/************************************************************/
/* Authors : Gustavo Rama, Gonzalo Tornaria
 * Date    : June 2020
 *
 * Eigenvalues for the orthogonal modular form of level 167, sign -1
 *
 * 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_167a.gp
 *      ? L167=lfunparamodular(form_167a);
 *
 * check the functional equation:
 *
 *      ? lfuncheckfeq(L167)
 *        *** lfuncheckfeq: Warning: #an = 557 < 854, results may be imprecise.
 *      %4 = -97
 *
 * compute the central value
 *
 *      ? lfun(L167, 2)
 *        *** lfun: Warning: #an = 557 < 721, results may be imprecise.
 *      %5 = 0.E-58
 *
 * compute the central derivative
 *
 *      ? lfun(L167, 2, 1)
 *        *** lfun: Warning: #an = 557 < 721, results may be imprecise.
 *      %6 = 0.11591529514599857918162186746901795845
 *
 * The format is
 *
 *      [level, class, dimension, root_numbers, ap_values, ap2_values]
 */

{form_167a=
[167, "a", 1, [[167, 1]], 
[
  [  2,     -8], [  3,    -10], [  5,     -4], [  7,    -14],
  [ 11,    -22], [ 13,     -4], [ 17,    -47], [ 19,    -12],
  [ 23,     41], [ 29,     50], [ 31,   -504], [ 37,   -102],
  [ 41,    174], [ 43,     30], [ 47,     42], [ 53,    156],
  [ 59,   -252], [ 61,    472], [ 67,    106], [ 71,   -481],
  [ 73,   -744], [ 79,    927], [ 83,   -632], [ 89,   -297],
  [ 97,      2], [101,   -992], [103,  -1222], [107,   1436],
  [109,   -954], [113,     19], [127,    516], [131,   -258],
  [137,   1080], [139,   1030], [149,   -974], [151,  -1119],
  [157,   1152], [163,    108], [167,  -2707], [173,   -182],
  [179,   2568], [181,  -2804], [191,  -3035], [193,    583],
  [197,   2276], [199,   6754], [211,    360], [223,   3569],
  [227,  -3346], [229,   2220], [233,  -2780], [239,  -3878],
  [241,   -819], [251,   6112], [257,  -5343], [263,   -808],
  [269,   3592], [271,   2954], [277,  -8334], [281,  -2942],
  [283,   6360], [293,   -856], [307,   3548], [311,  -6322],
  [313,  -9443], [317,    108], [331,   1596], [337,  -2129],
  [347,   1856], [349,    480], [353,   1704], [359,   4601],
  [367,   6298], [373,  -4998], [379,   7706], [383, -18293],
  [389,   5316], [397,   4324], [401,  -4679], [409,  -3476],
  [419,   -910], [421,   3552], [431,  -4878], [433,  15213],
  [439,  -6909], [443,  -7130], [449,  12908], [457,  -4005],
  [461,  -7334], [463,    -77], [467,  12248], [479,   6447],
  [487, -14197], [491,   1960], [499,   3288], [503,   1619],
  [509,  28510], [521,  -4650], [523, -21400], [541,    686],
  [547,  -4212], [557,  19530]
],[
  [  2,     10], [  3,     11], [  5,    -44], [  7,     -9],
  [ 11,    -67], [ 13,   -158], [ 17,    260], [ 19,     41],
  [ 23,   -198], [ 29,   -187], [ 31,   2744], [ 37,   -730],
  [ 41,    800], [ 43,    442], [ 47,  -5052]
]];}