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lfunc_lfunctions • Show schema
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{'Lhash': '2052579335187106779049323362203', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [230.44171945293493, 0.0], 'a6': [0.0, 0.0], 'a7': [343.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 78.72102642199872, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-343.0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '252.1', 'coefficient_field': 'CDF', 'conductor': 252, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-230.44171945293493, 0], [78125.0, 0]], [[1.0, 0], [-343.0, 0]], [[1.0, 0], [-5027.092036170545, 0], [19487171.0, 0]], [[1.0, 0], [13772.601266870439, 0], [62748517.0, 0]], [[1.0, 0], [32474.71176444077, 0], [410338673.0, 0]], [[1.0, 0], [-9651.950950152828, 0], [893871739.0, 0]], [[1.0, 0], [32034.47864225251, 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['1.61919959239364366267299229391621', '2.51020183650228963671319030700418', '4.17244927374621037037280666813736', '5.14765097337015763652225361744167', '6.35661771896507738405290366689301', '7.19742349634444734554011499595039', '8.495096268585817997387706021944778', '9.497938331525630254815875111195102', '10.09044807573988639224395868717770'], 'prelabel': '2-252-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.87248704828577, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.61919959239364366267299229392', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.51020183650228963671319030700', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.17244927374621037037280666814', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 78.72102642199872, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 252, 'conductor_radical': 42, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/252/8/a/c/1/2'], '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': '2-252-1.1-c7-0-16', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 1, 'prelabel': '2-252-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.87248704828577, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '1.61919959239364366267299229392', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2052579335187106779049323362203', 'Lhash_array': ['2052579335187106779049323362203'], 'factors': ['2-252-1.1-c7-0-16'], 'label': '2-252-1.1-c7-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/252/8/a/c/1/2'}