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'0.839961680932392632255188834272', 'prec': 107}}
-
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{'algebraic': True, 'analytic_conductor': 1995363.449276168, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 164648481361, 'conductor_radical': 91, 'degree': 8, 'dirichlet_coefficients': [1, -4, 5, 5, 36, -20, 0, 2, -31, -144, -95, 25, 52, 0, 180, -49, 146, 124, 48, 180, 0, 380, -121, 10, 651, -208, -214, 0, -440, -720, 283, 184, -475, -584, 0, -155, -209, -192, 260, 72, 93, 0, 526, -475, -1116, 484, 783, -245, 0, -2604, 730, 260, -340, 856, -3420, 0, 240, 1760, 922, 900, 141, -1132, 0, -611, 1872, 1900, -523, 730, -605, 0, 1468, -62, 47, 836, 3255, 240, 0, -1040, 1025, -1764, -243, -372, 1190, 0, 5256, -2104, -2200, -190, 2962, 4464, 0, -605, 1415, -3132, 1728, 920, -2715, 0, 2945, 3255], 'euler11': [1, 95, 7452, 379875, 16142470, 505613625, 13201672572, 224005030645, 3138428376721], 'euler13': [1, -52, 1014, -8788, 28561, 0, 0, 0, 0], 'euler17': [1, -146, 16532, -1364486, 113102822, -6703719718, 399042290708, -17313829968562, 582622237229761], 'euler19': [1, -48, 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22902048046490258711521], 'euler79': [1, -1025, 2071119, -1439609696, 1542926691608, -709783724906144, 503463047791197999, -122847885882183776975, 59091511031674153381441], 'euler83': [1, -1190, 2309473, -1949369070, 1975771812452, -1114623892428090, 755059964905624537, -222458903768373079570, 106890007738661124410161], 'euler89': [1, -2962, 5920469, -7608132226, 7558598583356, -5363497367230994, 2942362326714580709, -1037755667781571189058, 246990403565262140303521], 'euler97': [1, 2715, 4771625, 5953314954, 6129100067190, 5433429819012042, 3974630043019339625, 2064027324247144564155, 693842360995438000295041], 'euler_factors': [[1, 4, 11, 22, 74, 176, 704, 2048, 4096], [1, -5, 56, -221, 2014, -5967, 40824, -98415, 531441], [1, -36, 645, -8694, 102712, -1086750, 10078125, -70312500, 244140625], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 95, 7452, 379875, 16142470, 505613625, 13201672572, 224005030645, 3138428376721], [1, -52, 1014, -8788, 28561, 0, 0, 0, 0], [1, -146, 16532, -1364486, 113102822, -6703719718, 399042290708, -17313829968562, 582622237229761], [1, -48, 22109, -1039926, 209516732, -7132852434, 1040137383029, -15489009493392, 2213314919066161], [1, 121, 43427, 4124692, 758296736, 50185127564, 6428754551603, 217939472037023, 21914624432020321], [1, 440, 121385, 24466046, 4246931120, 596702395894, 72202628819585, 6383144229382360, 353814783205469041], [1, -283, 115883, -22509948, 5128506688, -670593860868, 102846589065323, -7482413071469893, 787662783788549761], [1, 209, 110126, 34693527, 6353129866, 1757331223131, 282553186517534, 27162003617171093, 6582952005840035281], [1, -93, 29038, -7679451, 6599220738, -529275442371, 137933526950158, -30446519898638373, 22563490300366186081], [1, -526, 389933, -128599950, 49380663820, -10224596224650, 2464908057785717, -264363713878779418, 39959630797262576401], [1, -783, 602263, -253090440, 102444830856, -26276608752120, 6491922561689527, -876279160439466561, 116191483108948578241], [1, 340, 376337, 45654214, 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106890007738661124410161], [1, -2962, 5920469, -7608132226, 7558598583356, -5363497367230994, 2942362326714580709, -1037755667781571189058, 246990403565262140303521], [1, 2715, 4771625, 5953314954, 6129100067190, 5433429819012042, 3974630043019339625, 2064027324247144564155, 693842360995438000295041]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/4/a/d'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '8-637e4-1.1-c3e4-0-0', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3, 3, 3], 'order_of_vanishing': 0, 'prelabel': '8-637e4-1.1-c3e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.130596763256966, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e4-0', 'trace_hash': 1810254072925470469, 'z1': {'__RealLiteral__': 0, 'data': '0.54517485489772946694852008339', 'prec': 103}}
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{'Lhash': '691091232040444628259332463244,818635792467717170550828263846,1064777929002660031433234230147,2580219288042898210915226433345', 'Lhash_array': ['691091232040444628259332463244', '818635792467717170550828263846', '1064777929002660031433234230147', '2580219288042898210915226433345'], 'label': '8-637e4-1.1-c3e4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/4/a/d'}