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lfunc_lfunctions • Show schema
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{'Lhash': '4021071012272117506347288848348', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.5, -2.598076211353316], 'a4': [-4.0, -6.928203230275509], 'a5': [0.0, -5.196152422706632], 'a6': [0.0, 0.0], 'a7': [9.0, -5.196152422706632], 'a8': [0.0, 0.0], 'a9': [-4.5, -7.794228634059948], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.301074490223885, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.5, 2.598076211353316]]], [13, [[1.0, 0], [32.5, 33.77499074759311]]]], 'bad_primes': [3, 13], 'central_character': '39.4', 'coefficient_field': 'CDF', 'conductor': 39, 'conductor_radical': 39, 'conjugate': '1725111646954398707904220904421', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [4.0, 6.928203230275509]], [[1.0, 0], [-1.5, 2.598076211353316]], [[1.0, 0], [0, 5.196152422706632], [-125.0, 0]], [[1.0, 0], [-9.0, 5.196152422706632], [171.5, -297.04671349806245]], [[1.0, 0], [-45.0, -25.98076211353316], [665.5, 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{'__RealLiteral__': 0, 'data': '0.20935380903', 'prec': 44}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.17206571869895288643449316524', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.77684931404360050921121243664', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.04493677831332736931288409360', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.301074490223885, 'bad_primes': [3, 13], 'central_character': '13.4', 'conductor': 39, 'conductor_radical': 39, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/39/4/j/a/4/1'], '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': '2-39-13.4-c3-0-6', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-39-13.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5169292963826246, 'root_angle': 0.20935380902961667, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '3.17206571869895288643449316524', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4021071012272117506347288848348', 'Lhash_array': ['4021071012272117506347288848348'], 'label': '2-39-13.4-c3-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/39/4/j/a/4/1'}