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lfunc_lfunctions • Show schema
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{'Lhash': '2149373700292036251895412815258', 'a10': [4.61596278244033, 13.191663733926548], 'a2': [1.6328178020120254, 2.5986146454732895], 'a3': [0.0, 0.0], 'a4': [-2.3511691446306555, 4.882253035786235], 'a5': [4.439702308796255, 1.0133330802176277], 'a6': [0.0, 0.0], 'a7': [10.763517961359366, -5.183437059269624], 'a8': [-4.327229122669233, 0.48756162687252075], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.11173489980375, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [29, [[1.0, 0], [18.682562598765816, -22.18021313565757]]]], 'bad_primes': [3, 29], 'central_character': '261.19', 'coefficient_field': 'CDF', 'conductor': 261, 'conductor_radical': 87, 'conjugate': '2420996386591148472766235966758', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.6328178020120254, -2.5986146454732895], [-1.7355349564702325, 3.6038754716096766]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.439702308796255, 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'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.69555688287061144396905382783', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.34190406427340968614934777042', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.09918749164545477369985064436', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.11173489980375, 'bad_primes': [3, 29], 'central_character': '29.19', 'conductor': 261, 'conductor_radical': 87, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/261/3/s/a/19/4'], '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': '2-261-29.19-c2-0-15', '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': '2-261-29.19-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6667836244816994, 'root_angle': -0.26032578023785713, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.69555688287061144396905382783', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2149373700292036251895412815258', 'Lhash_array': ['2149373700292036251895412815258'], 'label': '2-261-29.19-c2-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/261/3/s/a/19/4'}