F i_{22}.2

\begin{matrix}2^{10} : M_{22} \\ ≤ 2^{10} : M_{22}.2 \end{matrix} 284310 1a^{±} + 78a^{±} + 429a^{±} + 1430a^{±} + 3080a^{±}

+ 30030a^{±} + 32032a^{±} + 75075a^{±}

16

Character Numbers: [ 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 19, 20, 21, 22, 33, 34 ]

S_{1} S_{2}  S_{3} S_{4}  S_{5}  S_{6} S_{7}  S_{8}  S_{9} S_{10}  S_{11}  S_{12}  S_{13}  S_{14}  S_{15} S_{16}
χ_{1} 1 1 154 154 1024 1024 3696 3696 4928 4928 11264 11264 42240 42240 78848 78848
χ_{2} 1 −1 −154 154 1024 −1024 3696 −3696 −4928 4928 −11264 11264 42240 −42240 −78848 78848
χ_{3} 1 1 −77 −77 −320 −320 924  924 1232 1232 −1408 −1408 −5280 −5280  4928 4928
χ_{4} 1 −1  77 −77 −320  320 924 −924 −1232 1232  1408 −1408 −5280  5280 −4928 4928
χ_{5} 1 1  49 49 −176 −176 546  546 −532 −532  1184 1184 −960 −960 −112 −112
χ_{6} 1 −1 −49 49 −176  176 546 −546  532 −532 −1184 1184 −960  960  112 −112
χ_{7} 1 1 −35 −35 160  160 294  294 −364 −364 −400 −400  120  120  224 224
χ_{8} 1 −1  35 −35 160 −160 294 −294  364 −364  400 −400  120 −120 −224 224
χ_{9} 1 1  37 37  88  88 186  186  248 248  32  32  120  120 −712 −712
χ_{10} 1 −1 −37 37  88 −88 186 −186 −248 248  −32  32  120 −120  712 −712
χ_{11} 1 1  13 13 −32 −32  6  6 −28 −28 −112 −112  120  120  32  32
χ_{12} 1 −1 −13 13 −32  32  6  −6  28 −28  112 −112  120 −120  −32  32
χ_{13} 1 1 −17 −17 −20 −20 24  24  32  32  32  32  120  120 −172 −172
χ_{14} 1 −1  17 −17 −20  20 24 −24 −32  32  −32  32  120 −120  172 −172
χ_{15} 1 1  1  1  16  16 −30 −30  −4 −4  32  32 −96  −96  80  80
χ_{16} 1 −1 −1  1  16 −16 −30  30  4 −4  −32  32 −96  96  −80  80

Ramanujan Graphs: [ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 2, 3, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 2, 3, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 2, 3, 6, 8, 9, 11, 14, 15 ], [ 2, 3, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 2, 3, 8, 9, 11, 14, 15 ], [ 2, 3, 8, 14, 15 ], [ 2, 3, 9, 11, 14, 15 ], [ 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 2, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 2, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 2, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 2, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 2, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 2, 6, 8, 9, 11, 14, 15 ], [ 2, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 2, 8, 9, 11, 14, 15 ], [ 2, 8, 14, 15 ], [ 2, 9, 11, 14, 15 ], [ 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 3, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 3, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 3, 6, 8, 9, 11, 14, 15 ], [ 3, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 3, 8, 9, 11, 14, 15 ], [ 3, 8, 14, 15 ], [ 3, 9, 11, 14, 15 ], [ 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 4, 5, 7, 10, 12, 13, 16 ], [ 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 4, 7, 10, 12, 13, 16 ], [ 4, 7, 13, 16 ], [ 4, 10, 12, 13, 16 ], [ 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ], [ 5, 7, 10, 12, 13, 16 ], [ 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ] , [ 6, 8, 9, 11, 14, 15 ], [ 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 ] , [ 7, 10, 12, 13, 16 ], [ 7, 13, 16 ], [ 8, 9, 11, 14, 15 ], [ 8, 14, 15 ], [ 9, 11, 14, 15 ], [ 10, 12, 13, 16 ]