/************************************************************/ /* Authors : Gustavo Rama, Gonzalo Tornaria * Date : March 2023 * * Eigenvalues for the orthogonal modular form of level 97, sign +1 * * Please reference this data as * * Gustavo Rama and Gonzalo Tornaría, * Quinary orthogonal modular forms, 2023. * http://www.cmat.edu.uy/cnt/ * * See also: * * Gustavo Rama and Gonzalo Tornaría, * Computation of paramodular forms, * ANTS 2020. * * Example usage (gp/pari 2.15.0): * * ? \r lfunparamodular.gp * ? \r form_97a.gp * ? L97=lfunparamodular(form_97a); * * check the functional equation: * * ? lfuncheckfeq(L97) * %4 = -133 * * compute the central value * * ? lfun(L97, 2) * %5 = 0.19385684572538079033623425750447717545 * * The format is * * [level, class, dimension, root_numbers, ap_values, ap2_values] */ w = quadgen(5); {form_97a= [97, "a", 1, [[97, -1]], [ [ 2, -5 + w], [ 3, - 4*w], [ 5, -8 + 12*w], [ 7, 9 - 2*w], [ 11, -24 - 16*w], [ 13, -10 + 44*w], [ 17, 25 - 40*w], [ 19, -36 + 80*w], [ 23, 7 - 14*w], [ 29, -118 + 32*w], [ 31, 81 - 178*w], [ 37, 84 - 60*w], [ 41, 149 - 88*w], [ 43, 64 + 152*w], [ 47, -100 + 112*w], [ 53, 406 + 52*w], [ 59, -218 - 108*w], [ 61, -146 - 196*w], [ 67, 72 - 720*w], [ 71, -374 + 292*w], [ 73, 1064 - 128*w], [ 79, -752 + 1360*w], [ 83, -308 + 756*w], [ 89, 864 - 616*w], [ 97, -141 - 376*w], [101, -682 - 108*w], [103, -1009 + 642*w], [107, -430 + 208*w], [109, 772 - 24*w], [113, 144 - 1272*w], [127, 817 + 334*w], [131, 210 + 408*w], [137, 1415 + 240*w], [139, -1200 + 116*w], [149, -92 - 296*w], [151, 2376 - 1120*w], [157, -740 - 1632*w], [163, 854 - 2224*w], [167, -1109 + 130*w], [173, -380 + 80*w], [179, -902 + 796*w], [181, -452 + 912*w], [191, -1835 + 1670*w], [193, 1040 + 1120*w], [197, 1692 + 1052*w], [199, 797 - 874*w], [211, -1892 + 124*w], [223, -177 + 2546*w], [227, -1764 - 1972*w], [229, -1236 - 120*w], [233, -1184 + 2408*w], [239, 4619 + 1090*w], [241, 3722 - 2656*w], [251, 3036 - 1804*w], [257, -357 - 1024*w], [263, -753 + 2818*w], [269, -4072 + 7324*w], [271, 2041 + 182*w], [277, 1708 - 176*w], [281, -619 - 4120*w], [283, -3010 - 2344*w], [293, -6848 + 2864*w], [307, -676 - 1056*w], [311, 4829 - 1490*w], [313, 2356 - 5696*w], [317, -4228 + 1352*w], [331, -4160 + 264*w], [337, -2225 - 744*w], [347, 2516 + 2540*w], [349, 2498 - 1664*w], [353, 5285 - 2744*w], [359, 2315 + 1922*w], [367, 1117 + 6670*w], [373, 3164 - 2200*w], [379, -1342 - 2464*w], [383, -6639 + 78*w], [389, -7856 - 4360*w], [397, -5762 - 384*w], [401, 6162 + 5256*w], [409, 3142 - 1272*w], [419, 11722 - 10468*w], [421, 2280 + 1168*w], [431, -23704 + 5552*w], [433, 7705 - 2136*w], [439, 1326 + 4028*w], [443, 2622 + 1928*w], [449, -9039 + 4256*w], [457, -7593 + 2736*w], [461, 12768 + 3968*w], [463, 106 + 668*w], [467, -1360 - 6592*w], [479, 1322 + 8156*w], [487, -3852 + 10904*w], [491, -6726 - 7012*w], [499, -7946 - 1976*w], [503, 5766 + 6756*w], [509, -1638 - 4884*w], [521, -146 - 9872*w], [523, -13404 + 5548*w], [541, 12212 - 6900*w], [547, 7716 + 3672*w], [557, -2726 - 6152*w], [563, 284 + 5388*w], [569, 15564 - 15992*w], [571, -3768 + 5096*w], [577, 9738 - 1208*w], [587, -9916 - 7276*w], [593, 2878 - 3056*w], [599, 3424 - 6232*w], [601, 11273 - 6952*w], [607, -594 + 13396*w], [613, -3164 - 3560*w], [617, 9589 - 4064*w], [619, 7286 + 3212*w], [631, -20390 - 18060*w], [641, 4918 + 7640*w], [643, 25596 - 15820*w], [647, 18636 - 15928*w], [653, 12106 - 14720*w], [659, 3782 + 2292*w], [661, 10578 + 1440*w], [673, -21338 + 14688*w], [677, 2248 - 1904*w], [683, -3276 - 4504*w], [691, 1836 + 6520*w], [701, 7280 + 7376*w], [709, 10884 - 16452*w], [719, 28823 - 21558*w], [727, 11106 - 17812*w], [733, -23912 + 19200*w], [739, -24748 + 9520*w], [743, 986 + 6436*w], [751, -4614 - 5796*w], [757, -3582 + 3532*w], [761, -5571 + 8088*w], [769, -3122 + 6720*w], [773, 12810 - 8092*w], [787, -22504 + 28232*w], [797, 16174 + 4968*w], [809, -23228 + 26560*w], [811, 8688 - 8792*w], [821, -22604 + 5652*w], [823, -26876 + 29376*w], [827, 35496 - 18412*w], [829, 17794 - 6216*w], [839, -8963 - 4226*w], [853, -11910 - 4172*w], [857, 11430 - 25272*w], [859, -9982 + 13036*w], [863, 16663 - 14046*w], [877, 5378 + 13600*w], [881, -16434 + 2184*w], [883, -722 - 1992*w], [887, 21465 + 5966*w], [907, -13402 + 30700*w], [911, 9157 - 178*w], [919, 10283 + 250*w], [929, 11151 + 10424*w], [937, 7065 + 29448*w], [941, -31568 + 27608*w], [947, -10628 - 11180*w], [953, 1856 + 5168*w], [967, -2494 + 15884*w], [971, -5796 + 10008*w], [977, -13899 + 456*w], [983, -16964 + 4624*w], [991, 45581 - 11018*w], [997, 42490 - 18860*w] ],[ [ 2, 4 - 2*w], [ 3, -11 + 8*w], [ 5, 10 - 16*w], [ 7, 2 - 8*w], [11, -113 + 104*w], [13, 26 + 72*w], [17, -114 - 48*w], [19, -206 + 64*w], [23, -30 - 312*w], [29, 78 - 856*w], [31, -228 + 480*w] ]];}