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lfunc_lfunctions • Show schema
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{'Lhash': '3044838647726191209647879786673', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, -7.0710678118654755], 'a6': [0.0, 0.0], 'a7': [12.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.961857903394138, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '72.17', 'coefficient_field': 'CDF', 'conductor': 72, 'conductor_radical': 6, 'conjugate': '2037333571467530828089555886171', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 7.0710678118654755], [-25.0, 0]], [[1.0, 0], [-12.0, 0], [49.0, 0]], [[1.0, 0], [0, -5.656854249492381], [-121.0, 0]], [[1.0, 0], [8.0, 0], [169.0, 0]], [[1.0, 0], [0, 9.899494936611665], [-289.0, 0]], [[1.0, 0], [16.0, 0], [361.0, 0]], [[1.0, 0], [0, -39.59797974644666], [-529.0, 0]], [[1.0, 0], 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'14.84427364537398920610985588317817'], 'prelabel': '2-72-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4006633797576553, 'root_angle': 0.19591327601530362, 'root_number': '0.816496580927726 + 0.5773502691896257*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0979566380077', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.40195417189720467656724289281', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.41047057046745592853859020617', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.14129096528961839903305573819', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.961857903394138, 'bad_primes': [2, 3], 'central_character': '3.2', 'conductor': 72, 'conductor_radical': 6, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/72/3/e/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': '2-72-3.2-c2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-72-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4006633797576553, 'root_angle': 0.09795663800765181, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.40195417189720467656724289281', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3044838647726191209647879786673', 'Lhash_array': ['3044838647726191209647879786673'], 'label': '2-72-3.2-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/72/3/e/a/17/1'}