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lfunc_lfunctions • Show schema
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{'Lhash': '117306760929790292649455377097', 'a10': [0.975769248229062, -1.690081914396023], 'a2': [0.0, 2.3032665137821264], 'a3': [0.0, 0.0], 'a4': [-3.305036633510071, 0.0], 'a5': [-0.7337760976782444, -0.4236458275194475], 'a6': [0.0, 0.0], 'a7': [-0.35777731568650534, 2.621449101619209], 'a8': [0.0, -3.0058471772227042], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.35777731568650534, -2.621449101619209]]], [13, [[1.0, 0], [2.9232860268708456, 2.1105446702454955]]]], 'bad_primes': [3, 7, 13], 'central_character': '819.478', 'coefficient_field': 'CDF', 'conductor': 819, 'conductor_radical': 273, 'conjugate': '3129069208125109607428900820825', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -2.3032665137821264], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.7337760976782444, 0.4236458275194475], [2.5, 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'7.80455757961383449354054718668406', '9.220207426068496631117609629600372', '9.825833396177188890636937446374671'], 'prelabel': '2-819-91.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': 0.3927987458431339, 'root_number': '0.33045222088275494 + 0.9438227215497913*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.196399372922', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.092538717615619190739759191759', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.67730944594870939693081538607', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.80057601968878910493028596866', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'bad_primes': [3, 7, 13], 'central_character': '91.23', 'conductor': 819, 'conductor_radical': 273, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/819/2/bm/f/478/6'], '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': '2-819-91.23-c1-0-1', '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': '2-819-91.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': 0.19639937292156695, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.092538717615619190739759191759', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '117306760929790292649455377097', 'Lhash_array': ['117306760929790292649455377097'], 'label': '2-819-91.23-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/819/2/bm/f/478/6'}