##  MAXTORSTRUCTS.g                  (C) Frank Lübeck (2023)

# in GAP4
q := Indeterminate(Cyclotomics,"q");
# in GAP3 use instead:
##  q := Indeterminate(Cyclotomics);
##  q.name := "q";

# This file provides the data from the article
#    F.Lübeck, "Greatest common divisors of values of integer polynomials and
#    an application to maximal tori", ???
# in GAP readable format (with the small change above GAP3 or GAP4).
# Everything is collected in a record 'MAXTORSTRUCTS'. It is a record with
# components "F4", "2B2", "2E6", "2E6scmodZ", "2F4", "2G2", "3D4", "E6", 
# "E6scmodZ", "E7", "E7scmodZ", "E8", "G2" corresponding to the types of 
# considered exceptional groups.
# Each such component is again a record with components:
#   names:   names for F-conjugacy classes
#   reps:    representative of classes as Coxeter words in same order
#   eldivs:  the elementary divisors of the corresponding maximal tori in same order
#            (each entry of form [m, [ el.divs for q = 0(m), ..., el.divs for q = (m-1) mod m ] ])
# 
# There is a utility function for displaying cyclotomic polynomial factors of a polynomial in q,
# e.g.:
#     MAXTORSTRUCTS.ShowPhiFactors(MAXTORSTRUCTS.E8.eldivs[100][2][1][1]);


MAXTORSTRUCTS := 
rec(
2B2 := rec(
eldivs := [ [ 1, [ [ q^2-1 ] ] ], [ 1, [ [ q^2+(-E(8)+E(8)^3)*q+1 ] ] ], [ 1, [ [ q^2+(E(8)-E(8)^3)*q+1 ] ] ] ],
names := [ "", "('1')", "('1','2','1')" ] ),
2E6 := rec(
eldivs := [ [ 1, [ [ q+1, q+1, q+1, q+1, q+1, q+1 ] ] ], [ 1, [ [ q-1, q-1, q^2-1, q^2-1 ] ] ], [ 1, [ [ q+1, q+1, q^2-1, q^2-1 ] ] ], [ 1, [ [ q^2-q+1, q^2-q+1, q^2-q+1 ] ] ], [ 1, [ [ q+1, q+1, q+1, q^3+1 ] ] ], [ 3, [ [ q^3+1, q^3+1 ], [ q^3+1, q^3+1 ], [ 3, 1/3*q^3+1/3, q^3+1 ] ] ], [ 1, [ [ q^3+q^2+q+1, q^3+q^2+q+1 ] ] ], [ 1, [ [ q^2-1, q^4-1 ] ] ], [ 1, [ [ q+1, q^5+1 ] ] ], [ 1, [ [ q^2+q+1, q^4+q^2+1 ] ] ], [ 1, [ [ q^2-1, q^4+q^3-q-1 ] ] ], [ 1, [ [ q-1, q^5-q^4+q^3-q^2+q-1 ] ] ], [ 1, [ [ q^2-1, q^4-q^3+q-1 ] ] ], [ 1, [ [ q^6-q^3+1 ] ] ], [ 1, [ [ q^6-q^5+q^3-q+1 ] ] ], [ 1, [ [ q+1, q+1, q+1, q+1, q^2-1 ] ] ], [ 1, [ [ q^2-1, q^2-1, q^2-1 ] ] ], [ 1, [ [ q-1, q-1, q^4-1 ] ] ], [ 1, [ [ q+1, q+1, q^4-1 ] ] ], [ 1, [ [ q+1, q+1, q^4-q^3+q-1 ] ] ], [ 1, [ [ q^2-q+1, q^4-q^3+q-1 ] ] ], [ 3, [ [ q^6-1 ], [ q^6-1 ], [ 3, 1/3*q^6-1/3 ] ] ], [ 1, [ [ q^6-q^4+q^2-1 ] ] ], [ 1, [ [ q^6-q^5+q-1 ] ] ], [ 1, [ [ q^6+q^5+q^4-q^2-q-1 ] ] ] ],
names := [ "A_0", "4A_1", "2A_1", "3A_2", "A_2", "2A_2", "D_4(a_1)", "A_3+A_1", "A_4", "E_6(a_2)", "D_4", "A_5+A_1", "A_2+2A_1", "E_6(a_1)", "E_6", "A_1", "3A_1", "A_3+2A_1", "A_3", "A_2+A_1", "2A_2+A_1", "A_5", "D_5", "A_4+A_1", "D_5(a_1)" ],
reps := [ [ 1, 2, 3, 1, 4, 2, 3, 1, 4, 3, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 6, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 6, 5, 4, 3, 1 ], [  ], [ 3, 4, 3, 5, 4, 3 ], [ 1, 2, 4, 3, 1, 5, 4, 3, 6, 5, 4, 3 ], [ 1, 2, 3, 1, 4, 3, 1, 5, 4, 3, 1, 6, 5, 4, 3, 1 ], [ 2, 3, 4, 2, 3, 4, 6, 5, 4, 2, 3, 4, 5, 6 ], [ 1, 4, 2, 3, 1, 4, 3, 5, 4, 2, 3, 1, 4, 6, 5, 4, 3, 1 ], [ 1, 2 ], [ 4, 5, 4, 2, 3, 1, 4, 5 ], [ 4, 2, 5, 4, 2, 3, 4, 5, 6, 5, 4, 2, 3, 4, 5, 6 ], [ 2, 4 ], [ 1, 5 ], [ 5, 4 ], [ 1, 2, 5, 4 ], [ 1, 2, 3, 1, 4, 3 ], [ 1, 3, 1, 4, 3, 1, 5, 4, 3, 1, 6, 5, 4, 3, 1 ], [ 2 ], [ 1 ], [ 2, 3, 4, 3, 5, 4, 3 ], [ 1, 3, 4, 3, 5, 4, 3 ], [ 1, 3, 1, 4, 3 ], [ 1, 2, 5 ], [ 2, 5, 4 ], [ 1, 5, 4 ], [ 1, 2, 4 ] ] ),
2E6scmodZ := rec(
eldivs := [ [ 1, [ [ 1/3*q+1/3, q+1, q+1, q+1, q+1, q+1 ] ] ], [ 1, [ [ q-1, q-1, 1/3*q^2-1/3, q^2-1 ] ] ], [ 1, [ [ 1/3*q+1/3, q+1, q^2-1, q^2-1 ] ] ], [ 1, [ [ 1/3*q^2-1/3*q+1/3, q^2-q+1, q^2-q+1 ] ] ], [ 1, [ [ 1/3*q+1/3, q+1, q+1, q^3+1 ] ] ], [ 1, [ [ 1/3*q^3+1/3, q^3+1 ] ] ], [ 1, [ [ 1/3*q^3+1/3*q^2+1/3*q+1/3, q^3+q^2+q+1 ] ] ], [ 1, [ [ 1/3*q^2-1/3, q^4-1 ] ] ], [ 1, [ [ 1/3*q+1/3, q^5+1 ] ] ], [ 1, [ [ q^2+q+1, 1/3*q^4+1/3*q^2+1/3 ] ] ], [ 1, [ [ 1/3*q^2-1/3, q^4+q^3-q-1 ] ] ], [ 1, [ [ q-1, 1/3*q^5-1/3*q^4+1/3*q^3-1/3*q^2+1/3*q-1/3 ] ] ], [ 1, [ [ 1/3*q^2-1/3, q^4-q^3+q-1 ] ] ], [ 1, [ [ 1/3*q^6-1/3*q^3+1/3 ] ] ], [ 1, [ [ 1/3*q^6-1/3*q^5+1/3*q^3-1/3*q+1/3 ] ] ], [ 1, [ [ 1/3*q+1/3, q+1, q+1, q+1, q^2-1 ] ] ], [ 1, [ [ 1/3*q^2-1/3, q^2-1, q^2-1 ] ] ], [ 1, [ [ q-1, q-1, 1/3*q^4-1/3 ] ] ], [ 1, [ [ 1/3*q+1/3, q+1, q^4-1 ] ] ], [ 1, [ [ 1/3*q+1/3, q+1, q^4-q^3+q-1 ] ] ], [ 1, [ [ 1/3*q^2-1/3*q+1/3, q^4-q^3+q-1 ] ] ], [ 1, [ [ 1/3*q^6-1/3 ] ] ], [ 1, [ [ 1/3*q^6-1/3*q^4+1/3*q^2-1/3 ] ] ], [ 1, [ [ 1/3*q^6-1/3*q^5+1/3*q-1/3 ] ] ], [ 1, [ [ 1/3*q^6+1/3*q^5+1/3*q^4-1/3*q^2-1/3*q-1/3 ] ] ] ],
names := [ "A_0", "4A_1", "2A_1", "3A_2", "A_2", "2A_2", "D_4(a_1)", "A_3+A_1", "A_4", "E_6(a_2)", "D_4", "A_5+A_1", "A_2+2A_1", "E_6(a_1)", "E_6", "A_1", "3A_1", "A_3+2A_1", "A_3", "A_2+A_1", "2A_2+A_1", "A_5", "D_5", "A_4+A_1", "D_5(a_1)" ] ),
2F4 := rec(
eldivs := [ [ 1, [ [ q^2-1, q^2-1 ] ] ], [ 1, [ [ q^4+(E(8)-E(8)^3)*q^3+(-E(8)+E(8)^3)*q-1 ] ] ], [ 1, [ [ q^4-1 ] ] ], [ 1, [ [ q^4+(E(8)-E(8)^3)*q^3+q^2+(E(8)-E(8)^3)*q+1 ] ] ], [ 1, [ [ q^4+(-E(8)+E(8)^3)*q^3+q^2+(-E(8)+E(8)^3)*q+1 ] ] ], [ 1, [ [ q^4+(-E(8)+E(8)^3)*q^3+(E(8)-E(8)^3)*q-1 ] ] ], [ 1, [ [ q^4+1 ] ] ], [ 1, [ [ q^4-q^2+1 ] ] ], [ 1, [ [ q^2+1, q^2+1 ] ] ], [ 1, [ [ q^2+(E(8)-E(8)^3)*q+1, q^2+(E(8)-E(8)^3)*q+1 ] ] ], [ 1, [ [ q^2+(-E(8)+E(8)^3)*q+1, q^2+(-E(8)+E(8)^3)*q+1 ] ] ] ],
names := [ "2a", "8a", "4a", "24a", "24b", "8a", "8b", "12a", "4b", "8c", "8d" ] ),
2G2 := rec(
eldivs := [ [ 1, [ [ q^2-1 ] ] ], [ 1, [ [ q^2+(E(12)^7-E(12)^11)*q+1 ] ] ], [ 2, [ [ q^2+1 ], [ 2, 1/2*q^2+1/2 ] ] ], [ 1, [ [ q^2+(-E(12)^7+E(12)^11)*q+1 ] ] ] ],
names := [ "", "('1')", "('1','2','1')", "('1','2','1','2','1')" ] ),
3D4 := rec(
eldivs := [ [ 1, [ [ q^4-q^3+q-1 ] ] ], [ 1, [ [ q-1, q^3-1 ] ] ], [ 1, [ [ q+1, q^3+1 ] ] ], [ 1, [ [ q^4+q^3-q-1 ] ] ], [ 1, [ [ q^4-q^2+1 ] ] ], [ 1, [ [ q^2+q+1, q^2+q+1 ] ] ], [ 1, [ [ q^2-q+1, q^2-q+1 ] ] ] ],
names := [ "C_3", "~A_2", "C_3+A_1", "~A_2+A_1", "F_4", "~A_2+A_2", "F_4(a_1)" ],
reps := [ [ 1 ], [  ], [ 1, 2, 3, 1, 2, 3 ], [ 3 ], [ 1, 3 ], [ 1, 2, 3, 1, 2, 4, 3, 2 ], [ 1, 2, 3, 2 ] ] ),
E6 := rec(
eldivs := [ [ 1, [ [ q-1, q-1, q-1, q-1, q-1, q-1 ] ] ], [ 1, [ [ q+1, q+1, q^2-1, q^2-1 ] ] ], [ 1, [ [ q-1, q-1, q^2-1, q^2-1 ] ] ], [ 1, [ [ q^2+q+1, q^2+q+1, q^2+q+1 ] ] ], [ 1, [ [ q-1, q-1, q-1, q^3-1 ] ] ], [ 3, [ [ q^3-1, q^3-1 ], [ 3, 1/3*q^3-1/3, q^3-1 ], [ q^3-1, q^3-1 ] ] ], [ 1, [ [ q^3-q^2+q-1, q^3-q^2+q-1 ] ] ], [ 1, [ [ q^2-1, q^4-1 ] ] ], [ 1, [ [ q-1, q^5-1 ] ] ], [ 1, [ [ q^2-q+1, q^4+q^2+1 ] ] ], [ 1, [ [ q^2-1, q^4-q^3+q-1 ] ] ], [ 1, [ [ q+1, q^5+q^4+q^3+q^2+q+1 ] ] ], [ 1, [ [ q^2-1, q^4+q^3-q-1 ] ] ], [ 1, [ [ q^6+q^3+1 ] ] ], [ 1, [ [ q^6+q^5-q^3+q+1 ] ] ], [ 1, [ [ q-1, q-1, q-1, q-1, q^2-1 ] ] ], [ 1, [ [ q^2-1, q^2-1, q^2-1 ] ] ], [ 1, [ [ q+1, q+1, q^4-1 ] ] ], [ 1, [ [ q-1, q-1, q^4-1 ] ] ], [ 1, [ [ q-1, q-1, q^4+q^3-q-1 ] ] ], [ 1, [ [ q^2+q+1, q^4+q^3-q-1 ] ] ], [ 3, [ [ q^6-1 ], [ 3, 1/3*q^6-1/3 ], [ q^6-1 ] ] ], [ 1, [ [ q^6-q^4+q^2-1 ] ] ], [ 1, [ [ q^6+q^5-q-1 ] ] ], [ 1, [ [ q^6-q^5+q^4-q^2+q-1 ] ] ] ],
names := [ "A_0", "4A_1", "2A_1", "3A_2", "A_2", "2A_2", "D_4(a_1)", "A_3+A_1", "A_4", "E_6(a_2)", "D_4", "A_5+A_1", "A_2+2A_1", "E_6(a_1)", "E_6", "A_1", "3A_1", "A_3+2A_1", "A_3", "A_2+A_1", "2A_2+A_1", "A_5", "D_5", "A_4+A_1", "D_5(a_1)" ],
reps := [ [  ], [ 3, 4, 3, 2, 4, 3, 5, 4, 3, 2, 4, 5 ], [ 1, 4 ], [ 1, 3, 1, 4, 3, 1, 2, 4, 5, 4, 3, 1, 2, 4, 3, 5, 6, 5, 4, 3, 2, 4, 5, 6 ], [ 1, 3 ], [ 1, 3, 5, 6 ], [ 3, 4, 3, 2, 4, 5 ], [ 1, 4, 3, 6 ], [ 1, 4, 3, 2 ], [ 1, 2, 3, 1, 5, 4, 6, 5, 4, 2, 3, 4 ], [ 3, 4, 2, 5 ], [ 1, 2, 3, 4, 2, 3, 4, 6, 5, 4, 2, 3, 4, 5 ], [ 1, 3, 2, 5 ], [ 1, 3, 4, 3, 2, 4, 5, 6 ], [ 1, 4, 6, 2, 3, 5 ], [ 1 ], [ 1, 4, 6 ], [ 1, 3, 4, 3, 2, 4, 3, 5, 4, 3, 2, 4, 5 ], [ 1, 4, 3 ], [ 1, 3, 2 ], [ 1, 3, 2, 5, 6 ], [ 1, 4, 6, 3, 5 ], [ 1, 3, 4, 2, 5 ], [ 1, 4, 3, 2, 6 ], [ 1, 4, 2, 5, 4, 2, 3 ] ] ),
E6scmodZ := rec(
eldivs := [ [ 1, [ [ 1/3*q-1/3, q-1, q-1, q-1, q-1, q-1 ] ] ], [ 1, [ [ q+1, q+1, 1/3*q^2-1/3, q^2-1 ] ] ], [ 1, [ [ 1/3*q-1/3, q-1, q^2-1, q^2-1 ] ] ], [ 1, [ [ 1/3*q^2+1/3*q+1/3, q^2+q+1, q^2+q+1 ] ] ], [ 1, [ [ 1/3*q-1/3, q-1, q-1, q^3-1 ] ] ], [ 1, [ [ 1/3*q^3-1/3, q^3-1 ] ] ], [ 1, [ [ 1/3*q^3-1/3*q^2+1/3*q-1/3, q^3-q^2+q-1 ] ] ], [ 1, [ [ 1/3*q^2-1/3, q^4-1 ] ] ], [ 1, [ [ 1/3*q-1/3, q^5-1 ] ] ], [ 1, [ [ q^2-q+1, 1/3*q^4+1/3*q^2+1/3 ] ] ], [ 1, [ [ 1/3*q^2-1/3, q^4-q^3+q-1 ] ] ], [ 1, [ [ q+1, 1/3*q^5+1/3*q^4+1/3*q^3+1/3*q^2+1/3*q+1/3 ] ] ], [ 1, [ [ 1/3*q^2-1/3, q^4+q^3-q-1 ] ] ], [ 1, [ [ 1/3*q^6+1/3*q^3+1/3 ] ] ], [ 1, [ [ 1/3*q^6+1/3*q^5-1/3*q^3+1/3*q+1/3 ] ] ], [ 1, [ [ 1/3*q-1/3, q-1, q-1, q-1, q^2-1 ] ] ], [ 1, [ [ 1/3*q^2-1/3, q^2-1, q^2-1 ] ] ], [ 1, [ [ q+1, q+1, 1/3*q^4-1/3 ] ] ], [ 1, [ [ 1/3*q-1/3, q-1, q^4-1 ] ] ], [ 1, [ [ 1/3*q-1/3, q-1, q^4+q^3-q-1 ] ] ], [ 1, [ [ 1/3*q^2+1/3*q+1/3, q^4+q^3-q-1 ] ] ], [ 1, [ [ 1/3*q^6-1/3 ] ] ], [ 1, [ [ 1/3*q^6-1/3*q^4+1/3*q^2-1/3 ] ] ], [ 1, [ [ 1/3*q^6+1/3*q^5-1/3*q-1/3 ] ] ], [ 1, [ [ 1/3*q^6-1/3*q^5+1/3*q^4-1/3*q^2+1/3*q-1/3 ] ] ] ],
names := [ "A_0", "4A_1", "2A_1", "3A_2", "A_2", "2A_2", "D_4(a_1)", "A_3+A_1", "A_4", "E_6(a_2)", "D_4", "A_5+A_1", "A_2+2A_1", "E_6(a_1)", "E_6", "A_1", "3A_1", "A_3+2A_1", "A_3", "A_2+A_1", "2A_2+A_1", "A_5", "D_5", "A_4+A_1", "D_5(a_1)" ] ),
E7 := rec(
eldivs := [ [ 1, [ [ q-1, q-1, q-1, q-1, q-1, q-1, q-1 ] ] ], [ 1, [ [ q+1, q+1, q+1, q+1, q+1, q^2-1 ] ] ], [ 2, [ [ q+1, q^2-1, q^2-1, q^2-1 ], [ 2, q+1, 1/2*q^2-1/2, q^2-1, q^2-1 ] ] ], [ 1, [ [ q-1, q-1, q-1, q^2-1, q^2-1 ] ] ], [ 1, [ [ q+1, q^2-1, q^2-1, q^2-1 ] ] ], [ 1, [ [ q-1, q-1, q-1, q-1, q^3-1 ] ] ], [ 1, [ [ q^2+q+1, q^2+q+1, q^3-1 ] ] ], [ 1, [ [ q-1, q^3-1, q^3-1 ] ] ], [ 1, [ [ q-1, q^3-q^2+q-1, q^3-q^2+q-1 ] ] ], [ 2, [ [ q-1, q^2-1, q^4-1 ], [ 2, q-1, 1/2*q^2-1/2, q^4-1 ] ] ], [ 1, [ [ q+1, q+1, q+1, q^4-1 ] ] ], [ 2, [ [ q^3+q^2+q+1, q^4-1 ], [ 2, q^3+q^2+q+1, 1/2*q^4-1/2 ] ] ], [ 1, [ [ q-1, q^2-1, q^4-1 ] ] ], [ 1, [ [ q-1, q-1, q^5-1 ] ] ], [ 1, [ [ q+1, q+1, q+1, q^4-q^3+q-1 ] ] ], [ 1, [ [ q-1, q^2-1, q^4-q^3+q-1 ] ] ], [ 1, [ [ q^2-q+1, q^5-q^4+q^3-q^2+q-1 ] ] ], [ 1, [ [ q-1, q^2-1, q^4+q^3-q-1 ] ] ], [ 1, [ [ q^3+1, q^4-q^3+q-1 ] ] ], [ 2, [ [ q+1, q^6-1 ], [ 2, q+1, 1/2*q^6-1/2 ] ] ], [ 1, [ [ q+1, q^6-1 ] ] ], [ 1, [ [ q^7-1 ] ] ], [ 1, [ [ q+1, q^6-q^4+q^2-1 ] ] ], [ 2, [ [ q^7-q^6+q^5-q^4+q^3-q^2+q-1 ], [ 2, 1/2*q^7-1/2*q^6+1/2*q^5-1/2*q^4+1/2*q^3-1/2*q^2+1/2*q-1/2 ] ] ], [ 1, [ [ q^7-q^6+q^4-q^3+q-1 ] ] ], [ 1, [ [ q+1, q^6-q^5+q-1 ] ] ], [ 1, [ [ q+1, q^6+q^5+q^4-q^2-q-1 ] ] ], [ 1, [ [ q+1, q^6-q^5+q^4-q^2+q-1 ] ] ], [ 1, [ [ q^7-q^5-q^4+q^3+q^2-1 ] ] ], [ 1, [ [ q^7+q^6+q^5-q^2-q-1 ] ] ], [ 1, [ [ q+1, q+1, q+1, q+1, q+1, q+1, q+1 ] ] ], [ 1, [ [ q-1, q-1, q-1, q-1, q-1, q^2-1 ] ] ], [ 2, [ [ q-1, q^2-1, q^2-1, q^2-1 ], [ 2, q-1, 1/2*q^2-1/2, q^2-1, q^2-1 ] ] ], [ 1, [ [ q+1, q+1, q+1, q^2-1, q^2-1 ] ] ], [ 1, [ [ q-1, q^2-1, q^2-1, q^2-1 ] ] ], [ 1, [ [ q+1, q+1, q+1, q+1, q^3+1 ] ] ], [ 1, [ [ q^2-q+1, q^2-q+1, q^3+1 ] ] ], [ 1, [ [ q+1, q^3+1, q^3+1 ] ] ], [ 1, [ [ q+1, q^3+q^2+q+1, q^3+q^2+q+1 ] ] ], [ 2, [ [ q+1, q^2-1, q^4-1 ], [ 2, q+1, 1/2*q^2-1/2, q^4-1 ] ] ], [ 1, [ [ q-1, q-1, q-1, q^4-1 ] ] ], [ 2, [ [ q^3-q^2+q-1, q^4-1 ], [ 2, q^3-q^2+q-1, 1/2*q^4-1/2 ] ] ], [ 1, [ [ q+1, q^2-1, q^4-1 ] ] ], [ 1, [ [ q+1, q+1, q^5+1 ] ] ], [ 1, [ [ q-1, q-1, q-1, q^4+q^3-q-1 ] ] ], [ 1, [ [ q+1, q^2-1, q^4+q^3-q-1 ] ] ], [ 1, [ [ q^2+q+1, q^5+q^4+q^3+q^2+q+1 ] ] ], [ 1, [ [ q+1, q^2-1, q^4-q^3+q-1 ] ] ], [ 1, [ [ q^3-1, q^4+q^3-q-1 ] ] ], [ 2, [ [ q-1, q^6-1 ], [ 2, q-1, 1/2*q^6-1/2 ] ] ], [ 1, [ [ q-1, q^6-1 ] ] ], [ 1, [ [ q^7+1 ] ] ], [ 1, [ [ q-1, q^6-q^4+q^2-1 ] ] ], [ 2, [ [ q^7+q^6+q^5+q^4+q^3+q^2+q+1 ], [ 2, 1/2*q^7+1/2*q^6+1/2*q^5+1/2*q^4+1/2*q^3+1/2*q^2+1/2*q+1/2 ] ] ], [ 1, [ [ q^7+q^6-q^4-q^3+q+1 ] ] ], [ 1, [ [ q-1, q^6+q^5-q-1 ] ] ], [ 1, [ [ q-1, q^6-q^5+q^4-q^2+q-1 ] ] ], [ 1, [ [ q-1, q^6+q^5+q^4-q^2-q-1 ] ] ], [ 1, [ [ q^7-q^5+q^4+q^3-q^2+1 ] ] ], [ 1, [ [ q^7-q^6+q^5+q^2-q+1 ] ] ] ],
names := [ "A_0", "6A_1", "4A_1''", "2A_1", "4A_1'", "A_2", "3A_2", "2A_2", "D_4(a_1)", "A_3+A_1'", "A_3+3A_1", "D_4(a_1)+2A_1", "A_3+A_1''", "A_4", "D_4+2A_1", "D_4", "E_6(a_2)", "A_2+2A_1", "D_6(a_2)", "A_5+A_1''", "A_5+A_1'", "A_6", "D_5+A_1", "D_6(a_1)", "E_6(a_1)", "D_6", "A_3+A_2+A_1", "D_5(a_1)+A_1", "E_6", "A_4+A_2", "7A_1", "A_1", "3A_1'", "5A_1", "3A_1''", "D_4+3A_1", "E_7(a_4)", "D_6(a_2)+A_1", "2A_3+A_1", "A_3+2A_1''", "A_3", "D_4(a_1)+A_1", "A_3+2A_1'", "D_6+A_1", "A_2+A_1", "A_2+3A_1", "A_5+A_2", "D_4+A_1", "2A_2+A_1", "A_5'", "A_5''", "E_7(a_1)", "D_5", "A_7", "E_7", "A_4+A_1", "D_5(a_1)", "A_3+A_2", "E_7(a_2)", "E_7(a_3)" ],
reps := [ [  ], [ 7, 6, 7, 5, 6, 7, 4, 5, 6, 7, 2, 4, 5, 6, 7, 3, 4, 5, 6, 7, 2, 4, 5, 6, 3, 4, 5, 2, 4, 3 ], [ 5, 4, 5, 2, 4, 5, 3, 4, 5, 2, 4, 3 ], [ 7, 5 ], [ 7, 5, 2, 3 ], [ 7, 6 ], [ 6, 5, 6, 4, 5, 6, 2, 4, 3, 4, 5, 6, 2, 4, 5, 3, 1, 3, 4, 5, 2, 4, 3, 1 ], [ 7, 6, 4, 2 ], [ 5, 4, 5, 2, 4, 3 ], [ 7, 5, 6, 2 ], [ 7, 5, 4, 5, 2, 4, 5, 3, 4, 5, 2, 4, 3, 1 ], [ 7, 6, 7, 5, 6, 4, 5, 2, 4, 5, 3, 4, 5, 2, 4, 3 ], [ 7, 5, 6, 3 ], [ 7, 6, 5, 4 ], [ 7, 6, 5, 4, 5, 2, 4, 5, 3, 4, 5, 2, 4, 3 ], [ 5, 4, 2, 3 ], [ 1, 2, 3, 1, 5, 4, 6, 5, 4, 2, 3, 4 ], [ 7, 6, 4, 1 ], [ 7, 6, 7, 5, 6, 4, 5, 2, 4, 3 ], [ 1, 2, 3, 4, 2, 3, 4, 6, 5, 4, 2, 3, 4, 5 ], [ 7, 5, 2, 6, 4, 1 ], [ 7, 6, 5, 4, 3, 1 ], [ 7, 5, 2, 3, 4, 1 ], [ 3, 4, 2, 3, 4, 7, 6, 5 ], [ 6, 5, 4, 5, 2, 4, 3, 1 ], [ 7, 6, 5, 4, 2, 3 ], [ 7, 5, 6, 2, 3, 1 ], [ 7, 5, 4, 5, 2, 4, 3, 1 ], [ 6, 4, 1, 5, 3, 2 ], [ 7, 6, 4, 2, 3, 1 ], [ 7, 6, 7, 5, 6, 7, 4, 5, 6, 7, 2, 4, 5, 6, 7, 3, 4, 5, 6, 7, 2, 4, 5, 6, 3, 4, 5, 2, 4, 3, 1, 3, 4, 5, 6, 7, 2, 4, 5, 6, 3, 4, 5, 2, 4, 3, 1, 3, 4, 5, 6, 7, 2, 4, 5, 6, 3, 4, 5, 2, 4, 3, 1 ], [ 7 ], [ 7, 5, 2 ], [ 7, 5, 4, 5, 2, 4, 5, 3, 4, 5, 2, 4, 3 ], [ 7, 5, 3 ], [ 7, 6, 7, 5, 6, 7, 4, 5, 6, 7, 2, 4, 5, 6, 7, 3, 4, 5, 6, 7, 2, 4, 5, 6, 3, 4, 5, 2, 4, 3, 1 ], [ 7, 6, 7, 5, 6, 7, 4, 5, 6, 2, 4, 3, 4, 5, 2, 4, 3, 1, 3, 4, 2 ], [ 7, 6, 7, 5, 6, 4, 5, 6, 2, 4, 5, 6, 3, 4, 5, 6, 1, 3, 4, 5, 2, 4, 3 ], [ 7, 6, 7, 5, 6, 7, 4, 5, 6, 7, 2, 4, 5, 6, 7, 3, 4, 5, 6, 7, 2, 4, 5, 6, 3, 1, 3, 4, 5, 2, 4, 3, 1 ], [ 6, 5, 4, 5, 2, 4, 5, 3, 4, 5, 2, 4, 3 ], [ 7, 5, 6 ], [ 7, 5, 4, 5, 2, 4, 3 ], [ 7, 5, 6, 2, 3 ], [ 7, 6, 5, 4, 5, 2, 4, 5, 3, 4, 5, 2, 4, 3, 1 ], [ 7, 6, 4 ], [ 7, 5, 2, 3, 1 ], [ 7, 6, 5, 6, 4, 5, 6, 2, 4, 3, 4, 5, 6, 2, 4, 5, 3, 1, 3, 4, 5, 2, 4, 3, 1 ], [ 7, 5, 4, 2, 3 ], [ 7, 6, 4, 2, 1 ], [ 7, 5, 2, 6, 4 ], [ 7, 5, 3, 6, 4 ], [ 7, 6, 5, 4, 5, 2, 4, 3, 1 ], [ 6, 5, 4, 2, 3 ], [ 7, 6, 7, 5, 6, 4, 5, 2, 4, 5, 3, 4, 5, 2, 4, 3, 1 ], [ 7, 6, 5, 4, 2, 3, 1 ], [ 7, 5, 6, 4, 1 ], [ 3, 4, 2, 3, 4, 6, 5 ], [ 7, 5, 6, 3, 1 ], [ 7, 6, 7, 5, 6, 4, 5, 2, 4, 3, 1 ], [ 2, 4, 2, 3, 5, 4, 2, 7, 6, 5, 4, 3, 1 ] ] ),
E7scmodZ := rec(
eldivs := [ [ 1, [ [ 1/2*q-1/2, q-1, q-1, q-1, q-1, q-1, q-1 ] ] ], [ 1, [ [ 1/2*q+1/2, q+1, q+1, q+1, q+1, q^2-1 ] ] ], [ 2, [ [ 2, q+1, 1/4*q^2-1/4, q^2-1, q^2-1 ], [ q+1, 1/2*q^2-1/2, q^2-1, q^2-1 ] ] ], [ 1, [ [ 1/2*q-1/2, q-1, q-1, q^2-1, q^2-1 ] ] ], [ 1, [ [ 1/2*q+1/2, q^2-1, q^2-1, q^2-1 ] ] ], [ 1, [ [ 1/2*q-1/2, q-1, q-1, q-1, q^3-1 ] ] ], [ 1, [ [ q^2+q+1, q^2+q+1, 1/2*q^3-1/2 ] ] ], [ 1, [ [ 1/2*q-1/2, q^3-1, q^3-1 ] ] ], [ 1, [ [ 1/2*q-1/2, q^3-q^2+q-1, q^3-q^2+q-1 ] ] ], [ 2, [ [ q-1, 1/2*q^2-1/2, q^4-1 ], [ 2, q-1, 1/4*q^2-1/4, q^4-1 ] ] ], [ 1, [ [ 1/2*q+1/2, q+1, q+1, q^4-1 ] ] ], [ 2, [ [ 2, 1/2*q^3+1/2*q^2+1/2*q+1/2, 1/2*q^4-1/2 ], [ q^3+q^2+q+1, 1/2*q^4-1/2 ] ] ], [ 1, [ [ 1/2*q-1/2, q^2-1, q^4-1 ] ] ], [ 1, [ [ 1/2*q-1/2, q-1, q^5-1 ] ] ], [ 1, [ [ 1/2*q+1/2, q+1, q+1, q^4-q^3+q-1 ] ] ], [ 1, [ [ 1/2*q-1/2, q^2-1, q^4-q^3+q-1 ] ] ], [ 1, [ [ q^2-q+1, 1/2*q^5-1/2*q^4+1/2*q^3-1/2*q^2+1/2*q-1/2 ] ] ], [ 1, [ [ 1/2*q-1/2, q^2-1, q^4+q^3-q-1 ] ] ], [ 1, [ [ 1/2*q^3+1/2, q^4-q^3+q-1 ] ] ], [ 2, [ [ 2, q+1, 1/4*q^6-1/4 ], [ q+1, 1/2*q^6-1/2 ] ] ], [ 1, [ [ 1/2*q+1/2, q^6-1 ] ] ], [ 1, [ [ 1/2*q^7-1/2 ] ] ], [ 1, [ [ 1/2*q+1/2, q^6-q^4+q^2-1 ] ] ], [ 2, [ [ 1/2*q^7-1/2*q^6+1/2*q^5-1/2*q^4+1/2*q^3-1/2*q^2+1/2*q-1/2 ], [ 2, 1/4*q^7-1/4*q^6+1/4*q^5-1/4*q^4+1/4*q^3-1/4*q^2+1/4*q-1/4 ] ] ], [ 1, [ [ 1/2*q^7-1/2*q^6+1/2*q^4-1/2*q^3+1/2*q-1/2 ] ] ], [ 1, [ [ 1/2*q+1/2, q^6-q^5+q-1 ] ] ], [ 1, [ [ 1/2*q+1/2, q^6+q^5+q^4-q^2-q-1 ] ] ], [ 1, [ [ 1/2*q+1/2, q^6-q^5+q^4-q^2+q-1 ] ] ], [ 1, [ [ 1/2*q^7-1/2*q^5-1/2*q^4+1/2*q^3+1/2*q^2-1/2 ] ] ], [ 1, [ [ 1/2*q^7+1/2*q^6+1/2*q^5-1/2*q^2-1/2*q-1/2 ] ] ], [ 1, [ [ 1/2*q+1/2, q+1, q+1, q+1, q+1, q+1, q+1 ] ] ], [ 1, [ [ 1/2*q-1/2, q-1, q-1, q-1, q-1, q^2-1 ] ] ], [ 2, [ [ q-1, 1/2*q^2-1/2, q^2-1, q^2-1 ], [ 2, q-1, 1/4*q^2-1/4, q^2-1, q^2-1 ] ] ], [ 1, [ [ 1/2*q+1/2, q+1, q+1, q^2-1, q^2-1 ] ] ], [ 1, [ [ 1/2*q-1/2, q^2-1, q^2-1, q^2-1 ] ] ], [ 1, [ [ 1/2*q+1/2, q+1, q+1, q+1, q^3+1 ] ] ], [ 1, [ [ q^2-q+1, q^2-q+1, 1/2*q^3+1/2 ] ] ], [ 1, [ [ 1/2*q+1/2, q^3+1, q^3+1 ] ] ], [ 1, [ [ 1/2*q+1/2, q^3+q^2+q+1, q^3+q^2+q+1 ] ] ], [ 2, [ [ 2, q+1, 1/4*q^2-1/4, q^4-1 ], [ q+1, 1/2*q^2-1/2, q^4-1 ] ] ], [ 1, [ [ 1/2*q-1/2, q-1, q-1, q^4-1 ] ] ], [ 2, [ [ q^3-q^2+q-1, 1/2*q^4-1/2 ], [ 2, 1/2*q^3-1/2*q^2+1/2*q-1/2, 1/2*q^4-1/2 ] ] ], [ 1, [ [ 1/2*q+1/2, q^2-1, q^4-1 ] ] ], [ 1, [ [ 1/2*q+1/2, q+1, q^5+1 ] ] ], [ 1, [ [ 1/2*q-1/2, q-1, q-1, q^4+q^3-q-1 ] ] ], [ 1, [ [ 1/2*q+1/2, q^2-1, q^4+q^3-q-1 ] ] ], [ 1, [ [ q^2+q+1, 1/2*q^5+1/2*q^4+1/2*q^3+1/2*q^2+1/2*q+1/2 ] ] ], [ 1, [ [ 1/2*q+1/2, q^2-1, q^4-q^3+q-1 ] ] ], [ 1, [ [ 1/2*q^3-1/2, q^4+q^3-q-1 ] ] ], [ 2, [ [ q-1, 1/2*q^6-1/2 ], [ 2, q-1, 1/4*q^6-1/4 ] ] ], [ 1, [ [ 1/2*q-1/2, q^6-1 ] ] ], [ 1, [ [ 1/2*q^7+1/2 ] ] ], [ 1, [ [ 1/2*q-1/2, q^6-q^4+q^2-1 ] ] ], [ 2, [ [ 2, 1/4*q^7+1/4*q^6+1/4*q^5+1/4*q^4+1/4*q^3+1/4*q^2+1/4*q+1/4 ], [ 1/2*q^7+1/2*q^6+1/2*q^5+1/2*q^4+1/2*q^3+1/2*q^2+1/2*q+1/2 ] ] ], [ 1, [ [ 1/2*q^7+1/2*q^6-1/2*q^4-1/2*q^3+1/2*q+1/2 ] ] ], [ 1, [ [ 1/2*q-1/2, q^6+q^5-q-1 ] ] ], [ 1, [ [ 1/2*q-1/2, q^6-q^5+q^4-q^2+q-1 ] ] ], [ 1, [ [ 1/2*q-1/2, q^6+q^5+q^4-q^2-q-1 ] ] ], [ 1, [ [ 1/2*q^7-1/2*q^5+1/2*q^4+1/2*q^3-1/2*q^2+1/2 ] ] ], [ 1, [ [ 1/2*q^7-1/2*q^6+1/2*q^5+1/2*q^2-1/2*q+1/2 ] ] ] ],
names := [ "A_0", "6A_1", "4A_1''", "2A_1", "4A_1'", "A_2", "3A_2", "2A_2", "D_4(a_1)", "A_3+A_1'", "A_3+3A_1", "D_4(a_1)+2A_1", "A_3+A_1''", "A_4", "D_4+2A_1", "D_4", "E_6(a_2)", "A_2+2A_1", "D_6(a_2)", "A_5+A_1''", "A_5+A_1'", "A_6", "D_5+A_1", "D_6(a_1)", "E_6(a_1)", "D_6", "A_3+A_2+A_1", "D_5(a_1)+A_1", "E_6", "A_4+A_2", "7A_1", "A_1", "3A_1'", "5A_1", "3A_1''", "D_4+3A_1", "E_7(a_4)", "D_6(a_2)+A_1", "2A_3+A_1", "A_3+2A_1''", "A_3", "D_4(a_1)+A_1", "A_3+2A_1'", "D_6+A_1", "A_2+A_1", "A_2+3A_1", "A_5+A_2", "D_4+A_1", "2A_2+A_1", "A_5'", "A_5''", "E_7(a_1)", "D_5", "A_7", "E_7", "A_4+A_1", "D_5(a_1)", "A_3+A_2", "E_7(a_2)", "E_7(a_3)" ] ),
E8 := rec(
eldivs := [ [ 1, [ [ q-1, q-1, q-1, q-1, q-1, q-1, q-1, q-1 ] ] ], [ 1, [ [ q+1, q+1, q+1, q+1, q+1, q+1, q+1, q+1 ] ] ], [ 2, [ [ q^2-1, q^2-1, q^2-1, q^2-1 ], [ 2, 2, 1/2*q^2-1/2, 1/2*q^2-1/2, q^2-1, q^2-1 ] ] ], [ 1, [ [ q-1, q-1, q-1, q-1, q^2-1, q^2-1 ] ] ], [ 1, [ [ q+1, q+1, q+1, q+1, q^2-1, q^2-1 ] ] ], [ 1, [ [ q^2+1, q^2+1, q^2+1, q^2+1 ] ] ], [ 1, [ [ q^2-1, q^2-1, q^2-1, q^2-1 ] ] ], [ 1, [ [ q-1, q-1, q-1, q-1, q-1, q^3-1 ] ] ], [ 1, [ [ q+1, q+1, q+1, q+1, q+1, q^3+1 ] ] ], [ 1, [ [ q^2+q+1, q^2+q+1, q^2+q+1, q^2+q+1 ] ] ], [ 1, [ [ q^2-q+1, q^2-q+1, q^2-q+1, q^2-q+1 ] ] ], [ 3, [ [ q^2+q+1, q^3-1, q^3-1 ], [ 3, q^2+q+1, 1/3*q^3-1/3, q^3-1 ], [ q^2+q+1, q^3-1, q^3-1 ] ] ], [ 3, [ [ q^2-q+1, q^3+1, q^3+1 ], [ q^2-q+1, q^3+1, q^3+1 ], [ 3, q^2-q+1, 1/3*q^3+1/3, q^3+1 ] ] ], [ 1, [ [ q-1, q-1, q^3-1, q^3-1 ] ] ], [ 1, [ [ q+1, q+1, q^3+1, q^3+1 ] ] ], [ 1, [ [ q-1, q-1, q^3-q^2+q-1, q^3-q^2+q-1 ] ] ], [ 1, [ [ q+1, q+1, q^3+q^2+q+1, q^3+q^2+q+1 ] ] ], [ 2, [ [ q^4-1, q^4-1 ], [ 2, 2, 1/2*q^4-1/2, 1/2*q^4-1/2 ] ] ], [ 1, [ [ q-1, q-1, q^2-1, q^4-1 ] ] ], [ 1, [ [ q+1, q+1, q^2-1, q^4-1 ] ] ], [ 1, [ [ q^4+1, q^4+1 ] ] ], [ 1, [ [ q^4-1, q^4-1 ] ] ], [ 1, [ [ q-1, q-1, q-1, q^5-1 ] ] ], [ 1, [ [ q+1, q+1, q+1, q^5+1 ] ] ], [ 1, [ [ q^4+q^3+q^2+q+1, q^4+q^3+q^2+q+1 ] ] ], [ 1, [ [ q^4-q^3+q^2-q+1, q^4-q^3+q^2-q+1 ] ] ], [ 1, [ [ q+1, q+1, q^2-1, q^4+q^3-q-1 ] ] ], [ 1, [ [ q-1, q-1, q^2-1, q^4-q^3+q-1 ] ] ], [ 1, [ [ q^4+q^2+1, q^4+q^2+1 ] ] ], [ 1, [ [ q-1, q-1, q^2-1, q^4+q^3-q-1 ] ] ], [ 1, [ [ q+1, q+1, q^2-1, q^4-q^3+q-1 ] ] ], [ 1, [ [ q^4-q^2+1, q^4-q^2+1 ] ] ], [ 1, [ [ q^3-2*q^2+2*q-1, q^5-q^4+q^3-q^2+q-1 ] ] ], [ 1, [ [ q^3+2*q^2+2*q+1, q^5+q^4+q^3+q^2+q+1 ] ] ], [ 2, [ [ q^2-1, q^6-1 ], [ 2, 2, 1/2*q^2-1/2, 1/2*q^6-1/2 ] ] ], [ 1, [ [ q^2-1, q^6-1 ] ] ], [ 1, [ [ q^4+q^3-q-1, q^4+q^3-q-1 ] ] ], [ 1, [ [ q^4-q^3+q-1, q^4-q^3+q-1 ] ] ], [ 1, [ [ q^2+1, q^6+1 ] ] ], [ 1, [ [ q^2-1, q^6-1 ] ] ], [ 1, [ [ q-1, q^7-1 ] ] ], [ 1, [ [ q+1, q^7+1 ] ] ], [ 1, [ [ q^2-1, q^6-q^4+q^2-1 ] ] ], [ 2, [ [ q-1, q^7-q^6+q^5-q^4+q^3-q^2+q-1 ], [ 2*q-2, 1/2*q^7-1/2*q^6+1/2*q^5-1/2*q^4+1/2*q^3-1/2*q^2+1/2*q-1/2 ] ] ], [ 2, [ [ q+1, q^7+q^6+q^5+q^4+q^3+q^2+q+1 ], [ 2*q+2, 1/2*q^7+1/2*q^6+1/2*q^5+1/2*q^4+1/2*q^3+1/2*q^2+1/2*q+1/2 ] ] ], [ 1, [ [ q-1, q^7-q^6+q^4-q^3+q-1 ] ] ], [ 1, [ [ q+1, q^7+q^6-q^4-q^3+q+1 ] ] ], [ 3, [ [ q^8+q^7+q^6+q^5+q^4+q^3+q^2+q+1 ], [ 3, 1/3*q^8+1/3*q^7+1/3*q^6+1/3*q^5+1/3*q^4+1/3*q^3+1/3*q^2+1/3*q+1/3 ], [ q^8+q^7+q^6+q^5+q^4+q^3+q^2+q+1 ] ] ], [ 3, [ [ q^8-q^7+q^6-q^5+q^4-q^3+q^2-q+1 ], [ q^8-q^7+q^6-q^5+q^4-q^3+q^2-q+1 ], [ 3, 1/3*q^8-1/3*q^7+1/3*q^6-1/3*q^5+1/3*q^4-1/3*q^3+1/3*q^2-1/3*q+1/3 ] ] ], [ 1, [ [ q^2-1, q^6+q^5-q-1 ] ] ], [ 1, [ [ q^2-1, q^6-q^5+q-1 ] ] ], [ 1, [ [ q^8-q^6+q^4-q^2+1 ] ] ], [ 1, [ [ q^3-q^2+q-1, q^5+q^3-q^2-1 ] ] ], [ 1, [ [ q^3+q^2+q+1, q^5+q^3+q^2+1 ] ] ], [ 1, [ [ q^2+q+1, q^6+q^5-q^3+q+1 ] ] ], [ 1, [ [ q^2-q+1, q^6-q^5+q^3-q+1 ] ] ], [ 1, [ [ q-1, q^7-q^5-q^4+q^3+q^2-1 ] ] ], [ 1, [ [ q+1, q^7-q^5+q^4+q^3-q^2+1 ] ] ], [ 1, [ [ q^2-1, q^6+q^5+q^4-q^2-q-1 ] ] ], [ 1, [ [ q^2-1, q^6-q^5+q^4-q^2+q-1 ] ] ], [ 1, [ [ q^8-q^4+1 ] ] ], [ 1, [ [ q-1, q^7+q^6+q^5-q^2-q-1 ] ] ], [ 1, [ [ q+1, q^7-q^6+q^5+q^2-q+1 ] ] ], [ 1, [ [ q^8-q^7+q^5-q^4+q^3-q+1 ] ] ], [ 1, [ [ q^8+q^7-q^5-q^4-q^3+q+1 ] ] ], [ 1, [ [ q-1, q-1, q-1, q-1, q-1, q-1, q^2-1 ] ] ], [ 1, [ [ q+1, q+1, q+1, q+1, q+1, q+1, q^2-1 ] ] ], [ 1, [ [ q-1, q-1, q^2-1, q^2-1, q^2-1 ] ] ], [ 1, [ [ q+1, q+1, q^2-1, q^2-1, q^2-1 ] ] ], [ 1, [ [ q-1, q-1, q-1, q-1, q^4-1 ] ] ], [ 1, [ [ q+1, q+1, q+1, q+1, q^4-1 ] ] ], [ 2, [ [ q^2-1, q^2-1, q^4-1 ], [ 2, 2, 1/2*q^2-1/2, 1/2*q^2-1/2, q^4-1 ] ] ], [ 2, [ [ q-1, q^3-q^2+q-1, q^4-1 ], [ 2*q-2, q^3-q^2+q-1, 1/2*q^4-1/2 ] ] ], [ 2, [ [ q+1, q^3+q^2+q+1, q^4-1 ], [ 2*q+2, q^3+q^2+q+1, 1/2*q^4-1/2 ] ] ], [ 1, [ [ q^2+1, q^2+1, q^4-1 ] ] ], [ 1, [ [ q^2-1, q^2-1, q^4-1 ] ] ], [ 1, [ [ q-1, q-1, q-1, q-1, q^4+q^3-q-1 ] ] ], [ 1, [ [ q+1, q+1, q+1, q+1, q^4-q^3+q-1 ] ] ], [ 1, [ [ q^2+q+1, q^2+q+1, q^4+q^3-q-1 ] ] ], [ 1, [ [ q^2-q+1, q^2-q+1, q^4-q^3+q-1 ] ] ], [ 1, [ [ q^2-1, q^2-1, q^4+q^3-q-1 ] ] ], [ 1, [ [ q^2-1, q^2-1, q^4-q^3+q-1 ] ] ], [ 1, [ [ q-1, q^3-1, q^4+q^3-q-1 ] ] ], [ 1, [ [ q+1, q^3+1, q^4-q^3+q-1 ] ] ], [ 3, [ [ q^2+q+1, q^6-1 ], [ 3, q^2+q+1, 1/3*q^6-1/3 ], [ q^2+q+1, q^6-1 ] ] ], [ 3, [ [ q^2-q+1, q^6-1 ], [ q^2-q+1, q^6-1 ], [ 3, q^2-q+1, 1/3*q^6-1/3 ] ] ], [ 1, [ [ q-1, q-1, q^6-1 ] ] ], [ 1, [ [ q+1, q+1, q^6-1 ] ] ], [ 1, [ [ q-1, q-1, q^6-q^4+q^2-1 ] ] ], [ 1, [ [ q+1, q+1, q^6-q^4+q^2-1 ] ] ], [ 2, [ [ q^8-1 ], [ 2, 2, 1/4*q^8-1/4 ] ] ], [ 1, [ [ q^8-1 ] ] ], [ 1, [ [ q-1, q-1, q^6+q^5-q-1 ] ] ], [ 1, [ [ q+1, q+1, q^6-q^5+q-1 ] ] ], [ 1, [ [ q+1, q+1, q^6+q^5+q^4-q^2-q-1 ] ] ], [ 1, [ [ q-1, q-1, q^6-q^5+q^4-q^2+q-1 ] ] ], [ 1, [ [ q-1, q-1, q^6+q^5+q^4-q^2-q-1 ] ] ], [ 1, [ [ q+1, q+1, q^6-q^5+q^4-q^2+q-1 ] ] ], [ 1, [ [ q^8+q^6-q^2-1 ] ] ], [ 1, [ [ q^8-q^6+q^2-1 ] ] ], [ 1, [ [ q^8+q^7-q^6-2*q^5+2*q^3+q^2-q-1 ] ] ], [ 1, [ [ q^8-q^7-q^6+2*q^5-2*q^3+q^2+q-1 ] ] ], [ 1, [ [ q^8+q^7-q-1 ] ] ], [ 1, [ [ q^8-q^7+q-1 ] ] ], [ 1, [ [ q^8-q^6+q^5-q^3+q^2-1 ] ] ], [ 1, [ [ q^8-q^6-q^5+q^3+q^2-1 ] ] ], [ 1, [ [ q^8+q^7+q^6+q^5-q^3-q^2-q-1 ] ] ], [ 1, [ [ q^8-q^7+q^6-q^5+q^3-q^2+q-1 ] ] ], [ 1, [ [ q^8+q^7-q^5+q^3-q-1 ] ] ], [ 1, [ [ q^8-q^7+q^5-q^3+q-1 ] ] ], [ 1, [ [ q^8+2*q^7+2*q^6+q^5-q^3-2*q^2-2*q-1 ] ] ], [ 1, [ [ q^8-2*q^7+2*q^6-q^5+q^3-2*q^2+2*q-1 ] ] ] ],
names := [ "A_0", "8A_1", "4A_1'", "2A_1", "6A_1", "2D_4(a_1)", "4A_1''", "A_2", "D_4+4A_1", "4A_2", "E_8(a_8)", "3A_2", "E_7(a_4)+A_1", "2A_2", "2D_4", "D_4(a_1)", "2A_3+2A_1", "2A_3'", "A_3+A_1", "A_3+3A_1", "D_8(a_3)", "2A_3''", "A_4", "D_6+2A_1", "2A_4", "E_8(a_6)", "A_2+4A_1", "D_4", "E_6(a_2)+A_2", "A_2+2A_1", "D_4+2A_1", "E_8(a_3)", "E_6(a_2)", "A_5+A_2+A_1", "A_5+A_1'", "D_4+A_2", "2A_2+2A_1", "D_6(a_2)", "D_8(a_1)", "A_5+A_1''", "A_6", "D_8", "D_5+A_1", "D_6(a_1)", "A_7+A_1", "E_6(a_1)", "E_7+A_1", "A_8", "E_8(a_4)", "A_4+2A_1", "D_6", "E_8(a_2)", "D_4(a_1)+A_2", "D_5(a_1)+A_3", "E_6+A_2", "E_8(a_7)", "E_6", "E_7(a_2)+A_1", "A_3+A_2+A_1", "D_5(a_1)+A_1", "E_8(a_1)", "A_4+A_2", "D_8(a_2)", "E_8(a_5)", "E_8", "A_1", "7A_1", "3A_1", "5A_1", "A_3", "A_3+4A_1", "A_3+2A_1'", "D_4(a_1)+A_1", "2A_3+A_1", "D_4(a_1)+A_3", "A_3+2A_1''", "A_2+A_1", "D_4+3A_1", "3A_2+A_1", "E_7(a_4)", "A_2+3A_1", "D_4+A_1", "2A_2+A_1", "D_6(a_2)+A_1", "A_5+A_2", "E_6(a_2)+A_1", "A_5", "A_5+2A_1", "D_5", "D_5+2A_1", "A_7'", "A_7''", "A_4+A_1", "D_6+A_1", "A_3+A_2+2A_1", "D_5(a_1)", "A_3+A_2", "D_4+A_3", "D_5(a_1)+A_2", "D_7", "E_6+A_1", "E_7(a_2)", "A_6+A_1", "E_7(a_1)", "E_6(a_1)+A_1", "E_7", "A_4+A_3", "D_7(a_1)", "D_5+A_2", "D_7(a_2)", "A_4+A_2+1", "E_7(a_3)" ],
reps := [ [  ], [ 8, 7, 8, 6, 7, 8, 5, 6, 7, 8, 4, 5, 6, 7, 8, 2, 4, 5, 6, 7, 8, 3, 4, 5, 6, 7, 8, 2, 4, 5, 6, 7, 3, 4, 5, 6, 2, 4, 5, 3, 4, 2, 1, 3, 4, 5, 6, 7, 8, 2, 4, 5, 6, 7, 3, 4, 5, 6, 2, 4, 5, 3, 4, 2, 1, 3, 4, 5, 6, 7, 8, 2, 4, 5, 6, 7, 3, 4, 5, 6, 2, 4, 5, 3, 4, 2, 1, 3, 4, 5, 6, 7, 8, 2, 4, 5, 6, 3, 4, 5, 2, 4, 3, 1, 3, 4, 5, 6, 7, 2, 4, 5, 6, 3, 4, 5, 2, 4, 3, 1 ], [ 5, 4, 5, 2, 4, 5, 3, 4, 5, 2, 4, 3 ], [ 6, 1 ], [ 7, 6, 7, 5, 6, 7, 4, 5, 6, 7, 2, 4, 5, 6, 7, 3, 4, 5, 6, 7, 2, 4, 5, 6, 3, 4, 5, 2, 4, 3 ], [ 8, 7, 6, 7, 5, 6, 4, 5, 6, 7, 2, 4, 5, 6, 3, 4, 5, 6, 7, 8, 2, 4, 5, 6, 3, 4, 5, 1, 3, 4, 5, 6, 7, 8, 2, 4, 5, 6, 7, 3, 4, 5, 6, 2, 4, 5, 3, 4, 2, 1, 3, 4, 5, 6, 7, 2, 4, 5, 3, 1 ], [ 7, 5, 2, 3 ], [ 6, 7 ], [ 1, 2, 3, 1, 4, 2, 3, 1, 4, 3, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 6, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 6, 5, 4, 3, 1, 7, 6, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 6, 5, 4, 3, 1, 7, 6, 5, 4, 2, 3, 4, 5, 6, 7, 8 ], [ 8, 7, 8, 6, 7, 5, 6, 7, 4, 2, 4, 5, 3, 4, 5, 6, 7, 8, 2, 4, 5, 6, 3, 4, 5, 2, 1, 3, 4, 5, 6, 7, 8, 2, 4, 5, 6, 7, 3, 4, 5, 6, 2, 4, 5, 3, 4, 1, 3, 4, 5, 6, 7, 8, 2, 4, 5, 6, 7, 3, 4, 5, 6, 2, 4, 5, 3, 4, 2, 1, 3, 4, 5, 6, 2, 4, 5, 3, 4, 1 ], [ 5, 6, 4, 3, 4, 5, 6, 7, 8, 2, 4, 5, 6, 3, 4, 2, 1, 3, 4, 5, 6, 7, 8, 2, 4, 5, 6, 7, 3, 4, 5, 2, 1, 3, 4, 5, 6, 7, 8, 2 ], [ 6, 5, 2, 4, 5, 6, 3, 4, 5, 2, 4, 3, 1, 3, 4, 5, 6, 2, 4, 5, 3, 4, 1, 3 ], [ 2, 3, 4, 2, 3, 4, 5, 4, 2, 3, 1, 4, 5, 6, 8, 7, 6, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 6, 5, 4, 3, 1, 7, 6, 5, 4, 2, 3, 4, 5, 6, 7 ], [ 7, 8, 2, 4 ], [ 2, 4, 2, 5, 4, 2, 6, 5, 4, 2, 3, 4, 5, 6, 7, 6, 5, 4, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 6, 5, 4, 3, 1, 7, 8 ], [ 4, 2, 4, 3, 4, 5 ], [ 1, 2, 3, 1, 4, 2, 3, 1, 4, 3, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 6, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 6, 5, 4, 3, 1, 7, 6, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 6, 5, 4, 3, 1, 7, 8, 7, 6, 5, 4, 2, 3, 4, 5, 6, 7, 8 ], [ 2, 3, 4, 2, 3, 4, 6, 5, 7, 6, 5, 4, 2, 3, 4, 5 ], [ 3, 7, 6, 8 ], [ 1, 2, 3, 4, 2, 3, 4, 5, 4, 2, 3, 4, 5, 7 ], [ 4, 5, 6, 7, 3, 4, 5, 2, 4, 3, 1, 3, 4, 5, 6, 7, 8, 2, 4, 5, 3, 4, 2, 1, 3, 4, 5, 6, 7, 8 ], [ 7, 6, 8, 1, 4, 3 ], [ 5, 6, 3, 4 ], [ 3, 4, 3, 5, 4, 3, 6, 5, 4, 3, 8, 7, 6, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 6, 5, 4, 3, 7, 6, 5, 4, 2 ], [ 7, 5, 6, 2, 4, 5, 3, 4, 5, 6, 7, 8, 2, 4, 5, 6, 7, 1, 3, 4, 5, 6, 7, 8, 2, 4, 5, 6, 7, 3, 4, 5, 2, 4, 3, 1, 3, 4, 5, 6, 7, 8, 2, 4, 5, 6, 3, 4 ], [ 8, 7, 6, 7, 5, 4, 5, 6, 2, 4, 3, 4, 5, 6, 7, 1, 3, 4, 5, 6, 2, 4, 5, 3 ], [ 8, 7, 5, 4, 5, 2, 4, 5, 3, 4, 5, 2, 4, 3 ], [ 5, 4, 2, 3 ], [ 1, 2, 3, 1, 4, 2, 3, 1, 4, 5, 4, 2, 3, 1, 4, 3, 6, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 6, 5, 4, 3, 1, 7, 6, 5, 4, 2, 3, 4, 5, 6, 7, 8, 7 ], [ 7, 4, 5, 1 ], [ 5, 4, 5, 2, 4, 5, 3, 4, 5, 6, 7, 2, 4, 3 ], [ 8, 7, 6, 7, 5, 2, 4, 3, 4, 5, 2, 4, 1, 3, 4, 5, 6, 2, 4, 5 ], [ 3, 4, 2, 3, 5, 4, 2, 3, 1, 4, 5, 6 ], [ 4, 3, 5, 4, 2, 3, 4, 5, 6, 5, 4, 2, 3, 4, 5, 6, 7, 6, 5, 4, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 6, 5, 4, 3, 1, 7, 8 ], [ 2, 3, 4, 2, 3, 4, 5, 4, 2, 3, 1, 4, 5, 6 ], [ 8, 7, 5, 2, 4, 3 ], [ 7, 8, 5, 2, 3, 1 ], [ 6, 5, 6, 7, 4, 2, 4, 5, 3, 4 ], [ 5, 4, 6, 5, 4, 2, 3, 7, 6, 5, 4, 2, 3, 8, 7, 6, 5, 4, 2, 3, 1, 4 ], [ 6, 4, 5, 2, 7, 1 ], [ 8, 5, 6, 7, 2, 4 ], [ 2, 7, 6, 5, 4, 2, 3, 4, 8, 7, 6, 5, 4, 2, 3, 1, 4, 3 ], [ 8, 5, 6, 2, 3, 4 ], [ 2, 4, 2, 3, 4, 5, 6, 7 ], [ 2, 4, 2, 5, 4, 2, 3, 6, 5, 4, 2, 3, 4, 5, 6, 7, 6, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 6, 5, 4, 3, 1, 7, 8 ], [ 5, 3, 4, 5, 6, 2, 4, 1 ], [ 3, 4, 3, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 8, 7, 6 ], [ 1, 3, 4, 3, 1, 5, 4, 2, 3, 4, 5, 8, 7, 6, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 6, 5, 7, 6 ], [ 2, 3, 4, 3, 1, 5, 4, 2, 3, 4, 5, 6, 7, 8 ], [ 6, 7, 8, 5, 2, 1 ], [ 7, 5, 6, 2, 3, 4 ], [ 6, 7, 8, 5, 6, 7, 4, 5, 3, 4, 2, 1 ], [ 7, 8, 4, 2, 3, 4, 5, 2 ], [ 1, 3, 1, 4, 5, 4, 3, 6, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 7, 6, 5, 4, 2, 3, 1, 4, 3, 5, 4, 2, 6, 5, 4, 3, 1, 7, 6, 5, 4, 2, 3, 4, 5, 6, 7, 8 ], [ 1, 2, 3, 4, 2, 3, 1, 4, 3, 5, 4, 2, 3, 1, 4, 5, 6, 5, 4, 2, 3, 4, 5, 6, 8, 7 ], [ 1, 2, 3, 1, 4, 2, 5, 4, 2, 3, 1, 4, 6, 5, 4, 2, 3, 4, 5, 6, 7, 8 ], [ 6, 4, 1, 5, 3, 2 ], [ 1, 2, 3, 1, 4, 2, 3, 1, 4, 3, 5, 4, 3, 1, 6, 5, 4, 2, 3, 4, 5, 6, 7, 8 ], [ 5, 7, 6, 2, 1, 3 ], [ 8, 1, 2, 3, 4, 2, 5, 4 ], [ 8, 7, 6, 2, 4, 5, 3, 4, 1, 3 ], [ 8, 7, 6, 5, 3, 1 ], [ 3, 4, 2, 3, 5, 4, 2, 3, 4, 6, 5, 4, 2, 3, 7, 6, 5, 4, 2, 3, 1, 4, 5, 6, 7, 8 ], [ 8, 6, 5, 4, 2, 3, 4, 5, 6, 7, 1, 3, 4, 5, 2, 4 ], [ 7, 8, 6, 2, 1, 3, 4, 5 ], [ 3 ], [ 7, 6, 7, 5, 6, 7, 4, 5, 6, 7, 2, 4, 5, 6, 7, 3, 4, 5, 6, 7, 2, 4, 5, 6, 3, 4, 5, 2, 4, 3, 1, 3, 4, 5, 6, 7, 2, 4, 5, 6, 3, 4, 5, 2, 4, 3, 1, 3, 4, 5, 6, 7, 2, 4, 5, 6, 3, 4, 5, 2, 4, 3, 1 ], [ 8, 6, 1 ], [ 7, 5, 4, 5, 2, 4, 5, 3, 4, 5, 2, 4, 3 ], [ 4, 1, 3 ], [ 2, 3, 4, 2, 3, 4, 5, 4, 2, 3, 4, 5, 6, 5, 4, 2, 3, 4, 5, 6, 7, 6, 5, 4, 2, 3, 4, 5, 6, 7, 8 ], [ 2, 3, 4, 2, 3, 4, 5, 4, 2, 3, 4, 5, 6 ], [ 8, 5, 4, 2, 3, 4, 2 ], [ 2, 4, 2, 3, 4, 5, 4, 2, 3, 1, 4, 3, 5, 6, 5, 4, 2, 3, 4, 5, 6, 7, 6, 5, 4, 2, 3, 1, 4, 3, 5, 6, 7 ], [ 2, 3, 4, 5, 4, 2, 3, 4, 5, 7, 6, 8, 7, 6, 5, 4, 2, 3, 4, 5, 6 ], [ 8, 5, 2, 4, 1 ], [ 4, 2, 1 ], [ 2, 3, 4, 2, 3, 4, 5, 4, 2, 3, 4, 5, 6, 5, 4, 2, 3, 4, 5, 6, 7, 6, 5, 4, 2, 3, 1, 4, 5, 6, 7 ], [ 8, 5, 6, 4, 5, 6, 3, 4, 5, 6, 2, 4, 3, 1, 3, 4, 5, 6, 2, 4, 5, 3, 4, 2, 1 ], [ 5, 2, 4, 5, 1, 3, 4, 5, 6, 2, 4, 5, 3, 4, 2, 1, 3, 4, 5, 6, 7 ], [ 8, 5, 2, 3, 1 ], [ 7, 5, 4, 2, 3 ], [ 8, 6, 5, 3, 1 ], [ 2, 3, 4, 2, 3, 1, 4, 5, 4, 2, 6, 5, 4, 2, 3, 1, 4, 3, 5, 4, 6, 5, 7 ], [ 1, 2, 3, 1, 4, 2, 3, 5, 4, 2, 3, 1, 4, 3, 5, 4, 6, 5, 4, 2, 3, 4, 5, 6, 7 ], [ 1, 2, 3, 4, 2, 6, 5, 4, 2, 3, 4, 5, 8 ], [ 7, 5, 2, 6, 4 ], [ 8, 2, 3, 4, 2, 3, 4, 5, 4, 2, 3, 1, 4, 5, 6 ], [ 2, 3, 5, 1, 4 ], [ 2, 3, 4, 2, 3, 4, 5, 4, 2, 3, 4, 5, 7, 6, 8 ], [ 2, 3, 5, 6, 5, 4, 2, 3, 4, 7, 6, 5, 4, 2, 3, 1, 4 ], [ 4, 6, 8, 1, 3, 5, 7 ], [ 5, 6, 2, 4, 1 ], [ 6, 7, 5, 4, 5, 2, 4, 5, 1, 3, 4, 5, 2, 4, 3 ], [ 2, 3, 4, 2, 3, 4, 5, 4, 2, 3, 1, 4, 5, 8, 7 ], [ 4, 2, 5, 4, 2, 3, 1 ], [ 7, 6, 4, 2, 3 ], [ 2, 3, 4, 2, 3, 4, 5, 7, 6, 5, 4, 2, 3, 4, 5, 6, 8 ], [ 1, 4, 2, 5, 4, 2, 3, 7, 8 ], [ 6, 7, 8, 5, 4, 2, 3 ], [ 8, 6, 4, 1, 2, 3, 5 ], [ 4, 2, 5, 4, 3, 1, 6, 5, 7, 6, 5 ], [ 8, 6, 7, 2, 4, 5, 1 ], [ 5, 3, 4, 5, 6, 7, 2, 4, 1 ], [ 8, 5, 6, 3, 4, 2, 1, 3, 4 ], [ 6, 7, 5, 2, 4, 3, 1 ], [ 8, 6, 7, 4, 1, 2, 3 ], [ 7, 8, 5, 6, 4, 2, 4, 3, 4 ], [ 7, 8, 4, 5, 2, 3, 1 ], [ 4, 3, 5, 4, 2, 3, 4, 5, 6, 8, 7 ], [ 8, 6, 7, 5, 2, 3, 1 ], [ 2, 4, 2, 3, 1, 6, 5, 4, 2, 3, 4, 5, 7 ] ] ),
F4 := rec(
eldivs := [ [ 1, [ [ q-1, q-1, q-1, q-1 ] ] ], [ 1, [ [ q+1, q+1, q+1, q+1 ] ] ], [ 2, [ [ q^2-1, q^2-1 ], [ 2, 1/2*q^2-1/2, q^2-1 ] ] ], [ 1, [ [ q-1, q^3-1 ] ] ], [ 1, [ [ q+1, q^3+1 ] ] ], [ 1, [ [ q^2+1, q^2+1 ] ] ], [ 1, [ [ q-1, q^3-1 ] ] ], [ 1, [ [ q+1, q^3+1 ] ] ], [ 1, [ [ q^2+q+1, q^2+q+1 ] ] ], [ 1, [ [ q^2-q+1, q^2-q+1 ] ] ], [ 1, [ [ q^4-q^2+1 ] ] ], [ 1, [ [ q-1, q-1, q^2-1 ] ] ], [ 1, [ [ q+1, q+1, q^2-1 ] ] ], [ 1, [ [ q^4+q^3-q-1 ] ] ], [ 1, [ [ q^4-q^3+q-1 ] ] ], [ 2, [ [ q^4-1 ], [ 2, 1/2*q^4-1/2 ] ] ], [ 1, [ [ q-1, q-1, q^2-1 ] ] ], [ 1, [ [ q+1, q+1, q^2-1 ] ] ], [ 1, [ [ q^4+q^3-q-1 ] ] ], [ 1, [ [ q^4-q^3+q-1 ] ] ], [ 2, [ [ q^4-1 ], [ 2, 1/2*q^4-1/2 ] ] ], [ 1, [ [ q^2-1, q^2-1 ] ] ], [ 1, [ [ q-1, q^3-q^2+q-1 ] ] ], [ 1, [ [ q+1, q^3+q^2+q+1 ] ] ], [ 1, [ [ q^4+1 ] ] ] ],
names := [ "A_0", "4A_1", "2A_1", "A_2", "D_4", "D_4(a_1)", "~A_2", "C_3+A_1", "A_2+~A_2", "F_4(a_1)", "F_4", "A_1", "3A_1", "~A_2+A_1", "C_3", "A_3", "~A_1", "2A_1+~A_1", "A_2+~A_1", "B_3", "B_2+A_1", "A_1+~A_1", "B_2", "A_3+~A_1", "B_4" ],
reps := [ [  ], [ 1, 2, 1, 3, 2, 1, 3, 2, 3, 4, 3, 2, 1, 3, 2, 3, 4, 3, 2, 1, 3, 2, 3, 4 ], [ 2, 3, 2, 3 ], [ 2, 1 ], [ 2, 3, 2, 3, 4, 3, 2, 1, 3, 4 ], [ 3, 2, 4, 3, 2, 1, 3, 2, 4, 3, 2, 1 ], [ 4, 3 ], [ 1, 2, 1, 4, 3, 2, 1, 3, 2, 3 ], [ 3, 2, 1, 4, 3, 2, 1, 3, 2, 3, 4, 3, 2, 1, 3, 2 ], [ 3, 2, 4, 3, 2, 1, 3, 2 ], [ 4, 3, 2, 1 ], [ 1 ], [ 2, 3, 2, 3, 4, 3, 2, 3, 4 ], [ 1, 4, 3 ], [ 4, 3, 2 ], [ 2, 3, 2, 1, 3 ], [ 3 ], [ 1, 2, 1, 3, 2, 1, 3, 2, 3 ], [ 2, 1, 4 ], [ 3, 2, 1 ], [ 2, 4, 3, 2, 3 ], [ 1, 3 ], [ 3, 2 ], [ 2, 3, 2, 3, 4, 3, 2, 1, 3, 2, 4, 3, 2, 1 ], [ 2, 4, 3, 2, 1, 3 ] ] ),
G2 := rec(
eldivs := [ [ 1, [ [ q-1, q-1 ] ] ], [ 1, [ [ q^2-1 ] ] ], [ 1, [ [ q^2-1 ] ] ], [ 1, [ [ q^2-q+1 ] ] ], [ 1, [ [ q^2+q+1 ] ] ], [ 1, [ [ q+1, q+1 ] ] ] ],
names := [ "A_0", "~A_1", "A_1", "G_2", "A_2", "A_1+~A_1" ],
reps := [ [  ], [ 2 ], [ 1 ], [ 1, 2 ], [ 1, 2, 1, 2 ], [ 1, 2, 1, 2, 1, 2 ] ] ),
PhiFactorNames := [ "Phi8'", "Phi8''", "Phi12'", "Phi12''", "Phi24'", "Phi24''" ],
PhiFactors := [ q^2+(E(8)-E(8)^3)*q+1, q^2+(-E(8)+E(8)^3)*q+1, q^2+(E(12)^7-E(12)^11)*q+1, q^2+(-E(12)^7+E(12)^11)*q+1, q^4+(E(8)-E(8)^3)*q^3+q^2+(E(8)-E(8)^3)*q+1, q^4+(-E(8)+E(8)^3)*q^3+q^2+(-E(8)+E(8)^3)*q+1 ],
              Phis := [ q-1, q+1, q^2+q+1, q^2+1, q^4+q^3+q^2+q+1, q^2-q+1, q^6+q^5+q^4+q^3+q^2+q+1, q^4+1, q^6+q^3+1, q^4-q^3+q^2-q+1,, q^4-q^2+1,, q^6-q^5+q^4-q^3+q^2-q+1, q^8-q^7+q^5-q^4+q^3-q+1,,, q^6-q^3+1,, q^8-q^6+q^4-q^2+1,,,, q^8-q^4+1,,,,,, q^8+q^7-q^5-q^4-q^3+q+1 ] );

MAXTORSTRUCTS.ShowPhiFactors := function ( pol )
    local  res, phi, i;
    res := "";
    for i  in [ 1 .. 30 ]  do
        if IsBound( MAXTORSTRUCTS.Phis[i] )  then
            while
             Degree( pol ) >= Degree( MAXTORSTRUCTS.Phis[i] ) and 0*q =
                   pol mod MAXTORSTRUCTS.Phis[i] do
                Append( res, "Phi" );
                Append( res, String( i ) );
                Add( res, ' ' );
                pol := pol / MAXTORSTRUCTS.Phis[i];
            od;
        fi;
    od;
    for i  in [ 1 .. 6 ]  do
        phi := MAXTORSTRUCTS.PhiFactors[i];
        while Degree( pol ) >= Degree( phi ) and 0*q =  pol mod phi do
            Append( res, MAXTORSTRUCTS.PhiFactorNames[i] );
            pol := pol / phi;
        od;
    od;
    if pol <> q ^ 0  then
        res := Concatenation( "(", String( pol ), ") ", res );
    fi;
    if res[Length( res )] = ' '  then
        Unbind( res[Length( res )] );
    fi;
    return res;
end;