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lfunc_lfunctions • Show schema
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{'Lhash': '1313277278055991625896905729688,2040971457834719006581920274505', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5137059648879263, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -2, 1]], [313, [1, -2, 1]]], 'bad_primes': [2, 3, 313], 'central_character': '3756.1', 'coefficient_field': '1.1.1.1', 'conductor': 14107536, 'conductor_radical': 1878, 'degree': 4, 'euler_factors': [[1], [1, -2, 1], [1, 0, -1, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, 0, -1, 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, -1, 0, 1], [1, 0, -1, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 2, 3, 2, 1], [1, 0, -2, 0, 1], [1, 0, -1, 0, 1], [1, 2, 3, 2, 1], [1, 0, -1, 0, 1], [1, -2, 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['1.03599310237343597690680986043820', '1.61004259175774456264277347381375', '2.14323717241113469601512258149173', '2.41197936041089706818323620495666', '2.94541026064580168649098360661782', '3.47866879129007037207351525505970', '3.86300676578161777553435165841513', '4.14219077583304853849486602760746', '4.52169411030607859650399790657312', '4.74602307009875378489814719920988', '5.71273002538015404164899343796917', '6.00451322326766499426072678000356', '6.37742232697386040078138806973835', '6.79700923728156894971029763593247', '7.07760382964634302775289750309402', '7.37170171053222653955698977228466', '8.211717875853318985983843868171749', '8.290814093835749620584621269982644', '8.378741355072920119261002382737044', '8.785851370520609655250561535334451'], 'prelabel': '4-3756e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3691194934882627, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0e2-0', 'trace_hash': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.5137059648879263, 'bad_primes': [2, 3, 313], 'central_character': '1.1', 'conductor': 14107536, 'conductor_radical': 1878, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0], 'euler11': [1, 0, -2, 0, 1], 'euler13': [1, -2, 3, -2, 1], 'euler17': [1, 0, -1, 0, 1], 'euler19': [1, 4, 6, 4, 1], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 2, 0, 1], 'euler29': [1, 0, -2, 0, 1], 'euler3': [1, -2, 1, 0, 0], '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, -1, 0, 1], 'euler53': [1, 0, -1, 0, 1], 'euler59': [1, 0, -1, 0, 1], 'euler61': [1, 0, -2, 0, 1], 'euler67': [1, 0, -2, 0, 1], 'euler7': [1, 0, -2, 0, 1], 'euler71': [1, 0, -2, 0, 1], 'euler73': [1, 0, -2, 0, 1], 'euler79': [1, 2, 3, 2, 1], 'euler83': [1, 0, -2, 0, 1], 'euler89': [1, 0, -1, 0, 1], 'euler97': [1, 2, 3, 2, 1], 'euler_factors': [[1, 0, 0, 0, 0], [1, -2, 1, 0, 0], [1, 0, -1, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, 0, -1, 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, -1, 0, 1], [1, 0, -1, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 2, 3, 2, 1], [1, 0, -2, 0, 1], [1, 0, -1, 0, 1], [1, 2, 3, 2, 1]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3756/1/g/c'], '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': '4-3756e2-1.1-c0e2-0-2', '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': '4-3756e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3691194934882627, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 429787036536699905, 'z1': {'__RealLiteral__': 0, 'data': '1.03599310237343597690680986044', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1313277278055991625896905729688,2040971457834719006581920274505', 'Lhash_array': ['1313277278055991625896905729688', '2040971457834719006581920274505'], 'label': '4-3756e2-1.1-c0e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3756/1/g/c'}