HN

A_{11} ≤ A_{12} 13680000 1a + 133ab + 760a + 3344a + 8910a + 9405a + 16929a + 35112ab + 267520a + 365750a + 406296a + 653125a + 1185030a + 2031480a + 2375000a + 2407680a + 3878280a

19

Character Numbers:[ 1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 18, 20, 23, 24, 32, 39, 40, 41, 47 ]

S_{1} S_{2}  S_{3}  S_{4}  S_{5}  S_{6}  S_{7}  S_{8}  S_{9}  S_{10}
χ_{1} 1 11 2772 2772 16632 20790  30240  30240 83160 9979 2
χ_{2} 1 11 −1188 −1188  792 4950 −4320r5 4320r5 3960 475 2
χ_{3} 1 11 −1188 −1188  792 4950 4320r5 −4320r5 3960 475 2
χ_{4} 1 11  792  792 −1188 2970 −6480 −6480 −5940 −7128
χ_{5} 1 11  72  72 1332 990  1440  1440 6660 7992
χ_{6} 1 11  492  492 −88 1030  2880  2880 −440 −528
χ_{7} 1 −1 −168  168 1428 1050  0  0 2100
χ_{8} 1 11  372  372  632 310 −1440 −1440 3160 3792
χ_{9} 1 11 −288 −288 −108 450 −720r5  720r5 −540 −648
χ_{10} 1 11 −288 −288 −108 450  720r5 −720r5 −540 −648
χ_{11} 1 11  72  72 −18 −90  360  360 −90 −108
χ_{12} 1 11 −108 −108  72 −90  0  0  360  432
χ_{13} 1 11  72  72 −68  10  −240  −240 −340 −408
χ_{14} 1 −1 −72  72  180  90  0  0  468 −648
χ_{15} 1 −1  72 −72  68 250  0  0  100 −168
χ_{16} 1 −1  12 −12  208 −50  0  0 −400  192
χ_{17} 1 −1  36 −36 −144 −18  0  0  144  0
χ_{18} 1 −1 −48  48 −102 150  0  0 −150  252
χ_{19} 1 −1  −8  8 −12 −150  0  0  100 −88

S_{11}  S_{12}  S_{13}  S_{14}  S_{15}  S_{16}  S_{17}  S_{18}  S_{19}
χ_{1} 103950 362880 369600 831600 1247400 1995840 1995840 2494800 3991680
χ_{2} 24750 17280 52800 −118800 −59400 95040r5 −95040r5 −118800 190080
χ_{3} 24750 17280 52800 −118800 −59400 −95040r5 95040r5 −118800 190080
χ_{4} 14850  6480 13200  59400  0 −71280 −71280  0 71280
χ_{5} 4950  2880 −26400  3600 −3600 −12960 −12960 −7200 31680
χ_{6} 5150 −1920  4800  10800 −6600  7680  7680 −13200 −21120
χ_{7} −1050 −10080  0  0 25200  0  0 −25200 10080
χ_{8} 1550 −1920  4800 −3600  4200  960  960  8400 −21120
χ_{9} 2250  −720 −1200 −1800  3600 −2160r5  2160r5  7200 −7920
χ_{10} 2250  −720 −1200 −1800  3600  2160r5 −2160r5  7200 −7920
χ_{11} −450  180  600 −1800  1800  −3240  −3240  3600  1980
χ_{12} −450  0  9 60  2160 −1080  0  0 −2160  0
χ_{13}  50  80 −1200  −600  −800  2160  2160 −1600  880
χ_{14}  −90  1440  0  0  −720  0  0  720 −1440
χ_{15} −250  −480  0  0 −1200  0  0  1200  480
χ_{16}  50  320  0  0  400  0  0  −400  −320
χ_{17}  18  576  0  0  1008  0  0 −1008  −576
χ_{18} −150 −180  0  0  0  0  0  0  180
χ_{19}  150  −480  0  0  −400  0  0  400  480

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