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lfunc_lfunctions • Show schema
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{'Lhash': '1182612040435261980913290489946,2621164886880241677504202494097', 'a10': 0, 'a2': 2, 'a3': 0, 'a4': 3, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 4, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.7651852663939254, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [7, [1]], [17, [1, 0, 1]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.1', 'coefficient_field': '1.1.1.1', 'conductor': 11102224, 'conductor_radical': 238, 'degree': 4, 'euler_factors': [[1, -2, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, -4, 6, -4, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 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'3.15546472061134942580040113142244', '3.50207615625483771515222682220555', '4.05546430443564320995967653250829', '4.19642928662406139554867024404738', '4.84989405626378519022573792706198', '5.42316652431438731144289533028471', '5.47196184114791683729290094088111', '5.95268570667967206761893156752674', '5.99821582395933511915893744867114', '6.63573805565276938472088701074395', '7.04115919702666259433507616078828', '7.26929135940430910527311972029713', '7.932166059349246756991103152182662', '8.048066470631121885324039611231134', '8.430633300389028200049488011712156', '8.910798471797272718739241120260767'], 'prelabel': '4-3332e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e2-0', 'trace_hash': 1296575929646230095, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.932916404743028582333596457171', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.06773450539787846026591481102', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.10603401765731893028781930880', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.7651852663939254, 'bad_primes': [2, 7, 17], 'central_character': '1.1', 'conductor': 11102224, 'conductor_radical': 238, 'degree': 4, 'dirichlet_coefficients': [1, 2, 0, 3, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 5, 0, -4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6], 'euler11': [1, 0, 2, 0, 1], 'euler13': [1, 0, 2, 0, 1], 'euler17': [1, 0, 1, 0, 0], 'euler19': [1, 0, -2, 0, 1], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, 0, 2, 0, 1], 'euler29': [1, 0, -2, 0, 1], 'euler3': [1, 0, 2, 0, 1], 'euler31': [1, 0, 2, 0, 1], 'euler37': [1, 0, -2, 0, 1], 'euler41': [1, 0, 2, 0, 1], 'euler43': [1, 0, -2, 0, 1], 'euler47': [1, 0, -2, 0, 1], 'euler5': [1, 0, 2, 0, 1], 'euler53': [1, -4, 6, -4, 1], 'euler59': [1, 0, -2, 0, 1], 'euler61': [1, 0, 2, 0, 1], 'euler67': [1, 0, -2, 0, 1], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, 2, 0, 1], 'euler73': [1, 0, 2, 0, 1], 'euler79': [1, 0, 2, 0, 1], 'euler83': [1, 0, -2, 0, 1], 'euler89': [1, 0, 2, 0, 1], 'euler97': [1, 0, 2, 0, 1], 'euler_factors': [[1, -2, 1, 0, 0], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 0, 0, 0], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 1, 0, 0], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, -4, 6, -4, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1]], 'index': 7, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/g/h', 'ArtinRepresentation/2.3332.8t11.c'], 'is_instance_Artin': True, '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': '4-3332e2-1.1-c0e2-0-7', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'prelabel': '4-3332e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 1296575929646230095, 'z1': {'__RealLiteral__': 0, 'data': '0.932916404743028582333596457171', 'prec': 107}}
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lfunc_instances • Show schema
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id: 24608327
{'Lhash': '1182612040435261980913290489946,2621164886880241677504202494097', 'Lhash_array': ['1182612040435261980913290489946', '2621164886880241677504202494097'], 'label': '4-3332e2-1.1-c0e2-0-7', 'type': 'Artin', 'url': 'ArtinRepresentation/2.3332.8t11.c'}
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id: 19902532
{'Lhash': '1182612040435261980913290489946,2621164886880241677504202494097', 'Lhash_array': ['1182612040435261980913290489946', '2621164886880241677504202494097'], 'label': '4-3332e2-1.1-c0e2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/g/h'}