/************************************************************/
/* Authors : Gustavo Rama, Gonzalo Tornaria
 * Date    : March 2023
 *
 * Eigenvalues for the orthogonal modular form of level 79, 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_89a.gp
 *      ? L89=lfunparamodular(form_89a);
 *
 * check the functional equation:
 *
 *      ? lfuncheckfeq(L89)
 *      %4 = -132
 *
 * compute the central value
 *
 *      ? lfun(L89, 2)
 *      %5 = 0.17697433808159553250320665695808915202
 *
 * The format is
 *
 *      [level, class, dimension, root_numbers, ap_values, ap2_values]
 */


{form_89a=
[89, "a", 1, [[89, -1]],
[
  [  2,     -4], [  3,     -6], [  5,     16], [  7,    -17],
  [ 11,     -2], [ 13,    -46], [ 17,     66], [ 19,     42],
  [ 23,     49], [ 29,    -64], [ 31,    218], [ 37,     -6],
  [ 41,     91], [ 43,    -16], [ 47,   -307], [ 53,    -10],
  [ 59,   -260], [ 61,    196], [ 67,    368], [ 71,   1221],
  [ 73,   -282], [ 79,   -558], [ 83,    220], [ 89,   -166],
  [ 97,   -312], [101,    856], [103,    525], [107,    838],
  [109,  -1132], [113,   -849], [127,    371], [131,   -410],
  [137,    514], [139,  -1874], [149,  -3332], [151,  -3236],
  [157,    766], [163,   -456], [167,      4], [173,   3144],
  [179,   6386], [181,  -2432], [191,  -2167], [193,   6256],
  [197,   1494], [199,   1560], [211,  -1240], [223,    -95],
  [227,  -1416], [229,    838], [233,  -1584], [239,   2895],
  [241,   1538], [251,   2770], [257,   3650], [263,  -2364],
  [269,    854], [271,    704], [277,   2030], [281,  -5129],
  [283,  -8300], [293,  -3420], [307,  -3490], [311,   5766],
  [313,   -951], [317,  -5770], [331,   2190], [337,   2133],
  [347,  -1888], [349,    264], [353,   6125], [359,    297],
  [367,   1006], [373,   9670], [379,  -2748], [383,    505],
  [389,   2760], [397,  -8094], [401,   3729], [409, -13890],
  [419,  -6106], [421,  -1418], [431,   -915], [433,  13845],
  [439,   4305], [443,   3476], [449,   2442], [457,   7648],
  [461, -14420], [463,   3555], [467,  -5584], [479, -16212],
  [487,  -3846], [491, -20232], [499,   3334], [503,  -3403],
  [509,  11100], [521,  14525], [523, -19740], [541,   9496],
  [547,  25146], [557,   8352], [563,  -2546], [569,  -1589],
  [571, -19340], [577,  19796], [587,  10072], [593,  16625],
  [599,  15755], [601,  -5838], [607,  12384], [613, -20932],
  [617, -12763], [619,   7568], [631, -13874], [641,  -3616],
  [643,  12126], [647,  23528], [653,   3056], [659,   3636],
  [661,  16872], [673,  17185], [677, -23300], [683,   6836],
  [691,  12062], [701, -46592], [709,  -4678], [719,   -605],
  [727,   2045], [733,  13140], [739, -12600], [743,  15812],
  [751,  12590], [757, -19960], [761, -31620], [769,   9756],
  [773,   4770], [787,  27508], [797, -16476], [809, -20604],
  [811,  10632], [821,   7006], [823,   1358], [827, -36200],
  [829, -11512], [839,   2873], [853, -21450], [857,   3945],
  [859,  45254], [863,   9232], [877, -13596], [881,  58658],
  [883, -36084], [887,  40274], [907, -32768], [911, -12895],
  [919,  40652], [929,  20081], [937,  -7613], [941,  28062],
  [947,  17874], [953,  41919], [967, -18341], [971, -20020],
  [977,   4950], [983, -28476], [991,  28737], [997,  -8954]
],[
  [ 2,    2], [ 3,  -6], [ 5,   27], [ 7,  -14], [11, -183],
  [13,  -66], [17,  57], [19,  -20], [23, -466], [29, -210],
  [31,  552]
]];}