HS

A_{8} ≤ A_{8}.2 2200 1a + 22a + 77a + 154abc + 175a + 693a + 770a

9

Character Numbers: [ 1, 2, 3, 4, 5, 6, 7, 9, 10 ]

S_{1} S_{2} S_{3} S_{4} S_{5} S_{6}  S_{7} S_{8} S_{9}
χ_{1} 1 1 28 28 105 105 336 336 1260
χ_{2} 1 −1 0 0 −35 35 −112 112 0
χ_{3} 1 1 −12 −12 25 25  16 16 −60
χ_{4} 1 1 8 8 15 15 −24 −24 0
χ_{5} 1 −1 −10 10 15 −15 −12 12  0
χ_{6} 1 −1 10 −10 15 −15 −12 12  0
χ_{7} 1 1 6 6 −5 −5 28 28 −60
χ_{8} 1 1 −2 −2 −5 −5 −4 −4 20
χ_{9} 1 −1  0  0 −5  5  8 −8  0

Ramanujan Graphs: [ 2, 3, 4, 5, 6, 7, 8 ], [ 2, 3, 4, 5, 6, 7, 8, 9 ] , [ 2, 3, 4, 5, 6, 9 ], [ 2, 3, 4, 5, 7, 8, 9 ], [ 2, 3, 4, 5, 8, 9 ], [ 2, 3, 4, 5, 9 ], [ 2, 3, 4, 6, 7, 8, 9 ], [ 2, 3, 4, 6, 7, 9 ], [ 2, 3, 4, 6, 9 ], [ 2, 3, 4, 7, 8, 9 ], [ 2, 3, 5, 6, 7, 8, 9 ], [ 2, 3, 5, 6, 9 ], [ 2, 3, 5, 7, 8, 9 ], [ 2, 3, 5, 8, 9 ], [ 2, 3, 5, 9 ], [ 2, 3, 6, 7, 8, 9 ], [ 2, 3, 6, 7, 9 ], [ 2, 3, 6, 9 ], [ 2, 3, 7, 8, 9 ], [ 2, 3, 9 ], [ 2, 4, 5, 6, 7, 8, 9 ], [ 2, 4, 5, 6, 9 ], [ 2, 4, 5, 7, 8, 9 ], [ 2, 4, 5, 8, 9 ], [ 2, 4, 5, 9 ], [ 2, 4, 6, 7, 8, 9 ], [ 2, 4, 6, 7, 9 ], [ 2, 4, 6, 9 ], [ 2, 4, 7, 8, 9 ], [ 2, 4, 9 ], [ 2, 5, 6, 7, 8, 9 ], [ 2, 5, 6, 9 ], [ 2, 5, 7, 8, 9 ], [ 2, 5, 8, 9 ], [ 2, 5, 9 ], [ 2, 6, 7, 8, 9 ], [ 2, 6, 7, 9 ], [ 2, 6, 9 ], [ 2, 7, 8, 9 ], [ 2, 9 ], [ 3, 4, 5, 6, 7, 8 ], [ 3, 4, 5, 6, 7, 8, 9 ], [ 3, 4, 5, 6, 9 ], [ 3, 4, 5, 7, 8, 9 ], [ 3, 4, 5, 8, 9 ], [ 3, 4, 5, 9 ], [ 3, 4, 6, 7, 8, 9 ], [ 3, 4, 6, 7, 9 ], [ 3, 4, 6, 9 ], [ 3, 4, 7, 8, 9 ], [ 3, 5, 6, 7, 8, 9 ], [ 3, 5, 6, 9 ], [ 3, 5, 7, 8, 9 ], [ 3, 5, 8, 9 ], [ 3, 5, 9 ], [ 3, 6, 7, 8, 9 ], [ 3, 6, 7, 9 ], [ 3, 6, 9 ], [ 3, 7, 8, 9 ], [ 4, 5, 6, 7, 8, 9 ], [ 4, 5, 6, 9 ], [ 4, 5, 7, 8, 9 ], [ 4, 5, 8, 9 ], [ 4, 5, 9 ], [ 4, 6, 7, 8, 9 ], [ 4, 6, 7, 9 ], [ 4, 6, 9 ], [ 4, 7, 8, 9 ], [ 5, 6, 7, 8, 9 ], [ 5, 6, 9 ], [ 5, 7, 8, 9 ], [ 5, 8, 9 ], [ 5, 9 ], [ 6, 7, 8, 9 ], [ 6, 7, 9 ], [ 6, 9 ], [ 7, 8, 9 ], [ 9 ]