# Stored data for newform 1573.4.a.a, downloaded from the LMFDB on 23 April 2024. {"label": "1573.4.a.a", "space_label": "1573.4.a", "level": 1573, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 67110437, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 2012405640596685218, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-5, 1]]], "qexp_display": "q+5q^{2}-7q^{3}+17q^{4}-7q^{5}-35q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 25168, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 92.81000443902998, "hecke_ring_index": 1, "level_radical": 143, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [1573, 1, [365, 1211], [1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [11, 13], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.981", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.964", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.938", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[11, -1], [13, 1]], "trace_display": [5, -7, -7, 13], "traces": [0, 1, 5, -7, 17, -7, -35, 13, 45, 22, -35, 0, -119, -13, 65, 49, 89, -77, 110, 126, -119, -91, 0, -96, -315, -76, -65, 35, 221, 82, 245, 196, 85, 0, -385, -91, 374, -131, 630, 91, -315, -336, -455, 201, 0, -154, -480, -105, -623, -174, -380, 539, -221, -432, 175, 0, 585, -882, 410, -294, 833, 56, 980, 286, -287, 91, 0, 478, -1309, 672, -455, 9, 990, -98, -655, 532, 2142, 0, 455, -1304, -623, -839, -1680, 308, -1547, 539, 1005, -574, 0, -1190, -770, -169, -1632, -1372, -525, -882, -595, 70, -870, 0, -1292, -420, 2695, 588, -585, 637, -2160, 684, 595, -373, 0, 917, 1157, -1734, -4410, 672, 1394, -286, -1470, -1001, 2205, 0, 280, 2352, 3332, 1407, 1430, -1892, -2115, -1407, 455, -1435, 0, 1638, 2390, -245, -3465, -1776, 3360, 1869, -1547, 735, 45, 0, 1958, -574, -490, 1218, -2227, -2466, 2660, 3323, 5670, -1694, 0, -1372, 1547, -2730, -6520, 3024, -595, -1248, -4195, -544, -5712, 0, 1540, -1624, -4095, 169, 2695, 2772, 3417, 336, -2870, -988, 0, 2058, -5950, -3029, -2618, -28, -845, -392, -4320, 917, -6860, 0, -1785, 455, -4410, 422, 2009, -492, 350, -637, -2958, -2991, 0, -70, -3420, -3346, -2100, 1066, 9163, 2352, 2940, -2112, -1157, 0, 3185, -2851, -7344, -63, 3420, -1407, 1575, 2548, -1865, 686, 0, 1001, 4585, 217, 1105, -1672, -8670, 2576, -14994, 455, 3360, 0, 3690, -3061, -1430, 735, -4998, 9128, -5005, 3477, 4361, 1610, 0, 4928, 952, 1218, 11760, -1638, 8820, -2156, 7035, 1008, 4862, 0, -9460, -3773, -8279, 6041, -7035, -1703, 1547, 1804, -7175, 3708, 0, 3024, 8190, 8330, 8126, 8344, -1225, 1617, -6853, 1183, -8880, 0, 11424, 3820, 9345, 4312, -4095, 6214, 3675, 5292, 153, 6174, 0, -4368, 1870, 1016, -2870, -490, -1666, 903, 6090, 2058, -5895, 0, -12330, 1248, 9044, 2613, 16615, 2940, 11214, -392, -8470, -2114, 0, -4116, -6860, 3402, 4095, -10689, -13650, -2002, -22168, -7054, 15120, 0, 2009, -4788, -6240, -9702, -14263, 988, -2720, 2611, -15120, -1365, 0, 9704, 5236, -2882, -8120, -3346, -8099, 10449, 845, 12138, 9163, 0, 13860, -6721, 9045, -4704, 1680, 621, -9758, -12481, -4940, -455, 0, -1400, 10290, -63, -20230, 7007, -15145, 4968, -6930, 9017, -140, 0, -2873, 686, -1960, 8722, -8544, -7392, 4585, -5616, -23324, -10012, 0, -9849, -4725, -1066, 2275, -3372, -14994, 13244, 2110, -847, 14805, 0, -2460, 4422, 1190, 11314, -3185, 7392, -7830, 10045, -14955, 9128, 0, 1862, -350, -11466, -6764, 6820, -16730, -2548, -7140, 5873, 5330, 0, 24255, 12992, 11760, 12432, 9996, -3822, -10560, -2156, -1105, -13083, 0, -7343, 10829, -5059, -14255, -2310, -19440, 5852, -315, 728, 11628, 0, -7035, -3243, 3115, 11599, 12740, 4018, -6341, -12096, 3430, 17374, 0, -3828, 5005, 989, 15589, 8330, 1085, 17262, -3731, -14474, -8360, 0, -29478, -23261, 12880, 1183, -39690, 1594, 2275, -2695, 11424, 5915, 0, -11072, 7298, 9604, -15305, 1260, -4862, 6214, 3675, 19110, -13230, 0, 45640, -9576, -17017, -9504, 17385, 12033, 4165, 1703, 8050, 8736, 0, -490, 24640, -2280, 2520, 3808, 6090, -16767, 39984, -6314, -8190, 0, 17444, 117, -10780, 12840, 23919, 11368, 5040, 2198, 12870, 2940, 0, -1183, -32164, -17066, -18865, -1274, -24475, 4410, 30205, -4116, -23919, 0, -8515, -2352, 4095, 2583, 9020, -18620, -24395, 6916, 18540, -15092, 0, -2951, 15120, -6468, 27846, 4368, 41650, -4788, 21510, 21203, 41720, 0, -4165, 16833, 8085, 196, -6545, 2611, 5915, 8615, -30192, 1232, 0, 10332, 30240, -16952, 19100, -6419, 31773, -8535, 21560, -2613, -8099, 0, 31070, 4641, 12495, 12138, 26460, -10907, 405, 4793, 30870, 5563, 0, -2954, -21840, 7296, -6314, 24038, 5080, 3444, -9758, 4004, -2450, 0, -4410, 2002, 4515, -21224, 20706, 24696, 10290, 20937, -11659, -4354, 0, 7007, -41922, 490, 6240, 7310, 23940, 7595, 13065, 10516, 56491, 0, 14700, 826, 10710, -7462, -1960, 1365, -28798, -14590, -10570, -16464, 0, 4888, -20580, -11004, -23324, -3360, 17010, -15470, 8099, -349, -53445, 0, -46410, 10087, -10010, -4975, -58680, 19957, -35270, 13244, 51408, 2262, 0, 198, 14805, 3950, -23940, -3682, -21216, 9849, -48510, 10402, -37755, 0, 4940, -17836, -9248, -31680, 13055, 10045, -29904, -2156, -6825, -21940, 0, -31374, 48520, -7007, 13860, -11466, -14410, -7872, -27608, -1519, -16730, 0, -7735, -18013, 52245, -2660, 2873, 10640, 60690, 910, 24255, -18032, 0, -9336, 47124, 12432, -33605, -3185, 17889, 5616, -23520, 4200, 5712, 0, 3105, -13083, -25830, 25872, -62405, 21427, -16796, -9872, -2275, -16506, 0, -5145, -7000, -5460, 34986, 28450, -315, -28688, -53550, -18816, 35035, 0, -51493, -24339, 24840, 32718, -13706, 7644, 45085, -11270, -476, -6232, 0, -22834, -7605, -11843, 3430, -15477, -6664, -7875, 43610, -8526, -8160, 0, -36960, 2140, 15589, 11466, -28080, -31971, -61740, 17262, -50060, 6776, 0, 8892, -49245, -7432, -9345, -7056, -5330, -23261, 7735, 20176, -16860, 0, -39690, 9478, 66220, -4849, 7174, 11858, -4235, 3822, 57953, 12096, 0, -42287, -8364, 17941, 22110, -14896, 3150, 11921, 56570, -42336, -10829, 0, 36960, 2870, -15486, 19110, 50225, -6664, -50847, -25956, 45640, -22542, 0, -728, 9310, -21168, -1190, -1442, -57330, 8085, -6460, -26180, 34100, 0, -56882, 8736, -12740, -58408, -18900, -30207, 29365, -21140, 18122, -11319, 0, 3808, 47971, 25326, 64960, -3718, 39984, -569, 62160, -8538, 26460, 0, -19110, 32702, -35904, -21154, -10780, -26740, 3731, 13398, -65415, 11368, 0, 6860, -36715, -2184, 28665, -17665, -25295, -43498, -48467, -1183, -11550, 0, -38448, -37044, 29260, 12576, -1071, -36687, 3640, -19404, 30780, -36806, 0, 4900, -23919, 30576, -16215, -13697, 2975, -2352, 57995, -7112, 43316, 0, 20090, -6214, -16785, 1540, -60480, 18291, 11662, -6239, 86870, -6321, 0, 133, -19140, -26003, 17017, -14406, 4945, 31248, 41265, -24596, 41650, 0, 3689, -13230, 86310, 21203, -27495, -8736, -72370, 16072, -28424, 33264, 0, -18291, -78030, 196, -116305, -38253, 43792, -9240, 5915, 36374, -78498, 0, 7970, 2744, 7735, -18655, -13475, 27648, 30240, 14798, 29575, -117, 0, 9956, -55360, 12936, 6970, 756, 48020, -21924, -52037, -23814, 6300, 0, -12870, -20846, 31070, 74823, 12495, 41321, 95550, 32256, -26166, -3185, 0, 54966, 155176, 1274, -47880, 49378, -45045, 44553, -47520, -2954, 59109, 0, 60165, -23088, -14063, 8625, 8515, 15048, 27370, 3444, 43680, 27907, 0, 67914, -2450, -16443, 83776, 24297, -11400, -6916, 4984, -45414, 19040, 0, 20706, -8206, -83835, -8981, 105840, 20937, -31570, 9555, -27846, -19296, 0, -17414, 16660, -67928, 585, 490, -36652, 23702, 64200, -4585, 63315, 0, 56840, 22638, 17136, 23422, 10990, -54432, 25454, -39846, 14700, -73143, 0, -5922, -5915, -7462, -85140, -38148, -85330, -7086, -64141, -23429, -6370, 0, -56143, 25536, 22050, 16952, 102697, 47047, -20580, 26920, -63315, -10152, 0, 14784, -28951, -4312, -11760, 56070, 8099, -4347, 12915, -32058, 30668, 0, -93100, 87367, -64575, 4095, 34580, 38820, 63036, 10907, -75460, 19957, 0, 43199, -14755, 9800, 51408, -14670, -32340, -26404, 73710, 441, 21840, 0, 141610, -504, -23940, -22022, 42542, -10742, 106015, -15276, 141848, -34776, 0, -4004, -11025, 10080, 84165, -63119, 27489, -17836, 980, -34480, 22099, 0, 13055, 30156, 20111, 29234, 43075, -4802, -79920, -52542, 6160, -35490, 0, -61054, 51660, -15916, 59808, -7007, -84760, -11760, 64940, -24738, -32095, 0, 84105, 39312, -42675, -1519, 73304, 2882, -13065, 70084, -7735, -37044, 0, 57974, 105638, 30954, 23205, 16704, 33075, -42380, 60690, 7462, 89964, 0, -54535, -18032, 801, 23604, 23965, -36806, 104958, -7072, 27815, -41624, 0, -3185, -14770, -25676, -74256, 5929, 36480, -30240, -46530, 38773, 120190, 0, 17272, 15470, 17220, 7056, -25830, 7035, 20020, -15892, -8330, 21427, 0, -79198, -8722, -21112, 10010, -8951, 15351, -51744, -106120, 7980, 54810, 0, 123480, -31570, 34986, -20902, 104685, 2197, -11135, -63896, -21770, 14691, 0, -27552, 35035, -13034, -110970, 11802, 2450, -24339, 21216, 36036, 36550, 0, 47348, 58280, 37975, -47740, 44421, -11270, 52580, -693, 149535, 17836, 0, 4368, 49980, 65116, 4130, -34496, -36162, 65296, -37310, 41472, -6664, 0, 6825, 81774, -76230, 13224, -72950, -90944, -35938, -38313, -82320, -2072, 0, -39072, 24440, 11466, -69972, -59969, -55020, 26754, -61740, 7546, -16800, 0, 57834, 15092, -77350, 16482, 7735, -24857, -1745, 41118, -181713, -39377, 0, -7056, -122850, 51401, 50435, -19656, -34034, -910, -24875, 35413, -116056, 0, 99785, -364, -119918, -3675, 66220, -65856, 136080, 60228, 11310, -40964, 0, -28126, 990, -61019, 57953, -5096, 19750, 63068, -81396, -42287, -18410, 0, -56160, -7226, 49245, -52367, -164934, 22701, 52010, 11921, -74671, 66106, 0, -81193, 16796, 14910, -89180, -69424, -24480, -12628, -158400, 18046, 44387, 0, 50225, 84672, -28560, 5460, -10780, -25956, -23205, -121618, -109700, 42203, 0, 52724, -156870, -6090, 164968, 32832, -35035, 964, 27412, -6923, -57330, 0, -48994, 39396, -39360, -58310, -73080, 5486, -7595, -7644, -56882, -54252, 0, 100408, 26117, -58408, -90065, 101318, 177633, 1134, -13300, -6396, 7605, 0, 53200, -11319, 206346, 28224, 4550, 73106, 47971, -81725, -90160, -8610, 0, -8281, -46680, 78276, 124740, -33492, 62160, -11158, -114257, 59439, -15925, 0, 17085, 64603, 28080, -38883, -79968, 16420, 21000, -41405, 15120, -26740, 0, -12348, 10557, 77504, -65415, -8892, -51086, -910, 129360, -30184, -212177, 0, 107135, -41965, -44460, -8820, -49360, -5376, -7735, -43498, -82530, -43498, 0, -46100, -25725, -23716, -23800, -60060, -27300, -37044, 92610, 4849, 142250, 0, -1071, -14268, -143440, -20459, -105910, 67032, -94080, 21735, 119119, 6326, 0, -15120, -136305, 52479, -121695, 30576, 84456, -84231, 163590, -10876, -13090, 0, 38220, -11921, 153289, -7112, -56350, -76342, -1260, -27456, -31160, 106258, 0, 58494, -114170, 3430, -15041, -20580, -59215, 67228, 11662, 15960, -77385, 0, -17640, -6321, -39375, -11968, 148274, 22542, -42630, -71192, 27552, 117369, 0, 22344, -125664, -37063, 10700, 44198, 41265, -79851, 57330, 17773, -95472, 0, -159855, 693, -122108, -11830, 86310, -819, -170204, 53933, 33880, -8736, 0, -89880, 44460, 33896, -167433, -164304, -37160, -35728, -8925, -18291, -35280, 0, -18122, -15386, -116305, 68950, 20475, 91630, 100880, -20580, -57324, 44016, 0, -34104, -78498, 3718, 47390, -97298, 225148, -4256, -24245, 119462, 18990, 0, 59290, -32431, -14399, 8918, 19110, 14798, 171325, -35424, 60480, -105714, 0, -45888, -211435, -21616, -22140, 28812, 89705, 13013, 75174, -27585, -74480, 0, 6230, -87318, 59605, -23814, 192338, 7392, -211680, -35532, -28665, 2821, 0, -18081, 125664, 74823, 14350, 58345, -14790, 130340, 95550, 102732, 170765, 0, -33320, -21736, -134595, 38808, -129780, -38810, 155176, 105644, -112710, 18870, 0, 49378, -3640, 20657, 31654, 33488, -105840, -26331, -3150, -10290, -7210, 0, -194922, 61507, 40425, -30576, 21812, -17402, -130900, 5915, 115940, 33516, 0, -115407, -150570, 61495, 43680, -66638, -43316, 107856, -292040, 67914, -37380, 0, -151035, 84782, 99841, 48848, -105700, -117831, 47970, -18291, -56595, 66094, 0, -616, 19040, -39793, 45815, -864, 126630, -18277, 220864, -82404, -18590, 0, 105840, -60305, -2845, -84672, 211344, 9555, -42690, 1960, 52332, -5390, 0, 24596, -64974, -72324, 163510, -67928, -95040, -10990, -105770, 118664, -36652, 0, -133700, -5868, 27495, 20174, 66990, 96773, -222411, -15659, 56840, 59745, 0, 45201, 34300, -36328, -124831, 18291, -10920, 9408, 56693, 43975, -88325, 0, -86003, -73143, -217490, 20930, -128295, -32487, -5915, -149940, -39270, -490, 0, -84966, -36720, 27720, -185220, 22099, 99484, 64064, 62880, 18655, -2835, 0, -183435, -33551, 12376, 119765, -97020, -24108, 60876, -38941, -184030, 47047, 0, 32340, 24500, 9284, -63315, -73752, 152880, -118316, -55131, -51072, -68485, 0, -10045, -21294, -11760, -168266, 197183, -64780, -35560, -4347, 114660, -10824, 0, 13755, 68306, 104468, -31070, -28028, -33197, 87367, 7700, -118158, -205632, 0, 91455, -45276, 30870, 52906, -31195, 3185, 295358, 13104, -31605, -33392, 0, 148568, 665, -67536, -65076, 9800, -130015, -172872, 45045, 4592, -72030, 0, 16813, -65802, 156240, -684, 81613, 40530, -122980, 30478, 141610, 23088, 0, 121240, 9765, -49049, -66150, -70838, 293454, -22150, 106015, -1540, -107627, 0, -43680, -34776, -246058, -51170, 80360, 78533, -75240, -40420, 166320, -53165, 0, -63119, -91455, -24297, -154326, 16730, 980, 124047, -395437, 22794, -191265, 0, 115920, 125184, -46200, -52668, 20111, -5782, 181870, -74004, -74970, 7448, 0, 23452, 27098, -57624, 13720, 20897, 20475, -9555, -93275, -61054, -45815, 0, 138240, 102130, 59808, 48204, 73990, 8820, 100555, 51744, -585, 24962, 0, -39106, 49780, -34216, -188224, 28721, 64680, 39312, -23534, 77028, 3780, 0, 163268, -116354, -109620, 80544, -137745, 70084, -119070, -17696, 21420, 108290, 0, -70838, -25454, -54647, -104230, 2443, 105638, -44739, 374115, -154021, 33075, 0, 206605, 108472, 324870, 7462, 161280, -70609, -24990, 96502, -15925, 10976, 0, 34825, 274830, 23604, 410760, 21021, 6370, -62722, -162792, 115572, 246890, 0, -89089, -92708, 222765, -12369, -161568, -29568, -14770, -15834, 156465, -73824, 0, 5929, 204561, 315, -115440, -52920, -103635, 133518, 43125, -27650, 28951, 0, 75240, 35280, 72450, 25774, 17220, -114198, 148512, -17026, 139535, -30954, 0, 32058, 339570, 49660, -8330, -72814, -82215, 39196, 221760, -79198, 121485, 0, -38760, -53788, -34580, -8358, 4760, 56056, -227070, -51744, 64736, 74088, 0, 221760, 54810, 56592, -41030, -43199, -285039, -70315, -44905, 80782, 209328, 0, 104685, -3430, -107338, -11900, 47775, 99104, -73710, 153580, -96480, -67193, 0, 68796, -87070, 219618, -56252, -13034, -339640, -79646, 1989, 22022, 2450, 0, -97020, 87409, 118510, 80262, 218280, -92941, -22925, 127538, 125223, 55104, 0, 52628, 193256, -47740, 113190, 4774, 45360, 58464, 117110, 2081, 37366, 0, -272160, 17836, 24310, -72924, -199230, 126091, 49980, -21105, -365715, 13208, 0, 63764, -29610, -179905, -20111, 4900, -37310, -74480, -168388, 86184, -190740, 0, -290122, -6370, -35430, 66852, -169785, 35490, -117145, 56672, -21658, -90944, 0, 114240, -84915, 65352, 127680, 11739, 74970, -70716, 84760, -87024, 271845, 0, 235235, 738, -69972, 10010, 134600, -125636, -125223, 26754, -50760, -39312, 0, 58011, 73920, -46998, -76635, -29400, -21560, -23408, -39984, 93688, 280350, 0, 7735, 178673, -21735, 43948, 43911, 91581, -160290, 92587, 81180, -121709, 0, -181104, -316540, 16224, 436835, 51401, -127715, -67342, 20475, -12726, 117572, 0, 194100, 69104, 166860, 35413, 54535, -34974, -256564, 115542, 99785, 46520, 0, -16688, 215995, 16170, -50167, -8036, 49000, 7072, 136080, 38220, -73350, 0, -109956, -108339, -132020, -199150, 145782, 134706, 2205, -25004, 74256, -45640, 0, -5096, 374850, -9056, -2520, 131712, -81396, 145572, -110110, -146823, 40630, 0, -53710, -218484, 360451, -27482, -76380, 76494, 375480, -127248, -173880, 22701, 0, -229026, -20020, 145684, -21805, -24150, 50400, -53508, 286161, -81193, -315595, 0, 72765, 35420, -89180, 21112, 3332, 145152, -172400, 43624, 162855, 44226, 0, 18566, 44387, 159838, 150780, 38514, 53235, 84672, 146170, -50155, 146455, 0, -24010, -138957, -158064, 108339, -262710, -121618, 20944, -2197, -177450, 55125, 0, 1764, -305270, -78680, 175644, 26796, -79580, -19756, 57120, -92798, -35035, 0, -288184, -29472, -58800, -6923, 171900, -14980, -123690, -91702, -109123, -23942, 0, -36036, 166341, 90440, 196560, 110495, -145095, 223797, -7595, -6720, 194040, 0, 14410, -120834, -44421, 9648, 350420, -119392, 26117, 10780, -185220, -98420, 0, 101318, 289870, -62244, 279630, -4368, 154770, 188480, 78897, 52024, 83520, 0, 65415, -7336, -211900, 22176, 206346, -126126, 37310, -19208, 238140, 162827, 0, -164024, -185419, -138458, -90160, -141232, 765, 89068, 118020, 12844, 81481, 0, -184030, -86832, 277830, -9100, -35360, -66346, 94571, -11158, -208120, -166642, 0, 33943, -15925, -106928, -50218, -74079, -128380, 18865, -196560, -55277, 29645, 0, 124032, -26754, -151200, 18270, -182138, -41405, 193865, -84672, 408646, 54103, 0, -52414, 45720, 132902, 77350, 77504, 58548, 126152, 35280, -125587, -51086, 0, 35175, 40320, 68068, 104272, -79460, 39377, -22050, 136752, 107135, -37466, 0, 23963, -395990, -8820, -8330, 296352, -105560, -151419, 34034, 238, -44755, 0, 40635, -43498, -258720, 116524, -360808, -68798, 39900, 112987, 108402, 364, 0, -133770, 419832, -213038, -157850, 135837, 92610, 46648, -104510, -143913, 355929, 0, 10985, 81576, 37597, -56448, -319480, -215082, -74018, 157794, 73455, 177282, 0, 190038, -137760, 5096, 119119, 47049, -65170, 117040, -219474, 66528, 59010, 0, 8330, -89630, -121695, 10094, 56160, -159866, 180180, -84231, 124270, -56595, 0, -82159, 45220, -27691, 291400, -41650, 129115, -11921, -238700, 25256, 117585, 0, -56350, -27342, 178772, -238392, -3465, -61152, 295747, 1125, 89180, 98784, 0, 183568, 21840, -76739, 132300, -5320, 325580, 211449, 14042, 8073, -172480, 0, -266490, 147980, 326480, 15960, -126854, -146274, 207360, 35574, -17640, -37086, 0, -162253, 23205, -26656, 408870, 103686, -150766, -255584, 66120, -177282, -248030, 0, -454720, 117369, -95130, -5915, -191565, 13872, -279888, -65664, -10360, 3983, 0, 44198, -195360, 165844, 83096, 59766, 57330, -18200, -185220, 213817, -299845, 0, -187068, -214851, 133770, -62618, -122108, -228914, 37730, -5486, -57120, -819, 0, 148078, 153090, -180810, 75460, 45360, -262990, 84040, 82410, -89880, -26117, 0, -124285, -93786, -5933, -18816, 205590, 169496, -481005, -79576, -196885, 35808, 0, 6396, -35280, -164444, -242970, 64584, 257005, -15386, 171479, 15288, -98280, 0, -90090, 172527, -4550, 123655, -84575, 31920, 177065, 117221, -110840, 136708, 0, 78969, 339269, 189882, -1820, 8281, -317430, -59094, -18375, -2583, 225148, 0, -329280, -55267, 269136, 119462, 301140, 116424, 38454, 210810, -204820, 62832, 0, -88032, -140630, 8918, 3366, -245334, -305095, 256809, 171325, 38883, -25480, 0, 67150, -30870, 315340, -255871, -215460, 113386, -211435, 257642, -62594, 60368, 0, -44688, -111072, -34300, -36130, 200970, 167433, -97580, -261835, -96096, -436590, 0, 113505, 910, 176834, 95879, 59605, -142578, -71315, 90776, 330530, 16464, 0, 75168, -405965, 166464, 44460, 22352, 74550, -223776, -303212, -18081, -347120, 0, -48416, 219422, -63140, -130156, -538560, 43498, 90230, 130340, 117495, 79674, 0, 2450, 170765, -72282, 423360, 11256, 96432, -128037, 27300, -1179, -36652, 0, -129780, 43673, -61425, -237522, -608090, 105644, -372980, 19866, 211015, -13858, 0, 235494, 263620, -931, -533358, 20657, -30450, -146708, 436680, 182021, 164160, 0, -119119, -43836, 4820, 45276, 26180, 45750, -34615, 53564, -194922, -218736, 0, 141463, -129690, -30576, 196980, 172172, -133824, 210210, -291550, 151335, -144536, 0, 27430, -51984, -25823, -40908, -38220, 92610, -150570, -11011, -271260, 17386, 0, -148421, 502040, 124544, 192465, 99542, -292040, 27456, -306221, -156541, 506590, 0, 470205, -112504, 5670, 196898, -45220, 12838, -31980, -232848, 15041, -117831, 0, 138803, 180880, 57486, -56595, 247235, 546210, 53303, 141120, -1372, 15470, 0, 365530, 69559, 45815, 267771, -408625, 147082, -306544, 28348, -43050, -14700, 0, -137403, -41405, -102884, -158712, -254618, 391380, -60305, 246708, 96096, -167460, 0, 211344, -28149, -55790, 37063, -302445, -8624, 297195, -160608, -54145, 134155, 0, 130585, -57687, -52134, 323015, -72324, 95472, -193536, -194415, -233240, -211680, 0, 82100, -46508, 71400, 118664, -207025, 151247, 29904, 819, -133700, 41888, 0, 30870, -61740, -69692, 27945, 99708, 387520, 24206, -222411, 20580, -44460, 0, -48790, 59745, -4550, -5292, 439824, -99659, -150920, -20594, -561645, 153468, 0, 18291, 364259, 142711, -209825, 74844, -87932, 231040, -44100, -51786, -167824, 0, -26880, 88660, -20475, 37747, -217490, 145922, -280602, 5740, -217490, -32487, 0, -235158, -230500, 213864, -87465, -33124, -118580, -289247, -63000, 131784, -300300, 0, -92820, -225792, -185220, -310716, 183162, 95935, 24245, 76349, 483650, 147754, 0, 125048, -2835, -384762, -71340, 70317, -487696, -33551, -102295, -8918, -101150, 0, 335160, 237473, -319872, -155188, 108675, -38941, 315315, 32751, 31630, -311871, 0, -96768, -75600, 168896, -269581, 20678, 262395, -5880, -413763, 418698, 152880, 0, 223560, -13013, -421155, -135072, 556206, 161616, -54380, 133243, 44198, 96078, 0, -60375, 129948, -168266, -59605, -143584, 405765, 23940, -35560, 51156, -191590, 0, -381710, -24108, -2492, -256158, -137280, -2821, -105944, -195349, 531290, 50218, 0, -28028, 292470, -213444, -388178, 157264, 17150, -3024, -14365, 115101, -102900, 0, -201331, -101682, 336140, -170079, 30870, 181632, 79800, 170824, -263109, 21736, 0, -67240, -34888, -34440, -31605, 317898, -133875, -95459, -59840, 148568, 392490, 0, 112710, -145313, -144942, -25872, -355960, -13055, 203040, -172872, 586845, -65767, 0, 62867, 111720, -33488, -332640, -20944, -185315, -146559, 36380, 166474, 220990, 0, 81613, -30030, -399255, -205413, 194922, 30478, 88865, 135072, -252720, -194616, 0, 201320, -543507, 121898, 3465, 76076, -116620, -5915, -59150, 213488, 293454, 0, -4095, -343980, -450540, -3430, 269665, 48216, 115192, -9744, -43680, -165914, 0, 32928, -449400, -51170, 151164, 109909, 169480, -250194, -443205], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "13.4.a.a", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0], [1], [5], [-7], [17], [-7], [-35], [13], [45], [22], [-35], [0], [-119], [-13], [65], [49], [89], [-77], [110], [126], [-119], [-91], [0], [-96], [-315], [-76], [-65], [35], [221], [82], [245], [196], [85], [0], [-385], [-91], [374], [-131], [630], [91], [-315], [-336], [-455], [201], [0], [-154], [-480], [-105], [-623], [-174], [-380], [539], [-221], [-432], [175], [0], [585], [-882], [410], [-294], [833], [56], [980], [286], [-287], [91], [0], [478], [-1309], [672], [-455], [9], [990], [-98], [-655], [532], [2142], [0], [455], [-1304], [-623], [-839], [-1680], [308], [-1547], [539], [1005], [-574], [0], [-1190], [-770], [-169], [-1632], [-1372], [-525], [-882], [-595], [70], [-870], [0], [-1292]]}