HN.2

S_{11} ≤ S_{12} 13680000 1a^{+} + 133ab + 760a^{+} + 3344a^{+} +

8910a^{+} + 9405a^{+} + 16929a^{+} + 35112ab
+ 267520a^{+} + 365750a^{+} + 406296a^{+} +
653125a^{+} + 1185030a^{+} + 2031480a^{+} +
2375000a^{+} + 2407680a^{+} + 3878280a^{+}

17

Character Numbers: [ 1, 3, 4, 6, 9, 11, 13, 15, 20, 24, 27, 29, 36, 47, 49, 51, 63 ]

S_{1} S_{2}  S_{3}  S_{4}  S_{5}  S_{6}  S_{7}  S_{8}  S_{9}
χ_{1} 1 11 2772 2772 16632 20790 60480 83160 99792
χ_{2} 1 11 −1188 −1188  792 4950  0 3960 4752
χ_{3} 1 11  792  792 −1188 2970 −12960 −5940 −7128
χ_{4} 1 11  72  72 1332 990  2880 6660 7992
χ_{5} 1 11  492  492 −88 1030  5760 −440 −528
χ_{6} 1 −1 −168  168 1428 1050  0 2100 −3528
χ_{7} 1 11  372  372  632 310 −2880 3160 3792
χ_{8} 1 11 −288 −288 −108 450  0 −540 −648
χ_{9} 1 11  72  72 −18 −90  720 −90 −108
χ_{10} 1 11 −108 −108  72 −90  0  360  432
χ_{11} 1 11  72  72 −68  10 −480 −340 −408
χ_{12} 1 −1 −72  72  180  90  0  468
χ_{13} 1 −1  72 −72  68 250  0  100 −168
χ_{14} 1 −1  12 −12  208 −50  0 −400  192
χ_{15} 1 −1  36 −36 −144 −18  0  144  0
χ_{16} 1 −1 −48  48 −102 150  0 −150  252
χ_{17} 1 −1  −8  8 −12 −150  0  100 −88

S_{10}  S_{11}  S_{12}  S_{13}  S_{14}  S_{15}  S_{16}  S_{17}
χ_{1} 103950 362880 369600 831600 1247400 2494800 3991680 3991680
χ_{2} 24750 17280 52800 −118800 −59400 −118800 190080  0
χ_{3} 14850  6480 13200  59400  0  0 71280 −142560
χ_{4} 4950  2880 −26400  3600 −3600 −7200 31680 −25920
χ_{5} 5150 −1920  4800  10800 −6600 −13200 −21120  15360
χ_{6} −1050 −10080  0  0 25200 −25200 10080  0
χ_{7} 1550 −1920  4800 −3600  4200  8400 −21120  1920
χ_{8} 2250 −720 −1200 −1800  3600  7200 −7920  0
χ_{9} −450  180  600 −1800  1800  3600  1980 −6480
χ_{10} −450  0  960  2160 −1080 −2160  0  0
χ_{11}  50  80 −1200  −600  −800 −1600  880  4320
χ_{12}  −90  1440  0  0  −720  720 −1440  0
χ_{13} −250 −480  0  0 −1200  1200  480  0
χ_{14}  50  320  0  0  400  −400  −320  0
χ_{15}  18  576  0  0  1008 −1008  −576  0
χ_{16} −150 −180  0  0  0  0  180  0
χ_{17}  150 −480  0  0  −400  400  480  0

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