# Stored data for newform 361.4.a.m, downloaded from the LMFDB on 02 May 2024.
{"label": "361.4.a.m", "space_label": "361.4.a", "level": 361, "weight": 4, "hecke_orbit": 13, "hecke_orbit_code": 54043195595555177, "dim": 12, "is_polredabs": true, "trace_hash": 986540919428215097, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [69312, -136800, -37488, 129304, 18132, -39798, -5463, 5259, 774, -303, -48, 6, 1]]], "qexp_display": "q+(-1+\\beta _{1})q^{2}+(-2+\\beta _{4})q^{3}+(4+\\cdots)q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 5776, "fricke_eigenval": -1, "atkin_lehner_string": "-", "analytic_conductor": 21.299689512072362, "hecke_ring_index": 1, "level_radical": 19, "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": [361, 1, [2], [1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [19], "conrey_indexes": [1], "field_disc": 622428011944628295246705009, "field_disc_factorization": [[3, 17], [1259, 1], [3828265672964977, 1]], "field_poly": [87552, 115776, -80856, -110145, 31905, 35973, -7080, -4893, 846, 287, -48, -6, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.971", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "276.283", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11982.487", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 12, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[19, -1]], "trace_display": [-6, -18, 12, -3], "traces": [0, 12, -6, -18, 36, 12, 24, -3, -75, 54, -84, -39, -219, -6, -108, -261, 48, 75, -132, 0, -99, -288, 63, -30, 1086, -168, 639, -870, -357, -582, 522, -591, -231, 213, -1152, -948, -228, 36, 0, 168, -552, -600, -411, 1371, -1935, 1569, -1728, -738, -1908, 639, -1788, -705, 24, -1428, -1938, -522, -2319, 0, -1410, -2640, 132, -1320, 1953, 171, 1785, -2433, -3732, -1974, 438, -1767, 2991, -2178, -3306, -1524, -297, -666, 0, 1893, 462, -3864, -1632, 672, -516, -1071, -1437, 1953, -2934, -759, 1101, -4263, -57, -1278, 2556, -1224, 543, 0, -795, -294, 4731, 1320, 186, 1296, 1353, 237, 294, 2283, 1215, -1158, 6858, 4506, 4017, 84, 2541, 336, 0, 2262, 4029, -1215, 4065, -6660, -321, -3483, 5739, 5877, 9678, -1311, 8910, -5628, -2400, 2595, 3192, -1788, 8805, 0, -7578, -1737, 4206, -1008, 738, 438, 51, 4827, -912, -3282, 171, 5193, -1842, 3702, 17040, 1212, 8187, -408, 0, 6591, 16182, -4488, 2055, -8790, 7239, -15087, 16503, 7632, 21603, -6369, -465, 165, 405, -2790, 11826, -5166, -873, 0, 3264, -10188, 10692, 2943, -15744, 8754, -5283, -1539, 1278, -1116, -8763, 1449, 4002, -7212, 16545, 3012, -471, 393, 0, 5292, 10329, -4185, 6693, -7365, -150, -3789, 21735, -768, 3750, 4188, 3636, -9354, 2238, 8337, -1521, 897, 5649, 0, -13614, -2391, 7971, 2835, 6987, 7116, -1254, -1287, -3387, -7665, 2640, -645, 18354, 1056, -20802, -2079, 18645, -5028, 0, 6588, -3744, -15042, -14670, -5238, -16308, -5679, -19521, 13122, 2520, -12189, 5229, -5898, -3420, -3468, -1479, -20748, -1548, 0, -11307, 3327, 5637, 1764, 23388, -9150, 39903, -25725, -12864, -9078, 25839, -7662, 1065, 8076, 2325, -15576, -9036, 6444, 0, 14280, 9750, -9744, -6273, 15222, 6501, 3540, -11475, -6531, -13122, 18327, 5232, -19557, 22782, -40848, 3963, -1374, -11340, 0, -5562, -40332, 4098, -14967, 7020, -13080, 5700, -7191, -20340, -19131, -14922, -8454, 22896, -32775, -8640, -6744, -1851, 1104, 0, 14520, -1089, -8274, 16380, 6228, -20565, 18525, -11703, 17292, -22770, -5475, -28674, -5652, -2661, -14706, -34725, 3522, -11268, 0, -25872, 5142, 63, -18855, 32565, 21162, -11859, -21303, -38028, -28632, 17799, -35865, 9171, 15210, -27957, -13569, 7362, -36837, 0, -777, -45354, 8418, -2052, 8652, -30468, -447, -4596, -16326, 13797, 2919, -37527, -11538, -44181, 22809, 17460, 3942, -5385, 0, -10344, -4020, -25092, 1233, 20256, -11946, 43296, -4713, 6402, -9000, -20910, 11265, -25524, -1329, 315, -8535, -23316, 8052, 0, 28404, 18000, -21180, -8595, 1872, 43725, -9174, -99, 15060, 17757, 6711, 25251, 30843, 18360, -21585, -504, 16116, -13992, 0, 6069, 10506, 25797, 26460, -23007, -3795, -19647, -20814, 18867, 11706, -29199, 1611, -1032, -3786, 8208, 34680, -4047, 45279, 0, -37965, 33795, 20760, 23499, -3528, -17655, 31014, 5844, -25476, -17364, 45060, 17811, -42864, 50637, 37980, -46407, 27411, 47649, 0, 17673, -13782, 18393, -26919, 4788, 15924, -68799, 70341, 36108, 39978, 45555, 46653, -3633, 4035, -13746, 49002, -8820, -10443, 0, 21690, -46239, -4962, -18264, -22110, -9417, -27747, 31716, 18843, 25224, -58605, -1671, 50892, -16371, 59943, 43380, -39936, -4113, 0, 7554, 78735, -2046, 65388, -59583, -16392, 40149, 27303, 57777, 43533, -25536, 14187, -22446, 38136, 52326, 2421, 35490, 7968, 0, -44613, 52674, 50580, 8967, -6270, 77271, -14349, 2205, -6768, -1653, -19557, 20994, 50637, -37422, -35466, 35265, 33792, 636, 0, 32184, -26928, -58170, -53724, -108891, 13155, -83337, 50019, 7347, 25464, -12534, 84066, -588, -46656, 62553, -10914, -29421, 8025, 0, -31098, 20583, 16362, -15108, -11505, 31707, 9708, 6990, -25650, 14622, 8925, 25848, -4644, 8715, 65289, -5199, -5511, 24018, 0, 72666, 86256, -50382, 75756, -45717, 23124, -95481, 1077, -14469, 62466, -21222, -57243, -36666, 72984, -53307, 35913, -28074, -24429, 0, -58020, -73755, 28230, 22953, 12561, -3447, 11643, 14337, -24198, 10716, -17571, 38283, 26358, -68976, 64302, 6414, 82875, 12450, 0, 70902, 36306, 50583, -38304, -38625, -24117, 23055, 122745, 52590, -44664, -9633, 11625, -53952, -48570, 32676, 16854, -10434, -8658, 0, -31341, -61998, 3519, -56406, -21828, 38880, -5673, 15315, 17958, -52284, 11214, -34854, 77163, 80262, -76872, -24705, -51972, -19749, 0, -26703, -17568, -39273, 43206, 41265, -41469, -12597, -73083, 22290, 77646, 46359, -87129, 32073, 17688, 6741, -74718, -19038, 14274, 0, -23142, 18771, 52506, -25302, 64242, -54111, 85263, -52752, -108939, -76035, 27342, -10176, -49611, 56838, 19392, 17133, 21078, -41706, 0, 2844, 4857, -49191, -55713, 88446, -59772, 55134, 3408, 6180, 30720, -14559, 81261, -111264, -89634, -47025, -38337, 20253, 14157, 0, -4884, -70059, 87612, 81747, 12135, -44160, -38358, -125406, 3891, -88149, -28233, 2877, 76857, -50724, -91653, -8418, -86064, 55614, 0, 48054, 52425, -131379, 30576, 144774, 44958, 132600, -103857, 33996, -10188, 76851, -43353, -86574, 190884, -152031, 2520, 63924, 41841, 0, -47316, 8130, 13101, 24513, 92892, 24939, 47856, -83970, -21864, 4527, 94917, -166965, 43446, -45960, -849, -46254, 83046, -73461, 0, 85986, -74268, -56004, -143121, -49053, 19899, -4437, -32601, 23841, -69444, -54030, 1149, -27762, -126618, -21168, 67518, 16791, -29697, 0, -96780, -139017, -3276, 73692, 79965, -1617, 33813, -55962, -29643, -96813, -10599, -45942, 39108, -113031, 1713, -40578, -59136, -50643, 0, -5847, 35358, 68730, 68649, 31575, -62952, 7119, -18033, -110235, -72870, -56061, -164004, 77178, 76911, -114012, -80562, -118464, -115356, 0, -124134, 7206, 20208, -123135, 81678, -89319, 40644, 14316, -96126, -120084, 63855, -5502, 13860, 108633, -42213, -94392, 80766, -96288, 0, 93849, -45681, 1629, -58182, 44109, -79770, -47424, 61947, 33678, 65484, -810, 71199, -19752, -151608, -42567, -22863, -129792, 69234, 0, 143661, -68925, -131514, -101190, -75444, 31902, 75807, -68937, 87567, -25692, -116370, -14028, 40386, 22989, -228, 54216, 41508, 43452, 0, 6132, 33660, -111270, 181086, -72966, 71628, -59694, -84357, -13476, 72735, 67323, -19947, -48975, 3084, 37803, 40803, 33354, 35352, 0, -31389, -46809, 157812, -73824, -72090, 47274, -31593, 17214, -64374, -66045, 42609, 44505, -50754, -6669, -27816, -49137, 52944, 45495, 0, -152961, 16770, 91320, -92769, -21117, -5070, 39828, 85803, -158289, -34581, 200169, 193947, 8208, 55686, 88047, -10413, 11031, -32712, 0, 73710, 126585, 1254, 49155, 39642, 37875, 19137, 115152, -2547, 193545, -79887, -2577, 23778, 103803, 131967, -135, -174822, -37152, 0, -21564, 111744, -143748, -69, -54678, -15570, -76452, -5397, 103770, -56910, -153678, -44175, -68517, 109095, 134718, 52842, 78570, 36234, 0, 103092, 5313, -98196, 118440, -68880, -34401, 24609, -86430, 126570, 219948, -2499, 206055, -114720, -134328, 24159, 59280, -324, 103854, 0, -36486, -48336, 93414, -98604, -55686, 15009, -36375, 141753, 77919, -48630, -91986, 150411, 241206, -162822, -149655, -10422, 72693, 81639, 0, -31854, 91029, -3990, -77700, -157827, -129072, -141987, 150504, 10686, 96531, 179142, -47721, 96114, 79704, 43920, -28176, 57513, -51954, 0, -97347, 22758, 305058, 177075, -79968, 44754, -13977, 3201, 98559, 163479, -118041, -160581, 52086, 88302, 361740, 86658, -119427, -1296, 0, 52050, 83739, -43524, 75174, 75108, 147771, -40077, 250086, -31749, 48984, -122781, -15468, -231084, 172179, 65376, 205698, 119400, 98034, 0, -66279, -121314, 18171, 26022, -19197, 185646, -96306, 100320, 72753, 10995, -41025, 128370, 118956, -130293, 46314, 76224, 100194, -163266, 0, 194742, 150543, -51621, 107163, -158490, 77031, -163584, 157176, 196200, -123306, -65664, 177339, -132729, -223839, 9912, 179139, -22029, 233730, 0, 8466, 110838, 173598, 25386, -101367, 42360, -32244, -104928, 39366, -64644, 203691, -83211, -102417, 210774, -202179, 16860, 11175, 63162, 0, 77388, -58224, -57183, 145203, 29079, 242421, -190479, -75297, 44274, 474939, 7851, -70692, 47688, -26235, 94212, 43284, 21834, 116592, 0, -32976, -158319, -181347, -66804, -89949, -87576, -14445, 135387, -194037, 3516, -269562, 20937, 14877, -7134, 262920, 90384, 16866, 18540, 0, 54537, 392490, -87837, 36186, -16122, -40209, 127140, 29754, 191202, 35442, 68139, 134139, -13848, -52206, -9933, -237306, -38994, -223962, 0, 46863, -31428, 274563, 38862, 75366, 10434, 44694, -155061, -149256, -86448, -83262, 1839, 300186, -57165, -54333, 80721, -51639, 41409, 0, -103155, -124101, -99360, -288867, -40065, -183945, 51993, 79098, 65892, -83886, 24471, 72123, -153969, 101169, -88677, -137448, -44244, -1056, 0, -293103, -83220, 2826, -84192, 186291, -21426, 209616, -75765, 10224, -59805, 196140, -61080, -228057, -9432, 96390, -118482, 35748, -103113, 0, 177534, -36684, -44814, 123429, -122568, -94848, -150855, -54654, -65307, 132726, -250260, -134298, 70662, 3090, -187692, 59169, -216720, -165384, 0, -106407, 1320, -32769, 79257, 104250, -79623, 70596, -99720, -95808, -128343, 191142, 54267, 19704, -105078, 228327, -241029, 339048, 38085, 0, 44256, 47670, 97860, -55002, -30048, -97761, 52947, 260130, -141318, -255918, 87648, -241587, -48480, 270513, -122271, 92541, 15588, 30315, 0, -61170, -192429, -43092, -170706, 106818, 63198, 28866, 28959, -141042, -78162, 221433, -28995, 392598, 3999, -254802, -28566, -40983, 61926, 0, 25440, -109680, -112194, -51159, 96852, -164775, 67161, -110085, 70932, 127437, 124635, 46473, -160677, -51693, 73620, -225561, -211722, 325281, 0, 133344, 29586, -70161, -44925, 64728, 178935, 147915, -438543, -195360, -166821, -121467, -59055, -8205, 67095, -208134, -82020, -167319, -160566, 0, -87960, -76293, -32484, -10746, -50127, -220518, -92850, -219648, 48114, 15990, -63759, 177231, -314025, -423372, -137715, 70350, 73410, -450207, 0, 98799, -232350, 394782, 74493, 283413, -101094, 352803, -137331, -117534, -507894, -15498, -123186, 34770, 28722, -345633, -122313, -28122, -25158, 0, 121320, 253497, -214407, -145836, 202818, 120582, 18189, -129930, -69540, -131112, 60933, 85146, -43776, 484107, -342441, 112836, 102390, -94239, 0, -230298, -70278, -126147, -151920, -8733, -6528, -24360, 40287, 14643, 172116, -104967, -339867, 379005, -89919, 86970, -189630, -91299, -57492, 0, 99141, 17562, -269082, 7659, 35346, 28104, 155553, -282993, -25923, -273099, -76935, -297153, 212688, -347532, 4134, -16269, -239484, -113298, 0, -61206, -90264, -89751, 179484, 327762, -76881, 244989, -101421, -96954, 181041, 227088, -63951, -217530, -278490, 3390, -114069, 186789, 268872, 0, 125874, -161703, -77802, -173028, -11907, 54663, -248373, -210090, 134568, -267528, -104361, -172356, 224490, -187296, -234492, 292284, -105588, -531, 0, -246054, -281076, 128541, -162480, 80127, -100410, -50895, -30909, -79254, 2310, 116595, 22491, -272076, 213180, 152862, 27675, 260997, -157860, 0, 31260, 117120, 240357, 226869, 154020, -81429, 116307, 195501, 9387, 59097, 360621, -51624, -165288, 253605, -55782, -230817, 17052, -158664, 0, 171396, 9819, -236361, -142668, 45720, 156243, -55431, -65067, 95076, -219666, -242217, 83766, 46152, 210579, -370392, 25800, 130392, -126450, 0, -236178, -133221, -36540, 417006, -120825, -148878, 95589, 44595, 165801, 32589, -291819, -204045, -122280, -160479, 167625, 24105, 123123, 473301, 0, -50229, 87621, 216690, 287244, 18015, 123963, 221613, 71601, 170820, -25950, -46347, -77295, 83907, -64437, 33573, -101010, -64851, -100548, 0, 27864, 47004, 79926, -153582, -163608, 119742, -140295, -106389, -245358, -67716, 146295, 473754, 62784, 123318, 99870, -42783, -314646, 355869, 0, -86985, 239838, 433950, -117573, -14625, -366282, -154470, -60219, -253101, 571254, 223485, 141216, 114015, -65730, 552816, -125364, 87258, -41283, 0, 177714, 195144, -66567, -224079, 171237, -160020, 12996, 567804, 150453, 392178, -42699, 113571, -198690, 337992, 173781, 275652, -59868, -259473, 0, 409932, -82749, -398139, 147699, -212652, 193368, -341430, 167667, 142620, 133245, -7833, 178635, -193329, -35490, -282237, 334272, -196428, 334266, 0, 50370, -46395, -32700, 210459, -89286, 92826, 11241, 49401, 169668, -151410, -150345, 201825, 49371, -173199, 123090, 40020, 227562, 262905, 0, -270093, 195690, -140124, -83991, -538650, 338406, 162081, -106260, 163962, -88350, 126300, -326424, -26106, 265452, 340236, -23592, 158730, -28164, 0, -338037, 19767, 290913, -121887, -207591, 81075, -184899, 236982, -175620, 396564, -156009, -141990, 58560, -259731, 231372, 99024, 49509, -378081, 0, 294207, 20928, 73359, -136998, 122589, -211980, -107658, 559239, -7488, 51303, -342564, 301233, -189996, 73602, 407082, -15186, -150873, -53844, 0, -100692, 185904, 301758, 31554, 286404, 197934, -30999, 169842, -127008, 160359, 75159, 285978, 455247, -83700, 55374, -24321, 181428, -236727, 0, -53976, 233079, 316002, 143754, -314601, 168912, -340527, 331584, 281799, 30720, -167079, 176655, -231594, 116604, 120981, 338262, -62301, 184809, 0, -19119, -106584, -175602, 106617, -272832, 62214, -19812, -151773, 111804, 52767, 177543, -55092, -131457, 34206, -48873, -122685, 65088, 383583, 0, 125094, 106761, -455334, 15978, -190887, -32571, -395817, -57291, 357, 163857, 102891, 576252, 434841, -371529, -183312, 238884, 236652, 323769, 0, -150750, -168717, -185358, -49803, -466686, 306654, -311532, -18258, 88269, 472590, -217137, -577461, -149268, -61662, -7020, -45840, 223545, 288993, 0, 266385, 58314, -32304, 407508, -497052, -182982, -112119, 251958, 293172, -67140, -309585, -116109, 188199, 65367, 405126, 308664, -537081, -513954, 0, -123678, 166377, 276648, 212763, 52356, 289836, 109683, 64716, -396744, -508713, -135519, 434922, -4566, -45765, 256371, -422322, 137826, 79848, 0, 271446, -71736, 148218, -340452, -102549, -119967, -195480, 541974, 127065, 19287, 166158, 126696, 36237, 118632, -60375, -45021, -147603, -307638, 0, -107481, -69579, -195894, -217785, -127137, 175380, 262488, 17061, 288522, 51474, -29253, -62427, 271971, 302058, 393888, 353832, -54282, 21375, 0, 336621, 422676, -216108, 351255, -17784, 118326, -155850, -435672, 322347, 422862, -295977, -203811, -475455, 60018, -658380, 343494, -434772, 419355, 0, -194922, 146211, 466104, 210105, 359199, 279615, 171348, -219225, -289104, -161763, 294444, 777156, 421110, -222561, 118245, 121629, 691245, -331152, 0, -291921, 208926, 248304, 215640, -258909, -137577, 76791, -38169, 190947, -15582, 123354, -298044, -223884, -192582, -101244, 145149, 14079, 96120, 0, -5187, -56439, 174006, -389274, 88962, -200145, 394131, 58665, -101793, 15942, 298755, -155964, -104046, 341526, 125319, -155055, -3075, -28104, 0, 257517, -25596, -387429, 100134, 178953, 60864, -245943, 101391, -14904, 181782, -49554, -131436, -66093, 239805, 132966, 20706, -334581, 264990, 0, 59250, -584232, -104181, -538053, 288306, -256779, -9309, -322125, -28113, -248535, -81747, 282018, 288930, 117636, -514548, -353736, -90720, 188985, 0, -108921, -197442, -597588, -568302, 223092, -96153, 113445, 326319, 194655, -86421, 241293, 319545, -601908, -369198, -196296, -515616, 436893, 271257, 0, 348537, -79509, 274218, -104598, 279198, -814962, 66843, -557772, -229953, -196434, -107238, -338592, 284244, 1821, 2478, -33948, -501126, -401640, 0, -130980, 525918, -111828, 102147, 273753, -199638, 37440, -191721, -717342, 339726, 190158, 220977, 49518, -3819, -244926, -492156, 309522, -106575, 0, -422076, -364110, 507678, 592572, 123387, 61701, 93285, 55845, -485718, -578007, 313383, -981570, 140937, 261579, 236709, 15051, 83634, -3276, 0, -511383, 139404, 143343, -74271, 481098, 173286, 707388, -269031, -68424, -149892, -128094, 327765, -63558, -229575, -408387, 501924, -44937, -206001, 0, -303003, 301023, 31521, 102387, 122118, 437526, 139122, 164085, 263886, -13149, 31926, 202965, 32235, -266025, -35949, -105048, -115311, -2283, 0, 228345, -350574, -250788, -32592, -505641, 106191, -358428, -259731, 480420, -225084, 7623, -334398, 114267, 461088, -424728, -31863, -3522, -885282, 0, -360927, -808140, -92622, 7230, 265350, -217344, 400146, -582159, -249228, -595050, 27561, -610287, -508980, -200007, 481170, -639876, 410205, -54036, 0, 621366, -190332, 123615, -710571, -10701, -211821, 113784, 307395, -289584, -47454, -268467, -384699, -705978, -300150, -382098, -510504, -764814, 40902, 0, 437763, -506883, -154734, 240063, 225405, -371856, 180375, -227448, -102885, -371769, -552687, -451269, 735948, -132105, -594225, 176763, -199794, -216240, 0, 650331, 305262, -596787, 378474, 395646, -320706, 238500, -379203, 24798, 337683, 332901, -899883, 222897, 315762, 352899, -25788, 309258, 783036, 0, -102288, -477843, -224436, 30228, 3486, 376782, 258726, -335715, 142650, 272601, 871821, -723426, -46194, -446931, -599244, 257943, 336972, -145395, 0, -490419, 66963, -230013, 54000, 72069, -297369, -428694, -225567, -4062, -50412, -239688, 745491, 31239, -525492, 104325, 316320, -387096, -77502, 0, -232986, 32976, 284424, 79068, 215442, 182775, -100167, -323970, -66810, -486042, 34059, 351234, 71175, 248292, -335760, -465657, -64602, -396114, 0, 27771, 444708, -94461, 425742, 643308, 112869, -509211, -82707, -368073, -801258, -207780, 266721, -937935, 563910, -63063, -101751, 183522, -770304, 0, 230799, 147966, 904368, -821352, 380994, 74391, 102957, -43314, -499575, 89892, -353781, -177261, -34596, 39558, -221142, 142530, -165780, -69435, 0, 39462, 23964, -616791, -356958, 206976, -82254, 811656, 386235, 122295, -22902, 261969, -162849, 251355, -365757, -485283, -558834, 797166, 236625, 0, -194994, -491787, -301512, 6525, -46989, 355248, -30906, -297501, -54906, -425403, -158391, -215889, 919080, 30393, -91578, 273777, -106866, 157092, 0, -161556, 1182, 301926, -153120, -244497, -381525, 9345, -383931, 452682, 160377, 111186, -518523, -75228, -460980, 174855, -362691, -735960, 857508, 0, -722898, -291390, 41838, 285018, -19419, -558825, 403191, 637191, -385854, 138822, 501573, 468519, -270252, 165882, 461244, -369342, 207306, -52581, 0, 266022, -352674, 151425, -370665, 51927, 360222, 102537, -47373, -236235, 186507, 118908, 473955, 507234, 26286, -166812, 1134984, -16770, -310494, 0, -75552, 161574, -12903, 111579, -245466, -365748, -555444, 44214, 202047, 560610, -341820, 783558, -180138, 50883, 482922, 420435, 128016, 404028, 0, 436842, 294594, 658743, 328338, 136293, 466950, 487266, 10461, 790878, -38166, 124257, 15639, -493011, 553677, -525531, -135024, -129258, -187575, 0, 265848, 976854, -253866, -38415, 136890, 430404, 379653, -380406, 279678, 308370, 341613, 388491, 230031, 360588, -267462, 592212, 596142, -228798, 0, -311568, -411390, -322701, -274521, -616539, 189954, -728916, 239415, -139725, 215988, 1560, 69717, 290583, -209706, 774801, -345897, 43440, 92232, 0, 12807, 654903, 153693, 215940, -601917, -553557, -355905, 476997, 364914, -45177, 6942, -474642, 89274, 307116, 116724, -662577, -1139850, 557763, 0, 157281, -169215, 66261, 547107, -161655, -187638, 214617, 80487, -554955, 679536, -588456, 24981, -192390, 46920, 26592, 9468, -157986, 456018, 0, 26892, 36612, 143925, -265014, 220746, -141579, -271581, 355377, -285228, -255672, -240870, 233157, -132630, 114489, 608007, -81978, -342222, -257706, 0, 153684, -27924, -28974, 117492, 113691, -784137, 300750, 294042, 566805, -461667, 263658, 582999, -521124, -49380, 725055, 482316, 579504, -570018, 0, 347091, 131973, -232392, 94923, -688620, 545085, -425226, -490389, 512841, -69516, 29991, 65652, -583011, 193029, -285822, -286515, 368481, 598605, 0, -45627, -334758, -704550, 551604, -1028850, 215409, -867135, -117831, 277965, -273663, 264708, -117384, 924123, 197007, 107988, 617337, 621510, -136929, 0, -542385, 472593, 273987, -347415, -651624, 830907, -266181, 447204, 229992, 802134, -307869, 951315, -290154, -200565, 458394, 47556, 553020, 365628, 0, 35472, 818184, 474075, -317910, -445410, 582774, -404721, 979227, -287481, 235998, -325206, -263265, 1102308, 14418, 129891, -19314, -777720, 41688, 0, 309552, -232389, -392019, 34578, 256500, 853737, -220089, 771429, -279462, 934713, -707676, 832749, 165453, -1172403, 139329, 600729, -262005, 224721, 0, -32142, 758733, 475080, 77265, 51678, 278682, 354306, 268032, -110292, 308157, 157800, -327000, 427254, -10797, 703497, 123006, -99666, 714042, 0, -195492, -89325, -55812, -252234, -227583, -334881, -466242, 511872, -74697, 650229, 370263, 213501, -655824, 2292, -124698, -189546, 9186, -635901, 0, 353010, -947238, 305298, 437016, -431889, -392295, 269223, -120135, 151413, -38874, -44703, 175494, -207432, -9744, 351819, 337614, 14214, -266457, 0, 648690, 261192, -759168, 448467, -66729, -731094, -199671, 740154, 489210, -314595, -719691, -157863, -690576, -222927, 130986, 370176, 227799, -87597, 0, -867552, 329760, 503532, -24726, -244167, 515370, -686436, -235341, -176619, -125490, -289488, -437097, 214974, 942396, 449391, -104892, 937821, -964944, 0, -21867, -414225, 287223, -204414, -256464, -25776, 34647, 355719, 27885, 122466, -316281, -605691, 300360, -417690, 584013, 710289, -472890, 111654, 0, -121125, -841350, 826323, -379650, 18858, 848163, 6852, 625440, -911835, -125697, 237075, 733935, -957600, 266475, 211554, -697734, -366012, 189138, 0, 287328, 1097097, -191025, -536610, 95982, 513627, -880557, 887043, 165234, 659265, 243087, 410256, 958938, -163968, -416646, 129420, -808896, -638211, 0, -829743, 339534, 633399, -106380, -82203, -504933, -25413, -717927, 497154, 1106799, -564516, -52827, 130884, -722010, 388500, -122994, 610467, 583200, 0, 487704, 632154, -62880, 1065357, -166449, 287034, 329877, -740376, -267294, -83550, 1184787, -723255, -589980, 834993, -654573, 929223, 67437, 1509171, 0, 142599, -132078, 188289, 42747, 437694, 300906, -564588, -73077, 1030128, 46932, 421608, 736341, 808413, -329898, -199284, 153483, 1143204, 370392, 0, 27504, 202026, -802035, 316899, -852360, -808485, 296745, 201420, 1051161, -504882, -687057, -748878, -165024, -213903, 281082, -258276, 455049, 128514, 0, -572358, -164592, -845892, 123891, 468927, -206772, 902820, -435243, -614928, -804846, -544557, -266181, -142944, 843246, 707850, -714006, -800925, -775362, 0, 630948, 107793, -140682, 880056, 330132, -188130, 25293, 77568, 496296, -88578, -20517, 231648, -651291, 549030, -638142, 140844, 164160, 315297, 0, 717726, -1205982, 292848, -497277, 64722, -104583, -343161, 136542, -278172, -788172, -526587, 435900, 248160, -847875, -258423, -413082, 113538, 251397, 0, 490782, 253392, 168285, 324651, 164868, -37233, 637056, -396873, 526743, 263412, 504435, 483930, -703518, 581019, 328890, -306702, -678111, -833466, 0, -368625, 502470, -9225, 107151, 802401, 129174, 612201, -540309, -329040, 147063, 1017027, -613461, 311835, 316572, -1760199, 240744, -605247, 14376, 0, 398322, 117294, -521910, -360951, 760734, -513429, -33384, -519579, -305796, 657297, 473661, 510831, -479424, -29292, 134700, -487815, 149532, 773004, 0, -797013, -341043, -194022, 88602, 243393, -284964, 417510, 10131, -427071, -9057, 13209, -221127, 169332, -478158, 408621, 505386, 315669], "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": "19.4.e.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], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [4, -1, 1, -2, 0, -1, 1, 0, 0, 0, 0, 0], [2, 0, -1, 1, -1, 1, -1, 0, -2, 0, -1, 1], [4, -3, 1, -1, 0, 0, 1, -1, 0, -1, 0, 0], [1, -2, 0, 0, -1, -1, 1, -1, 4, 1, 0, -2], [-8, 3, -1, 1, 1, 1, 1, 3, -7, 0, -1, 1], [4, 2, -1, 1, -4, 1, -5, 2, 3, 0, 0, 1], [-8, -1, 0, 0, 2, -4, 0, -1, 11, -1, 4, -2], [-6, -2, -1, 11, 1, 3, -1, -2, -3, 3, 2, -1], [-25, 10, -4, 2, -1, 5, -2, 1, 4, 0, 1, 1], [-8, 6, 3, 0, 1, 1, -2, 1, -6, -4, 4, -2], [-13, -4, -3, 12, -2, 11, -9, -2, -12, 6, -2, 0], [-19, 0, 1, -7, 6, -10, 4, -3, 12, 3, -1, -1], [15, -6, 2, -32, -4, -12, 8, -1, 17, -5, 4, -2], [7, -6, -1, 5, -2, 5, -1, 4, -6, -3, 4, 3], [-10, 0, -4, 34, -5, -1, -3, 0, 7, 5, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-9, -8, -1, 45, -3, 15, -9, 3, -53, 0, -7, 1], [-21, 0, -2, -13, -6, 10, 6, 6, 11, -8, -3, 2], [14, -12, 0, -10, -10, 0, -15, -2, 20, 0, -6, -4], [23, -14, -6, -34, -10, -12, 13, 3, 5, 4, -8, 1], [105, -21, 4, -37, -8, -13, -4, 3, 26, 3, 2, -4], [-9, -12, 2, 29, -5, 7, 4, 6, -6, -8, 1, -1], [67, -4, -1, -9, 5, -5, 21, -3, 25, 6, -7, 7], [-47, -34, 5, -20, 7, -9, 29, -14, -31, 4, -1, -3], [-26, -26, 2, -7, 5, -4, -14, -11, 97, 2, 11, -3], [-33, -8, 1, 35, -1, -14, -6, 1, -24, -6, -2, 7], [43, -7, 1, 68, -8, 23, -15, 7, -119, -5, -10, 6], [-51, 10, 16, -69, -1, -4, 16, -4, 37, -3, -2, -4], [-25, 19, -16, 63, -11, 30, -12, -1, -101, 0, -11, 13], [13, -22, 10, -53, 6, 10, -9, 3, -27, -13, 10, -1], [-86, 14, -7, -44, -8, -15, 1, 9, 35, -11, -4, 2], [-81, 18, -4, -81, 2, -5, 0, -2, -28, 14, -8, 7], [-5, -41, 3, 38, 5, 0, -16, -13, -66, 6, -9, -11], [25, -14, 21, 66, 13, -34, 35, -4, 4, -2, 3, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, -16, 11, 100, 8, 4, 17, -16, -42, 6, 20, -8], [-19, -39, 5, -94, 12, -27, 23, -25, 169, 23, 4, -6], [-65, 2, 0, -24, 17, 24, -8, 10, 37, 2, -3, 20], [-31, -39, 11, -155, 27, -13, 25, -8, 106, -5, 27, -5], [122, -12, -7, -63, 18, -8, -16, -15, 56, -13, -1, 3], [-183, -5, -25, 126, 14, 35, -18, -13, 59, 19, 2, 2], [110, 34, 0, -51, -29, 23, -19, 27, 57, -29, 7, 2], [-154, 18, -8, 2, -18, 6, -4, 20, -144, -4, 8, 0], [-71, 20, 12, -22, 5, -6, -20, 20, 98, -6, -27, -4], [-175, 46, -10, 199, -18, 23, -6, 8, -175, 26, -30, 4], [37, 30, 8, 78, 14, -36, 17, 3, -103, -11, 22, -11], [-154, -14, -9, -102, 20, -7, -11, -5, 101, 5, 12, 2], [-76, -18, 19, 52, 33, -33, -4, -11, -136, 35, 7, -22], [-17, 65, 3, -128, -6, -9, -17, 25, -53, -9, -22, 8], [-132, 14, 18, 44, -41, 21, -13, 15, -4, 6, 12, 6], [-176, 10, -16, -113, 20, 13, -8, 29, -76, -21, -10, 4], [-23, 0, 3, 21, 4, -26, 67, -16, 39, 12, 13, -2], [-229, 21, -35, 277, -1, 79, -73, 18, -80, -39, -23, 13], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-114, 5, -32, 180, 10, -6, -30, 21, -123, -11, -2, 18], [-280, 30, 8, -40, 17, 22, -16, 16, 153, -2, 28, -4], [5, 16, -3, -128, 8, -61, 51, -12, 340, -8, 66, -20], [-141, 54, 2, -75, 0, 23, -44, -12, -62, -10, -20, 7], [108, 27, 16, -83, 51, 34, 54, 18, 4, 15, 5, 5], [22, 64, 27, 105, -8, -69, 9, 12, -82, 39, -26, 11], [137, -44, 20, -17, 65, -66, -8, -22, 242, 19, 31, -25], [-228, 40, 8, -126, -17, -15, -64, -12, 17, -21, 20, -3], [-304, 37, -35, 9, 33, 3, 94, -11, 165, 6, -7, 13], [-142, -86, 35, 12, 15, -31, 44, -1, 55, -12, 32, -36], [91, -67, 2, 66, 14, -16, 32, -28, -154, 22, -24, -2], [-112, 26, -27, -110, -41, -10, -3, 44, 60, 15, -53, 10], [333, -63, 35, -25, -27, -65, 103, 18, -44, -19, 5, -17], [-93, -66, -30, -56, 0, -64, 91, -59, 43, 8, 18, -21], [-296, -65, -18, -42, 81, 41, 7, -63, 100, 16, 13, -7], [-179, -52, 30, -111, -3, 83, -42, -50, -53, 56, 6, -31], [-139, 204, -9, -3, 13, 23, -95, 87, -331, -36, -41, 39], [-55, 36, 10, 100, -24, -58, 32, -6, 16, 24, 9, -38], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [164, 148, 7, 11, -56, -52, 31, 24, -135, -19, -39, 4], [15, 88, -17, -150, -20, -5, -101, 38, 26, -10, -62, 10], [-361, 18, 13, 55, 4, 55, 13, -16, 10, 12, -40, -43], [-281, 134, -29, -10, -24, 131, -123, 32, -90, -16, -6, 0], [-11, 182, -16, 37, -99, 27, 5, 19, 53, -2, 14, -12], [-31, -28, 50, -172, 7, -43, 31, 7, 198, -66, 31, -29], [-148, 0, -41, -36, 7, 116, -79, -50, 21, 3, 7, 8], [-162, 67, -24, 173, 7, 84, -46, 8, -430, 11, -65, 29], [167, 12, -8, 21, -67, 87, 10, 0, 114, -7, -3, 25], [-346, 76, -45, 382, 50, 129, -21, -39, -169, -17, 8, 20], [-69, 98, -49, 127, -40, 7, -20, -5, -37, -25, 4, 28], [118, -233, 30, 46, 28, 50, -95, -47, 11, -29, 58, -20], [-326, 0, -85, 34, -8, 60, -119, 4, -232, -39, -52, 58], [-38, 65, 0, -105, 35, -10, 96, -22, 230, 35, 31, 13], [-97, -102, -3, 247, -6, 71, 33, -8, 6, 2, 8, -31], [284, -82, 58, 0, 18, -104, 72, -12, 118, -26, 50, -2], [-106, 110, -19, 114, -117, 39, 30, -21, 140, 30, -10, -6], [-14, -130, 40, 213, 77, 78, 32, -79, 89, 66, 81, -15], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-8, -90, 77, -166, 63, -184, 65, -67, 296, 8, 71, -47], [-18, 74, -21, 161, -35, 18, -15, -10, -132, -52, 10, 46], [506, 91, -5, -27, -59, -87, 47, 47, -333, -12, -91, 69], [45, 160, 20, 98, 4, -99, 23, 31, 12, 54, 20, -4], [67, -83, -40, 70, -26, 78, -70, -46, -240, 28, -56, 22]]}