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lfunc_lfunctions • Show schema
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{'Lhash': '1793916845020500070793833662540', 'a10': [-8.744562646538029, 0.0], 'a2': [-2.715194527703128, 0.0], 'a3': [0.0, 0.0], 'a4': [5.372281323269014, 0.0], 'a5': [3.2206026335561817, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.3722813232690143, 0.0], 'a8': [-9.156399794815492, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 19], 'central_character': '171.1', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '1793916845020500070793833662540', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.715194527703128, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.2206026335561817, 0], [5.0, 0]], [[1.0, 0], [2.3722813232690143, 0], [7.0, 0]], [[1.0, 0], [-2.2097864218500747, 0], [11.0, 0]], [[1.0, 0], [-2.0, 0], [13.0, 0]], [[1.0, 0], 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'9.076706445399730109013520526548194', '9.648678097466539583770747806205730', '10.25351083202929888879644431080105', '11.36248191326633025355074091442368', '12.50784271909754991397912871153560'], 'prelabel': '2-171-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, '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': '1.41515086625409323007548048294', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.92918446423028069714030795006', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.00298913510787374330974131618', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'bad_primes': [3, 19], 'central_character': '1.1', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/2/a/e/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': '2-171-1.1-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': '2-171-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.41515086625409323007548048294', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1793916845020500070793833662540', 'Lhash_array': ['1793916845020500070793833662540'], 'label': '2-171-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/a/e/1/1'}