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lfunc_lfunctions • Show schema
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{'Lhash': '3162021536343784910358546392868', 'a10': [5.0, 0.0], 'a2': [0.0, 2.23606797749979], 'a3': [0.0, 0.0], 'a4': [-3.0, 0.0], 'a5': [0.0, -2.23606797749979], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, -2.23606797749979], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.3593268090957619, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 2.23606797749979]]]], 'bad_primes': [3, 5], 'central_character': '45.19', 'coefficient_field': 'CDF', 'conductor': 45, 'conductor_radical': 15, 'conjugate': '5870194140457500382378227509886', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.23606797749979], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.23606797749979]], [[1.0, 0], [0, 0], [-7.0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [0, 0], [-13.0, 0]], [[1.0, 0], [0, 4.47213595499958], [-17.0, 0]], [[1.0, 0], [4.0, 0], [19.0, 0]], [[1.0, 0], [0, -8.94427190999916], 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'root_angle': -0.25, 'root_number': '6.123233995736766e-17 - 1.0*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.49439517148849264400889437608', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.10424053282794606423576741067', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.52566376180141557577636495203', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.3593268090957619, 'bad_primes': [3, 5], 'central_character': '5.4', 'conductor': 45, 'conductor_radical': 15, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/45/2/b/a/19/2'], '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': '2-45-5.4-c1-0-0', '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': '2-45-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5994387450738915, 'root_angle': -0.25, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.49439517148849264400889437608', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3162021536343784910358546392868', 'Lhash_array': ['3162021536343784910358546392868'], 'factors': ['2-45-5.4-c1-0-0'], 'label': '2-45-5.4-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/45/2/b/a/19/2'}