# Stored data for newform 2205.4.a.a, downloaded from the LMFDB on 25 April 2024.
{"label": "2205.4.a.a", "space_label": "2205.4.a", "level": 2205, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 67111069, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 2189989361751766799, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [5, 1]], [11, [50, 1]], [13, [-20, 1]], [17, [10, 1]]], "qexp_display": "q-5q^{2}+17q^{4}-5q^{5}-45q^{8}+5^{2}q^{10}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 35280, "fricke_eigenval": -1, "atkin_lehner_string": "++-", "analytic_conductor": 130.09921156265804, "hecke_ring_index": 1, "level_radical": 105, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [2205, 1, [1226, 442, 1081], [1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 1, "level_primes": [3, 5, 7], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.006", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.999", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.946", "prec": 17}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[3, 1], [5, 1], [7, -1]], "trace_display": [-5, 0, -5, 0], "traces": [0, 1, -5, 0, 17, -5, 0, 0, -45, 0, 25, -50, 0, 20, 0, 0, 89, -10, 0, 44, -85, 0, 250, -120, 0, 25, -100, 0, 0, 50, 0, -108, -85, 0, 50, 0, 0, -40, -220, 0, 225, 400, 0, 280, -850, 0, 600, -280, 0, 0, -125, 0, 340, 610, 0, 250, 0, 0, -250, 50, 0, 518, 540, 0, -287, -100, 0, -180, -170, 0, 0, -700, 0, 410, 200, 0, 748, 0, 0, -516, -445, 0, -2000, 660, 0, 50, -1400, 0, 2250, -1500, 0, 0, -2040, 0, 1400, -220, 0, 1630, 0, 0, 425, -450, 0, -770, -900, 0, -3050, -660, 0, 1754, -1250, 0, 0, 310, 0, 600, 850, 0, -250, 0, 0, 1169, -2590, 0, -1836, -125, 0, -1070, 2115, 0, 500, 1950, 0, 0, 900, 0, 450, -1050, 0, -1676, 0, 0, 3500, -1000, 0, -250, -2050, 0, -680, -2050, 0, 448, -1980, 0, 0, 540, 0, 100, 2580, 0, 425, 0, 0, -1900, 6800, 0, -3300, 1920, 0, -1797, -250, 0, 4760, 2550, 0, 0, -4450, 0, 7500, -3650, 0, 4342, 0, 0, 5400, 200, 0, 500, -4760, 0, 1100, 3500, 0, 3350, -8150, 0, 0, -90, 0, -3664, -1125, 0, 2250, 0, 0, -2000, 3850, 0, 1780, -2200, 0, -268, 10370, 0, 3300, -1400, 0, 0, -8770, 0, 4250, -200, 0, 3670, 0, 0, -1550, 3760, 0, 1434, -3000, 0, -2250, 3450, 0, 1400, 850, 0, 0, 4900, 0, -4822, -5845, 0, 8806, 0, 0, 880, 4860, 0, 625, -4650, 0, 6000, 5350, 0, -8279, 5130, 0, 0, -1700, 0, -9750, 1280, 0, -3050, 0, 0, -3060, 3350, 0, -5512, -890, 0, 5250, -1250, 0, 4920, 8380, 0, 0, -4500, 0, 6900, -11900, 0, 5000, 0, 0, -4813, 1250, 0, 6970, 1530, 0, -250, 1800, 0, 10250, -2400, 0, 0, -2240, 0, 3916, -2590, 0, -3040, 0, 0, -2700, -5700, 0, -3110, -500, 0, -8772, 950, 0, -2500, 1435, 0, 0, -440, 0, 500, 9500, 0, -18000, 0, 0, 2292, 11220, 0, -9600, 900, 0, -7730, 8985, 0, 850, 5400, 0, 0, -12600, 0, -12750, 1120, 0, -1186, 0, 0, 4250, 3630, 0, 3500, -25500, 0, 18250, 1800, 0, -4923, -21710, 0, 0, -2050, 0, -8490, -10680, 0, -1000, 0, 0, 100, -2500, 0, 12600, 1000, 0, -8084, -3740, 0, -17500, -9480, 0, 0, -16750, 0, 27710, 10950, 0, 1200, 0, 0, 450, 2580, 0, -13840, 18320, 0, 2225, -9300, 0, -2160, -7650, 0, 0, 2000, 0, 2854, 10000, 0, -13090, 0, 0, -3300, -1700, 0, 11000, 1150, 0, -11162, 1340, 0, -27450, -250, 0, 0, -11220, 0, 7000, 1200, 0, -1510, 0, 0, 29818, -5280, 0, -424, -11250, 0, 1000, -12360, 0, 7500, -18350, 0, 0, 1300, 0, -20000, 5270, 0, -18800, 0, 0, -7190, -7170, 0, 10200, -150, 0, 2670, 4450, 0, -17250, 1180, 0, 0, -7000, 0, -2250, -14000, 0, 1100, 0, 0, -24500, -14100, 0, -800, 24110, 0, 19873, -8150, 0, -9850, -23310, 0, 0, 2450, 0, -500, -4400, 0, -9612, 0, 0, -17036, -2125, 0, 23250, -20600, 0, 2250, -30000, 0, -18190, 5750, 0, 0, 24475, 0, -25650, 3850, 0, 14000, 0, 0, 4500, -15500, 0, 13940, 33150, 0, -6400, 1080, 0, 2233, 15250, 0, 0, 8000, 0, 3300, 8100, 0, -16750, 0, 0, -20478, 27560, 0, 850, -8770, 0, 12040, -17850, 0, 6250, 2200, 0, 0, -24600, 0, -28492, -23550, 0, 5600, 0, 0, 22500, -6120, 0, -1550, -34500, 0, 31500, 11700, 0, -8188, -17000, 0, 0, -3000, 0, -11690, 24065, 0, -4250, 0, 0, -30500, -18450, 0, -7650, 21060, 0, -4752, 1250, 0, -3560, -22910, 0, 0, -34850, 0, 12000, 1400, 0, 11002, 0, 0, 7616, -5845, 0, -4630, -3740, 0, 12950, -5600, 0, 24040, 15200, 0, 0, 1890, 0, -19244, 9180, 0, 28500, 0, 0, 625, 15550, 0, 1700, 400, 0, 15892, 23220, 0, -4750, 5350, 0, 0, 12500, 0, -10575, 12600, 0, -7260, 0, 0, 2200, 7400, 0, -2500, -2500, 0, -32300, 4790, 0, -9750, 35600, 0, 0, 1450, 0, -11818, -11460, 0, -29700, 0, 0, -6000, 32640, 0, -4500, -25900, 0, 5550, 38650, 0, -30549, 12930, 0, 0, -2250, 0, -27000, -32580, 0, 5250, 0, 0, 24920, 12200, 0, -10228, 43350, 0, -5600, 8380, 0, -4000, 5930, 0, 0, -8350, 0, -1760, 14350, 0, -18150, 0, 0, -14954, -17500, 0, 67500, 12960, 0, 5000, -62050, 0, -9000, 29400, 0, 0, 24615, 0, 73814, 1250, 0, 16330, 0, 0, 10250, -2800, 0, -30800, 42450, 0, 10200, 9000, 0, -9524, 3400, 0, 0, 28600, 0, 10250, -500, 0, 8500, 0, 0, -8252, -24920, 0, -5000, -2240, 0, -24920, 40420, 0, 9900, 27900, 0, 0, 59500, 0, 47400, 1000, 0, 11506, 0, 0, 56950, -12510, 0, -2700, -73350, 0, -54750, 17600, 0, 35000, -6000, 0, 0, -500, 0, 1100, -1530, 0, -12900, 0, 0, 10360, 69200, 0, -62288, -4490, 0, 2800, -2125, 0, 46500, -20500, 0, 0, 10800, 0, 20250, -28600, 0, -10068, 0, 0, -10000, 9500, 0, 12320, -14270, 0, -34000, 14250, 0, 6830, 34650, 0, 0, 8920, 0, 3534, 16500, 0, -5740, 0, 0, -9600, -37400, 0, -5750, -8000, 0, -21889, 55810, 0, -4556, 8985, 0, 0, 54290, 0, 1250, 4800, 0, -5160, 0, 0, 29700, 7670, 0, -25804, -23800, 0, -6000, -400, 0, -12750, 7550, 0, 0, 25800, 0, -3600, -78930, 0, 26400, 0, 0, -35100, 2120, 0, 22250, -18700, 0, -2980, -3400, 0, 61800, -35880, 0, 0, -37500, 0, 62390, -12320, 0, 18250, 0, 0, -6500, -5400, 0, -6100, 100000, 0, -13950, -21710, 0, 45240, 63920, 0, 0, -33200, 0, -33000, 35950, 0, 24378, 0, 0, 35356, -27000, 0, 750, -14000, 0, -1000, -13350, 0, -4250, -25700, 0, 0, 58650, 0, -5900, -2500, 0, -52890, 0, 0, 23800, 38050, 0, -48000, 4450, 0, 70000, 29640, 0, 8200, -5500, 0, 0, -15170, 0, -17500, 83300, 0, 70500, 0, 0, -18127, 4000, 0, -81974, -16750, 0, -5470, -52605, 0, 40750, 15150, 0, 0, 49250, 0, 46102, -31190, 0, 75000, 0, 0, -12250, -7560, 0, 450, 2500, 0, 14960, -33600, 0, 32672, 9180, 0, 0, 18320, 0, 4740, 85180, 0, 5625, 0, 0, -500, -79050, 0, 103000, 26840, 0, 38054, -11250, 0, 102000, 47230, 0, 0, 48150, 0, -28750, 15150, 0, 338, 0, 0, -56143, 10000, 0, -10320, 87210, 0, -19250, -40200, 0, -15570, -70000, 0, 0, -5180, 0, 49124, -8900, 0, 77500, 0, 0, 11000, -69700, 0, -87750, 21300, 0, 8148, 21760, 0, -5400, 1340, 0, 0, -11165, 0, -51850, -17850, 0, 15010, 0, 0, -40000, -81500, 0, -94, -16500, 0, -16020, -2000, 0, 7000, 56950, 0, 0, 13200, 0, 33600, 102390, 0, -93704, 0, 0, -30970, 2870, 0, 43850, -30650, 0, -44360, -60200, 0, 47250, 29050, 0, 0, -21250, 0, -11000, -16320, 0, 1000, 0, 0, 83640, 36050, 0, 22500, 75420, 0, 117750, -18350, 0, 660, -28000, 0, 0, 2200, 0, -49060, -76500, 0, 30600, 0, 0, -22234, 7750, 0, 117300, 38500, 0, -18800, -62300, 0, -58500, 1800, 0, 0, 40940, 0, 45000, -7170, 0, 4320, 0, 0, 15000, -72100, 0, 50930, 58450, 0, -81821, -30000, 0, 22792, 11250, 0, 0, -28760, 0, -17250, 152500, 0, 36490, 0, 0, 11988, 26010, 0, -105300, -7000, 0, 33000, 23760, 0, -4250, 4250, 0, 0, 3400, 0, 114550, -34980, 0, 20000, 0, 0, 92250, -56990, 0, -24500, -40800, 0, -7000, -87700, 0, -3998, -55010, 0, 0, 24110, 0, 7000, -20160, 0, 29225, 0, 0, -11700, 23150, 0, -12628, -43470, 0, -73200, -44030, 0, 28000, 48640, 0, 0, -120200, 0, -51680, -83850, 0, -24108, 0, 0, -9450, -4400, 0, -53220, 96220, 0, -24300, -4100, 0, -15500, -96900, 0, 0, 14000, 0, -15886, -3125, 0, -52870, 0, 0, 23250, -4500, 0, -2000, -75150, 0, 32600, -79460, 0, -45924, -30000, 0, 0, 16150, 0, -26750, -43200, 0, -7920, 0, 0, -42500, 14370, 0, 6916, 41395, 0, -63000, -13640, 0, -25650, 36300, 0, 0, 45900, 0, 86572, -7480, 0, -37000, 0, 0, 53150, 12500, 0, 8500, -44750, 0, -35430, 85500, 0, -23950, 1640, 0, 0, 48750, 0, -34000, -9000, 0, -6400, 0, 0, -7250, 54300, 0, -20738, 59090, 0, 38964, 15250, 0, -58790, 58740, 0, 0, 8100, 0, -30240, 30000, 0, -86400, 0, 0, -15400, 15300, 0, 129500, 5160, 0, -16750, -27750, 0, -131410, -30800, 0, 0, 80865, 0, -64650, 27560, 0, -6000, 0, 0, 4450, -96300, 0, -14000, 91800, 0, 162900, 14600, 0, -49053, -26250, 0, 0, -88110, 0, 6250, -23800, 0, -61000, 0, 0, -28658, 51140, 0, -114750, -24600, 0, 18040, 19040, 0, -41900, -13200, 0, 0, 20000, 0, -20162, 53500, 0, -96536, 0, 0, 41750, -62160, 0, 22500, 8800, 0, -105750, 24600, 0, -6600, 61710, 0, 0, -34500, 0, 35080, 74770, 0, 59500, 0, 0, 105070, -133500, 0, -64800, 49540, 0, -34066, -25000, 0, 164250, 50370, 0, 0, 30600, 0, -147000, 39800, 0, -97500, 0, 0, -83691, 24065, 0, 78410, -195390, 0, -6250, 16950, 0, -21060, -81650, 0, 0, 30240, 0, 56396, -34850, 0, 14000, 0, 0, -7650, 154000, 0, -144330, 6200, 0, -22888, 34440, 0, -45000, 1250, 0, 0, 47620, 0, -9000, -31100, 0, 96940, 0, 0, -143000, 53040, 0, 98526, -51250, 0, 1700, 94430, 0, 12000, -22500, 0, 0, -18450, 0, -22704, 41260, 0, 23800, 0, 0, 52500, 17000, 0, 11200, 63900, 0, 15000, 124600, 0, -137428, -16000, 0, 0, -19580, 0, -139500, -9840, 0, 12950, 0, 0, -157500, 83800, 0, 16692, -161160, 0, -5000, 15200, 0, 30500, -57530, 0, 0, 21600, 0, -44350, -150750, 0, 62550, 0, 0, -44286, 13500, 0, 145070, -70530, 0, 28500, 186150, 0, -88000, 117500, 0, 0, -175000, 0, 20400, 15550, 0, 25510, 0, 0, 2500, 72650, 0, 23380, -5500, 0, 4050, 29040, 0, -9916, 43860, 0, 0, -25400, 0, -4750, -51800, 0, -235280, 0, 0, -11200, 164880, 0, 22450, 12500, 0, 95200, -14000, 0, -7175, 41600, 0, 0, -158100, 0, 102500, -103320, 0, -81954, 0, 0, -36720, -29930, 0, 2200, -40050, 0, 143000, -40950, 0, -37862, 50340, 0, 0, -2500, 0, 22780, 34000, 0, -47500, 0, 0, 84000, -61600, 0, 48518, -107730, 0, 102500, 90000, 0, -71250, -65880, 0, 0, -34150, 0, -68530, -16300, 0, -21400, 0, 0, -44600, -11460, 0, 88330, -17670, 0, -56100, -22400, 0, 3730, 42300, 0, 0, 127040, 0, -114206, 48000, 0, 99000, 0, 0, -4500, 19550, 0, 40000, -49200, 0, 91079, 109445, 0, -189754, 38650, 0, 0, 12060, 0, -44925, -66000, 0, 77040, 0, 0, -51850, -111270, 0, 96836, -4250, 0, -24000, 39000, 0, -27000, 25800, 0, 0, 110350, 0, 2500, -58740, 0, -38350, 0, 0, 4500, 129020, 0, 63000, 10600, 0, 102860, 20400, 0, 2000, -5000, 0, 0, 63750, 0, -25670, -72290, 0, -5600, 0, 0, -129000, 11200, 0, 115522, 18000, 0, 156106, 5930, 0, -12080, -89760, 0, 0, 7700, 0, 123010, 175500, 0, -7208, 0, 0, 39396, -21250, 0, 93500, 112000, 0, -18150, 14900, 0, 9000, 25900, 0, 0, -210120, 0, 179400, -17500, 0, -13710, 0, 0, 127500, -21000, 0, -33770, -165150, 0, 61600, 35760, 0, 29226, -91250, 0, 0, 95000, 0, -9000, 22100, 0, 27000, 0, 0, 74202, 30500, 0, -340000, 24615, 0, -33520, 27590, 0, 108550, -89850, 0, 0, -226200, 0, -169200, 61920, 0, 6600, 0, 0, 166000, -50600, 0, 10250, 165000, 0, -122230, -5400, 0, 39208, -64530, 0, 0, 42450, 0, -96000, -176780, 0, 53400, 0, 0, 71720, -2550, 0, 70000, -112760, 0, -1107, 5000, 0, 45390, -17540, 0, 0, -14350, 0, 128500, 89850, 0, 35082, 0, 0, -155250, -500, 0, -82560, 20060, 0, 12500, -32700, 0, -138710, 264450, 0, 0, -85170, 0, -3584, -63000, 0, -190250, 0, 0, -5000, 240000, 0, -4250, -21600, 0, -55944, -238000, 0, -148200, 40420, 0, 0, -41000, 0, 18700, -155050, 0, -127500, 0, 0, 75850, 34780, 0, -79200, 87500, 0, -220500, 55890, 0, 47400, -239700, 0, 0, -19800, 0, -3100, 90635, 0, -13600, 0, 0, -112000, 216990, 0, 83750, 6450, 0, 72440, 27350, 0, 104041, -41000, 0, 0, -138550, 0, -75750, -9000, 0, -54750, 0, 0, -167450, 60450, 0, -37052, -44030, 0, 155950, -6000, 0, -33880, -375000, 0, 0, -24400, 0, 8960, 41650, 0, 37800, 0, 0, 182500, -2250, 0, -8500, -25170, 0, -12900, -39600, 0, 168000, 51450, 0, 0, -163360, 0, 30996, 69200, 0, -53840, 0, 0, -91600, -217100, 0, 1170, -23700, 0, -289612, -143210, 0, 72136, -11125, 0, 0, -74700, 0, 46500, 2500, 0, 209250, 0, 0, 172132, -350200, 0, -134200, 10800, 0, -130270, -190270, 0, 38250, -78400, 0, 0, -270000, 0, -236150, -113700, 0, -130334, 0, 0, -95230, -29040, 0, -10000, 97750, 0, -75750, -99900, 0, 2000, -1690, 0, 0, -14270, 0, 180000, 84915, 0, -50000, 0, 0, -7260, 51600, 0, -230850, -11690, 0, -35000, 65450, 0, 201000, -50160, 0, 0, 77850, 0, 238000, 43650, 0, 77176, 0, 0, 25900, 16500, 0, 19440, -245620, 0, 8500, 131100, 0, -75160, -263500, 0, 0, 20600, 0, 88874, -55000, 0, 236980, 0, 0, -5750, 173550, 0, -106500, -55350, 0, -175000, -40740, 0, -57600, 55810, 0, 0, 18360, 0, -6700, -3300, 0, 4770, 0, 0, 37961, 20500, 0, -38000, 137250, 0, 89250, -167500, 0, 1250, -75050, 0, 0, 112200, 0, -49892, 136000, 0, 407500, 0, 0, 109910, 470, 0, 56100, 81350, 0, 102670, 15300, 0, 10000, 13640, 0, 0, -35000, 0, -150750, -104550, 0, -6000, 0, 0, -66000, 10700, 0, -44182, -168000, 0, -348126, 7550, 0, 4500, 248040, 0, 0, 38400, 0, 244000, 154850, 0, -21150, 0, 0, -9316, -149090, 0, 153250, -2000, 0, 26400, 221800, 0, 204680, 183200, 0, 0, -93450, 0, -145250, 2120, 0, -79880, 0, 0, 56250, 75600, 0, 74960, 37400, 0, 81600, -166320, 0, -25423, -5000, 0, 0, -89870, 0, 61800, -221400, 0, -180250, 0, 0, -7962, -112500, 0, -149164, -37500, 0, -19500, -400350, 0, 91750, -195600, 0, 0, -3300, 0, 95200, 49090, 0, 55924, 0, 0, -11000, -167300, 0, -6500, 245300, 0, 202500, 51000, 0, -156748, -104040, 0, 0, 100000, 0, -20720, 111170, 0, -26350, 0, 0, -44280, -310500, 0, -192500, 141460, 0, -43594, 94000, 0, 59500, 71830, 0, 0, 198900, 0, -9000, 170800, 0, 12742, 0, 0, -139196, 35950, 0, 170670, -89000, 0, 35850, -25800, 0, 147820, -21600, 0, 0, -132070, 0, 51436, -51000, 0, 360500, 0, 0, 750, -254650, 0, -198730, -21450, 0, 111432, 216585, 0, 150000, -13350, 0, 0, -113960, 0, -22250, 13400, 0, 54000, 0, 0, 143800, -73000, 0, 10500, 86250, 0, -518500, 73690, 0, -5900, -34850, 0, 0, -67050, 0, -4022, -59940, 0, -68850, 0, 0, 207280, 358020, 0, 35000, 87300, 0, 86840, -165000, 0, -80784, 75790, 0, 0, 11250, 0, -21250, 16760, 0, 70000, 0, 0, 11480, 92400, 0, 80412, -389470, 0, 174900, -5500, 0, 118410, -100000, 0, 0, 143450, 0, 147830, -182450, 0, 284950, 0, 0, -17574, 122500, 0, 108000, 103710, 0, 70500, 23800, 0, 438500, -47600, 0, 0, 19990, 0, 187034, 4000, 0, 33000, 0, 0, -120550, 173250, 0, -47080, -35000, 0, 39872, 122430, 0, 20000, -99365, 0, 0, -135680, 0, 40750, 58500, 0, -78710, 0, 0, 10000, 93060, 0, 217350, 49250, 0, 19660, 366000, 0, 116550, -85600, 0, 0, -95200, 0, -243200, 169920, 0, 55728, 0, 0, 408680, -183500, 0, -12250, 136800, 0, 419250, -158450, 0, 79200, 120540, 0, 0, 2500, 0, -138620, 32130, 0, 22000, 0, 0, 110770, 266100, 0, -327148, -201450, 0, 7200, 48060, 0, 20500, 70000, 0, 0, 77500, 0, 256500, 85800, 0, -170800, 0, 0, -70000, 85180, 0, -188000, 79430, 0, 10625, 207200, 0, -1350, 139950, 0, 0, -210480, 0, 67000, -116250, 0, 8900, 0, 0, 103000, 6800, 0, 375750, -71700, 0, -188362, -163000, 0, 270164, -11250, 0, 0, 43860, 0, 150000, -41850, 0, 20500, 0, 0, -42750, 14000, 0, 90324, 90950, 0, 216000, 143080, 0, -28750, 39600, 0, 0, 126450, 0, -165048, 112500, 0, -71850, 0, 0, -81920, -34580, 0, -122375, -1800, 0, -172500, 214200, 0, 68200, -4480, 0, 0, 128250, 0, -123420, -71280, 0, -19250, 0, 0, -229500, 137450, 0, -75000, -432860, 0, 19800, -70000, 0, -73280, 125800, 0, 0, -150600, 0, 88150, -265750, 0, -42500, 0, 0, -37200, -22500, 0, 223750, -46200, 0, 77500, 177150, 0, -169100, -131700, 0, 0, 81430, 0, -8200, -69700, 0, 136430, 0, 0, -165750, 113050, 0, 145040, -114800, 0, 45000, 28000, 0, -245000, 32000, 0, 0, 176190, 0, -5400, 24650, 0, -271500, 0, 0, -73744, 103690, 0, -200906, -11165, 0, -74150, -103140, 0, -76250, 241100, 0, 0, 293950, 0, -56100, -39430, 0, -47004, 0, 0, -40500, -161920, 0, -40000, 151200, 0, -102000, -1000, 0, -52588, 170880, 0, 0, -16500, 0, 27880, 77000, 0, -40500, 0, 0, -174120, -440300, 0, -25800, 188400, 0, 38574, 83750, 0, 94350, -32170, 0, 0, 347850, 0, 154000, -67850, 0, -16400, 0, 0, -159933, 102390, 0, -139580, 219810, 0, -137800, -40400, 0, 163490, 30000, 0, 0, -44000, 0, -235544, -4250, 0, 481500, 0, 0, 43850, 70000, 0, -243000, -250200, 0, -51908, -553860, 0, -73000, -60200, 0, 0, 245265, 0, 89250, -91050, 0, -5360, 0, 0, 440550, -72000, 0, -68686, -31250, 0, -80360, 203070, 0, -11000, 207400, 0, 0, 162000, 0, 232500, 143290, 0, -173876, 0, 0, 14650, 226950, 0, 123000, 19000, 0, -14000, -90200, 0, -50400, 123610, 0, 0, 142460, 0, 66000, -140280, 0, 117750, 0, 0, -68000, 221350, 0, 14828, 53370, 0, -267500, -28000, 0, -45880, 482680, 0, 0, -33700, 0, 120780, -141950, 0, 310800, 0, 0, 223223, -112500, 0, -29920, 81500, 0, 30600, 413950, 0, -123000, -174450, 0, 0, 33000, 0, -163350, 7750, 0, -256500, 0, 0, 172500, -90200, 0, 26310, -175400, 0, -254218, 63870, 0, -19200, -157500, 0, 0, -239180, 0, -58500, -525350, 0, 127500, 0, 0, -195348, 220320, 0, -247700, 40940, 0, 144110, 170330, 0, 85000, 163550, 0, 0, -324850, 0, -251850, -145040, 0, 19712, 0, 0, -81000, 17970, 0, 15000, 499800, 0, -199000, -224200, 0, -50400, 487500, 0, 0, 58450, 0, 83870, 221535, 0, -120325, 0, 0, -64000, -392050, 0, 386438, -192630, 0, 73400, 21250, 0, -84750, 134320, 0, 0, 105300, 0, 277610, 143150, 0, -280000, 0, 0, -151200, 152500, 0, -5740, -281980, 0, 92250, 128400, 0, 20640, -47600, 0, 0, 96720, 0, -22500, 38250, 0, -523600, 0, 0, -105300, 382050, 0, -31000, -28450, 0, -25500, 114440, 0, -253800, 23760, 0, 0, 153000, 0, -6250, 75200, 0, -28430, 0, 0, -161908, -18190, 0, -167500, 17800, 0, 155500, -20260, 0, 114550, -484700, 0, 0, -8400, 0, -315788, 486200, 0, -265200, 0, 0, 28680, -492630, 0, 174250, 275600, 0, 4400, -4500, 0, -472150, -38500, 0, 0, -60000, 0, 44500, 164000, 0, -7000, 0, 0, 92250, 266000, 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": "45.4.a.a", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0], [1], [-5], [0], [17], [-5], [0], [0], [-45], [0], [25], [-50], [0], [20], [0], [0], [89], [-10], [0], [44], [-85], [0], [250], [-120], [0], [25], [-100], [0], [0], [50], [0], [-108], [-85], [0], [50], [0], [0], [-40], [-220], [0], [225], [400], [0], [280], [-850], [0], [600], [-280], [0], [0], [-125], [0], [340], [610], [0], [250], [0], [0], [-250], [50], [0], [518], [540], [0], [-287], [-100], [0], [-180], [-170], [0], [0], [-700], [0], [410], [200], [0], [748], [0], [0], [-516], [-445], [0], [-2000], [660], [0], [50], [-1400], [0], [2250], [-1500], [0], [0], [-2040], [0], [1400], [-220], [0], [1630], [0], [0], [425]]}