HS

4.2^{4} : S_{5} 5775 1a + 77a + 154a + 175a + 693a + 825a + 1056a + 1386a + 1408a

9

Character Numbers: [ 1, 3, 4, 7, 9, 13, 16, 17, 18 ]

S_{1} S_{2} S_{3} S_{4} S_{5} S_{6} S_{7}  S_{8}  S_{9}
χ_{1} 1 30 80 128 480 640 960 1536 1920
χ_{2} 1 15 20 −32 60 80  0  96 −240
χ_{3} 1 15 20  8 60 −20  0 −144  60
χ_{4} 1 −3 14 40 −48 68 36 −48 −60
χ_{5} 1 5 −10  8  0 20 −60  16  20
χ_{6} 1 7  4  0 −28 −32 16  32  0
χ_{7} 1 −5 10 −12 −10 10 −20 −4  30
χ_{8} 1 −5  0  8 20 −20  0  16 −20
χ_{9} 1 0 −10 −7  0 10 30 −24  0

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