# Stored data for newform 1008.4.a.ba, downloaded from the LMFDB on 24 April 2024.
{"label": "1008.4.a.ba", "space_label": "1008.4.a", "level": 1008, "weight": 4, "hecke_orbit": 27, "hecke_orbit_code": 117093590378742768, "dim": 2, "is_polredabs": true, "nf_label": "2.2.57.1", "trace_hash": 56705023516977781, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-48, 6, 1]], [11, [-1416, 6, 1]]], "qexp_display": "q+(-3-\\beta )q^{5}-7q^{7}+(-3+5\\beta )q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 16128, "fricke_eigenval": 1, "atkin_lehner_string": "--+", "analytic_conductor": 59.47392528578654, "hecke_ring_index": 2, "level_radical": 42, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [1008, 1, [127, 757, 785, 577], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [2, 3, 7], "conrey_indexes": [1], "field_disc": 57, "field_disc_factorization": [[3, 1], [19, 1]], "field_poly": [-14, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.013", "prec": 17}, {"__RealLiteral__": 0, "data": "1.966", "prec": 17}, {"__RealLiteral__": 0, "data": "0.044", "prec": 17}, {"__RealLiteral__": 0, "data": "9.259", "prec": 17}, {"__RealLiteral__": 0, "data": "0.861", "prec": 17}, {"__RealLiteral__": 0, "data": "61.129", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [3, -1], [7, 1]], "trace_display": [0, 0, -6, -14], "traces": [0, 2, 0, 0, 0, -6, 0, -14, 0, 0, 0, -6, 0, 16, 0, 0, 0, 6, 0, -64, 0, 0, 0, 6, 0, -118, 0, 0, 0, 252, 0, -40, 0, 0, 0, 42, 0, -248, 0, 0, 0, 450, 0, -376, 0, 0, 0, -12, 0, 98, 0, 0, 0, 1104, 0, -552, 0, 0, 0, 804, 0, -428, 0, 0, 0, 636, 0, -148, 0, 0, 0, 954, 0, 1072, 0, 0, 0, 42, 0, 572, 0, 0, 0, 1944, 0, -132, 0, 0, 0, -366, 0, -112, 0, 0, 0, -1176, 0, 808, 0, 0, 0, -1146, 0, 2912, 0, 0, 0, 1050, 0, -500, 0, 0, 0, 180, 0, 1920, 0, 0, 0, -42, 0, 206, 0, 0, 0, 420, 0, 2252, 0, 0, 0, 1968, 0, 448, 0, 0, 0, 1824, 0, -1528, 0, 0, 0, -3468, 0, 612, 0, 0, 0, 1200, 0, 2048, 0, 0, 0, 4224, 0, 4780, 0, 0, 0, -42, 0, -2380, 0, 0, 0, 1044, 0, -162, 0, 0, 0, -3858, 0, 826, 0, 0, 0, 1110, 0, 1048, 0, 0, 0, 2796, 0, 552, 0, 0, 0, 690, 0, 5656, 0, 0, 0, -864, 0, 3416, 0, 0, 0, -1764, 0, -3060, 0, 0, 0, 7032, 0, -3184, 0, 0, 0, -1608, 0, 280, 0, 0, 0, -636, 0, 7016, 0, 0, 0, -3804, 0, 2920, 0, 0, 0, 13152, 0, -3840, 0, 0, 0, -954, 0, 2776, 0, 0, 0, -294, 0, -8720, 0, 0, 0, 7524, 0, -9708, 0, 0, 0, -5550, 0, 1736, 0, 0, 0, -2058, 0, -3084, 0, 0, 0, 3498, 0, 4496, 0, 0, 0, 3774, 0, 4000, 0, 0, 0, 1224, 0, -1408, 0, 0, 0, -3150, 0, -9694, 0, 0, 0, 1638, 0, 4200, 0, 0, 0, 11676, 0, 2632, 0, 0, 0, -2820, 0, -4840, 0, 0, 0, 1956, 0, -3788, 0, 0, 0, 1920, 0, -7596, 0, 0, 0, 1176, 0, -5048, 0, 0, 0, 84, 0, -15328, 0, 0, 0, 6600, 0, 5980, 0, 0, 0, -20400, 0, -686, 0, 0, 0, -6378, 0, -14348, 0, 0, 0, -2730, 0, -1152, 0, 0, 0, 9114, 0, 4746, 0, 0, 0, -3900, 0, 5840, 0, 0, 0, -7728, 0, -8036, 0, 0, 0, 10224, 0, -5488, 0, 0, 0, -14376, 0, 3864, 0, 0, 0, -7716, 0, -1920, 0, 0, 0, -7872, 0, -3812, 0, 0, 0, 1272, 0, 24304, 0, 0, 0, -9516, 0, 6232, 0, 0, 0, -5628, 0, -11304, 0, 0, 0, 6228, 0, 544, 0, 0, 0, 330, 0, 2996, 0, 0, 0, -10590, 0, 5740, 0, 0, 0, -23448, 0, 10016, 0, 0, 0, -15546, 0, -6996, 0, 0, 0, -19908, 0, 7200, 0, 0, 0, -4452, 0, -6764, 0, 0, 0, -8298, 0, -14620, 0, 0, 0, -20244, 0, 1036, 0, 0, 0, 14808, 0, 11984, 0, 0, 0, 1308, 0, 10328, 0, 0, 0, -18156, 0, 1160, 0, 0, 0, -12186, 0, -612, 0, 0, 0, -6678, 0, -8176, 0, 0, 0, 15264, 0, 1956, 0, 0, 0, -16710, 0, -7504, 0, 0, 0, -16944, 0, 19416, 0, 0, 0, -66, 0, -1624, 0, 0, 0, -4224, 0, 8630, 0, 0, 0, -6660, 0, -12840, 0, 0, 0, -294, 0, -16064, 0, 0, 0, 17916, 0, -916, 0, 0, 0, -24480, 0, -4004, 0, 0, 0, 4776, 0, -19424, 0, 0, 0, -16692, 0, 14508, 0, 0, 0, 19056, 0, 22004, 0, 0, 0, -11982, 0, 27148, 0, 0, 0, -13608, 0, -4452, 0, 0, 0, 7308, 0, -47968, 0, 0, 0, 22134, 0, 924, 0, 0, 0, 37074, 0, -3620, 0, 0, 0, 2802, 0, -9568, 0, 0, 0, -23352, 0, -2660, 0, 0, 0, 3672, 0, 18752, 0, 0, 0, 2562, 0, -5434, 0, 0, 0, -2796, 0, -21508, 0, 0, 0, -15648, 0, 784, 0, 0, 0, 14496, 0, -1744, 0, 0, 0, 19884, 0, -35472, 0, 0, 0, -22524, 0, 1848, 0, 0, 0, 9954, 0, -5732, 0, 0, 0, 8232, 0, 24012, 0, 0, 0, 21804, 0, 35680, 0, 0, 0, -28626, 0, -5656, 0, 0, 0, 37758, 0, 1596, 0, 0, 0, 10200, 0, -9328, 0, 0, 0, 18264, 0, 3060, 0, 0, 0, 11196, 0, -16688, 0, 0, 0, 8022, 0, 13612, 0, 0, 0, 69648, 0, 3792, 0, 0, 0, 25872, 0, -20384, 0, 0, 0, -23076, 0, 35408, 0, 0, 0, 1608, 0, -1040, 0, 0, 0, -30336, 0, -24412, 0, 0, 0, 11034, 0, 16692, 0, 0, 0, -7350, 0, -6256, 0, 0, 0, 18480, 0, -30836, 0, 0, 0, 65442, 0, 3500, 0, 0, 0, 46104, 0, -1220, 0, 0, 0, 6414, 0, -22264, 0, 0, 0, 6120, 0, -11412, 0, 0, 0, -25284, 0, 14288, 0, 0, 0, -1260, 0, -28048, 0, 0, 0, 37998, 0, 3840, 0, 0, 0, 204, 0, -13440, 0, 0, 0, 22380, 0, 3488, 0, 0, 0, 25608, 0, 44864, 0, 0, 0, -70152, 0, -2524, 0, 0, 0, -45846, 0, -83960, 0, 0, 0, 294, 0, 13968, 0, 0, 0, 32796, 0, -610, 0, 0, 0, 11430, 0, -1442, 0, 0, 0, 34140, 0, 80356, 0, 0, 0, 14226, 0, -7096, 0, 0, 0, -16338, 0, 39732, 0, 0, 0, 29064, 0, 35752, 0, 0, 0, -2940, 0, 16492, 0, 0, 0, 69966, 0, -28912, 0, 0, 0, -30828, 0, -15764, 0, 0, 0, 46896, 0, 47400, 0, 0, 0, 44208, 0, 3084, 0, 0, 0, -42132, 0, 17384, 0, 0, 0, -67950, 0, 21528, 0, 0, 0, -13776, 0, 46472, 0, 0, 0, 17892, 0, 2320, 0, 0, 0, 2010, 0, -3136, 0, 0, 0, -3024, 0, 48076, 0, 0, 0, 77658, 0, -27720, 0, 0, 0, -72678, 0, 4472, 0, 0, 0, -23940, 0, -816, 0, 0, 0, -12768, 0, 88962, 0, 0, 0, -35436, 0, 58268, 0, 0, 0, -2136, 0, 10696, 0, 0, 0, -10344, 0, 41568, 0, 0, 0, 44184, 0, -47340, 0, 0, 0, -47640, 0, -22216, 0, 0, 0, -30768, 0, 40828, 0, 0, 0, 24276, 0, -4200, 0, 0, 0, -38064, 0, 79648, 0, 0, 0, -7098, 0, -4284, 0, 0, 0, 77826, 0, 34060, 0, 0, 0, -16290, 0, -32360, 0, 0, 0, -43086, 0, 50752, 0, 0, 0, 2820, 0, -24664, 0, 0, 0, -8400, 0, 1248, 0, 0, 0, 42534, 0, 16364, 0, 0, 0, -5496, 0, -14336, 0, 0, 0, 33180, 0, 8264, 0, 0, 0, 76236, 0, 13756, 0, 0, 0, -6624, 0, 38600, 0, 0, 0, -17280, 0, -65928, 0, 0, 0, -29568, 0, 99764, 0, 0, 0, 51552, 0, -45488, 0, 0, 0, 32862, 0, -33460, 0, 0, 0, -11490, 0, 3048, 0, 0, 0, 52926, 0, 10848, 0, 0, 0, -25152, 0, -49100, 0, 0, 0, -105072, 0, -87832, 0, 0, 0, 294, 0, -66992, 0, 0, 0, 32304, 0, -44904, 0, 0, 0, -6600, 0, 16660, 0, 0, 0, 26124, 0, 78832, 0, 0, 0, -3192, 0, -114056, 0, 0, 0, -51492, 0, 62944, 0, 0, 0, 56250, 0, -39684, 0, 0, 0, -7308, 0, -104152, 0, 0, 0, 23964, 0, 45300, 0, 0, 0, -46554, 0, 1134, 0, 0, 0, 15042, 0, 36180, 0, 0, 0, 438, 0, -1584, 0, 0, 0, -80580, 0, -117296, 0, 0, 0, -10380, 0, 1152, 0, 0, 0, 27006, 0, 67504, 0, 0, 0, 2682, 0, 7188, 0, 0, 0, 56220, 0, -5782, 0, 0, 0, 79440, 0, 30440, 0, 0, 0, -6672, 0, 26464, 0, 0, 0, 3900, 0, -75780, 0, 0, 0, -80208, 0, 60520, 0, 0, 0, -7770, 0, -1368, 0, 0, 0, 148608, 0, -87928, 0, 0, 0, 21600, 0, -7336, 0, 0, 0, -70560, 0, -69136, 0, 0, 0, 56526, 0, -99400, 0, 0, 0, -77430, 0, 16764, 0, 0, 0, -128340, 0, -90760, 0, 0, 0, -19572, 0, -58604, 0, 0, 0, -102078, 0, -30760, 0, 0, 0, 4776, 0, -3864, 0, 0, 0, -18060, 0, -40224, 0, 0, 0, 90948, 0, -83444, 0, 0, 0, -66504, 0, 17288, 0, 0, 0, -9732, 0, -90976, 0, 0, 0, -4830, 0, -25952, 0, 0, 0, 7872, 0, 68052, 0, 0, 0, -51048, 0, -39592, 0, 0, 0, 60384, 0, 114816, 0, 0, 0, 9006, 0, -48024, 0, 0, 0, -61770, 0, -33618, 0, 0, 0, 78732, 0, 93360, 0, 0, 0, 6048, 0, 47164, 0, 0, 0, -22260, 0, -26096, 0, 0, 0, -49740, 0, -23912, 0, 0, 0, 37704, 0, 25472, 0, 0, 0, -71052, 0, -9828, 0, 0, 0, -18924, 0, 11304, 0, 0, 0, 120, 0, 94496, 0, 0, 0, 12348, 0, -30016, 0, 0, 0, -20880, 0, -95096, 0, 0, 0, -17502, 0, 21420, 0, 0, 0, -87882, 0, -44664, 0, 0, 0, 28398, 0, 66752, 0, 0, 0, 654, 0, -24884, 0, 0, 0, -139296, 0, -14248, 0, 0, 0, -49224, 0, -26460, 0, 0, 0, 91728, 0, -56392, 0, 0, 0, -87108, 0, 22288, 0, 0, 0, -47604, 0, 77384, 0, 0, 0, -53520, 0, -100520, 0, 0, 0, 33672, 0, -17472, 0, 0, 0, 23166, 0, 55568, 0, 0, 0, 11256, 0, -40812, 0, 0, 0, 61200, 0, 6996, 0, 0, 0, -86580, 0, -1960, 0, 0, 0, -76866, 0, 49876, 0, 0, 0, -63816, 0, 81728, 0, 0, 0, -70296, 0, 141840, 0, 0, 0, 104208, 0, -35272, 0, 0, 0, 4452, 0, -20048, 0, 0, 0, 111834, 0, 59568, 0, 0, 0, 134196, 0, -49112, 0, 0, 0, 16836, 0, 17048, 0, 0, 0, -185820, 0, 22168, 0, 0, 0, 3456, 0, -71452, 0, 0, 0, -48834, 0, -83964, 0, 0, 0, 26628, 0, -2624, 0, 0, 0, -53136, 0, -52364, 0, 0, 0, -157866, 0, -20440, 0, 0, 0, 41394, 0, 46240, 0, 0, 0, 26718, 0, -3984, 0, 0, 0, -101406, 0, 59872, 0, 0, 0, -110184, 0, 106520, 0, 0, 0, -92064, 0, 31932, 0, 0, 0, 46350, 0, -105060, 0, 0, 0, -13872, 0, 26880, 0, 0, 0, 18156, 0, -35336, 0, 0, 0, 36408, 0, 58204, 0, 0, 0, -129264, 0, -68356, 0, 0, 0, -61650, 0, 101272, 0, 0, 0, 6678, 0, -28204, 0, 0, 0, -8412, 0, -10942, 0, 0, 0, -128748, 0, -19432, 0, 0, 0, 108840, 0, -100892, 0, 0, 0, -200370, 0, 90032, 0, 0, 0, 62256, 0, 60288, 0, 0, 0, 40104, 0, 180648, 0, 0, 0, 2058, 0, -1956, 0, 0, 0, -65106, 0, 137660, 0, 0, 0, 40380, 0, 61040, 0, 0, 0, 78828, 0, -58728, 0, 0, 0, -68280, 0, 215380, 0, 0, 0, 636, 0, 15080, 0, 0, 0, 16944, 0, 92848, 0, 0, 0, -52668, 0, -121144, 0, 0, 0, -43560, 0, -104100, 0, 0, 0, -103176, 0, 67956, 0, 0, 0, -66546, 0, -189680, 0, 0, 0, 57000, 0, -21856, 0, 0, 0, 78594, 0, 57568, 0, 0, 0, -85200, 0, -104064, 0, 0, 0, 38850, 0, -91688, 0, 0, 0, 73314, 0, 69856, 0, 0, 0, -122844, 0, -12152, 0, 0, 0, -102936, 0, 12840, 0, 0, 0, 26616, 0, -59144, 0, 0, 0, 221952, 0, -21316, 0, 0, 0, 34464, 0, -88632, 0, 0, 0, 14406, 0, 162928, 0, 0, 0, 155160, 0, -22662, 0, 0, 0, -17916, 0, 21588, 0, 0, 0, -54234, 0, 60172, 0, 0, 0, -85332, 0, 19112, 0, 0, 0, 208194, 0, 44644, 0, 0, 0, 232056, 0, 31712, 0, 0, 0, -24486, 0, 66456, 0, 0, 0, 133218, 0, -139184, 0, 0, 0, 75288, 0, -31472, 0, 0, 0, 49632, 0, -129216, 0, 0, 0, -86352, 0, -87192, 0, 0, 0, 89688, 0, 149376, 0, 0, 0, 54456, 0, -14508, 0, 0, 0, -26418, 0, 55440, 0, 0, 0, 58572, 0, -95780, 0, 0, 0, 131352, 0, -28000, 0, 0, 0, 55224, 0, 9012, 0, 0, 0, 8718, 0, 37400, 0, 0, 0, 11232, 0, 5312, 0, 0, 0, -132792, 0, 164128, 0, 0, 0, -8568, 0, -256980, 0, 0, 0, 41202, 0, 3188, 0, 0, 0, 133764, 0, 9856, 0, 0, 0, -29604, 0, -12616, 0, 0, 0, 191796, 0, 31540, 0, 0, 0, 184620, 0, -162604, 0, 0, 0, 178146, 0, 41100, 0, 0, 0, 22050, 0, -242284, 0, 0, 0, -53760, 0, 202732, 0, 0, 0, 95280, 0, 67858, 0, 0, 0, 215166, 0, 36328, 0, 0, 0, 82680, 0, 93072, 0, 0, 0, 254058, 0, -27424, 0, 0, 0, 69540, 0, -138696, 0, 0, 0, -11466, 0, -145520, 0, 0, 0, -2802, 0, 140724, 0, 0, 0, 68712, 0, -29400, 0, 0, 0, 115044, 0, -180992, 0, 0, 0, -81864, 0, 224576, 0, 0, 0, -27384, 0, 206528, 0, 0, 0, 90342, 0, 96592, 0, 0, 0, -81732, 0, -172584, 0, 0, 0, 141552, 0, -8340, 0, 0, 0, 168684, 0, -18424, 0, 0, 0, -70314, 0, -100352, 0, 0, 0, 126864, 0, 91768, 0, 0, 0, 75372, 0, 20184, 0, 0, 0, 136656, 0, -144352, 0, 0, 0, 19740, 0, -102032, 0, 0, 0, -117594, 0, -192472, 0, 0, 0, -186336, 0, 33880, 0, 0, 0, -159564, 0, 50352, 0, 0, 0, 15648, 0, -94496, 0, 0, 0, 203028, 0, 252252, 0, 0, 0, 110952, 0, 244980, 0, 0, 0, -13692, 0, -37156, 0, 0, 0, 19320, 0, 4224, 0, 0, 0, 92352, 0, 26516, 0, 0, 0, -175056, 0, 29216, 0, 0, 0, 42480, 0, 14576, 0, 0, 0, 50154, 0, -75790, 0, 0, 0, 149148, 0, 159384, 0, 0, 0, -13440, 0, 137092, 0, 0, 0, 70158, 0, -1848, 0, 0, 0, -265020, 0, 53172, 0, 0, 0, -27804, 0, -56416, 0, 0, 0, -210444, 0, 70668, 0, 0, 0, 138084, 0, 74876, 0, 0, 0, -144720, 0, -20800, 0, 0, 0, -8232, 0, -46064, 0, 0, 0, 119412, 0, 206188, 0, 0, 0, -23982, 0, 35336, 0, 0, 0, -213024, 0, 111832, 0, 0, 0, -94620, 0, 18608, 0, 0, 0, -1800, 0, -11588, 0, 0, 0, 93960, 0, -47632, 0, 0, 0, -588, 0, -24012, 0, 0, 0, 5490, 0, 32360, 0, 0, 0, 768, 0, 107296, 0, 0, 0, 84792, 0, -28632, 0, 0, 0, 313260, 0, -1596, 0, 0, 0, -63204, 0, -25224, 0, 0, 0, -28782, 0, -251888, 0, 0, 0, -46200, 0, 154232, 0, 0, 0, -328824, 0, -225544, 0, 0, 0, 76566, 0, -41860, 0, 0, 0, -18264, 0, 70944, 0, 0, 0, -130800, 0, -78088, 0, 0, 0, 213648, 0, 159376, 0, 0, 0, -122976, 0, 19160, 0, 0, 0, 142800, 0, 50044, 0, 0, 0, -207450, 0, -35616, 0, 0, 0, -84432, 0, 4802, 0, 0, 0, -99384, 0, 179280, 0, 0, 0, -181896, 0, 34640, 0, 0, 0, 197220, 0, 81720, 0, 0, 0, 45090, 0, 46720, 0, 0, 0, 44646, 0, -3792, 0, 0, 0, -4848, 0, 60460, 0, 0, 0, -81942, 0, 100436, 0, 0, 0, 56946, 0, -233056, 0, 0, 0, -528, 0, 69048, 0, 0, 0, 166146, 0, -161580, 0, 0, 0, -8424, 0, -33808, 0, 0, 0, 19110, 0, 185152, 0, 0, 0, -88398, 0, 129160, 0, 0, 0, 13044, 0, 8064, 0, 0, 0, -156000, 0, -14376, 0, 0, 0, 86088, 0, 292992, 0, 0, 0, -34740, 0, 130748, 0, 0, 0, 277572, 0, -65560, 0, 0, 0, -63798, 0, -54000, 0, 0, 0, -183180, 0, 194776, 0, 0, 0, 76506, 0, -33222, 0, 0, 0, 5934, 0, -16692, 0, 0, 0, -309840, 0, -166072, 0, 0, 0, 133962, 0, -89292, 0, 0, 0, 93384, 0, 66320, 0, 0, 0, 27300, 0, -209984, 0, 0, 0, -306504, 0, -38316, 0, 0, 0, -18480, 0, -40880, 0, 0, 0, -235872, 0, -122560, 0, 0, 0, 1344, 0, -143244, 0, 0, 0, -43200, 0, -95792, 0, 0, 0, -421722, 0, 35788, 0, 0, 0, 54096, 0, 256356, 0, 0, 0, -143184, 0, 176556, 0, 0, 0, 235686, 0, 56252, 0, 0, 0, -118248, 0, -182912, 0, 0, 0, -326298, 0, 178960, 0, 0, 0, -87516, 0, 25092, 0, 0, 0, -37188, 0, 27264, 0, 0, 0, -71568, 0, -115264, 0, 0, 0, -14262, 0, -79576, 0, 0, 0, 1932, 0, 38416, 0, 0, 0, -113484, 0, -147256, 0, 0, 0, 300504, 0, 160200, 0, 0, 0, 25284, 0, -241312, 0, 0, 0, -3810, 0, 44896, 0, 0, 0, 100632, 0, 236924, 0, 0, 0, -352836, 0, 183184, 0, 0, 0, 94170, 0, -27048, 0, 0, 0, 227370, 0, -145240, 0, 0, 0, 166524, 0, -363064, 0, 0, 0, 72042, 0, -203252, 0, 0, 0, 190320, 0, 423608, 0, 0, 0, 54012, 0, -68996, 0, 0, 0, -76842, 0, 227612, 0, 0, 0, 30792, 0, 13440, 0, 0, 0, -238188, 0, -115760, 0, 0, 0, -125640, 0, 263620, 0, 0, 0, -304332, 0, -142704, 0, 0, 0, -284064, 0, -128592, 0, 0, 0, 55104, 0, 32732, 0, 0, 0, -25608, 0, -229632, 0, 0, 0, 2082, 0, 26684, 0, 0, 0, 58758, 0, -51036, 0, 0, 0, -38406, 0, 319280, 0, 0, 0, -92208, 0, 54688, 0, 0, 0, 210060, 0, -353704, 0, 0, 0, -8904, 0, 312110, 0, 0, 0, -86976, 0, -114312, 0, 0, 0, -134076, 0, -170128, 0, 0, 0, -100908, 0, 16080, 0, 0, 0, -281904, 0, -151676, 0, 0, 0, 103548, 0, -13968, 0, 0, 0, 354510, 0, -279012, 0, 0, 0, 66612, 0, -347800, 0, 0, 0, -77640, 0, -163712, 0, 0, 0, -123918, 0, -43624, 0, 0, 0, 142104, 0, -361024, 0, 0, 0, -11430, 0, -320448, 0, 0, 0, -34482, 0, -119920, 0, 0, 0, -36300, 0, 9800, 0, 0, 0, 39396, 0, 238164, 0, 0, 0, 308286, 0, 31504, 0, 0, 0, 309300, 0, 79128, 0, 0, 0, -115284, 0, 189000, 0, 0, 0, -301968, 0, -264164, 0, 0, 0, -144408, 0, -181736, 0, 0, 0, -171630, 0, -162180, 0, 0, 0, -43596, 0, 164808, 0, 0, 0, -78048, 0, -39732, 0, 0, 0, 39936, 0, -3808, 0, 0, 0, -368328, 0, 542020, 0, 0, 0, 105198, 0, -403224, 0, 0, 0, -124482, 0, -131268, 0, 0, 0, 279576, 0, -237736, 0, 0, 0, -2310, 0, 232664, 0, 0, 0, -382848, 0, -21632, 0, 0, 0, 268416, 0, -20972, 0, 0, 0, 251460, 0, -223968, 0, 0, 0, 152148, 0], "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": "21.4.a.c", "char_is_minimal": false, "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, 0], [1, 0], [0, 0], [0, 0], [0, 0], [-3, -1], [0, 0], [-7, 0], [0, 0], [0, 0], [0, 0], [-3, 5], [0, 0], [8, -6], [0, 0], [0, 0], [0, 0], [3, 1], [0, 0], [-32, 12], [0, 0], [0, 0], [0, 0], [3, -17], [0, 0], [-59, 6], [0, 0], [0, 0], [0, 0], [126, -12], [0, 0], [-20, -36], [0, 0], [0, 0], [0, 0], [21, 7], [0, 0], [-124, -18], [0, 0], [0, 0], [0, 0], [225, 15], [0, 0], [-188, 24], [0, 0], [0, 0], [0, 0], [-6, 34], [0, 0], [49, 0], [0, 0], [0, 0], [0, 0], [552, -2], [0, 0], [-276, -12], [0, 0], [0, 0], [0, 0], [402, -58], [0, 0], [-214, 36], [0, 0], [0, 0], [0, 0], [318, 10], [0, 0], [-74, -54], [0, 0], [0, 0], [0, 0], [477, -15], [0, 0], [536, 6], [0, 0], [0, 0], [0, 0], [21, -35], [0, 0], [286, 54], [0, 0], [0, 0], [0, 0], [972, 48], [0, 0], [-66, -6], [0, 0], [0, 0], [0, 0], [-183, 71], [0, 0], [-56, 42], [0, 0], [0, 0], [0, 0], [-588, -4], [0, 0], [404, 138], [0, 0], [0, 0], [0, 0]]}