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  • lfunc_lfunctions • Show schema
    {'Lhash': '1839066533970681623074116384815', 'a10': [-211.37806115282262, 0.0], 'a2': [-8.455122446112904, 0.0], 'a3': [-26.775479849487027, 0.0], 'a4': [39.489095578762274, 0.0], 'a5': [25.0, 0.0], 'a6': [226.38996068084154, 0.0], 'a7': [22.292731177966708, 0.0], 'a8': [-63.321220129077815, 0.0], 'a9': [473.9263211702858, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.821110089713937, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 7}, 'bad_lfactors': [[5, [[1.0, 0], [-25.0, 0]]], [11, [[1.0, 0], [-121.0, 0]]]], 'bad_primes': [5, 11], 'central_character': '55.1', 'coefficient_field': 'CDF', 'conductor': 55, 'conductor_radical': 55, 'conjugate': '1839066533970681623074116384815', 'degree': 2, 'euler_factors': [[[1.0, 0], [8.455122446112904, 0], [32.0, 0]], [[1.0, 0], [26.775479849487027, 0], [243.0, 0]], [[1.0, 0], [-25.0, 0]], [[1.0, 0], [-22.292731177966708, 0], [16807.0, 0]], [[1.0, 0], [-121.0, 0]], [[1.0, 0], [225.5471161503267, 0], 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['1.45076769074978056359026672148776', '4.96281994733437368358485169981565', '6.38925775015976217417957842780553', '7.50277514409221844094750648785668', '9.261939384966243794412727035963431', '10.20101213022699922747536131390592', '11.18204680035488534572594079097314', '11.98294298539494008226114611749573', '13.53538190619253896261462190285884'], 'prelabel': '2-55-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.970035368428116, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.45076769074978056359026672149', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '4.96281994733437368358485169982', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '6.38925775015976217417957842781', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 8.821110089713937, 'bad_primes': [5, 11], 'central_character': '1.1', 'conductor': 55, 'conductor_radical': 55, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/55/6/a/a/1/1'], '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': '2-55-1.1-c5-0-6', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-55-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.970035368428116, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.45076769074978056359026672149', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1839066533970681623074116384815', 'Lhash_array': ['1839066533970681623074116384815'], 'factors': ['2-55-1.1-c5-0-6'], 'label': '2-55-1.1-c5-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/55/6/a/a/1/1'}