F i_{22}.2

\begin{matrix}2^{6} : S_{6}(2) \\ ≤ 2^{7} : S_{6}(2) \end{matrix} 1389960 1a^{±} + 429a^{±} + 1430a^{±} + 3080a^{±} + 13650a^{±}

+ 30030a^{±} + 45045a^{±} + 75075a^{±} + 205920a^{±} + 320320a^{±}

20

Character Numbers: [ 1, 2, 5, 6, 9, 10, 13, 14, 17, 18, 19, 20, 25, 26, 33, 34, 46, 47, 52, 53 ]

S_{1}  S_{2}  S_{3}  S_{4}  S_{5}  S_{6}  S_{7}  S_{8}  S_{9}  S_{10}
χ_{1}  1  1  135  135 1260 1260  2304 2304 8640  8640
χ_{2}  1 −1  135 −135 −1260 1260  2304 −2304 8640 −8640
χ_{3} 1680 1680 1260 1260 8960 8960 −10080 −1680 −1680 −10080
χ_{4} −1680 1680 −1260 1260 8960 −8960 −10080 −1680 1680 10080
χ_{5} 1008 1008 −2268 −2268 −1792 −1792 −3024 6048 6048 −3024
χ_{6} −1008 1008 2268 −2268 −1792 1792 −3024 6048 −6048  3024
χ_{7}  96  96 1368 1368 −1408 −1408 −1440  120  120 −1440
χ_{8} −96  96 −1368 1368 −1408 1408 −1440  120 −120  1440
χ_{9}  312 312 −576 −576 −256 −256  1152 −960 −960  1152
χ_{10} −312 312  576 −576 −256  256  1152 −960  960 −1152
χ_{11}  240 240  180  180 −256 −256  720 −672 −672  720
χ_{12} −240 240 −180  180 −256  256  720 −672  672 −720
χ_{13} −144 −144 −432 −432  512  512  0  0  0  0
χ_{14}  144 −144  432 −432  512 −512  0  0  0  0
χ_{15} −48 −48 −36 −36 −256 −256  288  48  48  288
χ_{16}  48 −48  36 −36 −256  256  288  48 −48 −288
χ_{17}  0  0  0  0  224  224  0 −252 −252  0
χ_{18}  0  0  0  0  224 −224  0 −252  252  0
χ_{19} −12 −12  72  72 −112 −112 −144  228  228 −144
χ_{20}  12 −12 −72  72 −112  112 −144  228 −228  144

S_{11}  S_{12}  S_{13}  S_{14}  S_{15}  S_{16}  S_{17}  S_{18}  S_{19}  S_{20}
χ_{1} 10080 10080 45360 45360 143360 143360 241920 241920 241920 241920
χ_{2} −10080 10080 −45360 45360 143360 −143360 241920 241920 −241920 −241920
χ_{3}  1680 1680  1260 1260 8960  8960 −10080 −1680 −1680 −10080
χ_{4} −1680 1680 −1260 1260 8960 −8960 −10080 −1680  1680  10080
χ_{5}  1008 1008 −2268 −2268 −1792 −1792 −3024 6048  6048 −3024
χ_{6} −1008 1008  2268 −2268 −1792  1792 −3024 6048 −6048  3024
χ_{7}  96  96  1368 1368 −1408 −1408 −1440  120  120 −1440
χ_{8}  −96  96 −1368 1368 −1408  1408 −1440  120  −120  1440
χ_{9}  312 312 −576 −576 −256  −256  1152 −960  −960  1152
χ_{10} −312 312  576 −576 −256  256  1152 −960  960 −1152
χ_{11}  240 240  180  180 −256  −256  720 −672  −672  720
χ_{12} −240 240 −180  180 −256  256  720 −672  672  −720
χ_{13} −144 −144 −432 −432  512  512  0  0  0  0
χ_{14}  144 −144  432 −432  512  −512  0  0  0  0
χ_{15}  −48 −48  −36 −36 −256  −256  288  48  48  288
χ_{16}  48 −48  36 −36 −256  256  288  48  −48  −288
χ_{17}  0  0  0  0  224  224  0 −252  −252  0
χ_{18}  0  0  0  0  224  −224  0 −252  252  0
χ_{19}  −12 −12  72  72 −112  −112 −144  228  228  −144
χ_{20}  12 −12  −72  72 −112  112 −144  228  −228  144

Ramanujan Graphs: [ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ] , [ 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ], [ 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ], [ 2, 3, 4, 5, 6, 7, 9, 11, 13, 14, 15, 16, 17, 18, 19, 20 ], [ 2, 3, 4, 5, 6, 7, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ], [ 2, 3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20 ], [ 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ], [ 2, 3, 4, 5, 6, 8, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20 ], [ 2, 3, 4, 5, 6, 8, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ], [ 2, 3, 4, 5, 6, 8, 13, 14, 15, 16, 17, 18, 19, 20 ], [ 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ], [ 2, 3, 4, 5, 6, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ], [ 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ], [ 2, 3, 4, 5, 7, 8, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ], [ 2, 3, 4, 5, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ], [ 2, 3, 4, 5, 7, 9, 11, 13, 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