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lfunc_lfunctions • Show schema
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{'Lhash': '2752471599122510860784877097435', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.23606797749979, 2.0], 'a4': [0.0, 0.0], 'a5': [2.23606797749979, -4.47213595499958], 'a6': [0.0, 0.0], 'a7': [0.0, 8.0], 'a8': [0.0, 0.0], 'a9': [1.0, 8.94427190999916], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6348815861617816, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-2.23606797749979, -2.0]]], [5, [[1.0, 0], [-2.23606797749979, 4.47213595499958]]]], 'bad_primes': [2, 3, 5], 'central_character': '60.29', 'coefficient_field': 'CDF', 'conductor': 60, 'conductor_radical': 30, 'conjugate': '3272900973037698327595905435683', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.23606797749979, -2.0]], [[1.0, 0], [-2.23606797749979, 4.47213595499958]], [[1.0, 0], [0, -8.0], [-49.0, 0]], [[1.0, 0], [0, 8.94427190999916], [-121.0, 0]], [[1.0, 0], [0, 12.0], [-169.0, 0]], [[1.0, 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'11.30211096781844578266825975357640', '12.87789159468169518770330368802164', '13.78758732139391218205172937444425', '14.47621702430565846663890279211652'], 'prelabel': '2-60-15.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2786248809411545, 'root_angle': -0.060068427575398396, 'root_number': '0.9296181273332772 - 0.3685242696666948*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0600684275754', 'prec': 54}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.17131723727890984097766088136', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.08223328678377031679040300796', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.70381367980156212657825159348', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6348815861617816, 'bad_primes': [2, 3, 5], 'central_character': '15.14', 'conductor': 60, 'conductor_radical': 30, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/60/3/b/a/29/4'], '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': '2-60-15.14-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': '2-60-15.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2786248809411545, 'root_angle': -0.060068427575398396, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.17131723727890984097766088136', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2752471599122510860784877097435', 'Lhash_array': ['2752471599122510860784877097435'], 'factors': ['2-60-15.14-c2-0-1'], 'label': '2-60-15.14-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/60/3/b/a/29/4'}