/************************************************************/ /* Authors : Gustavo Rama, Gonzalo Tornaría * Date : April 2023 * * Eigenvalues for the orthogonal modular form of level 94, 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 2.15.3): * * ? \r lfunparamodular.gp * ? \r form_94a.gp * ? L94=lfunparamodular(form_94a); * * check the functional equation: * * ? lfuncheckfeq(L94) * %4 = -133 * * compute the central value * * ? lfun(L94, 2) * %5 = 0.17815783617895789653725754803907877238 * * The format is * * [level, class, dimension, root_numbers, ap_values, ap2_values] */ {form_94a= [94, "a", 1, [[2, 1], [47, -1]], [ [ 2, -5], [ 3, -1], [ 5, -13], [ 7, 8], [ 11, -12], [ 13, -59], [ 17, -13], [ 19, 44], [ 23, 75], [ 29, 59], [ 31, 228], [ 37, -102], [ 41, -7], [ 43, -210], [ 47, 548], [ 53, -491], [ 59, -43], [ 61, 859], [ 67, -417], [ 71, -165], [ 73, -1272], [ 79, 488], [ 83, 81], [ 89, -1013], [ 97, 1039], [101, 1596], [103, 670], [107, 468], [109, -151], [113, -294], [127, 1021], [131, -289], [137, 1492], [139, -1352], [149, -672], [151, -537], [157, 740], [163, 909], [167, 41], [173, 2412], [179, -883], [181, 2987], [191, -4957], [193, -4530], [197, -3416], [199, -749], [211, -1554], [223, 1283], [227, 3845], [229, 2117], [233, 4829], [239, -3950], [241, 6741], [251, 349], [257, -360], [263, -1281], [269, -1660], [271, 1016], [277, -992], [281, 2550], [283, -3547], [293, -8454], [307, 1017], [311, -4915], [313, -7126], [317, 547], [331, 418], [337, 12721], [347, -2393], [349, -1107], [353, -312], [359, 1125], [367, 11405], [373, 9657], [379, 4993], [383, 2042], [389, -3998], [397, 1337], [401, -8513], [409, -7478], [419, 3452], [421, -5162], [431, -2851], [433, 4331], [439, -3906], [443, -3249], [449, 4755], [457, -14655], [461, 449], [463, -744], [467, 18469], [479, 11544], [487, -4718], [491, 5543], [499, 19108], [503, 549], [509, -18244], [521, -4881], [523, 10959], [541, -6229], [547, 3747], [557, -13600], [563, 20294], [569, 3435], [571, -3906], [577, -17158], [587, 12796], [593, 12018], [599, -15221], [601, -903], [607, 6589], [613, -7864], [617, 9937], [619, 15201], [631, -22073], [641, 14272], [643, -4239], [647, 10920], [653, -204], [659, 11795], [661, -25881], [673, 3563], [677, -9731], [683, 17960], [691, -16548], [701, 5757], [709, -2126], [719, 3990], [727, -30576], [733, -7875], [739, -31734], [743, -5984], [751, -4056], [757, 26453], [761, -20901], [769, 22547], [773, 35172], [787, -37044], [797, 274], [809, -4698], [811, -1559], [821, -12989], [823, 10001], [827, -19787], [829, 1199], [839, -12205], [853, -9269], [857, -3982], [859, -33376], [863, 17342], [877, 44023], [881, 992], [883, -36483], [887, 51547], [907, -7070], [911, 44259], [919, 4675], [929, -50706], [937, -19364], [941, -27898], [947, -52029], [953, -5955], [967, 35629], [971, 67269], [977, 5075], [983, -37059], [991, -11485], [997, 56793] ],[ [ 3, -17], [ 5, 9], [ 7, -12], [11, -150], [13, 115], [17, -351], [19, -42], [23, -795], [29, -54], [31, 488] ]];}