HN.2

\begin{matrix}2.HS.2 \\ ≤ 4.HS.2 \end{matrix} 3078000 1a^{+} + 760a^{+} + 3344a^{+} + 8910a^{+} + 9405a^{+}

+ 16929a^{+} + 214016a^{±} + 267520a^{+} +
270864a^{+} + 365750a^{+} + 653125a^{+} +
1053360a^{+}

13

Character Numbers: [ 1, 4, 6, 9, 11, 13, 18, 19, 20, 22, 24, 29, 33 ]

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 1408 1408 4400 11550 35200 35200 246400 354816 354816 554400 1478400
χ_{2} 1 −1 352 −352  0  0 4400 −4400  0 22176 −22176  0  0
χ_{3} 1 1 208 208 −100 1050 2200 2200 −5600 2016  2016 −12600  8400
χ_{4} 1 1 −112 −112 600  150 1000 1000 −4400 −864 −864  7200 −3600
χ_{5} 1 1 208 208 200 −1050 1000 1000 2800 2016  2016  0 −8400
χ_{6} 1 1 128 128 400  750  0  0 3200 −2304 −2304  0  0
χ_{7} 1 1 −47 −47 −100  0 250  250  700 −504 −504  0  0
χ_{8} 1 −1 −53  53  0  0 350 −350  0 −504  504  0  0
χ_{9} 1 1  28  28 −100  150 −50 −50 −200  396  396  900 −1500
χ_{10} 1 −1  72 −72  0  0 100 −100  0 −504  504  0  0
χ_{11} 1 1 −32 −32  80  30 −80 −80  160  576  576 −720  −480
χ_{12} 1 1  16  16  8 −90 −56 −56 −272 −288 −288  0  1008
χ_{13} 1 −1 −8  8  0  0 −100  100  0  216 −216  0  0

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