# Stored data for newform 825.4.a.u, downloaded from the LMFDB on 28 April 2024.
{"label": "825.4.a.u", "space_label": "825.4.a", "level": 825, "weight": 4, "hecke_orbit": 21, "hecke_orbit_code": 90071992614519609, "dim": 4, "is_polredabs": true, "nf_label": "4.4.91035289.2", "trace_hash": 404423371474994068, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-4, 1, 1]], [7, [303074, -7047, -1127, 11, 1]]], "qexp_display": "q+\\beta _{3}q^{2}+3q^{3}+(-4-\\beta _{3})q^{4}+3\\beta _{3}q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 13200, "fricke_eigenval": 1, "atkin_lehner_string": "--+", "analytic_conductor": 48.67657575473601, "hecke_ring_index": 4, "level_radical": 165, "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": [825, 1, [551, 727, 376], [1, 1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 1, "level_primes": [3, 5, 11], "conrey_indexes": [1], "field_disc": 91035289, "field_disc_factorization": [[17, 2], [19, 1], [59, 1], [281, 1]], "field_poly": [19616, 286, -285, -2, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.078", "prec": 17}, {"__RealLiteral__": 0, "data": "3.740", "prec": 17}, {"__RealLiteral__": 0, "data": "0.454", "prec": 17}, {"__RealLiteral__": 0, "data": "36.715", "prec": 20}, {"__RealLiteral__": 0, "data": "6.474", "prec": 17}, {"__RealLiteral__": 0, "data": "540.455", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, -1], [11, 1]], "trace_display": [-2, 12, 0, -11], "traces": [0, 4, -2, 12, -14, 0, -6, -11, 6, 36, 0, -44, -42, 25, -3, 0, -78, 85, -18, 118, 0, -33, 22, -10, 18, 0, -157, 108, 47, 251, 0, -135, 246, -132, 289, 0, -126, 419, -76, 75, 0, -103, -9, 15, 154, 0, -420, 665, -234, 1003, 0, 255, 57, -116, -54, 0, 77, 354, 189, 951, 0, -350, -213, -99, 1538, 0, 66, 266, -629, -30, 0, 1526, 54, -566, 1091, 0, -396, 121, -471, 2567, 0, 324, 9, -961, 141, 0, 1837, 753, -66, 1053, 0, 2150, 460, -405, 2209, 0, 738, -172, -1819, -396, 0, 3004, 867, -2331, 1627, 0, 432, 1525, -378, 2045, 0, 1257, 87, -298, -228, 0, -1193, 225, -1793, 1941, 0, 484, 634, -309, 753, 0, -27, 1721, -4250, 45, 0, 1927, 462, -4803, 1210, 0, -3519, 2611, -1260, 4425, 0, 1995, 716, -275, -702, 0, 1898, 3009, -2767, 1915, 0, 1864, 364, 765, 33, 0, 171, -1198, -4573, -348, 0, 5309, -162, 132, 403, 0, -3931, 4426, 231, 3717, 0, 1062, -1897, 5498, 567, 0, 858, 2853, -4173, -2395, 0, -1973, 7170, -1050, 4660, 0, -639, -935, -4869, -297, 0, 4358, 4614, 1334, 154, 0, -2193, 5156, 198, 801, 0, 798, -1162, 6756, -1887, 0, 1599, -90, -2655, -1298, 0, -1536, 32, 4578, 5859, 0, 162, -5928, 5667, -1698, 0, -140, 3273, -4252, -1195, 0, -8538, 7751, -1188, 6231, 0, 363, -3083, 4767, -1413, 0, -2011, 7701, -3427, 9720, 0, -9696, -242, 972, 766, 0, 27, -12385, 2883, -2883, 0, 10612, 423, 110, -7499, 0, -11182, -2325, 5511, 5413, 0, 2259, -14691, 16878, -198, 0, -4339, 3159, -2274, -5414, 0, 10079, 3315, 6450, -3915, 0, 1380, -10370, 6483, -1215, 0, -7553, 6627, 2465, -6820, 0, 1727, -7493, 2214, -9041, 0, -516, 366, 1943, -5457, 0, -13677, -1188, -14889, -10105, 0, -3886, -1544, 9012, -2556, 0, 2601, -21584, -517, -6993, 0, 5347, 4881, 19927, -4246, 0, -5695, -2936, 1296, -2761, 0, 4575, -22723, -2311, -1134, 0, 4252, 6135, 313, -10315, 0, 1958, 7775, 3771, -3726, 0, 261, -17368, 17309, -894, 0, 1485, -684, -9835, -20267, 0, -3616, -8004, -3579, 10865, 0, 675, -2706, 973, -5379, 0, -39, 5823, 3025, -13092, 0, -6184, 5823, 1452, -15770, 0, 1902, -19531, -6180, -927, 0, 17304, 2259, 10604, -3179, 0, -26959, -21587, -81, 9770, 0, 5163, -9948, 8853, -12750, 0, -3166, 135, 534, -3040, 0, -3431, 15997, 5781, -4890, 0, 1386, -36346, -19517, -14409, 0, 10293, 3630, -31821, -10854, 0, -36664, -4609, -10557, 7178, 0, 7833, 7725, 32181, -3780, 0, -7277, 13275, 836, -20451, 0, -6171, 6208, 5985, -4288, 0, 2148, -42172, -11959, -825, 0, 4540, -2106, -4647, -19680, 0, -13847, 8716, 5694, -14351, 0, 9027, 6972, 22557, -8301, 0, -23612, 5745, -3473, -17677, 0, 1133, 9730, 5592, -15359, 0, 1092, -32650, -16741, 2295, 0, -19960, 99, -18365, -177, 0, -14309, 6252, 513, 9924, 0, -3594, 15919, -165, -13719, 0, -4337, -1044, 14316, 16892, 0, -10970, -4400, 15927, -1694, 0, -486, -39003, -5574, 396, 0, 24095, 1209, 19070, -27051, 0, -1575, -1031, -11793, 29220, 0, 13278, 7036, 12108, 693, 0, 4620, 11151, 615, -32794, 0, -52, 34134, 3186, 24189, 0, -5691, -7315, -20531, 16494, 0, 26271, 1701, 4184, 6983, 0, -15426, -14778, 2574, 9568, 0, 8559, 23551, 29174, -12519, 0, -14374, -7185, 31046, -11033, 0, 8517, 20027, -5919, 25449, 0, 21510, -6668, -6529, -3150, 0, 19969, 13980, 19943, 34918, 0, -24183, 18551, -1917, 9191, 0, -2805, 1915, -27802, -14607, 0, 25585, -891, -13980, 47403, 0, 10847, -627, 13074, 45235, 0, 13842, 2417, 17245, 4002, 0, -8212, 462, 1276, -18614, 0, -18405, 7693, -6579, 36099, 0, 15468, 11337, 48574, 594, 0, 7229, 2403, -7587, 25513, 0, 43588, 25998, 2394, -5912, 0, -3486, 16486, 6220, 20268, 0, -14912, -5661, -7650, -3488, 0, -847, -19935, 4797, -39872, 0, -270, 7297, -35210, -7965, 0, -5637, -3894, 9038, 41479, 0, 22598, 40035, -4608, 24520, 0, 96, -2239, -2079, 13734, 0, -18553, 17577, -22660, 1487, 0, 4037, 20873, 486, -10461, 0, -17784, -4780, -16372, 17001, 0, 1371, -5094, 10113, -4465, 0, 19783, -23266, -420, 47085, 0, 9819, 62889, -13978, -12756, 0, 3850, -3585, -18968, -25724, 0, -32177, 17477, -25614, 77275, 0, 23253, 2343, -49083, -3564, 0, 6881, 18693, 27375, 85060, 0, 28400, -18376, 1089, 10292, 0, -9249, -10815, -58753, 14301, 0, 24588, -4239, 6379, -16918, 0, 3687, -34771, -6033, -1511, 0, 23103, 41691, 48315, -10281, 0, 6555, 29160, -2396, 54868, 0, 44624, 37500, -29088, 2069, 0, -726, 12175, -87470, 2916, 0, 33364, 2298, -76235, 43587, 0, -26540, -2926, 81, 28305, 0, -37155, 53772, -40112, 8649, 0, -19072, -8649, 6919, 21564, 0, 32493, 25155, 31836, -11825, 0, 1269, -27522, 21550, 330, 0, -6218, -22497, -83658, -7484, 0, 35311, 94210, -33546, -76760, 0, -6975, -2170, 43374, 16533, 0, -1006, 16239, -76136, -24655, 0, -16786, -29403, 6777, -39321, 0, -44073, 45559, -15734, 50634, 0, 29732, -594, -8830, 42126, 0, 16313, -13276, -13017, 56475, 0, 9477, -20353, 6226, -6822, 0, -43887, -16242, 766, 2743, 0, 49587, 9640, 30237, -12001, 0, 9945, -23255, -70382, 19350, 0, 30287, -11745, -37964, -8265, 0, 11373, -8151, 4140, 25064, 0, -31110, 22473, -15886, 19449, 0, 4356, -3645, 21437, -7148, 0, 31081, -5967, -22659, -64, 0, 19881, -1331, 7872, 7395, 0, 371, -20460, -9292, 82184, 0, -70549, -94973, 5181, -54434, 0, -22479, 57196, -45323, 6642, 0, -28625, -27123, 43392, -28237, 0, 128762, -70517, -1548, 14750, 0, 1098, 42281, -23807, 5829, 0, -63453, -16371, 7794, -6412, 0, 14281, 83458, -41031, -80227, 0, -3564, 40620, 21757, -44667, 0, 12189, -30315, -12267, 47787, 0, 22000, -99, -11658, 95110, 0, -4632, 1908, -15645, 27036, 0, -29885, -7668, 10571, 32118, 0, -8183, 22848, 7803, -36381, 0, -64752, -14908, 37155, -1551, 0, 77565, -20979, 34621, -16515, 0, 62121, -4759, 16041, -68644, 0, 14643, 68804, 112304, 59781, 0, -17047, -12738, -88783, -38307, 0, -20207, -17409, -17085, -201038, 0, -8808, 29933, 2067, 3888, 0, -53196, -8283, 57956, 59840, 0, -9895, 9106, 13725, 43184, 0, -68169, 30828, 726, -6933, 0, -81937, -3402, 26958, 43395, 0, 13710, -49800, 12756, -11583, 0, 18405, -64807, -30404, 939, 0, -13938, -30945, 76591, -107391, 0, 39836, -25413, 5874, 27537, 0, 23325, 155744, -11176, 11313, 0, -23650, -11178, 28655, -49484, 0, -18736, -109932, 783, -41570, 0, -52104, -5060, 107978, 51927, 0, 75605, -2682, 43478, 118415, 0, -25996, -185784, 4455, 35618, 0, -2052, 85564, -14889, -29505, 0, 18742, -60801, 77362, -24299, 0, -1121, -41392, -10848, -16579, 0, -24012, 65889, -8063, -10737, 0, -4166, 32595, 153893, 56323, 0, 77044, -52086, 2025, -33462, 0, -8118, -40328, -67004, 2919, 0, -12558, -16137, -8621, 66941, 0, 17458, 1892, -117, -78527, 0, 17469, 14958, 101248, 9075, 0, -9390, -39276, 20009, 83577, 0, -99131, -23953, -18552, -60343, 0, 17469, 8421, 3179, 4356, 0, -32606, -47310, -41307, -76362, 0, 32621, 49010, 5706, -217006, 0, -58593, 45631, 147632, -18540, 0, -2857, -2781, 6562, -188166, 0, -33044, -89013, 51912, -93519, 0, 6777, -52387, 37709, 31812, 0, -81833, -9537, 48774, 28297, 0, 22962, 23809, -80877, 24818, 0, -64761, -35445, 25641, -243, 0, -7572, 29310, 79531, 43168, 0, 4124, -38803, 15489, -17897, 0, -29844, -27996, -15263, 26559, 0, 25998, -38250, 35879, -29539, 0, 18919, -39491, -9498, 34862, 0, 405, 89956, 73975, 1602, 0, -4752, -9120, 35262, -277456, 0, 86746, 10633, -10293, -47239, 0, 47991, -16775, 60873, 17343, 0, -91926, -14670, -127287, 105099, 0, -86898, -146971, 4158, -142404, 0, -109038, 156119, -93709, -58551, 0, 48007, -43227, 87433, -22495, 0, -9010, -121924, 30879, -10454, 0, 10890, 65173, 9528, -95463, 0, -193559, -32562, 192888, -9654, 0, 46884, 123451, -109992, -118300, 0, -13827, -11312, -140482, -31671, 0, 38046, 21534, 89824, -75750, 0, 29862, -957, 23499, 10299, 0, 23175, 34537, -9984, 96543, 0, 18664, -11340, 3278, -28685, 0, -466, -56797, -21831, -156928, 0, 39825, -74071, 135733, 2508, 0, 51498, -61353, 28263, -33365, 0, -22705, 107106, -18513, -99399, 0, 18624, 249367, -12776, 17955, 0, -84192, -12864, -143338, -95925, 0, 13123, -79952, 6444, -204402, 0, -126516, 6497, -125115, -35877, 0, -35284, -2475, 228717, 79963, 0, 39382, 5207, 13620, 148505, 0, -6318, -139248, 19723, -13941, 0, -165010, -59040, -56682, -47300, 0, -53796, 93969, -41541, -21351, 0, 26148, -8927, -90639, 17082, 0, 31147, -43053, 20533, -104882, 0, -59066, -83357, 27081, 15434, 0, 20916, 98977, -47433, 67671, 0, -5324, -24903, -105267, -155417, 0, 23282, -168831, -70836, 81055, 0, 17235, -6974, 15761, -10419, 0, 148476, -53031, 95196, -556, 0, 1048, -205267, 3399, 27667, 0, 29190, 12975, -174765, 16776, 0, -18037, -46077, 37850, -8283, 0, 45613, -45314, 3276, -27837, 0, -97950, 32459, 80008, -50223, 0, 113437, 6885, 131788, 294953, 0, 140876, 62844, -59880, 17784, 0, 297, 166262, 21724, -55095, 0, 43971, -531, -163670, 37121, 0, 15293, -18931, -42927, 90470, 0, 18756, -77030, -176738, 1539, 0, 36123, 29772, 46750, 43297, 0, -119506, -7579, -10782, -56947, 0, 47757, -11907, -27303, -495, 0, 28633, -41157, -54686, -75231, 0, 21921, 106178, -13011, -230467, 0, -3132, -23695, 170598, 42948, 0, 54764, 50676, -13868, -86054, 0, -21197, 23112, -32910, -12764, 0, -13200, 46853, -56161, 47781, 0, -112253, -5082, 39381, 89869, 0, 81750, -71982, -1458, 184010, 0, -117009, 52916, 52833, -16722, 0, 20939, 1188, 34537, 39598, 0, 126675, 33980, 72285, -13310, 0, 3627, -188452, 40409, 57210, 0, -53779, -81153, -133288, -122988, 0, 96760, 198558, -4725, 62720, 0, -3093, -23344, -102414, -35379, 0, 38709, 87660, 14888, -53941, 0, 12099, -103873, 39834, 195929, 0, 21108, -28721, 98173, 36324, 0, 38695, 2079, -82868, 269254, 0, -60630, -74687, 13860, 47007, 0, 33453, 124302, 30929, 1845, 0, 163294, -98382, 91996, -48675, 0, 27971, -70723, -156, 94182, 0, 102402, -164220, 94412, 9558, 0, -265962, 72567, -7711, 29490, 0, 96310, 222836, -17073, -123133, 0, -21945, 4374, -49171, -61593, 0, 88296, 49482, -58231, 272618, 0, -106844, -7876, 78813, 43127, 0, 5103, -12581, -18683, 12552, 0, 117267, 20949, 3025, 77223, 0, 33166, -62963, -46278, 122281, 0, -44334, -59576, -141016, 7722, 0, -69994, 28704, 103258, 35348, 0, 106210, 211483, 25677, -111036, 0, 70653, 62197, 94239, 87522, 0, 3907, -37557, -150621, -20819, 0, -20878, 6163, -43122, -106367, 0, -21555, 171171, 83729, 93138, 0, -53478, -33099, 5743, 109417, 0, -97831, 47907, 25551, 376280, 0, 60081, 139884, 30437, -17757, 0, -267305, 76347, -105548, 5499, 0, 41670, 281974, 64530, -21065, 0, -20004, -95239, -269148, -19587, 0, 61720, -9450, 51957, 74507, 0, -151528, -140097, 59907, 184947, 0, 41940, 67684, -16204, 59829, 0, -20504, 104754, -143079, -18037, 0, 60626, 515, -72549, 114481, 0, 55653, -4004, -160352, -5751, 0, 60367, 27573, -21212, 325382, 0, -100517, -120847, -8415, 30651, 0, 5745, 149402, -62144, -83406, 0, 145915, -43821, -67519, -363, 0, 15680, 129037, 76755, 150432, 0, -2673, -122645, 358741, -41940, 0, -31904, 142209, 86504, 63340, 0, 8924, 69585, 32541, 122091, 0, -1881, 44125, -188190, 39222, 0, -84667, 135705, -208222, -75356, 0, -201305, 13178, 41526, 133618, 0, 7251, 47213, -153579, 51735, 0, 240192, 12006, 50303, 232687, 0, -28569, 164830, -24636, 60465, 0, 1386, -93758, -49614, 3828, 0, -2650, -55842, -182253, -91461, 0, 81211, 239248, -55215, -126429, 0, 23079, 115273, 114562, -19737, 0, -68650, 108297, -76132, -262678, 0, -58399, -104509, 46404, -48410, 0, 34011, -310454, -45779, 145722, 0, -20207, 1782, -156339, 276740, 0, 58541, 180667, 21687, -3624, 0, 7209, 33479, -1452, -22761, 0, 82975, 76539, -5559, 197584, 0, -50910, 50540, 130764, -4433, 0, 77994, -180271, -124494, 7182, 0, -204032, -17736, -22052, -57360, 0, 137945, 94131, -10458, 190594, 0, 49458, -15173, 52714, 18660, 0, 43241, 60804, 98482, -241560, 0, 142843, 159227, -44736, 220320, 0, -16983, -48686, 95991, -22950, 0, -72246, -10464, -60926, 94748, 0, 3633, -96776, -2541, -31827, 0, -59805, -4105, 99212, 14391, 0, 68519, -119616, -137373, -40887, 0, 110897, -19169, -810, 138331, 0, 21891, 143275, 43636, -105630, 0, -14502, -23895, -104512, 55460, 0, -152000, 44866, -16911, 31265, 0, -11682, 22149, -185770, 27114, 0, 162873, 124437, -21881, -104249, 0, 12462, 20867, 67794, 103335, 0, 120105, -339797, -146202, -13824, 0, 201470, 73560, -60478, -74697, 0, -29517, 263201, 288, -43723, 0, -6717, -196356, 158485, -6237, 0, -125524, 41202, -185572, 221142, 0, -151160, 212645, -55659, 34774, 0, 52731, 37169, 87184, -67980, 0, -27423, 4461, -306279, -201972, 0, -9438, 29914, 12111, -63648, 0, 62619, 179867, -306046, 1458, 0, -246022, -31383, 112617, -111777, 0, -54437, 6474, -53352, 135808, 0, -14340, -206937, 45903, -49116, 0, -3816, 51003, -107232, -31573, 0, 39546, 378171, 4113, 26345, 0, -15282, -62342, 238578, 30339, 0, 347101, -13395, 101491, 42359, 0, 26197, -68096, 59349, -26943, 0, -69798, 170422, -23413, -1260, 0, 21703, 141255, -142180, -114252, 0, -105704, -319558, 29457, 178895, 0, 188667, -78870, -243996, -41934, 0, 62351, -38268, -119844, -20800, 0, 109760, -29696, 11550, -164504, 0, -10755, -169560, 111854, -56904, 0, 314712, -77172, 64766, -51260, 0, -94806, -64185, -96531, 80943, 0, 52431, -133137, -81425, -76842, 0, 87698, 231825, 94617, 188624, 0, -42440, -65168, 69759, 185992, 0, 7029, 106115, -83770, -147249, 0, 227373, -10692, -49341, -43020, 0, -256779, 10285, 20643, 25981, 0, 56079, -222738, 318068, 82125, 0, 175162, 255180, 53559, -396528, 0, 96155, 204189, 85200, 63060, 0, -55128, -446682, -128773, 3267, 0, 55171, 30876, -379098, -170973, 0, -47555, 198712, -27747, -332230, 0, -32445, -12570, 43602, -176259, 0, -243489, 42903, 55861, 7079, 0, -47938, -219130, 73764, 102174, 0, -12717, -152273, 92574, 19137, 0, -106214, -50754, 8699, -52936, 0, 28732, 540874, 11061, 98344, 0, -104313, -23046, -14674, -18099, 0, -44845, -4533, -7449, -162002, 0, -8555, -134154, 69309, -1694, 0, 125073, -291207, 120175, 144945, 0, 306475, -30843, -26557, 98282, 0, -48108, 7706, 19665, -54772, 0, 87480, -319850, 312306, -7188, 0, 24123, 164604, 17363, -171693, 0, -187868, 47245, 133872, -10115, 0, 112500, -56716, -260613, -87264, 0, -240074, 6207, 237704, -91361, 0, -109871, -559738, -2178, -69084, 0, 36525, 47022, 58311, -262410, 0, 390769, 8748, 103034, -8811, 0, 234993, -90057, 100092, 68978, 0, 6894, -412165, 382322, -228705, 0, -196473, 130761, 123630, -125507, 0, -234840, -38592, -79620, 106615, 0, -8778, -76915, 68270, 243, 0, -342618, 84915, -18542, -194284, 0, 170755, 12782, -111465, 44145, 0, 161316, -205454, 19315, -120336, 0, 348178, 25947, -74316, 39343, 0, -74473, 11394, -57216, -35793, 0, -25947, -211729, 200539, 20757, 0, -149558, 64692, 9147, -296201, 0, -218240, 88246, 97479, -19801, 0, 75465, -170428, -234038, 95508, 0, -147487, -35475, 543774, -291295, 0, -17589, -7845, 3807, -221434, 0, -82566, 184068, -37868, 64650, 0, -269143, 990, 150524, 238348, 0, -72979, 110036, -18654, -4585, 0, -67491, 273095, 29205, -250974, 0, 127690, -22452, 29359, -91164, 0, -467613, 375555, 105933, 14278, 0, 282630, -396434, -3890, -100638, 0, -4535, -230280, 19871, 131476, 0, -105337, -153531, -20925, -224961, 0, -6510, -89388, 25902, 130122, 0, 16896, 49599, 91678, -57108, 0, -190659, -194932, -3018, 70314, 0, 48717, -352, 40650, -228408, 0, 63706, -73965, 251948, -156928, 0, -118701, -153550, -50358, 194683, 0, -88209, 13906, 16467, 20331, 0, 273332, -117963, 364688, -64449, 0, -205269, -22606, -132219, 346164, 0, 136677, 179158, 307068, -47202, 0, -53291, 151902, 45361, -49905, 0, -3788, -107398, 89196, 137091, 0, -1782, -391755, 221584, -26490, 0, 117338, 126378, -275747, -246315, 0, -281543, 65208, 48939, -281323, 0, -39828, 123877, 11755, -39051, 0, -189485, 169425, -62337, -79891, 0, -395276, -284138, 28431, -52428, 0, -61059, -376535, -270434, 18678, 0, -15583, -20466, 354933, 159641, 0, -45528, 157685, -131661, 48113, 0, -48726, 17857, 300809, 2298, 0, -219252, 8229, -56290, -630704, 0, 1540, -124372, 148761, 35931, 0, 28920, -43473, -12216, 90711, 0, -409547, -36003, -399808, 70960, 0, -93350, -28066, 29835, -157038, 0, -69765, -7446, 46772, -211146, 0, 124704, 58050, -123404, 450433, 0, -234521, 481554, 90861, 13145, 0, -35235, 299896, 69441, -113892, 0, -53306, -24795, 182652, 70273, 0, 169472, -333201, 34119, 37396, 0, -24453, -204492, -200565, 12420, 0, 93918, 75192, -101655, -180723, 0, 56904, 141306, -93330, 226321, 0, 67419, -85261, 18692, -47658, 0, 297236, 58347, 267550, -17701, 0, -427323, -535453, 13068, -351622, 0, -10935, -49314, 743838, 64311, 0, -194179, -21444, -124613, -68541, 0, -45302, 140085, 93243, -197498, 0, -17901, -251858, -42789, -67977, 0, -350332, -192, -240733, -85201, 0, -257976, -44730, 59643, -184066, 0, -3993, -35016, 40416, 23616, 0, -241794, 22185, 104881, -320395, 0, 56859, 33913, 1113, -58964, 0, -61380, -514395, 1510, -27876, 0, 380085, 246552, -52437, 67715, 0, -16909, -7832, -211647, -20768, 0, -284919, 125924, -51033, 15543, 0, -404553, -163302, 99699, -78040, 0, 24993, 386, -67437, -35163, 0, 171588, 239445, -231997, -135969, 0, 297400, 19926, -27822, -143080, 0, 22121, -215724, -85875, 380954, 0, -81369, 140934, 72625, 130176, 0, 67322, -84711, 62196, -82504, 0, -86834, 119284, 386286, -286047, 0, -211551, 158248, 37697, -4644, 0, -40568, 44250, 211886, -35821, 0, -273541, 248423, 3294, -106920, 0, 126843, -69983, -101454, -71421, 0, -2673, 17487, -97278, 670098, 0, 212383, 92960, -190359, 4225, 0, -49113, 122555, 248094, 23382, 0, 106656, -19236, 269662, -266111, 0, -328203, -415078, 42843, 237228, 0, 250374, 2662, -371246, -123093, 0, -104625, -240681, -96139, -342658, 0, 159771, -109002, -10692, 43777, 0, 121860, -341825, 272213, 65271, 0, 420162, -134001, -14518, -8426, 0, 138481, 257088, 36567, 106486, 0, -90945, -72604, 306422, -36801, 0, 352436, 143361, -65002, -284043, 0, 244828, -382888, 66000, 215031, 0, -297, 230976, -97575, -34974, 0, 384253, 285330, -202022, -368545, 0, -134335, 136235, -13896, -406823, 0, 5724, -38641, -80726, -46935, 0, 304874, 81108, -31713, 301488, 0, 267750, 150719, -89655, -19180, 0, -23004, -253575, 222313, 31713, 0, -194470, 96354, -101924, -36351, 0, 152300, 464564, -24549, 159665, 0, 68544, -158393, -259843, 23409, 0, -472028, -109143, -285831, 255831, 0, -116732, -321800, -194256, -176444, 0, -44724, -2290, -120216, 111465, 0, 93652, -4653, -98345, 426750, 0, -81196, 6089, 232695, -252574, 0, -62937, 158529, -1210, 103863, 0, 461190, -49545, 6139, -66524, 0, -3661, 602823, 186363, 82489, 0, -14277, 74354, -88534, 48123, 0, -128938, -205932, -205784, -21322, 0, 550718, -640378, 43929, 127796, 0, 206412, -61639, 514637, 336912, 0, 123002, 179343, -321877, 484607, 0, 75822, -41958, -51141, -44449, 0, -38214, 25575, 196031, -266349, 0, 180659, -114921, 82896, -127233, 0, 33347, -181618, -60621, -201492, 0, -52227, 124939, -360725, -51255, 0, -311994, -603114, -157677, -59543, 0, 301812, -215181, -26424, -150482, 0, 89799, -597368, -100029, 6201, 0, 77428, 11664, -1212, 74115, 0, 133814, 179312, -159588, 215192, 0, -24849, 78724, 345271, 173868, 0, -205604, 179520, 56440, -174150, 0, 516950, 161601, -29685, -201608, 0, 27318, 43238, -387764, 41175, 0, 126952, 129552, -185658, 67277, 0, 111021, -744399, -204507, 529280, 0, 92484, -26315, -205400, 2178, 0, -98919, -20799, -138569, 312290, 0, 90429, 635170, -245811, -64530, 0, -10206, 625147, -194668, 80874, 0, 283829, 130185, 77117, -186372, 0, 47729, -485148, 41130, 356323, 0, -149400, 284001, -722037, 38268, 0, -401333, -34749, -62758, 168797, 0, -78947, 425523, 55215, 35700, 0, -194421, 807285, 25014, -91212, 0, 330033, 2817, 362266, 321380, 0, -153629, 676056, -41814, 59554, 0, -92835, 451473, 302253, 229773, 0, -8836, -322173, -660708, 659181, 0, 138714, 63688, 119508, -307614, 0, -76239, -532176, -330050, 17622, 0, -110869, 82611, 268362, 167376, 0, 14028, -205593, 69975, 51026, 0, 467232, -36465, -718948, -33528, 0, -101144, 33939, 229551, -294208, 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": "825.4.a.u", "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, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [3, 0, 0, 0], [-4, 0, 0, -1], [0, 0, 0, 0], [0, 0, 0, 3], [-3, 0, 1, -1], [-4, 0, 0, -11], [9, 0, 0, 0], [0, 0, 0, 0], [-11, 0, 0, 0], [-12, 0, 0, -3], [2, 1, 1, -9], [-2, 1, -1, -2], [0, 0, 0, 0], [-12, 0, 0, 15], [31, 0, 1, 19], [0, 0, 0, 9], [29, -1, -2, 0], [0, 0, 0, 0], [-9, 0, 3, -3], [0, 0, 0, -11], [-15, -2, 2, -26], [-12, 0, 0, -33], [0, 0, 0, 0], [-34, 1, 3, 9], [27, 0, 0, 0], [14, -1, -3, 6], [72, -3, 3, 17], [0, 0, 0, 0], [-42, -3, -3, -15], [92, 0, 0, 61], [-33, 0, 0, 0], [78, 1, -1, 12], [0, 0, 0, 0], [-36, 0, 0, -9], [143, -1, 3, 75], [-4, -2, -2, 31], [6, 3, 3, -27], [0, 0, 0, 0], [-27, 4, -3, -1], [-6, 3, -3, -6], [58, 3, -1, 109], [44, 0, 0, 11], [0, 0, 0, 0], [-100, 2, -10, 15], [241, 1, -3, 151], [-36, 0, 0, 45], [212, -1, -5, -75], [0, 0, 0, 0], [93, 0, 3, 57], [26, -5, -7, 27], [-18, 8, 8, 18], [0, 0, 0, 27], [0, 0, 0, 0], [34, -11, 7, 26], [87, -3, -6, 0], [74, 3, -15, 61], [199, 5, 15, -85], [0, 0, 0, 0], [-74, 4, -18, 36], [-66, -3, -9, -21], [-27, 0, 9, -9], [340, 0, 0, -89], [0, 0, 0, 0], [0, 0, 0, -33], [106, 14, 6, 76], [-202, -1, -3, -88], [-45, -6, 6, -78], [0, 0, 0, 0], [425, 4, 2, 86], [-36, 0, 0, -99], [-94, -20, -2, 96], [306, 3, -7, 70], [0, 0, 0, 0], [-112, 6, 10, -31], [33, 0, -11, 11], [-102, 3, 9, 27], [545, 2, 11, -199], [0, 0, 0, 0], [81, 0, 0, 0], [-10, -3, 19, -34], [-370, 7, -5, -257], [42, -3, -9, 18], [0, 0, 0, 0], [434, -1, 13, -57], [216, -9, 9, 51], [44, 0, 0, 121], [156, -5, -15, -207], [0, 0, 0, 0], [780, -12, 6, 482], [160, 6, 2, 89], [-126, -9, -9, -45], [598, -3, 7, 88], [0, 0, 0, 0], [276, 0, 0, 183], [-41, -10, 32, -12], [-310, -5, 1, 289], [-99, 0, 0, 0], [0, 0, 0, 0]]}