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lfunc_lfunctions • Show schema
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{'Lhash': '2975140527348818702398435881317', 'a10': [-2.723617149194944, 0.0], 'a2': [2.723617149194944, 0.0], 'a3': [-2.2929762073560798, 0.0], 'a4': [5.418090375388794, 0.0], 'a5': [-1.0, 0.0], 'a6': [-6.245189321051, 0.0], 'a7': [3.827098945662206, 0.0], 'a8': [9.309569563907104, 0.0], 'a9': [2.257739887501071, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.4772324373936878, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [1.0, 0]]], [37, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 37], 'central_character': '185.1', 'coefficient_field': 'CDF', 'conductor': 185, 'conductor_radical': 185, 'conjugate': '2975140527348818702398435881317', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.723617149194944, 0], [2.0, 0]], [[1.0, 0], [2.2929762073560798, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.827098945662206, 0], [7.0, 0]], [[1.0, 0], [4.418090375388794, 0], [11.0, 0]], [[1.0, 0], [3.6758302628898645, 0], 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'5.71100562208432374945143308111240', '7.05876834498019419392193677384463', '7.918525139150551152019140953404113', '10.60771610289190051814467976225565', '11.01565153991037924670571636370145', '11.84267740631140168356801220595413', '12.46255944100228155947207988645418'], 'prelabel': '2-185-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2154145125814846, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.34697204956410755155792042680', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.33455911454823304428546661972', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.04539116693120770066126784883', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.4772324373936878, 'bad_primes': [5, 37], 'central_character': '1.1', 'conductor': 185, 'conductor_radical': 185, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/185/2/a/e/1/5'], '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': '2-185-1.1-c1-0-7', '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': '2-185-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2154145125814846, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.34697204956410755155792042680', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2975140527348818702398435881317', 'Lhash_array': ['2975140527348818702398435881317'], 'factors': ['2-185-1.1-c1-0-7'], 'label': '2-185-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/185/2/a/e/1/5'}