# Stored data for newform 784.4.a.ba, downloaded from the LMFDB on 18 April 2024.
{"label": "784.4.a.ba", "space_label": "784.4.a", "level": 784, "weight": 4, "hecke_orbit": 27, "hecke_orbit_code": 117093590378742544, "dim": 2, "is_polredabs": true, "nf_label": "2.2.37.1", "trace_hash": 1381329834587366932, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [-37, 0, 1]], [5, [-99, -14, 1]]], "qexp_display": "q-\\beta q^{3}+(7-2\\beta )q^{5}+10q^{9}+(-2^{4}+\\cdots)q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 12544, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 46.25749744450064, "hecke_ring_index": 2, "level_radical": 14, "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": "0.003", "prec": 17}, "analytic_rank_proved": true, "char_values": [784, 1, [687, 197, 689], [1, 1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [2, 7], "conrey_indexes": [1], "field_disc": 37, "field_disc_factorization": [[37, 1]], "field_poly": [-9, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.046", "prec": 17}, {"__RealLiteral__": 0, "data": "2.001", "prec": 17}, {"__RealLiteral__": 0, "data": "0.264", "prec": 17}, {"__RealLiteral__": 0, "data": "9.940", "prec": 17}, {"__RealLiteral__": 0, "data": "2.281", "prec": 17}, {"__RealLiteral__": 0, "data": "69.570", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [7, -1]], "trace_display": [0, 0, 14, 0], "traces": [0, 2, 0, 0, 0, 14, 0, 0, 0, 20, 0, -32, 0, 28, 0, 148, 0, 154, 0, -224, 0, 0, 0, -68, 0, 144, 0, 0, 0, -236, 0, -196, 0, 518, 0, 0, 0, 346, 0, -296, 0, 420, 0, 344, 0, 140, 0, 84, 0, 0, 0, 296, 0, -438, 0, 812, 0, 222, 0, -56, 0, -98, 0, 0, 0, -396, 0, -336, 0, 518, 0, -896, 0, -966, 0, 2072, 0, 0, 0, 52, 0, -1798, 0, 392, 0, 1670, 0, 2072, 0, -294, 0, 0, 0, 518, 0, -1124, 0, 420, 0, -320, 0, 1022, 0, 2212, 0, 0, 0, 3384, 0, -2262, 0, 3108, 0, 1468, 0, 560, 0, 280, 0, 0, 0, 1476, 0, -888, 0, 3402, 0, 2896, 0, 0, 0, -1064, 0, 0, 0, -2516, 0, 1582, 0, 504, 0, -1110, 0, -2520, 0, 2492, 0, 0, 0, -30, 0, -612, 0, 1540, 0, -336, 0, -658, 0, -3108, 0, 0, 0, 152, 0, 1258, 0, 1288, 0, -2818, 0, -2240, 0, 5726, 0, 0, 0, 2738, 0, -3192, 0, 196, 0, 5476, 0, 8638, 0, -392, 0, 0, 0, 1212, 0, -2138, 0, 0, 0, -1756, 0, 4228, 0, 518, 0, 0, 0, 1164, 0, -680, 0, 5138, 0, 344, 0, -4144, 0, 2408, 0, 0, 0, -1480, 0, 972, 0, 1456, 0, 1440, 0, -8232, 0, -546, 0, 0, 0, -5026, 0, -1632, 0, -9842, 0, -9384, 0, -8302, 0, 0, 0, 0, 0, -4024, 0, -6512, 0, -10416, 0, 4714, 0, 13468, 0, -8022, 0, 0, 0, -2360, 0, 6996, 0, -9282, 0, -4440, 0, 5726, 0, 5852, 0, 0, 0, 12200, 0, 3466, 0, -1960, 0, 1292, 0, -4368, 0, -15022, 0, 0, 0, 3216, 0, 5624, 0, 3780, 0, 5084, 0, -8806, 0, -3024, 0, 0, 0, -7844, 0, 10266, 0, 5208, 0, 666, 0, 5068, 0, -5334, 0, 0, 0, -14190, 0, 18280, 0, -4662, 0, -16360, 0, -6272, 0, 1036, 0, 0, 0, -5968, 0, 3460, 0, -1316, 0, 1388, 0, -10360, 0, 6762, 0, 0, 0, -1406, 0, -6120, 0, 1260, 0, 5032, 0, 7098, 0, -14560, 0, 0, 0, -6220, 0, 12036, 0, -16576, 0, -9722, 0, 7588, 0, 4200, 0, 0, 0, 11226, 0, 6660, 0, -11592, 0, 5472, 0, 4144, 0, -7756, 0, 0, 0, 3440, 0, 3298, 0, -3164, 0, -17242, 0, -19320, 0, -12026, 0, 0, 0, -7674, 0, -4816, 0, -12586, 0, 16220, 0, 7490, 0, -16576, 0, 0, 0, -10280, 0, 11248, 0, -29064, 0, -6316, 0, 840, 0, 19376, 0, 0, 0, 11988, 0, -3996, 0, -1372, 0, -2960, 0, 9170, 0, -18340, 0, 0, 0, 7960, 0, -10938, 0, 21756, 0, 9484, 0, -12936, 0, 9842, 0, 0, 0, -16890, 0, -5032, 0, -532, 0, -864, 0, -10878, 0, 21112, 0, 0, 0, -24420, 0, -5504, 0, -9912, 0, -4380, 0, 18788, 0, -7588, 0, 0, 0, 14188, 0, -18412, 0, 20202, 0, -8448, 0, -9884, 0, 8120, 0, 0, 0, 21096, 0, 296, 0, 12096, 0, -8534, 0, -8288, 0, 4326, 0, 0, 0, -3774, 0, 16816, 0, -9114, 0, -8732, 0, 5418, 0, 6664, 0, 0, 0, -13020, 0, -18396, 0, -560, 0, 9432, 0, 14364, 0, -26418, 0, 0, 0, -26950, 0, 20128, 0, -13762, 0, -13568, 0, -980, 0, 32648, 0, 0, 0, 47360, 0, 23914, 0, 4816, 0, 35150, 0, 9632, 0, -10444, 0, 0, 0, 35286, 0, 11248, 0, 17094, 0, 9608, 0, -16254, 0, -6216, 0, 0, 0, -14748, 0, -3960, 0, 40712, 0, 23506, 0, 10360, 0, 42, 0, 0, 0, -26418, 0, 20628, 0, 25172, 0, -3360, 0, -22820, 0, 17780, 0, 0, 0, 5616, 0, -18190, 0, 24864, 0, -17572, 0, -12600, 0, -8806, 0, 0, 0, 19134, 0, -61568, 0, 39074, 0, -9376, 0, 12432, 0, 28560, 0, 0, 0, -8960, 0, -40354, 0, -28616, 0, 25456, 0, 51324, 0, 20062, 0, 0, 0, 10530, 0, -41932, 0, -9660, 0, 2104, 0, 34566, 0, -18648, 0, 0, 0, 22528, 0, -44400, 0, 39900, 0, -308, 0, -35224, 0, 35070, 0, 0, 0, 12210, 0, 2352, 0, -22078, 0, 68228, 0, 6300, 0, -25592, 0, 0, 0, 26024, 0, 28788, 0, -33152, 0, -35540, 0, -29428, 0, -1554, 0, 0, 0, 10426, 0, 520, 0, 10290, 0, 6336, 0, 6216, 0, 2268, 0, 0, 0, -15984, 0, 41024, 0, 33600, 0, 15986, 0, 26488, 0, 25774, 0, 0, 0, 9002, 0, -4664, 0, 36260, 0, -14688, 0, 43302, 0, 3920, 0, 0, 0, -11828, 0, -6216, 0, 15400, 0, -29116, 0, -25900, 0, 67522, 0, 0, 0, 16700, 0, -11736, 0, 56532, 0, 36408, 0, -20482, 0, 392, 0, 0, 0, -49704, 0, -14672, 0, -35224, 0, -53446, 0, -22960, 0, 57498, 0, 0, 0, -23276, 0, -54168, 0, -30324, 0, 2028, 0, -2940, 0, 5096, 0, 0, 0, 36556, 0, -40346, 0, 34440, 0, 40034, 0, 41468, 0, -38528, 0, 0, 0, 59762, 0, -18828, 0, 4144, 0, -38568, 0, 966, 0, -3108, 0, 0, 0, 9608, 0, -8806, 0, 16688, 0, 37086, 0, -51800, 0, -36302, 0, 0, 0, -66230, 0, 9992, 0, 10220, 0, -11240, 0, -15414, 0, -44408, 0, 0, 0, -5692, 0, 22618, 0, 45584, 0, -69726, 0, -6776, 0, 4200, 0, 0, 0, -23670, 0, 42624, 0, -14532, 0, 48632, 0, 15022, 0, 67788, 0, 0, 0, 28768, 0, -12738, 0, -75180, 0, 17316, 0, 37632, 0, -46158, 0, 0, 0, 41628, 0, 36520, 0, 10220, 0, -28320, 0, -51856, 0, 31080, 0, 0, 0, -17916, 0, 66304, 0, 4032, 0, 111936, 0, 22120, 0, -35406, 0, 0, 0, -3034, 0, 67556, 0, -67732, 0, -68968, 0, -20146, 0, -20496, 0, 0, 0, 8888, 0, -7604, 0, -40404, 0, -6868, 0, 42672, 0, -94276, 0, 0, 0, -36748, 0, 33840, 0, -27398, 0, 8096, 0, -16058, 0, 16464, 0, 0, 0, 7696, 0, 19158, 0, -26376, 0, -22620, 0, 7812, 0, 8428, 0, 0, 0, -11696, 0, -31684, 0, -48174, 0, -23240, 0, 34454, 0, -52836, 0, 0, 0, 6640, 0, -21238, 0, 39732, 0, 69532, 0, 51800, 0, 12726, 0, 0, 0, 14680, 0, 15320, 0, 36540, 0, -59052, 0, 5376, 0, 40096, 0, 0, 0, 27372, 0, -69130, 0, 5600, 0, 14358, 0, -59668, 0, -51282, 0, 0, 0, -87170, 0, -49432, 0, 16100, 0, 48880, 0, -25172, 0, 27272, 0, 0, 0, -118104, 0, 31034, 0, -45920, 0, -95312, 0, 32648, 0, -32074, 0, 0, 0, 46196, 0, 24768, 0, -59570, 0, 31536, 0, -10626, 0, -49728, 0, 0, 0, 52132, 0, 14760, 0, -33208, 0, -96804, 0, -81844, 0, 74186, 0, 0, 0, -31746, 0, 44540, 0, -30492, 0, 15096, 0, 57414, 0, -71260, 0, 0, 0, -78608, 0, 114938, 0, -79772, 0, 14486, 0, -22904, 0, 34020, 0, 0, 0, 11678, 0, 63936, 0, -30730, 0, -33204, 0, 2072, 0, -23800, 0, 0, 0, 28960, 0, 132634, 0, -12152, 0, 33226, 0, -49812, 0, -53886, 0, 0, 0, 13644, 0, 27404, 0, 0, 0, -25752, 0, -101486, 0, -88060, 0, 0, 0, -75648, 0, 29822, 0, -25032, 0, -86778, 0, -10640, 0, 70294, 0, 0, 0, -65046, 0, -1512, 0, -74424, 0, 34780, 0, 45346, 0, -53256, 0, 0, 0, 43444, 0, -89834, 0, -31080, 0, -90082, 0, -85568, 0, 36260, 0, 0, 0, 143562, 0, -65120, 0, 32340, 0, -6864, 0, 39886, 0, -27132, 0, 0, 0, -47952, 0, -27078, 0, -10864, 0, 15820, 0, 44352, 0, 67046, 0, 0, 0, -80302, 0, -96008, 0, -16576, 0, -40592, 0, -5558, 0, 5040, 0, 0, 0, -85344, 0, -14208, 0, -44520, 0, -16616, 0, -60088, 0, -18802, 0, 0, 0, 18870, 0, -47376, 0, 39186, 0, 180856, 0, 30702, 0, 58492, 0, 0, 0, 154656, 0, 16662, 0, -25200, 0, -67884, 0, 40600, 0, -116550, 0, 0, 0, -6602, 0, 96792, 0, 17276, 0, -41456, 0, 24920, 0, 47152, 0, 0, 0, -65564, 0, 45684, 0, 163968, 0, 61346, 0, 5460, 0, 3794, 0, 0, 0, -118560, 0, 83268, 0, -46102, 0, -97056, 0, -33712, 0, -52836, 0, 0, 0, 28304, 0, -300, 0, -35364, 0, 113194, 0, 151256, 0, 87920, 0, 0, 0, 122988, 0, 121032, 0, 21070, 0, -6120, 0, 120442, 0, -40992, 0, 0, 0, 4372, 0, 89088, 0, 60088, 0, 66956, 0, -7812, 0, -138446, 0, 0, 0, 3858, 0, -69560, 0, 18046, 0, 103752, 0, -165760, 0, 66024, 0, 0, 0, -3360, 0, -17328, 0, -67704, 0, 99974, 0, 41664, 0, -94556, 0, 0, 0, -7026, 0, 4136, 0, -6580, 0, -163036, 0, -35812, 0, 89096, 0, 0, 0, 137580, 0, -216080, 0, -79128, 0, 59188, 0, 52836, 0, -15806, 0, 0, 0, -111074, 0, -107380, 0, -103670, 0, -7696, 0, 113680, 0, 25340, 0, 0, 0, -99696, 0, -133054, 0, 70448, 0, -16002, 0, 65520, 0, -41958, 0, 0, 0, 111708, 0, 1520, 0, 61992, 0, 34080, 0, -180264, 0, 72632, 0, 0, 0, 124616, 0, 62670, 0, 92008, 0, -21386, 0, -100716, 0, -52374, 0, 0, 0, -20622, 0, 13464, 0, 90650, 0, 9624, 0, -35350, 0, 12880, 0, 0, 0, -141344, 0, 111888, 0, 44632, 0, -40398, 0, 20720, 0, 35364, 0, 0, 0, -28180, 0, 16384, 0, 146272, 0, -84804, 0, 70672, 0, 121240, 0, 0, 0, 169064, 0, -35340, 0, 201376, 0, 15050, 0, -68180, 0, 168350, 0, 0, 0, -11278, 0, 39516, 0, 14140, 0, 29408, 0, 57260, 0, 142884, 0, 0, 0, -29304, 0, -175274, 0, 71792, 0, -30858, 0, -2632, 0, 86968, 0, 0, 0, -63440, 0, -31792, 0, 10878, 0, -6648, 0, -180138, 0, -35224, 0, 0, 0, 59512, 0, -46546, 0, -60592, 0, 126564, 0, -74592, 0, 89250, 0, 0, 0, 217782, 0, -139428, 0, -10668, 0, -31920, 0, 89614, 0, -146636, 0, 0, 0, 5296, 0, 38554, 0, -63196, 0, 20988, 0, 187376, 0, 1960, 0, 0, 0, 1456, 0, -160136, 0, 133868, 0, 152772, 0, 122248, 0, 21168, 0, 0, 0, -93092, 0, 54836, 0, 23968, 0, -258260, 0, -138124, 0, 66626, 0, 0, 0, 78686, 0, -84852, 0, 86380, 0, 82664, 0, 84462, 0, 17612, 0, 0, 0, -9688, 0, -50912, 0, 22484, 0, -38986, 0, -3920, 0, 113316, 0, 0, 0, 54538, 0, 19608, 0, -170772, 0, 36112, 0, 18858, 0, -35616, 0, 0, 0, 54072, 0, -70770, 0, 31080, 0, 112260, 0, 83272, 0, 46102, 0, 0, 0, 47318, 0, 12120, 0, 98756, 0, -57000, 0, -33152, 0, -160412, 0, 0, 0, 4736, 0, 79170, 0, -145404, 0, -21380, 0, -32088, 0, -63434, 0, 0, 0, -90044, 0, 4472, 0, -63714, 0, 172988, 0, 155554, 0, 0, 0, 0, 0, -54004, 0, -43808, 0, 72240, 0, -186522, 0, -79772, 0, 164892, 0, 0, 0, -17560, 0, -180544, 0, 174468, 0, 142968, 0, 88452, 0, 57428, 0, 0, 0, -24512, 0, -73870, 0, 42280, 0, 138982, 0, -162680, 0, 181818, 0, 0, 0, -98010, 0, -155400, 0, -15204, 0, -37936, 0, -8806, 0, -116256, 0, 0, 0, -6808, 0, -70662, 0, 241920, 0, 106634, 0, -47124, 0, -110992, 0, 0, 0, 24654, 0, 95212, 0, -27972, 0, -10376, 0, -18536, 0, 98420, 0, 0, 0, -30168, 0, 11640, 0, -8400, 0, -99846, 0, 209272, 0, -170030, 0, 0, 0, 153106, 0, -12928, 0, 179228, 0, 61132, 0, -80962, 0, -27160, 0, 0, 0, 151420, 0, 98510, 0, 39368, 0, 53252, 0, 180796, 0, 51380, 0, 0, 0, 46728, 0, 290524, 0, 3108, 0, 47936, 0, -136752, 0, 42448, 0, 0, 0, 3440, 0, 137850, 0, -152740, 0, 243312, 0, -70728, 0, -58912, 0, 0, 0, 100710, 0, 12160, 0, 70448, 0, -137996, 0, 71596, 0, 91168, 0, 0, 0, 30960, 0, 156288, 0, -11648, 0, 10180, 0, 24080, 0, -87444, 0, 0, 0, -20202, 0, 54152, 0, -153034, 0, -58312, 0, -62874, 0, -32732, 0, 0, 0, 37496, 0, -245746, 0, 46620, 0, -206310, 0, -47936, 0, -199430, 0, 0, 0, -133854, 0, 25160, 0, -127092, 0, -271832, 0, 169904, 0, 30240, 0, 0, 0, 87764, 0, -14622, 0, -170464, 0, 9720, 0, 137760, 0, 98490, 0, 0, 0, -47382, 0, -156060, 0, -131572, 0, -124776, 0, -115878, 0, 14560, 0, 0, 0, -141160, 0, -112998, 0, 38808, 0, 167788, 0, 18648, 0, 14448, 0, 0, 0, -129456, 0, 319160, 0, -152404, 0, -60828, 0, -392994, 0, 193312, 0, 0, 0, 50356, 0, 88468, 0, -82320, 0, -43474, 0, -21084, 0, -343434, 0, 0, 0, -142478, 0, 1036, 0, 47348, 0, -10304, 0, -5460, 0, 149772, 0, 0, 0, 21312, 0, 52666, 0, 256452, 0, -158730, 0, -154112, 0, 36554, 0, 0, 0, -39338, 0, 74336, 0, 116032, 0, 8144, 0, 22274, 0, -6216, 0, 0, 0, -231864, 0, -50260, 0, 25032, 0, 100266, 0, -140896, 0, -164388, 0, 0, 0, -309690, 0, 72884, 0, -159628, 0, -16320, 0, 72548, 0, -78680, 0, 0, 0, -9304, 0, 288594, 0, -270396, 0, 6396, 0, 84616, 0, 167314, 0, 0, 0, 243630, 0, -68376, 0, 130284, 0, 71736, 0, -102564, 0, -195496, 0, 0, 0, -93840, 0, -113642, 0, -261072, 0, 163170, 0, 239568, 0, -126238, 0, 0, 0, 183980, 0, 100616, 0, -83020, 0, 16848, 0, -54684, 0, -95312, 0, 0, 0, 195224, 0, 100048, 0, 105308, 0, -66938, 0, 0, 0, -252574, 0, 0, 0, 50912, 0, -5688, 0, -67816, 0, 148, 0, 58800, 0, -30912, 0, 0, 0, -162284, 0, -187468, 0, -95312, 0, -19372, 0, -36484, 0, 213934, 0, 0, 0, -180830, 0, -40240, 0, -145488, 0, -150896, 0, 186480, 0, 25088, 0, 0, 0, 150072, 0, -74902, 0, 32144, 0, 110704, 0, 13328, 0, 368900, 0, 0, 0, 115092, 0, -316416, 0, -326858, 0, 155424, 0, 213038, 0, -104160, 0, 0, 0, 84308, 0, 23606, 0, -230552, 0, -267676, 0, -22792, 0, -100534, 0, 0, 0, 47140, 0, -75336, 0, 119084, 0, 1184, 0, 1946, 0, 18396, 0, 0, 0, -281712, 0, 238114, 0, -228956, 0, -269748, 0, -215040, 0, 46620, 0, 0, 0, -142844, 0, 96200, 0, -280980, 0, 113728, 0, -80220, 0, -337568, 0, 0, 0, -128612, 0, 81520, 0, -89656, 0, -165760, 0, 60984, 0, 55510, 0, 0, 0, 89922, 0, 347732, 0, 146076, 0, -2280, 0, 136598, 0, -165760, 0, 0, 0, 174632, 0, 212164, 0, 144984, 0, -77768, 0, -219632, 0, 82278, 0, 0, 0, -221926, 0, 83800, 0, 139664, 0, 69960, 0, -70546, 0, 26824, 0, 0, 0, -361044, 0, 279598, 0, 91168, 0, -35532, 0, -259084, 0, -92820, 0, 0, 0, 64314, 0, 105672, 0, -79604, 0, -90632, 0, -73038, 0, 47068, 0, 0, 0, 75480, 0, -68508, 0, -228592, 0, -226514, 0, -112560, 0, -311920, 0, 0, 0, -69274, 0, -44616, 0, 57260, 0, 177232, 0, 187712, 0, -234136, 0, 0, 0, -146088, 0, 261664, 0, -212800, 0, 45156, 0, 58520, 0, 152866, 0, 0, 0, 152662, 0, -97612, 0, -73990, 0, 38184, 0, -334096, 0, -419664, 0, 0, 0, 97360, 0, -147690, 0, 25900, 0, 180044, 0, 150864, 0, -8806, 0, 0, 0, 111118, 0, 122000, 0, -95172, 0, -36372, 0, 124320, 0, -51408, 0, 0, 0, -240796, 0, 67442, 0, 28224, 0, 34660, 0, 328972, 0, 217182, 0, 0, 0, -86292, 0, -82052, 0, 97384, 0, 84160, 0, -5068, 0, 176204, 0, 0, 0, 308448, 0, 37888, 0, 486332, 0, 219828, 0, -488992, 0, -146048, 0, 0, 0, 12920, 0, 187168, 0, 84714, 0, -266548, 0, -9632, 0, 267288, 0, 0, 0, 127692, 0, -139326, 0, -43680, 0, 18172, 0, 207396, 0, -16058, 0, 0, 0, -30126, 0, -137640, 0, -66024, 0, -151648, 0, 255374, 0, -7756, 0, 0, 0, 283272, 0, -84000, 0, 177912, 0, 125430, 0, 151032, 0, -89628, 0, 0, 0, 15234, 0, 164864, 0, 176638, 0, 247744, 0, -177030, 0, 362600, 0, 0, 0, -122432, 0, 32160, 0, -226912, 0, -20682, 0, 170940, 0, -132734, 0, 0, 0, 56980, 0, -15068, 0, 260372, 0, -95608, 0, -314538, 0, -16856, 0, 0, 0, -329056, 0, 193656, 0, 106708, 0, 19612, 0, -69384, 0, 37800, 0, 0, 0, -22704, 0, -145632, 0, -199220, 0, -3024, 0, 136752, 0, 20944, 0, 0, 0, 50840, 0, -284754, 0, -357672, 0, -129870, 0, -9884, 0, -83160, 0, 0, 0, -148346, 0, 359900, 0, -227920, 0, 113112, 0, 60774, 0, 133644, 0, 0, 0, 360816, 0, -421134, 0, 156800, 0, -36188, 0, -30240, 0, -250530, 0, 0, 0, -264180, 0, -300248, 0, -229278, 0, -304140, 0, -315042, 0, 359800, 0, 0, 0, -291724, 0, -32074, 0, 155400, 0, 318204, 0, 148260, 0, 27454, 0, 0, 0, -133856, 0, 133348, 0, -244412, 0, -206984, 0, -49728, 0, 149520, 0, 0, 0, 205720, 0, -20638, 0, -44912, 0, 102660, 0, -76776, 0, -32914, 0, 0, 0, 247542, 0, -287984, 0, 441854, 0, -2268, 0, 123144, 0, 52080, 0, 0, 0, -15780, 0, 74592, 0, 92512, 0, -43422, 0, 582232, 0, -119686, 0, 0, 0, -11322, 0, -166216, 0, 202622, 0, -314352, 0, -31794, 0, 210868, 0, 0, 0, -68112, 0, -194574, 0, 50680, 0, 300780, 0, -264152, 0, 217042, 0, 0, 0, -71296, 0, 10656, 0, 107912, 0, 176500, 0, -53340, 0, -461608, 0, 0, 0, 333148, 0, -184384, 0, 383208, 0, 138972, 0, 68628, 0, 158466, 0, 0, 0, 195866, 0, 100360, 0, -37814, 0, -85160, 0, 309162, 0, 122248, 0, 0, 0, 27424, 0, -141900, 0, 170940, 0, -26468, 0, 271432, 0, 25774, 0, 0, 0, 209346, 0, -86256, 0, 98070, 0, 182800, 0, -250138, 0, -69048, 0, 0, 0, 149740, 0, -57792, 0, -101528, 0, -104306, 0, -18396, 0, 79254, 0, 0, 0, 290550, 0, -201724, 0, 276276, 0, 197984, 0, 435120, 0, 371980, 0, 0, 0, -163600, 0, -300718, 0, -138432, 0, -378066, 0, -230664, 0, 54950, 0, 0, 0, -69456, 0, -404368, 0, -62720, 0, 430432, 0, -340228, 0, 180264, 0, 0, 0, 197368, 0, -5106, 0, -241416, 0, 405974, 0, -17612, 0, 4998, 0, 0, 0, 353646, 0, -164088, 0, -127708, 0, -57424, 0, 24878, 0, 164276, 0, 0, 0, 178880, 0, 286230, 0, 89096, 0, 75564, 0, -69832, 0, 337218, 0, 0, 0, -280556, 0, -59680, 0, 186606, 0, 436, 0, 127946, 0, -242368, 0, 0, 0, -408924, 0, -185100, 0, 508032, 0, -311054, 0, -454300, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "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": "28.4.e.a", "char_is_minimal": false, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [0, 0], [0, -1], [0, 0], [7, -2], [0, 0], [0, 0], [0, 0], [10, 0], [0, 0], [-16, -7], [0, 0], [14, 4], [0, 0], [74, -7], [0, 0], [77, -4], [0, 0], [-112, -3], [0, 0], [0, 0], [0, 0], [-34, -7], [0, 0], [72, -28], [0, 0], [0, 17], [0, 0], [-118, -28], [0, 0], [-98, -7], [0, 0], [259, 16], [0, 0], [0, 0], [0, 0], [173, -42], [0, 0], [-148, -14], [0, 0], [210, 12], [0, 0], [172, 0], [0, 0], [70, -20], [0, 0], [42, 15], [0, 0], [0, 0], [0, 0], [148, -77], [0, 0], [-219, 42], [0, 0], [406, -17], [0, 0], [111, 112], [0, 0], [-28, -37], [0, 0], [-49, -74], [0, 0], [0, 0], [0, 0], [-198, 0], [0, 0], [-168, -7], [0, 0], [259, 34], [0, 0], [-448, 56], [0, 0], [-483, 20], [0, 0], [1036, -72], [0, 0], [0, 0], [0, 0], [26, 133], [0, 0], [-899, 0], [0, 0], [196, 88], [0, 0], [835, -182], [0, 0], [1036, 118], [0, 0], [-147, 60], [0, 0], [0, 0], [0, 0], [259, 98], [0, 0], [-562, 203], [0, 0], [210, -76], [0, 0], [-160, -70], [0, 0]]}