# Stored data for newform 1840.4.a.x, downloaded from the LMFDB on 18 April 2024.
{"label": "1840.4.a.x", "space_label": "1840.4.a", "level": 1840, "weight": 4, "hecke_orbit": 24, "hecke_orbit_code": 103582791496632112, "dim": 8, "is_polredabs": true, "trace_hash": 2049149849740083886, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [33856, 83904, 16400, -22173, 462, 1029, -67, -12, 1]], [7, [-575432512, 511740376, -70422072, -8737786, 501889, 31419, -1184, -31, 1]]], "qexp_display": "q+(2-\\beta _{1})q^{3}+5q^{5}+(3+\\beta _{1}+\\beta _{3}+\\cdots)q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 29440, "fricke_eigenval": 1, "atkin_lehner_string": "+--", "analytic_conductor": 108.56351441056273, "hecke_ring_index": 32, "level_radical": 230, "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": [1840, 1, [1151, 1381, 737, 1201], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 1, "level_primes": [2, 5, 23], "conrey_indexes": [1], "field_disc": 148477966787842535129937, "field_disc_factorization": [[3, 1], [7, 1], [281, 1], [2251198949, 1], [11176929713, 1]], "field_poly": [124632, 36684, -45582, -7035, 4492, 335, -123, -4, 1], "hecke_ring_index_factorization": [[2, 5]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.110", "prec": 17}, {"__RealLiteral__": 0, "data": "7.014", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "125.612", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3370.252", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [5, -1], [23, -1]], "trace_display": [0, 12, 40, 31], "traces": [0, 8, 0, 12, 0, 40, 0, 31, 0, 62, 0, 35, 0, -54, 0, 60, 0, -11, 0, 107, 0, -148, 0, 184, 0, 200, 0, 405, 0, 37, 0, 290, 0, 289, 0, 155, 0, -172, 0, 311, 0, 308, 0, 538, 0, 310, 0, 1035, 0, 585, 0, 387, 0, 46, 0, 175, 0, 286, 0, 1256, 0, 399, 0, 1234, 0, -270, 0, 1598, 0, 276, 0, 750, 0, 177, 0, 300, 0, -1228, 0, 1292, 0, 380, 0, 2094, 0, -55, 0, 2245, 0, 484, 0, 679, 0, -2111, 0, 535, 0, -2225, 0, 2117, 0, -1292, 0, 2839, 0, -740, 0, 3040, 0, 761, 0, 2648, 0, -4338, 0, 920, 0, -1752, 0, 2526, 0, -761, 0, 4958, 0, 1000, 0, 2665, 0, -1374, 0, 3451, 0, -1485, 0, 2025, 0, -1859, 0, 4845, 0, -465, 0, 7532, 0, 185, 0, 4625, 0, -1341, 0, 3668, 0, -3041, 0, 1450, 0, -3336, 0, 7656, 0, 713, 0, 6866, 0, 1445, 0, 5512, 0, -150, 0, 2192, 0, -6103, 0, 775, 0, -498, 0, 7183, 0, 5659, 0, 6871, 0, -860, 0, 3109, 0, -3853, 0, 4536, 0, -4383, 0, 1555, 0, -3546, 0, 3528, 0, 8036, 0, 12318, 0, 1540, 0, 1426, 0, -4336, 0, 58, 0, -1530, 0, 2690, 0, 3111, 0, 7185, 0, 7244, 0, 6896, 0, 1550, 0, 1832, 0, 4360, 0, -9407, 0, -1885, 0, 5175, 0, 13996, 0, 809, 0, 15848, 0, 7122, 0, 2925, 0, 4041, 0, -2234, 0, 2325, 0, 805, 0, 1935, 0, 15675, 0, 1010, 0, 28054, 0, 2611, 0, 230, 0, -4866, 0, 3989, 0, -2505, 0, 14949, 0, 875, 0, 14691, 0, -13486, 0, 15682, 0, 10464, 0, 1430, 0, -10902, 0, -51, 0, -20941, 0, 3424, 0, 6280, 0, 20965, 0, -1242, 0, 11204, 0, -2866, 0, 1995, 0, -2943, 0, 5301, 0, -11305, 0, -7827, 0, 6170, 0, -3455, 0, 852, 0, 34004, 0, 5388, 0, -1350, 0, -6802, 0, 8724, 0, 6137, 0, 11108, 0, 7990, 0, 11839, 0, -12072, 0, 5042, 0, 24380, 0, 1380, 0, 16359, 0, 15403, 0, -16138, 0, 7243, 0, 3750, 0, 8703, 0, -300, 0, 13307, 0, 20240, 0, 885, 0, 6018, 0, 22073, 0, -17492, 0, -23446, 0, 1500, 0, 13193, 0, 1169, 0, 32907, 0, -4780, 0, -6140, 0, 2680, 0, 3553, 0, -253, 0, -2921, 0, 6460, 0, 1600, 0, -37555, 0, 28938, 0, 15588, 0, 1900, 0, 7472, 0, -646, 0, -6480, 0, -10666, 0, 10470, 0, 33273, 0, -14974, 0, 28885, 0, 22470, 0, -275, 0, -3428, 0, -8141, 0, -10424, 0, -12327, 0, 11225, 0, 2461, 0, 11690, 0, 60201, 0, 26962, 0, 2420, 0, -35522, 0, 17891, 0, 4481, 0, -24034, 0, 3395, 0, 17680, 0, -15105, 0, 37791, 0, -1472, 0, -10555, 0, -6318, 0, -18518, 0, -31158, 0, 8448, 0, 2675, 0, 11122, 0, -16972, 0, 30868, 0, -3404, 0, -11125, 0, -48579, 0, 41041, 0, -18759, 0, -36950, 0, 10585, 0, 44434, 0, -10463, 0, 25064, 0, -19249, 0, -6460, 0, -35470, 0, -12317, 0, -4346, 0, -4907, 0, 14195, 0, 4688, 0, -48685, 0, 49150, 0, 10674, 0, -3700, 0, -35784, 0, 4232, 0, -88, 0, -26157, 0, 15200, 0, 58059, 0, -48550, 0, -5427, 0, 10020, 0, 3805, 0, -4600, 0, -25503, 0, 20922, 0, -39504, 0, 13240, 0, -40070, 0, -16722, 0, 48328, 0, -14094, 0, -21690, 0, -82382, 0, 42188, 0, 41095, 0, -76272, 0, 4600, 0, -26157, 0, -90207, 0, 35312, 0, 29870, 0, -8760, 0, -22656, 0, -52977, 0, -16506, 0, 214, 0, 12630, 0, -43586, 0, 5839, 0, 8430, 0, 64178, 0, -3805, 0, -29608, 0, 40612, 0, -36545, 0, -108742, 0, 24790, 0, 29097, 0, 21341, 0, 9315, 0, 44732, 0, 5000, 0, -8399, 0, 16378, 0, 23440, 0, -41710, 0, 13325, 0, -54906, 0, -24999, 0, 85952, 0, 57966, 0, -6870, 0, -18563, 0, -70774, 0, 11217, 0, -85126, 0, 17255, 0, 29706, 0, -37888, 0, -10451, 0, 48769, 0, -7425, 0, 851, 0, -79432, 0, -86251, 0, -30955, 0, 10125, 0, -55962, 0, 56424, 0, 40838, 0, 32078, 0, -9295, 0, -116388, 0, 7348, 0, 55746, 0, -156577, 0, 24225, 0, -31119, 0, -43761, 0, 47579, 0, 74728, 0, -2325, 0, -60544, 0, -103761, 0, 38132, 0, 6670, 0, 37660, 0, -61875, 0, -16375, 0, 50696, 0, -2350, 0, 925, 0, -24457, 0, -11053, 0, 20720, 0, -98648, 0, 23125, 0, 37920, 0, 50387, 0, -34893, 0, 74583, 0, -6705, 0, -69264, 0, -47192, 0, -9968, 0, -24270, 0, 18340, 0, -92476, 0, 6647, 0, 7862, 0, -34549, 0, -15205, 0, -71164, 0, -45040, 0, -33233, 0, -71196, 0, 7250, 0, 12776, 0, -50122, 0, -63841, 0, 46645, 0, -16680, 0, 51652, 0, -90613, 0, -22952, 0, -57868, 0, 38280, 0, -89234, 0, -5760, 0, 48322, 0, 6294, 0, 3565, 0, -18815, 0, 39411, 0, 42315, 0, -44288, 0, 34330, 0, -42920, 0, -86573, 0, 22220, 0, 73465, 0, 7225, 0, -16048, 0, -112186, 0, 25797, 0, -24764, 0, 27560, 0, -93758, 0, 920, 0, 11317, 0, -66670, 0, -750, 0, -48304, 0, 3116, 0, -3956, 0, -167697, 0, 10960, 0, 13313, 0, 1303, 0, -70321, 0, 3905, 0, -30515, 0, -72684, 0, -11644, 0, -300, 0, -74705, 0, 3875, 0, -119457, 0, 21510, 0, 120990, 0, -37019, 0, -2490, 0, -65587, 0, -108914, 0, 64364, 0, -39702, 0, 35915, 0, 7153, 0, -5725, 0, -25156, 0, 84196, 0, 28295, 0, -38816, 0, -88388, 0, -28078, 0, -94374, 0, 34355, 0, -61652, 0, 69418, 0, 73301, 0, 33145, 0, -4300, 0, -10043, 0, 31793, 0, 27791, 0, -109655, 0, 15545, 0, -7975, 0, -21500, 0, -5209, 0, 7084, 0, -19265, 0, -98290, 0, -98579, 0, -51684, 0, 10851, 0, 22680, 0, -68674, 0, -34651, 0, -13252, 0, -34406, 0, -21915, 0, 8405, 0, -85741, 0, -53945, 0, -160508, 0, 7775, 0, 5421, 0, -87056, 0, 65240, 0, -15433, 0, -17730, 0, -138836, 0, 12374, 0, 34873, 0, 3705, 0, 17640, 0, -11532, 0, 7532, 0, 116109, 0, -71108, 0, 40180, 0, -72098, 0, -27864, 0, 111822, 0, -84316, 0, 61590, 0, -125826, 0, -6912, 0, 34525, 0, -58923, 0, 7700, 0, -117016, 0, 70909, 0, 15950, 0, -47021, 0, 7130, 0, -133053, 0, -97870, 0, 143527, 0, -32431, 0, -21680, 0, -43153, 0, 50238, 0, -25807, 0, -81297, 0, 290, 0, -60724, 0, -78413, 0, -54139, 0, 39853, 0, -7650, 0, -115441, 0, 20421, 0, -55173, 0, 96778, 0, 13450, 0, 8774, 0, -27642, 0, 23805, 0, -20975, 0, 15555, 0, -2999, 0, 153124, 0, 11511, 0, -128888, 0, 35925, 0, -658, 0, 65992, 0, 129360, 0, 79823, 0, 36220, 0, 41138, 0, -60751, 0, 53000, 0, 176184, 0, 34480, 0, -65563, 0, -230232, 0, 264068, 0, 70974, 0, 7750, 0, 13455, 0, -109098, 0, -93513, 0, 65375, 0, 9160, 0, -82505, 0, -1330, 0, 30051, 0, 110476, 0, 21800, 0, -88150, 0, -14346, 0, 63831, 0, -139489, 0, -47035, 0, -74030, 0, -120360, 0, 163662, 0, -144584, 0, -9425, 0, -253743, 0, 153440, 0, 62430, 0, 8901, 0, 25875, 0, -25640, 0, 45424, 0, 185566, 0, 50855, 0, 69980, 0, -113878, 0, -1069, 0, 60008, 0, 182109, 0, 4045, 0, -19431, 0, 75742, 0, 98044, 0, 19144, 0, 79240, 0, 10387, 0, 121618, 0, -75694, 0, 71410, 0, 35610, 0, 44790, 0, 1058, 0, -14336, 0, -118171, 0, 14625, 0, -186521, 0, -32081, 0, 5881, 0, 221308, 0, 20205, 0, -130130, 0, -101142, 0, 143030, 0, -21722, 0, -11170, 0, -17050, 0, -101746, 0, -128070, 0, 138696, 0, 11625, 0, 35590, 0, -120192, 0, 42254, 0, 57186, 0, 4025, 0, -112329, 0, 56487, 0, 63719, 0, 158936, 0, 9675, 0, -95249, 0, -115136, 0, 306371, 0, 123722, 0, 78375, 0, -30559, 0, 71214, 0, 231783, 0, 57878, 0, 5050, 0, 7331, 0, 12802, 0, 152731, 0, -111251, 0, 140270, 0, -64080, 0, -669, 0, 6578, 0, 163644, 0, 13055, 0, -141725, 0, 148658, 0, -94526, 0, 34262, 0, 1150, 0, -14681, 0, 74719, 0, 109884, 0, -92490, 0, -24330, 0, -63108, 0, -33080, 0, 193572, 0, -162972, 0, 19945, 0, -78368, 0, 150486, 0, 124966, 0, 251774, 0, -12525, 0, 28888, 0, -58153, 0, 289219, 0, -20407, 0, 74745, 0, 261713, 0, -242698, 0, -117214, 0, 122369, 0, 4375, 0, 114904, 0, 18708, 0, -34337, 0, 129487, 0, 73455, 0, -79164, 0, 160726, 0, 139826, 0, 161402, 0, -67430, 0, 297498, 0, 64460, 0, 166712, 0, 9177, 0, 78410, 0, -472088, 0, 77204, 0, 144532, 0, -181680, 0, 52320, 0, -55125, 0, -99768, 0, 278471, 0, -25103, 0, 7150, 0, 160693, 0, -83193, 0, 230622, 0, 222191, 0, -54510, 0, -134406, 0, -120236, 0, 260470, 0, -112516, 0, -255, 0, -47261, 0, 28382, 0, 53282, 0, -59929, 0, -104705, 0, 103575, 0, 250281, 0, -68085, 0, -62829, 0, 17120, 0, 101900, 0, 292160, 0, 162794, 0, 137543, 0, 31400, 0, -185936, 0, 23822, 0, 275141, 0, -17124, 0, 104825, 0, 6802, 0, 42892, 0, 383925, 0, 55008, 0, -6210, 0, -49723, 0, 51407, 0, -101352, 0, 2824, 0, 56020, 0, 195590, 0, 67664, 0, 206938, 0, -38872, 0, -14330, 0, -79198, 0, -76894, 0, -210399, 0, 99844, 0, 9975, 0, -239115, 0, 11170, 0, 158505, 0, 164436, 0, -14715, 0, 33388, 0, 55814, 0, 36754, 0, 146413, 0, 26505, 0, 49579, 0, -41407, 0, 279910, 0, 110634, 0, -56525, 0, -171925, 0, 119142, 0, 131024, 0, -63114, 0, -39135, 0, 25103, 0, -108284, 0, 248537, 0, 103153, 0, 30850, 0, 27022, 0, -10937, 0, 216339, 0, 24561, 0, -17275, 0, 6348, 0, -218494, 0, -54400, 0, 56262, 0, 4260, 0, -290844, 0, 92634, 0, 283030, 0, 125638, 0, 170020, 0, 73425, 0, -123720, 0, 283654, 0, -114416, 0, 26940, 0, 47569, 0, -65347, 0, -263231, 0, 70041, 0, -6750, 0, -120056, 0, 125464, 0, 280898, 0, 17250, 0, -34010, 0, -95412, 0, 245670, 0, -7751, 0, -118078, 0, 43620, 0, -250133, 0, 141577, 0, 407139, 0, -26642, 0, 30685, 0, -158293, 0, 251636, 0, -61793, 0, -226121, 0, 55540, 0, 275748, 0, -49854, 0, -213918, 0, 644268, 0, 39950, 0, -110038, 0, 4071, 0, -191700, 0, -76550, 0, 59195, 0, 125236, 0, -383752, 0, 267156, 0, 67780, 0, -60360, 0, -41324, 0, -151341, 0, -133465, 0, 7013, 0, 25210, 0, 21472, 0, 113427, 0, 50486, 0, 198385, 0, 121900, 0, -19250, 0, -66834, 0, 239116, 0, -215268, 0, 6900, 0, -116228, 0, -308536, 0, 242069, 0, -36754, 0, 81795, 0, -373818, 0, -137632, 0, -73459, 0, -128, 0, 77015, 0, 173760, 0, -97446, 0, 531913, 0, 42299, 0, -80690, 0, 92309, 0, 135238, 0, 83990, 0, -186110, 0, 36215, 0, -77573, 0, 35348, 0, -28244, 0, -290781, 0, 18750, 0, -350233, 0, -21800, 0, -213733, 0, 723, 0, 43515, 0, 377053, 0, -96620, 0, -120690, 0, 250146, 0, -1500, 0, -402917, 0, 395322, 0, 83240, 0, -578281, 0, 66535, 0, -35043, 0, 56696, 0, 301587, 0, 34418, 0, 101200, 0, 29716, 0, 74198, 0, -181720, 0, -94305, 0, 4425, 0, 210936, 0, -226366, 0, 71286, 0, 287573, 0, 30090, 0, -96344, 0, -341906, 0, -28850, 0, 189824, 0, 110365, 0, 227643, 0, -205316, 0, 528047, 0, 57962, 0, -87460, 0, 477882, 0, -15900, 0, -168304, 0, 8740, 0, -117230, 0, -376587, 0, 4176, 0, 277711, 0, -316654, 0, 7500, 0, -82452, 0, 149967, 0, 74987, 0, -514310, 0, 65965, 0, -60180, 0, -2443, 0, 283586, 0, 28720, 0, 5845, 0, -290327, 0, -6992, 0, 298016, 0, -106617, 0, 164535, 0, 195704, 0, 48162, 0, 158430, 0, 325734, 0, -23900, 0, -122970, 0, 265270, 0, -268436, 0, -475818, 0, -30700, 0, 237263, 0, 43674, 0, 200305, 0, -172992, 0, 13400, 0, -63419, 0, 179420, 0, -274439, 0, 58474, 0, 17765, 0, -346708, 0, 442853, 0, -24266, 0, 183057, 0, -1265, 0, -246120, 0, -95617, 0, 24542, 0, -83519, 0, -14605, 0, 279946, 0, -150564, 0, 529827, 0, 244106, 0, 32300, 0, -394776, 0, -152405, 0, -571692, 0, -73331, 0, 8000, 0, -173874, 0, -136177, 0, 399806, 0, 190923, 0, -187775, 0, -3314, 0, 207286, 0, 51635, 0, 117855, 0, 144690, 0, 7280, 0, 194595, 0, 346029, 0, -488860, 0, 77940, 0, -381073, 0, 513819, 0, -35070, 0, -94712, 0, 9500, 0, 345521, 0, 84745, 0, 194548, 0, 466118, 0, 37360, 0, -238395, 0, -184492, 0, 157380, 0, 20852, 0, -3230, 0, 11132, 0, -681135, 0, 208984, 0, -240863, 0, -32400, 0, -188833, 0, 235629, 0, -170384, 0, 126007, 0, -53330, 0, -436294, 0, 282683, 0, 207943, 0, -306904, 0, 52350, 0, 76094, 0, -712724, 0, 30992, 0, -50722, 0, 166365, 0, 72015, 0, -197590, 0, -59198, 0, 15617, 0, -74870, 0, -84778, 0, 197275, 0, -206674, 0, 252878, 0, 144425, 0, -69390, 0, 21140, 0, 199980, 0, 55172, 0, 112350, 0, -195467, 0, 372470, 0, 28206, 0, -343338, 0, -1375, 0, -25241, 0, -66042, 0, -158273, 0, 580396, 0, -17140, 0, -298703, 0, -48553, 0, -318121, 0, -622578, 0, -40705, 0, 174826, 0, -409534, 0, 328652, 0, 490707, 0, -52120, 0, 40568, 0, -319846, 0, -362226, 0, 17313, 0, -61635, 0, 65433, 0, -79930, 0, -166568, 0, 5658, 0, 56125, 0, 294218, 0, -138715, 0, -587877, 0, 134034, 0, 12305, 0, -110850, 0, 84850, 0, 18193, 0, 114440, 0, 58450, 0, -70833, 0, -214342, 0, -108135, 0, 60738, 0, 301005, 0, -8301, 0, -404753, 0, 827680, 0, 202566, 0, 134810, 0, 174063, 0, 214981, 0, 186853, 0, -446769, 0, 12100, 0, 182890, 0, -105082, 0, -51175, 0, -442954, 0, -177610, 0, -335638, 0, -61349, 0, -669920, 0, 259002, 0, 89455, 0, 441674, 0, 83664, 0, -307404, 0, -262876, 0, 22405, 0, -219428, 0, 115584, 0, 78861, 0, -677439, 0, -120170, 0, 34266, 0, 256957, 0, -125044, 0, 376268, 0, 16975, 0, 48691, 0, 306268, 0, -26336, 0, -153801, 0, 88400, 0, 340065, 0, -894689, 0, 66528, 0, -161003, 0, -75525, 0, -483, 0, 30628, 0, -301854, 0, 288199, 0, 188955, 0, 31792, 0, 500444, 0, 422412, 0, -145290, 0, -7360, 0, 761888, 0, -179474, 0, 160554, 0, -29716, 0, -52775, 0, -95813, 0, -270026, 0, -192922, 0, 29730, 0, -31590, 0, 157301, 0, 216942, 0, -19955, 0, -893658, 0, -92590, 0, -202537, 0, -375425, 0, 306498, 0, 130257, 0, -155790, 0, -181420, 0, -300335, 0, 193314, 0, -395480, 0, 42240, 0, -340523, 0, 65297, 0, 120315, 0, 177684, 0, 13375, 0, 298071, 0, -27003, 0, -504136, 0, -457823, 0, 55610, 0, 613621, 0, 341926, 0, -129806, 0, 52010, 0, -84860, 0, 79426, 0, -123246, 0, -109332, 0, 161430, 0, 154340, 0, -355074, 0, 164556, 0, 188981, 0, 324268, 0, -17020, 0, -293973, 0, -204252, 0, -115510, 0, 333476, 0, -55625, 0, -7749, 0, 682458, 0, -14235, 0, 153113, 0, -242895, 0, -5128, 0, -171732, 0, -35309, 0, -709074, 0, 205205, 0, -342475, 0, -301296, 0, -79368, 0, 286304, 0, -93795, 0, -111483, 0, -204997, 0, 69920, 0, 34968, 0, -184750, 0, -138436, 0, 452961, 0, 447970, 0, -123901, 0, 52925, 0, -178840, 0, 115330, 0, -208338, 0, -331934, 0, 222170, 0, 126668, 0, -65610, 0, -256674, 0, 332358, 0, -52315, 0, 439092, 0, -287701, 0, 353811, 0, -200326, 0, 125320, 0, 17503, 0, -164767, 0, -703789, 0, -201810, 0, -96245, 0, 19922, 0, -175034, 0, -137542, 0, 135477, 0, -32300, 0, -727345, 0, -138062, 0, 311315, 0, -21146, 0, -177350, 0, 57856, 0, -660544, 0, -292031, 0, -363251, 0, -61585, 0, -446580, 0, 282569, 0, -377124, 0, 60904, 0, -21730, 0, 322128, 0, -707816, 0, 445539, 0, -121402, 0, -24535, 0, -31519, 0, -331266, 0, -126881, 0, 422112, 0, 70975, 0, -583343, 0, 357301, 0, 377466, 0, -343959, 0, 23440, 0, 117578, 0, 158039, 0, -321858, 0, 264269, 0, -243425, 0, -272014, 0, -99774, 0, -864258, 0, -595255, 0, 245750, 0, -330024, 0, -433520, 0, 77280, 0, 376520, 0, 53370, 0, 476597, 0, -1007029, 0, -223541, 0, -222360, 0, -18500, 0, 227778, 0, 251460, 0, -1117091, 0, 304787, 0, -178920, 0, 454882, 0, -527650, 0, -334500, 0, 25396, 0, 21160, 0, 31842, 0, -654048, 0, -371360, 0, 16336, 0, -440, 0, -187775, 0, -248442, 0, -658037, 0, 98383, 0, -130785, 0, -650500, 0, 20522, 0, -18744, 0, 287287, 0, 76000, 0, 644845, 0, -117746, 0, 140874, 0, -564692, 0, 290295, 0, 53085, 0, -260170, 0, -40296, 0, -85649, 0, -242750, 0, -480737, 0, -624411, 0, -61460, 0, 56442, 0, -27135, 0, -127268, 0, 304952, 0, -573126, 0, -676063, 0, 50100, 0, -293219, 0, 344930, 0, 20804, 0, -407992, 0, 19025, 0, -159244, 0, 145944, 0, -418519, 0, -153268, 0, -23000, 0, 58098, 0, 72106, 0, 64066, 0, -425894, 0, -127515, 0, 610370, 0, -58033, 0, -739530, 0, 48561, 0, 104610, 0, 580506, 0, -436854, 0, -707808, 0, -153855, 0, -197520, 0, -113720, 0, -318162, 0, 300270, 0, -138744, 0, 66200, 0, 274989, 0, -72324, 0, 114825, 0, -17503, 0, -200350, 0, -211203, 0, 234197, 0, -229092, 0, -148801, 0, -83610, 0, 614130, 0, -259954, 0, 181396, 0, -744340, 0, 241640, 0, 249772, 0, -372878, 0, -371792, 0, -103690, 0, -70470, 0, -516054, 0, -378184, 0, 489472, 0, 137347, 0, -108450, 0, -1014074, 0, 114034, 0, 233561, 0, 579043, 0, -411910, 0, 581376, 0, 543264, 0, -712653, 0, -461720, 0, 210940, 0, -400991, 0, -150784, 0, -216519, 0, -949550, 0, 205475, 0, -289125, 0, 119299, 0, 305089, 0, 165195, 0, -381360, 0, 2252, 0, 930510, 0, -228234, 0, 120356, 0, 23000, 0, -694855, 0, -578141, 0, -667560, 0, 140410, 0, -130785, 0, 121978, 0, -207034, 0, 265552, 0, 19969, 0, -451035, 0, -78153, 0, 358592, 0, -564021, 0, 220357, 0, 176560, 0, -394695, 0, 462899, 0, -691028, 0, -51355, 0, 149350, 0, 172874, 0, 523400, 0, 61295, 0, -128792, 0, -43800, 0, 597666, 0, -99432, 0, 315960, 0, -219656, 0, -113280, 0, -485828, 0, 441054, 0, 105057, 0, 338453, 0, -264885, 0, 251195, 0, 188523, 0, 412540, 0, 370589, 0, -82530, 0, -414427, 0, -32732, 0, 87018, 0, 345492, 0, 1070, 0, -31602, 0, -826047, 0, -1012367, 0, -653725, 0, 63150, 0, -404464, 0, 43730, 0, 509130, 0, 403862, 0, -217930, 0, -760708, 0, 394388, 0, -422876, 0, -188835, 0, 29195, 0, 66824, 0, -405328, 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": "920.4.a.c", "char_is_minimal": false, "conrey_index": 1, "id": null, "nf_label": 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, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [9, -2, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 1, -1, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-6, -1, 0, 0, 1, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [10, -5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 1, -1, 1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [15, -1, 0, -1, 2, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-17, -9, -4, 6, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [23, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [25, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [54, -2, 5, -3, -3, 0, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [9, -8, 2, 3, 3, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [32, 7, -2, 0, 3, 2, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0], [42, -6, 8, -7, -2, 5, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [15, 5, 0, 5, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-15, -10, 1, 0, 3, 0, -2, 1], [0, 0, 0, 0, 0, 0, 0, 0], [29, 14, 0, 3, 0, 3, 4, 1], [0, 0, 0, 0, 0, 0, 0, 0], [49, -20, 2, -4, 0, 1, 5, -1], [0, 0, 0, 0, 0, 0, 0, 0], [59, 14, 1, 4, -7, -1, -6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [45, -10, 5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [125, 8, 4, -1, -1, 2, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [77, -16, 2, 11, 1, -5, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0], [40, 19, 3, -1, 1, 6, -5, -2], [0, 0, 0, 0, 0, 0, 0, 0], [20, -26, 0, -2, -6, -1, -7, -2], [0, 0, 0, 0, 0, 0, 0, 0], [25, 0, 5, -5, 0, 5, -5, 0], [0, 0, 0, 0, 0, 0, 0, 0], [52, -24, -2, -10, 1, -5, 2, -1], [0, 0, 0, 0, 0, 0, 0, 0], [159, 1, -6, -2, 4, -13, 4, 2], [0, 0, 0, 0, 0, 0, 0, 0], [62, -41, -17, 9, 2, -9, 14, -6], [0, 0, 0, 0, 0, 0, 0, 0], [124, 27, -19, 34, 0, -15, 12, -3], [0, 0, 0, 0, 0, 0, 0, 0], [-30, -5, 0, 0, 5, 5, -5, 0], [0, 0, 0, 0, 0, 0, 0, 0], [220, -25, 11, -16, 11, 6, 9, 3], [0, 0, 0, 0, 0, 0, 0, 0], [46, -23, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [83, 9, -13, 20, 3, -10, -5, 0], [0, 0, 0, 0, 0, 0, 0, 0], [25, -11, 5, 5, -26, -5, -13, 4], [0, 0, 0, 0, 0, 0, 0, 0], [50, -25, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-163, 14, -21, -6, 12, 6, 4, -3], [0, 0, 0, 0, 0, 0, 0, 0], [187, -48, -3, -4, -15, -13, -5, -5], [0, 0, 0, 0, 0, 0, 0, 0], [86, -58, 11, -24, -18, 0, -9, 6], [0, 0, 0, 0, 0, 0, 0, 0], [245, 7, -18, 14, 6, 1, 19, 3], [0, 0, 0, 0, 0, 0, 0, 0], [-10, 0, 0, 5, -5, 5, -5, 5], [0, 0, 0, 0, 0, 0, 0, 0], [318, -97, -6, 25, -13, -14, 2, -1], [0, 0, 0, 0, 0, 0, 0, 0], [48, 23, 1, 14, 1, -15, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [114, -57, -11, -17, -4, 15, -7, -5], [0, 0, 0, 0, 0, 0, 0, 0], [-276, -3, -24, 13, 10, 9, 12, 2], [0, 0, 0, 0, 0, 0, 0, 0], [75, -5, 0, -5, 10, -5, 0, 5], [0, 0, 0, 0, 0, 0, 0, 0], [-315, 56, -9, 15, 20, 3, 21, 6], [0, 0, 0, 0, 0, 0, 0, 0], [341, -90, 37, -67, -3, 16, -7, 3], [0, 0, 0, 0, 0, 0, 0, 0]]}