# Stored data for newform 625.4.a.c, downloaded from the LMFDB on 05 May 2024.
{"label": "625.4.a.c", "space_label": "625.4.a", "level": 625, "weight": 4, "hecke_orbit": 3, "hecke_orbit_code": 9007199321850481, "dim": 14, "is_polredabs": true, "trace_hash": 489061921449222361, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [210176, 1072768, 1065840, -1114088, -885776, 408250, 260815, -68315, -35820, 5595, 2444, -213, -80, 3, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+\\beta _{7}q^{3}+(4+\\beta _{2})q^{4}+(1-\\beta _{3}+\\cdots)q^{6}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 10000, "fricke_eigenval": 1, "atkin_lehner_string": "+", "analytic_conductor": 36.876193753587884, "hecke_ring_index": 500, "level_radical": 5, "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": 0, "analytic_rank_proved": true, "char_values": [625, 1, [2], [1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 1, "level_primes": [5], "conrey_indexes": [1], "field_disc": 209909212038639041682156397470703125, "field_disc_factorization": [[3, 2], [5, 10], [839, 1], [654839, 1], [306859171, 1], [14166199079, 1]], "field_poly": [210176, -1072768, 1065840, 1114088, -885776, -408250, 260815, 68315, -35820, -5595, 2444, 213, -80, -3, 1], "hecke_ring_index_factorization": [[2, 2], [5, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.257", "prec": 17}, {"__RealLiteral__": 0, "data": "11.942", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "418.392", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "24005.447", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 14, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[5, 1]], "trace_display": [-3, -1, 0, -8], "traces": [0, 14, -3, -1, 57, 0, 33, -8, -60, 143, 0, 103, -143, 139, 154, 0, 269, 107, -276, 165, 0, 208, 24, 39, 390, 0, 293, 740, -859, 415, 0, 493, -693, 478, 379, 0, 894, -313, 1495, 826, 0, 873, 1674, -86, 1044, 0, 343, -2293, -3571, 672, 0, 1003, 2072, -701, 975, 0, 1745, -385, 1580, 1645, 0, 1253, 369, 2104, 1272, 0, 1466, 1097, 1811, 1106, 0, 2073, -7590, -4451, 2424, 0, 1760, 3554, -3932, 1825, 0, 1214, -3381, 3209, 2419, 0, 2593, -935, 6640, 3085, 0, 1878, 8197, 2183, 3234, 0, 5213, -3043, -4084, 3286, 0, 2628, 5884, -5491, 4500, 0, 3278, -418, 5035, 1225, 0, 4598, -1448, 2579, 2095, 0, 4675, 238, -6265, 5664, 0, 637, -4526, -3592, 3999, 0, 5308, 6457, 95, 5936, 0, 6693, -5916, 3640, 6784, 0, 985, -8733, 17363, 4055, 0, 5223, 4624, 4823, 1538, 0, 5768, -443, -1784, 4910, 0, 3348, -1625, -2641, -4452, 0, -1967, 1002, -11515, 5291, 0, 4618, 7947, -3161, 3579, 0, -8227, 787, -6855, -2467, 0, 3045, 142, -41, -11075, 0, 358, 9730, 2845, 6125, 0, -1497, -4301, 12058, -15460, 0, -17869, 2374, -13399, -4160, 0, 5453, -6608, 4554, -6681, 0, -19549, 6047, 9138, -1080, 0, -2997, -24416, 4290, -20286, 0, -13867, 13998, -9311, 4170, 0, -1657, 1512, -27617, -24211, 0, -17160, -22426, 7085, -624, 0, 8628, 13919, 7919, -9161, 0, -32682, -8483, 16380, -4735, 0, 3906, 14170, -5331, -26119, 0, -3690, 5465, 82, 14945, 0, -7257, 22621, 7364, -20826, 0, -37904, 11980, 16090, -5129, 0, 20988, -36208, 373, -9236, 0, -29051, 9722, -36897, 3784, 0, -3815, 18944, -39451, -27090, 0, -5895, -45660, -21294, 2665, 0, 3973, 29777, 22408, -26226, 0, -40977, 15627, 33695, 2311, 0, 12463, 2444, 20299, -8931, 0, -21314, -18736, -2676, -13823, 0, -8217, -27488, 21154, -37796, 0, -435, 17035, 36770, 19281, 0, -7182, -58181, -1832, -25195, 0, -27647, 9722, -27238, -4119, 0, 16523, 5355, -17691, 974, 0, -18640, -4063, -50827, 4500, 0, -12452, 20464, -11175, -32943, 0, -3177, 9900, 8825, 13774, 0, -6447, -26163, 9734, -35221, 0, -17602, -21103, 4149, -1814, 0, 22706, 3310, -970, 18965, 0, -5362, 39657, 40600, 3730, 0, 3655, -4376, -7471, -33225, 0, 27535, 22624, -35425, 20895, 0, -14731, 29679, -24638, -4016, 0, -53209, -26093, 19839, 2916, 0, 13098, 7129, 17959, 14438, 0, 18465, 20130, 13620, 12845, 0, -16792, -11526, 9399, 7185, 0, 2723, -30482, 20096, 14755, 0, 34068, 61085, 29593, -22501, 0, -12642, -38633, -43410, 5090, 0, -4022, -18336, 3178, 21964, 0, -10175, 17789, 440, -6395, 0, 23758, 23732, -26620, -27644, 0, 24838, -22390, -22940, 33985, 0, 10303, -26021, -28291, 5105, 0, -1174, 32584, 35801, -11443, 0, 35373, 3815, 15199, 15558, 0, -33225, 16230, 65393, 40625, 0, -5271, 20774, 38324, -20391, 0, -7212, -36180, -8469, 4540, 0, 15941, -8433, -80362, 4244, 0, -15215, 24562, 9625, 19045, 0, 44423, 15178, 2149, 7100, 0, -2047, -4633, -13741, 25934, 0, 52378, -69925, -67592, -30345, 0, 19682, 71563, -63745, 39125, 0, 26343, -107446, 89308, -9299, 0, -26532, -39563, 48035, 37216, 0, 16563, 50094, 8985, -4405, 0, -2117, -10506, -14647, 27610, 0, 41073, 7459, 42799, 42710, 0, -3594, 28728, 48586, 65015, 0, 45918, 10012, 18935, -25666, 0, 53878, 6794, 18662, 40746, 0, 36223, -75985, -28621, 41669, 0, -20282, -8031, -77862, -11247, 0, 58090, 15385, 4293, -12010, 0, 71280, -28095, 89265, 34289, 0, 14693, 141924, -42957, 3689, 0, 15381, -16503, -156164, 62276, 0, 79075, 120040, -64540, 11644, 0, 245, -121678, -21732, 58106, 0, -30509, -51496, 24199, 53479, 0, 14358, 7612, -14725, 35085, 0, 9573, 28524, 50298, 4238, 0, -6396, 105507, 65116, 51836, 0, 54268, 16764, 20988, 54025, 0, 49993, 14177, 126681, -21215, 0, 79293, -22718, 85224, 97190, 0, 102600, -87030, 27758, 68950, 0, 11248, -9121, -20461, 12104, 0, 62331, 56942, -4670, -61850, 0, 34438, -8923, 6099, 107204, 0, -49740, 39317, -69167, 18325, 0, -5695, -67906, -107790, 42006, 0, 85628, 13735, -79624, 87764, 0, 203, -108095, -28442, 44839, 0, 66693, -5263, 18080, 14871, 0, 51873, -24481, -89026, 61469, 0, -31910, 55297, 59160, -46675, 0, -15064, 29157, -11101, -44420, 0, 49073, -61682, -12393, 13415, 0, -9007, 7334, 20543, -29850, 0, 6333, -17620, 53946, -57874, 0, 74681, -52241, 57309, 51914, 0, -37676, -39113, -6877, -3216, 0, -104162, 84168, 78879, 38270, 0, -33905, -86365, -34931, 37186, 0, -69977, 73122, 47798, -103291, 0, -61035, -53176, -129465, -46439, 0, -55032, 10960, 30360, 36044, 0, -8022, -60436, 13870, -85215, 0, 38455, 19715, -54672, -97612, 0, 70425, -12910, -24630, 73725, 0, -76322, 106247, -1082, -79951, 0, -45161, -89893, 84165, -154777, 0, 44898, 158939, -50071, -8946, 0, -117357, 91704, -131547, -4185, 0, -128435, -96526, 47484, -156850, 0, 4503, 98333, 101042, -12526, 0, -4422, -141928, 7378, 10885, 0, -94535, 10462, 35255, 50387, 0, -16387, 68084, 5050, -55906, 0, 24933, 19105, -491, -81345, 0, -106422, 12857, -4531, -100034, 0, 8960, 33674, -41210, -31260, 0, -70854, -60366, -8885, -145188, 0, -44204, 52537, -199479, -151044, 0, 55588, -161300, 32633, 99829, 0, -71695, 51957, 133435, 16349, 0, -116810, 61984, 57763, -36246, 0, -46614, 250715, -93085, -14045, 0, -74527, -41475, 26293, -16772, 0, -113732, -41960, 109210, -130734, 0, -52667, 56509, 88749, -26605, 0, -42035, -262063, 46864, -67095, 0, -19382, 9922, -194059, -91125, 0, 61860, 95825, -88895, 52435, 0, -163371, 43069, -236797, 101899, 0, 78918, 41116, -63456, -183349, 0, 58703, -88701, 92439, -38872, 0, -39220, -157248, -124, -121475, 0, -212494, -63011, 11809, 78605, 0, -202, -77053, -70823, -125100, 0, 37338, 197905, 171209, 89175, 0, -17907, 29087, 157520, 105436, 0, -40597, 115322, 51479, 143104, 0, -11467, -20973, -154200, -177496, 0, 10498, -167528, 117825, 3005, 0, -30880, -43029, 171990, 17785, 0, -124797, 8638, 87468, -202020, 0, 191, 84222, 5356, -184524, 0, 100253, 2805, 128, 48414, 0, 30505, 89584, 62560, 18865, 0, -176532, 201884, 5568, 73958, 0, 81453, -238717, 32495, -51505, 0, -83865, -76563, -254742, 122564, 0, -99075, 55617, -230028, -23304, 0, -65077, -337301, -217207, -76035, 0, -14374, 231657, 260820, -189379, 0, -46117, 2570, 62449, 65231, 0, 142125, -88645, 109285, 119584, 0, -162243, -95686, 27734, -114776, 0, -99684, 40657, 236960, -38030, 0, 101823, 101062, 166980, -34831, 0, -34112, 41477, -172947, -116445, 0, -143930, 183909, -30941, -164610, 0, 57155, -41846, 89565, 41696, 0, 22013, 167109, -93967, -149727, 0, 10173, -88363, -102010, 71885, 0, -2324, 87539, -33940, 278279, 0, -35222, -43595, -14126, -41505, 0, 34018, -48636, -7791, -55144, 0, 7880, 136568, -28845, 137595, 0, -192077, -5926, -99309, -225883, 0, 46075, -187780, 264571, -288250, 0, 56373, -8345, -195311, -84242, 0, 94877, 96534, -71357, -21165, 0, -151447, -294056, -56400, 52765, 0, 83053, 3360, 58605, 88700, 0, -125842, -143863, -46436, 82658, 0, -75714, -130376, 32034, 16141, 0, -35807, -43480, 91609, 112040, 0, -4009, 146384, -40880, -212305, 0, 30048, -85608, -7200, 96475, 0, 27645, 200730, -156148, 177036, 0, -51202, 44719, 204239, -16986, 0, -66954, 40137, -87049, -306506, 0, 131553, -191036, 93894, 283159, 0, 90745, -125063, -140087, -34786, 0, -133927, 85240, 205489, -240539, 0, 232095, 111335, 219306, -82855, 0, -19014, 32570, 103358, 239159, 0, 139488, 35327, 150483, -60434, 0, -1710, -89792, -43731, 413489, 0, 108358, -262213, -225315, -15065, 0, -25315, 250577, -279962, 220354, 0, 151598, 289285, -71710, 44209, 0, -96482, 155899, -219056, 107670, 0, 6586, 88724, -306398, -416719, 0, 244498, 338660, -42251, 61284, 0, -154464, -212525, 328128, -96520, 0, -37750, -32866, 106019, 82529, 0, 201146, 119200, 5704, -2306, 0, -63217, -258453, -22927, 154399, 0, -111505, 127214, -88695, 133461, 0, -36827, -63726, 175004, 246704, 0, 174843, -10903, 97530, 77140, 0, 7793, 68195, 263614, -114840, 0, 136033, -189170, -173055, 154275, 0, -196412, 157209, 106698, 149469, 0, 205378, 72529, -89385, -111213, 0, -3192, -245131, 320579, -81396, 0, -69405, 221297, 184595, 8176, 0, -82039, -174991, -149221, -118745, 0, 160713, -214980, -361874, -156545, 0, 145523, -140836, -181206, 120884, 0, 137478, -34643, -289065, 209290, 0, 39258, 24575, -250447, 34389, 0, 52160, 59110, -68107, 72650, 0, 128150, 319602, -200840, 353400, 0, 295635, -355595, 74307, 376315, 0, -69812, -266861, 282983, -63155, 0, 241731, 137774, 4121, -65415, 0, 218826, -301150, 38425, -151896, 0, 246190, -1523, -177722, -75955, 0, -283784, -137286, 83989, -82631, 0, 264578, -35149, 159735, -28545, 0, 12483, 166380, 26733, 262434, 0, -174511, -250983, -33910, 279251, 0, 10858, 361558, 233939, 190540, 0, 204343, 34912, 239840, -36422, 0, 121485, 177719, 169438, 441791, 0, 200082, 205420, 68910, 234945, 0, -41387, -195031, -233930, 87214, 0, 169626, 45837, -4061, 19696, 0, 185616, -2033, -49692, 111545, 0, -216505, 111924, 321608, -172494, 0, -218260, -82332, -213455, 491289, 0, 325403, 64800, -290479, 21925, 0, 140148, 301560, -253319, -106046, 0, 269598, -100285, 79107, -8124, 0, 174023, -99806, 53855, 466868, 0, 219343, 16747, -53180, -195463, 0, 234548, 166405, -24521, 583700, 0, 109078, 173942, 85043, 375804, 0, -52877, -9841, 31218, 257665, 0, 214176, -147940, 240456, -111374, 0, 304958, -51555, 63880, 137408, 0, 295925, -901, -113932, -193810, 0, -116707, 146599, -252567, -122915, 0, -249615, 227354, -15690, -242285, 0, 75923, -181853, 105174, 164728, 0, 171355, 195945, -95460, 125222, 0, -74805, -4900, -275451, 373735, 0, -32669, -29033, 9672, -55815, 0, 258065, -234780, -128461, 331805, 0, 136375, 46695, 132505, 309535, 0, -28124, 188909, -276837, -253578, 0, 214841, -190543, 70025, -157694, 0, 61038, -199589, -199861, 201039, 0, 2863, -103581, 200679, 174475, 0, -439422, 150974, 173790, -579020, 0, -210617, 31888, -88229, 83141, 0, -123677, -71688, 416408, -117002, 0, 214713, 214504, 150675, -178430, 0, -82627, 40455, 163069, -266601, 0, 169488, 171287, 88913, -48795, 0, -26654, -5758, 393524, -221764, 0, -61540, -310710, 70252, 99060, 0, 14115, -24711, 342619, 355359, 0, -11599, -6641, 381555, 154701, 0, 93193, -36135, -171560, -211176, 0, -114845, -141361, 264626, 113709, 0, -293134, -55336, -48671, -574226, 0, -108170, -137740, -219930, -117215, 0, -72217, 76717, -95882, -483285, 0, 33798, -96815, -89130, -42690, 0, -112162, 40149, -203026, -168015, 0, -225392, 373024, -149246, 52640, 0, -88379, -117493, -239491, 30988, 0, -90140, -258812, -288360, 220495, 0, -31752, -294002, -370067, 370084, 0, -86915, -265693, 22421, -438134, 0, 173193, 349789, 85617, -269996, 0, -253515, -113125, -93052, 58025, 0, -120244, 257039, -27041, -48554, 0, -537149, -225212, -507954, -400426, 0, -148962, 1235, 242335, 414374, 0, 103005, -113253, 105992, 161047, 0, -84802, -228335, 331490, -786636, 0, 147536, 255632, -259810, -236925, 0, 23945, 400989, -53531, 109920, 0, -77592, 5964, 360085, -132445, 0, 46623, -160921, -180482, 188950, 0, -42784, -444043, 485932, 135411, 0, 197888, 56344, 18918, 211200, 0, -26850, 184207, -22862, 10380, 0, 52213, -118136, 5533, 119369, 0, -484122, 140185, 385699, -409111, 0, 9393, -206015, 253540, -246721, 0, -499780, -11908, -94965, -551130, 0, -38524, 498109, 17309, -229775, 0, 117097, -394033, 35065, 24565, 0, -26772, 54320, 243900, 215345, 0, -233265, 326546, -13835, 53691, 0, -247753, 246232, 417103, 328739, 0, 8591, -34386, -138880, 136206, 0, 50610, -165268, -89346, -672158, 0, 151818, -20133, 146828, 10380, 0, -175142, -193561, 45448, 348615, 0, -328557, 202475, -335153, -196215, 0, 30050, -27563, -414587, -669611, 0, -554834, 41484, -595405, 457256, 0, -50577, 530058, 4949, -331841, 0, 51233, -106366, 205960, -356400, 0, 112278, 12257, -294251, -328341, 0, -448615, -6252, -80540, 485594, 0, -84557, -113196, -228652, -733745, 0, 30333, 483067, 356290, 233237, 0, 137193, -434690, -95551, -169571, 0, 176815, 324, -721382, 367455, 0, -83492, 110324, -85702, -318928, 0, -357172, -145830, 197360, 131710, 0, -138494, 269927, 578339, -352326, 0, 61823, 289767, 179512, -370684, 0, -176487, -63996, 177979, -892170, 0, -249865, -16673, -328775, -123175, 0, 152070, 19417, 280743, 214142, 0, -807385, -115020, -51305, 234584, 0, -165392, -127396, 188078, 115978, 0, -12239, 475015, 43504, 172875, 0, 89343, -150296, -357219, -261431, 0, 100240, -573630, -270797, -167396, 0, 18248, 537119, -7631, -441900, 0, -633074, -275820, 439716, 106170, 0, 78463, 82165, -392427, 4823, 0, -245100, 102024, -81685, -15144, 0, -381012, -99496, 164535, 217014, 0, 24171, 544357, 124250, -349252, 0, 298143, -456803, -333000, -692344, 0, -419920, -214585, 44945, -302679, 0, 139343, -31245, -235116, 469915, 0, 175136, 311817, -668369, -463200, 0, 314183, 9253, 161519, -175426, 0, 67112, 303697, -2122, 604315, 0, 115185, -466776, 206670, 572229, 0, -49274, -270061, 65090, -307845, 0, 354266, -206186, 237553, 49224, 0, -274695, 81654, 363353, -264394, 0, -216292, -893311, 351743, -670956, 0, -304267, 214252, -451491, -218734, 0, 409358, -485190, 12549, -10490, 0, -115100, -303575, -56958, 133350, 0, -96642, 64516, -127822, 447639, 0, -634792, -264096, -401515, 126646, 0, 26413, 108899, -337741, -101006, 0, 47057, 258450, 153260, 236664, 0, 13373, 268719, -8665, -690510, 0, -426810, 439695, 356641, 103000, 0, 102658, 508674, -8962, 243054, 0, 408973, -325575, 297300, 340211, 0, -461782, 458345, -639692, -1062791, 0, -452957, -976466, 187928, 367620, 0, -59445, 314895, 232739, -200817, 0, -187390, 127590, 449163, -220565, 0, -38902, 25259, 396108, -206726, 0, 60786, -788163, 12972, 155511, 0, 335556, 119620, 223194, -1156731, 0, 251175, -330223, 570125, 505680, 0, 185885, -260862, -409931, 904474, 0, -525720, 605408, -465270, 403269, 0, 49603, 845272, -328129, -77235, 0, -5702, 85327, -1110110, 602056, 0, -155582, 318514, -539634, -905260, 0, 685953, 33237, 109499, -383335, 0, -32892, 272082, 140960, -744309, 0, -219330, -329716, 297095, 298005, 0, 89738, 293804, 135364, 456719, 0, -42348, -329035, 186155, 257451, 0, -89552, -48450, 101309, -202945, 0, -192600, 204346, -354225, 141655, 0, 169175, 327019, 361419, 637061, 0, -822562, 412681, 171142, -472305, 0, 531650, -615455, -491332, 63598, 0, -162797, 230649, 232195, 371760, 0, 404883, -249851, 667429, -119896, 0, -214040, -124023, 82045, -63655, 0, 1461, 359042, 370908, 779090, 0, 89298, -232947, -136520, -35330, 0, -104989, -35196, -19432, -598335, 0, 177473, -172358, 13992, -212435, 0, 215673, 514464, 111709, 158613, 0, 446684, -431180, 637028, -45609, 0, 286826, -136156, 173628, 1028880, 0, -513377, 237210, 83285, 130955, 0, 464663, 279579, 302615, 316838, 0, 482300, 18497, 370655, -202103, 0, 32463, 294124, 87574, 183094, 0, -158210, 80, -985855, -272656, 0, 574760, -311135, -286251, -495060, 0, -464548, -86395, -360442, 118974, 0, 274893, -47366, -610862, -116001, 0, 706793, -101476, -227260, 345216, 0, -179442, -178546, 306798, -224661, 0, -428865, 540864, 343102, 341545, 0, -262982, -884046, -168275, 622755, 0, -532562, -267625, 184121, 196170, 0, 238798, -390748, 270598, -29651, 0, 303093, -138640, -98628, 224591, 0, 174071, -76856, -512621, 229785, 0, 231713, 444512, 222623, -189413, 0, -128109, -359755, -6261, -482870, 0, -720745, 529510, 494215, 392044, 0, -1417, -1111752, -684425, 305965, 0, 641706, 273389, -734479, 33366, 0, 250818, -653120, 41360, -1054196, 0, 169793, -28293, 594713, 470825, 0, -108725, 289780, -283616, -636402, 0, -336802, -350946, -1035710, 199981, 0, 272118, 467807, 161998, 635584, 0, 613018, 335899, 284495, 843726, 0, -26390, -234995, -223852, -583595, 0, 200676, -272143, 334301, 266835, 0, 497188, 160139, 235309, -816185, 0, 143660, 574051, -312358, 288896, 0, 23693, 146024, 937478, -285131, 0, -39602, 616957, 711318, 227130, 0, 61895, 1195404, 394564, -316647, 0, 157420, 219217, -139107, 580880, 0, 264965, -307171, -230119, -11822, 0, -400252, -289325, 379026, 233885, 0, 172183, 102635, 55964, 728490, 0, -116402, 370484, -865155, -145554, 0, 115341, -473235, 100188, -466631, 0, 60598, 63620, 206875, 290034, 0, 304648, -626726, 182129, 832285, 0, -146862, -535205, 1191937, -304085, 0, 283183, 563944, -315019, 1023015, 0, 573766, -172253, 514881, -79130, 0, 345628, 449562, 16078, -768112, 0, 424900, -112978, -324082, 387564, 0, 288488, 220819, 476830, 1479754, 0, -218647, -289642, -308249, -168464, 0, 441773, -500538, -727962, 557084, 0, 747450, 853427, -385130, 494067, 0, -69687, -475371, 422639, 372560, 0, 768743, -323242, 804955, 73675, 0, 812753, 451315, 330984, 368520, 0, -169985, -568196, -734400, 225560, 0, -182946, 1003804, -469035, 226704, 0, 216061, -89815, 427380, -180413, 0, 892663, -352158, -305760, -619252, 0, 826043, -818183, -44974, 70775, 0, 69475, -102166, -213551, 1393210, 0, -985452, 125940, -208209, -126456, 0, 401681, 417345, 74348, 709189, 0, 80625, -346693, 466613, 1066021, 0, 311723, 628848, -36900, -350036, 0, 424453, -72733, -65551, 152435, 0, -240220, -531218, -1042047, 935975, 0, -39150, -182210, -712845, 264085, 0, 14348, -406441, 439353, -525302, 0, 532263, 294567, -820804, 815216, 0, 522808, 252405, -674461, -227396, 0, 1261225, 319957, 254885, 143024, 0, 508428, 277384, 80363, -562155, 0, -915364, 533695, -70875, 396045, 0, -554747, -191900, 372384, 103130, 0, 28383, 260599, 67350, 461779, 0, 705961, -609010, 794539, 532950, 0, 76920, -164945, -109060, 645546, 0, 364498, -191498, 194720, 85115, 0, 284907, 343320, 107580, 742210, 0, -216357, -953741, 504709, -473841, 0, 293166, 197602, 184600, 73111, 0, -163907, -797341, 238880, -1056102, 0, 698540, 365450, 359240, -116035, 0, 254074, -125292, -216206, 778241, 0, -473730, 304963, -66369, 447770, 0, 391338, 634220, -146237, 273114, 0, -124032, -394288, 686220, 407201, 0, -471432, 593308, -241912, 498689, 0, -385502, -724306, 730850, -398986, 0, 219598, -515758, -72647, -270218, 0, -601782, 834500, -315960, 395135, 0, 450990, 953914, -528082, 319910, 0, 558431, -493490, 276976, -668814, 0, 184453, 745287, -153176, -387776, 0, 164810, 153677, -469467, -116079, 0, -380471, -322221, -721950, -656717, 0, 77213, 331295, -417931, -77535, 0, -96552, -1033418, -337747, 1051774, 0, -55080, 370477, -639676, -762615, 0, 305383, 689795, -115442, -221111, 0, -276324, 347434, -1150931, 60735, 0, 4238, -709135, -351221, 894040, 0, -166900, -298802, -196310, -296460, 0, 193570, 1063144, 311243, 338244, 0, -129230, -534813, 1109020, -487189, 0, -87739, -312466, 46560, -1495916, 0, 458223, 443132, -272347, -730395, 0, 22998, 365068, 454069, -405315, 0, -175379, 683004, 289930, 177014, 0, -581047, -443983, -434627, 888958, 0, -237922, -1011783, 749913, 232060, 0, -486152, -354235, 909189, 547708, 0, 191000, 91817, -453040, -4075, 0, -59223, -367333, 516144, -957145, 0, -756365, -103560, -443065, -449250, 0, 120323, 657294, 1268908, 181633, 0, -397918, 42572, 74801, -611214, 0, 313383, 1227605, -198421, -851385, 0, -413438, -854275, -387902, 657735, 0, 81578, 558749, 664750, -490656, 0, -152045, -102920, 541200, -313725, 0, -493157, 758837, 719818, -739956, 0, -528940, 185574, -772169, -108433, 0, -422697, -902796, 290723, -883770, 0, 324938, 228304, -1147450, 418350, 0, 151486, -329333, -659351, 1149979, 0, -676732, 101565, -16778, 343010, 0, -207924, -382846, -826786, -595186, 0, 179041, 145477, -290046, -292543, 0, -638122, 545354, -227120, -618715, 0, -255795, -579593, -59117, -692356, 0, -314835, -787446, -968933, -637550, 0, -414175, -480065, -106548, 535295, 0, 79373, -1279365, -475315, -75472, 0, 666778, 74587, 1321160, 245036, 0, 53778, -738656, -116971, -927251, 0, -129659, 968094, 42765, 274303, 0, -1307202, 828580, 172735, 216458, 0, -748332, 41178, 824285, -573765, 0, -265704, -16446, 234078, -257245, 0, -348877, 74444, 432507, -293823, 0, 750920, -242975, -324861, -644905, 0, -523310, 1008247, -767154, -717521, 0, -572057, -310750, 438164, 1188500, 0, -55017, -476909, -400185, -551302, 0, -641672, -856651, 733919, 2924, 0, 452340, -51038, 288830, -452509, 0, 168923, -333355, -86980, 553345, 0, 424298, -115076, 312285, -877130, 0, -83655, 150495, 913014, 725645, 0, -570765, -414196, 282185, 674065, 0, -195512, 765048, -34863, 257039, 0, 1362956, 216977, -338995, -392930, 0, -100085, -1556181, -942387, 20204, 0, -217277, 452747, 8968, -1103689, 0, -592607, 414604, -336141, -978610, 0, -346312, -829920, -398854, -561595, 0, 160446, -668736, -112907, -515672, 0, -268701, 404087, -141850, -22180, 0, 128403, 704469, -319790, -344636, 0, 216260, -125013, 368913, -128880, 0, -990202, 691002, -576630, 269286, 0, -106405, -494845, -763887, 110375, 0, -411142, 224934, -504315, -188475, 0, -1176439, 696974, 740232, -22159, 0, -210787, -632605, 1393569, -7972, 0, 184630, 492772, -320520, -484910, 0, -60482, 603589, -160051, -499255, 0, -106072, 126146, 661075, 282235, 0, -93947, -478858, 347018, -169406, 0, -89039, -991970, -82430, -1814379, 0, 21316, -29667, -1103920, -895215, 0, -826552, 172195, -310716, 509329, 0, -624577, 244714, -378507, 57860, 0, -620253, 919322, 1266100, 922640, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "25.4.d.a", "char_is_minimal": true, "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, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, -1, 0, 0, 1, -1, -1, 0, 0, 1, 0, 0], [-1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [-5, -3, 0, -4, 0, 0, -1, 0, 0, 1, -1, -1, 0, 0], [11, 1, 0, 1, 0, 0, -1, 2, 1, 0, 1, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 1, 1, -4, 0, -1, -3, 0, -1, 1, -1, 0, 0, -1], [-6, 2, -4, 3, 2, 1, -4, 5, 3, -1, 1, -2, 2, 0], [13, -2, 1, 6, -1, 2, 0, 1, -1, 0, -1, -1, 0, 0], [12, 4, 1, 1, 1, 2, 1, 5, 2, 0, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [17, 4, 4, -3, -1, -1, -1, -4, 4, 1, 0, 1, 0, 1], [10, -1, 1, 7, -2, 1, -3, 2, 1, 1, -1, 1, 0, 2], [-27, -14, -4, -18, 1, -4, 8, 0, -5, 0, 0, 2, -1, -2], [12, -3, -2, 3, 2, 1, -7, -3, -4, -3, 1, -1, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [14, -19, 5, 3, -3, -3, 14, 0, -11, 0, 0, 2, -2, 0], [-18, -13, 9, -50, 0, -6, -3, 7, 6, 2, 1, 1, -1, -1], [14, -10, 6, 25, -1, 2, 9, 1, -6, 1, 1, 3, 0, 0], [14, 14, 4, -5, -2, 2, 20, -19, -13, -1, 1, 2, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [36, -31, 5, 10, 1, -1, 20, -4, 7, -1, -1, -1, 1, 2], [64, -5, 3, 19, 0, -6, -4, 12, 4, -3, 1, 1, 0, -1], [-48, -19, -3, 28, 0, 3, 11, -1, -10, 0, -1, 1, -1, 3], [24, 3, -1, -11, 2, 2, -17, -2, 1, -2, 1, -4, 5, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [45, -1, 6, 16, -1, -1, -16, 5, 3, 4, -2, 0, -7, -2], [-37, -11, -3, 11, -3, 5, -23, 12, 12, 1, -2, -1, -6, -1], [23, -18, -4, -27, 1, -3, 25, 11, -6, -4, 5, 3, 1, -1], [22, -14, 3, -35, 1, 4, 0, 17, 16, 2, -6, -3, -1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [63, 72, 5, 47, 2, -2, -28, 4, -11, -6, 5, 0, 1, 3], [-13, -7, -2, 25, -5, 10, -28, 6, 1, 3, -4, 7, -8, 0], [66, -27, 4, -88, 5, -3, 27, 4, -11, -5, 5, -1, 5, 2], [46, 17, -3, -41, -2, 1, 22, 16, 16, 2, 1, -4, 5, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [89, 28, -1, 44, 2, -3, -20, 0, 19, -1, -2, -7, 0, -2], [176, -14, 0, 83, 8, -2, -26, 23, 15, -5, 5, -4, 0, -6], [10, -21, 4, 18, -3, 3, 24, 15, 3, -2, 2, -7, 3, 7], [37, -26, 15, -67, -9, 3, -68, -15, -2, 11, -5, 4, -15, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [83, -48, -9, 63, 13, 2, 34, 31, 6, -3, -1, -10, 11, 0], [-206, 6, -11, -71, -1, 13, -34, 5, -4, -5, -5, 1, -1, 1], [-149, -38, -17, 180, 1, 4, 7, 9, 3, -4, -3, -13, -2, 1], [26, 20, -13, -62, 5, 4, 13, -3, 3, 7, -5, -6, -5, -9], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [132, -65, -11, 77, -2, -6, 54, -1, 6, -1, 5, 1, 0, -7], [256, -30, 5, 193, -2, 22, -52, -8, 11, 15, -6, -1, -7, 3], [14, -42, 13, 79, 2, -20, 41, 18, 15, -3, 8, -7, 8, -11], [10, -73, 2, -121, -11, -1, -21, -13, -18, 12, -6, 15, -19, -8], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [174, 54, -8, 128, 4, -5, 29, -13, -10, -16, 11, -13, 29, 7], [-127, 13, 7, -187, 18, -12, -12, 16, -14, -9, 11, 0, 18, 4], [35, -64, 19, -168, 1, -2, 24, -23, -13, 2, -5, -1, 0, 5], [57, 52, -5, -76, -5, -8, -13, 19, -16, -9, 11, -3, 1, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [132, 67, -19, 93, -6, 4, -73, 23, 23, 10, -3, -3, -1, -1], [-61, -72, 29, -191, -9, -34, 24, -31, 0, 5, -1, 2, 1, -2], [22, -51, -24, -290, -7, 10, 8, 1, 13, 21, -4, 24, -22, -9], [-8, 0, 2, -161, -7, -19, 62, -20, -32, -8, -5, 4, -6, -5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [196, 33, -33, 235, 8, 16, -40, -3, -37, -11, 11, 16, 0, -8], [166, -32, -9, 181, -6, -16, -16, -26, -18, 6, -6, -3, -1, -3], [140, -40, 26, 16, -4, 20, -20, -43, -6, 12, -11, 3, -3, -3], [26, -83, -30, -175, 9, -10, 13, 24, 15, -2, 4, -4, 17, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [238, -38, -15, 181, -13, 21, -40, -61, 4, 13, 3, 11, -17, 1], [-675, -8, -40, -272, 1, 2, 8, -20, -3, -8, 4, -18, 17, 14], [-229, -49, -1, 140, 8, -21, 38, -6, 10, 8, -7, 10, 3, -5], [51, 6, 13, -287, 7, -36, 88, 58, 40, -15, 4, -9, 22, 9], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [237, -50, 0, 217, -4, 23, -50, 12, -19, 20, -3, 10, -13, -1], [325, 54, -39, 185, 9, -29, 22, -11, -28, -21, 9, -12, 33, 4], [-121, -29, -20, 338, -11, 41, -49, -57, -7, 16, -21, 21, -26, -1], [72, 105, -35, -107, 17, -1, -36, 31, 35, -22, 12, -4, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [192, -22, -30, 164, 3, 15, -38, 55, 41, 3, -13, 8, -12, 4], [-322, -112, 19, -161, -32, -7, 28, -84, -15, 23, -14, 13, -29, -1], [260, 48, -43, 60, -19, 42, -31, -7, 35, 7, -11, 7, -15, -6], [19, -76, -5, -314, 3, -6, 31, -123, -13, 12, -1, 19, 6, -5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [341, -31, 1, 334, -4, 42, 8, -87, -20, 5, -20, 8, -11, 5], [-125, 103, 21, -56, 24, -10, -5, 18, -37, -22, 19, -23, 31, 13], [292, -37, 35, -404, 0, -58, -3, -35, 26, -16, -15, -45, 19, 7], [149, -27, 9, -168, 13, 2, -22, -75, 17, 5, 6, -4, -9, 7], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [146, -3, 14, 66, -19, -9, 106, 25, -49, 14, -14, -9, 5, 23], [685, 29, -2, 281, 1, 54, 40, -93, -44, -1, -3, 24, 13, 16], [195, 109, -18, 49, 16, 1, 13, 67, 65, -17, 15, -1, 13, -2], [28, 196, 5, -323, 7, -22, 33, 41, 20, -24, 14, 1, 25, 18], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [518, 126, 25, 298, -5, -9, 70, 9, 71, -9, 8, 18, -6, -7], [-413, 43, 22, -374, 12, 19, -65, -20, -29, 23, 13, 15, -13, -32], [-176, 53, 16, 310, -8, -19, 21, -65, -12, -14, 29, 21, 17, 5], [180, -51, -28, -78, -16, 36, -30, 53, -10, 1, 15, 44, -17, 12], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}