/************************************************************/
/* Authors : Gustavo Rama, Gonzalo Tornaría
 * Date    : April 2023
 *
 * Eigenvalues for the orthogonal modular form of level 69, 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_69a.gp
 *      ? L69=lfunparamodular(form_69a);
 *
 * check the functional equation:
 *
 *      ? lfuncheckfeq(L69)
 *      %4 = -130
 *
 * compute the central value
 *
 *      ? lfun(L69, 2)
 *      %5 = 0.13446662785124384499438516751506897157
 *
 * The format is
 *
 *      [level, class, dimension, root_numbers, ap_values, ap2_values]
 */


{form_69a=
[69, "a", 1, [[3, -1], [23, 1]],
[
  [  2,     -6], [  3,     -4], [  5,      8], [  7,    -12],
  [ 11,      2], [ 13,    -35], [ 17,     50], [ 19,     22],
  [ 23,   -155], [ 29,    -85], [ 31,    -63], [ 37,    152],
  [ 41,   -119], [ 43,   -332], [ 47,    369], [ 53,    500],
  [ 59,   -240], [ 61,     88], [ 67,    250], [ 71,    597],
  [ 73,   -389], [ 79,    234], [ 83,   -656], [ 89,   -342],
  [ 97,  -1342], [101,   -780], [103,    776], [107,   -526],
  [109,   1194], [113,  -1542], [127,   1087], [131,   1073],
  [137,    854], [139,   -685], [149,  -1028], [151,    849],
  [157,   2370], [163,    667], [167,   1876], [173,   1392],
  [179,   4011], [181,  -1368], [191,   -722], [193,   -593],
  [197,  -3805], [199,  -2370], [211,  -2776], [223,  -1008],
  [227,    720], [229,  -4102], [233,    681], [239,  -7007],
  [241,    592], [251,  -2080], [257,  -2859], [263,   2510],
  [269,   2743], [271,    696], [277,   4671], [281,    610],
  [283,  12562], [293,   1030], [307,  -6836], [311,   5297],
  [313,   2010], [317,   5404], [331,   5203], [337,  13026],
  [347, -14008], [349,   1875], [353, -11553], [359,  -2166],
  [367,   2472], [373,  -2412], [379,  -3192], [383,   -336],
  [389,  -7182], [397,   6993], [401,  -4224], [409,  -3093],
  [419,  10284], [421,   1298], [431,   2732], [433,   1036],
  [439,   5783], [443,    753], [449,   5912], [457, -26430],
  [461,  14643], [463,  24504], [467,   -346], [479,  -4980],
  [487,    399], [491,  -1161], [499,   6053], [503, -23942],
  [509,  11635], [521,    502], [523,   8580], [541,  -1697],
  [547,  -3681], [557,  -3294], [563,   -996], [569,   1288],
  [571,  -1208], [577, -10633], [587,     21], [593, -23332],
  [599,  10668], [601, -23425], [607, -12900], [613, -12958],
  [617,   7404], [619,  16056], [631,  19332], [641,   6838],
  [643,    566], [647,  -4963], [653,   2441], [659,  21376],
  [661,  15008], [673,  -9855], [677,   7324], [683, -10997],
  [691,  -1128], [701,  25902], [709,   3126], [719,  29892],
  [727, -43454], [733,   7434], [739,   -357], [743, -42380],
  [751, -14052], [757,  18724], [761,  -5061], [769,  19968],
  [773,  -4654], [787, -12852], [797,  31896], [809, -14000],
  [811, -18975], [821,   1756], [823, -14051], [827,  14888],
  [829,  17144], [839,   4740], [853, -41628], [857,  15661],
  [859, -12215], [863,    747], [877, -20076], [881,  22930],
  [883,  32888], [887,    493], [907, -29670], [911, -22122],
  [919,  18280], [929,  42417], [937,  27436], [941,  21490],
  [947, -21843], [953,  12920], [967,   7675], [971,  20426],
  [977,  33216], [983, -56554], [991, -28520], [997,  -29428]
],[
  [ 2,    5], [ 5,  -32], [ 7,  -40], [11, -148], [13,  170],
  [17, -140], [19, -112], [29, -450], [31,   32]
]];}