/************************************************************/ /* Authors : Gustavo Rama, Gonzalo Tornaria * Date : June 2020 * Update : April 2021 (added eigenvalues 2000-3000) * * Eigenvalues for the (non-lift) orthogonal modular form of level 61 * * Please reference this data as * * Gustavo Rama and Gonzalo Tornaría, * Quinary orthogonal modular forms, 2020. * http://www.cmat.edu.uy/cnt/ * * See also: * * Gustavo Rama and Gonzalo Tornaría, * Computation of paramodular forms, * ANTS 2020. * * Example usage (gp/pari 2.11.4): * * ? \r lfunparamodular.gp * ? \r form_61a.gp * ? L61=lfunparamodular(form_61a); * * check the functional equation: * * ? lfuncheckfeq(L61) * %4 = -124 * * compute the central value * * ? lfun(L61, 2) * %5 = 0.11755572262228832083489179991258553768 * * the same with more precision * * ? \p 104 * ? lfun(L61, 2) * %6 = 0.11755572262228832083489179991258553770693255690936719273956500014576750295105978992025051562572197380169 * * The computation of ap_s for all p up to 2000 took ~ 1 core-year. * Wall time: 10 days in a 36 core computer (dual xeon 6240). * * UPDATE: implemented grouping of neighbours in orbits by the * action of the group of autometries gave a 10x improvement. * * Computation for p up to 2000 now takes ~ 37.5 core-days. * Computation for p in the range 2000 - 3000 took ~ 137 core-days. * Total wall time: ~ 4.8 days in the same 36 core computer. * * The format is * * [level, class, dimension, root_numbers, ap_values, ap2_values] */ {form_61a= [61, "a", 1, [[61, -1]], [ [ 2, -7], [ 3, -3], [ 5, 3], [ 7, -9], [ 11, -4], [ 13, -3], [ 17, 37], [ 19, -75], [ 23, 10], [ 29, 212], [ 31, -6], [ 37, -88], [ 41, -3], [ 43, 547], [ 47, -147], [ 53, -108], [ 59, -45], [ 61, 145], [ 67, -632], [ 71, -650], [ 73, 859], [ 79, -978], [ 83, 931], [ 89, -571], [ 97, 453], [ 101, 830], [ 103, 1246], [ 107, 707], [ 109, -378], [ 113, -225], [ 127, 1607], [ 131, -1399], [ 137, -861], [ 139, 1938], [ 149, 157], [ 151, 2356], [ 157, -414], [ 163, -11], [ 167, -1852], [ 173, -2021], [ 179, 1444], [ 181, 442], [ 191, -366], [ 193, -2790], [ 197, -815], [ 199, -2753], [ 211, -3519], [ 223, 100], [ 227, -2302], [ 229, -813], [ 233, -1136], [ 239, 5251], [ 241, 5366], [ 251, 4478], [ 257, -1794], [ 263, 4270], [ 269, 7959], [ 271, -2409], [ 277, 1592], [ 281, 7566], [ 283, -737], [ 293, -6777], [ 307, 1350], [ 311, 4001], [ 313, 2685], [ 317, 7560], [ 331, -6732], [ 337, -5228], [ 347, 2829], [ 349, 4999], [ 353, -18397], [ 359, 3871], [ 367, 3171], [ 373, -6977], [ 379, 8517], [ 383, 5665], [ 389, -194], [ 397, -1484], [ 401, -2484], [ 409, -12944], [ 419, -1919], [ 421, 21564], [ 431, -1559], [ 433, -4556], [ 439, -4476], [ 443, 7725], [ 449, -8444], [ 457, -2673], [ 461, -5217], [ 463, -2666], [ 467, -672], [ 479, -1129], [ 487, 467], [ 491, -4973], [ 499, -3859], [ 503, 4091], [ 509, 10085], [ 521, -2290], [ 523, 11663], [ 541, 16984], [ 547, -6079], [ 557, -28136], [ 563, 591], [ 569, -13725], [ 571, 16866], [ 577, 21984], [ 587, 3770], [ 593, 16344], [ 599, -3720], [ 601, -5680], [ 607, -4355], [ 613, -4118], [ 617, 1816], [ 619, 2865], [ 631, -416], [ 641, 29818], [ 643, 4806], [ 647, 2677], [ 653, 20114], [ 659, -35935], [ 661, -10673], [ 673, 4206], [ 677, 24858], [ 683, -19831], [ 691, 33693], [ 701, -8116], [ 709, 4409], [ 719, 103], [ 727, -21097], [ 733, 21508], [ 739, -12441], [ 743, 914], [ 751, -10979], [ 757, 17029], [ 761, 9824], [ 769, 2507], [ 773, -34168], [ 787, 14729], [ 797, -23959], [ 809, 16393], [ 811, -8860], [ 821, -17840], [ 823, -23390], [ 827, -22068], [ 829, 24032], [ 839, 21701], [ 853, 48113], [ 857, 4346], [ 859, 34291], [ 863, 17510], [ 877, 4474], [ 881, -3063], [ 883, -34159], [ 887, -23122], [ 907, -31038], [ 911, -37242], [ 919, -11955], [ 929, -24813], [ 937, -58018], [ 941, 26630], [ 947, 20736], [ 953, -1103], [ 967, -334], [ 971, 19843], [ 977, -41663], [ 983, -32746], [ 991, -935], [ 997, 30390], [1009, 11118], [1013, -20536], [1019, 462], [1021, -7651], [1031, 54316], [1033, 2563], [1039, 11235], [1049, 411], [1051, -65175], [1061, 23262], [1063, -35319], [1069, 24429], [1087, -2764], [1091, 15048], [1093, 14547], [1097, 22168], [1103, -4111], [1109, -658], [1117, 55945], [1123, -6963], [1129, -20038], [1151, -39009], [1153, -41796], [1163, 4589], [1171, -36144], [1181, -33241], [1187, -17287], [1193, -4171], [1201, 15811], [1213, 56010], [1217, -47775], [1223, 78799], [1229, 18068], [1231, 11438], [1237, 81218], [1249, -2411], [1259, 26701], [1277, 148889], [1279, -67208], [1283, -10099], [1289, -38714], [1291, -2562], [1297, 79855], [1301, 36483], [1303, -27721], [1307, -30587], [1319, 52454], [1321, 86867], [1327, -36629], [1361, 61071], [1367, 37629], [1373, -18395], [1381, 22327], [1399, 30693], [1409, 9506], [1423, 5697], [1427, 49802], [1429, 36966], [1433, -121431], [1439, -79391], [1447, 166798], [1451, -147192], [1453, -10072], [1459, -31711], [1471, 29585], [1481, 74726], [1483, -33974], [1487, 7686], [1489, -41035], [1493, 4571], [1499, -44751], [1511, -7767], [1523, -46617], [1531, -46868], [1543, 40789], [1549, -118777], [1553, -182430], [1559, 24295], [1567, -19757], [1571, -99669], [1579, 12851], [1583, -18865], [1597, -37755], [1601, 43451], [1607, -52934], [1609, 78784], [1613, -126113], [1619, -58080], [1621, 22723], [1627, -63421], [1637, 10050], [1657, -16179], [1663, 6321], [1667, 83671], [1669, -15937], [1693, 86919], [1697, -87300], [1699, 8495], [1709, -98693], [1721, 32691], [1723, 22207], [1733, -43219], [1741, -103999], [1747, -40397], [1753, 36623], [1759, -4644], [1777, -13302], [1783, -139672], [1787, 128594], [1789, 54484], [1801, -128651], [1811, 81801], [1823, -2022], [1831, -10329], [1847, 104444], [1861, 10775], [1867, -21969], [1871, 55191], [1873, -57063], [1877, 133982], [1879, 129715], [1889, 55151], [1901, 109657], [1907, 84579], [1913, -26989], [1931, -29075], [1933, -5565], [1949, -41269], [1951, -61911], [1973, -64460], [1979, -25896], [1987, -32928], [1993, 44415], [1997, 24049], [1999, 321], [2003, 26190], [2011, -9179], [2017, -183910], [2027, -37998], [2029, -140587], [2039, -96603], [2053, -5748], [2063, 41757], [2069, 191767], [2081, 12735], [2083, 70717], [2087, 7743], [2089, -23571], [2099, 143772], [2111, -4415], [2113, 24801], [2129, -40986], [2131, -57679], [2137, 91012], [2141, -69734], [2143, 66752], [2153, -70600], [2161, 39474], [2179, -225828], [2203, -11009], [2207, 41517], [2213, 35327], [2221, -132399], [2237, 36970], [2239, -85987], [2243, 9287], [2251, 200948], [2267, 59674], [2269, -138269], [2273, 77456], [2281, 306824], [2287, 74275], [2293, 49235], [2297, -151994], [2309, -179141], [2311, 67994], [2333, 20604], [2339, 59378], [2341, 42480], [2347, 113192], [2351, 204068], [2357, 133893], [2371, -63891], [2377, 29805], [2381, -19300], [2383, -153944], [2389, 32668], [2393, 75581], [2399, 2847], [2411, 26395], [2417, 53137], [2423, 121664], [2437, 9229], [2441, 206404], [2447, -60146], [2459, 53870], [2467, -153720], [2473, -18093], [2477, 22144], [2503, 176231], [2521, -59004], [2531, -53758], [2539, -180100], [2543, 53611], [2549, -118011], [2551, -57762], [2557, -163239], [2579, 146498], [2591, -139869], [2593, -49503], [2609, -49815], [2617, 85348], [2621, 4362], [2633, -8160], [2647, -21852], [2657, 66121], [2659, -159508], [2663, -46755], [2671, 225540], [2677, -930], [2683, 227296], [2687, -77922], [2689, 20445], [2693, 11761], [2699, -66427], [2707, 165824], [2711, -288610], [2713, 30597], [2719, 149479], [2729, 25612], [2731, -205479], [2741, 55513], [2749, -60184], [2753, 46101], [2767, -255501], [2777, -156], [2789, 81745], [2791, 81975], [2797, -26429], [2801, 187593], [2803, -7785], [2819, 117112], [2833, 144390], [2837, -120318], [2843, -14978], [2851, -232370], [2857, 1578], [2861, -72978], [2879, 9449], [2887, 107896], [2897, 69275], [2903, 44628], [2909, -52717], [2917, 62700], [2927, 90747], [2939, 176516], [2953, 119705], [2957, 164570], [2963, -51631], [2969, 88715], [2971, 161758], [2999, 151368] ], [ [ 2, 7], [ 3, -9], [ 5, -9], [ 7, -42], [11, 36], [13, -57], [17, 176], [19, 32], [23, 76], [29, -66], [31,-2080], [37,-1482], [41,-2099], [43, 2524], [47,-1164], [53,-5610], [59,-1608], [67, 1208], [71, 568], [73, 762], [79, 7630], [83, 6844], [89, 2320], [97,-5789] ]];}