HN.2

\begin{matrix}2.HS.2 \\ ≤ 4.HS.2 \end{matrix} 3078000 1a^{±} + 3344a^{±} + 8910a^{±} + 9405a^{±} + 16929a^{±} +

214016a^{±} + 267520a^{±} + 365750a^{±} + 653125a^{±}

18

Character Numbers: [ 1, 2, 6, 7, 9, 10, 11, 12, 13, 14, 18, 1 9, 20, 21, 24, 25, 29, 30 ]

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}  S_{17}  S_{18}
χ_{1} 1  1  1408 1408 2200  2200  5775 5775 35200  35200  123200 123200 277200  277200 354816  354816  739200 739200
χ_{2} 1 −1 −1408 1408 2200 −2200 −5775 5775 35200 −35200 −123200 123200 277200 −277200 354816 −354816 −739200 739200
χ_{3} 1  1  208  208 −50  −50  525  525 2200  2200  −2800 −2800 −6300  −6300  2016  2016  4200  4200
χ_{4} 1 −1 −208  208 −50  50 −525  525 2200 −2200  2800 −2800 −6300  6300  2016  −2016  −4200  4200
χ_{5} 1  1 −112 −112 300  300  75  75 1000  1000  −2200 −2200  3600  3600  −864  −864  −1800 −1800
χ_{6} 1 −1  112 −112 300 −300  −75  75 1000 −1000  2200 −2200  3600  −3600  −864  864  1800 −1800
χ_{7} 1  1  208  208 100  100 −525 −525 1000  1000  1400  1400  0  0  2016  2016  −4200 −4200
χ_{8} 1 −1 −208  208 100 −100  525 −525 1000 −1000  −1400  1400  0  0  2016  −2016  4200 −4200
χ_{9} 1  1  128  128 200  200  375  375  0  0  1600  1600  0  0 −2304  −2304  0  0
χ_{10} 1 −1 −128  128 200 −200 −375  375  0  0  −1600  1600  0  0 −2304  2304  0  0
χ_{11} 1  1  −47 −47 −50  −50  0  0  250  250  350  350  0  0  −504  −504  0  0
χ_{12} 1 −1  47 −47 −50  50  0  0  250  −250  −350  350  0  0  −504  504  0  0
χ_{13} 1  1  28  28 −50  −50  75  75  −50  −50  −100  −100  450  450  396  396  −750  −750
χ_{14} 1 −1  −28  28 −50  50  −75  75  −50  50  100  −100  450  −450  396  −396  750  −750
χ_{15} 1  1  −32 −32  40  40  15  15  −80  −80  80  80  −360  −360  576  576  −240  −240
χ_{16} 1 −1  32 −32  40  −40  −15  15  −80  80  −80  80  −360  360  576  −576  240  −240
χ_{17} 1  1  16  16  4  4  −45 −45  −56  −56  −136  −136  0  0  −288  −288  504  504
χ_{18} 1 −1  −16  16  4  −4  45 −45  −56  56  136  −136  0  0  −288  288  −504  504

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