/************************************************************/
/* Authors : Gustavo Rama, Gonzalo Tornaria
* Date : June 2020
*
* 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 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).
*
* 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]
],[
[ 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]
]];}