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lfunc_lfunctions • Show schema
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{'Lhash': '1685288585085569943813034996492', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.9510565162951535, -0.30901699437494745], 'a5': [0.30901699437494745, 0.9510565162951535], 'a6': [0.0, 0.0], 'a7': [-0.8090169943749475, -0.41221474770752686], 'a8': [0.0, 0.0], 'a9': [-0.5877852522924731, 0.8090169943749475], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5215229382014875, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-0.30901699437494745, -0.9510565162951535]]], [11, [[1.0, 0], [-0.9510565162951535, -0.30901699437494745]]], [19, [[1.0, 0], [0.30901699437494745, -0.9510565162951535]]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.227', 'coefficient_field': 'CDF', 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': '2294757531927720578519281429219', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.9510565162951535, 0.30901699437494745]], [[1.0, 0], [0, 0], 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'8.686988729004464045132040470627140', '9.132504659882844439741009379473858', '9.808288829702025144776560349953761'], 'prelabel': '2-1045-1045.227-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7221654507115994, 'root_angle': -0.15407497710965348, 'root_number': '0.88512172158526668576821149320447 - 0.46535957922657361620988162258572*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07703748855482674', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.32945827878924088114668928209', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.82967988266207884503276162076', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.56061288568117692154673103124', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5215229382014875, 'bad_primes': [5, 11, 19], 'central_character': '1045.227', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1045/1/br/b/227/1'], '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': '2-1045-1045.227-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1045-1045.227-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7221654507115994, 'root_angle': -0.07703748855482674, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.32945827878924088114668928209', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1685288585085569943813034996492', 'Lhash_array': ['1685288585085569943813034996492'], 'label': '2-1045-1045.227-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1045/1/br/b/227/1'}