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lfunc_lfunctions • Show schema
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{'Lhash': '1979983349460698398341626503566', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, -4.301691043097465], 'a4': [0.0, 0.0], 'a5': [8.58257569495584, -7.16515138991168], 'a6': [0.0, 0.0], 'a7': [0.0, 28.31620690750261], 'a8': [0.0, 0.0], 'a9': [8.49545416973504, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.440305600918503, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-8.58257569495584, 7.16515138991168]]]], 'bad_primes': [2, 5], 'central_character': '160.129', 'coefficient_field': 'CDF', 'conductor': 160, 'conductor_radical': 10, 'conjugate': '1571458183207068826341542253409', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 4.301691043097465], [-27.0, 0]], [[1.0, 0], [-8.58257569495584, 7.16515138991168]], [[1.0, 0], [0, -28.31620690750261], [-343.0, 0]], [[1.0, 0], [-65.23579590120015, 0], [1331.0, 0]], [[1.0, 0], [0, 33.66969722017664], [-2197.0, 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['1.56193145737809749519729641611041', '3.79901246545787289774327788112009', '4.38488680841972823627493930141489', '6.41569996542694090543482118312251', '6.91814675587438902916009517372250', '8.689632895719970032627158829019377', '9.807126889867510990824131643388910', '10.42455702716189583744869285012406', '11.18540610345079145280014272559270', '12.65102516625626719740727689626452'], 'prelabel': '2-160-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.072508031058422, 'root_angle': 0.27857349808488796, 'root_number': '0.6408706230767846 + 0.7676489070383504*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.139286749042', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.56193145737809749519729641611', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.79901246545787289774327788112', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.38488680841972823627493930141', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.440305600918503, 'bad_primes': [2, 5], 'central_character': '5.4', 'conductor': 160, 'conductor_radical': 10, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/160/4/c/d/129/3'], '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': '2-160-5.4-c3-0-10', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-160-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.072508031058422, 'root_angle': 0.13928674904244398, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.56193145737809749519729641611', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1979983349460698398341626503566', 'Lhash_array': ['1979983349460698398341626503566'], 'label': '2-160-5.4-c3-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/160/4/c/d/129/3'}