O′N.2

L_{3}(7) ≤ L_{3}(7).2 491040 1a^{±} + 10944a^{±} + 26752a^{±} + 32395ab + 37696a^{±} + 52668a^{±} + 85064a^{±}

13

Character Numbers: [ 1, 2, 3, 4, 7, 8, 9, 10, 11, 12, 13, 20 , 21 ]

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}
χ_{1} 1 1  912 11172 11172 11172 12768 32928 32928 52136 52136 117306 156408
χ_{2} 1 1 −912 −11172 −11172 11172 12768 −32928 −32928 52136 52136 117306 −156408
χ_{3} 1 1  98  238  238 392 −212  −28  −28 161 161 −504  −518
χ_{4} 1 1 −98 −238 −238 392 −212  28  28 161 161 −504  518
χ_{5} 1 1 −42r2  84r2  84r2 −42 222 105r2 105r2 161 161 −504 −336r2
χ_{6} 1 1 42r2 −84r2 −84r2 −42 222 −105r2 −105r2 161 161 −504  336r2
χ_{7} 1 1  0  0  0  84  96  0  0 −280 −280  378  0
χ_{8} 1 −1  0  −84  84  0  0 −294  294 −343 343  0  0
χ_{9} 1 −1  0  84  −84  0  0  294 −294 −343 343  0  0
χ_{10} 1 1  8r7 −26r7 −26r7 −112 −128  80r7  80r7  56  56  126 −116r7
χ_{11} 1 1 −8r7  26r7  26r7 −112 −128 −80r7 −80r7  56  56  126  116r7
χ_{12} 1 −1  0  114 −114  0  0  −96  96 152 −152  0  0
χ_{13} 1 −1  0 −114  114  0  0  96  −96 152 −152  0  0

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