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lfunc_lfunctions • Show schema
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{'Lhash': '845137287754579420044668053671,1461898618837111438940517079417', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.35329522822271664, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [1, 1, 1]], [397, [1, -2, 1]]], 'bad_primes': [3, 397], 'central_character': '1191.1', 'coefficient_field': '1.1.1.1', 'conductor': 1418481, 'conductor_radical': 1191, 'degree': 4, 'euler_factors': [[1, 0, 2, 0, 1], [1, 1, 1], [1, 0, -1, 0, 1], [1, 3, 4, 3, 1], [1, 0, 1, 0, 1], [1, -3, 4, -3, 1], [1, 0, 2, 0, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, -2, 3, -2, 1], [1, 0, -1, 0, 1], [1, -2, 3, -2, 1], [1, 0, 1, 0, 1], [1, 0, 2, 0, 1], [1, 0, -1, 0, 1], [1, 3, 4, 3, 1], [1, -2, 3, -2, 1], [1, 0, 2, 0, 1], [1, -1, 0, -1, 1], [1, 1, 0, 1, 1], [1, 0, -2, 0, 1], [1, 0, -1, 0, 1], [1, 1, 0, 1, 1], [1, 0, -1, 0, 1], [1, 0, 1, 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['0.66669576585410825697822313883760', '1.15323466779719063038657096546593', '2.93245060061195969706874171784727', '3.18975106289151085018506111104081', '3.70031432019657060922039545342784', '3.93147918738295870543552061143076', '4.48797240556585259461349637436015', '5.23803889531485341861914378000192', '5.74841708359112710365280960320421', '5.86500816419121904623155290347561', '6.35862807686730366278487955414898', '6.41477002112533212718053879528216', '7.32506943170227492889266914056857', '7.61901046915063473830617132673086', '8.423800458865870935332890082359577', '8.698895641271596281357618521882139', '9.112086111019762132601855847827587', '9.281008776609150354845338294198068', '9.719650491537961470731312083947733', '9.910804776469886212801322055978068'], 'prelabel': '4-1191e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7709646101124914, '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': 1402250129553201090, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.66669576585410825697822313884', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.15323466779719063038657096547', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.93245060061195969706874171785', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.35329522822271664, 'bad_primes': [3, 397], 'central_character': '1.1', 'conductor': 1418481, 'conductor_radical': 1191, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, -2, 0, 0, -3, 0, 0, 0, 0, 2, 3, 0, 0, 3, 0, 0, 1, 0, 3, 0, 0, 0, 1, 0, 1, 6, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, 0, 2, 0, 0, 0, 0, -3, 5, 0, 0, -6, 0, 0, 0, 0, -1, 0, 0, 0, -3, 0, 0, -4, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, -1, -2, 0, 0, -1, 0, -1, 0, 0, -6, 0, 0, 0, 0, 0, 0, -9, 0, 2, 0, 0, 0, -1, 0, 0, -2], 'euler11': [1, 0, 1, 0, 1], 'euler13': [1, -3, 4, -3, 1], 'euler17': [1, 0, 2, 0, 1], 'euler19': [1, -1, 0, -1, 1], 'euler2': [1, 0, 2, 0, 1], 'euler23': [1, 0, 1, 0, 1], 'euler29': [1, 0, 1, 0, 1], 'euler3': [1, 1, 1, 0, 0], 'euler31': [1, 2, 3, 2, 1], 'euler37': [1, -2, 3, -2, 1], 'euler41': [1, 0, -1, 0, 1], 'euler43': [1, -2, 3, -2, 1], 'euler47': [1, 0, 1, 0, 1], 'euler5': [1, 0, -1, 0, 1], 'euler53': [1, 0, 2, 0, 1], 'euler59': [1, 0, -1, 0, 1], 'euler61': [1, 3, 4, 3, 1], 'euler67': [1, -2, 3, -2, 1], 'euler7': [1, 3, 4, 3, 1], 'euler71': [1, 0, 2, 0, 1], 'euler73': [1, -1, 0, -1, 1], 'euler79': [1, 1, 0, 1, 1], 'euler83': [1, 0, -2, 0, 1], 'euler89': [1, 0, -1, 0, 1], 'euler97': [1, 1, 0, 1, 1], 'euler_factors': [[1, 0, 2, 0, 1], [1, 1, 1, 0, 0], [1, 0, -1, 0, 1], [1, 3, 4, 3, 1], [1, 0, 1, 0, 1], [1, -3, 4, -3, 1], [1, 0, 2, 0, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, -2, 3, -2, 1], [1, 0, -1, 0, 1], [1, -2, 3, -2, 1], [1, 0, 1, 0, 1], [1, 0, 2, 0, 1], [1, 0, -1, 0, 1], [1, 3, 4, 3, 1], [1, -2, 3, -2, 1], [1, 0, 2, 0, 1], [1, -1, 0, -1, 1], [1, 1, 0, 1, 1], [1, 0, -2, 0, 1], [1, 0, -1, 0, 1], [1, 1, 0, 1, 1]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1191/1/j/a'], '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': '4-1191e2-1.1-c0e2-0-1', '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': '4-1191e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7709646101124914, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 1402250129553201090, 'z1': {'__RealLiteral__': 0, 'data': '0.66669576585410825697822313884', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '845137287754579420044668053671,1461898618837111438940517079417', 'Lhash_array': ['845137287754579420044668053671', '1461898618837111438940517079417'], 'label': '4-1191e2-1.1-c0e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1191/1/j/a'}