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lfunc_lfunctions • Show schema
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{'Lhash': '1470792431671924708242434724233', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 3.0454748755547754], 'a6': [0, 0], 'a7': [0.4186267395829792, 0], 'a8': [0, 0], 'a9': [3.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.7098088857877, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 19], 'central_character': '1216.609', 'coefficient_field': 'CDF', 'conductor': 1216, 'conductor_radical': 38, 'conjugate': '1364327438581842411514370028361', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-3.0, 0]], [[1.0, 0], [0, -3.0454748755547754], [-5.0, 0]], [[1.0, 0], [-0.4186267395829792, 0], [7.0, 0]], [[1.0, 0], [0, 5.274917217635375], [-11.0, 0]], [[1.0, 0], [0, 2.6268481359717963], [-13.0, 0]], [[1.0, 0], [-3.274917217635375, 0], [17.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [-3.4641016151377544, 0], [23.0, 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'5.08125226995704370886455274260375', '6.46191594304986749037570577901910', '7.33854353491412972697410023201680', '8.010055151699358258045728763597167', '9.073469064690954494689098126823650', '9.589479855352754269226960857229779'], 'prelabel': '2-1216-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.11605662429098, 'root_angle': -0.08333333333333333, 'root_number': '0.96592582628906828674974319972889736763390483900840455041 - 0.2588190451025207623488988376240483283490689013199305139*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.04166666666666667', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16025064904092767914570652128', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.04456391096378707103181693170', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.82484768759651005478387558909', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.7098088857877, 'bad_primes': [2, 19], 'central_character': '8.5', 'conductor': 1216, 'conductor_radical': 38, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1216/2/c/i/609/8'], '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': '2-1216-8.5-c1-0-17', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1216-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.11605662429098, 'root_angle': -0.041666666666666664, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16025064904092767914570652128', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1470792431671924708242434724233', 'Lhash_array': ['1470792431671924708242434724233'], 'label': '2-1216-8.5-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1216/2/c/i/609/8'}