F i_{22}.2

{O_{8}^{+}(2).2 ≤ \atop O_{8}^{+}(2).3.2 × 2} 370656 1a^{+} + 429a^{±} + 1001a^{+} + 3080a^{+} +

10725a^{−} + 13650a^{+} + 45045a^{+} + 48048a^{±}
+ 50050a^{−} + 75075a^{±}

13

Character Numbers: [ 1, 5, 6, 7, 13, 16, 17, 25, 27, 28, 30, 33, 34 ]

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 2 2 1575 1575 3150 3150 22400 22400 44800 44800 226800
χ_{2} 1 1 −1 −1 315 315 −315 −315 2240 2240 −2240 −2240  0
χ_{3} 1 −1 −1 1 315 −315 315 −315 −2240 2240 −2240 2240  0
χ_{4} 1 −1 2 −2 −225 225 450 −450 −800 800 1600 −1600 0
χ_{5} 1 1 2 2 171 171 342 342  −64 −64 −128 −128 −648
χ_{6} 1 −1 2 −2  63 −63 −126 126 −224  224  448 −448  0
χ_{7} 1 1 2 2  −9  −9 −18 −18  224  224  448  448 −1296
χ_{8} 1 1 2 2  −9  −9 −18 −18  −64 −64 −128 −128  432
χ_{9} 1 1 −1 −1 −45 −45  45  45  80  80  −80  −80  0
χ_{10} 1 −1 −1 1 −45  45 −45  45  −80  80  −80  80  0
χ_{11} 1 −1 2 −2  −9  9  18 −18  64 −64 −128  128  0
χ_{12} 1 1 −1 −1  27  27 −27 −27  −64 −64  64  64  0
χ_{13} 1 −1 −1 1  27 −27  27 −27  64 −64  64  −64  0

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