# Stored data for newform 1344.4.a.bq, downloaded from the LMFDB on 20 April 2024.
{"label": "1344.4.a.bq", "space_label": "1344.4.a", "level": 1344, "weight": 4, "hecke_orbit": 43, "hecke_orbit_code": 189151184416671040, "dim": 2, "is_polredabs": true, "nf_label": "2.2.337.1", "trace_hash": 1090643161714687896, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[5, [-328, -6, 1]], [11, [-168, 26, 1]]], "qexp_display": "q+3q^{3}+(3+\\beta )q^{5}-7q^{7}+9q^{9}+(-13+\\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": 21504, "fricke_eigenval": -1, "atkin_lehner_string": "+-+", "analytic_conductor": 79.29856704771538, "hecke_ring_index": 2, "level_radical": 42, "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": [1344, 1, [127, 1093, 449, 577], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [2, 3, 7], "conrey_indexes": [1], "field_disc": 337, "field_disc_factorization": [[337, 1]], "field_poly": [-84, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.951", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.077", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "57.964", "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], [3, -1], [7, 1]], "trace_display": [0, 6, 6, -14], "traces": [0, 2, 0, 6, 0, 6, 0, -14, 0, 18, 0, -26, 0, -96, 0, 18, 0, 78, 0, -40, 0, -42, 0, 22, 0, 442, 0, 54, 0, -204, 0, 96, 0, -78, 0, -42, 0, -504, 0, -288, 0, -102, 0, -296, 0, 54, 0, -780, 0, 98, 0, 234, 0, -192, 0, -752, 0, -120, 0, -212, 0, 100, 0, -126, 0, -1636, 0, -212, 0, 66, 0, -534, 0, 1128, 0, 1326, 0, 182, 0, 468, 0, 162, 0, 824, 0, -1788, 0, -612, 0, -2118, 0, 672, 0, 288, 0, -120, 0, 400, 0, -234, 0, 362, 0, -1624, 0, -126, 0, -1658, 0, -652, 0, -1512, 0, 1564, 0, -3304, 0, -864, 0, -546, 0, -1650, 0, -306, 0, 4620, 0, 2388, 0, -888, 0, -3440, 0, 280, 0, 162, 0, 2024, 0, -984, 0, -2340, 0, 2596, 0, -612, 0, 294, 0, 5184, 0, -2096, 0, 702, 0, -10496, 0, -4340, 0, -576, 0, -154, 0, -1964, 0, -2256, 0, 3204, 0, 2910, 0, -360, 0, 2114, 0, -3094, 0, -636, 0, -2966, 0, 6104, 0, 300, 0, -164, 0, 1008, 0, -378, 0, -30, 0, -2696, 0, -4908, 0, -1856, 0, -3960, 0, -636, 0, 1428, 0, 7108, 0, 198, 0, 520, 0, 912, 0, -1602, 0, -11672, 0, -672, 0, 3384, 0, 300, 0, -9848, 0, 3978, 0, 1340, 0, -1096, 0, 546, 0, -7240, 0, 4400, 0, 1404, 0, 6614, 0, 5232, 0, 486, 0, 294, 0, 1920, 0, 2472, 0, 3308, 0, 3084, 0, -5364, 0, 9690, 0, 3528, 0, -1836, 0, -3130, 0, -12708, 0, -6354, 0, -714, 0, -13112, 0, 2016, 0, -9790, 0, -2304, 0, 864, 0, 1872, 0, -1624, 0, -360, 0, 714, 0, -718, 0, 1200, 0, -5734, 0, -10072, 0, -702, 0, 5684, 0, 2072, 0, 1086, 0, 11084, 0, -8352, 0, -4872, 0, -12124, 0, 6964, 0, -378, 0, 4672, 0, 2652, 0, -4974, 0, -1560, 0, -29304, 0, -1956, 0, 5460, 0, -8736, 0, -4536, 0, 712, 0, -9652, 0, 4692, 0, 9536, 0, -686, 0, -9912, 0, -3446, 0, -1724, 0, -2592, 0, 15326, 0, -9016, 0, -1638, 0, 3978, 0, -12918, 0, -4950, 0, 10124, 0, 18096, 0, -918, 0, 1344, 0, -10652, 0, 13860, 0, 9792, 0, -2320, 0, 7164, 0, 1768, 0, 5264, 0, -2664, 0, -13676, 0, 10968, 0, -10320, 0, 40496, 0, -11876, 0, 840, 0, 4256, 0, 16960, 0, 486, 0, 5204, 0, 5360, 0, 6072, 0, 1484, 0, 34824, 0, -2952, 0, -7316, 0, 8096, 0, -7020, 0, 5106, 0, -700, 0, 7788, 0, -24878, 0, -12196, 0, -1836, 0, -440, 0, 4272, 0, 882, 0, -2086, 0, 11844, 0, 15552, 0, -15180, 0, -6088, 0, -6288, 0, 11452, 0, 1652, 0, 2106, 0, 16074, 0, -12740, 0, -31488, 0, -3932, 0, 1484, 0, -13020, 0, 14632, 0, -8840, 0, -1728, 0, -17556, 0, 21496, 0, -462, 0, 48380, 0, 11400, 0, -5892, 0, 15930, 0, -7956, 0, -6768, 0, 3738, 0, -4032, 0, 9612, 0, -16544, 0, -61596, 0, 8730, 0, -4234, 0, -7896, 0, -1080, 0, 14000, 0, 3400, 0, 6342, 0, -34074, 0, -17128, 0, -9282, 0, 36096, 0, -7242, 0, -1908, 0, -9932, 0, 15920, 0, -8898, 0, -1274, 0, 7776, 0, 18312, 0, 62748, 0, 22652, 0, 900, 0, 4080, 0, -3276, 0, -492, 0, 25288, 0, 35776, 0, 3024, 0, 11620, 0, -19572, 0, -1134, 0, -232, 0, 19684, 0, -90, 0, -15358, 0, 1084, 0, -8088, 0, -5768, 0, 14628, 0, -14724, 0, -6156, 0, -1920, 0, -5568, 0, 37486, 0, 12516, 0, -11880, 0, 25794, 0, -7604, 0, -1908, 0, 12574, 0, 29520, 0, 4284, 0, 23960, 0, -908, 0, 21324, 0, -2384, 0, -9088, 0, 594, 0, 14826, 0, 35446, 0, 1560, 0, -23700, 0, -21020, 0, 2736, 0, -18448, 0, -4704, 0, -4806, 0, 26776, 0, 33544, 0, -35016, 0, 9372, 0, 12192, 0, -2016, 0, -388, 0, -45368, 0, 10152, 0, -14466, 0, -9124, 0, 900, 0, 840, 0, -2244, 0, -29544, 0, -12084, 0, -2400, 0, 11934, 0, 14146, 0, -2800, 0, 4020, 0, 29666, 0, 55948, 0, -3288, 0, 33480, 0, 21536, 0, 1638, 0, 18616, 0, -26220, 0, -21720, 0, 19076, 0, 10080, 0, 13200, 0, -2534, 0, -51660, 0, 4212, 0, 54976, 0, 57664, 0, 19842, 0, 9312, 0, 11368, 0, 15696, 0, -45084, 0, 2520, 0, 1458, 0, 20808, 0, 32288, 0, 882, 0, 1408, 0, 21124, 0, 5760, 0, 38218, 0, 3420, 0, 7416, 0, 11606, 0, -25904, 0, 9924, 0, 36848, 0, -42636, 0, 9252, 0, -22710, 0, 4564, 0, -16092, 0, 29048, 0, 12876, 0, 29070, 0, 24098, 0, -43488, 0, 10584, 0, 2040, 0, 14356, 0, -5508, 0, -42676, 0, -44656, 0, -9390, 0, -10948, 0, -26368, 0, -38124, 0, 7554, 0, -50640, 0, -19062, 0, -21404, 0, 23128, 0, -2142, 0, 8340, 0, 4080, 0, -39336, 0, 41288, 0, 5920, 0, 6048, 0, 30712, 0, 17228, 0, -29370, 0, -37066, 0, -2968, 0, -6912, 0, 3822, 0, 81056, 0, 2592, 0, -65124, 0, -27970, 0, 5616, 0, 138138, 0, 11550, 0, -4872, 0, -12284, 0, -7180, 0, -1080, 0, -45638, 0, 11328, 0, 2142, 0, -3234, 0, -42860, 0, -2154, 0, -45176, 0, 7480, 0, 3600, 0, -32340, 0, 1604, 0, -17202, 0, -8634, 0, -4160, 0, -30216, 0, 25508, 0, -16716, 0, -2106, 0, 15600, 0, -13616, 0, 17052, 0, -9792, 0, 28908, 0, 6216, 0, 8876, 0, -52360, 0, 3258, 0, 54978, 0, -43064, 0, 33252, 0, 24080, 0, 10312, 0, -25056, 0, 40460, 0, -103296, 0, -14616, 0, 18322, 0, -1960, 0, -36372, 0, 3024, 0, -10420, 0, 20892, 0, 13814, 0, -38192, 0, -1134, 0, -57850, 0, -67624, 0, 14016, 0, -39964, 0, -101864, 0, 7956, 0, -14168, 0, 117570, 0, -14922, 0, -22916, 0, 91172, 0, -4680, 0, 30520, 0, 6888, 0, -87912, 0, -44688, 0, 9336, 0, -5868, 0, 21832, 0, -6916, 0, 16380, 0, 50664, 0, 47576, 0, -26208, 0, -133200, 0, -81284, 0, -13608, 0, -18172, 0, 20040, 0, 2136, 0, 3840, 0, 16064, 0, -28956, 0, 37626, 0, 4284, 0, 14076, 0, 5342, 0, 51884, 0, 28608, 0, 21942, 0, -100648, 0, -2058, 0, -59710, 0, -15664, 0, -29736, 0, -28452, 0, -13480, 0, -10338, 0, -36288, 0, 15040, 0, -5172, 0, 79582, 0, -81636, 0, -7776, 0, 59352, 0, 14672, 0, 45978, 0, -39196, 0, -22608, 0, -27048, 0, -52380, 0, 2236, 0, -4914, 0, 51408, 0, -130120, 0, 11934, 0, -104256, 0, -42280, 0, -38754, 0, 73472, 0, -117828, 0, -14850, 0, 56592, 0, -78480, 0, 30372, 0, -84842, 0, 30380, 0, 54288, 0, -19506, 0, 45384, 0, -2754, 0, -79742, 0, 57976, 0, 4032, 0, 5504, 0, 26540, 0, -31956, 0, 4240, 0, 81272, 0, 41580, 0, 1078, 0, 45408, 0, 29376, 0, 2240, 0, 59288, 0, -6960, 0, -12312, 0, 13748, 0, 21492, 0, -77428, 0, -45760, 0, 5304, 0, -28952, 0, 15088, 0, 15792, 0, 65268, 0, -2000, 0, -7992, 0, -32698, 0, 33548, 0, -41028, 0, -22428, 0, 8296, 0, 32904, 0, -131940, 0, 660, 0, -30960, 0, 17338, 0, -20370, 0, 121488, 0, -5666, 0, 10404, 0, -35628, 0, -15954, 0, 97352, 0, 2520, 0, -56228, 0, -5616, 0, 12768, 0, -66532, 0, 1416, 0, 50880, 0, -14798, 0, -7344, 0, 1458, 0, -22542, 0, 58548, 0, 15612, 0, 12316, 0, 21658, 0, 16080, 0, -50624, 0, 7848, 0, 18216, 0, 32720, 0, 76608, 0, 4452, 0, 23772, 0, 3932, 0, 104472, 0, 30192, 0, -3920, 0, -8856, 0, 20762, 0, -118136, 0, -21948, 0, 43184, 0, -113560, 0, 24288, 0, 45648, 0, -42728, 0, -21060, 0, -123520, 0, 4240, 0, 15318, 0, -73294, 0, -49704, 0, -2100, 0, 3382, 0, 20308, 0, 23364, 0, -97244, 0, -49424, 0, -74634, 0, 1148, 0, -46092, 0, -36588, 0, -29938, 0, -62120, 0, -5508, 0, 42664, 0, -7056, 0, -1320, 0, 107988, 0, -82856, 0, 12816, 0, -15724, 0, 67052, 0, 2646, 0, -115224, 0, -59864, 0, -6258, 0, 38532, 0, 158336, 0, 35532, 0, 210, 0, 40208, 0, 46656, 0, -99024, 0, -23036, 0, -45540, 0, 10680, 0, 18872, 0, -18264, 0, 28064, 0, 44848, 0, -18864, 0, -14042, 0, 79560, 0, 34356, 0, 14694, 0, 28398, 0, 4956, 0, -72540, 0, -136896, 0, 6318, 0, 12992, 0, -27484, 0, 48222, 0, 228988, 0, -22560, 0, -38220, 0, 37796, 0, 27720, 0, -94464, 0, -5432, 0, 58728, 0, -11796, 0, -52820, 0, 122892, 0, 4452, 0, 6828, 0, -64920, 0, -39060, 0, -91144, 0, -98112, 0, 43896, 0, -9996, 0, -38816, 0, -26520, 0, -58432, 0, -65560, 0, -5184, 0, 104218, 0, -49756, 0, -52668, 0, 6310, 0, 79768, 0, 64488, 0, -159870, 0, 8632, 0, -1386, 0, -4174, 0, 76276, 0, 145140, 0, -145280, 0, 97664, 0, 34200, 0, -3640, 0, -42140, 0, -17676, 0, -26544, 0, 78776, 0, 47790, 0, -103468, 0, -6384, 0, -23868, 0, 52996, 0, 88048, 0, -20304, 0, 114416, 0, -1184, 0, 11214, 0, -56264, 0, 163984, 0, -12096, 0, 112930, 0, -9360, 0, 28836, 0, 81704, 0, -76188, 0, -49632, 0, -30576, 0, -137196, 0, -184788, 0, 40532, 0, 4704, 0, 26190, 0, -84446, 0, 86804, 0, -12702, 0, -8776, 0, -146544, 0, -23688, 0, 150184, 0, 19584, 0, -3240, 0, -9072, 0, -125096, 0, 42000, 0, -2100, 0, 57488, 0, 10200, 0, -51294, 0, 67424, 0, 19026, 0, 82548, 0, 68936, 0, -102222, 0, -22244, 0, 137856, 0, -51384, 0, 40796, 0, 44152, 0, -27846, 0, -16480, 0, -27660, 0, 108288, 0, 68878, 0, -262324, 0, -21726, 0, -9380, 0, 53024, 0, -5724, 0, 76704, 0, 3468, 0, -29796, 0, 133518, 0, 7672, 0, 47760, 0, -214142, 0, 142520, 0, -26694, 0, -686, 0, 35760, 0, -3822, 0, -57378, 0, -58048, 0, 23328, 0, -375432, 0, 4496, 0, 54936, 0, 50680, 0, 31196, 0, 188244, 0, -69838, 0, -55260, 0, 67956, 0, 184896, 0, -30800, 0, 2700, 0, -125940, 0, -63400, 0, 12240, 0, 73544, 0, -63652, 0, -9828, 0, -15888, 0, -38956, 0, -1476, 0, -38382, 0, 129608, 0, 75864, 0, -46298, 0, -38764, 0, 107328, 0, -21292, 0, -51086, 0, 9072, 0, -58612, 0, -36624, 0, 34860, 0, 42360, 0, 143924, 0, -58716, 0, -193690, 0, 64560, 0, -3402, 0, 235216, 0, 136448, 0, -696, 0, -71176, 0, 21624, 0, 59052, 0, -2058, 0, 202164, 0, -270, 0, -10762, 0, 162028, 0, -46074, 0, 86076, 0, -13440, 0, 3252, 0, 35444, 0, 152096, 0, -24264, 0, 210040, 0, -13420, 0, -17304, 0, -188500, 0, 121576, 0, 43884, 0, -119952, 0, -131256, 0, -44172, 0, -23156, 0, -27080, 0, -18468, 0, -103528, 0, 27780, 0, -5760, 0, -10200, 0, -21588, 0, -16704, 0, -162498, 0, 75704, 0, 112458, 0, -196904, 0, 9960, 0, 37548, 0, 118110, 0, -200928, 0, -35640, 0, -21648, 0, 155496, 0, 77382, 0, -67830, 0, 83128, 0, -22812, 0, -38754, 0, 4096, 0, -5724, 0, -33572, 0, -24696, 0, 37722, 0, -190312, 0, -127344, 0, 88560, 0, 182248, 0, 289728, 0, 12852, 0, 140800, 0, 139172, 0, 71880, 0, 113600, 0, -113096, 0, -2724, 0, 21910, 0, -8000, 0, 63972, 0, -91736, 0, 57338, 0, -7152, 0, -219540, 0, 88956, 0, -27264, 0, -167238, 0, -137396, 0, 1782, 0, 32748, 0, 31864, 0, 44478, 0, 144754, 0, -200028, 0, 106338, 0, 200216, 0, -170504, 0, 4680, 0, 4998, 0, 166872, 0, -71100, 0, 38410, 0, -167744, 0, -63060, 0, -63576, 0, 91784, 0, 8208, 0, -158864, 0, 21720, 0, -55344, 0, 19952, 0, -152696, 0, -14112, 0, 5584, 0, 202112, 0, -14418, 0, -7240, 0, 133788, 0, 80328, 0, 68530, 0, 113920, 0, 100632, 0, -2812, 0, -211964, 0, -105048, 0, -224568, 0, 16128, 0, 28116, 0, 21624, 0, 72204, 0, 36576, 0, 56450, 0, 30312, 0, -6048, 0, -120768, 0, 32480, 0, -1164, 0, 24120, 0, 14336, 0, -136104, 0, -13104, 0, 43276, 0, 30456, 0, 243598, 0, 337980, 0, -43398, 0, -70628, 0, 11368, 0, -27372, 0, -27540, 0, 105624, 0, 2700, 0, -69916, 0, 242820, 0, 2520, 0, 20404, 0, 110796, 0, -6732, 0, 84222, 0, -42500, 0, -88632, 0, -4998, 0, -180540, 0, -36252, 0, 503808, 0, 41660, 0, -7200, 0, 7600, 0, 5026, 0, 35802, 0, 225890, 0, 15672, 0, 42438, 0, 33160, 0, 167936, 0, -8400, 0, 31674, 0, 267632, 0, 12060, 0, -319572, 0, -114288, 0, 88998, 0, 40138, 0, 58608, 0, 167844, 0, -116922, 0, 54468, 0, -9864, 0, 160728, 0, 70504, 0, 100440, 0, -261076, 0, 13040, 0, 64608, 0, 376216, 0, -31744, 0, 4914, 0, 49776, 0, 100784, 0, 55848, 0, 48662, 0, 129960, 0, -78660, 0, -39788, 0, 60280, 0, -65160, 0, 117872, 0, 102164, 0, 57228, 0, 87644, 0, -14504, 0, 30240, 0, -205146, 0, -109928, 0, 39600, 0, -115056, 0, -88, 0, -7602, 0, 49876, 0, -50328, 0, -154980, 0, -157976, 0, -154872, 0, 12636, 0, -77588, 0, -155824, 0, 164928, 0, -34982, 0, 7976, 0, 172992, 0, -31280, 0, 58464, 0, 59526, 0, -31604, 0, -160232, 0, 27936, 0, 169968, 0, -40120, 0, 34104, 0, 100908, 0, 25476, 0, 47088, 0, -296680, 0, -123660, 0, -135252, 0, 84868, 0, 203292, 0, 7560, 0, 34552, 0, 66080, 0, 4374, 0, 172800, 0, -48748, 0, 62424, 0, -375408, 0, -187584, 0, 96864, 0, 92992, 0, 274536, 0, 2646, 0, 46010, 0, 163954, 0, 4224, 0, 46420, 0, -172736, 0, 63372, 0, -32704, 0, -20324, 0, 17280, 0, -358890, 0, -29016, 0, 114654, 0, -231500, 0, -18564, 0, 10260, 0, 261404, 0, -92456, 0, 22248, 0, 99180, 0, 337292, 0, 34818, 0, -3068, 0, -62724, 0, -77712, 0, -80272, 0, -3632, 0, 29772, 0, 10920, 0, -53696, 0, 110544, 0, -206964, 0, 38660, 0, -127908, 0, -9958, 0, 205128, 0, 27756, 0, 222528, 0, -17792, 0, -68130, 0, -189156, 0, -250104, 0, 13692, 0, -47736, 0, 22436, 0, -48276, 0, 52176, 0, 33000, 0, 87144, 0, -38220, 0, -62988, 0, 38628, 0, 166062, 0, -42920, 0, 87210, 0, 208464, 0, 61152, 0, 72294, 0, -68472, 0, 317392, 0, -130464, 0, 151804, 0, -70692, 0, 31752, 0, -46908, 0, -298920, 0, 6120, 0, -182578, 0, -29904, 0, 43068, 0, -4984, 0, -23128, 0, -16524, 0, -205336, 0, -274120, 0, -128028, 0, 234842, 0, 67564, 0, -133968, 0, -103080, 0, 283840, 0, -28170, 0, -112224, 0, -105328, 0, -32844, 0, -92400, 0, -142992, 0, -79104, 0, -153232, 0, -6600, 0, -114372, 0, -66752, 0, 184452, 0, 22662, 0, 27070, 0, -210384, 0, -151920, 0, -157376, 0, 4802, 0, -57186, 0, 339480, 0, -84048, 0, -64212, 0, 136, 0, -47760, 0, 69384, 0, -248916, 0, -92984, 0, -6426, 0, 64178, 0, 371480, 0, 25020, 0, 24122, 0, -48384, 0, 12240, 0, -130256, 0, -23340, 0, -118008, 0, 263522, 0, 12068, 0, 123864, 0, 135394, 0, -603008, 0, 17760, 0, 92976, 0, -10848, 0, 18144, 0, -93634, 0, -122708, 0, 92136, 0, 182376, 0, -42080, 0, 51684, 0, -107282, 0, -80480, 0, -88110, 0, 332494, 0, 56120, 0, -111198, 0, 204988, 0, 63112, 0, -8904, 0, 68800, 0, -46440, 0, -20736, 0, 492056, 0, -72688, 0, 11466, 0, 113524, 0, 319796, 0, 243168, 0, -330692, 0, 159064, 0, 7776, 0, -27846, 0, -238352, 0, -195372, 0, 88388, 0, -37320, 0, -83910, 0, -296090, 0, 90426, 0, 16848, 0, -50766, 0, 238572, 0, 414414, 0, 182352, 0, -277744, 0, 34650, 0, -5862, 0, -303196, 0, -14616, 0, -243720, 0, 62344, 0, -36852, 0, -70868, 0, -368896, 0, -21540, 0, 91784, 0, 38852, 0, -3240, 0, -211152, 0, -126672, 0, -136914, 0, -478080, 0, -245672, 0, 33984, 0, 90080, 0, 216036, 0, 6426, 0, 185440, 0, 432720, 0, -9702, 0, -120938, 0, -2244, 0, -128580, 0, -9408, 0, 138524, 0, -6462, 0, -40480, 0, -15276, 0, -135528, 0, -254786, 0, 74564, 0, 22440, 0, 104984, 0, 389624, 0, 10800, 0, 133770, 0, -187344, 0, -97020, 0, 119740, 0, -163492, 0, 4812, 0, 201156, 0, -409344, 0, -51606, 0, -68544, 0, 19680, 0, -25902, 0, -95866, 0, -94664, 0, -12480, 0, 14212, 0, 16240, 0, -90648, 0, 40284, 0, 80280, 0, 76524, 0, -23080, 0, -316920, 0, -50148, 0, -80292, 0, -9136, 0, -6318, 0, -241054, 0, -272080, 0, 46800, 0, -12376, 0, 27564, 0, -40848, 0, 218284, 0, 91584, 0, 51156, 0, -387098, 0, -36848, 0, -29376, 0, -174378, 0, -270776, 0, 86724, 0, -188308, 0, -133872, 0, 18648, 0, -203110, 0, -60644, 0, 26628, 0, -51920, 0, 291496, 0, -157080, 0, 95732, 0, 244132, 0, 9774, 0, -242546, 0, -244980, 0, 164934, 0, -173336, 0, -76776, 0, -129192, 0, -47300, 0, -157008, 0, 99756, 0, 25640, 0, -70940, 0, 72240, 0, 36732, 0, 12240, 0, 30936, 0, -392832, 0, 85056, 0, -75168, 0, -283472, 0, -210652, 0, 121380, 0, -218136, 0, -11680, 0, -309888, 0, -29318, 0, 83132, 0, -43848, 0, -105770, 0, 287500, 0, 54966, 0, 102918, 0, 168848, 0, -5880, 0, 824464, 0, 319200, 0, -109116, 0, 127172, 0, 23704, 0, 9072, 0, -29792, 0, -60946, 0, -31260, 0, -40800, 0, -133640, 0, 62676, 0, -417732, 0, -118720, 0, 41442, 0, 200060, 0, -117208, 0, -114576, 0, -103680, 0, 95892, 0, -3402, 0, -226092, 0, -89376, 0, -173550, 0, -2798, 0, -463060, 0, -202872, 0, -36428, 0, -371176, 0, 42048, 0, -551592, 0, 316848, 0, -119892, 0, 265006, 0, -37520, 0, -305592, 0, 68840, 0, 41920, 0, 23868, 0, -274734, 0, -333360, 0, -42504, 0, -8066, 0, 9808, 0, 352710, 0, -193556, 0, 15744, 0, -44766, 0, -10388, 0, 114156, 0, -68748, 0, 238902, 0, 402608, 0, 273516, 0, 92292, 0, -243768, 0, -14040, 0, 180596, 0, -54320, 0, 91560, 0, 266304, 0, -136852, 0, 20664, 0, 154328, 0, -39752, 0, -263736, 0, -19390, 0, -36924, 0, -134064, 0, 51212, 0, 17928, 0, 28008, 0, -136608, 0, 230052, 0, -17604, 0, 209920, 0, -56672, 0, 65496, 0, -174856, 0, 140500, 0, -20748, 0, 49810, 0, 30176, 0, 49140, 0, 241762, 0, 261412, 0, 151992, 0, 1488, 0, -305688, 0, 142728, 0, -35742, 0, 200888, 0, -78624, 0, 103056, 0, 86800, 0, -399600, 0, 165648, 0, 4900, 0, -243852, 0, 16612, 0, 390792, 0, -40824, 0, -375196, 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": "168.4.a.g", "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], [3, 0], [0, 0], [3, 1], [0, 0], [-7, 0], [0, 0], [9, 0], [0, 0], [-13, -1], [0, 0], [-48, -2], [0, 0], [9, 3], [0, 0], [39, -3], [0, 0], [-20, 0], [0, 0], [-21, 0], [0, 0], [11, -5], [0, 0], [221, 6], [0, 0], [27, 0], [0, 0], [-102, 0], [0, 0], [48, -16], [0, 0], [-39, -3], [0, 0], [-21, -7], [0, 0], [-252, 2], [0, 0], [-144, -6], [0, 0], [-51, 11], [0, 0], [-148, -16], [0, 0], [27, 9], [0, 0], [-390, 10], [0, 0], [49, 0], [0, 0], [117, -9], [0, 0], [-96, -18], [0, 0], [-376, -16], [0, 0], [-60, 0], [0, 0], [-106, -14], [0, 0], [50, 16], [0, 0], [-63, 0], [0, 0], [-818, -54], [0, 0], [-106, 2], [0, 0], [33, -15], [0, 0], [-267, -11], [0, 0], [564, 10], [0, 0], [663, 18], [0, 0], [91, 7], [0, 0], [234, 58], [0, 0], [81, 0], [0, 0], [412, 48], [0, 0], [-894, 30], [0, 0], [-306, 0], [0, 0], [-1059, 27], [0, 0], [336, 14], [0, 0], [144, -48], [0, 0], [-60, -20], [0, 0], [200, 70], [0, 0], [-117, -9], [0, 0]]}