He.2

\begin{matrix}2^{2}.L_{3}(4).S_{3} \\ ≤ 2^{2}.L_{3}(4).D_{12} \end{matrix} 16660 1a^{+} + 51ab + 680a^{+} + 1029ab + 1275a^{+}

+ 1920a^{+} + 4352a^{+} + 6272a^{+}

8

Character Numbers: [ 1, 3, 5, 7, 8, 11, 15, 17 ]

S_{1} S_{2} S_{3} S_{4} S_{5}  S_{6}  S_{7}  S_{8}
χ_{1} 1 1 210 1344 1344 1440 3360 8960
χ_{2} 1 1 70 224 224 −240 −280  0
χ_{3} 1 1 42  0  0  12 168 −224
χ_{4} 1 −1  0 −64 64  0  0  0
χ_{5} 1 1 14  0  0  96 −112  0
χ_{6} 1 1 −28 35 35  12  28 −84
χ_{7} 1 1  0 −21 −21 −30  0  70
χ_{8} 1 −1  0 21 −21  0  0  0

Ramanujan Graphs: [ 1, 2 ], [ 1, 2, 3, 4, 5, 6, 7, 8 ], [ 1, 2, 3, 4, 5, 7, 8 ], [ 1, 2, 3, 4, 6, 7, 8 ], [ 1, 2, 3, 4, 6, 8 ], [ 1, 2, 3, 4, 7, 8 ], [ 1, 2, 3, 5, 6, 7, 8 ], [ 1, 2, 3, 5, 6, 8 ], [ 1, 2, 3, 5, 7, 8 ], [ 1, 2, 3, 6, 8 ], [ 1, 2, 3, 7, 8 ], [ 1, 2, 3, 8 ], [ 1, 2, 4, 5, 6, 7, 8 ], [ 1, 2, 4, 5, 6, 8 ], [ 1, 2, 4, 5, 7, 8 ], [ 1, 2, 4, 6 ], [ 1, 2, 4, 6, 8 ], [ 1, 2, 4, 7, 8 ], [ 1, 2, 5, 6 ], [ 1, 2, 5, 6, 8 ], [ 1, 2, 5, 7, 8 ], [ 1, 3, 4, 5, 6, 7, 8 ], [ 1, 3, 4, 5, 7, 8 ], [ 1, 3, 4, 6, 7, 8 ], [ 1, 3, 4, 6, 8 ], [ 1, 3, 4, 7, 8 ], [ 1, 3, 5, 6, 7, 8 ], [ 1, 3, 5, 6, 8 ], [ 1, 3, 5, 7, 8 ], [ 1, 3, 6, 8 ], [ 1, 3, 7, 8 ], [ 1, 3, 8 ], [ 1, 4, 5, 6, 7, 8 ], [ 1, 4, 5, 6, 8 ], [ 1, 4, 5, 7, 8 ], [ 1, 4, 6 ], [ 1, 4, 6, 8 ], [ 1, 4, 7, 8 ], [ 1, 5, 6 ], [ 1, 5, 6, 8 ], [ 1, 5, 7, 8 ], [ 2, 3, 4, 5, 6, 7, 8 ], [ 2, 3, 4, 5, 7, 8 ], [ 2, 3, 4, 6, 7, 8 ], [ 2, 3, 4, 6, 8 ], [ 2, 3, 4, 7, 8 ], [ 2, 3, 5, 6, 7, 8 ], [ 2, 3, 5, 6, 8 ], [ 2, 3, 5, 7, 8 ], [ 2, 3, 6, 8 ], [ 2, 3, 7, 8 ], [ 2, 3, 8 ], [ 2, 4, 5, 6, 7, 8 ], [ 2, 4, 5, 6, 8 ], [ 2, 4, 5, 7, 8 ], [ 2, 4, 6 ], [ 2, 4, 6, 8 ], [ 2, 4, 7, 8 ], [ 2, 5, 6 ], [ 2, 5, 6, 8 ], [ 2, 5, 7, 8 ], [ 3, 4, 5, 6, 7, 8 ], [ 3, 4, 5, 7, 8 ], [ 3, 4, 6, 7, 8 ], [ 3, 4, 6, 8 ], [ 3, 4, 7, 8 ], [ 3, 5, 6, 7, 8 ], [ 3, 5, 6, 8 ], [ 3, 5, 7, 8 ], [ 3, 6, 8 ], [ 3, 7, 8 ], [ 3, 8 ], [ 4, 5, 6, 7, 8 ], [ 4, 5, 6, 8 ], [ 4, 5, 7, 8 ], [ 4, 6 ], [ 4, 6, 8 ], [ 4, 7, 8 ], [ 5, 6 ], [ 5, 6, 8 ], [ 5, 7, 8 ]