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lfunc_lfunctions • Show schema
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{'Lhash': '441094834258125205776351776834', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.9135454576426009, 0.4067366430758002], 'a4': [-0.9945218953682733, 0.10452846326765347], 'a5': [-0.8660254037844386, 0.5], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.6691306063588582, -0.7431448254773942], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.235185906266681, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.9135454576426009, -0.4067366430758002]]], [5, [[1.0, 0], [0.8660254037844386, -0.5]]], [11, [[1.0, 0], [-0.7431448254773942, -0.6691306063588582]]]], 'bad_primes': [3, 5, 11], 'central_character': '2475.1517', 'coefficient_field': 'CDF', 'conductor': 2475, 'conductor_radical': 165, 'conjugate': '1703691294842508040161926987904', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.9945218953682733, -0.10452846326765347]], [[1.0, 0], [0.9135454576426009, -0.4067366430758002]], [[1.0, 0], 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'3.24682282797172278565610893940265', '4.24203784044498925855324971486910', '4.77650846126238704484370296876328', '5.57610124468669227544170777455762', '6.42742905851784212120760030224146', '7.26805200965122652796902631447583', '8.092431121892733698128471006431901', '8.811062182766307582848446852262336'], 'prelabel': '2-2475-2475.1517-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.111389178580879, 'root_angle': -0.8422222222222223, 'root_number': '-0.87964857286661650104740898756879 - 0.47562420907027522752532724010081*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4211111111111111', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.34796247024117681910921952118', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.41164161481259750925904123865', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.24682282797172278565610893940', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.235185906266681, 'bad_primes': [3, 5, 11], 'central_character': '2475.1517', 'conductor': 2475, 'conductor_radical': 165, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2475/1/fy/a/1517/1'], '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': '2-2475-2475.1517-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2475-2475.1517-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.111389178580879, 'root_angle': -0.42111111111111116, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.34796247024117681910921952118', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '441094834258125205776351776834', 'Lhash_array': ['441094834258125205776351776834'], 'label': '2-2475-2475.1517-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2475/1/fy/a/1517/1'}