, 1, 3, 16 ], [ 37, 1, 3, 16 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 8 ], 
  [ 41, 1, 6, 16 ], [ 41, 1, 9, 16 ], [ 42, 1, 2, 16 ], [ 43, 1, 4, 16 ], 
  [ 44, 1, 8, 8 ], [ 45, 1, 5, 16 ], [ 48, 1, 5, 8 ], [ 48, 1, 6, 16 ], 
  [ 50, 1, 11, 16 ], [ 51, 1, 8, 16 ], [ 52, 1, 9, 16 ], [ 53, 1, 8, 16 ] ]

    k = 19: F-action on Pi is (2,5)      [56,1,19]
      Dynkin type is ^2A_3(q) + A_1(q) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 2 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 3 modulo 60:   1/32 ( q^4-9*q^3+29*q^2-47*q+42 )
        q congruent 4 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 5 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 7 modulo 60:   1/32 ( q^4-9*q^3+29*q^2-47*q+42 )
        q congruent 8 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 9 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 11 modulo 60:   1/32 ( q^4-9*q^3+29*q^2-47*q+42 )
        q congruent 13 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 16 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 17 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 19 modulo 60:   1/32 ( q^4-9*q^3+29*q^2-47*q+42 )
        q congruent 21 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 23 modulo 60:   1/32 ( q^4-9*q^3+29*q^2-47*q+42 )
        q congruent 25 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 27 modulo 60:   1/32 ( q^4-9*q^3+29*q^2-47*q+42 )
        q congruent 29 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 31 modulo 60:   1/32 ( q^4-9*q^3+29*q^2-47*q+42 )
        q congruent 32 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 37 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 41 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 43 modulo 60:   1/32 ( q^4-9*q^3+29*q^2-47*q+42 )
        q congruent 47 modulo 60:   1/32 ( q^4-9*q^3+29*q^2-47*q+42 )
        q congruent 49 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 53 modulo 60:   1/32 phi1 ( q^3-8*q^2+21*q-22 )
        q congruent 59 modulo 60:   1/32 ( q^4-9*q^3+29*q^2-47*q+42 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 69, 5, 7, 69, 68, 3, 82, 31, 19, 72 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 4 ], [ 4, 1, 1, 4 ], 
  [ 4, 1, 2, 6 ], [ 6, 1, 2, 8 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 3 ], 
  [ 10, 1, 1, 4 ], [ 10, 1, 2, 2 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], 
  [ 13, 1, 1, 8 ], [ 13, 1, 3, 8 ], [ 13, 1, 4, 8 ], [ 16, 1, 3, 8 ], 
  [ 19, 1, 2, 8 ], [ 20, 1, 3, 16 ], [ 20, 1, 4, 8 ], [ 22, 1, 3, 16 ], 
  [ 23, 1, 1, 4 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 6 ], 
  [ 25, 1, 1, 8 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], 
  [ 28, 1, 2, 8 ], [ 28, 1, 3, 8 ], [ 28, 1, 4, 4 ], [ 31, 1, 3, 16 ], 
  [ 34, 1, 3, 16 ], [ 35, 1, 6, 16 ], [ 35, 1, 7, 16 ], [ 35, 1, 8, 8 ], 
  [ 39, 1, 1, 8 ], [ 39, 1, 2, 8 ], [ 39, 1, 4, 8 ], [ 40, 1, 2, 16 ], 
  [ 41, 1, 1, 16 ], [ 41, 1, 4, 16 ], [ 41, 1, 6, 16 ], [ 43, 1, 3, 32 ], 
  [ 43, 1, 8, 16 ], [ 44, 1, 9, 16 ], [ 48, 1, 5, 16 ], [ 51, 1, 10, 32 ], 
  [ 52, 1, 2, 16 ], [ 52, 1, 4, 16 ], [ 53, 1, 6, 32 ] ]

    k = 20: F-action on Pi is (2,5)      [56,1,20]
      Dynkin type is ^2A_3(q) + A_1(q) + T(phi2^4)
      Order of center |Z^F|: phi2^4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/96 phi1 ( q^3-24*q^2+197*q-582 )
        q congruent 2 modulo 60:   1/96 ( q^4-24*q^3+188*q^2-544*q+512 )
        q congruent 3 modulo 60:   1/96 ( q^4-25*q^3+221*q^2-815*q+1050 )
        q congruent 4 modulo 60:   1/96 ( q^4-24*q^3+188*q^2-480*q+192 )
        q congruent 5 modulo 60:   1/96 ( q^4-25*q^3+221*q^2-843*q+1190 )
        q congruent 7 modulo 60:   1/96 ( q^4-25*q^3+221*q^2-815*q+1050 )
        q congruent 8 modulo 60:   1/96 ( q^4-24*q^3+188*q^2-544*q+512 )
        q congruent 9 modulo 60:   1/96 ( q^4-25*q^3+221*q^2-779*q+774 )
        q congruent 11 modulo 60:   1/96 ( q^4-25*q^3+221*q^2-879*q+1658 )
        q congruent 13 modulo 60:   1/96 phi1 ( q^3-24*q^2+197*q-582 )
        q congruent 16 modulo 60:   1/96 q ( q^3-24*q^2+188*q-480 )
        q congruent 17 modulo 60:   1/96 ( q^4-25*q^3+221*q^2-843*q+1190 )
        q congruent 19 modulo 60:   1/96 ( q^4-25*q^3+221*q^2-815*q+1242 )
        q congruent 21 modulo 60:   1/96 phi1 ( q^3-24*q^2+197*q-582 )
        q congruent 23 modulo 60:   1/96 ( q^4-25*q^3+221*q^2-879*q+1658 )
        q congruent 25 modulo 60:   1/96 phi1 ( q^3-24*q^2+197*q-582 )
        q congruent 27 modulo 60:   1/96 ( q^4-25*q^3+221*q^2-815*q+1050 )
        q congruent 29 modulo 60:   1/96 ( q^4-25*q^3+221*q^2-843*q+1382 )
        q congruent 31 modulo 60:   1/96 ( q^4-25*q^3+221*q^2-815*q+1050 )
        q congruent 32 modulo 60:   1/96 ( q^4-24*q^3+188*q^2-544*q+512 )
        q congruent 37 modulo 60:   1/96 phi1 ( q^3-24*q^2+197*q-582 )
        q congruent 41 modulo 60:   1/96 ( q^4-25*q^3+221*q^2-843*q+1190 )
        q congruent 43 modulo 60:   1/96 ( q^4-25*q^3+221*q^2-815*q+1050 )
        q congruent 47 modulo 60:   1/96 ( q^4-25*q^3+221*q^2-879*q+1658 )
        q congruent 49 modulo 60:   1/96 ( q^4-25*q^3+221*q^2-779*q+774 )
        q congruent 53 modulo 60:   1/96 ( q^4-25*q^3+221*q^2-843*q+1190 )
        q congruent 59 modulo 60:   1/96 ( q^4-25*q^3+221*q^2-879*q+1850 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 2, 5, 67, 69, 5, 78, 9, 20, 71 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 20 ], [ 4, 1, 2, 34 ], 
  [ 5, 1, 2, 32 ], [ 6, 1, 2, 40 ], [ 7, 1, 2, 28 ], [ 8, 1, 2, 16 ], 
  [ 9, 1, 1, 7 ], [ 10, 1, 2, 14 ], [ 11, 1, 2, 36 ], [ 12, 1, 2, 68 ], 
  [ 13, 1, 4, 72 ], [ 14, 1, 2, 64 ], [ 15, 1, 2, 64 ], [ 16, 1, 3, 40 ], 
  [ 18, 1, 2, 64 ], [ 19, 1, 2, 72 ], [ 20, 1, 4, 56 ], [ 21, 1, 2, 48 ], 
  [ 22, 1, 4, 64 ], [ 23, 1, 2, 30 ], [ 24, 1, 2, 50 ], [ 25, 1, 3, 84 ], 
  [ 26, 1, 4, 48 ], [ 27, 1, 6, 48 ], [ 28, 1, 4, 84 ], [ 29, 1, 4, 96 ], 
  [ 30, 1, 3, 96 ], [ 31, 1, 4, 64 ], [ 34, 1, 4, 96 ], [ 35, 1, 8, 72 ], 
  [ 36, 1, 4, 96 ], [ 37, 1, 3, 96 ], [ 39, 1, 3, 72 ], [ 40, 1, 6, 144 ], 
  [ 41, 1, 9, 144 ], [ 42, 1, 6, 96 ], [ 43, 1, 13, 96 ], [ 44, 1, 10, 48 ], 
  [ 45, 1, 6, 96 ], [ 48, 1, 6, 96 ], [ 50, 1, 12, 96 ], [ 51, 1, 9, 96 ], 
  [ 52, 1, 10, 144 ], [ 53, 1, 20, 96 ] ]

i = 57: Pi = [ 1, 2, 5, 7 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [57,1,1]
      Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^4)
      Order of center |Z^F|: phi1^4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/384 ( q^4-40*q^3+574*q^2-3608*q+9601 )
        q congruent 2 modulo 60:   1/384 ( q^4-36*q^3+444*q^2-2096*q+2688 )
        q congruent 3 modulo 60:   1/384 ( q^4-40*q^3+574*q^2-3384*q+5985 )
        q congruent 4 modulo 60:   1/384 ( q^4-36*q^3+444*q^2-2224*q+3840 )
        q congruent 5 modulo 60:   1/384 ( q^4-40*q^3+574*q^2-3480*q+7425 )
        q congruent 7 modulo 60:   1/384 ( q^4-40*q^3+574*q^2-3512*q+7777 )
        q congruent 8 modulo 60:   1/384 ( q^4-36*q^3+444*q^2-2096*q+2688 )
        q congruent 9 modulo 60:   1/384 ( q^4-40*q^3+574*q^2-3480*q+7425 )
        q congruent 11 modulo 60:   1/384 ( q^4-40*q^3+574*q^2-3384*q+6369 )
        q congruent 13 modulo 60:   1/384 ( q^4-40*q^3+574*q^2-3608*q+9217 )
        q congruent 16 modulo 60:   1/384 ( q^4-36*q^3+444*q^2-2224*q+4224 )
        q congruent 17 modulo 60:   1/384 ( q^4-40*q^3+574*q^2-3480*q+7425 )
        q congruent 19 modulo 60:   1/384 ( q^4-40*q^3+574*q^2-3512*q+7777 )
        q congruent 21 modulo 60:   1/384 ( q^4-40*q^3+574*q^2-3480*q+7809 )
        q congruent 23 modulo 60:   1/384 ( q^4-40*q^3+574*q^2-3384*q+5985 )
        q congruent 25 modulo 60:   1/384 ( q^4-40*q^3+574*q^2-3608*q+9217 )
        q congruent 27 modulo 60:   1/384 ( q^4-40*q^3+574*q^2-3384*q+5985 )
        q congruent 29 modulo 60:   1/384 ( q^4-40*q^3+574*q^2-3480*q+7425 )
        q congruent 31 modulo 60:   1/384 ( q^4-40*q^3+574*q^2-3512*q+8161 )
        q congruent 32 modulo 60:   1/384 ( q^4-36*q^3+444*q^2-2096*q+2688 )
        q congruent 37 modulo 60:   1/384 ( q^4-40*q^3+574*q^2-3608*q+9217 )
        q congruent 41 modulo 60:   1/384 ( q^4-40*q^3+574*q^2-3480*q+7809 )
        q congruent 43 modulo 60:   1/384 ( q^4-40*q^3+574*q^2-3512*q+7777 )
        q congruent 47 modulo 60:   1/384 ( q^4-40*q^3+574*q^2-3384*q+5985 )
        q congruent 49 modulo 60:   1/384 ( q^4-40*q^3+574*q^2-3608*q+9217 )
        q congruent 53 modulo 60:   1/384 ( q^4-40*q^3+574*q^2-3480*q+7425 )
        q congruent 59 modulo 60:   1/384 ( q^4-40*q^3+574*q^2-3384*q+5985 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 66, 4, 4, 68, 66, 4, 4, 68, 4, 68, 68, 7 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 32 ], [ 4, 1, 1, 72 ], 
  [ 5, 1, 1, 96 ], [ 6, 1, 1, 128 ], [ 7, 1, 1, 32 ], [ 8, 1, 1, 16 ], 
  [ 9, 1, 1, 7 ], [ 10, 1, 1, 8 ], [ 11, 1, 1, 32 ], [ 12, 1, 1, 96 ], 
  [ 13, 1, 1, 144 ], [ 14, 1, 1, 96 ], [ 15, 1, 1, 192 ], [ 16, 1, 1, 384 ], 
  [ 17, 1, 1, 384 ], [ 18, 1, 1, 64 ], [ 19, 1, 1, 128 ], [ 20, 1, 1, 192 ], 
  [ 21, 1, 1, 16 ], [ 22, 1, 1, 64 ], [ 23, 1, 1, 24 ], [ 24, 1, 1, 56 ], 
  [ 25, 1, 1, 144 ], [ 28, 1, 1, 96 ], [ 30, 1, 1, 192 ], [ 31, 1, 1, 192 ], 
  [ 32, 1, 1, 384 ], [ 33, 1, 1, 768 ], [ 34, 1, 1, 64 ], [ 35, 1, 1, 384 ], 
  [ 37, 1, 1, 96 ], [ 39, 1, 1, 48 ], [ 40, 1, 1, 192 ], [ 41, 1, 1, 288 ], 
  [ 47, 1, 1, 384 ], [ 48, 1, 1, 192 ], [ 49, 1, 1, 768 ], [ 52, 1, 1, 192 ] ]

    k = 2: F-action on Pi is ()      [57,1,2]
      Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^3 phi2)
      Order of center |Z^F|: phi1^3 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/96 phi1 ( q^3-19*q^2+115*q-241 )
        q congruent 2 modulo 60:   1/96 q ( q^3-16*q^2+76*q-96 )
        q congruent 3 modulo 60:   1/96 phi1 ( q^3-19*q^2+115*q-201 )
        q congruent 4 modulo 60:   1/96 q ( q^3-16*q^2+76*q-112 )
        q congruent 5 modulo 60:   1/96 phi1 ( q^3-19*q^2+115*q-225 )
        q congruent 7 modulo 60:   1/96 phi1 ( q^3-19*q^2+115*q-217 )
        q congruent 8 modulo 60:   1/96 q ( q^3-16*q^2+76*q-96 )
        q congruent 9 modulo 60:   1/96 phi1 ( q^3-19*q^2+115*q-225 )
        q congruent 11 modulo 60:   1/96 phi1 ( q^3-19*q^2+115*q-201 )
        q congruent 13 modulo 60:   1/96 phi1 ( q^3-19*q^2+115*q-241 )
        q congruent 16 modulo 60:   1/96 q ( q^3-16*q^2+76*q-112 )
        q congruent 17 modulo 60:   1/96 phi1 ( q^3-19*q^2+115*q-225 )
        q congruent 19 modulo 60:   1/96 phi1 ( q^3-19*q^2+115*q-217 )
        q congruent 21 modulo 60:   1/96 phi1 ( q^3-19*q^2+115*q-225 )
        q congruent 23 modulo 60:   1/96 phi1 ( q^3-19*q^2+115*q-201 )
        q congruent 25 modulo 60:   1/96 phi1 ( q^3-19*q^2+115*q-241 )
        q congruent 27 modulo 60:   1/96 phi1 ( q^3-19*q^2+115*q-201 )
        q congruent 29 modulo 60:   1/96 phi1 ( q^3-19*q^2+115*q-225 )
        q congruent 31 modulo 60:   1/96 phi1 ( q^3-19*q^2+115*q-217 )
        q congruent 32 modulo 60:   1/96 q ( q^3-16*q^2+76*q-96 )
        q congruent 37 modulo 60:   1/96 phi1 ( q^3-19*q^2+115*q-241 )
        q congruent 41 modulo 60:   1/96 phi1 ( q^3-19*q^2+115*q-225 )
        q congruent 43 modulo 60:   1/96 phi1 ( q^3-19*q^2+115*q-217 )
        q congruent 47 modulo 60:   1/96 phi1 ( q^3-19*q^2+115*q-201 )
        q congruent 49 modulo 60:   1/96 phi1 ( q^3-19*q^2+115*q-241 )
        q congruent 53 modulo 60:   1/96 phi1 ( q^3-19*q^2+115*q-225 )
        q congruent 59 modulo 60:   1/96 phi1 ( q^3-19*q^2+115*q-201 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 4, 68, 4, 68, 68, 3, 4, 68, 68, 7, 68, 7, 7, 69 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 36 ], 
  [ 6, 1, 1, 32 ], [ 7, 1, 1, 8 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 6 ], 
  [ 10, 1, 2, 2 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 72 ], 
  [ 16, 1, 1, 96 ], [ 19, 1, 1, 32 ], [ 20, 1, 1, 48 ], [ 20, 1, 2, 48 ], 
  [ 22, 1, 2, 16 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 42 ], [ 24, 1, 2, 14 ], 
  [ 25, 1, 1, 72 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 24 ], [ 31, 1, 2, 48 ], 
  [ 33, 1, 1, 192 ], [ 34, 1, 2, 16 ], [ 35, 1, 1, 96 ], [ 35, 1, 3, 96 ], 
  [ 39, 1, 1, 24 ], [ 39, 1, 4, 12 ], [ 40, 1, 1, 48 ], [ 41, 1, 1, 144 ], 
  [ 41, 1, 6, 72 ], [ 47, 1, 2, 96 ], [ 48, 1, 2, 48 ], [ 49, 1, 1, 192 ], 
  [ 49, 1, 9, 192 ], [ 52, 1, 1, 48 ], [ 52, 1, 2, 48 ] ]

    k = 3: F-action on Pi is (5,7)      [57,1,3]
      Dynkin type is A_1(q) + A_1(q) + A_1(q^2) + T(phi1^3 phi2)
      Order of center |Z^F|: phi1^3 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 ( q^3-13*q^2+51*q-55 )
        q congruent 2 modulo 60:   1/32 q ( q^3-12*q^2+44*q-48 )
        q congruent 3 modulo 60:   1/32 ( q^4-14*q^3+64*q^2-98*q+15 )
        q congruent 4 modulo 60:   1/32 q ( q^3-12*q^2+44*q-48 )
        q congruent 5 modulo 60:   1/32 phi1 ( q^3-13*q^2+51*q-55 )
        q congruent 7 modulo 60:   1/32 ( q^4-14*q^3+64*q^2-98*q+15 )
        q congruent 8 modulo 60:   1/32 q ( q^3-12*q^2+44*q-48 )
        q congruent 9 modulo 60:   1/32 phi1 ( q^3-13*q^2+51*q-55 )
        q congruent 11 modulo 60:   1/32 ( q^4-14*q^3+64*q^2-98*q+15 )
        q congruent 13 modulo 60:   1/32 phi1 ( q^3-13*q^2+51*q-55 )
        q congruent 16 modulo 60:   1/32 q ( q^3-12*q^2+44*q-48 )
        q congruent 17 modulo 60:   1/32 phi1 ( q^3-13*q^2+51*q-55 )
        q congruent 19 modulo 60:   1/32 ( q^4-14*q^3+64*q^2-98*q+15 )
        q congruent 21 modulo 60:   1/32 phi1 ( q^3-13*q^2+51*q-55 )
        q congruent 23 modulo 60:   1/32 ( q^4-14*q^3+64*q^2-98*q+15 )
        q congruent 25 modulo 60:   1/32 phi1 ( q^3-13*q^2+51*q-55 )
        q congruent 27 modulo 60:   1/32 ( q^4-14*q^3+64*q^2-98*q+15 )
        q congruent 29 modulo 60:   1/32 phi1 ( q^3-13*q^2+51*q-55 )
        q congruent 31 modulo 60:   1/32 ( q^4-14*q^3+64*q^2-98*q+15 )
        q congruent 32 modulo 60:   1/32 q ( q^3-12*q^2+44*q-48 )
        q congruent 37 modulo 60:   1/32 phi1 ( q^3-13*q^2+51*q-55 )
        q congruent 41 modulo 60:   1/32 phi1 ( q^3-13*q^2+51*q-55 )
        q congruent 43 modulo 60:   1/32 ( q^4-14*q^3+64*q^2-98*q+15 )
        q congruent 47 modulo 60:   1/32 ( q^4-14*q^3+64*q^2-98*q+15 )
        q congruent 49 modulo 60:   1/32 phi1 ( q^3-13*q^2+51*q-55 )
        q congruent 53 modulo 60:   1/32 phi1 ( q^3-13*q^2+51*q-55 )
        q congruent 59 modulo 60:   1/32 ( q^4-14*q^3+64*q^2-98*q+15 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 70, 68, 19, 68, 19, 7, 76 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 10 ], 
  [ 4, 1, 2, 6 ], [ 5, 1, 1, 16 ], [ 6, 1, 1, 16 ], [ 7, 1, 1, 8 ], 
  [ 8, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 11, 1, 1, 8 ], 
  [ 12, 1, 1, 8 ], [ 13, 1, 1, 16 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], 
  [ 13, 1, 4, 8 ], [ 14, 1, 1, 16 ], [ 15, 1, 1, 16 ], [ 16, 1, 1, 16 ], 
  [ 16, 1, 2, 16 ], [ 18, 1, 1, 16 ], [ 19, 1, 1, 16 ], [ 20, 1, 1, 16 ], 
  [ 20, 1, 3, 16 ], [ 21, 1, 1, 8 ], [ 22, 1, 1, 16 ], [ 23, 1, 1, 6 ], 
  [ 23, 1, 2, 2 ], [ 24, 1, 1, 12 ], [ 25, 1, 1, 12 ], [ 25, 1, 2, 8 ], 
  [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 28, 1, 1, 8 ], [ 28, 1, 3, 8 ], 
  [ 30, 1, 1, 16 ], [ 30, 1, 2, 16 ], [ 31, 1, 1, 16 ], [ 33, 1, 2, 32 ], 
  [ 34, 1, 1, 16 ], [ 35, 1, 1, 16 ], [ 35, 1, 2, 16 ], [ 35, 1, 5, 16 ], 
  [ 35, 1, 6, 16 ], [ 37, 1, 1, 16 ], [ 37, 1, 2, 8 ], [ 39, 1, 1, 8 ], 
  [ 39, 1, 2, 4 ], [ 40, 1, 3, 16 ], [ 41, 1, 1, 16 ], [ 41, 1, 2, 8 ], 
  [ 41, 1, 4, 16 ], [ 47, 1, 3, 32 ], [ 48, 1, 1, 16 ], [ 48, 1, 4, 16 ], 
  [ 48, 1, 7, 16 ], [ 49, 1, 2, 32 ], [ 52, 1, 3, 16 ] ]

    k = 4: F-action on Pi is (5,7)      [57,1,4]
      Dynkin type is A_1(q) + A_1(q) + A_1(q^2) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 ( q^3-9*q^2+23*q-11 )
        q congruent 2 modulo 60:   1/16 ( q^4-8*q^3+16*q^2-16 )
        q congruent 3 modulo 60:   1/16 ( q^4-10*q^3+32*q^2-42*q+27 )
        q congruent 4 modulo 60:   1/16 q^2 ( q^2-8*q+16 )
        q congruent 5 modulo 60:   1/16 ( q^4-10*q^3+32*q^2-34*q-5 )
        q congruent 7 modulo 60:   1/16 ( q^4-10*q^3+32*q^2-34*q+19 )
        q congruent 8 modulo 60:   1/16 ( q^4-8*q^3+16*q^2-16 )
        q congruent 9 modulo 60:   1/16 phi1 ( q^3-9*q^2+23*q-19 )
        q congruent 11 modulo 60:   1/16 ( q^4-10*q^3+32*q^2-34*q+3 )
        q congruent 13 modulo 60:   1/16 phi1 ( q^3-9*q^2+23*q-11 )
        q congruent 16 modulo 60:   1/16 q^2 ( q^2-8*q+16 )
        q congruent 17 modulo 60:   1/16 ( q^4-10*q^3+32*q^2-34*q-5 )
        q congruent 19 modulo 60:   1/16 ( q^4-10*q^3+32*q^2-34*q+19 )
        q congruent 21 modulo 60:   1/16 phi1 ( q^3-9*q^2+23*q-19 )
        q congruent 23 modulo 60:   1/16 ( q^4-10*q^3+32*q^2-34*q+3 )
        q congruent 25 modulo 60:   1/16 phi1 ( q^3-9*q^2+23*q-11 )
        q congruent 27 modulo 60:   1/16 ( q^4-10*q^3+32*q^2-42*q+27 )
        q congruent 29 modulo 60:   1/16 ( q^4-10*q^3+32*q^2-34*q-5 )
        q congruent 31 modulo 60:   1/16 ( q^4-10*q^3+32*q^2-34*q+19 )
        q congruent 32 modulo 60:   1/16 ( q^4-8*q^3+16*q^2-16 )
        q congruent 37 modulo 60:   1/16 phi1 ( q^3-9*q^2+23*q-11 )
        q congruent 41 modulo 60:   1/16 ( q^4-10*q^3+32*q^2-34*q-5 )
        q congruent 43 modulo 60:   1/16 ( q^4-10*q^3+32*q^2-34*q+19 )
        q congruent 47 modulo 60:   1/16 ( q^4-10*q^3+32*q^2-34*q+3 )
        q congruent 49 modulo 60:   1/16 phi1 ( q^3-9*q^2+23*q-11 )
        q congruent 53 modulo 60:   1/16 ( q^4-10*q^3+32*q^2-34*q-5 )
        q congruent 59 modulo 60:   1/16 ( q^4-10*q^3+32*q^2-34*q+3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 19, 3, 72, 7, 76, 69, 20 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], 
  [ 4, 1, 1, 6 ], [ 4, 1, 2, 6 ], [ 6, 1, 1, 8 ], [ 6, 1, 2, 8 ], 
  [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 4 ], 
  [ 12, 1, 2, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], 
  [ 13, 1, 4, 8 ], [ 16, 1, 1, 8 ], [ 16, 1, 2, 8 ], [ 16, 1, 3, 8 ], 
  [ 16, 1, 4, 8 ], [ 17, 1, 2, 16 ], [ 17, 1, 3, 16 ], [ 19, 1, 1, 8 ], 
  [ 19, 1, 2, 8 ], [ 20, 1, 1, 8 ], [ 20, 1, 2, 8 ], [ 20, 1, 3, 8 ], 
  [ 20, 1, 4, 8 ], [ 22, 1, 2, 8 ], [ 22, 1, 3, 8 ], [ 23, 1, 1, 2 ], 
  [ 23, 1, 2, 2 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 25, 1, 1, 4 ], 
  [ 25, 1, 2, 8 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 28, 1, 1, 4 ], 
  [ 28, 1, 2, 4 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], [ 31, 1, 2, 8 ], 
  [ 31, 1, 3, 8 ], [ 32, 1, 2, 16 ], [ 32, 1, 4, 16 ], [ 33, 1, 2, 16 ], 
  [ 33, 1, 6, 16 ], [ 34, 1, 2, 8 ], [ 34, 1, 3, 8 ], [ 35, 1, 1, 8 ], 
  [ 35, 1, 2, 8 ], [ 35, 1, 3, 8 ], [ 35, 1, 4, 8 ], [ 35, 1, 5, 8 ], 
  [ 35, 1, 6, 8 ], [ 35, 1, 7, 8 ], [ 35, 1, 8, 8 ], [ 39, 1, 2, 4 ], 
  [ 39, 1, 4, 4 ], [ 40, 1, 2, 8 ], [ 40, 1, 3, 8 ], [ 41, 1, 2, 8 ], 
  [ 41, 1, 4, 16 ], [ 41, 1, 6, 8 ], [ 47, 1, 4, 16 ], [ 47, 1, 9, 16 ], 
  [ 48, 1, 2, 8 ], [ 48, 1, 5, 8 ], [ 49, 1, 2, 16 ], [ 49, 1, 8, 16 ], 
  [ 52, 1, 3, 8 ], [ 52, 1, 4, 8 ] ]

    k = 5: F-action on Pi is ()      [57,1,5]
      Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/64 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 2 modulo 60:   1/64 q ( q^3-8*q^2+20*q-16 )
        q congruent 3 modulo 60:   1/64 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 4 modulo 60:   1/64 q ( q^3-8*q^2+20*q-16 )
        q congruent 5 modulo 60:   1/64 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 7 modulo 60:   1/64 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 8 modulo 60:   1/64 q ( q^3-8*q^2+20*q-16 )
        q congruent 9 modulo 60:   1/64 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 11 modulo 60:   1/64 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 13 modulo 60:   1/64 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 16 modulo 60:   1/64 q ( q^3-8*q^2+20*q-16 )
        q congruent 17 modulo 60:   1/64 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 19 modulo 60:   1/64 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 21 modulo 60:   1/64 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 23 modulo 60:   1/64 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 25 modulo 60:   1/64 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 27 modulo 60:   1/64 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 29 modulo 60:   1/64 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 31 modulo 60:   1/64 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 32 modulo 60:   1/64 q ( q^3-8*q^2+20*q-16 )
        q congruent 37 modulo 60:   1/64 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 41 modulo 60:   1/64 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 43 modulo 60:   1/64 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 47 modulo 60:   1/64 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 49 modulo 60:   1/64 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 53 modulo 60:   1/64 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 59 modulo 60:   1/64 phi1 ( q^3-11*q^2+39*q-45 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 68, 68, 7, 68, 7, 3, 69, 68, 7, 7, 69, 7, 69, 69, 5 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 12 ], 
  [ 9, 1, 1, 7 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 24 ], 
  [ 13, 1, 4, 24 ], [ 20, 1, 2, 32 ], [ 20, 1, 3, 32 ], [ 23, 1, 1, 4 ], 
  [ 23, 1, 2, 4 ], [ 24, 1, 1, 28 ], [ 24, 1, 2, 28 ], [ 25, 1, 1, 24 ], 
  [ 25, 1, 3, 24 ], [ 28, 1, 2, 16 ], [ 28, 1, 3, 16 ], [ 35, 1, 3, 64 ], 
  [ 35, 1, 6, 64 ], [ 37, 1, 2, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 3, 8 ], 
  [ 39, 1, 4, 16 ], [ 41, 1, 1, 48 ], [ 41, 1, 6, 96 ], [ 41, 1, 9, 48 ], 
  [ 48, 1, 3, 32 ], [ 48, 1, 4, 32 ], [ 49, 1, 5, 128 ], [ 49, 1, 9, 128 ], 
  [ 52, 1, 2, 32 ], [ 52, 1, 9, 32 ] ]

    k = 6: F-action on Pi is ()      [57,1,6]
      Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^3)
      Order of center |Z^F|: phi1 phi2^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/96 phi1 ( q^3-15*q^2+75*q-117 )
        q congruent 2 modulo 60:   1/96 ( q^4-12*q^3+44*q^2-64*q+32 )
        q congruent 3 modulo 60:   1/96 ( q^4-16*q^3+90*q^2-216*q+189 )
        q congruent 4 modulo 60:   1/96 q ( q^3-12*q^2+44*q-48 )
        q congruent 5 modulo 60:   1/96 ( q^4-16*q^3+90*q^2-208*q+165 )
        q congruent 7 modulo 60:   1/96 ( q^4-16*q^3+90*q^2-216*q+189 )
        q congruent 8 modulo 60:   1/96 ( q^4-12*q^3+44*q^2-64*q+32 )
        q congruent 9 modulo 60:   1/96 phi1 ( q^3-15*q^2+75*q-117 )
        q congruent 11 modulo 60:   1/96 ( q^4-16*q^3+90*q^2-232*q+237 )
        q congruent 13 modulo 60:   1/96 phi1 ( q^3-15*q^2+75*q-117 )
        q congruent 16 modulo 60:   1/96 q ( q^3-12*q^2+44*q-48 )
        q congruent 17 modulo 60:   1/96 ( q^4-16*q^3+90*q^2-208*q+165 )
        q congruent 19 modulo 60:   1/96 ( q^4-16*q^3+90*q^2-216*q+189 )
        q congruent 21 modulo 60:   1/96 phi1 ( q^3-15*q^2+75*q-117 )
        q congruent 23 modulo 60:   1/96 ( q^4-16*q^3+90*q^2-232*q+237 )
        q congruent 25 modulo 60:   1/96 phi1 ( q^3-15*q^2+75*q-117 )
        q congruent 27 modulo 60:   1/96 ( q^4-16*q^3+90*q^2-216*q+189 )
        q congruent 29 modulo 60:   1/96 ( q^4-16*q^3+90*q^2-208*q+165 )
        q congruent 31 modulo 60:   1/96 ( q^4-16*q^3+90*q^2-216*q+189 )
        q congruent 32 modulo 60:   1/96 ( q^4-12*q^3+44*q^2-64*q+32 )
        q congruent 37 modulo 60:   1/96 phi1 ( q^3-15*q^2+75*q-117 )
        q congruent 41 modulo 60:   1/96 ( q^4-16*q^3+90*q^2-208*q+165 )
        q congruent 43 modulo 60:   1/96 ( q^4-16*q^3+90*q^2-216*q+189 )
        q congruent 47 modulo 60:   1/96 ( q^4-16*q^3+90*q^2-232*q+237 )
        q congruent 49 modulo 60:   1/96 phi1 ( q^3-15*q^2+75*q-117 )
        q congruent 53 modulo 60:   1/96 ( q^4-16*q^3+90*q^2-208*q+165 )
        q congruent 59 modulo 60:   1/96 ( q^4-16*q^3+90*q^2-232*q+237 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 3, 7, 69, 7, 69, 69, 5, 7, 69, 69, 5, 69, 5, 5, 67 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 36 ], 
  [ 6, 1, 2, 32 ], [ 7, 1, 2, 8 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 24 ], [ 13, 1, 4, 72 ], 
  [ 16, 1, 3, 96 ], [ 19, 1, 2, 32 ], [ 20, 1, 3, 48 ], [ 20, 1, 4, 48 ], 
  [ 22, 1, 3, 16 ], [ 23, 1, 2, 12 ], [ 24, 1, 1, 14 ], [ 24, 1, 2, 42 ], 
  [ 25, 1, 3, 72 ], [ 28, 1, 3, 24 ], [ 28, 1, 4, 24 ], [ 31, 1, 3, 48 ], 
  [ 33, 1, 8, 192 ], [ 34, 1, 3, 16 ], [ 35, 1, 6, 96 ], [ 35, 1, 8, 96 ], 
  [ 39, 1, 3, 24 ], [ 39, 1, 4, 12 ], [ 40, 1, 6, 48 ], [ 41, 1, 6, 72 ], 
  [ 41, 1, 9, 144 ], [ 47, 1, 7, 96 ], [ 48, 1, 5, 48 ], [ 49, 1, 5, 192 ], 
  [ 49, 1, 10, 192 ], [ 52, 1, 9, 48 ], [ 52, 1, 10, 48 ] ]

    k = 7: F-action on Pi is (5,7)      [57,1,7]
      Dynkin type is A_1(q) + A_1(q) + A_1(q^2) + T(phi1 phi2 phi4)
      Order of center |Z^F|: phi1 phi2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^2 phi2 ( q-3 )
        q congruent 2 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 3 modulo 60:   1/16 phi1^2 phi2 ( q-3 )
        q congruent 4 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 5 modulo 60:   1/16 phi1^2 phi2 ( q-3 )
        q congruent 7 modulo 60:   1/16 phi1^2 phi2 ( q-3 )
        q congruent 8 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 9 modulo 60:   1/16 phi1^2 phi2 ( q-3 )
        q congruent 11 modulo 60:   1/16 phi1^2 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/16 phi1^2 phi2 ( q-3 )
        q congruent 16 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 17 modulo 60:   1/16 phi1^2 phi2 ( q-3 )
        q congruent 19 modulo 60:   1/16 phi1^2 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/16 phi1^2 phi2 ( q-3 )
        q congruent 23 modulo 60:   1/16 phi1^2 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/16 phi1^2 phi2 ( q-3 )
        q congruent 27 modulo 60:   1/16 phi1^2 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/16 phi1^2 phi2 ( q-3 )
        q congruent 31 modulo 60:   1/16 phi1^2 phi2 ( q-3 )
        q congruent 32 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 37 modulo 60:   1/16 phi1^2 phi2 ( q-3 )
        q congruent 41 modulo 60:   1/16 phi1^2 phi2 ( q-3 )
        q congruent 43 modulo 60:   1/16 phi1^2 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/16 phi1^2 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/16 phi1^2 phi2 ( q-3 )
        q congruent 53 modulo 60:   1/16 phi1^2 phi2 ( q-3 )
        q congruent 59 modulo 60:   1/16 phi1^2 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 19, 73, 76, 18, 72, 18, 20, 74 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 39, 1, 4, 4 ], 
  [ 39, 1, 5, 4 ], [ 41, 1, 5, 8 ], [ 41, 1, 6, 8 ], [ 41, 1, 8, 16 ], 
  [ 49, 1, 4, 16 ], [ 49, 1, 7, 16 ], [ 52, 1, 5, 8 ], [ 52, 1, 8, 8 ] ]

    k = 8: F-action on Pi is (5,7)      [57,1,8]
      Dynkin type is A_1(q) + A_1(q) + A_1(q^2) + T(phi2^2 phi4)
      Order of center |Z^F|: phi2^2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 2 modulo 60:   1/32 q^3 ( q-2 )
        q congruent 3 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 4 modulo 60:   1/32 q^3 ( q-2 )
        q congruent 5 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 7 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 8 modulo 60:   1/32 q^3 ( q-2 )
        q congruent 9 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 11 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 16 modulo 60:   1/32 q^3 ( q-2 )
        q congruent 17 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 19 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 23 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 27 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 31 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 32 modulo 60:   1/32 q^3 ( q-2 )
        q congruent 37 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 41 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 43 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 53 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 59 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 76, 18, 20, 74, 20, 74, 71, 17 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 3 ], 
  [ 10, 1, 2, 4 ], [ 13, 1, 4, 8 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 12 ], 
  [ 25, 1, 3, 8 ], [ 39, 1, 3, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 5, 8 ], 
  [ 41, 1, 8, 16 ], [ 41, 1, 9, 16 ], [ 48, 1, 9, 16 ], [ 49, 1, 4, 32 ], 
  [ 52, 1, 5, 16 ] ]

    k = 9: F-action on Pi is (5,7)      [57,1,9]
      Dynkin type is A_1(q) + A_1(q) + A_1(q^2) + T(phi1 phi2^3)
      Order of center |Z^F|: phi1 phi2^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 ( q^3-9*q^2+27*q-27 )
        q congruent 2 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 3 modulo 60:   1/32 ( q^4-10*q^3+36*q^2-62*q+51 )
        q congruent 4 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 5 modulo 60:   1/32 phi1 ( q^3-9*q^2+27*q-27 )
        q congruent 7 modulo 60:   1/32 ( q^4-10*q^3+36*q^2-62*q+51 )
        q congruent 8 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 9 modulo 60:   1/32 phi1 ( q^3-9*q^2+27*q-27 )
        q congruent 11 modulo 60:   1/32 ( q^4-10*q^3+36*q^2-62*q+51 )
        q congruent 13 modulo 60:   1/32 phi1 ( q^3-9*q^2+27*q-27 )
        q congruent 16 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 17 modulo 60:   1/32 phi1 ( q^3-9*q^2+27*q-27 )
        q congruent 19 modulo 60:   1/32 ( q^4-10*q^3+36*q^2-62*q+51 )
        q congruent 21 modulo 60:   1/32 phi1 ( q^3-9*q^2+27*q-27 )
        q congruent 23 modulo 60:   1/32 ( q^4-10*q^3+36*q^2-62*q+51 )
        q congruent 25 modulo 60:   1/32 phi1 ( q^3-9*q^2+27*q-27 )
        q congruent 27 modulo 60:   1/32 ( q^4-10*q^3+36*q^2-62*q+51 )
        q congruent 29 modulo 60:   1/32 phi1 ( q^3-9*q^2+27*q-27 )
        q congruent 31 modulo 60:   1/32 ( q^4-10*q^3+36*q^2-62*q+51 )
        q congruent 32 modulo 60:   1/32 q ( q^3-8*q^2+20*q-16 )
        q congruent 37 modulo 60:   1/32 phi1 ( q^3-9*q^2+27*q-27 )
        q congruent 41 modulo 60:   1/32 phi1 ( q^3-9*q^2+27*q-27 )
        q congruent 43 modulo 60:   1/32 ( q^4-10*q^3+36*q^2-62*q+51 )
        q congruent 47 modulo 60:   1/32 ( q^4-10*q^3+36*q^2-62*q+51 )
        q congruent 49 modulo 60:   1/32 phi1 ( q^3-9*q^2+27*q-27 )
        q congruent 53 modulo 60:   1/32 phi1 ( q^3-9*q^2+27*q-27 )
        q congruent 59 modulo 60:   1/32 ( q^4-10*q^3+36*q^2-62*q+51 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 7, 76, 69, 20, 69, 20, 5, 71 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 6 ], 
  [ 4, 1, 2, 10 ], [ 5, 1, 2, 16 ], [ 6, 1, 2, 16 ], [ 7, 1, 2, 8 ], 
  [ 8, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 4 ], [ 11, 1, 2, 8 ], 
  [ 12, 1, 2, 8 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], 
  [ 13, 1, 4, 16 ], [ 14, 1, 2, 16 ], [ 15, 1, 2, 16 ], [ 16, 1, 3, 16 ], 
  [ 16, 1, 4, 16 ], [ 18, 1, 2, 16 ], [ 19, 1, 2, 16 ], [ 20, 1, 2, 16 ], 
  [ 20, 1, 4, 16 ], [ 21, 1, 2, 8 ], [ 22, 1, 4, 16 ], [ 23, 1, 1, 2 ], 
  [ 23, 1, 2, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 4 ], [ 25, 1, 2, 8 ], 
  [ 25, 1, 3, 12 ], [ 25, 1, 4, 8 ], [ 28, 1, 2, 8 ], [ 28, 1, 4, 8 ], 
  [ 30, 1, 3, 16 ], [ 30, 1, 4, 16 ], [ 31, 1, 4, 16 ], [ 33, 1, 6, 32 ], 
  [ 34, 1, 4, 16 ], [ 35, 1, 3, 16 ], [ 35, 1, 4, 16 ], [ 35, 1, 7, 16 ], 
  [ 35, 1, 8, 16 ], [ 37, 1, 2, 8 ], [ 37, 1, 3, 16 ], [ 39, 1, 2, 4 ], 
  [ 39, 1, 3, 8 ], [ 40, 1, 2, 16 ], [ 41, 1, 2, 8 ], [ 41, 1, 4, 16 ], 
  [ 41, 1, 9, 16 ], [ 47, 1, 10, 32 ], [ 48, 1, 3, 16 ], [ 48, 1, 6, 16 ], 
  [ 48, 1, 10, 16 ], [ 49, 1, 8, 32 ], [ 52, 1, 4, 16 ] ]

    k = 10: F-action on Pi is ()      [57,1,10]
      Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi2^4)
      Order of center |Z^F|: phi2^4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/384 phi1 ( q^3-31*q^2+327*q-1209 )
        q congruent 2 modulo 60:   1/384 ( q^4-28*q^3+252*q^2-848*q+896 )
        q congruent 3 modulo 60:   1/384 ( q^4-32*q^3+358*q^2-1632*q+2457 )
        q congruent 4 modulo 60:   1/384 ( q^4-28*q^3+252*q^2-720*q+384 )
        q congruent 5 modulo 60:   1/384 ( q^4-32*q^3+358*q^2-1664*q+2745 )
        q congruent 7 modulo 60:   1/384 ( q^4-32*q^3+358*q^2-1632*q+2457 )
        q congruent 8 modulo 60:   1/384 ( q^4-28*q^3+252*q^2-848*q+896 )
        q congruent 9 modulo 60:   1/384 ( q^4-32*q^3+358*q^2-1536*q+1593 )
        q congruent 11 modulo 60:   1/384 ( q^4-32*q^3+358*q^2-1760*q+3993 )
        q congruent 13 modulo 60:   1/384 phi1 ( q^3-31*q^2+327*q-1209 )
        q congruent 16 modulo 60:   1/384 q ( q^3-28*q^2+252*q-720 )
        q congruent 17 modulo 60:   1/384 ( q^4-32*q^3+358*q^2-1664*q+2745 )
        q congruent 19 modulo 60:   1/384 ( q^4-32*q^3+358*q^2-1632*q+2841 )
        q congruent 21 modulo 60:   1/384 phi1 ( q^3-31*q^2+327*q-1209 )
        q congruent 23 modulo 60:   1/384 ( q^4-32*q^3+358*q^2-1760*q+3993 )
        q congruent 25 modulo 60:   1/384 phi1 ( q^3-31*q^2+327*q-1209 )
        q congruent 27 modulo 60:   1/384 ( q^4-32*q^3+358*q^2-1632*q+2457 )
        q congruent 29 modulo 60:   1/384 ( q^4-32*q^3+358*q^2-1664*q+3129 )
        q congruent 31 modulo 60:   1/384 ( q^4-32*q^3+358*q^2-1632*q+2457 )
        q congruent 32 modulo 60:   1/384 ( q^4-28*q^3+252*q^2-848*q+896 )
        q congruent 37 modulo 60:   1/384 phi1 ( q^3-31*q^2+327*q-1209 )
        q congruent 41 modulo 60:   1/384 ( q^4-32*q^3+358*q^2-1664*q+2745 )
        q congruent 43 modulo 60:   1/384 ( q^4-32*q^3+358*q^2-1632*q+2457 )
        q congruent 47 modulo 60:   1/384 ( q^4-32*q^3+358*q^2-1760*q+3993 )
        q congruent 49 modulo 60:   1/384 ( q^4-32*q^3+358*q^2-1536*q+1593 )
        q congruent 53 modulo 60:   1/384 ( q^4-32*q^3+358*q^2-1664*q+2745 )
        q congruent 59 modulo 60:   1/384 ( q^4-32*q^3+358*q^2-1760*q+4377 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 7, 69, 69, 5, 69, 5, 5, 67, 69, 5, 5, 67, 5, 67, 67, 2 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 2, 32 ], [ 4, 1, 2, 72 ], 
  [ 5, 1, 2, 96 ], [ 6, 1, 2, 128 ], [ 7, 1, 2, 32 ], [ 8, 1, 2, 16 ], 
  [ 9, 1, 1, 7 ], [ 10, 1, 2, 8 ], [ 11, 1, 2, 32 ], [ 12, 1, 2, 96 ], 
  [ 13, 1, 4, 144 ], [ 14, 1, 2, 96 ], [ 15, 1, 2, 192 ], [ 16, 1, 3, 384 ], 
  [ 17, 1, 4, 384 ], [ 18, 1, 2, 64 ], [ 19, 1, 2, 128 ], [ 20, 1, 4, 192 ], 
  [ 21, 1, 2, 16 ], [ 22, 1, 4, 64 ], [ 23, 1, 2, 24 ], [ 24, 1, 2, 56 ], 
  [ 25, 1, 3, 144 ], [ 28, 1, 4, 96 ], [ 30, 1, 3, 192 ], [ 31, 1, 4, 192 ], 
  [ 32, 1, 3, 384 ], [ 33, 1, 8, 768 ], [ 34, 1, 4, 64 ], [ 35, 1, 8, 384 ], 
  [ 37, 1, 3, 96 ], [ 39, 1, 3, 48 ], [ 40, 1, 6, 192 ], [ 41, 1, 9, 288 ], 
  [ 47, 1, 8, 384 ], [ 48, 1, 6, 192 ], [ 49, 1, 10, 768 ], 
  [ 52, 1, 10, 192 ] ]

    k = 11: F-action on Pi is (5,7)      [57,1,11]
      Dynkin type is A_1(q) + A_1(q) + A_1(q^2) + T(phi1^2 phi4)
      Order of center |Z^F|: phi1^2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 phi2 ( q^2-8*q+15 )
        q congruent 2 modulo 60:   1/32 q^2 ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/32 phi1 phi2 ( q^2-8*q+15 )
        q congruent 4 modulo 60:   1/32 q^2 ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/32 phi1 phi2 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/32 phi1 phi2 ( q^2-8*q+15 )
        q congruent 8 modulo 60:   1/32 q^2 ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/32 phi1 phi2 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/32 phi1 phi2 ( q^2-8*q+15 )
        q congruent 13 modulo 60:   1/32 phi1 phi2 ( q^2-8*q+15 )
        q congruent 16 modulo 60:   1/32 q^2 ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/32 phi1 phi2 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/32 phi1 phi2 ( q^2-8*q+15 )
        q congruent 21 modulo 60:   1/32 phi1 phi2 ( q^2-8*q+15 )
        q congruent 23 modulo 60:   1/32 phi1 phi2 ( q^2-8*q+15 )
        q congruent 25 modulo 60:   1/32 phi1 phi2 ( q^2-8*q+15 )
        q congruent 27 modulo 60:   1/32 phi1 phi2 ( q^2-8*q+15 )
        q congruent 29 modulo 60:   1/32 phi1 phi2 ( q^2-8*q+15 )
        q congruent 31 modulo 60:   1/32 phi1 phi2 ( q^2-8*q+15 )
        q congruent 32 modulo 60:   1/32 q^2 ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/32 phi1 phi2 ( q^2-8*q+15 )
        q congruent 41 modulo 60:   1/32 phi1 phi2 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/32 phi1 phi2 ( q^2-8*q+15 )
        q congruent 47 modulo 60:   1/32 phi1 phi2 ( q^2-8*q+15 )
        q congruent 49 modulo 60:   1/32 phi1 phi2 ( q^2-8*q+15 )
        q congruent 53 modulo 60:   1/32 phi1 phi2 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/32 phi1 phi2 ( q^2-8*q+15 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 70, 16, 19, 73, 19, 73, 76, 18 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 9, 1, 1, 3 ], 
  [ 10, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 12 ], 
  [ 25, 1, 1, 8 ], [ 39, 1, 1, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 1, 16 ], 
  [ 41, 1, 5, 8 ], [ 41, 1, 8, 16 ], [ 48, 1, 8, 16 ], [ 49, 1, 7, 32 ], 
  [ 52, 1, 8, 16 ] ]

    k = 12: F-action on Pi is (2,5,7)      [57,1,12]
      Dynkin type is A_1(q) + A_1(q^3) + T(phi1^2 phi3)
      Order of center |Z^F|: phi1^2 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 phi1 phi2 ( q^2-4*q+2 )
        q congruent 2 modulo 60:   1/12 q phi2 ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/12 q phi2 ( q^2-5*q+6 )
        q congruent 4 modulo 60:   1/12 q phi1 ( q^2-2*q-2 )
        q congruent 5 modulo 60:   1/12 q phi2 ( q^2-5*q+6 )
        q congruent 7 modulo 60:   1/12 phi1 phi2 ( q^2-4*q+2 )
        q congruent 8 modulo 60:   1/12 q phi2 ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/12 q phi2 ( q^2-5*q+6 )
        q congruent 11 modulo 60:   1/12 q phi2 ( q^2-5*q+6 )
        q congruent 13 modulo 60:   1/12 phi1 phi2 ( q^2-4*q+2 )
        q congruent 16 modulo 60:   1/12 q phi1 ( q^2-2*q-2 )
        q congruent 17 modulo 60:   1/12 q phi2 ( q^2-5*q+6 )
        q congruent 19 modulo 60:   1/12 phi1 phi2 ( q^2-4*q+2 )
        q congruent 21 modulo 60:   1/12 q phi2 ( q^2-5*q+6 )
        q congruent 23 modulo 60:   1/12 q phi2 ( q^2-5*q+6 )
        q congruent 25 modulo 60:   1/12 phi1 phi2 ( q^2-4*q+2 )
        q congruent 27 modulo 60:   1/12 q phi2 ( q^2-5*q+6 )
        q congruent 29 modulo 60:   1/12 q phi2 ( q^2-5*q+6 )
        q congruent 31 modulo 60:   1/12 phi1 phi2 ( q^2-4*q+2 )
        q congruent 32 modulo 60:   1/12 q phi2 ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/12 phi1 phi2 ( q^2-4*q+2 )
        q congruent 41 modulo 60:   1/12 q phi2 ( q^2-5*q+6 )
        q congruent 43 modulo 60:   1/12 phi1 phi2 ( q^2-4*q+2 )
        q congruent 47 modulo 60:   1/12 q phi2 ( q^2-5*q+6 )
        q congruent 49 modulo 60:   1/12 phi1 phi2 ( q^2-4*q+2 )
        q congruent 53 modulo 60:   1/12 q phi2 ( q^2-5*q+6 )
        q congruent 59 modulo 60:   1/12 q phi2 ( q^2-5*q+6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 14, 87, 83, 40 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], 
  [ 7, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], 
  [ 11, 1, 1, 2 ], [ 17, 1, 5, 12 ], [ 18, 1, 1, 4 ], [ 19, 1, 1, 2 ], 
  [ 21, 1, 1, 4 ], [ 22, 1, 1, 4 ], [ 24, 1, 1, 2 ], [ 33, 1, 3, 6 ], 
  [ 34, 1, 1, 4 ], [ 40, 1, 5, 6 ], [ 47, 1, 5, 12 ], [ 49, 1, 3, 6 ], 
  [ 52, 1, 6, 6 ] ]

    k = 13: F-action on Pi is (2,5,7)      [57,1,13]
      Dynkin type is A_1(q) + A_1(q^3) + T(phi1 phi2 phi3)
      Order of center |Z^F|: phi1 phi2 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 phi1^2 ( q^2-2 )
        q congruent 2 modulo 60:   1/12 q^2 phi2 ( q-2 )
        q congruent 3 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 4 modulo 60:   1/12 q phi1 ( q^2-2 )
        q congruent 5 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 7 modulo 60:   1/12 phi1^2 ( q^2-2 )
        q congruent 8 modulo 60:   1/12 q^2 phi2 ( q-2 )
        q congruent 9 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 11 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 13 modulo 60:   1/12 phi1^2 ( q^2-2 )
        q congruent 16 modulo 60:   1/12 q phi1 ( q^2-2 )
        q congruent 17 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 19 modulo 60:   1/12 phi1^2 ( q^2-2 )
        q congruent 21 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 23 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 25 modulo 60:   1/12 phi1^2 ( q^2-2 )
        q congruent 27 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 29 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 31 modulo 60:   1/12 phi1^2 ( q^2-2 )
        q congruent 32 modulo 60:   1/12 q^2 phi2 ( q-2 )
        q congruent 37 modulo 60:   1/12 phi1^2 ( q^2-2 )
        q congruent 41 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 43 modulo 60:   1/12 phi1^2 ( q^2-2 )
        q congruent 47 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 49 modulo 60:   1/12 phi1^2 ( q^2-2 )
        q congruent 53 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 59 modulo 60:   1/12 q phi1 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 83, 35, 37, 88 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], 
  [ 7, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], 
  [ 19, 1, 1, 2 ], [ 22, 1, 2, 4 ], [ 24, 1, 2, 2 ], [ 33, 1, 3, 6 ], 
  [ 34, 1, 2, 4 ], [ 40, 1, 5, 6 ], [ 47, 1, 6, 12 ], [ 49, 1, 3, 6 ], 
  [ 52, 1, 6, 6 ] ]

    k = 14: F-action on Pi is (2,5,7)      [57,1,14]
      Dynkin type is A_1(q) + A_1(q^3) + T(phi1 phi2 phi6)
      Order of center |Z^F|: phi1 phi2 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 2 modulo 60:   1/12 phi2 ( q^3-4*q^2+6*q-4 )
        q congruent 3 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 4 modulo 60:   1/12 q^2 phi1 ( q-2 )
        q congruent 5 modulo 60:   1/12 phi2 ( q^3-5*q^2+8*q-6 )
        q congruent 7 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 8 modulo 60:   1/12 phi2 ( q^3-4*q^2+6*q-4 )
        q congruent 9 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 11 modulo 60:   1/12 phi2 ( q^3-5*q^2+8*q-6 )
        q congruent 13 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 16 modulo 60:   1/12 q^2 phi1 ( q-2 )
        q congruent 17 modulo 60:   1/12 phi2 ( q^3-5*q^2+8*q-6 )
        q congruent 19 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 21 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 23 modulo 60:   1/12 phi2 ( q^3-5*q^2+8*q-6 )
        q congruent 25 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 27 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 29 modulo 60:   1/12 phi2 ( q^3-5*q^2+8*q-6 )
        q congruent 31 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 32 modulo 60:   1/12 phi2 ( q^3-4*q^2+6*q-4 )
        q congruent 37 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 41 modulo 60:   1/12 phi2 ( q^3-5*q^2+8*q-6 )
        q congruent 43 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 47 modulo 60:   1/12 phi2 ( q^3-5*q^2+8*q-6 )
        q congruent 49 modulo 60:   1/12 q^2 phi1 ( q-3 )
        q congruent 53 modulo 60:   1/12 phi2 ( q^3-5*q^2+8*q-6 )
        q congruent 59 modulo 60:   1/12 phi2 ( q^3-5*q^2+8*q-6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 87, 38, 35, 84 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], 
  [ 7, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], 
  [ 19, 1, 2, 2 ], [ 22, 1, 3, 4 ], [ 24, 1, 1, 2 ], [ 33, 1, 7, 6 ], 
  [ 34, 1, 3, 4 ], [ 40, 1, 4, 6 ], [ 47, 1, 11, 12 ], [ 49, 1, 6, 6 ], 
  [ 52, 1, 7, 6 ] ]

    k = 15: F-action on Pi is (2,5,7)      [57,1,15]
      Dynkin type is A_1(q) + A_1(q^3) + T(phi2^2 phi6)
      Order of center |Z^F|: phi2^2 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q^2 phi1^2
        q congruent 2 modulo 60:   1/12 phi2 ( q^3-2*q^2+2*q-4 )
        q congruent 3 modulo 60:   1/12 q^2 phi1^2
        q congruent 4 modulo 60:   1/12 q^3 phi1
        q congruent 5 modulo 60:   1/12 phi2 ( q^3-3*q^2+4*q-6 )
        q congruent 7 modulo 60:   1/12 q^2 phi1^2
        q congruent 8 modulo 60:   1/12 phi2 ( q^3-2*q^2+2*q-4 )
        q congruent 9 modulo 60:   1/12 q^2 phi1^2
        q congruent 11 modulo 60:   1/12 phi2 ( q^3-3*q^2+4*q-6 )
        q congruent 13 modulo 60:   1/12 q^2 phi1^2
        q congruent 16 modulo 60:   1/12 q^3 phi1
        q congruent 17 modulo 60:   1/12 phi2 ( q^3-3*q^2+4*q-6 )
        q congruent 19 modulo 60:   1/12 q^2 phi1^2
        q congruent 21 modulo 60:   1/12 q^2 phi1^2
        q congruent 23 modulo 60:   1/12 phi2 ( q^3-3*q^2+4*q-6 )
        q congruent 25 modulo 60:   1/12 q^2 phi1^2
        q congruent 27 modulo 60:   1/12 q^2 phi1^2
        q congruent 29 modulo 60:   1/12 phi2 ( q^3-3*q^2+4*q-6 )
        q congruent 31 modulo 60:   1/12 q^2 phi1^2
        q congruent 32 modulo 60:   1/12 phi2 ( q^3-2*q^2+2*q-4 )
        q congruent 37 modulo 60:   1/12 q^2 phi1^2
        q congruent 41 modulo 60:   1/12 phi2 ( q^3-3*q^2+4*q-6 )
        q congruent 43 modulo 60:   1/12 q^2 phi1^2
        q congruent 47 modulo 60:   1/12 phi2 ( q^3-3*q^2+4*q-6 )
        q congruent 49 modulo 60:   1/12 q^2 phi1^2
        q congruent 53 modulo 60:   1/12 phi2 ( q^3-3*q^2+4*q-6 )
        q congruent 59 modulo 60:   1/12 phi2 ( q^3-3*q^2+4*q-6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 40, 84, 88, 15 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], 
  [ 7, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], 
  [ 11, 1, 2, 2 ], [ 17, 1, 6, 12 ], [ 18, 1, 2, 4 ], [ 19, 1, 2, 2 ], 
  [ 21, 1, 2, 4 ], [ 22, 1, 4, 4 ], [ 24, 1, 2, 2 ], [ 33, 1, 7, 6 ], 
  [ 34, 1, 4, 4 ], [ 40, 1, 4, 6 ], [ 47, 1, 12, 12 ], [ 49, 1, 6, 6 ], 
  [ 52, 1, 7, 6 ] ]

    k = 16: F-action on Pi is (1,2)(5,7)      [57,1,16]
      Dynkin type is A_1(q^2) + A_1(q^2) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 2 modulo 60:   1/32 q ( q^3-4*q^2+8 )
        q congruent 3 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 4 modulo 60:   1/32 q ( q^3-4*q^2+8 )
        q congruent 5 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 7 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 8 modulo 60:   1/32 q ( q^3-4*q^2+8 )
        q congruent 9 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 11 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 16 modulo 60:   1/32 q ( q^3-4*q^2+8 )
        q congruent 17 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 19 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 23 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 27 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 31 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 32 modulo 60:   1/32 q ( q^3-4*q^2+8 )
        q congruent 37 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 41 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 43 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 53 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
        q congruent 59 modulo 60:   1/32 phi1^2 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 7, 76, 76, 22 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], [ 5, 1, 1, 8 ], 
  [ 5, 1, 2, 8 ], [ 8, 1, 1, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 3 ], 
  [ 13, 1, 2, 8 ], [ 13, 1, 3, 8 ], [ 14, 1, 1, 8 ], [ 14, 1, 2, 8 ], 
  [ 21, 1, 1, 4 ], [ 21, 1, 2, 4 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 4 ], 
  [ 25, 1, 1, 8 ], [ 25, 1, 3, 8 ], [ 30, 1, 2, 16 ], [ 30, 1, 4, 16 ], 
  [ 37, 1, 1, 8 ], [ 37, 1, 2, 8 ], [ 37, 1, 3, 8 ], [ 37, 1, 4, 16 ], 
  [ 39, 1, 2, 8 ], [ 41, 1, 2, 16 ], [ 48, 1, 7, 16 ], [ 48, 1, 10, 16 ] ]

    k = 17: F-action on Pi is (1,2)(5,7)      [57,1,17]
      Dynkin type is A_1(q^2) + A_1(q^2) + T(phi1 phi2 phi4)
      Order of center |Z^F|: phi1 phi2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^3 phi2
        q congruent 2 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 3 modulo 60:   1/16 phi1^3 phi2
        q congruent 4 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 5 modulo 60:   1/16 phi1^3 phi2
        q congruent 7 modulo 60:   1/16 phi1^3 phi2
        q congruent 8 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 9 modulo 60:   1/16 phi1^3 phi2
        q congruent 11 modulo 60:   1/16 phi1^3 phi2
        q congruent 13 modulo 60:   1/16 phi1^3 phi2
        q congruent 16 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 17 modulo 60:   1/16 phi1^3 phi2
        q congruent 19 modulo 60:   1/16 phi1^3 phi2
        q congruent 21 modulo 60:   1/16 phi1^3 phi2
        q congruent 23 modulo 60:   1/16 phi1^3 phi2
        q congruent 25 modulo 60:   1/16 phi1^3 phi2
        q congruent 27 modulo 60:   1/16 phi1^3 phi2
        q congruent 29 modulo 60:   1/16 phi1^3 phi2
        q congruent 31 modulo 60:   1/16 phi1^3 phi2
        q congruent 32 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 37 modulo 60:   1/16 phi1^3 phi2
        q congruent 41 modulo 60:   1/16 phi1^3 phi2
        q congruent 43 modulo 60:   1/16 phi1^3 phi2
        q congruent 47 modulo 60:   1/16 phi1^3 phi2
        q congruent 49 modulo 60:   1/16 phi1^3 phi2
        q congruent 53 modulo 60:   1/16 phi1^3 phi2
        q congruent 59 modulo 60:   1/16 phi1^3 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 76, 22, 18, 75 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 3 ], 
  [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], 
  [ 25, 1, 1, 4 ], [ 25, 1, 3, 4 ], [ 39, 1, 2, 4 ], [ 39, 1, 5, 4 ], 
  [ 41, 1, 2, 8 ], [ 41, 1, 5, 8 ], [ 48, 1, 8, 8 ], [ 48, 1, 9, 8 ] ]

    k = 18: F-action on Pi is (1,2)(5,7)      [57,1,18]
      Dynkin type is A_1(q^2) + A_1(q^2) + T(phi4^2)
      Order of center |Z^F|: phi4^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 phi2 ( q^2-13 )
        q congruent 2 modulo 60:   1/32 ( q^4-12*q^2+32 )
        q congruent 3 modulo 60:   1/32 ( q^4-14*q^2+45 )
        q congruent 4 modulo 60:   1/32 q^2 ( q^2-12 )
        q congruent 5 modulo 60:   1/32 phi1 phi2 ( q^2-13 )
        q congruent 7 modulo 60:   1/32 ( q^4-14*q^2+45 )
        q congruent 8 modulo 60:   1/32 ( q^4-12*q^2+32 )
        q congruent 9 modulo 60:   1/32 phi1 phi2 ( q^2-13 )
        q congruent 11 modulo 60:   1/32 phi1 phi2 ( q^2-13 )
        q congruent 13 modulo 60:   1/32 ( q^4-14*q^2+45 )
        q congruent 16 modulo 60:   1/32 q^2 ( q^2-12 )
        q congruent 17 modulo 60:   1/32 ( q^4-14*q^2+45 )
        q congruent 19 modulo 60:   1/32 phi1 phi2 ( q^2-13 )
        q congruent 21 modulo 60:   1/32 phi1 phi2 ( q^2-13 )
        q congruent 23 modulo 60:   1/32 ( q^4-14*q^2+45 )
        q congruent 25 modulo 60:   1/32 phi1 phi2 ( q^2-13 )
        q congruent 27 modulo 60:   1/32 ( q^4-14*q^2+45 )
        q congruent 29 modulo 60:   1/32 phi1 phi2 ( q^2-13 )
        q congruent 31 modulo 60:   1/32 phi1 phi2 ( q^2-13 )
        q congruent 32 modulo 60:   1/32 ( q^4-12*q^2+32 )
        q congruent 37 modulo 60:   1/32 ( q^4-14*q^2+45 )
        q congruent 41 modulo 60:   1/32 phi1 phi2 ( q^2-13 )
        q congruent 43 modulo 60:   1/32 ( q^4-14*q^2+45 )
        q congruent 47 modulo 60:   1/32 ( q^4-14*q^2+45 )
        q congruent 49 modulo 60:   1/32 phi1 phi2 ( q^2-13 )
        q congruent 53 modulo 60:   1/32 ( q^4-14*q^2+45 )
        q congruent 59 modulo 60:   1/32 phi1 phi2 ( q^2-13 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 22, 75, 75, 6 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 5, 1, 3, 16 ], [ 5, 1, 4, 16 ], [ 9, 1, 1, 3 ], 
  [ 32, 1, 5, 32 ], [ 37, 1, 5, 16 ], [ 39, 1, 5, 8 ], [ 41, 1, 5, 16 ] ]

    k = 19: F-action on Pi is (1,2,5,7)      [57,1,19]
      Dynkin type is A_1(q^4) + T(phi8)
      Order of center |Z^F|: phi8
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 2 modulo 60:   1/8 q^4
        q congruent 3 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 4 modulo 60:   1/8 q^4
        q congruent 5 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 7 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 8 modulo 60:   1/8 q^4
        q congruent 9 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 11 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 13 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 16 modulo 60:   1/8 q^4
        q congruent 17 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 19 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 21 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 23 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 25 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 27 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 29 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 31 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 32 modulo 60:   1/8 q^4
        q congruent 37 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 41 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 43 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 47 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 49 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 53 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 59 modulo 60:   1/8 phi1 phi2 phi4
      Fusion of maximal tori of C^F in those of G^F:
        [ 92, 21 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 9, 1, 1, 1 ] ]

    k = 20: F-action on Pi is (1,2,5,7)      [57,1,20]
      Dynkin type is A_1(q^4) + T(phi1 phi2 phi4)
      Order of center |Z^F|: phi1 phi2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1^2 phi2^2
        q congruent 2 modulo 60:   1/8 q^2 ( q^2-2 )
        q congruent 3 modulo 60:   1/8 phi1^2 phi2^2
        q congruent 4 modulo 60:   1/8 q^2 ( q^2-2 )
        q congruent 5 modulo 60:   1/8 phi1^2 phi2^2
        q congruent 7 modulo 60:   1/8 phi1^2 phi2^2
        q congruent 8 modulo 60:   1/8 q^2 ( q^2-2 )
        q congruent 9 modulo 60:   1/8 phi1^2 phi2^2
        q congruent 11 modulo 60:   1/8 phi1^2 phi2^2
        q congruent 13 modulo 60:   1/8 phi1^2 phi2^2
        q congruent 16 modulo 60:   1/8 q^2 ( q^2-2 )
        q congruent 17 modulo 60:   1/8 phi1^2 phi2^2
        q congruent 19 modulo 60:   1/8 phi1^2 phi2^2
        q congruent 21 modulo 60:   1/8 phi1^2 phi2^2
        q congruent 23 modulo 60:   1/8 phi1^2 phi2^2
        q congruent 25 modulo 60:   1/8 phi1^2 phi2^2
        q congruent 27 modulo 60:   1/8 phi1^2 phi2^2
        q congruent 29 modulo 60:   1/8 phi1^2 phi2^2
        q congruent 31 modulo 60:   1/8 phi1^2 phi2^2
        q congruent 32 modulo 60:   1/8 q^2 ( q^2-2 )
        q congruent 37 modulo 60:   1/8 phi1^2 phi2^2
        q congruent 41 modulo 60:   1/8 phi1^2 phi2^2
        q congruent 43 modulo 60:   1/8 phi1^2 phi2^2
        q congruent 47 modulo 60:   1/8 phi1^2 phi2^2
        q congruent 49 modulo 60:   1/8 phi1^2 phi2^2
        q congruent 53 modulo 60:   1/8 phi1^2 phi2^2
        q congruent 59 modulo 60:   1/8 phi1^2 phi2^2
      Fusion of maximal tori of C^F in those of G^F:
        [ 22, 92 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 5, 1, 3, 4 ], [ 5, 1, 4, 4 ], [ 8, 1, 1, 2 ], 
  [ 8, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 21, 1, 1, 2 ], [ 21, 1, 2, 2 ], 
  [ 37, 1, 4, 4 ], [ 37, 1, 5, 4 ] ]

i = 58: Pi = [ 1, 3, 5, 6 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [58,1,1]
      Dynkin type is A_2(q) + A_2(q) + T(phi1^4)
      Order of center |Z^F|: phi1^4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/288 ( q^4-34*q^3+423*q^2-2368*q+5722 )
        q congruent 2 modulo 60:   1/288 ( q^4-34*q^3+400*q^2-1824*q+2304 )
        q congruent 3 modulo 60:   1/288 ( q^4-34*q^3+415*q^2-2124*q+3474 )
        q congruent 4 modulo 60:   1/288 ( q^4-34*q^3+408*q^2-2032*q+3520 )
        q congruent 5 modulo 60:   1/288 ( q^4-34*q^3+415*q^2-2160*q+4050 )
        q congruent 7 modulo 60:   1/288 ( q^4-34*q^3+423*q^2-2332*q+4858 )
        q congruent 8 modulo 60:   1/288 ( q^4-34*q^3+400*q^2-1824*q+2304 )
        q congruent 9 modulo 60:   1/288 ( q^4-34*q^3+415*q^2-2160*q+4050 )
        q congruent 11 modulo 60:   1/288 ( q^4-34*q^3+415*q^2-2124*q+3762 )
        q congruent 13 modulo 60:   1/288 ( q^4-34*q^3+423*q^2-2368*q+5434 )
        q congruent 16 modulo 60:   1/288 ( q^4-34*q^3+408*q^2-2032*q+3808 )
        q congruent 17 modulo 60:   1/288 ( q^4-34*q^3+415*q^2-2160*q+4050 )
        q congruent 19 modulo 60:   1/288 ( q^4-34*q^3+423*q^2-2332*q+4858 )
        q congruent 21 modulo 60:   1/288 ( q^4-34*q^3+415*q^2-2160*q+4338 )
        q congruent 23 modulo 60:   1/288 ( q^4-34*q^3+415*q^2-2124*q+3474 )
        q congruent 25 modulo 60:   1/288 ( q^4-34*q^3+423*q^2-2368*q+5434 )
        q congruent 27 modulo 60:   1/288 ( q^4-34*q^3+415*q^2-2124*q+3474 )
        q congruent 29 modulo 60:   1/288 ( q^4-34*q^3+415*q^2-2160*q+4050 )
        q congruent 31 modulo 60:   1/288 ( q^4-34*q^3+423*q^2-2332*q+5146 )
        q congruent 32 modulo 60:   1/288 ( q^4-34*q^3+400*q^2-1824*q+2304 )
        q congruent 37 modulo 60:   1/288 ( q^4-34*q^3+423*q^2-2368*q+5434 )
        q congruent 41 modulo 60:   1/288 ( q^4-34*q^3+415*q^2-2160*q+4338 )
        q congruent 43 modulo 60:   1/288 ( q^4-34*q^3+423*q^2-2332*q+4858 )
        q congruent 47 modulo 60:   1/288 ( q^4-34*q^3+415*q^2-2124*q+3474 )
        q congruent 49 modulo 60:   1/288 ( q^4-34*q^3+423*q^2-2368*q+5434 )
        q congruent 53 modulo 60:   1/288 ( q^4-34*q^3+415*q^2-2160*q+4050 )
        q congruent 59 modulo 60:   1/288 ( q^4-34*q^3+415*q^2-2124*q+3474 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 8, 66, 4, 77, 8, 77, 14 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 36 ], 
  [ 5, 1, 1, 72 ], [ 6, 1, 1, 36 ], [ 7, 1, 1, 36 ], [ 8, 1, 1, 24 ], 
  [ 9, 1, 1, 9 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 12 ], [ 12, 1, 1, 36 ], 
  [ 14, 1, 1, 144 ], [ 15, 1, 1, 72 ], [ 16, 1, 1, 72 ], [ 17, 1, 1, 72 ], 
  [ 18, 1, 1, 72 ], [ 19, 1, 1, 36 ], [ 20, 1, 1, 144 ], [ 21, 1, 1, 72 ], 
  [ 22, 1, 1, 72 ], [ 23, 1, 1, 36 ], [ 24, 1, 1, 36 ], [ 25, 1, 1, 144 ], 
  [ 26, 1, 1, 72 ], [ 27, 1, 1, 24 ], [ 29, 1, 1, 144 ], [ 31, 1, 1, 144 ], 
  [ 32, 1, 1, 72 ], [ 34, 1, 1, 72 ], [ 36, 1, 1, 144 ], [ 37, 1, 1, 288 ], 
  [ 38, 1, 1, 144 ], [ 39, 1, 1, 72 ], [ 40, 1, 1, 144 ], [ 42, 1, 1, 72 ], 
  [ 43, 1, 1, 288 ], [ 46, 1, 1, 144 ], [ 50, 1, 1, 144 ], [ 51, 1, 1, 288 ] ]

    k = 2: F-action on Pi is ()      [58,1,2]
      Dynkin type is A_2(q) + A_2(q) + T(phi1^3 phi2)
      Order of center |Z^F|: phi1^3 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/48 phi1 ( q^3-15*q^2+72*q-118 )
        q congruent 2 modulo 60:   1/48 q ( q^3-16*q^2+76*q-96 )
        q congruent 3 modulo 60:   1/48 ( q^4-16*q^3+83*q^2-146*q+42 )
        q congruent 4 modulo 60:   1/48 q ( q^3-16*q^2+80*q-128 )
        q congruent 5 modulo 60:   1/48 phi1 ( q^3-15*q^2+68*q-90 )
        q congruent 7 modulo 60:   1/48 ( q^4-16*q^3+87*q^2-178*q+70 )
        q congruent 8 modulo 60:   1/48 q ( q^3-16*q^2+76*q-96 )
        q congruent 9 modulo 60:   1/48 phi1 ( q^3-15*q^2+68*q-90 )
        q congruent 11 modulo 60:   1/48 ( q^4-16*q^3+83*q^2-146*q+42 )
        q congruent 13 modulo 60:   1/48 phi1 ( q^3-15*q^2+72*q-118 )
        q congruent 16 modulo 60:   1/48 q ( q^3-16*q^2+80*q-128 )
        q congruent 17 modulo 60:   1/48 phi1 ( q^3-15*q^2+68*q-90 )
        q congruent 19 modulo 60:   1/48 ( q^4-16*q^3+87*q^2-178*q+70 )
        q congruent 21 modulo 60:   1/48 phi1 ( q^3-15*q^2+68*q-90 )
        q congruent 23 modulo 60:   1/48 ( q^4-16*q^3+83*q^2-146*q+42 )
        q congruent 25 modulo 60:   1/48 phi1 ( q^3-15*q^2+72*q-118 )
        q congruent 27 modulo 60:   1/48 ( q^4-16*q^3+83*q^2-146*q+42 )
        q congruent 29 modulo 60:   1/48 phi1 ( q^3-15*q^2+68*q-90 )
        q congruent 31 modulo 60:   1/48 ( q^4-16*q^3+87*q^2-178*q+70 )
        q congruent 32 modulo 60:   1/48 q ( q^3-16*q^2+76*q-96 )
        q congruent 37 modulo 60:   1/48 phi1 ( q^3-15*q^2+72*q-118 )
        q congruent 41 modulo 60:   1/48 phi1 ( q^3-15*q^2+68*q-90 )
        q congruent 43 modulo 60:   1/48 ( q^4-16*q^3+87*q^2-178*q+70 )
        q congruent 47 modulo 60:   1/48 ( q^4-16*q^3+83*q^2-146*q+42 )
        q congruent 49 modulo 60:   1/48 phi1 ( q^3-15*q^2+72*q-118 )
        q congruent 53 modulo 60:   1/48 phi1 ( q^3-15*q^2+68*q-90 )
        q congruent 59 modulo 60:   1/48 ( q^4-16*q^3+83*q^2-146*q+42 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 77, 4, 68, 30, 77, 30, 83 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 12 ], 
  [ 5, 1, 1, 24 ], [ 6, 1, 1, 24 ], [ 7, 1, 1, 12 ], [ 8, 1, 1, 12 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 8 ], 
  [ 12, 1, 1, 12 ], [ 14, 1, 1, 24 ], [ 15, 1, 1, 24 ], [ 16, 1, 1, 24 ], 
  [ 17, 1, 1, 48 ], [ 18, 1, 1, 12 ], [ 19, 1, 1, 12 ], [ 20, 1, 1, 24 ], 
  [ 20, 1, 2, 24 ], [ 21, 1, 1, 12 ], [ 22, 1, 1, 36 ], [ 22, 1, 2, 12 ], 
  [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 26, 1, 1, 12 ], [ 26, 1, 3, 12 ], 
  [ 27, 1, 1, 12 ], [ 27, 1, 2, 4 ], [ 29, 1, 1, 24 ], [ 29, 1, 2, 24 ], 
  [ 31, 1, 1, 24 ], [ 31, 1, 2, 24 ], [ 32, 1, 1, 24 ], [ 34, 1, 1, 12 ], 
  [ 34, 1, 2, 12 ], [ 36, 1, 2, 24 ], [ 38, 1, 1, 72 ], [ 38, 1, 5, 24 ], 
  [ 39, 1, 4, 12 ], [ 42, 1, 1, 12 ], [ 42, 1, 4, 12 ], [ 43, 1, 2, 48 ], 
  [ 46, 1, 1, 24 ], [ 46, 1, 2, 24 ], [ 50, 1, 2, 24 ], [ 50, 1, 4, 24 ], 
  [ 51, 1, 2, 48 ] ]

    k = 3: F-action on Pi is ()      [58,1,3]
      Dynkin type is A_2(q) + A_2(q) + T(phi1^2 phi3)
      Order of center |Z^F|: phi1^2 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/72 phi1 ( q^3-6*q^2+3*q+38 )
        q congruent 2 modulo 60:   1/72 q phi2 ( q^2-8*q+12 )
        q congruent 3 modulo 60:   1/72 q phi2 ( q^2-8*q+15 )
        q congruent 4 modulo 60:   1/72 phi1 ( q^3-6*q^2+32 )
        q congruent 5 modulo 60:   1/72 q phi2 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/72 phi1 ( q^3-6*q^2+3*q+38 )
        q congruent 8 modulo 60:   1/72 q phi2 ( q^2-8*q+12 )
        q congruent 9 modulo 60:   1/72 q phi2 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/72 q phi2 ( q^2-8*q+15 )
        q congruent 13 modulo 60:   1/72 phi1 ( q^3-6*q^2+3*q+38 )
        q congruent 16 modulo 60:   1/72 phi1 ( q^3-6*q^2+32 )
        q congruent 17 modulo 60:   1/72 q phi2 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/72 phi1 ( q^3-6*q^2+3*q+38 )
        q congruent 21 modulo 60:   1/72 q phi2 ( q^2-8*q+15 )
        q congruent 23 modulo 60:   1/72 q phi2 ( q^2-8*q+15 )
        q congruent 25 modulo 60:   1/72 phi1 ( q^3-6*q^2+3*q+38 )
        q congruent 27 modulo 60:   1/72 q phi2 ( q^2-8*q+15 )
        q congruent 29 modulo 60:   1/72 q phi2 ( q^2-8*q+15 )
        q congruent 31 modulo 60:   1/72 phi1 ( q^3-6*q^2+3*q+38 )
        q congruent 32 modulo 60:   1/72 q phi2 ( q^2-8*q+12 )
        q congruent 37 modulo 60:   1/72 phi1 ( q^3-6*q^2+3*q+38 )
        q congruent 41 modulo 60:   1/72 q phi2 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/72 phi1 ( q^3-6*q^2+3*q+38 )
        q congruent 47 modulo 60:   1/72 q phi2 ( q^2-8*q+15 )
        q congruent 49 modulo 60:   1/72 phi1 ( q^3-6*q^2+3*q+38 )
        q congruent 53 modulo 60:   1/72 q phi2 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/72 q phi2 ( q^2-8*q+15 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 8, 77, 14, 77, 30, 83, 14, 83, 12 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 8 ], [ 6, 1, 1, 18 ], 
  [ 8, 1, 1, 12 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 17, 1, 1, 36 ], 
  [ 22, 1, 1, 36 ], [ 27, 1, 1, 12 ], [ 27, 1, 5, 6 ], [ 38, 1, 1, 72 ], 
  [ 38, 1, 3, 36 ], [ 42, 1, 3, 18 ], [ 46, 1, 3, 36 ], [ 50, 1, 3, 36 ] ]

    k = 4: F-action on Pi is (5,6)      [58,1,4]
      Dynkin type is A_2(q) + ^2A_2(q) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 q phi1 ( q^2-5*q+6 )
        q congruent 2 modulo 60:   1/24 q^2 ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/24 q phi1 ( q^2-5*q+6 )
        q congruent 4 modulo 60:   1/24 q^2 ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/24 q phi1 ( q^2-5*q+6 )
        q congruent 7 modulo 60:   1/24 q phi1 ( q^2-5*q+6 )
        q congruent 8 modulo 60:   1/24 q^2 ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/24 q phi1 ( q^2-5*q+6 )
        q congruent 11 modulo 60:   1/24 q phi1 ( q^2-5*q+6 )
        q congruent 13 modulo 60:   1/24 q phi1 ( q^2-5*q+6 )
        q congruent 16 modulo 60:   1/24 q^2 ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/24 q phi1 ( q^2-5*q+6 )
        q congruent 19 modulo 60:   1/24 q phi1 ( q^2-5*q+6 )
        q congruent 21 modulo 60:   1/24 q phi1 ( q^2-5*q+6 )
        q congruent 23 modulo 60:   1/24 q phi1 ( q^2-5*q+6 )
        q congruent 25 modulo 60:   1/24 q phi1 ( q^2-5*q+6 )
        q congruent 27 modulo 60:   1/24 q phi1 ( q^2-5*q+6 )
        q congruent 29 modulo 60:   1/24 q phi1 ( q^2-5*q+6 )
        q congruent 31 modulo 60:   1/24 q phi1 ( q^2-5*q+6 )
        q congruent 32 modulo 60:   1/24 q^2 ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/24 q phi1 ( q^2-5*q+6 )
        q congruent 41 modulo 60:   1/24 q phi1 ( q^2-5*q+6 )
        q congruent 43 modulo 60:   1/24 q phi1 ( q^2-5*q+6 )
        q congruent 47 modulo 60:   1/24 q phi1 ( q^2-5*q+6 )
        q congruent 49 modulo 60:   1/24 q phi1 ( q^2-5*q+6 )
        q congruent 53 modulo 60:   1/24 q phi1 ( q^2-5*q+6 )
        q congruent 59 modulo 60:   1/24 q phi1 ( q^2-5*q+6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 68, 28, 69, 7, 82, 27, 81, 36 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 6 ], 
  [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 12, 1, 2, 6 ], 
  [ 16, 1, 2, 12 ], [ 16, 1, 4, 12 ], [ 23, 1, 1, 6 ], [ 23, 1, 2, 6 ], 
  [ 25, 1, 1, 12 ], [ 25, 1, 2, 12 ], [ 25, 1, 3, 12 ], [ 25, 1, 4, 12 ], 
  [ 32, 1, 2, 12 ], [ 37, 1, 2, 24 ], [ 39, 1, 2, 12 ], [ 40, 1, 1, 12 ], 
  [ 40, 1, 2, 12 ], [ 40, 1, 3, 12 ], [ 40, 1, 6, 12 ], [ 43, 1, 8, 24 ], 
  [ 51, 1, 3, 24 ], [ 51, 1, 6, 24 ] ]

    k = 5: F-action on Pi is (5,6)      [58,1,5]
      Dynkin type is A_2(q) + ^2A_2(q) + T(phi1 phi2 phi4)
      Order of center |Z^F|: phi1 phi2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 phi2 ( q^2-2*q+2 )
        q congruent 2 modulo 60:   1/8 q^3 ( q-2 )
        q congruent 3 modulo 60:   1/8 phi1 phi2 ( q^2-2*q+2 )
        q congruent 4 modulo 60:   1/8 q^3 ( q-2 )
        q congruent 5 modulo 60:   1/8 phi1 phi2 ( q^2-2*q+2 )
        q congruent 7 modulo 60:   1/8 phi1 phi2 ( q^2-2*q+2 )
        q congruent 8 modulo 60:   1/8 q^3 ( q-2 )
        q congruent 9 modulo 60:   1/8 phi1 phi2 ( q^2-2*q+2 )
        q congruent 11 modulo 60:   1/8 phi1 phi2 ( q^2-2*q+2 )
        q congruent 13 modulo 60:   1/8 phi1 phi2 ( q^2-2*q+2 )
        q congruent 16 modulo 60:   1/8 q^3 ( q-2 )
        q congruent 17 modulo 60:   1/8 phi1 phi2 ( q^2-2*q+2 )
        q congruent 19 modulo 60:   1/8 phi1 phi2 ( q^2-2*q+2 )
        q congruent 21 modulo 60:   1/8 phi1 phi2 ( q^2-2*q+2 )
        q congruent 23 modulo 60:   1/8 phi1 phi2 ( q^2-2*q+2 )
        q congruent 25 modulo 60:   1/8 phi1 phi2 ( q^2-2*q+2 )
        q congruent 27 modulo 60:   1/8 phi1 phi2 ( q^2-2*q+2 )
        q congruent 29 modulo 60:   1/8 phi1 phi2 ( q^2-2*q+2 )
        q congruent 31 modulo 60:   1/8 phi1 phi2 ( q^2-2*q+2 )
        q congruent 32 modulo 60:   1/8 q^3 ( q-2 )
        q congruent 37 modulo 60:   1/8 phi1 phi2 ( q^2-2*q+2 )
        q congruent 41 modulo 60:   1/8 phi1 phi2 ( q^2-2*q+2 )
        q congruent 43 modulo 60:   1/8 phi1 phi2 ( q^2-2*q+2 )
        q congruent 47 modulo 60:   1/8 phi1 phi2 ( q^2-2*q+2 )
        q congruent 49 modulo 60:   1/8 phi1 phi2 ( q^2-2*q+2 )
        q congruent 53 modulo 60:   1/8 phi1 phi2 ( q^2-2*q+2 )
        q congruent 59 modulo 60:   1/8 phi1 phi2 ( q^2-2*q+2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 72, 19, 96, 20, 76, 60, 95, 59, 99 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], 
  [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], [ 12, 1, 2, 2 ], 
  [ 16, 1, 2, 4 ], [ 16, 1, 4, 4 ], [ 32, 1, 2, 4 ], [ 39, 1, 5, 4 ], 
  [ 43, 1, 9, 8 ], [ 51, 1, 4, 8 ], [ 51, 1, 7, 8 ] ]

    k = 6: F-action on Pi is (5,6)      [58,1,6]
      Dynkin type is A_2(q) + ^2A_2(q) + T(phi3 phi6)
      Order of center |Z^F|: phi3 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 2 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 3 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 4 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 5 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 7 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 8 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 9 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 11 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 13 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 16 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 17 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 19 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 21 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 23 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 25 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 27 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 29 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 31 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 32 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 37 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 41 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 43 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 47 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 49 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 53 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 59 modulo 60:   1/12 q^2 phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 35, 87, 33, 88, 40, 86, 34, 85, 29 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 40, 1, 4, 6 ], 
  [ 40, 1, 5, 6 ] ]

    k = 7: F-action on Pi is ()      [58,1,7]
      Dynkin type is A_2(q) + A_2(q) + T(phi1 phi2 phi3)
      Order of center |Z^F|: phi1 phi2 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 phi1^3 ( q+2 )
        q congruent 2 modulo 60:   1/24 q^2 phi2 ( q-2 )
        q congruent 3 modulo 60:   1/24 q phi1^2 phi2
        q congruent 4 modulo 60:   1/24 q phi1 ( q^2-4 )
        q congruent 5 modulo 60:   1/24 q phi1^2 phi2
        q congruent 7 modulo 60:   1/24 phi1^3 ( q+2 )
        q congruent 8 modulo 60:   1/24 q^2 phi2 ( q-2 )
        q congruent 9 modulo 60:   1/24 q phi1^2 phi2
        q congruent 11 modulo 60:   1/24 q phi1^2 phi2
        q congruent 13 modulo 60:   1/24 phi1^3 ( q+2 )
        q congruent 16 modulo 60:   1/24 q phi1 ( q^2-4 )
        q congruent 17 modulo 60:   1/24 q phi1^2 phi2
        q congruent 19 modulo 60:   1/24 phi1^3 ( q+2 )
        q congruent 21 modulo 60:   1/24 q phi1^2 phi2
        q congruent 23 modulo 60:   1/24 q phi1^2 phi2
        q congruent 25 modulo 60:   1/24 phi1^3 ( q+2 )
        q congruent 27 modulo 60:   1/24 q phi1^2 phi2
        q congruent 29 modulo 60:   1/24 q phi1^2 phi2
        q congruent 31 modulo 60:   1/24 phi1^3 ( q+2 )
        q congruent 32 modulo 60:   1/24 q^2 phi2 ( q-2 )
        q congruent 37 modulo 60:   1/24 phi1^3 ( q+2 )
        q congruent 41 modulo 60:   1/24 q phi1^2 phi2
        q congruent 43 modulo 60:   1/24 phi1^3 ( q+2 )
        q congruent 47 modulo 60:   1/24 q phi1^2 phi2
        q congruent 49 modulo 60:   1/24 phi1^3 ( q+2 )
        q congruent 53 modulo 60:   1/24 q phi1^2 phi2
        q congruent 59 modulo 60:   1/24 q phi1^2 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 77, 30, 83, 30, 81, 37, 83, 37, 79 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 6, 1, 1, 6 ], 
  [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 17, 1, 1, 12 ], [ 22, 1, 2, 12 ], 
  [ 27, 1, 2, 4 ], [ 27, 1, 5, 6 ], [ 38, 1, 3, 36 ], [ 38, 1, 5, 24 ], 
  [ 42, 1, 3, 6 ], [ 46, 1, 3, 12 ], [ 50, 1, 6, 12 ] ]

    k = 8: F-action on Pi is ()      [58,1,8]
      Dynkin type is A_2(q) + A_2(q) + T(phi3^2)
      Order of center |Z^F|: phi3^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/72 phi1 ( q^3+3*q^2-6*q-16 )
        q congruent 2 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 3 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 4 modulo 60:   1/72 phi1 ( q^3+3*q^2-6*q-16 )
        q congruent 5 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 7 modulo 60:   1/72 phi1 ( q^3+3*q^2-6*q-16 )
        q congruent 8 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 9 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 11 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 13 modulo 60:   1/72 phi1 ( q^3+3*q^2-6*q-16 )
        q congruent 16 modulo 60:   1/72 phi1 ( q^3+3*q^2-6*q-16 )
        q congruent 17 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 19 modulo 60:   1/72 phi1 ( q^3+3*q^2-6*q-16 )
        q congruent 21 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 23 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 25 modulo 60:   1/72 phi1 ( q^3+3*q^2-6*q-16 )
        q congruent 27 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 29 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 31 modulo 60:   1/72 phi1 ( q^3+3*q^2-6*q-16 )
        q congruent 32 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 37 modulo 60:   1/72 phi1 ( q^3+3*q^2-6*q-16 )
        q congruent 41 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 43 modulo 60:   1/72 phi1 ( q^3+3*q^2-6*q-16 )
        q congruent 47 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 49 modulo 60:   1/72 phi1 ( q^3+3*q^2-6*q-16 )
        q congruent 53 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 59 modulo 60:   1/72 q phi2 ( q^2+q-6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 14, 83, 12, 83, 37, 79, 12, 79, 10 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 27, 1, 5, 12 ], [ 38, 1, 3, 72 ], 
  [ 40, 1, 5, 36 ] ]

    k = 9: F-action on Pi is ()      [58,1,9]
      Dynkin type is A_2(q) + A_2(q) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 ( q^3-5*q^2+6*q-6 )
        q congruent 2 modulo 60:   1/32 q^2 ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/32 ( q^4-6*q^3+11*q^2-8*q+6 )
        q congruent 4 modulo 60:   1/32 q^2 ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/32 phi1 ( q^3-5*q^2+6*q-6 )
        q congruent 7 modulo 60:   1/32 ( q^4-6*q^3+11*q^2-8*q+6 )
        q congruent 8 modulo 60:   1/32 q^2 ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/32 phi1 ( q^3-5*q^2+6*q-6 )
        q congruent 11 modulo 60:   1/32 ( q^4-6*q^3+11*q^2-8*q+6 )
        q congruent 13 modulo 60:   1/32 phi1 ( q^3-5*q^2+6*q-6 )
        q congruent 16 modulo 60:   1/32 q^2 ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/32 phi1 ( q^3-5*q^2+6*q-6 )
        q congruent 19 modulo 60:   1/32 ( q^4-6*q^3+11*q^2-8*q+6 )
        q congruent 21 modulo 60:   1/32 phi1 ( q^3-5*q^2+6*q-6 )
        q congruent 23 modulo 60:   1/32 ( q^4-6*q^3+11*q^2-8*q+6 )
        q congruent 25 modulo 60:   1/32 phi1 ( q^3-5*q^2+6*q-6 )
        q congruent 27 modulo 60:   1/32 ( q^4-6*q^3+11*q^2-8*q+6 )
        q congruent 29 modulo 60:   1/32 phi1 ( q^3-5*q^2+6*q-6 )
        q congruent 31 modulo 60:   1/32 ( q^4-6*q^3+11*q^2-8*q+6 )
        q congruent 32 modulo 60:   1/32 q^2 ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/32 phi1 ( q^3-5*q^2+6*q-6 )
        q congruent 41 modulo 60:   1/32 phi1 ( q^3-5*q^2+6*q-6 )
        q congruent 43 modulo 60:   1/32 ( q^4-6*q^3+11*q^2-8*q+6 )
        q congruent 47 modulo 60:   1/32 ( q^4-6*q^3+11*q^2-8*q+6 )
        q congruent 49 modulo 60:   1/32 phi1 ( q^3-5*q^2+6*q-6 )
        q congruent 53 modulo 60:   1/32 phi1 ( q^3-5*q^2+6*q-6 )
        q congruent 59 modulo 60:   1/32 ( q^4-6*q^3+11*q^2-8*q+6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 68, 30, 68, 7, 81, 30, 81, 37 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 4 ], 
  [ 5, 1, 1, 8 ], [ 6, 1, 1, 12 ], [ 7, 1, 1, 4 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 2, 4 ], [ 11, 1, 1, 4 ], [ 12, 1, 1, 4 ], [ 15, 1, 1, 8 ], 
  [ 16, 1, 1, 8 ], [ 17, 1, 1, 24 ], [ 19, 1, 1, 4 ], [ 20, 1, 2, 16 ], 
  [ 22, 1, 2, 24 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 4, 16 ], 
  [ 26, 1, 3, 8 ], [ 27, 1, 2, 8 ], [ 29, 1, 2, 16 ], [ 31, 1, 2, 16 ], 
  [ 32, 1, 1, 8 ], [ 34, 1, 2, 8 ], [ 38, 1, 5, 48 ], [ 39, 1, 3, 8 ], 
  [ 40, 1, 3, 16 ], [ 42, 1, 4, 8 ], [ 43, 1, 12, 32 ], [ 46, 1, 2, 16 ], 
  [ 50, 1, 5, 16 ], [ 51, 1, 5, 32 ] ]

    k = 10: F-action on Pi is (1,3)(5,6)      [58,1,10]
      Dynkin type is ^2A_2(q) + ^2A_2(q) + T(phi1 phi2 phi6)
      Order of center |Z^F|: phi1 phi2 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 q phi1^3
        q congruent 2 modulo 60:   1/24 q phi2 ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/24 q phi1^3
        q congruent 4 modulo 60:   1/24 q^2 phi1 ( q-2 )
        q congruent 5 modulo 60:   1/24 phi1^2 phi2 ( q-2 )
        q congruent 7 modulo 60:   1/24 q phi1^3
        q congruent 8 modulo 60:   1/24 q phi2 ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/24 q phi1^3
        q congruent 11 modulo 60:   1/24 phi1^2 phi2 ( q-2 )
        q congruent 13 modulo 60:   1/24 q phi1^3
        q congruent 16 modulo 60:   1/24 q^2 phi1 ( q-2 )
        q congruent 17 modulo 60:   1/24 phi1^2 phi2 ( q-2 )
        q congruent 19 modulo 60:   1/24 q phi1^3
        q congruent 21 modulo 60:   1/24 q phi1^3
        q congruent 23 modulo 60:   1/24 phi1^2 phi2 ( q-2 )
        q congruent 25 modulo 60:   1/24 q phi1^3
        q congruent 27 modulo 60:   1/24 q phi1^3
        q congruent 29 modulo 60:   1/24 phi1^2 phi2 ( q-2 )
        q congruent 31 modulo 60:   1/24 q phi1^3
        q congruent 32 modulo 60:   1/24 q phi2 ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/24 q phi1^3
        q congruent 41 modulo 60:   1/24 phi1^2 phi2 ( q-2 )
        q congruent 43 modulo 60:   1/24 q phi1^3
        q congruent 47 modulo 60:   1/24 phi1^2 phi2 ( q-2 )
        q congruent 49 modulo 60:   1/24 q phi1^3
        q congruent 53 modulo 60:   1/24 phi1^2 phi2 ( q-2 )
        q congruent 59 modulo 60:   1/24 phi1^2 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 78, 31, 84, 31, 82, 38, 84, 38, 80 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 6, 1, 2, 6 ], 
  [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 4, 12 ], [ 22, 1, 3, 12 ], 
  [ 27, 1, 3, 4 ], [ 27, 1, 4, 6 ], [ 38, 1, 8, 24 ], [ 38, 1, 11, 36 ], 
  [ 42, 1, 5, 6 ], [ 46, 1, 4, 12 ], [ 50, 1, 7, 12 ] ]

    k = 11: F-action on Pi is (1,3)(5,6)      [58,1,11]
      Dynkin type is ^2A_2(q) + ^2A_2(q) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 ( q^3-5*q^2+10*q-10 )
        q congruent 2 modulo 60:   1/32 q ( q^3-6*q^2+12*q-8 )
        q congruent 3 modulo 60:   1/32 ( q^4-6*q^3+15*q^2-24*q+18 )
        q congruent 4 modulo 60:   1/32 q ( q^3-6*q^2+12*q-8 )
        q congruent 5 modulo 60:   1/32 phi1 ( q^3-5*q^2+10*q-10 )
        q congruent 7 modulo 60:   1/32 ( q^4-6*q^3+15*q^2-24*q+18 )
        q congruent 8 modulo 60:   1/32 q ( q^3-6*q^2+12*q-8 )
        q congruent 9 modulo 60:   1/32 phi1 ( q^3-5*q^2+10*q-10 )
        q congruent 11 modulo 60:   1/32 ( q^4-6*q^3+15*q^2-24*q+18 )
        q congruent 13 modulo 60:   1/32 phi1 ( q^3-5*q^2+10*q-10 )
        q congruent 16 modulo 60:   1/32 q ( q^3-6*q^2+12*q-8 )
        q congruent 17 modulo 60:   1/32 phi1 ( q^3-5*q^2+10*q-10 )
        q congruent 19 modulo 60:   1/32 ( q^4-6*q^3+15*q^2-24*q+18 )
        q congruent 21 modulo 60:   1/32 phi1 ( q^3-5*q^2+10*q-10 )
        q congruent 23 modulo 60:   1/32 ( q^4-6*q^3+15*q^2-24*q+18 )
        q congruent 25 modulo 60:   1/32 phi1 ( q^3-5*q^2+10*q-10 )
        q congruent 27 modulo 60:   1/32 ( q^4-6*q^3+15*q^2-24*q+18 )
        q congruent 29 modulo 60:   1/32 phi1 ( q^3-5*q^2+10*q-10 )
        q congruent 31 modulo 60:   1/32 ( q^4-6*q^3+15*q^2-24*q+18 )
        q congruent 32 modulo 60:   1/32 q ( q^3-6*q^2+12*q-8 )
        q congruent 37 modulo 60:   1/32 phi1 ( q^3-5*q^2+10*q-10 )
        q congruent 41 modulo 60:   1/32 phi1 ( q^3-5*q^2+10*q-10 )
        q congruent 43 modulo 60:   1/32 ( q^4-6*q^3+15*q^2-24*q+18 )
        q congruent 47 modulo 60:   1/32 ( q^4-6*q^3+15*q^2-24*q+18 )
        q congruent 49 modulo 60:   1/32 phi1 ( q^3-5*q^2+10*q-10 )
        q congruent 53 modulo 60:   1/32 phi1 ( q^3-5*q^2+10*q-10 )
        q congruent 59 modulo 60:   1/32 ( q^4-6*q^3+15*q^2-24*q+18 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 69, 31, 69, 7, 82, 31, 82, 38 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 4 ], 
  [ 5, 1, 2, 8 ], [ 6, 1, 2, 12 ], [ 7, 1, 2, 4 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 2, 4 ], [ 15, 1, 2, 8 ], 
  [ 16, 1, 3, 8 ], [ 17, 1, 4, 24 ], [ 19, 1, 2, 4 ], [ 20, 1, 3, 16 ], 
  [ 22, 1, 3, 24 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ], [ 25, 1, 2, 16 ], 
  [ 26, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 29, 1, 3, 16 ], [ 31, 1, 3, 16 ], 
  [ 32, 1, 3, 8 ], [ 34, 1, 3, 8 ], [ 38, 1, 8, 48 ], [ 39, 1, 1, 8 ], 
  [ 40, 1, 2, 16 ], [ 42, 1, 2, 8 ], [ 43, 1, 3, 32 ], [ 46, 1, 5, 16 ], 
  [ 50, 1, 8, 16 ], [ 51, 1, 10, 32 ] ]

    k = 12: F-action on Pi is (1,3)(5,6)      [58,1,12]
      Dynkin type is ^2A_2(q) + ^2A_2(q) + T(phi1 phi2^3)
      Order of center |Z^F|: phi1 phi2^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/48 phi1 ( q^3-11*q^2+40*q-54 )
        q congruent 2 modulo 60:   1/48 ( q^4-12*q^3+48*q^2-80*q+48 )
        q congruent 3 modulo 60:   1/48 ( q^4-12*q^3+51*q^2-106*q+102 )
        q congruent 4 modulo 60:   1/48 q ( q^3-12*q^2+44*q-48 )
        q congruent 5 modulo 60:   1/48 ( q^4-12*q^3+55*q^2-126*q+130 )
        q congruent 7 modulo 60:   1/48 ( q^4-12*q^3+51*q^2-106*q+102 )
        q congruent 8 modulo 60:   1/48 ( q^4-12*q^3+48*q^2-80*q+48 )
        q congruent 9 modulo 60:   1/48 phi1 ( q^3-11*q^2+40*q-54 )
        q congruent 11 modulo 60:   1/48 ( q^4-12*q^3+55*q^2-138*q+178 )
        q congruent 13 modulo 60:   1/48 phi1 ( q^3-11*q^2+40*q-54 )
        q congruent 16 modulo 60:   1/48 q ( q^3-12*q^2+44*q-48 )
        q congruent 17 modulo 60:   1/48 ( q^4-12*q^3+55*q^2-126*q+130 )
        q congruent 19 modulo 60:   1/48 ( q^4-12*q^3+51*q^2-106*q+102 )
        q congruent 21 modulo 60:   1/48 phi1 ( q^3-11*q^2+40*q-54 )
        q congruent 23 modulo 60:   1/48 ( q^4-12*q^3+55*q^2-138*q+178 )
        q congruent 25 modulo 60:   1/48 phi1 ( q^3-11*q^2+40*q-54 )
        q congruent 27 modulo 60:   1/48 ( q^4-12*q^3+51*q^2-106*q+102 )
        q congruent 29 modulo 60:   1/48 ( q^4-12*q^3+55*q^2-126*q+130 )
        q congruent 31 modulo 60:   1/48 ( q^4-12*q^3+51*q^2-106*q+102 )
        q congruent 32 modulo 60:   1/48 ( q^4-12*q^3+48*q^2-80*q+48 )
        q congruent 37 modulo 60:   1/48 phi1 ( q^3-11*q^2+40*q-54 )
        q congruent 41 modulo 60:   1/48 ( q^4-12*q^3+55*q^2-126*q+130 )
        q congruent 43 modulo 60:   1/48 ( q^4-12*q^3+51*q^2-106*q+102 )
        q congruent 47 modulo 60:   1/48 ( q^4-12*q^3+55*q^2-138*q+178 )
        q congruent 49 modulo 60:   1/48 phi1 ( q^3-11*q^2+40*q-54 )
        q congruent 53 modulo 60:   1/48 ( q^4-12*q^3+55*q^2-126*q+130 )
        q congruent 59 modulo 60:   1/48 ( q^4-12*q^3+55*q^2-138*q+178 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 67, 5, 78, 5, 69, 31, 78, 31, 84 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 12 ], 
  [ 5, 1, 2, 24 ], [ 6, 1, 2, 24 ], [ 7, 1, 2, 12 ], [ 8, 1, 2, 12 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], 
  [ 12, 1, 2, 12 ], [ 14, 1, 2, 24 ], [ 15, 1, 2, 24 ], [ 16, 1, 3, 24 ], 
  [ 17, 1, 4, 48 ], [ 18, 1, 2, 12 ], [ 19, 1, 2, 12 ], [ 20, 1, 3, 24 ], 
  [ 20, 1, 4, 24 ], [ 21, 1, 2, 12 ], [ 22, 1, 3, 12 ], [ 22, 1, 4, 36 ], 
  [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 26, 1, 2, 12 ], [ 26, 1, 4, 12 ], 
  [ 27, 1, 3, 4 ], [ 27, 1, 6, 12 ], [ 29, 1, 3, 24 ], [ 29, 1, 4, 24 ], 
  [ 31, 1, 3, 24 ], [ 31, 1, 4, 24 ], [ 32, 1, 3, 24 ], [ 34, 1, 3, 12 ], 
  [ 34, 1, 4, 12 ], [ 36, 1, 3, 24 ], [ 38, 1, 8, 24 ], [ 38, 1, 12, 72 ], 
  [ 39, 1, 4, 12 ], [ 42, 1, 2, 12 ], [ 42, 1, 6, 12 ], [ 43, 1, 4, 48 ], 
  [ 46, 1, 5, 24 ], [ 46, 1, 6, 24 ], [ 50, 1, 9, 24 ], [ 50, 1, 11, 24 ], 
  [ 51, 1, 8, 48 ] ]

    k = 13: F-action on Pi is (1,3)(5,6)      [58,1,13]
      Dynkin type is ^2A_2(q) + ^2A_2(q) + T(phi6^2)
      Order of center |Z^F|: phi6^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 2 modulo 60:   1/72 phi2 ( q^3-3*q^2-6*q+16 )
        q congruent 3 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 4 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 5 modulo 60:   1/72 phi2 ( q^3-3*q^2-6*q+16 )
        q congruent 7 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 8 modulo 60:   1/72 phi2 ( q^3-3*q^2-6*q+16 )
        q congruent 9 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 11 modulo 60:   1/72 phi2 ( q^3-3*q^2-6*q+16 )
        q congruent 13 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 16 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 17 modulo 60:   1/72 phi2 ( q^3-3*q^2-6*q+16 )
        q congruent 19 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 21 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 23 modulo 60:   1/72 phi2 ( q^3-3*q^2-6*q+16 )
        q congruent 25 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 27 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 29 modulo 60:   1/72 phi2 ( q^3-3*q^2-6*q+16 )
        q congruent 31 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 32 modulo 60:   1/72 phi2 ( q^3-3*q^2-6*q+16 )
        q congruent 37 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 41 modulo 60:   1/72 phi2 ( q^3-3*q^2-6*q+16 )
        q congruent 43 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 47 modulo 60:   1/72 phi2 ( q^3-3*q^2-6*q+16 )
        q congruent 49 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 53 modulo 60:   1/72 phi2 ( q^3-3*q^2-6*q+16 )
        q congruent 59 modulo 60:   1/72 phi2 ( q^3-3*q^2-6*q+16 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 15, 84, 13, 84, 38, 80, 13, 80, 11 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 27, 1, 4, 12 ], [ 38, 1, 11, 72 ], 
  [ 40, 1, 4, 36 ] ]

    k = 14: F-action on Pi is (1,3)(5,6)      [58,1,14]
      Dynkin type is ^2A_2(q) + ^2A_2(q) + T(phi2^2 phi6)
      Order of center |Z^F|: phi2^2 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/72 q phi1^2 ( q-3 )
        q congruent 2 modulo 60:   1/72 phi2 ( q^3-6*q^2+12*q-8 )
        q congruent 3 modulo 60:   1/72 q phi1^2 ( q-3 )
        q congruent 4 modulo 60:   1/72 q^2 phi1 ( q-4 )
        q congruent 5 modulo 60:   1/72 phi2 ( q^3-6*q^2+15*q-14 )
        q congruent 7 modulo 60:   1/72 q phi1^2 ( q-3 )
        q congruent 8 modulo 60:   1/72 phi2 ( q^3-6*q^2+12*q-8 )
        q congruent 9 modulo 60:   1/72 q phi1^2 ( q-3 )
        q congruent 11 modulo 60:   1/72 phi2 ( q^3-6*q^2+15*q-14 )
        q congruent 13 modulo 60:   1/72 q phi1^2 ( q-3 )
        q congruent 16 modulo 60:   1/72 q^2 phi1 ( q-4 )
        q congruent 17 modulo 60:   1/72 phi2 ( q^3-6*q^2+15*q-14 )
        q congruent 19 modulo 60:   1/72 q phi1^2 ( q-3 )
        q congruent 21 modulo 60:   1/72 q phi1^2 ( q-3 )
        q congruent 23 modulo 60:   1/72 phi2 ( q^3-6*q^2+15*q-14 )
        q congruent 25 modulo 60:   1/72 q phi1^2 ( q-3 )
        q congruent 27 modulo 60:   1/72 q phi1^2 ( q-3 )
        q congruent 29 modulo 60:   1/72 phi2 ( q^3-6*q^2+15*q-14 )
        q congruent 31 modulo 60:   1/72 q phi1^2 ( q-3 )
        q congruent 32 modulo 60:   1/72 phi2 ( q^3-6*q^2+12*q-8 )
        q congruent 37 modulo 60:   1/72 q phi1^2 ( q-3 )
        q congruent 41 modulo 60:   1/72 phi2 ( q^3-6*q^2+15*q-14 )
        q congruent 43 modulo 60:   1/72 q phi1^2 ( q-3 )
        q congruent 47 modulo 60:   1/72 phi2 ( q^3-6*q^2+15*q-14 )
        q congruent 49 modulo 60:   1/72 q phi1^2 ( q-3 )
        q congruent 53 modulo 60:   1/72 phi2 ( q^3-6*q^2+15*q-14 )
        q congruent 59 modulo 60:   1/72 phi2 ( q^3-6*q^2+15*q-14 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 9, 78, 15, 78, 31, 84, 15, 84, 13 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 8 ], [ 6, 1, 2, 18 ], 
  [ 8, 1, 2, 12 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ], [ 17, 1, 4, 36 ], 
  [ 22, 1, 4, 36 ], [ 27, 1, 4, 6 ], [ 27, 1, 6, 12 ], [ 38, 1, 11, 36 ], 
  [ 38, 1, 12, 72 ], [ 42, 1, 5, 18 ], [ 46, 1, 4, 36 ], [ 50, 1, 10, 36 ] ]

    k = 15: F-action on Pi is (1,3)(5,6)      [58,1,15]
      Dynkin type is ^2A_2(q) + ^2A_2(q) + T(phi2^4)
      Order of center |Z^F|: phi2^4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/288 phi1 ( q^3-25*q^2+210*q-630 )
        q congruent 2 modulo 60:   1/288 ( q^4-26*q^3+228*q^2-776*q+832 )
        q congruent 3 modulo 60:   1/288 ( q^4-26*q^3+235*q^2-876*q+1134 )
        q congruent 4 modulo 60:   1/288 ( q^4-26*q^3+220*q^2-600*q+288 )
        q congruent 5 modulo 60:   1/288 ( q^4-26*q^3+243*q^2-1016*q+1630 )
        q congruent 7 modulo 60:   1/288 ( q^4-26*q^3+235*q^2-876*q+1134 )
        q congruent 8 modulo 60:   1/288 ( q^4-26*q^3+228*q^2-776*q+832 )
        q congruent 9 modulo 60:   1/288 ( q^4-26*q^3+235*q^2-840*q+918 )
        q congruent 11 modulo 60:   1/288 ( q^4-26*q^3+243*q^2-1052*q+2134 )
        q congruent 13 modulo 60:   1/288 phi1 ( q^3-25*q^2+210*q-630 )
        q congruent 16 modulo 60:   1/288 q ( q^3-26*q^2+220*q-600 )
        q congruent 17 modulo 60:   1/288 ( q^4-26*q^3+243*q^2-1016*q+1630 )
        q congruent 19 modulo 60:   1/288 ( q^4-26*q^3+235*q^2-876*q+1422 )
        q congruent 21 modulo 60:   1/288 phi1 ( q^3-25*q^2+210*q-630 )
        q congruent 23 modulo 60:   1/288 ( q^4-26*q^3+243*q^2-1052*q+2134 )
        q congruent 25 modulo 60:   1/288 phi1 ( q^3-25*q^2+210*q-630 )
        q congruent 27 modulo 60:   1/288 ( q^4-26*q^3+235*q^2-876*q+1134 )
        q congruent 29 modulo 60:   1/288 ( q^4-26*q^3+243*q^2-1016*q+1918 )
        q congruent 31 modulo 60:   1/288 ( q^4-26*q^3+235*q^2-876*q+1134 )
        q congruent 32 modulo 60:   1/288 ( q^4-26*q^3+228*q^2-776*q+832 )
        q congruent 37 modulo 60:   1/288 phi1 ( q^3-25*q^2+210*q-630 )
        q congruent 41 modulo 60:   1/288 ( q^4-26*q^3+243*q^2-1016*q+1630 )
        q congruent 43 modulo 60:   1/288 ( q^4-26*q^3+235*q^2-876*q+1134 )
        q congruent 47 modulo 60:   1/288 ( q^4-26*q^3+243*q^2-1052*q+2134 )
        q congruent 49 modulo 60:   1/288 ( q^4-26*q^3+235*q^2-840*q+918 )
        q congruent 53 modulo 60:   1/288 ( q^4-26*q^3+243*q^2-1016*q+1630 )
        q congruent 59 modulo 60:   1/288 ( q^4-26*q^3+243*q^2-1052*q+2422 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 2, 67, 9, 67, 5, 78, 9, 78, 15 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 36 ], 
  [ 5, 1, 2, 72 ], [ 6, 1, 2, 36 ], [ 7, 1, 2, 36 ], [ 8, 1, 2, 24 ], 
  [ 9, 1, 1, 9 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 12 ], [ 12, 1, 2, 36 ], 
  [ 14, 1, 2, 144 ], [ 15, 1, 2, 72 ], [ 16, 1, 3, 72 ], [ 17, 1, 4, 72 ], 
  [ 18, 1, 2, 72 ], [ 19, 1, 2, 36 ], [ 20, 1, 4, 144 ], [ 21, 1, 2, 72 ], 
  [ 22, 1, 4, 72 ], [ 23, 1, 2, 36 ], [ 24, 1, 2, 36 ], [ 25, 1, 3, 144 ], 
  [ 26, 1, 4, 72 ], [ 27, 1, 6, 24 ], [ 29, 1, 4, 144 ], [ 31, 1, 4, 144 ], 
  [ 32, 1, 3, 72 ], [ 34, 1, 4, 72 ], [ 36, 1, 4, 144 ], [ 37, 1, 3, 288 ], 
  [ 38, 1, 12, 144 ], [ 39, 1, 3, 72 ], [ 40, 1, 6, 144 ], [ 42, 1, 6, 72 ], 
  [ 43, 1, 13, 288 ], [ 46, 1, 6, 144 ], [ 50, 1, 12, 144 ], 
  [ 51, 1, 9, 288 ] ]

    k = 16: F-action on Pi is (1,5)(3,6)      [58,1,16]
      Dynkin type is A_2(q^2) + T(phi1^3 phi2)
      Order of center |Z^F|: phi1^3 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/48 phi1 ( q^3-9*q^2+24*q-4 )
        q congruent 2 modulo 60:   1/48 q ( q^3-10*q^2+28*q-24 )
        q congruent 3 modulo 60:   1/48 ( q^4-10*q^3+29*q^2-20*q-12 )
        q congruent 4 modulo 60:   1/48 q ( q^3-10*q^2+32*q-32 )
        q congruent 5 modulo 60:   1/48 q phi1 ( q^2-9*q+20 )
        q congruent 7 modulo 60:   1/48 ( q^4-10*q^3+33*q^2-28*q-8 )
        q congruent 8 modulo 60:   1/48 q ( q^3-10*q^2+28*q-24 )
        q congruent 9 modulo 60:   1/48 q phi1 ( q^2-9*q+20 )
        q congruent 11 modulo 60:   1/48 ( q^4-10*q^3+29*q^2-20*q-12 )
        q congruent 13 modulo 60:   1/48 phi1 ( q^3-9*q^2+24*q-4 )
        q congruent 16 modulo 60:   1/48 q ( q^3-10*q^2+32*q-32 )
        q congruent 17 modulo 60:   1/48 q phi1 ( q^2-9*q+20 )
        q congruent 19 modulo 60:   1/48 ( q^4-10*q^3+33*q^2-28*q-8 )
        q congruent 21 modulo 60:   1/48 q phi1 ( q^2-9*q+20 )
        q congruent 23 modulo 60:   1/48 ( q^4-10*q^3+29*q^2-20*q-12 )
        q congruent 25 modulo 60:   1/48 phi1 ( q^3-9*q^2+24*q-4 )
        q congruent 27 modulo 60:   1/48 ( q^4-10*q^3+29*q^2-20*q-12 )
        q congruent 29 modulo 60:   1/48 q phi1 ( q^2-9*q+20 )
        q congruent 31 modulo 60:   1/48 ( q^4-10*q^3+33*q^2-28*q-8 )
        q congruent 32 modulo 60:   1/48 q ( q^3-10*q^2+28*q-24 )
        q congruent 37 modulo 60:   1/48 phi1 ( q^3-9*q^2+24*q-4 )
        q congruent 41 modulo 60:   1/48 q phi1 ( q^2-9*q+20 )
        q congruent 43 modulo 60:   1/48 ( q^4-10*q^3+33*q^2-28*q-8 )
        q congruent 47 modulo 60:   1/48 ( q^4-10*q^3+29*q^2-20*q-12 )
        q congruent 49 modulo 60:   1/48 phi1 ( q^3-9*q^2+24*q-4 )
        q congruent 53 modulo 60:   1/48 q phi1 ( q^2-9*q+20 )
        q congruent 59 modulo 60:   1/48 ( q^4-10*q^3+29*q^2-20*q-12 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 19, 87 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], 
  [ 6, 1, 1, 2 ], [ 6, 1, 2, 6 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 6 ], 
  [ 8, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 8 ], [ 11, 1, 1, 6 ], 
  [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], [ 17, 1, 3, 12 ], [ 18, 1, 1, 12 ], 
  [ 19, 1, 1, 6 ], [ 19, 1, 2, 6 ], [ 20, 1, 6, 24 ], [ 20, 1, 8, 24 ], 
  [ 21, 1, 1, 12 ], [ 22, 1, 1, 4 ], [ 22, 1, 3, 12 ], [ 23, 1, 1, 12 ], 
  [ 24, 1, 1, 12 ], [ 26, 1, 1, 12 ], [ 26, 1, 2, 12 ], [ 27, 1, 1, 12 ], 
  [ 27, 1, 3, 4 ], [ 32, 1, 4, 12 ], [ 34, 1, 1, 12 ], [ 34, 1, 3, 12 ], 
  [ 36, 1, 1, 24 ], [ 38, 1, 2, 8 ], [ 38, 1, 7, 24 ], [ 39, 1, 1, 24 ], 
  [ 42, 1, 1, 12 ], [ 42, 1, 2, 12 ], [ 43, 1, 6, 48 ], [ 46, 1, 7, 24 ], 
  [ 46, 1, 11, 24 ], [ 50, 1, 1, 24 ], [ 50, 1, 8, 24 ] ]

    k = 17: F-action on Pi is (1,5)(3,6)      [58,1,17]
      Dynkin type is A_2(q^2) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^2 ( q^2-2*q-4 )
        q congruent 2 modulo 60:   1/16 q ( q^3-4*q^2+8 )
        q congruent 3 modulo 60:   1/16 q phi2 ( q^2-5*q+6 )
        q congruent 4 modulo 60:   1/16 q ( q^3-4*q^2+8 )
        q congruent 5 modulo 60:   1/16 phi1^2 ( q^2-2*q-4 )
        q congruent 7 modulo 60:   1/16 q phi2 ( q^2-5*q+6 )
        q congruent 8 modulo 60:   1/16 q ( q^3-4*q^2+8 )
        q congruent 9 modulo 60:   1/16 phi1^2 ( q^2-2*q-4 )
        q congruent 11 modulo 60:   1/16 q phi2 ( q^2-5*q+6 )
        q congruent 13 modulo 60:   1/16 phi1^2 ( q^2-2*q-4 )
        q congruent 16 modulo 60:   1/16 q ( q^3-4*q^2+8 )
        q congruent 17 modulo 60:   1/16 phi1^2 ( q^2-2*q-4 )
        q congruent 19 modulo 60:   1/16 q phi2 ( q^2-5*q+6 )
        q congruent 21 modulo 60:   1/16 phi1^2 ( q^2-2*q-4 )
        q congruent 23 modulo 60:   1/16 q phi2 ( q^2-5*q+6 )
        q congruent 25 modulo 60:   1/16 phi1^2 ( q^2-2*q-4 )
        q congruent 27 modulo 60:   1/16 q phi2 ( q^2-5*q+6 )
        q congruent 29 modulo 60:   1/16 phi1^2 ( q^2-2*q-4 )
        q congruent 31 modulo 60:   1/16 q phi2 ( q^2-5*q+6 )
        q congruent 32 modulo 60:   1/16 q ( q^3-4*q^2+8 )
        q congruent 37 modulo 60:   1/16 phi1^2 ( q^2-2*q-4 )
        q congruent 41 modulo 60:   1/16 phi1^2 ( q^2-2*q-4 )
        q congruent 43 modulo 60:   1/16 q phi2 ( q^2-5*q+6 )
        q congruent 47 modulo 60:   1/16 q phi2 ( q^2-5*q+6 )
        q congruent 49 modulo 60:   1/16 phi1^2 ( q^2-2*q-4 )
        q congruent 53 modulo 60:   1/16 phi1^2 ( q^2-2*q-4 )
        q congruent 59 modulo 60:   1/16 q phi2 ( q^2-5*q+6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 7, 76, 40 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], 
  [ 6, 1, 1, 2 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 2 ], 
  [ 8, 1, 1, 4 ], [ 8, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], [ 11, 1, 2, 2 ], [ 17, 1, 2, 4 ], 
  [ 17, 1, 3, 4 ], [ 18, 1, 1, 4 ], [ 18, 1, 2, 4 ], [ 19, 1, 1, 2 ], 
  [ 19, 1, 2, 2 ], [ 20, 1, 6, 8 ], [ 20, 1, 7, 8 ], [ 21, 1, 1, 4 ], 
  [ 21, 1, 2, 4 ], [ 22, 1, 1, 4 ], [ 22, 1, 4, 4 ], [ 24, 1, 1, 2 ], 
  [ 24, 1, 2, 2 ], [ 26, 1, 2, 4 ], [ 26, 1, 3, 4 ], [ 27, 1, 2, 4 ], 
  [ 27, 1, 3, 4 ], [ 32, 1, 4, 4 ], [ 34, 1, 1, 4 ], [ 34, 1, 4, 4 ], 
  [ 36, 1, 2, 8 ], [ 36, 1, 3, 8 ], [ 37, 1, 4, 16 ], [ 38, 1, 2, 8 ], 
  [ 38, 1, 10, 8 ], [ 39, 1, 4, 4 ], [ 42, 1, 2, 4 ], [ 42, 1, 4, 4 ], 
  [ 43, 1, 7, 16 ], [ 46, 1, 8, 8 ], [ 46, 1, 11, 8 ], [ 50, 1, 2, 8 ], 
  [ 50, 1, 11, 8 ] ]

    k = 18: F-action on Pi is (1,5)(3,6)      [58,1,18]
      Dynkin type is A_2(q^2) + T(phi1 phi2 phi3)
      Order of center |Z^F|: phi1 phi2 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 phi1^3 ( q+2 )
        q congruent 2 modulo 60:   1/24 q^2 phi2 ( q-2 )
        q congruent 3 modulo 60:   1/24 q phi1^2 phi2
        q congruent 4 modulo 60:   1/24 q phi1 ( q^2-4 )
        q congruent 5 modulo 60:   1/24 q phi1^2 phi2
        q congruent 7 modulo 60:   1/24 phi1^3 ( q+2 )
        q congruent 8 modulo 60:   1/24 q^2 phi2 ( q-2 )
        q congruent 9 modulo 60:   1/24 q phi1^2 phi2
        q congruent 11 modulo 60:   1/24 q phi1^2 phi2
        q congruent 13 modulo 60:   1/24 phi1^3 ( q+2 )
        q congruent 16 modulo 60:   1/24 q phi1 ( q^2-4 )
        q congruent 17 modulo 60:   1/24 q phi1^2 phi2
        q congruent 19 modulo 60:   1/24 phi1^3 ( q+2 )
        q congruent 21 modulo 60:   1/24 q phi1^2 phi2
        q congruent 23 modulo 60:   1/24 q phi1^2 phi2
        q congruent 25 modulo 60:   1/24 phi1^3 ( q+2 )
        q congruent 27 modulo 60:   1/24 q phi1^2 phi2
        q congruent 29 modulo 60:   1/24 q phi1^2 phi2
        q congruent 31 modulo 60:   1/24 phi1^3 ( q+2 )
        q congruent 32 modulo 60:   1/24 q^2 phi2 ( q-2 )
        q congruent 37 modulo 60:   1/24 phi1^3 ( q+2 )
        q congruent 41 modulo 60:   1/24 q phi1^2 phi2
        q congruent 43 modulo 60:   1/24 phi1^3 ( q+2 )
        q congruent 47 modulo 60:   1/24 q phi1^2 phi2
        q congruent 49 modulo 60:   1/24 phi1^3 ( q+2 )
        q congruent 53 modulo 60:   1/24 q phi1^2 phi2
        q congruent 59 modulo 60:   1/24 q phi1^2 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 81, 59, 85 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], 
  [ 6, 1, 1, 2 ], [ 8, 1, 1, 4 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], 
  [ 17, 1, 2, 4 ], [ 22, 1, 1, 4 ], [ 27, 1, 3, 4 ], [ 27, 1, 5, 6 ], 
  [ 38, 1, 2, 8 ], [ 38, 1, 9, 12 ], [ 42, 1, 3, 6 ], [ 46, 1, 9, 12 ], 
  [ 50, 1, 3, 12 ] ]

    k = 19: F-action on Pi is (1,5,3,6)      [58,1,19]
      Dynkin type is ^2A_2(q^2) + T(phi1 phi2 phi4)
      Order of center |Z^F|: phi1 phi2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 phi2 ( q^2-2 )
        q congruent 2 modulo 60:   1/8 q^2 ( q^2-2 )
        q congruent 3 modulo 60:   1/8 phi1 phi2 ( q^2-2 )
        q congruent 4 modulo 60:   1/8 q^2 ( q^2-2 )
        q congruent 5 modulo 60:   1/8 phi1 phi2 ( q^2-2 )
        q congruent 7 modulo 60:   1/8 phi1 phi2 ( q^2-2 )
        q congruent 8 modulo 60:   1/8 q^2 ( q^2-2 )
        q congruent 9 modulo 60:   1/8 phi1 phi2 ( q^2-2 )
        q congruent 11 modulo 60:   1/8 phi1 phi2 ( q^2-2 )
        q congruent 13 modulo 60:   1/8 phi1 phi2 ( q^2-2 )
        q congruent 16 modulo 60:   1/8 q^2 ( q^2-2 )
        q congruent 17 modulo 60:   1/8 phi1 phi2 ( q^2-2 )
        q congruent 19 modulo 60:   1/8 phi1 phi2 ( q^2-2 )
        q congruent 21 modulo 60:   1/8 phi1 phi2 ( q^2-2 )
        q congruent 23 modulo 60:   1/8 phi1 phi2 ( q^2-2 )
        q congruent 25 modulo 60:   1/8 phi1 phi2 ( q^2-2 )
        q congruent 27 modulo 60:   1/8 phi1 phi2 ( q^2-2 )
        q congruent 29 modulo 60:   1/8 phi1 phi2 ( q^2-2 )
        q congruent 31 modulo 60:   1/8 phi1 phi2 ( q^2-2 )
        q congruent 32 modulo 60:   1/8 q^2 ( q^2-2 )
        q congruent 37 modulo 60:   1/8 phi1 phi2 ( q^2-2 )
        q congruent 41 modulo 60:   1/8 phi1 phi2 ( q^2-2 )
        q congruent 43 modulo 60:   1/8 phi1 phi2 ( q^2-2 )
        q congruent 47 modulo 60:   1/8 phi1 phi2 ( q^2-2 )
        q congruent 49 modulo 60:   1/8 phi1 phi2 ( q^2-2 )
        q congruent 53 modulo 60:   1/8 phi1 phi2 ( q^2-2 )
        q congruent 59 modulo 60:   1/8 phi1 phi2 ( q^2-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 75, 22, 100 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 5, 1, 3, 4 ], [ 5, 1, 4, 4 ], [ 9, 1, 1, 1 ], 
  [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 32, 1, 5, 4 ], [ 39, 1, 2, 4 ], 
  [ 43, 1, 11, 8 ] ]

    k = 20: F-action on Pi is (1,5,3,6)      [58,1,20]
      Dynkin type is ^2A_2(q^2) + T(phi12)
      Order of center |Z^F|: phi12
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 2 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 3 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 4 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 5 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 7 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 8 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 9 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 11 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 13 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 16 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 17 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 19 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 21 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 23 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 25 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 27 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 29 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 31 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 32 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 37 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 41 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 43 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 47 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 49 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 53 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 59 modulo 60:   1/12 q^2 phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 39, 100, 32 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]

    k = 21: F-action on Pi is (1,5,3,6)      [58,1,21]
      Dynkin type is ^2A_2(q^2) + T(phi4^2)
      Order of center |Z^F|: phi4^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 phi1 phi2 ( q^2-12 )
        q congruent 2 modulo 60:   1/24 ( q^4-10*q^2+24 )
        q congruent 3 modulo 60:   1/24 ( q^4-13*q^2+36 )
        q congruent 4 modulo 60:   1/24 q^2 ( q^2-10 )
        q congruent 5 modulo 60:   1/24 phi1 phi2 ( q^2-12 )
        q congruent 7 modulo 60:   1/24 ( q^4-13*q^2+36 )
        q congruent 8 modulo 60:   1/24 ( q^4-10*q^2+24 )
        q congruent 9 modulo 60:   1/24 phi1 phi2 ( q^2-12 )
        q congruent 11 modulo 60:   1/24 phi1 phi2 ( q^2-12 )
        q congruent 13 modulo 60:   1/24 ( q^4-13*q^2+36 )
        q congruent 16 modulo 60:   1/24 q^2 ( q^2-10 )
        q congruent 17 modulo 60:   1/24 ( q^4-13*q^2+36 )
        q congruent 19 modulo 60:   1/24 phi1 phi2 ( q^2-12 )
        q congruent 21 modulo 60:   1/24 phi1 phi2 ( q^2-12 )
        q congruent 23 modulo 60:   1/24 ( q^4-13*q^2+36 )
        q congruent 25 modulo 60:   1/24 phi1 phi2 ( q^2-12 )
        q congruent 27 modulo 60:   1/24 ( q^4-13*q^2+36 )
        q congruent 29 modulo 60:   1/24 phi1 phi2 ( q^2-12 )
        q congruent 31 modulo 60:   1/24 phi1 phi2 ( q^2-12 )
        q congruent 32 modulo 60:   1/24 ( q^4-10*q^2+24 )
        q congruent 37 modulo 60:   1/24 ( q^4-13*q^2+36 )
        q congruent 41 modulo 60:   1/24 phi1 phi2 ( q^2-12 )
        q congruent 43 modulo 60:   1/24 ( q^4-13*q^2+36 )
        q congruent 47 modulo 60:   1/24 ( q^4-13*q^2+36 )
        q congruent 49 modulo 60:   1/24 phi1 phi2 ( q^2-12 )
        q congruent 53 modulo 60:   1/24 ( q^4-13*q^2+36 )
        q congruent 59 modulo 60:   1/24 phi1 phi2 ( q^2-12 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 6, 75, 39 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 5, 1, 3, 12 ], [ 5, 1, 4, 12 ], [ 9, 1, 1, 3 ], 
  [ 32, 1, 5, 12 ], [ 37, 1, 5, 24 ], [ 39, 1, 5, 12 ], [ 43, 1, 10, 24 ] ]

    k = 22: F-action on Pi is (1,5)(3,6)      [58,1,22]
      Dynkin type is A_2(q^2) + T(phi1^2 phi6)
      Order of center |Z^F|: phi1^2 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/72 q phi1 ( q^2-8*q+19 )
        q congruent 2 modulo 60:   1/72 phi2 ( q^3-10*q^2+28*q-24 )
        q congruent 3 modulo 60:   1/72 q phi1 ( q^2-8*q+15 )
        q congruent 4 modulo 60:   1/72 q phi1 ( q^2-8*q+16 )
        q congruent 5 modulo 60:   1/72 phi2 ( q^3-10*q^2+31*q-30 )
        q congruent 7 modulo 60:   1/72 q phi1 ( q^2-8*q+19 )
        q congruent 8 modulo 60:   1/72 phi2 ( q^3-10*q^2+28*q-24 )
        q congruent 9 modulo 60:   1/72 q phi1 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/72 phi2 ( q^3-10*q^2+31*q-30 )
        q congruent 13 modulo 60:   1/72 q phi1 ( q^2-8*q+19 )
        q congruent 16 modulo 60:   1/72 q phi1 ( q^2-8*q+16 )
        q congruent 17 modulo 60:   1/72 phi2 ( q^3-10*q^2+31*q-30 )
        q congruent 19 modulo 60:   1/72 q phi1 ( q^2-8*q+19 )
        q congruent 21 modulo 60:   1/72 q phi1 ( q^2-8*q+15 )
        q congruent 23 modulo 60:   1/72 phi2 ( q^3-10*q^2+31*q-30 )
        q congruent 25 modulo 60:   1/72 q phi1 ( q^2-8*q+19 )
        q congruent 27 modulo 60:   1/72 q phi1 ( q^2-8*q+15 )
        q congruent 29 modulo 60:   1/72 phi2 ( q^3-10*q^2+31*q-30 )
        q congruent 31 modulo 60:   1/72 q phi1 ( q^2-8*q+19 )
        q congruent 32 modulo 60:   1/72 phi2 ( q^3-10*q^2+28*q-24 )
        q congruent 37 modulo 60:   1/72 q phi1 ( q^2-8*q+19 )
        q congruent 41 modulo 60:   1/72 phi2 ( q^3-10*q^2+31*q-30 )
        q congruent 43 modulo 60:   1/72 q phi1 ( q^2-8*q+19 )
        q congruent 47 modulo 60:   1/72 phi2 ( q^3-10*q^2+31*q-30 )
        q congruent 49 modulo 60:   1/72 q phi1 ( q^2-8*q+19 )
        q congruent 53 modulo 60:   1/72 phi2 ( q^3-10*q^2+31*q-30 )
        q congruent 59 modulo 60:   1/72 phi2 ( q^3-10*q^2+31*q-30 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 28, 96, 33 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], 
  [ 6, 1, 2, 6 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], [ 17, 1, 3, 12 ], 
  [ 22, 1, 3, 12 ], [ 27, 1, 1, 12 ], [ 27, 1, 4, 6 ], [ 38, 1, 4, 12 ], 
  [ 38, 1, 7, 24 ], [ 42, 1, 5, 18 ], [ 46, 1, 10, 36 ], [ 50, 1, 7, 36 ] ]

    k = 23: F-action on Pi is (1,5)(3,6)      [58,1,23]
      Dynkin type is A_2(q^2) + T(phi1 phi2 phi6)
      Order of center |Z^F|: phi1 phi2 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 q phi1^3
        q congruent 2 modulo 60:   1/24 q phi2 ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/24 q phi1^3
        q congruent 4 modulo 60:   1/24 q^2 phi1 ( q-2 )
        q congruent 5 modulo 60:   1/24 phi1^2 phi2 ( q-2 )
        q congruent 7 modulo 60:   1/24 q phi1^3
        q congruent 8 modulo 60:   1/24 q phi2 ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/24 q phi1^3
        q congruent 11 modulo 60:   1/24 phi1^2 phi2 ( q-2 )
        q congruent 13 modulo 60:   1/24 q phi1^3
        q congruent 16 modulo 60:   1/24 q^2 phi1 ( q-2 )
        q congruent 17 modulo 60:   1/24 phi1^2 phi2 ( q-2 )
        q congruent 19 modulo 60:   1/24 q phi1^3
        q congruent 21 modulo 60:   1/24 q phi1^3
        q congruent 23 modulo 60:   1/24 phi1^2 phi2 ( q-2 )
        q congruent 25 modulo 60:   1/24 q phi1^3
        q congruent 27 modulo 60:   1/24 q phi1^3
        q congruent 29 modulo 60:   1/24 phi1^2 phi2 ( q-2 )
        q congruent 31 modulo 60:   1/24 q phi1^3
        q congruent 32 modulo 60:   1/24 q phi2 ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/24 q phi1^3
        q congruent 41 modulo 60:   1/24 phi1^2 phi2 ( q-2 )
        q congruent 43 modulo 60:   1/24 q phi1^3
        q congruent 47 modulo 60:   1/24 phi1^2 phi2 ( q-2 )
        q congruent 49 modulo 60:   1/24 q phi1^3
        q congruent 53 modulo 60:   1/24 phi1^2 phi2 ( q-2 )
        q congruent 59 modulo 60:   1/24 phi1^2 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 82, 60, 86 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], 
  [ 6, 1, 2, 2 ], [ 8, 1, 2, 4 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], 
  [ 17, 1, 3, 4 ], [ 22, 1, 4, 4 ], [ 27, 1, 2, 4 ], [ 27, 1, 4, 6 ], 
  [ 38, 1, 4, 12 ], [ 38, 1, 10, 8 ], [ 42, 1, 5, 6 ], [ 46, 1, 10, 12 ], 
  [ 50, 1, 10, 12 ] ]

    k = 24: F-action on Pi is (1,5)(3,6)      [58,1,24]
      Dynkin type is A_2(q^2) + T(phi3 phi6)
      Order of center |Z^F|: phi3 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/36 q phi1^2 ( q+2 )
        q congruent 2 modulo 60:   1/36 q phi2^2 ( q-2 )
        q congruent 3 modulo 60:   1/36 q^2 phi1 phi2
        q congruent 4 modulo 60:   1/36 q phi1^2 ( q+2 )
        q congruent 5 modulo 60:   1/36 q phi2^2 ( q-2 )
        q congruent 7 modulo 60:   1/36 q phi1^2 ( q+2 )
        q congruent 8 modulo 60:   1/36 q phi2^2 ( q-2 )
        q congruent 9 modulo 60:   1/36 q^2 phi1 phi2
        q congruent 11 modulo 60:   1/36 q phi2^2 ( q-2 )
        q congruent 13 modulo 60:   1/36 q phi1^2 ( q+2 )
        q congruent 16 modulo 60:   1/36 q phi1^2 ( q+2 )
        q congruent 17 modulo 60:   1/36 q phi2^2 ( q-2 )
        q congruent 19 modulo 60:   1/36 q phi1^2 ( q+2 )
        q congruent 21 modulo 60:   1/36 q^2 phi1 phi2
        q congruent 23 modulo 60:   1/36 q phi2^2 ( q-2 )
        q congruent 25 modulo 60:   1/36 q phi1^2 ( q+2 )
        q congruent 27 modulo 60:   1/36 q^2 phi1 phi2
        q congruent 29 modulo 60:   1/36 q phi2^2 ( q-2 )
        q congruent 31 modulo 60:   1/36 q phi1^2 ( q+2 )
        q congruent 32 modulo 60:   1/36 q phi2^2 ( q-2 )
        q congruent 37 modulo 60:   1/36 q phi1^2 ( q+2 )
        q congruent 41 modulo 60:   1/36 q phi2^2 ( q-2 )
        q congruent 43 modulo 60:   1/36 q phi1^2 ( q+2 )
        q congruent 47 modulo 60:   1/36 q phi2^2 ( q-2 )
        q congruent 49 modulo 60:   1/36 q phi1^2 ( q+2 )
        q congruent 53 modulo 60:   1/36 q phi2^2 ( q-2 )
        q congruent 59 modulo 60:   1/36 q phi2^2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 36, 99, 29 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 27, 1, 4, 6 ], 
  [ 27, 1, 5, 6 ], [ 38, 1, 4, 12 ], [ 38, 1, 9, 12 ] ]

    k = 25: F-action on Pi is (1,5)(3,6)      [58,1,25]
      Dynkin type is A_2(q^2) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/144 phi1 ( q^3-11*q^2+34*q-12 )
        q congruent 2 modulo 60:   1/144 ( q^4-12*q^3+48*q^2-80*q+48 )
        q congruent 3 modulo 60:   1/144 ( q^4-12*q^3+41*q^2-30*q-36 )
        q congruent 4 modulo 60:   1/144 q ( q^3-12*q^2+48*q-64 )
        q congruent 5 modulo 60:   1/144 ( q^4-12*q^3+45*q^2-62*q+60 )
        q congruent 7 modulo 60:   1/144 ( q^4-12*q^3+45*q^2-46*q-24 )
        q congruent 8 modulo 60:   1/144 ( q^4-12*q^3+48*q^2-80*q+48 )
        q congruent 9 modulo 60:   1/144 q phi1 ( q^2-11*q+30 )
        q congruent 11 modulo 60:   1/144 ( q^4-12*q^3+45*q^2-62*q+24 )
        q congruent 13 modulo 60:   1/144 phi1 ( q^3-11*q^2+34*q-12 )
        q congruent 16 modulo 60:   1/144 q ( q^3-12*q^2+48*q-64 )
        q congruent 17 modulo 60:   1/144 ( q^4-12*q^3+45*q^2-62*q+60 )
        q congruent 19 modulo 60:   1/144 ( q^4-12*q^3+45*q^2-46*q-24 )
        q congruent 21 modulo 60:   1/144 q phi1 ( q^2-11*q+30 )
        q congruent 23 modulo 60:   1/144 ( q^4-12*q^3+45*q^2-62*q+24 )
        q congruent 25 modulo 60:   1/144 phi1 ( q^3-11*q^2+34*q-12 )
        q congruent 27 modulo 60:   1/144 ( q^4-12*q^3+41*q^2-30*q-36 )
        q congruent 29 modulo 60:   1/144 ( q^4-12*q^3+45*q^2-62*q+60 )
        q congruent 31 modulo 60:   1/144 ( q^4-12*q^3+45*q^2-46*q-24 )
        q congruent 32 modulo 60:   1/144 ( q^4-12*q^3+48*q^2-80*q+48 )
        q congruent 37 modulo 60:   1/144 phi1 ( q^3-11*q^2+34*q-12 )
        q congruent 41 modulo 60:   1/144 ( q^4-12*q^3+45*q^2-62*q+60 )
        q congruent 43 modulo 60:   1/144 ( q^4-12*q^3+45*q^2-46*q-24 )
        q congruent 47 modulo 60:   1/144 ( q^4-12*q^3+45*q^2-62*q+24 )
        q congruent 49 modulo 60:   1/144 phi1 ( q^3-11*q^2+34*q-12 )
        q congruent 53 modulo 60:   1/144 ( q^4-12*q^3+45*q^2-62*q+60 )
        q congruent 59 modulo 60:   1/144 ( q^4-12*q^3+45*q^2-62*q+24 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 72, 35 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], 
  [ 6, 1, 1, 6 ], [ 6, 1, 2, 6 ], [ 7, 1, 1, 18 ], [ 7, 1, 2, 18 ], 
  [ 9, 1, 1, 9 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 6 ], [ 11, 1, 1, 6 ], 
  [ 11, 1, 2, 6 ], [ 17, 1, 2, 12 ], [ 17, 1, 3, 12 ], [ 19, 1, 1, 18 ], 
  [ 19, 1, 2, 18 ], [ 20, 1, 5, 72 ], [ 20, 1, 8, 72 ], [ 22, 1, 2, 12 ], 
  [ 22, 1, 3, 12 ], [ 24, 1, 1, 18 ], [ 24, 1, 2, 18 ], [ 26, 1, 1, 36 ], 
  [ 26, 1, 4, 36 ], [ 27, 1, 1, 12 ], [ 27, 1, 6, 12 ], [ 32, 1, 4, 36 ], 
  [ 34, 1, 2, 36 ], [ 34, 1, 3, 36 ], [ 38, 1, 6, 24 ], [ 38, 1, 7, 24 ], 
  [ 39, 1, 4, 36 ], [ 42, 1, 1, 36 ], [ 42, 1, 6, 36 ], [ 43, 1, 5, 144 ], 
  [ 46, 1, 7, 72 ], [ 46, 1, 12, 72 ], [ 50, 1, 4, 72 ], [ 50, 1, 9, 72 ] ]

    k = 26: F-action on Pi is (1,5)(3,6)      [58,1,26]
      Dynkin type is A_2(q^2) + T(phi1 phi2^3)
      Order of center |Z^F|: phi1 phi2^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/48 q phi1^2 ( q-4 )
        q congruent 2 modulo 60:   1/48 q ( q^3-6*q^2+12*q-8 )
        q congruent 3 modulo 60:   1/48 ( q^4-6*q^3+9*q^2-4*q+12 )
        q congruent 4 modulo 60:   1/48 q^2 ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/48 phi1^2 ( q^2-4*q+4 )
        q congruent 7 modulo 60:   1/48 ( q^4-6*q^3+9*q^2-4*q+12 )
        q congruent 8 modulo 60:   1/48 q ( q^3-6*q^2+12*q-8 )
        q congruent 9 modulo 60:   1/48 q phi1^2 ( q-4 )
        q congruent 11 modulo 60:   1/48 ( q^4-6*q^3+13*q^2-12*q+16 )
        q congruent 13 modulo 60:   1/48 q phi1^2 ( q-4 )
        q congruent 16 modulo 60:   1/48 q^2 ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/48 phi1^2 ( q^2-4*q+4 )
        q congruent 19 modulo 60:   1/48 ( q^4-6*q^3+9*q^2-4*q+12 )
        q congruent 21 modulo 60:   1/48 q phi1^2 ( q-4 )
        q congruent 23 modulo 60:   1/48 ( q^4-6*q^3+13*q^2-12*q+16 )
        q congruent 25 modulo 60:   1/48 q phi1^2 ( q-4 )
        q congruent 27 modulo 60:   1/48 ( q^4-6*q^3+9*q^2-4*q+12 )
        q congruent 29 modulo 60:   1/48 phi1^2 ( q^2-4*q+4 )
        q congruent 31 modulo 60:   1/48 ( q^4-6*q^3+9*q^2-4*q+12 )
        q congruent 32 modulo 60:   1/48 q ( q^3-6*q^2+12*q-8 )
        q congruent 37 modulo 60:   1/48 q phi1^2 ( q-4 )
        q congruent 41 modulo 60:   1/48 phi1^2 ( q^2-4*q+4 )
        q congruent 43 modulo 60:   1/48 ( q^4-6*q^3+9*q^2-4*q+12 )
        q congruent 47 modulo 60:   1/48 ( q^4-6*q^3+13*q^2-12*q+16 )
        q congruent 49 modulo 60:   1/48 q phi1^2 ( q-4 )
        q congruent 53 modulo 60:   1/48 phi1^2 ( q^2-4*q+4 )
        q congruent 59 modulo 60:   1/48 ( q^4-6*q^3+13*q^2-12*q+16 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 69, 20, 88 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], 
  [ 6, 1, 1, 6 ], [ 6, 1, 2, 2 ], [ 7, 1, 1, 6 ], [ 7, 1, 2, 6 ], 
  [ 8, 1, 2, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 8 ], [ 11, 1, 1, 2 ], 
  [ 11, 1, 2, 6 ], [ 17, 1, 2, 12 ], [ 17, 1, 3, 4 ], [ 18, 1, 2, 12 ], 
  [ 19, 1, 1, 6 ], [ 19, 1, 2, 6 ], [ 20, 1, 5, 24 ], [ 20, 1, 7, 24 ], 
  [ 21, 1, 2, 12 ], [ 22, 1, 2, 12 ], [ 22, 1, 4, 4 ], [ 23, 1, 2, 12 ], 
  [ 24, 1, 2, 12 ], [ 26, 1, 3, 12 ], [ 26, 1, 4, 12 ], [ 27, 1, 2, 4 ], 
  [ 27, 1, 6, 12 ], [ 32, 1, 4, 12 ], [ 34, 1, 2, 12 ], [ 34, 1, 4, 12 ], 
  [ 36, 1, 4, 24 ], [ 38, 1, 6, 24 ], [ 38, 1, 10, 8 ], [ 39, 1, 3, 24 ], 
  [ 42, 1, 4, 12 ], [ 42, 1, 6, 12 ], [ 43, 1, 14, 48 ], [ 46, 1, 8, 24 ], 
  [ 46, 1, 12, 24 ], [ 50, 1, 5, 24 ], [ 50, 1, 12, 24 ] ]

    k = 27: F-action on Pi is (1,5)(3,6)      [58,1,27]
      Dynkin type is A_2(q^2) + T(phi2^2 phi3)
      Order of center |Z^F|: phi2^2 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/72 phi1^2 ( q^2-q-6 )
        q congruent 2 modulo 60:   1/72 q phi2 ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/72 q phi1 phi2 ( q-3 )
        q congruent 4 modulo 60:   1/72 q phi1 ( q^2-2*q-8 )
        q congruent 5 modulo 60:   1/72 q phi2 ( q^2-4*q+7 )
        q congruent 7 modulo 60:   1/72 phi1^2 ( q^2-q-6 )
        q congruent 8 modulo 60:   1/72 q phi2 ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/72 q phi1 phi2 ( q-3 )
        q congruent 11 modulo 60:   1/72 q phi2 ( q^2-4*q+7 )
        q congruent 13 modulo 60:   1/72 phi1^2 ( q^2-q-6 )
        q congruent 16 modulo 60:   1/72 q phi1 ( q^2-2*q-8 )
        q congruent 17 modulo 60:   1/72 q phi2 ( q^2-4*q+7 )
        q congruent 19 modulo 60:   1/72 phi1^2 ( q^2-q-6 )
        q congruent 21 modulo 60:   1/72 q phi1 phi2 ( q-3 )
        q congruent 23 modulo 60:   1/72 q phi2 ( q^2-4*q+7 )
        q congruent 25 modulo 60:   1/72 phi1^2 ( q^2-q-6 )
        q congruent 27 modulo 60:   1/72 q phi1 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/72 q phi2 ( q^2-4*q+7 )
        q congruent 31 modulo 60:   1/72 phi1^2 ( q^2-q-6 )
        q congruent 32 modulo 60:   1/72 q phi2 ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/72 phi1^2 ( q^2-q-6 )
        q congruent 41 modulo 60:   1/72 q phi2 ( q^2-4*q+7 )
        q congruent 43 modulo 60:   1/72 phi1^2 ( q^2-q-6 )
        q congruent 47 modulo 60:   1/72 q phi2 ( q^2-4*q+7 )
        q congruent 49 modulo 60:   1/72 phi1^2 ( q^2-q-6 )
        q congruent 53 modulo 60:   1/72 q phi2 ( q^2-4*q+7 )
        q congruent 59 modulo 60:   1/72 q phi2 ( q^2-4*q+7 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 27, 95, 34 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 2 ], 
  [ 6, 1, 1, 6 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ], [ 17, 1, 2, 12 ], 
  [ 22, 1, 2, 12 ], [ 27, 1, 5, 6 ], [ 27, 1, 6, 12 ], [ 38, 1, 6, 24 ], 
  [ 38, 1, 9, 12 ], [ 42, 1, 3, 18 ], [ 46, 1, 9, 36 ], [ 50, 1, 6, 36 ] ]

i = 59: Pi = [ 2, 3, 4, 5 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [59,1,1]
      Dynkin type is D_4(q) + T(phi1^4)
      Order of center |Z^F|: phi1^4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/1152 ( q^4-28*q^3+286*q^2-1260*q+2153 )
        q congruent 2 modulo 60:   1/1152 ( q^4-28*q^3+268*q^2-1008*q+1152 )
        q congruent 3 modulo 60:   1/1152 ( q^4-28*q^3+286*q^2-1260*q+1881 )
        q congruent 4 modulo 60:   1/1152 ( q^4-28*q^3+268*q^2-1008*q+1280 )
        q congruent 5 modulo 60:   1/1152 ( q^4-28*q^3+286*q^2-1260*q+2025 )
        q congruent 7 modulo 60:   1/1152 ( q^4-28*q^3+286*q^2-1260*q+2009 )
        q congruent 8 modulo 60:   1/1152 ( q^4-28*q^3+268*q^2-1008*q+1152 )
        q congruent 9 modulo 60:   1/1152 ( q^4-28*q^3+286*q^2-1260*q+2025 )
        q congruent 11 modulo 60:   1/1152 ( q^4-28*q^3+286*q^2-1260*q+1881 )
        q congruent 13 modulo 60:   1/1152 ( q^4-28*q^3+286*q^2-1260*q+2153 )
        q congruent 16 modulo 60:   1/1152 ( q^4-28*q^3+268*q^2-1008*q+1280 )
        q congruent 17 modulo 60:   1/1152 ( q^4-28*q^3+286*q^2-1260*q+2025 )
        q congruent 19 modulo 60:   1/1152 ( q^4-28*q^3+286*q^2-1260*q+2009 )
        q congruent 21 modulo 60:   1/1152 ( q^4-28*q^3+286*q^2-1260*q+2025 )
        q congruent 23 modulo 60:   1/1152 ( q^4-28*q^3+286*q^2-1260*q+1881 )
        q congruent 25 modulo 60:   1/1152 ( q^4-28*q^3+286*q^2-1260*q+2153 )
        q congruent 27 modulo 60:   1/1152 ( q^4-28*q^3+286*q^2-1260*q+1881 )
        q congruent 29 modulo 60:   1/1152 ( q^4-28*q^3+286*q^2-1260*q+2025 )
        q congruent 31 modulo 60:   1/1152 ( q^4-28*q^3+286*q^2-1260*q+2009 )
        q congruent 32 modulo 60:   1/1152 ( q^4-28*q^3+268*q^2-1008*q+1152 )
        q congruent 37 modulo 60:   1/1152 ( q^4-28*q^3+286*q^2-1260*q+2153 )
        q congruent 41 modulo 60:   1/1152 ( q^4-28*q^3+286*q^2-1260*q+2025 )
        q congruent 43 modulo 60:   1/1152 ( q^4-28*q^3+286*q^2-1260*q+2009 )
        q congruent 47 modulo 60:   1/1152 ( q^4-28*q^3+286*q^2-1260*q+1881 )
        q congruent 49 modulo 60:   1/1152 ( q^4-28*q^3+286*q^2-1260*q+2153 )
        q congruent 53 modulo 60:   1/1152 ( q^4-28*q^3+286*q^2-1260*q+2025 )
        q congruent 59 modulo 60:   1/1152 ( q^4-28*q^3+286*q^2-1260*q+1881 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 4, 3, 66, 70, 68, 4, 4, 16, 8, 28, 70, 70 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 12 ], [ 3, 1, 1, 32 ], [ 4, 1, 1, 24 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 1, 24 ], [ 11, 1, 1, 96 ], [ 12, 1, 1, 96 ], 
  [ 13, 1, 1, 144 ], [ 23, 1, 1, 24 ], [ 24, 1, 1, 72 ], [ 25, 1, 1, 48 ], 
  [ 27, 1, 1, 192 ], [ 28, 1, 1, 288 ], [ 39, 1, 1, 144 ], [ 40, 1, 1, 192 ], 
  [ 41, 1, 1, 288 ], [ 44, 1, 1, 576 ], [ 52, 1, 1, 576 ] ]

    k = 2: F-action on Pi is ()      [59,1,2]
      Dynkin type is D_4(q) + T(phi2^4)
      Order of center |Z^F|: phi2^4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/1152 phi1 ( q^3-19*q^2+123*q-297 )
        q congruent 2 modulo 60:   1/1152 ( q^4-20*q^3+124*q^2-240*q+128 )
        q congruent 3 modulo 60:   1/1152 ( q^4-20*q^3+142*q^2-420*q+441 )
        q congruent 4 modulo 60:   1/1152 q ( q^3-20*q^2+124*q-240 )
        q congruent 5 modulo 60:   1/1152 ( q^4-20*q^3+142*q^2-420*q+425 )
        q congruent 7 modulo 60:   1/1152 ( q^4-20*q^3+142*q^2-420*q+441 )
        q congruent 8 modulo 60:   1/1152 ( q^4-20*q^3+124*q^2-240*q+128 )
        q congruent 9 modulo 60:   1/1152 phi1 ( q^3-19*q^2+123*q-297 )
        q congruent 11 modulo 60:   1/1152 ( q^4-20*q^3+142*q^2-420*q+569 )
        q congruent 13 modulo 60:   1/1152 phi1 ( q^3-19*q^2+123*q-297 )
        q congruent 16 modulo 60:   1/1152 q ( q^3-20*q^2+124*q-240 )
        q congruent 17 modulo 60:   1/1152 ( q^4-20*q^3+142*q^2-420*q+425 )
        q congruent 19 modulo 60:   1/1152 ( q^4-20*q^3+142*q^2-420*q+441 )
        q congruent 21 modulo 60:   1/1152 phi1 ( q^3-19*q^2+123*q-297 )
        q congruent 23 modulo 60:   1/1152 ( q^4-20*q^3+142*q^2-420*q+569 )
        q congruent 25 modulo 60:   1/1152 phi1 ( q^3-19*q^2+123*q-297 )
        q congruent 27 modulo 60:   1/1152 ( q^4-20*q^3+142*q^2-420*q+441 )
        q congruent 29 modulo 60:   1/1152 ( q^4-20*q^3+142*q^2-420*q+425 )
        q congruent 31 modulo 60:   1/1152 ( q^4-20*q^3+142*q^2-420*q+441 )
        q congruent 32 modulo 60:   1/1152 ( q^4-20*q^3+124*q^2-240*q+128 )
        q congruent 37 modulo 60:   1/1152 phi1 ( q^3-19*q^2+123*q-297 )
        q congruent 41 modulo 60:   1/1152 ( q^4-20*q^3+142*q^2-420*q+425 )
        q congruent 43 modulo 60:   1/1152 ( q^4-20*q^3+142*q^2-420*q+441 )
        q congruent 47 modulo 60:   1/1152 ( q^4-20*q^3+142*q^2-420*q+569 )
        q congruent 49 modulo 60:   1/1152 phi1 ( q^3-19*q^2+123*q-297 )
        q congruent 53 modulo 60:   1/1152 ( q^4-20*q^3+142*q^2-420*q+425 )
        q congruent 59 modulo 60:   1/1152 ( q^4-20*q^3+142*q^2-420*q+569 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 5, 2, 69, 71, 67, 5, 5, 17, 27, 9, 71, 71 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 12 ], [ 3, 1, 2, 32 ], [ 4, 1, 2, 24 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 2, 24 ], [ 11, 1, 2, 96 ], [ 12, 1, 2, 96 ], 
  [ 13, 1, 4, 144 ], [ 23, 1, 2, 24 ], [ 24, 1, 2, 72 ], [ 25, 1, 3, 48 ], 
  [ 27, 1, 6, 192 ], [ 28, 1, 4, 288 ], [ 39, 1, 3, 144 ], [ 40, 1, 6, 192 ], 
  [ 41, 1, 9, 288 ], [ 44, 1, 10, 576 ], [ 52, 1, 10, 576 ] ]

    k = 3: F-action on Pi is ()      [59,1,3]
      Dynkin type is D_4(q) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/64 phi1^2 ( q^2-6*q+9 )
        q congruent 2 modulo 60:   1/64 q ( q^3-8*q^2+20*q-16 )
        q congruent 3 modulo 60:   1/64 phi1^2 ( q^2-6*q+9 )
        q congruent 4 modulo 60:   1/64 q ( q^3-8*q^2+20*q-16 )
        q congruent 5 modulo 60:   1/64 phi1^2 ( q^2-6*q+9 )
        q congruent 7 modulo 60:   1/64 phi1^2 ( q^2-6*q+9 )
        q congruent 8 modulo 60:   1/64 q ( q^3-8*q^2+20*q-16 )
        q congruent 9 modulo 60:   1/64 phi1^2 ( q^2-6*q+9 )
        q congruent 11 modulo 60:   1/64 phi1^2 ( q^2-6*q+9 )
        q congruent 13 modulo 60:   1/64 phi1^2 ( q^2-6*q+9 )
        q congruent 16 modulo 60:   1/64 q ( q^3-8*q^2+20*q-16 )
        q congruent 17 modulo 60:   1/64 phi1^2 ( q^2-6*q+9 )
        q congruent 19 modulo 60:   1/64 phi1^2 ( q^2-6*q+9 )
        q congruent 21 modulo 60:   1/64 phi1^2 ( q^2-6*q+9 )
        q congruent 23 modulo 60:   1/64 phi1^2 ( q^2-6*q+9 )
        q congruent 25 modulo 60:   1/64 phi1^2 ( q^2-6*q+9 )
        q congruent 27 modulo 60:   1/64 phi1^2 ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/64 phi1^2 ( q^2-6*q+9 )
        q congruent 31 modulo 60:   1/64 phi1^2 ( q^2-6*q+9 )
        q congruent 32 modulo 60:   1/64 q ( q^3-8*q^2+20*q-16 )
        q congruent 37 modulo 60:   1/64 phi1^2 ( q^2-6*q+9 )
        q congruent 41 modulo 60:   1/64 phi1^2 ( q^2-6*q+9 )
        q congruent 43 modulo 60:   1/64 phi1^2 ( q^2-6*q+9 )
        q congruent 47 modulo 60:   1/64 phi1^2 ( q^2-6*q+9 )
        q congruent 49 modulo 60:   1/64 phi1^2 ( q^2-6*q+9 )
        q congruent 53 modulo 60:   1/64 phi1^2 ( q^2-6*q+9 )
        q congruent 59 modulo 60:   1/64 phi1^2 ( q^2-6*q+9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 7, 5, 68, 76, 69, 3, 7, 18, 30, 31, 72, 76 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 8 ], 
  [ 13, 1, 2, 16 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 8 ], [ 23, 1, 1, 4 ], 
  [ 23, 1, 2, 4 ], [ 24, 1, 1, 12 ], [ 24, 1, 2, 12 ], [ 25, 1, 1, 8 ], 
  [ 25, 1, 3, 8 ], [ 28, 1, 2, 16 ], [ 28, 1, 3, 16 ], [ 39, 1, 1, 8 ], 
  [ 39, 1, 2, 16 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 16 ], [ 41, 1, 1, 16 ], 
  [ 41, 1, 2, 32 ], [ 41, 1, 6, 32 ], [ 41, 1, 9, 16 ], [ 44, 1, 5, 32 ], 
  [ 44, 1, 9, 32 ], [ 52, 1, 2, 32 ], [ 52, 1, 9, 32 ] ]

    k = 4: F-action on Pi is ()      [59,1,4]
      Dynkin type is D_4(q) + T(phi1^2 phi3)
      Order of center |Z^F|: phi1^2 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 2 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 3 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 4 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 5 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 7 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 8 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 9 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 11 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 13 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 16 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 17 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 19 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 21 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 23 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 25 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 27 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 29 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 31 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 32 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 37 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 41 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 43 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 47 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 49 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 53 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 59 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 8, 30, 27, 77, 97, 81, 30, 30, 53, 14, 36, 97, 97 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 6 ], [ 9, 1, 1, 3 ], 
  [ 12, 1, 1, 6 ], [ 23, 1, 1, 6 ], [ 25, 1, 1, 12 ], [ 27, 1, 5, 6 ], 
  [ 40, 1, 1, 12 ], [ 44, 1, 3, 18 ] ]

    k = 5: F-action on Pi is ()      [59,1,5]
      Dynkin type is D_4(q) + T(phi2^2 phi6)
      Order of center |Z^F|: phi2^2 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/36 q^2 phi1^2
        q congruent 2 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 3 modulo 60:   1/36 q^2 phi1^2
        q congruent 4 modulo 60:   1/36 q^2 phi1^2
        q congruent 5 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 7 modulo 60:   1/36 q^2 phi1^2
        q congruent 8 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 9 modulo 60:   1/36 q^2 phi1^2
        q congruent 11 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 13 modulo 60:   1/36 q^2 phi1^2
        q congruent 16 modulo 60:   1/36 q^2 phi1^2
        q congruent 17 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 19 modulo 60:   1/36 q^2 phi1^2
        q congruent 21 modulo 60:   1/36 q^2 phi1^2
        q congruent 23 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 25 modulo 60:   1/36 q^2 phi1^2
        q congruent 27 modulo 60:   1/36 q^2 phi1^2
        q congruent 29 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 31 modulo 60:   1/36 q^2 phi1^2
        q congruent 32 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 37 modulo 60:   1/36 q^2 phi1^2
        q congruent 41 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 43 modulo 60:   1/36 q^2 phi1^2
        q congruent 47 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 49 modulo 60:   1/36 q^2 phi1^2
        q congruent 53 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 59 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 28, 31, 9, 82, 98, 78, 31, 31, 54, 36, 15, 98, 98 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 3 ], 
  [ 12, 1, 2, 6 ], [ 23, 1, 2, 6 ], [ 25, 1, 3, 12 ], [ 27, 1, 4, 6 ], 
  [ 40, 1, 6, 12 ], [ 44, 1, 7, 18 ] ]

    k = 6: F-action on Pi is ()      [59,1,6]
      Dynkin type is D_4(q) + T(phi4^2)
      Order of center |Z^F|: phi4^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/96 phi1 phi2 ( q^2-9 )
        q congruent 2 modulo 60:   1/96 q^2 ( q^2-4 )
        q congruent 3 modulo 60:   1/96 phi1 phi2 ( q^2-9 )
        q congruent 4 modulo 60:   1/96 q^2 ( q^2-4 )
        q congruent 5 modulo 60:   1/96 phi1 phi2 ( q^2-9 )
        q congruent 7 modulo 60:   1/96 phi1 phi2 ( q^2-9 )
        q congruent 8 modulo 60:   1/96 q^2 ( q^2-4 )
        q congruent 9 modulo 60:   1/96 phi1 phi2 ( q^2-9 )
        q congruent 11 modulo 60:   1/96 phi1 phi2 ( q^2-9 )
        q congruent 13 modulo 60:   1/96 phi1 phi2 ( q^2-9 )
        q congruent 16 modulo 60:   1/96 q^2 ( q^2-4 )
        q congruent 17 modulo 60:   1/96 phi1 phi2 ( q^2-9 )
        q congruent 19 modulo 60:   1/96 phi1 phi2 ( q^2-9 )
        q congruent 21 modulo 60:   1/96 phi1 phi2 ( q^2-9 )
        q congruent 23 modulo 60:   1/96 phi1 phi2 ( q^2-9 )
        q congruent 25 modulo 60:   1/96 phi1 phi2 ( q^2-9 )
        q congruent 27 modulo 60:   1/96 phi1 phi2 ( q^2-9 )
        q congruent 29 modulo 60:   1/96 phi1 phi2 ( q^2-9 )
        q congruent 31 modulo 60:   1/96 phi1 phi2 ( q^2-9 )
        q congruent 32 modulo 60:   1/96 q^2 ( q^2-4 )
        q congruent 37 modulo 60:   1/96 phi1 phi2 ( q^2-9 )
        q congruent 41 modulo 60:   1/96 phi1 phi2 ( q^2-9 )
        q congruent 43 modulo 60:   1/96 phi1 phi2 ( q^2-9 )
        q congruent 47 modulo 60:   1/96 phi1 phi2 ( q^2-9 )
        q congruent 49 modulo 60:   1/96 phi1 phi2 ( q^2-9 )
        q congruent 53 modulo 60:   1/96 phi1 phi2 ( q^2-9 )
        q congruent 59 modulo 60:   1/96 phi1 phi2 ( q^2-9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 16, 18, 17, 73, 75, 74, 18, 18, 6, 53, 54, 75, 75 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 9, 1, 1, 3 ], [ 39, 1, 5, 24 ], [ 41, 1, 5, 48 ] ]

    k = 7: F-action on Pi is (2,3,5)      [59,1,7]
      Dynkin type is ^3D_4(q) + T(phi1^2 phi3)
      Order of center |Z^F|: phi1^2 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 2 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 3 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 4 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 5 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 7 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 8 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 9 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 11 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 13 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 16 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 17 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 19 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 21 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 23 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 25 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 27 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 29 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 31 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 32 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 37 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 41 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 43 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 47 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 49 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 53 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 59 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 14, 87, 83, 35, 12, 57, 33 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 1, 2 ], [ 10, 1, 1, 6 ], 
  [ 11, 1, 1, 6 ], [ 27, 1, 1, 12 ], [ 40, 1, 5, 6 ], [ 52, 1, 6, 18 ] ]

    k = 8: F-action on Pi is (2,5,3)      [59,1,8]
      Dynkin type is ^3D_4(q) + T(phi2^2 phi6)
      Order of center |Z^F|: phi2^2 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/36 q^2 phi1^2
        q congruent 2 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 3 modulo 60:   1/36 q^2 phi1^2
        q congruent 4 modulo 60:   1/36 q^2 phi1^2
        q congruent 5 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 7 modulo 60:   1/36 q^2 phi1^2
        q congruent 8 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 9 modulo 60:   1/36 q^2 phi1^2
        q congruent 11 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 13 modulo 60:   1/36 q^2 phi1^2
        q congruent 16 modulo 60:   1/36 q^2 phi1^2
        q congruent 17 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 19 modulo 60:   1/36 q^2 phi1^2
        q congruent 21 modulo 60:   1/36 q^2 phi1^2
        q congruent 23 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 25 modulo 60:   1/36 q^2 phi1^2
        q congruent 27 modulo 60:   1/36 q^2 phi1^2
        q congruent 29 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 31 modulo 60:   1/36 q^2 phi1^2
        q congruent 32 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 37 modulo 60:   1/36 q^2 phi1^2
        q congruent 41 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 43 modulo 60:   1/36 q^2 phi1^2
        q congruent 47 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 49 modulo 60:   1/36 q^2 phi1^2
        q congruent 53 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 59 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 35, 84, 88, 15, 34, 58, 13 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 3 ], [ 3, 1, 2, 2 ], [ 10, 1, 2, 6 ], 
  [ 11, 1, 2, 6 ], [ 27, 1, 6, 12 ], [ 40, 1, 4, 6 ], [ 52, 1, 7, 18 ] ]

    k = 9: F-action on Pi is (2,3,5)      [59,1,9]
      Dynkin type is ^3D_4(q) + T(phi3^2)
      Order of center |Z^F|: phi3^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/72 phi1 ( q^3+3*q^2-2*q-8 )
        q congruent 2 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 3 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 4 modulo 60:   1/72 phi1 ( q^3+3*q^2-2*q-8 )
        q congruent 5 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 7 modulo 60:   1/72 phi1 ( q^3+3*q^2-2*q-8 )
        q congruent 8 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 9 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 11 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 13 modulo 60:   1/72 phi1 ( q^3+3*q^2-2*q-8 )
        q congruent 16 modulo 60:   1/72 phi1 ( q^3+3*q^2-2*q-8 )
        q congruent 17 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 19 modulo 60:   1/72 phi1 ( q^3+3*q^2-2*q-8 )
        q congruent 21 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 23 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 25 modulo 60:   1/72 phi1 ( q^3+3*q^2-2*q-8 )
        q congruent 27 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 29 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 31 modulo 60:   1/72 phi1 ( q^3+3*q^2-2*q-8 )
        q congruent 32 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 37 modulo 60:   1/72 phi1 ( q^3+3*q^2-2*q-8 )
        q congruent 41 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 43 modulo 60:   1/72 phi1 ( q^3+3*q^2-2*q-8 )
        q congruent 47 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 49 modulo 60:   1/72 phi1 ( q^3+3*q^2-2*q-8 )
        q congruent 53 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 59 modulo 60:   1/72 q phi2 ( q^2+q-6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 12, 85, 79, 34, 10, 55, 29 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 27, 1, 5, 24 ], [ 40, 1, 5, 24 ] ]

    k = 10: F-action on Pi is (2,3,5)      [59,1,10]
      Dynkin type is ^3D_4(q) + T(phi6^2)
      Order of center |Z^F|: phi6^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 2 modulo 60:   1/72 phi2 ( q^3-3*q^2-2*q+8 )
        q congruent 3 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 4 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 5 modulo 60:   1/72 phi2 ( q^3-3*q^2-2*q+8 )
        q congruent 7 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 8 modulo 60:   1/72 phi2 ( q^3-3*q^2-2*q+8 )
        q congruent 9 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 11 modulo 60:   1/72 phi2 ( q^3-3*q^2-2*q+8 )
        q congruent 13 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 16 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 17 modulo 60:   1/72 phi2 ( q^3-3*q^2-2*q+8 )
        q congruent 19 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 21 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 23 modulo 60:   1/72 phi2 ( q^3-3*q^2-2*q+8 )
        q congruent 25 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 27 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 29 modulo 60:   1/72 phi2 ( q^3-3*q^2-2*q+8 )
        q congruent 31 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 32 modulo 60:   1/72 phi2 ( q^3-3*q^2-2*q+8 )
        q congruent 37 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 41 modulo 60:   1/72 phi2 ( q^3-3*q^2-2*q+8 )
        q congruent 43 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 47 modulo 60:   1/72 phi2 ( q^3-3*q^2-2*q+8 )
        q congruent 49 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 53 modulo 60:   1/72 phi2 ( q^3-3*q^2-2*q+8 )
        q congruent 59 modulo 60:   1/72 phi2 ( q^3-3*q^2-2*q+8 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 33, 80, 86, 13, 29, 56, 11 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 27, 1, 4, 24 ], [ 40, 1, 4, 24 ] ]

    k = 11: F-action on Pi is (2,3,5)      [59,1,11]
      Dynkin type is ^3D_4(q) + T(phi12)
      Order of center |Z^F|: phi12
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 2 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 3 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 4 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 5 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 7 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 8 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 9 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 11 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 13 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 16 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 17 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 19 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 21 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 23 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 25 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 27 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 29 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 31 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 32 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 37 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 41 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 43 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 47 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 49 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 53 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 59 modulo 60:   1/12 q^2 phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 57, 102, 101, 58, 55, 32, 56 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]

    k = 12: F-action on Pi is ()      [59,1,12]
      Dynkin type is D_4(q) + T(phi1^3 phi2)
      Order of center |Z^F|: phi1^3 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/96 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 2 modulo 60:   1/96 q ( q^3-12*q^2+44*q-48 )
        q congruent 3 modulo 60:   1/96 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 4 modulo 60:   1/96 q ( q^3-12*q^2+44*q-48 )
        q congruent 5 modulo 60:   1/96 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 7 modulo 60:   1/96 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 8 modulo 60:   1/96 q ( q^3-12*q^2+44*q-48 )
        q congruent 9 modulo 60:   1/96 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 11 modulo 60:   1/96 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 13 modulo 60:   1/96 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 16 modulo 60:   1/96 q ( q^3-12*q^2+44*q-48 )
        q congruent 17 modulo 60:   1/96 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 19 modulo 60:   1/96 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 21 modulo 60:   1/96 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 23 modulo 60:   1/96 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 25 modulo 60:   1/96 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 27 modulo 60:   1/96 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 29 modulo 60:   1/96 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 31 modulo 60:   1/96 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 32 modulo 60:   1/96 q ( q^3-12*q^2+44*q-48 )
        q congruent 37 modulo 60:   1/96 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 41 modulo 60:   1/96 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 43 modulo 60:   1/96 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 47 modulo 60:   1/96 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 49 modulo 60:   1/96 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 53 modulo 60:   1/96 phi1 ( q^3-11*q^2+39*q-45 )
        q congruent 59 modulo 60:   1/96 phi1 ( q^3-11*q^2+39*q-45 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 68, 69, 4, 19, 7, 68, 68, 73, 77, 82, 19, 19 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 12 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 8 ], 
  [ 12, 1, 1, 24 ], [ 13, 1, 1, 24 ], [ 23, 1, 1, 12 ], [ 24, 1, 1, 18 ], 
  [ 24, 1, 2, 6 ], [ 25, 1, 1, 24 ], [ 27, 1, 2, 16 ], [ 28, 1, 1, 24 ], 
  [ 28, 1, 2, 24 ], [ 39, 1, 1, 24 ], [ 39, 1, 4, 12 ], [ 40, 1, 1, 48 ], 
  [ 41, 1, 1, 48 ], [ 41, 1, 6, 24 ], [ 44, 1, 2, 48 ], [ 52, 1, 1, 48 ], 
  [ 52, 1, 2, 48 ] ]

    k = 13: F-action on Pi is ()      [59,1,13]
      Dynkin type is D_4(q) + T(phi1 phi2^3)
      Order of center |Z^F|: phi1 phi2^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/96 phi1 ( q^3-7*q^2+19*q-21 )
        q congruent 2 modulo 60:   1/96 q ( q^3-8*q^2+20*q-16 )
        q congruent 3 modulo 60:   1/96 phi1 ( q^3-7*q^2+19*q-21 )
        q congruent 4 modulo 60:   1/96 q ( q^3-8*q^2+20*q-16 )
        q congruent 5 modulo 60:   1/96 phi1 ( q^3-7*q^2+19*q-21 )
        q congruent 7 modulo 60:   1/96 phi1 ( q^3-7*q^2+19*q-21 )
        q congruent 8 modulo 60:   1/96 q ( q^3-8*q^2+20*q-16 )
        q congruent 9 modulo 60:   1/96 phi1 ( q^3-7*q^2+19*q-21 )
        q congruent 11 modulo 60:   1/96 phi1 ( q^3-7*q^2+19*q-21 )
        q congruent 13 modulo 60:   1/96 phi1 ( q^3-7*q^2+19*q-21 )
        q congruent 16 modulo 60:   1/96 q ( q^3-8*q^2+20*q-16 )
        q congruent 17 modulo 60:   1/96 phi1 ( q^3-7*q^2+19*q-21 )
        q congruent 19 modulo 60:   1/96 phi1 ( q^3-7*q^2+19*q-21 )
        q congruent 21 modulo 60:   1/96 phi1 ( q^3-7*q^2+19*q-21 )
        q congruent 23 modulo 60:   1/96 phi1 ( q^3-7*q^2+19*q-21 )
        q congruent 25 modulo 60:   1/96 phi1 ( q^3-7*q^2+19*q-21 )
        q congruent 27 modulo 60:   1/96 phi1 ( q^3-7*q^2+19*q-21 )
        q congruent 29 modulo 60:   1/96 phi1 ( q^3-7*q^2+19*q-21 )
        q congruent 31 modulo 60:   1/96 phi1 ( q^3-7*q^2+19*q-21 )
        q congruent 32 modulo 60:   1/96 q ( q^3-8*q^2+20*q-16 )
        q congruent 37 modulo 60:   1/96 phi1 ( q^3-7*q^2+19*q-21 )
        q congruent 41 modulo 60:   1/96 phi1 ( q^3-7*q^2+19*q-21 )
        q congruent 43 modulo 60:   1/96 phi1 ( q^3-7*q^2+19*q-21 )
        q congruent 47 modulo 60:   1/96 phi1 ( q^3-7*q^2+19*q-21 )
        q congruent 49 modulo 60:   1/96 phi1 ( q^3-7*q^2+19*q-21 )
        q congruent 53 modulo 60:   1/96 phi1 ( q^3-7*q^2+19*q-21 )
        q congruent 59 modulo 60:   1/96 phi1 ( q^3-7*q^2+19*q-21 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 69, 67, 7, 20, 5, 69, 69, 74, 81, 78, 20, 20 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 2, 12 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], 
  [ 12, 1, 2, 24 ], [ 13, 1, 4, 24 ], [ 23, 1, 2, 12 ], [ 24, 1, 1, 6 ], 
  [ 24, 1, 2, 18 ], [ 25, 1, 3, 24 ], [ 27, 1, 3, 16 ], [ 28, 1, 3, 24 ], 
  [ 28, 1, 4, 24 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 12 ], [ 40, 1, 6, 48 ], 
  [ 41, 1, 6, 24 ], [ 41, 1, 9, 48 ], [ 44, 1, 8, 48 ], [ 52, 1, 9, 48 ], 
  [ 52, 1, 10, 48 ] ]

    k = 14: F-action on Pi is (2,3,5)      [59,1,14]
      Dynkin type is ^3D_4(q) + T(phi1 phi2 phi3)
      Order of center |Z^F|: phi1 phi2 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 2 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 3 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 4 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 5 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 7 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 8 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 9 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 11 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 13 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 16 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 17 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 19 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 21 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 23 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 25 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 27 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 29 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 31 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 32 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 37 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 41 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 43 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 47 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 49 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 53 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 59 modulo 60:   1/12 q^2 phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 83, 40, 37, 88, 79, 101, 86 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 10, 1, 2, 2 ], 
  [ 11, 1, 1, 2 ], [ 27, 1, 2, 4 ], [ 40, 1, 5, 6 ], [ 52, 1, 6, 6 ] ]

    k = 15: F-action on Pi is (2,5,3)      [59,1,15]
      Dynkin type is ^3D_4(q) + T(phi1 phi2 phi6)
      Order of center |Z^F|: phi1 phi2 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 2 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 3 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 4 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 5 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 7 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 8 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 9 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 11 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 13 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 16 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 17 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 19 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 21 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 23 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 25 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 27 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 29 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 31 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 32 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 37 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 41 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 43 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 47 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 49 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 53 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 59 modulo 60:   1/12 q phi1 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 87, 38, 40, 84, 85, 102, 80 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 10, 1, 1, 2 ], 
  [ 11, 1, 2, 2 ], [ 27, 1, 3, 4 ], [ 40, 1, 4, 6 ], [ 52, 1, 7, 6 ] ]

    k = 16: F-action on Pi is ()      [59,1,16]
      Dynkin type is D_4(q) + T(phi1 phi2 phi4)
      Order of center |Z^F|: phi1 phi2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 phi2 ( q^2-2*q-1 )
        q congruent 2 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 3 modulo 60:   1/16 phi1 phi2 ( q^2-2*q-1 )
        q congruent 4 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 5 modulo 60:   1/16 phi1 phi2 ( q^2-2*q-1 )
        q congruent 7 modulo 60:   1/16 phi1 phi2 ( q^2-2*q-1 )
        q congruent 8 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 9 modulo 60:   1/16 phi1 phi2 ( q^2-2*q-1 )
        q congruent 11 modulo 60:   1/16 phi1 phi2 ( q^2-2*q-1 )
        q congruent 13 modulo 60:   1/16 phi1 phi2 ( q^2-2*q-1 )
        q congruent 16 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 17 modulo 60:   1/16 phi1 phi2 ( q^2-2*q-1 )
        q congruent 19 modulo 60:   1/16 phi1 phi2 ( q^2-2*q-1 )
        q congruent 21 modulo 60:   1/16 phi1 phi2 ( q^2-2*q-1 )
        q congruent 23 modulo 60:   1/16 phi1 phi2 ( q^2-2*q-1 )
        q congruent 25 modulo 60:   1/16 phi1 phi2 ( q^2-2*q-1 )
        q congruent 27 modulo 60:   1/16 phi1 phi2 ( q^2-2*q-1 )
        q congruent 29 modulo 60:   1/16 phi1 phi2 ( q^2-2*q-1 )
        q congruent 31 modulo 60:   1/16 phi1 phi2 ( q^2-2*q-1 )
        q congruent 32 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 37 modulo 60:   1/16 phi1 phi2 ( q^2-2*q-1 )
        q congruent 41 modulo 60:   1/16 phi1 phi2 ( q^2-2*q-1 )
        q congruent 43 modulo 60:   1/16 phi1 phi2 ( q^2-2*q-1 )
        q congruent 47 modulo 60:   1/16 phi1 phi2 ( q^2-2*q-1 )
        q congruent 49 modulo 60:   1/16 phi1 phi2 ( q^2-2*q-1 )
        q congruent 53 modulo 60:   1/16 phi1 phi2 ( q^2-2*q-1 )
        q congruent 59 modulo 60:   1/16 phi1 phi2 ( q^2-2*q-1 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 70, 76, 71, 19, 22, 20, 72, 76, 75, 97, 98, 18, 22 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 3 ], 
  [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], 
  [ 25, 1, 1, 4 ], [ 25, 1, 3, 4 ], [ 39, 1, 2, 4 ], [ 39, 1, 5, 4 ], 
  [ 41, 1, 2, 8 ], [ 41, 1, 5, 8 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 8 ] ]

    k = 17: F-action on Pi is (2,5)      [59,1,17]
      Dynkin type is ^2D_4(q) + T(phi1^3 phi2)
      Order of center |Z^F|: phi1^3 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/96 phi1 ( q^3-11*q^2+33*q-15 )
        q congruent 2 modulo 60:   1/96 q ( q^3-12*q^2+44*q-48 )
        q congruent 3 modulo 60:   1/96 ( q^4-12*q^3+44*q^2-48*q-9 )
        q congruent 4 modulo 60:   1/96 q ( q^3-12*q^2+44*q-48 )
        q congruent 5 modulo 60:   1/96 phi1 ( q^3-11*q^2+33*q-15 )
        q congruent 7 modulo 60:   1/96 ( q^4-12*q^3+44*q^2-48*q-9 )
        q congruent 8 modulo 60:   1/96 q ( q^3-12*q^2+44*q-48 )
        q congruent 9 modulo 60:   1/96 phi1 ( q^3-11*q^2+33*q-15 )
        q congruent 11 modulo 60:   1/96 ( q^4-12*q^3+44*q^2-48*q-9 )
        q congruent 13 modulo 60:   1/96 phi1 ( q^3-11*q^2+33*q-15 )
        q congruent 16 modulo 60:   1/96 q ( q^3-12*q^2+44*q-48 )
        q congruent 17 modulo 60:   1/96 phi1 ( q^3-11*q^2+33*q-15 )
        q congruent 19 modulo 60:   1/96 ( q^4-12*q^3+44*q^2-48*q-9 )
        q congruent 21 modulo 60:   1/96 phi1 ( q^3-11*q^2+33*q-15 )
        q congruent 23 modulo 60:   1/96 ( q^4-12*q^3+44*q^2-48*q-9 )
        q congruent 25 modulo 60:   1/96 phi1 ( q^3-11*q^2+33*q-15 )
        q congruent 27 modulo 60:   1/96 ( q^4-12*q^3+44*q^2-48*q-9 )
        q congruent 29 modulo 60:   1/96 phi1 ( q^3-11*q^2+33*q-15 )
        q congruent 31 modulo 60:   1/96 ( q^4-12*q^3+44*q^2-48*q-9 )
        q congruent 32 modulo 60:   1/96 q ( q^3-12*q^2+44*q-48 )
        q congruent 37 modulo 60:   1/96 phi1 ( q^3-11*q^2+33*q-15 )
        q congruent 41 modulo 60:   1/96 phi1 ( q^3-11*q^2+33*q-15 )
        q congruent 43 modulo 60:   1/96 ( q^4-12*q^3+44*q^2-48*q-9 )
        q congruent 47 modulo 60:   1/96 ( q^4-12*q^3+44*q^2-48*q-9 )
        q congruent 49 modulo 60:   1/96 phi1 ( q^3-11*q^2+33*q-15 )
        q congruent 53 modulo 60:   1/96 phi1 ( q^3-11*q^2+33*q-15 )
        q congruent 59 modulo 60:   1/96 ( q^4-12*q^3+44*q^2-48*q-9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 3, 70, 68, 72, 19, 28, 30, 89 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 2 ], 
  [ 4, 1, 2, 6 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], 
  [ 12, 1, 1, 8 ], [ 13, 1, 1, 12 ], [ 13, 1, 3, 24 ], [ 13, 1, 4, 12 ], 
  [ 23, 1, 1, 6 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 12 ], [ 25, 1, 2, 12 ], 
  [ 25, 1, 4, 4 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 24 ], [ 28, 1, 3, 24 ], 
  [ 39, 1, 1, 24 ], [ 39, 1, 2, 12 ], [ 40, 1, 3, 16 ], [ 41, 1, 3, 48 ], 
  [ 41, 1, 4, 24 ], [ 44, 1, 1, 48 ], [ 44, 1, 9, 48 ], [ 52, 1, 3, 48 ] ]

    k = 18: F-action on Pi is (2,5)      [59,1,18]
      Dynkin type is ^2D_4(q) + T(phi1 phi2^3)
      Order of center |Z^F|: phi1 phi2^3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/96 phi1 ( q^3-7*q^2+13*q-15 )
        q congruent 2 modulo 60:   1/96 q ( q^3-8*q^2+20*q-16 )
        q congruent 3 modulo 60:   1/96 ( q^4-8*q^3+20*q^2-28*q+39 )
        q congruent 4 modulo 60:   1/96 q ( q^3-8*q^2+20*q-16 )
        q congruent 5 modulo 60:   1/96 phi1 ( q^3-7*q^2+13*q-15 )
        q congruent 7 modulo 60:   1/96 ( q^4-8*q^3+20*q^2-28*q+39 )
        q congruent 8 modulo 60:   1/96 q ( q^3-8*q^2+20*q-16 )
        q congruent 9 modulo 60:   1/96 phi1 ( q^3-7*q^2+13*q-15 )
        q congruent 11 modulo 60:   1/96 ( q^4-8*q^3+20*q^2-28*q+39 )
        q congruent 13 modulo 60:   1/96 phi1 ( q^3-7*q^2+13*q-15 )
        q congruent 16 modulo 60:   1/96 q ( q^3-8*q^2+20*q-16 )
        q congruent 17 modulo 60:   1/96 phi1 ( q^3-7*q^2+13*q-15 )
        q congruent 19 modulo 60:   1/96 ( q^4-8*q^3+20*q^2-28*q+39 )
        q congruent 21 modulo 60:   1/96 phi1 ( q^3-7*q^2+13*q-15 )
        q congruent 23 modulo 60:   1/96 ( q^4-8*q^3+20*q^2-28*q+39 )
        q congruent 25 modulo 60:   1/96 phi1 ( q^3-7*q^2+13*q-15 )
        q congruent 27 modulo 60:   1/96 ( q^4-8*q^3+20*q^2-28*q+39 )
        q congruent 29 modulo 60:   1/96 phi1 ( q^3-7*q^2+13*q-15 )
        q congruent 31 modulo 60:   1/96 ( q^4-8*q^3+20*q^2-28*q+39 )
        q congruent 32 modulo 60:   1/96 q ( q^3-8*q^2+20*q-16 )
        q congruent 37 modulo 60:   1/96 phi1 ( q^3-7*q^2+13*q-15 )
        q congruent 41 modulo 60:   1/96 phi1 ( q^3-7*q^2+13*q-15 )
        q congruent 43 modulo 60:   1/96 ( q^4-8*q^3+20*q^2-28*q+39 )
        q congruent 47 modulo 60:   1/96 ( q^4-8*q^3+20*q^2-28*q+39 )
        q congruent 49 modulo 60:   1/96 phi1 ( q^3-7*q^2+13*q-15 )
        q congruent 53 modulo 60:   1/96 phi1 ( q^3-7*q^2+13*q-15 )
        q congruent 59 modulo 60:   1/96 ( q^4-8*q^3+20*q^2-28*q+39 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 5, 72, 69, 71, 20, 31, 27, 90 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 6 ], 
  [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 24 ], 
  [ 12, 1, 2, 8 ], [ 13, 1, 1, 12 ], [ 13, 1, 2, 24 ], [ 13, 1, 4, 12 ], 
  [ 23, 1, 1, 2 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 2, 4 ], 
  [ 25, 1, 4, 12 ], [ 27, 1, 6, 48 ], [ 28, 1, 2, 24 ], [ 28, 1, 4, 24 ], 
  [ 39, 1, 2, 12 ], [ 39, 1, 3, 24 ], [ 40, 1, 2, 16 ], [ 41, 1, 4, 24 ], 
  [ 41, 1, 10, 48 ], [ 44, 1, 5, 48 ], [ 44, 1, 10, 48 ], [ 52, 1, 4, 48 ] ]

    k = 19: F-action on Pi is (2,5)      [59,1,19]
      Dynkin type is ^2D_4(q) + T(phi1 phi2 phi3)
      Order of center |Z^F|: phi1 phi2 phi3
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 2 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 3 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 4 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 5 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 7 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 8 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 9 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 11 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 13 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 16 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 17 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 19 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 21 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 23 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 25 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 27 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 29 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 31 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 32 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 37 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 41 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 43 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 47 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 49 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 53 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 59 modulo 60:   1/12 q^2 phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 30, 27, 97, 81, 95, 59, 36, 37, 109 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], 
  [ 12, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 27, 1, 5, 6 ], 
  [ 40, 1, 3, 4 ], [ 44, 1, 3, 6 ] ]

    k = 20: F-action on Pi is (2,3)      [59,1,20]
      Dynkin type is ^2D_4(q) + T(phi1 phi2 phi6)
      Order of center |Z^F|: phi1 phi2 phi6
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 2 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 3 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 4 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 5 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 7 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 8 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 9 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 11 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 13 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 16 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 17 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 19 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 21 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 23 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 25 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 27 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 29 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 31 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 32 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 37 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 41 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 43 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 47 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 49 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 53 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 59 modulo 60:   1/12 q phi1 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 28, 31, 96, 82, 98, 60, 38, 36, 110 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], 
  [ 12, 1, 2, 2 ], [ 23, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 27, 1, 4, 6 ], 
  [ 40, 1, 2, 4 ], [ 44, 1, 7, 6 ] ]

    k = 21: F-action on Pi is (2,3)      [59,1,21]
      Dynkin type is ^2D_4(q) + T(phi1 phi2 phi4)
      Order of center |Z^F|: phi1 phi2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1^3 phi2
        q congruent 2 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 3 modulo 60:   1/16 phi1^3 phi2
        q congruent 4 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 5 modulo 60:   1/16 phi1^3 phi2
        q congruent 7 modulo 60:   1/16 phi1^3 phi2
        q congruent 8 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 9 modulo 60:   1/16 phi1^3 phi2
        q congruent 11 modulo 60:   1/16 phi1^3 phi2
        q congruent 13 modulo 60:   1/16 phi1^3 phi2
        q congruent 16 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 17 modulo 60:   1/16 phi1^3 phi2
        q congruent 19 modulo 60:   1/16 phi1^3 phi2
        q congruent 21 modulo 60:   1/16 phi1^3 phi2
        q congruent 23 modulo 60:   1/16 phi1^3 phi2
        q congruent 25 modulo 60:   1/16 phi1^3 phi2
        q congruent 27 modulo 60:   1/16 phi1^3 phi2
        q congruent 29 modulo 60:   1/16 phi1^3 phi2
        q congruent 31 modulo 60:   1/16 phi1^3 phi2
        q congruent 32 modulo 60:   1/16 q^3 ( q-2 )
        q congruent 37 modulo 60:   1/16 phi1^3 phi2
        q congruent 41 modulo 60:   1/16 phi1^3 phi2
        q congruent 43 modulo 60:   1/16 phi1^3 phi2
        q congruent 47 modulo 60:   1/16 phi1^3 phi2
        q congruent 49 modulo 60:   1/16 phi1^3 phi2
        q congruent 53 modulo 60:   1/16 phi1^3 phi2
        q congruent 59 modulo 60:   1/16 phi1^3 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 19, 20, 73, 76, 74, 18, 60, 59, 91 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 39, 1, 4, 4 ], 
  [ 39, 1, 5, 4 ], [ 41, 1, 7, 8 ], [ 41, 1, 8, 8 ], [ 52, 1, 5, 8 ], 
  [ 52, 1, 8, 8 ] ]

    k = 22: F-action on Pi is (2,5)      [59,1,22]
      Dynkin type is ^2D_4(q) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 phi4 ( q-3 )
        q congruent 2 modulo 60:   1/16 q^2 ( q^2-4*q+4 )
        q congruent 3 modulo 60:   1/16 phi1 phi4 ( q-3 )
        q congruent 4 modulo 60:   1/16 q^2 ( q^2-4*q+4 )
        q congruent 5 modulo 60:   1/16 phi1 phi4 ( q-3 )
        q congruent 7 modulo 60:   1/16 phi1 phi4 ( q-3 )
        q congruent 8 modulo 60:   1/16 q^2 ( q^2-4*q+4 )
        q congruent 9 modulo 60:   1/16 phi1 phi4 ( q-3 )
        q congruent 11 modulo 60:   1/16 phi1 phi4 ( q-3 )
        q congruent 13 modulo 60:   1/16 phi1 phi4 ( q-3 )
        q congruent 16 modulo 60:   1/16 q^2 ( q^2-4*q+4 )
        q congruent 17 modulo 60:   1/16 phi1 phi4 ( q-3 )
        q congruent 19 modulo 60:   1/16 phi1 phi4 ( q-3 )
        q congruent 21 modulo 60:   1/16 phi1 phi4 ( q-3 )
        q congruent 23 modulo 60:   1/16 phi1 phi4 ( q-3 )
        q congruent 25 modulo 60:   1/16 phi1 phi4 ( q-3 )
        q congruent 27 modulo 60:   1/16 phi1 phi4 ( q-3 )
        q congruent 29 modulo 60:   1/16 phi1 phi4 ( q-3 )
        q congruent 31 modulo 60:   1/16 phi1 phi4 ( q-3 )
        q congruent 32 modulo 60:   1/16 q^2 ( q^2-4*q+4 )
        q congruent 37 modulo 60:   1/16 phi1 phi4 ( q-3 )
        q congruent 41 modulo 60:   1/16 phi1 phi4 ( q-3 )
        q congruent 43 modulo 60:   1/16 phi1 phi4 ( q-3 )
        q congruent 47 modulo 60:   1/16 phi1 phi4 ( q-3 )
        q congruent 49 modulo 60:   1/16 phi1 phi4 ( q-3 )
        q congruent 53 modulo 60:   1/16 phi1 phi4 ( q-3 )
        q congruent 59 modulo 60:   1/16 phi1 phi4 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 69, 19, 7, 20, 76, 82, 81, 43 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], 
  [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 4 ], 
  [ 12, 1, 2, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 1, 2 ], 
  [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], 
  [ 25, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 1, 4 ], 
  [ 28, 1, 2, 4 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], [ 39, 1, 2, 4 ], 
  [ 39, 1, 4, 4 ], [ 40, 1, 2, 8 ], [ 40, 1, 3, 8 ], [ 41, 1, 4, 8 ], 
  [ 41, 1, 7, 8 ], [ 44, 1, 2, 8 ], [ 44, 1, 8, 8 ], [ 52, 1, 3, 8 ], 
  [ 52, 1, 4, 8 ] ]

    k = 23: F-action on Pi is (2,3)      [59,1,23]
      Dynkin type is ^2D_4(q) + T(phi1^2 phi4)
      Order of center |Z^F|: phi1^2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 phi2 ( q^2-6*q+9 )
        q congruent 2 modulo 60:   1/32 q^2 ( q^2-6*q+8 )
        q congruent 3 modulo 60:   1/32 phi1 phi2 ( q^2-6*q+9 )
        q congruent 4 modulo 60:   1/32 q^2 ( q^2-6*q+8 )
        q congruent 5 modulo 60:   1/32 phi1 phi2 ( q^2-6*q+9 )
        q congruent 7 modulo 60:   1/32 phi1 phi2 ( q^2-6*q+9 )
        q congruent 8 modulo 60:   1/32 q^2 ( q^2-6*q+8 )
        q congruent 9 modulo 60:   1/32 phi1 phi2 ( q^2-6*q+9 )
        q congruent 11 modulo 60:   1/32 phi1 phi2 ( q^2-6*q+9 )
        q congruent 13 modulo 60:   1/32 phi1 phi2 ( q^2-6*q+9 )
        q congruent 16 modulo 60:   1/32 q^2 ( q^2-6*q+8 )
        q congruent 17 modulo 60:   1/32 phi1 phi2 ( q^2-6*q+9 )
        q congruent 19 modulo 60:   1/32 phi1 phi2 ( q^2-6*q+9 )
        q congruent 21 modulo 60:   1/32 phi1 phi2 ( q^2-6*q+9 )
        q congruent 23 modulo 60:   1/32 phi1 phi2 ( q^2-6*q+9 )
        q congruent 25 modulo 60:   1/32 phi1 phi2 ( q^2-6*q+9 )
        q congruent 27 modulo 60:   1/32 phi1 phi2 ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/32 phi1 phi2 ( q^2-6*q+9 )
        q congruent 31 modulo 60:   1/32 phi1 phi2 ( q^2-6*q+9 )
        q congruent 32 modulo 60:   1/32 q^2 ( q^2-6*q+8 )
        q congruent 37 modulo 60:   1/32 phi1 phi2 ( q^2-6*q+9 )
        q congruent 41 modulo 60:   1/32 phi1 phi2 ( q^2-6*q+9 )
        q congruent 43 modulo 60:   1/32 phi1 phi2 ( q^2-6*q+9 )
        q congruent 47 modulo 60:   1/32 phi1 phi2 ( q^2-6*q+9 )
        q congruent 49 modulo 60:   1/32 phi1 phi2 ( q^2-6*q+9 )
        q congruent 53 modulo 60:   1/32 phi1 phi2 ( q^2-6*q+9 )
        q congruent 59 modulo 60:   1/32 phi1 phi2 ( q^2-6*q+9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 70, 72, 16, 19, 18, 73, 96, 97, 44 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 1, 4 ], [ 13, 1, 3, 8 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ], 
  [ 25, 1, 2, 8 ], [ 39, 1, 1, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 3, 16 ], 
  [ 41, 1, 8, 8 ], [ 44, 1, 6, 16 ], [ 52, 1, 8, 16 ] ]

    k = 24: F-action on Pi is (2,5)      [59,1,24]
      Dynkin type is ^2D_4(q) + T(phi2^2 phi4)
      Order of center |Z^F|: phi2^2 phi4
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1^3 phi2
        q congruent 2 modulo 60:   1/32 q^3 ( q-2 )
        q congruent 3 modulo 60:   1/32 phi1^3 phi2
        q congruent 4 modulo 60:   1/32 q^3 ( q-2 )
        q congruent 5 modulo 60:   1/32 phi1^3 phi2
        q congruent 7 modulo 60:   1/32 phi1^3 phi2
        q congruent 8 modulo 60:   1/32 q^3 ( q-2 )
        q congruent 9 modulo 60:   1/32 phi1^3 phi2
        q congruent 11 modulo 60:   1/32 phi1^3 phi2
        q congruent 13 modulo 60:   1/32 phi1^3 phi2
        q congruent 16 modulo 60:   1/32 q^3 ( q-2 )
        q congruent 17 modulo 60:   1/32 phi1^3 phi2
        q congruent 19 modulo 60:   1/32 phi1^3 phi2
        q congruent 21 modulo 60:   1/32 phi1^3 phi2
        q congruent 23 modulo 60:   1/32 phi1^3 phi2
        q congruent 25 modulo 60:   1/32 phi1^3 phi2
        q congruent 27 modulo 60:   1/32 phi1^3 phi2
        q congruent 29 modulo 60:   1/32 phi1^3 phi2
        q congruent 31 modulo 60:   1/32 phi1^3 phi2
        q congruent 32 modulo 60:   1/32 q^3 ( q-2 )
        q congruent 37 modulo 60:   1/32 phi1^3 phi2
        q congruent 41 modulo 60:   1/32 phi1^3 phi2
        q congruent 43 modulo 60:   1/32 phi1^3 phi2
        q congruent 47 modulo 60:   1/32 phi1^3 phi2
        q congruent 49 modulo 60:   1/32 phi1^3 phi2
        q congruent 53 modulo 60:   1/32 phi1^3 phi2
        q congruent 59 modulo 60:   1/32 phi1^3 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 72, 71, 18, 20, 17, 74, 98, 95, 45 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 9, 1, 1, 1 ], 
  [ 10, 1, 2, 4 ], [ 13, 1, 2, 8 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], 
  [ 25, 1, 4, 8 ], [ 39, 1, 3, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ], 
  [ 41, 1, 10, 16 ], [ 44, 1, 4, 16 ], [ 52, 1, 5, 16 ] ]

    k = 25: F-action on Pi is (2,3)      [59,1,25]
      Dynkin type is ^2D_4(q) + T(phi8)
      Order of center |Z^F|: phi8
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 2 modulo 60:   1/8 q^4
        q congruent 3 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 4 modulo 60:   1/8 q^4
        q congruent 5 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 7 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 8 modulo 60:   1/8 q^4
        q congruent 9 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 11 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 13 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 16 modulo 60:   1/8 q^4
        q congruent 17 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 19 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 21 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 23 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 25 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 27 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 29 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 31 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 32 modulo 60:   1/8 q^4
        q congruent 37 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 41 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 43 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 47 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 49 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 53 modulo 60:   1/8 phi1 phi2 phi4
        q congruent 59 modulo 60:   1/8 phi1 phi2 phi4
      Fusion of maximal tori of C^F in those of G^F:
        [ 89, 90, 44, 43, 45, 91, 110, 109, 21 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 9, 1, 1, 1 ] ]

i = 60: Pi = [ 2, 5, 7, 240 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [60,1,1]
      Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^4)
      Order of center |Z^F|: phi1^4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4608 ( q^4-40*q^3+562*q^2-3312*q+7397 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4608 ( q^4-40*q^3+562*q^2-3168*q+5445 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4608 ( q^4-40*q^3+562*q^2-3312*q+6885 )
        q congruent 7 modulo 60:   1/4608 ( q^4-40*q^3+562*q^2-3168*q+5957 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4608 ( q^4-40*q^3+562*q^2-3312*q+6885 )
        q congruent 11 modulo 60:   1/4608 ( q^4-40*q^3+562*q^2-3168*q+5445 )
        q congruent 13 modulo 60:   1/4608 ( q^4-40*q^3+562*q^2-3312*q+7397 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4608 ( q^4-40*q^3+562*q^2-3312*q+6885 )
        q congruent 19 modulo 60:   1/4608 ( q^4-40*q^3+562*q^2-3168*q+5957 )
        q congruent 21 modulo 60:   1/4608 ( q^4-40*q^3+562*q^2-3312*q+6885 )
        q congruent 23 modulo 60:   1/4608 ( q^4-40*q^3+562*q^2-3168*q+5445 )
        q congruent 25 modulo 60:   1/4608 ( q^4-40*q^3+562*q^2-3312*q+7397 )
        q congruent 27 modulo 60:   1/4608 ( q^4-40*q^3+562*q^2-3168*q+5445 )
        q congruent 29 modulo 60:   1/4608 ( q^4-40*q^3+562*q^2-3312*q+6885 )
        q congruent 31 modulo 60:   1/4608 ( q^4-40*q^3+562*q^2-3168*q+5957 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4608 ( q^4-40*q^3+562*q^2-3312*q+7397 )
        q congruent 41 modulo 60:   1/4608 ( q^4-40*q^3+562*q^2-3312*q+6885 )
        q congruent 43 modulo 60:   1/4608 ( q^4-40*q^3+562*q^2-3168*q+5957 )
        q congruent 47 modulo 60:   1/4608 ( q^4-40*q^3+562*q^2-3168*q+5445 )
        q congruent 49 modulo 60:   1/4608 ( q^4-40*q^3+562*q^2-3312*q+7397 )
        q congruent 53 modulo 60:   1/4608 ( q^4-40*q^3+562*q^2-3312*q+6885 )
        q congruent 59 modulo 60:   1/4608 ( q^4-40*q^3+562*q^2-3168*q+5445 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 66, 66, 4, 66, 4, 4, 68, 66, 4, 4, 68, 4, 68, 68, 3 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 1, 32 ], [ 4, 1, 1, 72 ], 
  [ 6, 1, 1, 128 ], [ 7, 1, 1, 96 ], [ 9, 1, 1, 15 ], [ 10, 1, 1, 24 ], 
  [ 11, 1, 1, 96 ], [ 12, 1, 1, 96 ], [ 13, 1, 1, 240 ], [ 16, 1, 1, 384 ], 
  [ 19, 1, 1, 384 ], [ 20, 1, 1, 576 ], [ 23, 1, 1, 24 ], [ 24, 1, 1, 168 ], 
  [ 25, 1, 1, 336 ], [ 26, 1, 1, 192 ], [ 27, 1, 1, 192 ], [ 28, 1, 1, 288 ], 
  [ 33, 1, 1, 768 ], [ 35, 1, 1, 1152 ], [ 39, 1, 1, 144 ], [ 40, 1, 1, 192 ],
  [ 41, 1, 1, 864 ], [ 42, 1, 1, 768 ], [ 43, 1, 1, 1152 ], [ 44, 1, 1, 576 ],
  [ 49, 1, 1, 2304 ], [ 52, 1, 1, 576 ], [ 53, 1, 1, 2304 ], 
  [ 59, 1, 1, 1152 ] ]

    k = 2: F-action on Pi is ()      [60,1,2]
      Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^2 phi3)
      Order of center |Z^F|: phi1^2 phi3 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/144 phi1 ( q^3-6*q^2+q+16 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/144 q phi2 ( q^2-8*q+15 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/144 q phi2 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/144 phi1 ( q^3-6*q^2+q+16 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/144 q phi2 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/144 q phi2 ( q^2-8*q+15 )
        q congruent 13 modulo 60:   1/144 phi1 ( q^3-6*q^2+q+16 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/144 q phi2 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/144 phi1 ( q^3-6*q^2+q+16 )
        q congruent 21 modulo 60:   1/144 q phi2 ( q^2-8*q+15 )
        q congruent 23 modulo 60:   1/144 q phi2 ( q^2-8*q+15 )
        q congruent 25 modulo 60:   1/144 phi1 ( q^3-6*q^2+q+16 )
        q congruent 27 modulo 60:   1/144 q phi2 ( q^2-8*q+15 )
        q congruent 29 modulo 60:   1/144 q phi2 ( q^2-8*q+15 )
        q congruent 31 modulo 60:   1/144 phi1 ( q^3-6*q^2+q+16 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/144 phi1 ( q^3-6*q^2+q+16 )
        q congruent 41 modulo 60:   1/144 q phi2 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/144 phi1 ( q^3-6*q^2+q+16 )
        q congruent 47 modulo 60:   1/144 q phi2 ( q^2-8*q+15 )
        q congruent 49 modulo 60:   1/144 phi1 ( q^3-6*q^2+q+16 )
        q congruent 53 modulo 60:   1/144 q phi2 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/144 q phi2 ( q^2-8*q+15 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 8, 77, 77, 30, 77, 30, 30, 81, 77, 30, 30, 81, 30, 81, 81, 27 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 18 ], 
  [ 6, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 13, 1, 1, 24 ], 
  [ 16, 1, 1, 24 ], [ 23, 1, 1, 6 ], [ 25, 1, 1, 12 ], [ 27, 1, 5, 6 ], 
  [ 33, 1, 1, 48 ], [ 40, 1, 1, 12 ], [ 42, 1, 3, 24 ], [ 44, 1, 3, 18 ], 
  [ 53, 1, 16, 72 ], [ 59, 1, 4, 36 ] ]

    k = 3: F-action on Pi is (  5,  7,240)      [60,1,3]
      Dynkin type is A_1(q) + A_1(q^3) + T(phi1^2 phi3)
      Order of center |Z^F|: phi1^2 phi3 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 7 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 11 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 13 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 19 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 21 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 23 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 25 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 27 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 29 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 31 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 41 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 43 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 47 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 49 modulo 60:   1/36 phi1^2 ( q^2-2*q-4 )
        q congruent 53 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
        q congruent 59 modulo 60:   1/36 q phi2 ( q^2-5*q+6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 14, 87, 83, 35 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], 
  [ 7, 1, 1, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 6 ], [ 11, 1, 1, 6 ], 
  [ 19, 1, 1, 6 ], [ 24, 1, 1, 6 ], [ 26, 1, 1, 12 ], [ 27, 1, 1, 12 ], 
  [ 33, 1, 3, 6 ], [ 40, 1, 5, 6 ], [ 42, 1, 1, 12 ], [ 49, 1, 3, 18 ], 
  [ 52, 1, 6, 18 ], [ 59, 1, 7, 36 ] ]

    k = 4: F-action on Pi is (  5,  7,240)      [60,1,4]
      Dynkin type is A_1(q) + A_1(q^3) + T(phi3^2)
      Order of center |Z^F|: phi3^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/72 phi1 ( q^3+3*q^2-2*q-8 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 7 modulo 60:   1/72 phi1 ( q^3+3*q^2-2*q-8 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 11 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 13 modulo 60:   1/72 phi1 ( q^3+3*q^2-2*q-8 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 19 modulo 60:   1/72 phi1 ( q^3+3*q^2-2*q-8 )
        q congruent 21 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 23 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 25 modulo 60:   1/72 phi1 ( q^3+3*q^2-2*q-8 )
        q congruent 27 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 29 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 31 modulo 60:   1/72 phi1 ( q^3+3*q^2-2*q-8 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/72 phi1 ( q^3+3*q^2-2*q-8 )
        q congruent 41 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 43 modulo 60:   1/72 phi1 ( q^3+3*q^2-2*q-8 )
        q congruent 47 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 49 modulo 60:   1/72 phi1 ( q^3+3*q^2-2*q-8 )
        q congruent 53 modulo 60:   1/72 q phi2 ( q^2+q-6 )
        q congruent 59 modulo 60:   1/72 q phi2 ( q^2+q-6 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 12, 85, 79, 34 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 1, 8 ], [ 6, 1, 1, 8 ], 
  [ 27, 1, 5, 24 ], [ 33, 1, 3, 24 ], [ 40, 1, 5, 24 ], [ 42, 1, 3, 24 ], 
  [ 59, 1, 9, 72 ] ]

    k = 5: F-action on Pi is (  2,  7)(  5,240)      [60,1,5]
      Dynkin type is A_1(q^2) + A_1(q^2) + T(phi1^2 phi3)
      Order of center |Z^F|: phi1^2 phi3 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/48 q phi1 phi2 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/48 q phi1 phi2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/48 q phi1 phi2 ( q-3 )
        q congruent 7 modulo 60:   1/48 q phi1 phi2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/48 q phi1 phi2 ( q-3 )
        q congruent 11 modulo 60:   1/48 q phi1 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/48 q phi1 phi2 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/48 q phi1 phi2 ( q-3 )
        q congruent 19 modulo 60:   1/48 q phi1 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/48 q phi1 phi2 ( q-3 )
        q congruent 23 modulo 60:   1/48 q phi1 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/48 q phi1 phi2 ( q-3 )
        q congruent 27 modulo 60:   1/48 q phi1 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/48 q phi1 phi2 ( q-3 )
        q congruent 31 modulo 60:   1/48 q phi1 phi2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/48 q phi1 phi2 ( q-3 )
        q congruent 41 modulo 60:   1/48 q phi1 phi2 ( q-3 )
        q congruent 43 modulo 60:   1/48 q phi1 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/48 q phi1 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/48 q phi1 phi2 ( q-3 )
        q congruent 53 modulo 60:   1/48 q phi1 phi2 ( q-3 )
        q congruent 59 modulo 60:   1/48 q phi1 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 30, 97, 97, 53 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 4 ], 
  [ 9, 1, 1, 3 ], [ 12, 1, 1, 6 ], [ 13, 1, 3, 8 ], [ 16, 1, 2, 8 ], 
  [ 23, 1, 1, 6 ], [ 25, 1, 1, 12 ], [ 27, 1, 5, 6 ], [ 33, 1, 4, 16 ], 
  [ 40, 1, 1, 12 ], [ 44, 1, 3, 18 ], [ 53, 1, 17, 24 ], [ 59, 1, 4, 36 ] ]

    k = 6: F-action on Pi is (  2,240,  7,  5)      [60,1,6]
      Dynkin type is A_1(q^4) + T(phi1 phi2 phi6)
      Order of center |Z^F|: phi1 phi2 phi6 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 q phi1^2 phi2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/24 q phi1^2 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/24 q phi1^2 phi2
        q congruent 7 modulo 60:   1/24 q phi1^2 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/24 q phi1^2 phi2
        q congruent 11 modulo 60:   1/24 q phi1^2 phi2
        q congruent 13 modulo 60:   1/24 q phi1^2 phi2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/24 q phi1^2 phi2
        q congruent 19 modulo 60:   1/24 q phi1^2 phi2
        q congruent 21 modulo 60:   1/24 q phi1^2 phi2
        q congruent 23 modulo 60:   1/24 q phi1^2 phi2
        q congruent 25 modulo 60:   1/24 q phi1^2 phi2
        q congruent 27 modulo 60:   1/24 q phi1^2 phi2
        q congruent 29 modulo 60:   1/24 q phi1^2 phi2
        q congruent 31 modulo 60:   1/24 q phi1^2 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/24 q phi1^2 phi2
        q congruent 41 modulo 60:   1/24 q phi1^2 phi2
        q congruent 43 modulo 60:   1/24 q phi1^2 phi2
        q congruent 47 modulo 60:   1/24 q phi1^2 phi2
        q congruent 49 modulo 60:   1/24 q phi1^2 phi2
        q congruent 53 modulo 60:   1/24 q phi1^2 phi2
        q congruent 59 modulo 60:   1/24 q phi1^2 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 60, 110 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], 
  [ 12, 1, 2, 2 ], [ 23, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 27, 1, 4, 6 ], 
  [ 33, 1, 9, 8 ], [ 40, 1, 2, 4 ], [ 44, 1, 7, 6 ], [ 59, 1, 20, 12 ] ]

    k = 7: F-action on Pi is (  2,240,  7,  5)      [60,1,7]
      Dynkin type is A_1(q^4) + T(phi1 phi2 phi3)
      Order of center |Z^F|: phi1 phi2 phi3 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 q phi1 phi2^2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/24 q phi1 phi2^2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/24 q phi1 phi2^2
        q congruent 7 modulo 60:   1/24 q phi1 phi2^2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/24 q phi1 phi2^2
        q congruent 11 modulo 60:   1/24 q phi1 phi2^2
        q congruent 13 modulo 60:   1/24 q phi1 phi2^2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/24 q phi1 phi2^2
        q congruent 19 modulo 60:   1/24 q phi1 phi2^2
        q congruent 21 modulo 60:   1/24 q phi1 phi2^2
        q congruent 23 modulo 60:   1/24 q phi1 phi2^2
        q congruent 25 modulo 60:   1/24 q phi1 phi2^2
        q congruent 27 modulo 60:   1/24 q phi1 phi2^2
        q congruent 29 modulo 60:   1/24 q phi1 phi2^2
        q congruent 31 modulo 60:   1/24 q phi1 phi2^2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/24 q phi1 phi2^2
        q congruent 41 modulo 60:   1/24 q phi1 phi2^2
        q congruent 43 modulo 60:   1/24 q phi1 phi2^2
        q congruent 47 modulo 60:   1/24 q phi1 phi2^2
        q congruent 49 modulo 60:   1/24 q phi1 phi2^2
        q congruent 53 modulo 60:   1/24 q phi1 phi2^2
        q congruent 59 modulo 60:   1/24 q phi1 phi2^2
      Fusion of maximal tori of C^F in those of G^F:
        [ 59, 109 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 2 ], [ 9, 1, 1, 1 ], 
  [ 12, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 27, 1, 5, 6 ], 
  [ 33, 1, 5, 8 ], [ 40, 1, 3, 4 ], [ 44, 1, 3, 6 ], [ 59, 1, 19, 12 ] ]

    k = 8: F-action on Pi is ()      [60,1,8]
      Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi2^2 phi6)
      Order of center |Z^F|: phi2^2 phi6 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/144 q phi1^2 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/144 q phi1^2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/144 phi2 ( q^3-6*q^2+13*q-16 )
        q congruent 7 modulo 60:   1/144 q phi1^2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/144 q phi1^2 ( q-3 )
        q congruent 11 modulo 60:   1/144 phi2 ( q^3-6*q^2+13*q-16 )
        q congruent 13 modulo 60:   1/144 q phi1^2 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/144 phi2 ( q^3-6*q^2+13*q-16 )
        q congruent 19 modulo 60:   1/144 q phi1^2 ( q-3 )
        q congruent 21 modulo 60:   1/144 q phi1^2 ( q-3 )
        q congruent 23 modulo 60:   1/144 phi2 ( q^3-6*q^2+13*q-16 )
        q congruent 25 modulo 60:   1/144 q phi1^2 ( q-3 )
        q congruent 27 modulo 60:   1/144 q phi1^2 ( q-3 )
        q congruent 29 modulo 60:   1/144 phi2 ( q^3-6*q^2+13*q-16 )
        q congruent 31 modulo 60:   1/144 q phi1^2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/144 q phi1^2 ( q-3 )
        q congruent 41 modulo 60:   1/144 phi2 ( q^3-6*q^2+13*q-16 )
        q congruent 43 modulo 60:   1/144 q phi1^2 ( q-3 )
        q congruent 47 modulo 60:   1/144 phi2 ( q^3-6*q^2+13*q-16 )
        q congruent 49 modulo 60:   1/144 q phi1^2 ( q-3 )
        q congruent 53 modulo 60:   1/144 phi2 ( q^3-6*q^2+13*q-16 )
        q congruent 59 modulo 60:   1/144 phi2 ( q^3-6*q^2+13*q-16 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 28, 82, 82, 31, 82, 31, 31, 78, 82, 31, 31, 78, 31, 78, 78, 9 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 4, 1, 2, 18 ], 
  [ 6, 1, 2, 8 ], [ 9, 1, 1, 3 ], [ 12, 1, 2, 6 ], [ 13, 1, 4, 24 ], 
  [ 16, 1, 3, 24 ], [ 23, 1, 2, 6 ], [ 25, 1, 3, 12 ], [ 27, 1, 4, 6 ], 
  [ 33, 1, 8, 48 ], [ 40, 1, 6, 12 ], [ 42, 1, 5, 24 ], [ 44, 1, 7, 18 ], 
  [ 53, 1, 18, 72 ], [ 59, 1, 5, 36 ] ]

    k = 9: F-action on Pi is (  2,  7)(  5,240)      [60,1,9]
      Dynkin type is A_1(q^2) + A_1(q^2) + T(phi2^2 phi6)
      Order of center |Z^F|: phi2^2 phi6 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/48 q phi1^2 phi2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/48 q phi1^2 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/48 q phi1^2 phi2
        q congruent 7 modulo 60:   1/48 q phi1^2 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/48 q phi1^2 phi2
        q congruent 11 modulo 60:   1/48 q phi1^2 phi2
        q congruent 13 modulo 60:   1/48 q phi1^2 phi2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/48 q phi1^2 phi2
        q congruent 19 modulo 60:   1/48 q phi1^2 phi2
        q congruent 21 modulo 60:   1/48 q phi1^2 phi2
        q congruent 23 modulo 60:   1/48 q phi1^2 phi2
        q congruent 25 modulo 60:   1/48 q phi1^2 phi2
        q congruent 27 modulo 60:   1/48 q phi1^2 phi2
        q congruent 29 modulo 60:   1/48 q phi1^2 phi2
        q congruent 31 modulo 60:   1/48 q phi1^2 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/48 q phi1^2 phi2
        q congruent 41 modulo 60:   1/48 q phi1^2 phi2
        q congruent 43 modulo 60:   1/48 q phi1^2 phi2
        q congruent 47 modulo 60:   1/48 q phi1^2 phi2
        q congruent 49 modulo 60:   1/48 q phi1^2 phi2
        q congruent 53 modulo 60:   1/48 q phi1^2 phi2
        q congruent 59 modulo 60:   1/48 q phi1^2 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 31, 98, 98, 54 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 6 ], 
  [ 9, 1, 1, 3 ], [ 12, 1, 2, 6 ], [ 13, 1, 2, 8 ], [ 16, 1, 4, 8 ], 
  [ 23, 1, 2, 6 ], [ 25, 1, 3, 12 ], [ 27, 1, 4, 6 ], [ 33, 1, 10, 16 ], 
  [ 40, 1, 6, 12 ], [ 44, 1, 7, 18 ], [ 53, 1, 15, 24 ], [ 59, 1, 5, 36 ] ]

    k = 10: F-action on Pi is (  5,240)      [60,1,10]
      Dynkin type is A_1(q) + A_1(q^2) + A_1(q) + T(phi1 phi2 phi6)
      Order of center |Z^F|: phi1 phi2 phi6 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 q phi1 phi2 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/24 q phi1 phi2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/24 q phi1 phi2 ( q-3 )
        q congruent 7 modulo 60:   1/24 q phi1 phi2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/24 q phi1 phi2 ( q-3 )
        q congruent 11 modulo 60:   1/24 q phi1 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/24 q phi1 phi2 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/24 q phi1 phi2 ( q-3 )
        q congruent 19 modulo 60:   1/24 q phi1 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/24 q phi1 phi2 ( q-3 )
        q congruent 23 modulo 60:   1/24 q phi1 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/24 q phi1 phi2 ( q-3 )
        q congruent 27 modulo 60:   1/24 q phi1 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/24 q phi1 phi2 ( q-3 )
        q congruent 31 modulo 60:   1/24 q phi1 phi2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/24 q phi1 phi2 ( q-3 )
        q congruent 41 modulo 60:   1/24 q phi1 phi2 ( q-3 )
        q congruent 43 modulo 60:   1/24 q phi1 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/24 q phi1 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/24 q phi1 phi2 ( q-3 )
        q congruent 53 modulo 60:   1/24 q phi1 phi2 ( q-3 )
        q congruent 59 modulo 60:   1/24 q phi1 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 28, 82, 96, 60, 82, 31, 60, 98 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 4, 1, 1, 2 ], 
  [ 4, 1, 2, 4 ], [ 6, 1, 2, 4 ], [ 9, 1, 1, 1 ], [ 12, 1, 2, 2 ], 
  [ 13, 1, 1, 4 ], [ 13, 1, 3, 4 ], [ 16, 1, 3, 4 ], [ 16, 1, 4, 4 ], 
  [ 23, 1, 1, 2 ], [ 25, 1, 2, 4 ], [ 27, 1, 4, 6 ], [ 33, 1, 6, 8 ], 
  [ 40, 1, 2, 4 ], [ 42, 1, 5, 12 ], [ 44, 1, 7, 6 ], [ 53, 1, 15, 12 ], 
  [ 53, 1, 18, 12 ], [ 59, 1, 20, 12 ] ]

    k = 11: F-action on Pi is (  5,240)      [60,1,11]
      Dynkin type is A_1(q) + A_1(q^2) + A_1(q) + T(phi1 phi2 phi3)
      Order of center |Z^F|: phi1 phi2 phi3 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/24 q phi1^2 phi2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/24 q phi1^2 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/24 q phi1^2 phi2
        q congruent 7 modulo 60:   1/24 q phi1^2 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/24 q phi1^2 phi2
        q congruent 11 modulo 60:   1/24 q phi1^2 phi2
        q congruent 13 modulo 60:   1/24 q phi1^2 phi2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/24 q phi1^2 phi2
        q congruent 19 modulo 60:   1/24 q phi1^2 phi2
        q congruent 21 modulo 60:   1/24 q phi1^2 phi2
        q congruent 23 modulo 60:   1/24 q phi1^2 phi2
        q congruent 25 modulo 60:   1/24 q phi1^2 phi2
        q congruent 27 modulo 60:   1/24 q phi1^2 phi2
        q congruent 29 modulo 60:   1/24 q phi1^2 phi2
        q congruent 31 modulo 60:   1/24 q phi1^2 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/24 q phi1^2 phi2
        q congruent 41 modulo 60:   1/24 q phi1^2 phi2
        q congruent 43 modulo 60:   1/24 q phi1^2 phi2
        q congruent 47 modulo 60:   1/24 q phi1^2 phi2
        q congruent 49 modulo 60:   1/24 q phi1^2 phi2
        q congruent 53 modulo 60:   1/24 q phi1^2 phi2
        q congruent 59 modulo 60:   1/24 q phi1^2 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 30, 81, 97, 59, 81, 27, 59, 95 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 4, 1, 1, 4 ], 
  [ 4, 1, 2, 2 ], [ 6, 1, 1, 4 ], [ 9, 1, 1, 1 ], [ 12, 1, 1, 2 ], 
  [ 13, 1, 2, 4 ], [ 13, 1, 4, 4 ], [ 16, 1, 1, 4 ], [ 16, 1, 2, 4 ], 
  [ 23, 1, 2, 2 ], [ 25, 1, 4, 4 ], [ 27, 1, 5, 6 ], [ 33, 1, 2, 8 ], 
  [ 40, 1, 3, 4 ], [ 42, 1, 3, 12 ], [ 44, 1, 3, 6 ], [ 53, 1, 16, 12 ], 
  [ 53, 1, 17, 12 ], [ 59, 1, 19, 12 ] ]

    k = 12: F-action on Pi is (  5,240,  7)      [60,1,12]
      Dynkin type is A_1(q) + A_1(q^3) + T(phi1 phi2 phi3)
      Order of center |Z^F|: phi1 phi2 phi3 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 7 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 11 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 13 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 19 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 21 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 23 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 25 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 27 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 29 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 31 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 41 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 43 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 47 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 49 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 53 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 59 modulo 60:   1/12 q^2 phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 83, 40, 37, 88 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 2 ], [ 6, 1, 1, 2 ], 
  [ 7, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 2 ], [ 11, 1, 1, 2 ], 
  [ 19, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 26, 1, 3, 4 ], [ 27, 1, 2, 4 ], 
  [ 33, 1, 3, 6 ], [ 40, 1, 5, 6 ], [ 42, 1, 4, 4 ], [ 49, 1, 3, 6 ], 
  [ 52, 1, 6, 6 ], [ 59, 1, 14, 12 ] ]

    k = 13: F-action on Pi is (  5,240,  7)      [60,1,13]
      Dynkin type is A_1(q) + A_1(q^3) + T(phi1 phi2 phi6)
      Order of center |Z^F|: phi1 phi2 phi6 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 7 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 11 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 13 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 19 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 21 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 23 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 25 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 27 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 29 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 31 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 41 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 43 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 47 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 49 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 53 modulo 60:   1/12 q phi1 phi2 ( q-2 )
        q congruent 59 modulo 60:   1/12 q phi1 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 87, 38, 40, 84 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], 
  [ 7, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], [ 11, 1, 2, 2 ], 
  [ 19, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 26, 1, 2, 4 ], [ 27, 1, 3, 4 ], 
  [ 33, 1, 7, 6 ], [ 40, 1, 4, 6 ], [ 42, 1, 2, 4 ], [ 49, 1, 6, 6 ], 
  [ 52, 1, 7, 6 ], [ 59, 1, 15, 12 ] ]

    k = 14: F-action on Pi is (  5,240,  7)      [60,1,14]
      Dynkin type is A_1(q) + A_1(q^3) + T(phi2^2 phi6)
      Order of center |Z^F|: phi2^2 phi6 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/36 q^2 phi1^2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/36 q^2 phi1^2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 7 modulo 60:   1/36 q^2 phi1^2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/36 q^2 phi1^2
        q congruent 11 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 13 modulo 60:   1/36 q^2 phi1^2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 19 modulo 60:   1/36 q^2 phi1^2
        q congruent 21 modulo 60:   1/36 q^2 phi1^2
        q congruent 23 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 25 modulo 60:   1/36 q^2 phi1^2
        q congruent 27 modulo 60:   1/36 q^2 phi1^2
        q congruent 29 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 31 modulo 60:   1/36 q^2 phi1^2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/36 q^2 phi1^2
        q congruent 41 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 43 modulo 60:   1/36 q^2 phi1^2
        q congruent 47 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 49 modulo 60:   1/36 q^2 phi1^2
        q congruent 53 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
        q congruent 59 modulo 60:   1/36 phi2 ( q^3-3*q^2+4*q-4 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 35, 84, 88, 15 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 2 ], [ 6, 1, 2, 2 ], 
  [ 7, 1, 2, 6 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 6 ], [ 11, 1, 2, 6 ], 
  [ 19, 1, 2, 6 ], [ 24, 1, 2, 6 ], [ 26, 1, 4, 12 ], [ 27, 1, 6, 12 ], 
  [ 33, 1, 7, 6 ], [ 40, 1, 4, 6 ], [ 42, 1, 6, 12 ], [ 49, 1, 6, 18 ], 
  [ 52, 1, 7, 18 ], [ 59, 1, 8, 36 ] ]

    k = 15: F-action on Pi is (  5,240,  7)      [60,1,15]
      Dynkin type is A_1(q) + A_1(q^3) + T(phi6^2)
      Order of center |Z^F|: phi6^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/72 phi2 ( q^3-3*q^2-2*q+8 )
        q congruent 7 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 11 modulo 60:   1/72 phi2 ( q^3-3*q^2-2*q+8 )
        q congruent 13 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/72 phi2 ( q^3-3*q^2-2*q+8 )
        q congruent 19 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 21 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 23 modulo 60:   1/72 phi2 ( q^3-3*q^2-2*q+8 )
        q congruent 25 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 27 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 29 modulo 60:   1/72 phi2 ( q^3-3*q^2-2*q+8 )
        q congruent 31 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 41 modulo 60:   1/72 phi2 ( q^3-3*q^2-2*q+8 )
        q congruent 43 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 47 modulo 60:   1/72 phi2 ( q^3-3*q^2-2*q+8 )
        q congruent 49 modulo 60:   1/72 q phi1 ( q^2-q-6 )
        q congruent 53 modulo 60:   1/72 phi2 ( q^3-3*q^2-2*q+8 )
        q congruent 59 modulo 60:   1/72 phi2 ( q^3-3*q^2-2*q+8 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 33, 80, 86, 13 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 3, 1, 2, 8 ], [ 6, 1, 2, 8 ], 
  [ 27, 1, 4, 24 ], [ 33, 1, 7, 24 ], [ 40, 1, 4, 24 ], [ 42, 1, 5, 24 ], 
  [ 59, 1, 10, 72 ] ]

    k = 16: F-action on Pi is (  5,  7,240)      [60,1,16]
      Dynkin type is A_1(q) + A_1(q^3) + T(phi12)
      Order of center |Z^F|: phi12 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 7 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 11 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 13 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 19 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 21 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 23 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 25 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 27 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 29 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 31 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 41 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 43 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 47 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 49 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 53 modulo 60:   1/12 q^2 phi1 phi2
        q congruent 59 modulo 60:   1/12 q^2 phi1 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 57, 102, 101, 58 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 1 ], [ 59, 1, 11, 12 ] ]

    k = 17: F-action on Pi is ()      [60,1,17]
      Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi2^4)
      Order of center |Z^F|: phi2^4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/4608 phi1 ( q^3-31*q^2+315*q-1053 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/4608 ( q^4-32*q^3+346*q^2-1512*q+2205 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/4608 ( q^4-32*q^3+346*q^2-1368*q+1565 )
        q congruent 7 modulo 60:   1/4608 ( q^4-32*q^3+346*q^2-1512*q+2205 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/4608 phi1 ( q^3-31*q^2+315*q-1053 )
        q congruent 11 modulo 60:   1/4608 ( q^4-32*q^3+346*q^2-1512*q+2717 )
        q congruent 13 modulo 60:   1/4608 phi1 ( q^3-31*q^2+315*q-1053 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/4608 ( q^4-32*q^3+346*q^2-1368*q+1565 )
        q congruent 19 modulo 60:   1/4608 ( q^4-32*q^3+346*q^2-1512*q+2205 )
        q congruent 21 modulo 60:   1/4608 phi1 ( q^3-31*q^2+315*q-1053 )
        q congruent 23 modulo 60:   1/4608 ( q^4-32*q^3+346*q^2-1512*q+2717 )
        q congruent 25 modulo 60:   1/4608 phi1 ( q^3-31*q^2+315*q-1053 )
        q congruent 27 modulo 60:   1/4608 ( q^4-32*q^3+346*q^2-1512*q+2205 )
        q congruent 29 modulo 60:   1/4608 ( q^4-32*q^3+346*q^2-1368*q+1565 )
        q congruent 31 modulo 60:   1/4608 ( q^4-32*q^3+346*q^2-1512*q+2205 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/4608 phi1 ( q^3-31*q^2+315*q-1053 )
        q congruent 41 modulo 60:   1/4608 ( q^4-32*q^3+346*q^2-1368*q+1565 )
        q congruent 43 modulo 60:   1/4608 ( q^4-32*q^3+346*q^2-1512*q+2205 )
        q congruent 47 modulo 60:   1/4608 ( q^4-32*q^3+346*q^2-1512*q+2717 )
        q congruent 49 modulo 60:   1/4608 phi1 ( q^3-31*q^2+315*q-1053 )
        q congruent 53 modulo 60:   1/4608 ( q^4-32*q^3+346*q^2-1368*q+1565 )
        q congruent 59 modulo 60:   1/4608 ( q^4-32*q^3+346*q^2-1512*q+2717 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 69, 69, 5, 69, 5, 5, 67, 69, 5, 5, 67, 5, 67, 67, 2 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 16 ], [ 3, 1, 2, 32 ], [ 4, 1, 2, 72 ], 
  [ 6, 1, 2, 128 ], [ 7, 1, 2, 96 ], [ 9, 1, 1, 15 ], [ 10, 1, 2, 24 ], 
  [ 11, 1, 2, 96 ], [ 12, 1, 2, 96 ], [ 13, 1, 4, 240 ], [ 16, 1, 3, 384 ], 
  [ 19, 1, 2, 384 ], [ 20, 1, 4, 576 ], [ 23, 1, 2, 24 ], [ 24, 1, 2, 168 ], 
  [ 25, 1, 3, 336 ], [ 26, 1, 4, 192 ], [ 27, 1, 6, 192 ], [ 28, 1, 4, 288 ], 
  [ 33, 1, 8, 768 ], [ 35, 1, 8, 1152 ], [ 39, 1, 3, 144 ], [ 40, 1, 6, 192 ],
  [ 41, 1, 9, 864 ], [ 42, 1, 6, 768 ], [ 43, 1, 13, 1152 ], 
  [ 44, 1, 10, 576 ], [ 49, 1, 10, 2304 ], [ 52, 1, 10, 576 ], 
  [ 53, 1, 20, 2304 ], [ 59, 1, 2, 1152 ] ]

    k = 18: F-action on Pi is ()      [60,1,18]
      Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi4^2)
      Order of center |Z^F|: phi4^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/384 phi1 phi2 ( q^2-9 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/384 phi1 phi2 ( q^2-9 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/384 phi1 phi2 ( q^2-9 )
        q congruent 7 modulo 60:   1/384 phi1 phi2 ( q^2-9 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/384 phi1 phi2 ( q^2-9 )
        q congruent 11 modulo 60:   1/384 phi1 phi2 ( q^2-9 )
        q congruent 13 modulo 60:   1/384 phi1 phi2 ( q^2-9 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/384 phi1 phi2 ( q^2-9 )
        q congruent 19 modulo 60:   1/384 phi1 phi2 ( q^2-9 )
        q congruent 21 modulo 60:   1/384 phi1 phi2 ( q^2-9 )
        q congruent 23 modulo 60:   1/384 phi1 phi2 ( q^2-9 )
        q congruent 25 modulo 60:   1/384 phi1 phi2 ( q^2-9 )
        q congruent 27 modulo 60:   1/384 phi1 phi2 ( q^2-9 )
        q congruent 29 modulo 60:   1/384 phi1 phi2 ( q^2-9 )
        q congruent 31 modulo 60:   1/384 phi1 phi2 ( q^2-9 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/384 phi1 phi2 ( q^2-9 )
        q congruent 41 modulo 60:   1/384 phi1 phi2 ( q^2-9 )
        q congruent 43 modulo 60:   1/384 phi1 phi2 ( q^2-9 )
        q congruent 47 modulo 60:   1/384 phi1 phi2 ( q^2-9 )
        q congruent 49 modulo 60:   1/384 phi1 phi2 ( q^2-9 )
        q congruent 53 modulo 60:   1/384 phi1 phi2 ( q^2-9 )
        q congruent 59 modulo 60:   1/384 phi1 phi2 ( q^2-9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 16, 73, 73, 18, 73, 18, 18, 74, 73, 18, 18, 74, 18, 74, 74, 17 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 39, 1, 5, 24 ], 
  [ 41, 1, 5, 48 ], [ 41, 1, 8, 96 ], [ 59, 1, 6, 96 ] ]

    k = 19: F-action on Pi is (  5,240)      [60,1,19]
      Dynkin type is A_1(q) + A_1(q^2) + A_1(q) + T(phi8)
      Order of center |Z^F|: phi8 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 7 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 11 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 13 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 19 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 21 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 23 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 25 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 27 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 29 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 31 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 41 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 43 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 47 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 49 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 53 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 59 modulo 60:   1/16 phi1 phi2 phi4
      Fusion of maximal tori of C^F in those of G^F:
        [ 89, 43, 44, 91, 43, 90, 91, 45 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 9, 1, 1, 1 ], [ 59, 1, 25, 8 ] ]

    k = 20: F-action on Pi is (  2,  7)(  5,240)      [60,1,20]
      Dynkin type is A_1(q^2) + A_1(q^2) + T(phi4^2)
      Order of center |Z^F|: phi4^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/128 phi1 phi2 ( q^2-9 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/128 phi1 phi2 ( q^2-9 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/128 phi1 phi2 ( q^2-9 )
        q congruent 7 modulo 60:   1/128 phi1 phi2 ( q^2-9 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/128 phi1 phi2 ( q^2-9 )
        q congruent 11 modulo 60:   1/128 phi1 phi2 ( q^2-9 )
        q congruent 13 modulo 60:   1/128 phi1 phi2 ( q^2-9 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/128 phi1 phi2 ( q^2-9 )
        q congruent 19 modulo 60:   1/128 phi1 phi2 ( q^2-9 )
        q congruent 21 modulo 60:   1/128 phi1 phi2 ( q^2-9 )
        q congruent 23 modulo 60:   1/128 phi1 phi2 ( q^2-9 )
        q congruent 25 modulo 60:   1/128 phi1 phi2 ( q^2-9 )
        q congruent 27 modulo 60:   1/128 phi1 phi2 ( q^2-9 )
        q congruent 29 modulo 60:   1/128 phi1 phi2 ( q^2-9 )
        q congruent 31 modulo 60:   1/128 phi1 phi2 ( q^2-9 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/128 phi1 phi2 ( q^2-9 )
        q congruent 41 modulo 60:   1/128 phi1 phi2 ( q^2-9 )
        q congruent 43 modulo 60:   1/128 phi1 phi2 ( q^2-9 )
        q congruent 47 modulo 60:   1/128 phi1 phi2 ( q^2-9 )
        q congruent 49 modulo 60:   1/128 phi1 phi2 ( q^2-9 )
        q congruent 53 modulo 60:   1/128 phi1 phi2 ( q^2-9 )
        q congruent 59 modulo 60:   1/128 phi1 phi2 ( q^2-9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 18, 75, 75, 6 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 9, 1, 1, 7 ], [ 39, 1, 5, 24 ], [ 41, 1, 5, 80 ], 
  [ 43, 1, 10, 64 ], [ 59, 1, 6, 96 ] ]

    k = 21: F-action on Pi is (  2,240,  7,  5)      [60,1,21]
      Dynkin type is A_1(q^4) + T(phi8)
      Order of center |Z^F|: phi8 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 7 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 11 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 13 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 19 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 21 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 23 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 25 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 27 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 29 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 31 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 41 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 43 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 47 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 49 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 53 modulo 60:   1/16 phi1 phi2 phi4
        q congruent 59 modulo 60:   1/16 phi1 phi2 phi4
      Fusion of maximal tori of C^F in those of G^F:
        [ 91, 21 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 9, 1, 1, 3 ], [ 59, 1, 25, 8 ] ]

    k = 22: F-action on Pi is (  2,  7)(  5,240)      [60,1,22]
      Dynkin type is A_1(q^2) + A_1(q^2) + T(phi1^4)
      Order of center |Z^F|: phi1^4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/1536 phi1 ( q^3-23*q^2+171*q-405 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/1536 ( q^4-24*q^3+194*q^2-624*q+693 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/1536 phi1 ( q^3-23*q^2+171*q-405 )
        q congruent 7 modulo 60:   1/1536 ( q^4-24*q^3+194*q^2-624*q+693 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/1536 phi1 ( q^3-23*q^2+171*q-405 )
        q congruent 11 modulo 60:   1/1536 ( q^4-24*q^3+194*q^2-624*q+693 )
        q congruent 13 modulo 60:   1/1536 phi1 ( q^3-23*q^2+171*q-405 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/1536 phi1 ( q^3-23*q^2+171*q-405 )
        q congruent 19 modulo 60:   1/1536 ( q^4-24*q^3+194*q^2-624*q+693 )
        q congruent 21 modulo 60:   1/1536 phi1 ( q^3-23*q^2+171*q-405 )
        q congruent 23 modulo 60:   1/1536 ( q^4-24*q^3+194*q^2-624*q+693 )
        q congruent 25 modulo 60:   1/1536 phi1 ( q^3-23*q^2+171*q-405 )
        q congruent 27 modulo 60:   1/1536 ( q^4-24*q^3+194*q^2-624*q+693 )
        q congruent 29 modulo 60:   1/1536 phi1 ( q^3-23*q^2+171*q-405 )
        q congruent 31 modulo 60:   1/1536 ( q^4-24*q^3+194*q^2-624*q+693 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/1536 phi1 ( q^3-23*q^2+171*q-405 )
        q congruent 41 modulo 60:   1/1536 phi1 ( q^3-23*q^2+171*q-405 )
        q congruent 43 modulo 60:   1/1536 ( q^4-24*q^3+194*q^2-624*q+693 )
        q congruent 47 modulo 60:   1/1536 ( q^4-24*q^3+194*q^2-624*q+693 )
        q congruent 49 modulo 60:   1/1536 phi1 ( q^3-23*q^2+171*q-405 )
        q congruent 53 modulo 60:   1/1536 phi1 ( q^3-23*q^2+171*q-405 )
        q congruent 59 modulo 60:   1/1536 ( q^4-24*q^3+194*q^2-624*q+693 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 70, 70, 16 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 12 ], [ 3, 1, 1, 32 ], [ 4, 1, 1, 24 ], 
  [ 4, 1, 2, 16 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 24 ], [ 11, 1, 1, 96 ], 
  [ 12, 1, 1, 96 ], [ 13, 1, 1, 144 ], [ 13, 1, 3, 32 ], [ 16, 1, 2, 128 ], 
  [ 20, 1, 3, 192 ], [ 23, 1, 1, 24 ], [ 24, 1, 1, 72 ], [ 25, 1, 1, 48 ], 
  [ 25, 1, 2, 96 ], [ 27, 1, 1, 192 ], [ 28, 1, 1, 288 ], [ 33, 1, 4, 256 ], 
  [ 35, 1, 5, 384 ], [ 39, 1, 1, 144 ], [ 40, 1, 1, 192 ], [ 41, 1, 1, 288 ], 
  [ 41, 1, 3, 192 ], [ 43, 1, 3, 384 ], [ 44, 1, 1, 576 ], [ 49, 1, 11, 768 ],
  [ 52, 1, 1, 576 ], [ 53, 1, 5, 768 ], [ 59, 1, 1, 1152 ] ]

    k = 23: F-action on Pi is (  2,240,  7,  5)      [60,1,23]
      Dynkin type is A_1(q^4) + T(phi1^3 phi2)
      Order of center |Z^F|: phi1^3 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/192 phi1 phi2 ( q^2-8*q+15 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/192 phi1 phi2 ( q^2-8*q+15 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/192 phi1 phi2 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/192 phi1 phi2 ( q^2-8*q+15 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/192 phi1 phi2 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/192 phi1 phi2 ( q^2-8*q+15 )
        q congruent 13 modulo 60:   1/192 phi1 phi2 ( q^2-8*q+15 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/192 phi1 phi2 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/192 phi1 phi2 ( q^2-8*q+15 )
        q congruent 21 modulo 60:   1/192 phi1 phi2 ( q^2-8*q+15 )
        q congruent 23 modulo 60:   1/192 phi1 phi2 ( q^2-8*q+15 )
        q congruent 25 modulo 60:   1/192 phi1 phi2 ( q^2-8*q+15 )
        q congruent 27 modulo 60:   1/192 phi1 phi2 ( q^2-8*q+15 )
        q congruent 29 modulo 60:   1/192 phi1 phi2 ( q^2-8*q+15 )
        q congruent 31 modulo 60:   1/192 phi1 phi2 ( q^2-8*q+15 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/192 phi1 phi2 ( q^2-8*q+15 )
        q congruent 41 modulo 60:   1/192 phi1 phi2 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/192 phi1 phi2 ( q^2-8*q+15 )
        q congruent 47 modulo 60:   1/192 phi1 phi2 ( q^2-8*q+15 )
        q congruent 49 modulo 60:   1/192 phi1 phi2 ( q^2-8*q+15 )
        q congruent 53 modulo 60:   1/192 phi1 phi2 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/192 phi1 phi2 ( q^2-8*q+15 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 19, 89 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 2 ], 
  [ 4, 1, 2, 6 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 12 ], [ 11, 1, 1, 24 ], 
  [ 12, 1, 1, 8 ], [ 13, 1, 1, 12 ], [ 13, 1, 3, 24 ], [ 13, 1, 4, 12 ], 
  [ 23, 1, 1, 6 ], [ 23, 1, 2, 2 ], [ 24, 1, 1, 12 ], [ 25, 1, 2, 12 ], 
  [ 25, 1, 4, 4 ], [ 27, 1, 1, 48 ], [ 28, 1, 1, 24 ], [ 28, 1, 3, 24 ], 
  [ 33, 1, 5, 32 ], [ 39, 1, 1, 24 ], [ 39, 1, 2, 12 ], [ 40, 1, 3, 16 ], 
  [ 41, 1, 3, 48 ], [ 41, 1, 4, 24 ], [ 44, 1, 1, 48 ], [ 44, 1, 9, 48 ], 
  [ 49, 1, 12, 96 ], [ 52, 1, 3, 48 ], [ 59, 1, 17, 96 ] ]

    k = 24: F-action on Pi is (  2,240,  7,  5)      [60,1,24]
      Dynkin type is A_1(q^4) + T(phi1 phi2^3)
      Order of center |Z^F|: phi1 phi2^3 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/192 phi1^2 phi2 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/192 phi1^2 phi2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/192 phi1^2 phi2 ( q-3 )
        q congruent 7 modulo 60:   1/192 phi1^2 phi2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/192 phi1^2 phi2 ( q-3 )
        q congruent 11 modulo 60:   1/192 phi1^2 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/192 phi1^2 phi2 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/192 phi1^2 phi2 ( q-3 )
        q congruent 19 modulo 60:   1/192 phi1^2 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/192 phi1^2 phi2 ( q-3 )
        q congruent 23 modulo 60:   1/192 phi1^2 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/192 phi1^2 phi2 ( q-3 )
        q congruent 27 modulo 60:   1/192 phi1^2 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/192 phi1^2 phi2 ( q-3 )
        q congruent 31 modulo 60:   1/192 phi1^2 phi2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/192 phi1^2 phi2 ( q-3 )
        q congruent 41 modulo 60:   1/192 phi1^2 phi2 ( q-3 )
        q congruent 43 modulo 60:   1/192 phi1^2 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/192 phi1^2 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/192 phi1^2 phi2 ( q-3 )
        q congruent 53 modulo 60:   1/192 phi1^2 phi2 ( q-3 )
        q congruent 59 modulo 60:   1/192 phi1^2 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 20, 90 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 6 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 6 ], 
  [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 2, 12 ], [ 11, 1, 2, 24 ], 
  [ 12, 1, 2, 8 ], [ 13, 1, 1, 12 ], [ 13, 1, 2, 24 ], [ 13, 1, 4, 12 ], 
  [ 23, 1, 1, 2 ], [ 23, 1, 2, 6 ], [ 24, 1, 2, 12 ], [ 25, 1, 2, 4 ], 
  [ 25, 1, 4, 12 ], [ 27, 1, 6, 48 ], [ 28, 1, 2, 24 ], [ 28, 1, 4, 24 ], 
  [ 33, 1, 9, 32 ], [ 39, 1, 2, 12 ], [ 39, 1, 3, 24 ], [ 40, 1, 2, 16 ], 
  [ 41, 1, 4, 24 ], [ 41, 1, 10, 48 ], [ 44, 1, 5, 48 ], [ 44, 1, 10, 48 ], 
  [ 49, 1, 16, 96 ], [ 52, 1, 4, 48 ], [ 59, 1, 18, 96 ] ]

    k = 25: F-action on Pi is (  2,  5,  7,240)      [60,1,25]
      Dynkin type is A_1(q^4) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 7 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 11 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 13 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 19 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 21 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 23 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 25 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 27 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 29 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 31 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 41 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 43 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 47 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 49 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 53 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 59 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 76, 43 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 4 ], 
  [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 1 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 11, 1, 1, 4 ], [ 11, 1, 2, 4 ], [ 12, 1, 1, 4 ], 
  [ 12, 1, 2, 4 ], [ 13, 1, 1, 4 ], [ 13, 1, 4, 4 ], [ 23, 1, 1, 2 ], 
  [ 23, 1, 2, 2 ], [ 24, 1, 1, 2 ], [ 24, 1, 2, 2 ], [ 25, 1, 2, 4 ], 
  [ 25, 1, 4, 4 ], [ 27, 1, 2, 8 ], [ 27, 1, 3, 8 ], [ 28, 1, 1, 4 ], 
  [ 28, 1, 2, 4 ], [ 28, 1, 3, 4 ], [ 28, 1, 4, 4 ], [ 33, 1, 5, 16 ], 
  [ 33, 1, 9, 16 ], [ 39, 1, 2, 4 ], [ 39, 1, 4, 4 ], [ 40, 1, 2, 8 ], 
  [ 40, 1, 3, 8 ], [ 41, 1, 4, 8 ], [ 41, 1, 7, 8 ], [ 43, 1, 11, 16 ], 
  [ 44, 1, 2, 8 ], [ 44, 1, 8, 8 ], [ 49, 1, 12, 16 ], [ 49, 1, 16, 16 ], 
  [ 52, 1, 3, 8 ], [ 52, 1, 4, 8 ], [ 59, 1, 22, 16 ] ]

    k = 26: F-action on Pi is (  2,  7)(  5,240)      [60,1,26]
      Dynkin type is A_1(q^2) + A_1(q^2) + T(phi2^4)
      Order of center |Z^F|: phi2^4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/1536 phi1^2 ( q^2-14*q+45 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/1536 phi2 ( q^3-17*q^2+91*q-147 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/1536 phi1^2 ( q^2-14*q+45 )
        q congruent 7 modulo 60:   1/1536 phi2 ( q^3-17*q^2+91*q-147 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/1536 phi1^2 ( q^2-14*q+45 )
        q congruent 11 modulo 60:   1/1536 phi2 ( q^3-17*q^2+91*q-147 )
        q congruent 13 modulo 60:   1/1536 phi1^2 ( q^2-14*q+45 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/1536 phi1^2 ( q^2-14*q+45 )
        q congruent 19 modulo 60:   1/1536 phi2 ( q^3-17*q^2+91*q-147 )
        q congruent 21 modulo 60:   1/1536 phi1^2 ( q^2-14*q+45 )
        q congruent 23 modulo 60:   1/1536 phi2 ( q^3-17*q^2+91*q-147 )
        q congruent 25 modulo 60:   1/1536 phi1^2 ( q^2-14*q+45 )
        q congruent 27 modulo 60:   1/1536 phi2 ( q^3-17*q^2+91*q-147 )
        q congruent 29 modulo 60:   1/1536 phi1^2 ( q^2-14*q+45 )
        q congruent 31 modulo 60:   1/1536 phi2 ( q^3-17*q^2+91*q-147 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/1536 phi1^2 ( q^2-14*q+45 )
        q congruent 41 modulo 60:   1/1536 phi1^2 ( q^2-14*q+45 )
        q congruent 43 modulo 60:   1/1536 phi2 ( q^3-17*q^2+91*q-147 )
        q congruent 47 modulo 60:   1/1536 phi2 ( q^3-17*q^2+91*q-147 )
        q congruent 49 modulo 60:   1/1536 phi1^2 ( q^2-14*q+45 )
        q congruent 53 modulo 60:   1/1536 phi1^2 ( q^2-14*q+45 )
        q congruent 59 modulo 60:   1/1536 phi2 ( q^3-17*q^2+91*q-147 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 5, 71, 71, 17 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 12 ], [ 3, 1, 2, 32 ], [ 4, 1, 1, 16 ], 
  [ 4, 1, 2, 24 ], [ 9, 1, 1, 3 ], [ 10, 1, 2, 24 ], [ 11, 1, 2, 96 ], 
  [ 12, 1, 2, 96 ], [ 13, 1, 2, 32 ], [ 13, 1, 4, 144 ], [ 16, 1, 4, 128 ], 
  [ 20, 1, 2, 192 ], [ 23, 1, 2, 24 ], [ 24, 1, 2, 72 ], [ 25, 1, 3, 48 ], 
  [ 25, 1, 4, 96 ], [ 27, 1, 6, 192 ], [ 28, 1, 4, 288 ], [ 33, 1, 10, 256 ], 
  [ 35, 1, 4, 384 ], [ 39, 1, 3, 144 ], [ 40, 1, 6, 192 ], [ 41, 1, 9, 288 ], 
  [ 41, 1, 10, 192 ], [ 43, 1, 12, 384 ], [ 44, 1, 10, 576 ], 
  [ 49, 1, 19, 768 ], [ 52, 1, 10, 576 ], [ 53, 1, 19, 768 ], 
  [ 59, 1, 2, 1152 ] ]

    k = 27: F-action on Pi is ()      [60,1,27]
      Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/256 phi1 ( q^3-11*q^2+43*q-65 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/256 ( q^4-12*q^3+54*q^2-108*q+81 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/256 phi1 ( q^3-11*q^2+43*q-65 )
        q congruent 7 modulo 60:   1/256 ( q^4-12*q^3+54*q^2-108*q+81 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/256 phi1 ( q^3-11*q^2+43*q-65 )
        q congruent 11 modulo 60:   1/256 ( q^4-12*q^3+54*q^2-108*q+81 )
        q congruent 13 modulo 60:   1/256 phi1 ( q^3-11*q^2+43*q-65 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/256 phi1 ( q^3-11*q^2+43*q-65 )
        q congruent 19 modulo 60:   1/256 ( q^4-12*q^3+54*q^2-108*q+81 )
        q congruent 21 modulo 60:   1/256 phi1 ( q^3-11*q^2+43*q-65 )
        q congruent 23 modulo 60:   1/256 ( q^4-12*q^3+54*q^2-108*q+81 )
        q congruent 25 modulo 60:   1/256 phi1 ( q^3-11*q^2+43*q-65 )
        q congruent 27 modulo 60:   1/256 ( q^4-12*q^3+54*q^2-108*q+81 )
        q congruent 29 modulo 60:   1/256 phi1 ( q^3-11*q^2+43*q-65 )
        q congruent 31 modulo 60:   1/256 ( q^4-12*q^3+54*q^2-108*q+81 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/256 phi1 ( q^3-11*q^2+43*q-65 )
        q congruent 41 modulo 60:   1/256 phi1 ( q^3-11*q^2+43*q-65 )
        q congruent 43 modulo 60:   1/256 ( q^4-12*q^3+54*q^2-108*q+81 )
        q congruent 47 modulo 60:   1/256 ( q^4-12*q^3+54*q^2-108*q+81 )
        q congruent 49 modulo 60:   1/256 phi1 ( q^3-11*q^2+43*q-65 )
        q congruent 53 modulo 60:   1/256 phi1 ( q^3-11*q^2+43*q-65 )
        q congruent 59 modulo 60:   1/256 ( q^4-12*q^3+54*q^2-108*q+81 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4, 68, 68, 7, 68, 3, 7, 69, 68, 7, 3, 69, 7, 69, 69, 5 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 12 ], 
  [ 9, 1, 1, 7 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 24 ], 
  [ 13, 1, 2, 16 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 24 ], [ 20, 1, 2, 32 ], 
  [ 20, 1, 3, 32 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 28 ], 
  [ 24, 1, 2, 28 ], [ 25, 1, 1, 24 ], [ 25, 1, 2, 32 ], [ 25, 1, 3, 24 ], 
  [ 25, 1, 4, 32 ], [ 28, 1, 2, 16 ], [ 28, 1, 3, 16 ], [ 35, 1, 3, 64 ], 
  [ 35, 1, 6, 64 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 16 ], [ 39, 1, 3, 8 ], 
  [ 39, 1, 4, 16 ], [ 41, 1, 1, 48 ], [ 41, 1, 2, 32 ], [ 41, 1, 4, 64 ], 
  [ 41, 1, 6, 96 ], [ 41, 1, 9, 48 ], [ 43, 1, 3, 64 ], [ 43, 1, 8, 64 ], 
  [ 43, 1, 12, 64 ], [ 44, 1, 5, 32 ], [ 44, 1, 9, 32 ], [ 49, 1, 5, 128 ], 
  [ 49, 1, 9, 128 ], [ 52, 1, 2, 32 ], [ 52, 1, 9, 32 ], [ 53, 1, 6, 128 ], 
  [ 53, 1, 9, 128 ], [ 59, 1, 3, 64 ] ]

    k = 28: F-action on Pi is ()      [60,1,28]
      Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2 phi4)
      Order of center |Z^F|: phi1 phi2 phi4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 7 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 11 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 19 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 23 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 27 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 31 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 41 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 43 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 53 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 59 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 70, 19, 19, 76, 19, 72, 76, 20, 19, 76, 72, 20, 76, 20, 20, 71 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 6 ], 
  [ 9, 1, 1, 3 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], 
  [ 13, 1, 4, 8 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], [ 25, 1, 1, 4 ], 
  [ 25, 1, 2, 8 ], [ 25, 1, 3, 4 ], [ 25, 1, 4, 8 ], [ 39, 1, 2, 4 ], 
  [ 39, 1, 5, 4 ], [ 41, 1, 2, 8 ], [ 41, 1, 4, 16 ], [ 41, 1, 5, 8 ], 
  [ 41, 1, 8, 16 ], [ 43, 1, 9, 16 ], [ 44, 1, 4, 8 ], [ 44, 1, 6, 8 ], 
  [ 53, 1, 11, 32 ], [ 53, 1, 13, 32 ], [ 59, 1, 16, 16 ] ]

    k = 29: F-action on Pi is (  2,  7)(  5,240)      [60,1,29]
      Dynkin type is A_1(q^2) + A_1(q^2) + T(phi1 phi2 phi4)
      Order of center |Z^F|: phi1 phi2 phi4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 7 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 11 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 19 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 23 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 27 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 31 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 41 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 43 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 53 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 59 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 72, 18, 18, 75 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 6 ], [ 4, 1, 2, 6 ], [ 9, 1, 1, 7 ], 
  [ 13, 1, 2, 12 ], [ 13, 1, 3, 12 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], 
  [ 25, 1, 1, 12 ], [ 25, 1, 3, 12 ], [ 39, 1, 2, 4 ], [ 39, 1, 5, 4 ], 
  [ 41, 1, 2, 24 ], [ 41, 1, 5, 24 ], [ 43, 1, 9, 16 ], [ 44, 1, 4, 8 ], 
  [ 44, 1, 6, 8 ], [ 53, 1, 10, 32 ], [ 53, 1, 14, 32 ], [ 59, 1, 16, 16 ] ]

    k = 30: F-action on Pi is (  5,240)      [60,1,30]
      Dynkin type is A_1(q) + A_1(q^2) + A_1(q) + T(phi2^2 phi4)
      Order of center |Z^F|: phi2^2 phi4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 7 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 11 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 19 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 23 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 27 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 31 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 41 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 43 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 53 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 59 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 72, 20, 18, 74, 20, 71, 74, 17 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 8 ], [ 4, 1, 2, 4 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 2, 4 ], [ 13, 1, 2, 16 ], [ 13, 1, 4, 8 ], 
  [ 23, 1, 2, 4 ], [ 24, 1, 2, 12 ], [ 25, 1, 3, 8 ], [ 25, 1, 4, 16 ], 
  [ 39, 1, 3, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 5, 8 ], [ 41, 1, 8, 16 ], 
  [ 41, 1, 9, 16 ], [ 41, 1, 10, 32 ], [ 43, 1, 9, 16 ], [ 44, 1, 4, 16 ], 
  [ 49, 1, 4, 32 ], [ 52, 1, 5, 16 ], [ 53, 1, 11, 32 ], [ 53, 1, 14, 32 ], 
  [ 59, 1, 24, 32 ] ]

    k = 31: F-action on Pi is (  5,240)      [60,1,31]
      Dynkin type is A_1(q) + A_1(q^2) + A_1(q) + T(phi1^2 phi4)
      Order of center |Z^F|: phi1^2 phi4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/64 phi1 phi2 ( q^2-8*q+15 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/64 phi1 phi2 ( q^2-8*q+15 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/64 phi1 phi2 ( q^2-8*q+15 )
        q congruent 7 modulo 60:   1/64 phi1 phi2 ( q^2-8*q+15 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/64 phi1 phi2 ( q^2-8*q+15 )
        q congruent 11 modulo 60:   1/64 phi1 phi2 ( q^2-8*q+15 )
        q congruent 13 modulo 60:   1/64 phi1 phi2 ( q^2-8*q+15 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/64 phi1 phi2 ( q^2-8*q+15 )
        q congruent 19 modulo 60:   1/64 phi1 phi2 ( q^2-8*q+15 )
        q congruent 21 modulo 60:   1/64 phi1 phi2 ( q^2-8*q+15 )
        q congruent 23 modulo 60:   1/64 phi1 phi2 ( q^2-8*q+15 )
        q congruent 25 modulo 60:   1/64 phi1 phi2 ( q^2-8*q+15 )
        q congruent 27 modulo 60:   1/64 phi1 phi2 ( q^2-8*q+15 )
        q congruent 29 modulo 60:   1/64 phi1 phi2 ( q^2-8*q+15 )
        q congruent 31 modulo 60:   1/64 phi1 phi2 ( q^2-8*q+15 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/64 phi1 phi2 ( q^2-8*q+15 )
        q congruent 41 modulo 60:   1/64 phi1 phi2 ( q^2-8*q+15 )
        q congruent 43 modulo 60:   1/64 phi1 phi2 ( q^2-8*q+15 )
        q congruent 47 modulo 60:   1/64 phi1 phi2 ( q^2-8*q+15 )
        q congruent 49 modulo 60:   1/64 phi1 phi2 ( q^2-8*q+15 )
        q congruent 53 modulo 60:   1/64 phi1 phi2 ( q^2-8*q+15 )
        q congruent 59 modulo 60:   1/64 phi1 phi2 ( q^2-8*q+15 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 70, 19, 16, 73, 19, 72, 73, 18 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 8 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 3, 16 ], 
  [ 23, 1, 1, 4 ], [ 24, 1, 1, 12 ], [ 25, 1, 1, 8 ], [ 25, 1, 2, 16 ], 
  [ 39, 1, 1, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 1, 16 ], [ 41, 1, 3, 32 ], 
  [ 41, 1, 5, 8 ], [ 41, 1, 8, 16 ], [ 43, 1, 9, 16 ], [ 44, 1, 6, 16 ], 
  [ 49, 1, 7, 32 ], [ 52, 1, 8, 16 ], [ 53, 1, 10, 32 ], [ 53, 1, 13, 32 ], 
  [ 59, 1, 23, 32 ] ]

    k = 32: F-action on Pi is (  2,240)(  5,  7)      [60,1,32]
      Dynkin type is A_1(q^2) + A_1(q^2) + T(phi1 phi2 phi4)
      Order of center |Z^F|: phi1 phi2 phi4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1^2 phi2^2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/32 phi1^2 phi2^2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/32 phi1^2 phi2^2
        q congruent 7 modulo 60:   1/32 phi1^2 phi2^2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/32 phi1^2 phi2^2
        q congruent 11 modulo 60:   1/32 phi1^2 phi2^2
        q congruent 13 modulo 60:   1/32 phi1^2 phi2^2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/32 phi1^2 phi2^2
        q congruent 19 modulo 60:   1/32 phi1^2 phi2^2
        q congruent 21 modulo 60:   1/32 phi1^2 phi2^2
        q congruent 23 modulo 60:   1/32 phi1^2 phi2^2
        q congruent 25 modulo 60:   1/32 phi1^2 phi2^2
        q congruent 27 modulo 60:   1/32 phi1^2 phi2^2
        q congruent 29 modulo 60:   1/32 phi1^2 phi2^2
        q congruent 31 modulo 60:   1/32 phi1^2 phi2^2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/32 phi1^2 phi2^2
        q congruent 41 modulo 60:   1/32 phi1^2 phi2^2
        q congruent 43 modulo 60:   1/32 phi1^2 phi2^2
        q congruent 47 modulo 60:   1/32 phi1^2 phi2^2
        q congruent 49 modulo 60:   1/32 phi1^2 phi2^2
        q congruent 53 modulo 60:   1/32 phi1^2 phi2^2
        q congruent 59 modulo 60:   1/32 phi1^2 phi2^2
      Fusion of maximal tori of C^F in those of G^F:
        [ 76, 22, 22, 75 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 2, 2 ], [ 9, 1, 1, 3 ], 
  [ 13, 1, 2, 4 ], [ 13, 1, 3, 4 ], [ 23, 1, 1, 2 ], [ 23, 1, 2, 2 ], 
  [ 25, 1, 1, 4 ], [ 25, 1, 3, 4 ], [ 39, 1, 2, 4 ], [ 39, 1, 5, 4 ], 
  [ 41, 1, 2, 8 ], [ 41, 1, 5, 8 ], [ 43, 1, 11, 16 ], [ 44, 1, 4, 8 ], 
  [ 44, 1, 6, 8 ], [ 59, 1, 16, 16 ] ]

    k = 33: F-action on Pi is (  5,240)      [60,1,33]
      Dynkin type is A_1(q) + A_1(q^2) + A_1(q) + T(phi1 phi2 phi4)
      Order of center |Z^F|: phi1 phi2 phi4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1^3 phi2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/32 phi1^3 phi2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/32 phi1^3 phi2
        q congruent 7 modulo 60:   1/32 phi1^3 phi2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/32 phi1^3 phi2
        q congruent 11 modulo 60:   1/32 phi1^3 phi2
        q congruent 13 modulo 60:   1/32 phi1^3 phi2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/32 phi1^3 phi2
        q congruent 19 modulo 60:   1/32 phi1^3 phi2
        q congruent 21 modulo 60:   1/32 phi1^3 phi2
        q congruent 23 modulo 60:   1/32 phi1^3 phi2
        q congruent 25 modulo 60:   1/32 phi1^3 phi2
        q congruent 27 modulo 60:   1/32 phi1^3 phi2
        q congruent 29 modulo 60:   1/32 phi1^3 phi2
        q congruent 31 modulo 60:   1/32 phi1^3 phi2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/32 phi1^3 phi2
        q congruent 41 modulo 60:   1/32 phi1^3 phi2
        q congruent 43 modulo 60:   1/32 phi1^3 phi2
        q congruent 47 modulo 60:   1/32 phi1^3 phi2
        q congruent 49 modulo 60:   1/32 phi1^3 phi2
        q congruent 53 modulo 60:   1/32 phi1^3 phi2
        q congruent 59 modulo 60:   1/32 phi1^3 phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 19, 76, 73, 18, 76, 20, 18, 74 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 2 ], [ 24, 1, 1, 6 ], [ 24, 1, 2, 6 ], [ 39, 1, 4, 4 ], 
  [ 39, 1, 5, 4 ], [ 41, 1, 5, 8 ], [ 41, 1, 6, 8 ], [ 41, 1, 7, 16 ], 
  [ 41, 1, 8, 16 ], [ 49, 1, 4, 16 ], [ 49, 1, 7, 16 ], [ 52, 1, 5, 8 ], 
  [ 52, 1, 8, 8 ], [ 59, 1, 21, 16 ] ]

    k = 34: F-action on Pi is (  2,  7)(  5,240)      [60,1,34]
      Dynkin type is A_1(q^2) + A_1(q^2) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/256 phi1 ( q^3-11*q^2+27*q+15 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/256 phi2 ( q^3-13*q^2+51*q-63 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/256 phi1 ( q^3-11*q^2+27*q+15 )
        q congruent 7 modulo 60:   1/256 phi2 ( q^3-13*q^2+51*q-63 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/256 phi1 ( q^3-11*q^2+27*q+15 )
        q congruent 11 modulo 60:   1/256 phi2 ( q^3-13*q^2+51*q-63 )
        q congruent 13 modulo 60:   1/256 phi1 ( q^3-11*q^2+27*q+15 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/256 phi1 ( q^3-11*q^2+27*q+15 )
        q congruent 19 modulo 60:   1/256 phi2 ( q^3-13*q^2+51*q-63 )
        q congruent 21 modulo 60:   1/256 phi1 ( q^3-11*q^2+27*q+15 )
        q congruent 23 modulo 60:   1/256 phi2 ( q^3-13*q^2+51*q-63 )
        q congruent 25 modulo 60:   1/256 phi1 ( q^3-11*q^2+27*q+15 )
        q congruent 27 modulo 60:   1/256 phi2 ( q^3-13*q^2+51*q-63 )
        q congruent 29 modulo 60:   1/256 phi1 ( q^3-11*q^2+27*q+15 )
        q congruent 31 modulo 60:   1/256 phi2 ( q^3-13*q^2+51*q-63 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/256 phi1 ( q^3-11*q^2+27*q+15 )
        q congruent 41 modulo 60:   1/256 phi1 ( q^3-11*q^2+27*q+15 )
        q congruent 43 modulo 60:   1/256 phi2 ( q^3-13*q^2+51*q-63 )
        q congruent 47 modulo 60:   1/256 phi2 ( q^3-13*q^2+51*q-63 )
        q congruent 49 modulo 60:   1/256 phi1 ( q^3-11*q^2+27*q+15 )
        q congruent 53 modulo 60:   1/256 phi1 ( q^3-11*q^2+27*q+15 )
        q congruent 59 modulo 60:   1/256 phi2 ( q^3-13*q^2+51*q-63 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 72, 72, 18 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 12 ], [ 4, 1, 2, 12 ], 
  [ 7, 1, 1, 16 ], [ 7, 1, 2, 16 ], [ 9, 1, 1, 11 ], [ 10, 1, 1, 4 ], 
  [ 10, 1, 2, 4 ], [ 13, 1, 1, 8 ], [ 13, 1, 2, 32 ], [ 13, 1, 3, 32 ], 
  [ 13, 1, 4, 8 ], [ 20, 1, 1, 32 ], [ 20, 1, 4, 32 ], [ 20, 1, 5, 64 ], 
  [ 20, 1, 8, 64 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 12 ], 
  [ 24, 1, 2, 12 ], [ 25, 1, 1, 40 ], [ 25, 1, 2, 16 ], [ 25, 1, 3, 40 ], 
  [ 25, 1, 4, 16 ], [ 26, 1, 1, 32 ], [ 26, 1, 4, 32 ], [ 28, 1, 2, 16 ], 
  [ 28, 1, 3, 16 ], [ 35, 1, 2, 64 ], [ 35, 1, 7, 64 ], [ 39, 1, 1, 8 ], 
  [ 39, 1, 2, 16 ], [ 39, 1, 3, 8 ], [ 39, 1, 4, 16 ], [ 41, 1, 1, 16 ], 
  [ 41, 1, 2, 96 ], [ 41, 1, 3, 32 ], [ 41, 1, 6, 32 ], [ 41, 1, 9, 16 ], 
  [ 41, 1, 10, 32 ], [ 43, 1, 1, 64 ], [ 43, 1, 5, 128 ], [ 43, 1, 8, 64 ], 
  [ 43, 1, 13, 64 ], [ 44, 1, 5, 32 ], [ 44, 1, 9, 32 ], [ 49, 1, 14, 128 ], 
  [ 49, 1, 20, 128 ], [ 52, 1, 2, 32 ], [ 52, 1, 9, 32 ], [ 53, 1, 2, 128 ], 
  [ 53, 1, 12, 128 ], [ 59, 1, 3, 64 ] ]

    k = 35: F-action on Pi is (  2,240,  7,  5)      [60,1,35]
      Dynkin type is A_1(q^4) + T(phi1^2 phi4)
      Order of center |Z^F|: phi1^2 phi4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 7 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 11 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 13 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 19 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 21 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 23 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 25 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 27 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 29 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 31 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 41 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 43 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 47 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 49 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 53 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
        q congruent 59 modulo 60:   1/64 phi1^2 phi2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 73, 44 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 2, 4 ], [ 7, 1, 2, 8 ], 
  [ 9, 1, 1, 1 ], [ 10, 1, 1, 4 ], [ 13, 1, 3, 8 ], [ 20, 1, 6, 16 ], 
  [ 20, 1, 8, 16 ], [ 23, 1, 1, 4 ], [ 24, 1, 1, 4 ], [ 25, 1, 2, 8 ], 
  [ 26, 1, 2, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 3, 16 ], 
  [ 41, 1, 8, 8 ], [ 43, 1, 6, 32 ], [ 44, 1, 6, 16 ], [ 49, 1, 17, 32 ], 
  [ 52, 1, 8, 16 ], [ 59, 1, 23, 32 ] ]

    k = 36: F-action on Pi is (  2,240,  7,  5)      [60,1,36]
      Dynkin type is A_1(q^4) + T(phi2^2 phi4)
      Order of center |Z^F|: phi2^2 phi4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/64 phi1^2 phi2^2
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/64 phi1^2 phi2^2
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/64 phi1^2 phi2^2
        q congruent 7 modulo 60:   1/64 phi1^2 phi2^2
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/64 phi1^2 phi2^2
        q congruent 11 modulo 60:   1/64 phi1^2 phi2^2
        q congruent 13 modulo 60:   1/64 phi1^2 phi2^2
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/64 phi1^2 phi2^2
        q congruent 19 modulo 60:   1/64 phi1^2 phi2^2
        q congruent 21 modulo 60:   1/64 phi1^2 phi2^2
        q congruent 23 modulo 60:   1/64 phi1^2 phi2^2
        q congruent 25 modulo 60:   1/64 phi1^2 phi2^2
        q congruent 27 modulo 60:   1/64 phi1^2 phi2^2
        q congruent 29 modulo 60:   1/64 phi1^2 phi2^2
        q congruent 31 modulo 60:   1/64 phi1^2 phi2^2
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/64 phi1^2 phi2^2
        q congruent 41 modulo 60:   1/64 phi1^2 phi2^2
        q congruent 43 modulo 60:   1/64 phi1^2 phi2^2
        q congruent 47 modulo 60:   1/64 phi1^2 phi2^2
        q congruent 49 modulo 60:   1/64 phi1^2 phi2^2
        q congruent 53 modulo 60:   1/64 phi1^2 phi2^2
        q congruent 59 modulo 60:   1/64 phi1^2 phi2^2
      Fusion of maximal tori of C^F in those of G^F:
        [ 74, 45 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 4, 1, 1, 4 ], [ 7, 1, 1, 8 ], 
  [ 9, 1, 1, 1 ], [ 10, 1, 2, 4 ], [ 13, 1, 2, 8 ], [ 20, 1, 5, 16 ], 
  [ 20, 1, 7, 16 ], [ 23, 1, 2, 4 ], [ 24, 1, 2, 4 ], [ 25, 1, 4, 8 ], 
  [ 26, 1, 3, 16 ], [ 39, 1, 3, 8 ], [ 39, 1, 5, 4 ], [ 41, 1, 8, 8 ], 
  [ 41, 1, 10, 16 ], [ 43, 1, 14, 32 ], [ 44, 1, 4, 16 ], [ 49, 1, 13, 32 ], 
  [ 52, 1, 5, 16 ], [ 59, 1, 24, 32 ] ]

    k = 37: F-action on Pi is (  2,240,  7,  5)      [60,1,37]
      Dynkin type is A_1(q^4) + T(phi1 phi2 phi4)
      Order of center |Z^F|: phi1 phi2 phi4 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 7 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 11 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 13 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 19 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 21 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 23 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 25 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 27 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 29 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 31 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 41 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 43 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 47 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 49 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 53 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
        q congruent 59 modulo 60:   1/32 phi1 phi2^2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 18, 91 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 7, 1, 1, 4 ], [ 7, 1, 2, 4 ], 
  [ 9, 1, 1, 5 ], [ 10, 1, 1, 2 ], [ 10, 1, 2, 2 ], [ 20, 1, 5, 8 ], 
  [ 20, 1, 6, 8 ], [ 20, 1, 7, 8 ], [ 20, 1, 8, 8 ], [ 24, 1, 1, 2 ], 
  [ 24, 1, 2, 2 ], [ 26, 1, 1, 8 ], [ 26, 1, 4, 8 ], [ 39, 1, 4, 4 ], 
  [ 39, 1, 5, 4 ], [ 41, 1, 7, 8 ], [ 41, 1, 8, 8 ], [ 43, 1, 5, 16 ], 
  [ 43, 1, 7, 16 ], [ 43, 1, 10, 16 ], [ 49, 1, 13, 16 ], [ 49, 1, 17, 16 ], 
  [ 52, 1, 5, 8 ], [ 52, 1, 8, 8 ], [ 59, 1, 21, 16 ] ]

    k = 38: F-action on Pi is (  2,  7)(  5,240)      [60,1,38]
      Dynkin type is A_1(q^2) + A_1(q^2) + T(phi1^2 phi2^2)
      Order of center |Z^F|: phi1^2 phi2^2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/128 phi1^2 ( q^2-2*q-7 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/128 phi2^2 ( q^2-6*q+9 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/128 phi1^2 ( q^2-2*q-7 )
        q congruent 7 modulo 60:   1/128 phi2^2 ( q^2-6*q+9 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/128 phi1^2 ( q^2-2*q-7 )
        q congruent 11 modulo 60:   1/128 phi2^2 ( q^2-6*q+9 )
        q congruent 13 modulo 60:   1/128 phi1^2 ( q^2-2*q-7 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/128 phi1^2 ( q^2-2*q-7 )
        q congruent 19 modulo 60:   1/128 phi2^2 ( q^2-6*q+9 )
        q congruent 21 modulo 60:   1/128 phi1^2 ( q^2-2*q-7 )
        q congruent 23 modulo 60:   1/128 phi2^2 ( q^2-6*q+9 )
        q congruent 25 modulo 60:   1/128 phi1^2 ( q^2-2*q-7 )
        q congruent 27 modulo 60:   1/128 phi2^2 ( q^2-6*q+9 )
        q congruent 29 modulo 60:   1/128 phi1^2 ( q^2-2*q-7 )
        q congruent 31 modulo 60:   1/128 phi2^2 ( q^2-6*q+9 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/128 phi1^2 ( q^2-2*q-7 )
        q congruent 41 modulo 60:   1/128 phi1^2 ( q^2-2*q-7 )
        q congruent 43 modulo 60:   1/128 phi2^2 ( q^2-6*q+9 )
        q congruent 47 modulo 60:   1/128 phi2^2 ( q^2-6*q+9 )
        q congruent 49 modulo 60:   1/128 phi1^2 ( q^2-2*q-7 )
        q congruent 53 modulo 60:   1/128 phi1^2 ( q^2-2*q-7 )
        q congruent 59 modulo 60:   1/128 phi2^2 ( q^2-6*q+9 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 7, 76, 76, 18 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 4, 1, 1, 4 ], [ 4, 1, 2, 4 ], 
  [ 9, 1, 1, 3 ], [ 10, 1, 1, 4 ], [ 10, 1, 2, 4 ], [ 13, 1, 1, 8 ], 
  [ 13, 1, 2, 16 ], [ 13, 1, 3, 16 ], [ 13, 1, 4, 8 ], [ 20, 1, 6, 32 ], 
  [ 20, 1, 7, 32 ], [ 23, 1, 1, 4 ], [ 23, 1, 2, 4 ], [ 24, 1, 1, 12 ], 
  [ 24, 1, 2, 12 ], [ 25, 1, 1, 8 ], [ 25, 1, 3, 8 ], [ 28, 1, 2, 16 ], 
  [ 28, 1, 3, 16 ], [ 39, 1, 1, 8 ], [ 39, 1, 2, 16 ], [ 39, 1, 3, 8 ], 
  [ 39, 1, 4, 16 ], [ 41, 1, 1, 16 ], [ 41, 1, 2, 32 ], [ 41, 1, 6, 32 ], 
  [ 41, 1, 7, 32 ], [ 41, 1, 9, 16 ], [ 43, 1, 7, 64 ], [ 44, 1, 5, 32 ], 
  [ 44, 1, 9, 32 ], [ 49, 1, 15, 64 ], [ 49, 1, 18, 64 ], [ 52, 1, 2, 32 ], 
  [ 52, 1, 9, 32 ], [ 59, 1, 3, 64 ] ]

    k = 39: F-action on Pi is (  2,  7)(  5,240)      [60,1,39]
      Dynkin type is A_1(q^2) + A_1(q^2) + T(phi1 phi2^3)
      Order of center |Z^F|: phi1 phi2^3 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/128 phi1^2 phi2 ( q-5 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/128 phi2 ( q^3-7*q^2+11*q+3 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/128 phi1^2 phi2 ( q-5 )
        q congruent 7 modulo 60:   1/128 phi2 ( q^3-7*q^2+11*q+3 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/128 phi1^2 phi2 ( q-5 )
        q congruent 11 modulo 60:   1/128 phi2 ( q^3-7*q^2+11*q+3 )
        q congruent 13 modulo 60:   1/128 phi1^2 phi2 ( q-5 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/128 phi1^2 phi2 ( q-5 )
        q congruent 19 modulo 60:   1/128 phi2 ( q^3-7*q^2+11*q+3 )
        q congruent 21 modulo 60:   1/128 phi1^2 phi2 ( q-5 )
        q congruent 23 modulo 60:   1/128 phi2 ( q^3-7*q^2+11*q+3 )
        q congruent 25 modulo 60:   1/128 phi1^2 phi2 ( q-5 )
        q congruent 27 modulo 60:   1/128 phi2 ( q^3-7*q^2+11*q+3 )
        q congruent 29 modulo 60:   1/128 phi1^2 phi2 ( q-5 )
        q congruent 31 modulo 60:   1/128 phi2 ( q^3-7*q^2+11*q+3 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/128 phi1^2 phi2 ( q-5 )
        q congruent 41 modulo 60:   1/128 phi1^2 phi2 ( q-5 )
        q congruent 43 modulo 60:   1/128 phi2 ( q^3-7*q^2+11*q+3 )
        q congruent 47 modulo 60:   1/128 phi2 ( q^3-7*q^2+11*q+3 )
        q congruent 49 modulo 60:   1/128 phi1^2 phi2 ( q-5 )
        q congruent 53 modulo 60:   1/128 phi1^2 phi2 ( q-5 )
        q congruent 59 modulo 60:   1/128 phi2 ( q^3-7*q^2+11*q+3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 69, 20, 20, 74 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 4 ], [ 3, 1, 2, 8 ], [ 4, 1, 1, 8 ], 
  [ 4, 1, 2, 12 ], [ 7, 1, 1, 8 ], [ 9, 1, 1, 3 ], [ 10, 1, 1, 2 ], 
  [ 10, 1, 2, 6 ], [ 11, 1, 2, 8 ], [ 12, 1, 2, 24 ], [ 13, 1, 2, 16 ], 
  [ 13, 1, 4, 24 ], [ 16, 1, 4, 32 ], [ 20, 1, 1, 16 ], [ 20, 1, 2, 16 ], 
  [ 20, 1, 5, 32 ], [ 20, 1, 7, 32 ], [ 23, 1, 2, 12 ], [ 24, 1, 1, 6 ], 
  [ 24, 1, 2, 18 ], [ 25, 1, 3, 24 ], [ 25, 1, 4, 16 ], [ 26, 1, 3, 16 ], 
  [ 27, 1, 3, 16 ], [ 28, 1, 3, 24 ], [ 28, 1, 4, 24 ], [ 33, 1, 10, 64 ], 
  [ 35, 1, 2, 32 ], [ 35, 1, 4, 32 ], [ 39, 1, 3, 24 ], [ 39, 1, 4, 12 ], 
  [ 40, 1, 6, 48 ], [ 41, 1, 6, 24 ], [ 41, 1, 7, 16 ], [ 41, 1, 9, 48 ], 
  [ 41, 1, 10, 32 ], [ 43, 1, 2, 32 ], [ 43, 1, 14, 64 ], [ 44, 1, 8, 48 ], 
  [ 49, 1, 14, 64 ], [ 49, 1, 15, 64 ], [ 49, 1, 19, 64 ], [ 52, 1, 9, 48 ], 
  [ 52, 1, 10, 48 ], [ 53, 1, 4, 64 ], [ 59, 1, 13, 96 ] ]

    k = 40: F-action on Pi is ()      [60,1,40]
      Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1^3 phi2)
      Order of center |Z^F|: phi1^3 phi2 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/384 phi1 ( q^3-17*q^2+87*q-135 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/384 ( q^4-18*q^3+104*q^2-198*q+63 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/384 phi1 ( q^3-17*q^2+87*q-135 )
        q congruent 7 modulo 60:   1/384 ( q^4-18*q^3+104*q^2-198*q+63 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/384 phi1 ( q^3-17*q^2+87*q-135 )
        q congruent 11 modulo 60:   1/384 ( q^4-18*q^3+104*q^2-198*q+63 )
        q congruent 13 modulo 60:   1/384 phi1 ( q^3-17*q^2+87*q-135 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/384 phi1 ( q^3-17*q^2+87*q-135 )
        q congruent 19 modulo 60:   1/384 ( q^4-18*q^3+104*q^2-198*q+63 )
        q congruent 21 modulo 60:   1/384 phi1 ( q^3-17*q^2+87*q-135 )
        q congruent 23 modulo 60:   1/384 ( q^4-18*q^3+104*q^2-198*q+63 )
        q congruent 25 modulo 60:   1/384 phi1 ( q^3-17*q^2+87*q-135 )
        q congruent 27 modulo 60:   1/384 ( q^4-18*q^3+104*q^2-198*q+63 )
        q congruent 29 modulo 60:   1/384 phi1 ( q^3-17*q^2+87*q-135 )
        q congruent 31 modulo 60:   1/384 ( q^4-18*q^3+104*q^2-198*q+63 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/384 phi1 ( q^3-17*q^2+87*q-135 )
        q congruent 41 modulo 60:   1/384 phi1 ( q^3-17*q^2+87*q-135 )
        q congruent 43 modulo 60:   1/384 ( q^4-18*q^3+104*q^2-198*q+63 )
        q congruent 47 modulo 60:   1/384 ( q^4-18*q^3+104*q^2-198*q+63 )
        q congruent 49 modulo 60:   1/384 phi1 ( q^3-17*q^2+87*q-135 )
        q congruent 53 modulo 60:   1/384 phi1 ( q^3-17*q^2+87*q-135 )
        q congruent 59 modulo 60:   1/384 ( q^4-18*q^3+104*q^2-198*q+63 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 66, 4, 4, 68, 4, 68, 68, 7, 4, 68, 68, 7, 68, 7, 7, 69 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 8 ], [ 3, 1, 1, 8 ], [ 4, 1, 1, 36 ], 
  [ 6, 1, 1, 32 ], [ 7, 1, 1, 8 ], [ 9, 1, 1, 7 ], [ 10, 1, 1, 6 ], 
  [ 10, 1, 2, 2 ], [ 11, 1, 1, 8 ], [ 12, 1, 1, 24 ], [ 13, 1, 1, 72 ], 
  [ 16, 1, 1, 96 ], [ 19, 1, 1, 32 ], [ 20, 1, 1, 48 ], [ 20, 1, 2, 48 ], 
  [ 23, 1, 1, 12 ], [ 24, 1, 1, 42 ], [ 24, 1, 2, 14 ], [ 25, 1, 1, 72 ], 
  [ 26, 1, 3, 16 ], [ 27, 1, 2, 16 ], [ 28, 1, 1, 24 ], [ 28, 1, 2, 24 ], 
  [ 33, 1, 1, 192 ], [ 35, 1, 1, 96 ], [ 35, 1, 3, 96 ], [ 39, 1, 1, 24 ], 
  [ 39, 1, 4, 12 ], [ 40, 1, 1, 48 ], [ 41, 1, 1, 144 ], [ 41, 1, 6, 72 ], 
  [ 42, 1, 4, 64 ], [ 43, 1, 2, 96 ], [ 44, 1, 2, 48 ], [ 49, 1, 1, 192 ], 
  [ 49, 1, 9, 192 ], [ 52, 1, 1, 48 ], [ 52, 1, 2, 48 ], [ 53, 1, 3, 192 ], 
  [ 59, 1, 12, 96 ] ]

    k = 41: F-action on Pi is ()      [60,1,41]
      Dynkin type is A_1(q) + A_1(q) + A_1(q) + A_1(q) + T(phi1 phi2^3)
      Order of center |Z^F|: phi1 phi2^3 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 60:   1/384 phi1 ( q^3-13*q^2+55*q-75 )
        q congruent 2 modulo 60:   0
        q congruent 3 modulo 60:   1/384 ( q^4-14*q^3+68*q^2-154*q+147 )
        q congruent 4 modulo 60:   0
        q congruent 5 modulo 60:   1/384 phi1 ( q^3-13*q^2+55*q-75 )
        q congruent 7 modulo 60:   1/384 ( q^4-14*q^3+68*q^2-154*q+147 )
        q congruent 8 modulo 60:   0
        q congruent 9 modulo 60:   1/384 phi1 ( q^3-13*q^2+55*q-75 )
        q congruent 11 modulo 60:   1/384 ( q^4-14*q^3+68*q^2-154*q+147 )
        q congruent 13 modulo 60:   1/384 phi1 ( q^3-13*q^2+55*q-75 )
        q congruent 16 modulo 60:   0
        q congruent 17 modulo 60:   1/384 phi1 ( q^3-13*q^2+55*q-75 )
        q congruent 19 modulo 60:   1/384 ( q^4-14*q^3+68*q^2-154*q+147 )
        q congruent 21 modulo 60:   1/384 phi1 ( q^3-13*q^2+55*q-75 )
        q congruent 23 modulo 60:   1/384 ( q^4-14*q^3+68*q^2-154*q+147 )
        q congruent 25 modulo 60:   1/384 phi1 ( q^3-13*q^2+55*q-75 )
        q congruent 27 modulo 60:   1/384 ( q^4-14*q^3+68*q^2-154*q+147 )
        q congruent 29 modulo 60:   1/384 phi1 ( q^3-13*q^2+55*q-75 )
        q congruent 31 modulo 60:   1/384 ( q^4-14*q^3+68*q^2-154*q+147 )
        q congruent 32 modulo 60:   0
        q congruent 37 modulo 60:   1/384 phi1 ( q^3-13*q^2+55*q-75 )
        q congruent 41 modulo 60:   1/384 phi1 ( q^3-13*q^2+55*q-75 )
        q congruent 43 modulo 60:   1/384 ( q^4-14*q^3+68*q^2-154*q+147 )
        q congruent 47 modulo 60:   1/384 ( q^4-14*q^3+68*q^2-154*q+147 )
        q congruent 49 modulo 60:   1/384 phi1 ( q^3-13*q^2+55*q-75 )
        q congruent 53 modulo 60:   1/384 phi1 ( q^3-13*q^2+55*q-75 )
        q congruent 59 modulo 60:   1/384 ( q^4-14*q^3+68*q^2-154*q+147 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 68, 7, 7, 69, 7, 69, 69, 5, 7, 69, 69, 5, 69