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lfunc_lfunctions • Show schema
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{'Lhash': '1674130648951067951874513583773', 'a10': [0.37025315969746336, 0.41807830536898566], 'a2': [0.08541974431807095, -0.2346888186894872], 'a3': [-2.2665947075770747, 0.3996618012768517], 'a4': [1.4843065773394537, 1.2454811015995464], 'a5': [-1.0659875644665475, 1.965622169289581], 'a6': [-0.09981578437694962, 0.5660834432478757], 'a7': [3.429828771611496, 1.9802125645642208], 'a8': [0.8516703472665964, -0.4917121042551915], 'a9': [2.1586441506588225, -0.7856822172126591], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.758578819202164, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [1.0659875644665475, -1.965622169289581]]], [19, [[1.0, 0], [-3.7683122446732744, 2.1908497955463466]]]], 'bad_primes': [5, 19], 'central_character': '95.4', 'coefficient_field': 'CDF', 'conductor': 95, 'conductor_radical': 95, 'conjugate': '3501398370646406088554535036035', 'degree': 2, 'euler_factors': [[[1.0, 0], 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{'__RealLiteral__': 0, 'data': '-0.165190358948', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.32065621918977940245200952704', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.85756499236941150788311735603', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.29244548082290166685267887270', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.758578819202164, 'bad_primes': [5, 19], 'central_character': '95.4', 'conductor': 95, 'conductor_radical': 95, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/95/2/p/a/4/5'], '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': '2-95-95.4-c1-0-1', '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': '2-95-95.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8709643042066443, 'root_angle': -0.16519035894787717, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.32065621918977940245200952704', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1674130648951067951874513583773', 'Lhash_array': ['1674130648951067951874513583773'], 'label': '2-95-95.4-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/95/2/p/a/4/5'}