/************************************************************/
/* Authors : Gustavo Rama, Gonzalo Tornaría
 * Date    : April 2023
 *
 * Eigenvalues for the orthogonal modular form of level 82, 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_82a.gp
 *      ? L82=lfunparamodular(form_82a);
 *
 * check the functional equation:
 *
 *      ? lfuncheckfeq(L82)
 *      %4 = -131
 *
 * compute the central value
 *
 *      ? lfun(L82, 2)
 *      %5 = 0.16004670997376354345098108851381046473
 *
 * The format is
 *
 *      [level, class, dimension, root_numbers, ap_values, ap2_values]
 */


{form_82a=
[82, "a", 1, [[2, 1], [41, -1]],
[
  [  2,     -5], [  3,     -4], [  5,     -2], [  7,     10],
  [ 11,    -40], [ 13,     28], [ 17,     46], [ 19,    -96],
  [ 23,     52], [ 29,     34], [ 31,     36], [ 37,   -278],
  [ 41,    -73], [ 43,   -252], [ 47,    -38], [ 53,    598],
  [ 59,    108], [ 61,    200], [ 67,    168], [ 71,    546],
  [ 73,    732], [ 79,   -522], [ 83,      4], [ 89,   -738],
  [ 97,  -1554], [101,    252], [103,   1296], [107,  -1100],
  [109,   -786], [113,   -168], [127,   2756], [131,   1044],
  [137,   -928], [139,   1024], [149,   -268], [151,   -562],
  [157,    196], [163,  -1792], [167,    390], [173,   1588],
  [179,  -1612], [181,   -774], [191,  -1930], [193,   2490],
  [197,  -1484], [199,   -694], [211,   7508], [223,    364],
  [227,  -1404], [229,   2234], [233,   2202], [239,   2858],
  [241,  -5544], [251,   2968], [257,  -1956], [263,  -3026],
  [269,  -6128], [271,   2372], [277,   -738], [281,  -1686],
  [283,  -2432], [293,  -2810], [307,  -2780], [311,  -6698],
  [313,  10068], [317,    528], [331,  -1208], [337,  11060],
  [347,   2136], [349,   3894], [353,  10548], [359,   -972],
  [367,  -5192], [373,  -5672], [379,   2956], [383,   2934],
  [389,  -8988], [397,   4154], [401,   1056], [409,   7680],
  [419,   8240], [421,   5116], [431,   -632], [433, -23892],
  [439, -18482], [443,   8808], [449,   7024], [457,  -4152],
  [461, -17982], [463,   -190], [467, -12252], [479,  -5186],
  [487,   1608], [491,  -7496], [499,   5400], [503,  18942],
  [509,   2212], [521,  25668], [523,  -1348], [541, -29330],
  [547,  12436], [557,    632], [563,   9408], [569,   8892],
  [571, -21076], [577,  12500], [587,  13176], [593,  -5832],
  [599,   2660], [601,   1970], [607,  -3128], [613,  -5378],
  [617,   2544], [619,     96], [631, -10728], [641,   8022],
  [643,  10524], [647,  19044], [653, -11574], [659, -46788],
  [661,   4170], [673, -39414], [677,   5962], [683, -20036],
  [691,  16172], [701, -32438], [709,  18620], [719,  15650],
  [727,  27158], [733,  -7580], [739,   4828], [743, -23092],
  [751,   7914], [757,   5742], [761,  29084], [769,  -6244],
  [773,    -34], [787,   9060], [797,  43236], [809,  -1924],
  [811,  29424], [821,  10942], [823, -37702], [827,  23912],
  [829,  -4782], [839,    294], [853,  32240], [857,  17520],
  [859,    392], [863,  -3480], [877,  10220], [881,   2496],
  [883,   6524], [887,   4458], [907,   4192], [911,  -5368],
  [919, -11858], [929,    390], [937,    394], [941,   8656],
  [947,   2272], [953,  -1432], [967, -28422], [971, -24640],
  [977,  -1358], [983, -15756], [991,   -590], [997,  -7478]
],[
  [ 3,   -2], [ 5,  -60], [ 7,    4], [11,  -54], [13,  -44],
  [17, -288], [19,   74], [23, -132], [29, -696], [31, -148]
]];}