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lfunc_lfunctions • Show schema
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{'Lhash': '442383075403970795748850733679', 'a10': [0, 1.154838536242769], 'a2': [-1.0, 0], 'a3': [0, 0], 'a4': [1.0, 0], 'a5': [0, -1.154838536242769], 'a6': [0, 0], 'a7': [-1.0, 0], 'a8': [-1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.116186243894532, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [-3.794729412566517, -2.144767746261253]]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '2394.1709', 'coefficient_field': 'CDF', 'conductor': 2394, 'conductor_radical': 798, 'conjugate': '1519234464228813395524628397181', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.154838536242769], [-5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, -2.906243352723809], [-11.0, 0]], [[1.0, 0], [0, -1.3832921397986973], [-13.0, 0]], [[1.0, 0], [0, -2.906243352723809], [-17.0, 0]], 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'3.17246725199094981257075067430538', '3.31112862158275651186014667865494', '4.99846117907972895752553536937244', '5.72992986208555849365122175993445', '6.63143817567202720842767614864994', '7.31918116266606818118979349300116', '7.911142995724033212553115306251485', '8.991284510765432676353832254610354'], 'prelabel': '2-2394-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.372206107206582, 'root_angle': -0.5321633792833692, 'root_number': '-0.1008723812678104877160579382779540107912101646975989082 - 0.9948993731515572101983463217893117156807834506535057588*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.26608168964168455', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.34897871331763152470663298116', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.70322534066303850513589124078', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.17246725199094981257075067431', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.116186243894532, 'bad_primes': [2, 3, 7, 19], 'central_character': '57.56', 'conductor': 2394, 'conductor_radical': 798, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2394/2/b/i/1709/4'], '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': '2-2394-57.56-c1-0-2', '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': '2-2394-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.372206107206582, 'root_angle': -0.2660816896416846, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.34897871331763152470663298116', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '442383075403970795748850733679', 'Lhash_array': ['442383075403970795748850733679'], 'label': '2-2394-57.56-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2394/2/b/i/1709/4'}