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lfunc_lfunctions • Show schema
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{'Lhash': '752418037796395108352471842641', 'a10': [-19505231.392747138, -7.866167727606496e-67], 'a2': [-209.73398448422128, 121.08997240017796], 'a3': [0, 0], 'a4': [21133.56283175172, -36604.40456954317], 'a5': [69749.895709729, 40270.12106396036], 'a6': [0, 0], 'a7': [-376400.09874436364, -651944.0949991802], 'a8': [0, 6268373.944447938], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.56882140101463, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '7.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '27.17', 'coefficient_field': 'CDF', 'conductor': 27, 'conductor_radical': 3, 'conjugate': '1071304956263472611268224928128', 'degree': 2, 'euler_factors': [[[1.0, 0], [209.73398448422128, -121.08997240017796], [8192.0, -14188.960215604242]], [[1.0, 0], [0, 0]], [[1.0, 0], [-69749.895709729, -40270.12106396036], [3051757812.5, 5285799583.645255]], [[1.0, 0], [376400.09874436364, 651944.0949991802], 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'rational': False, 'root_analytic_conductor': 5.793860664618595, 'root_angle': -0.2339912946983311, 'root_number': '0.1004161355602560229969267058266954318859934271782510791 - 0.9949455260058935939204542243911605111148392504939560864*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2339912946983311', 'prec': 64}, 'spectral_label': 'c14-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.59355317440068171987023550136', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.95586704562387199769422750398', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.06938029580611552386947681145', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 33.56882140101463, 'bad_primes': [3], 'central_character': '9.5', 'conductor': 27, 'conductor_radical': 3, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/27/15/d/a/17/1'], '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': '2-3e3-9.5-c14-0-3', 'motivic_weight': 14, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [14], 'order_of_vanishing': 0, 'prelabel': '2-3e3-9.5-c14-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.793860664618595, 'root_angle': -0.2339912946983311, 'self_dual': False, 'spectral_label': 'c14-0', 'z1': {'__RealLiteral__': 0, 'data': '0.59355317440068171987023550136', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '752418037796395108352471842641', 'Lhash_array': ['752418037796395108352471842641'], 'factors': ['2-3e3-9.5-c14-0-3'], 'label': '2-3e3-9.5-c14-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/27/15/d/a/17/1'}