/************************************************************/
/* Authors : Gustavo Rama, Gonzalo Tornaría
 * Date    : April 2023
 *
 * Eigenvalues for the orthogonal modular form of level 85, 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_85a.gp
 *      ? L85=lfunparamodular(form_85a);
 *
 * check the functional equation:
 *
 *      ? lfuncheckfeq(L85)
 *      %4 = -132
 *
 * compute the central value
 *
 *      ? lfun(L85, 2)
 *      %5 = 0.17022010735381646873356858989739705656
 *
 * The format is
 *
 *      [level, class, dimension, root_numbers, ap_values, ap2_values]
 */


{form_85a=
[85, "a", 1, [[5, -1], [17, 1]],
[
  [  2,     -4], [  3,     -8], [  5,      9], [  7,      8],
  [ 11,    -10], [ 13,     34], [ 17,     29], [ 19,    -20],
  [ 23,    -40], [ 29,    -28], [ 31,   -102], [ 37,    332],
  [ 41,    134], [ 43,   -294], [ 47,    254], [ 53,   -144],
  [ 59,    204], [ 61,   -330], [ 67,   -402], [ 71,   -106],
  [ 73,   -378], [ 79,    242], [ 83,   1062], [ 89,   -228],
  [ 97,  -1072], [101,    704], [103,   1018], [107,     -8],
  [109,   -786], [113,   -146], [127,  -1730], [131,   2362],
  [137,  -1822], [139,   -270], [149,  -2200], [151,    816],
  [157,   3280], [163,   3096], [167,   -824], [173,   1976],
  [179,  -2348], [181,  -4804], [191,   1044], [193,   -478],
  [197,   -816], [199,   -366], [211,   7294], [223,  -3982],
  [227,  -4956], [229,   8036], [233,   -116], [239,   -912],
  [241,   3650], [251,   7852], [257,  -8670], [263,   3362],
  [269,   -714], [271,  -6340], [277,  -2466], [281,  -2772],
  [283,   -924], [293,  -7244], [307,   2638], [311, -12846],
  [313,   -642], [317,   6310], [331,   2464], [337,   3548],
  [347,   4816], [349,  -1836], [353,   5516], [359,    564],
  [367,    112], [373,   5378], [379,   4930], [383,  -1242],
  [389,   5624], [397,  -2894], [401,   2208], [409,   3152],
  [419,  -6514], [421,  -6648], [431,   2626], [433,  -4058],
  [439,  -4358], [443,  12798], [449,   4426], [457,   9002],
  [461,    932], [463,   -990], [467,   5130], [479,   -654],
  [487, -16364], [491,  -9480], [499,  -2346], [503,   2084],
  [509,  -8256], [521,  -2948], [523, -20662], [541,   5108],
  [547,  -1016], [557,  10086], [563,   7462], [569,  22436],
  [571,  23622], [577,  13662], [587, -14186], [593,  -3772],
  [599, -18800], [601,  -1730], [607, -23680], [613,   5044],
  [617,   5006], [619,  -5618], [631,  15928], [641,  -6202],
  [643, -21236], [647, -23914], [653,  16288], [659, -16576],
  [661, -16268], [673,  -1038], [677,  12642], [683,  -1540],
  [691,  24618], [701, -28088], [709,   8660], [719,   8966],
  [727,   9802], [733, -34456], [739,   2052], [743,   4116],
  [751,   1266], [757,   1534], [761, -18560], [769,  -8140],
  [773,  23406], [787,  27960], [797,  16844], [809, -23876],
  [811,  -2338], [821,  43250], [823,  42864], [827,  34096],
  [829,  16424], [839,  31906], [853,  15928], [857,  18990],
  [859,  -6556], [863,  -9090], [877, -16878], [881, -23866],
  [883,  22294], [887, -39652], [907,   -536], [911,    162],
  [919, -30496], [929,  -4242], [937,  42084], [941,  12188],
  [947, -33160], [953,  43558], [967,  41042], [971, -29456],
  [977, -34456], [983,  -2828], [991,  -8422], [997,  24380]
],[
  [ 2,   -1], [ 3,    6], [ 7,  -50], [11, -180], [13, -136],
  [19, -308], [23, -550], [29,  108], [31, -820]
]];}