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lfunc_lfunctions • Show schema
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{'Lhash': '1849756982210492531354136975154', 'a10': [5.1975957828058075, 1.1419708793892769], 'a2': [0, -2.3798781233842137], 'a3': [0, 0], 'a4': [-3.6638198821627674, 0], 'a5': [-0.4798442694054354, 2.183975612757332], 'a6': [0, 0], 'a7': [0, 2.2839417587785538], 'a8': [0, 3.959688538810871], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.264516609202524, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.4798442694054354, -2.183975612757332]]], [23, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [3, 5, 23], 'central_character': '1035.829', 'coefficient_field': 'CDF', 'conductor': 1035, 'conductor_radical': 345, 'conjugate': '529014116323483687904687188631', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.3798781233842137], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.4798442694054354, -2.183975612757332]], [[1.0, 0], [0, -2.2839417587785538], [-7.0, 0]], [[1.0, 0], 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-0.9136887525153973, -0.5685807297043054], 'positive_zeros': ['1.45920096742545616899105700241489', '3.80994932912505844787301880577771', '4.50994509318557085187678786139419', '5.29418149790115400169438849422445', '6.28560590790786714862725535136106', '7.02822075285825543528488304112357', '7.82786858606984234264537654899041', '8.452502032070016011044762773885418', '9.233717727425825028791813722667299', '9.960484505796030029892940064512769'], 'prelabel': '2-1035-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.874807229920386, 'root_angle': -0.9311575353796755, 'root_number': '-0.9767035862654302665625344621031302434869636020089972830 - 0.214592881000855239369332660641119362339186162413585715*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.46557876768983775', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.45920096742545616899105700241', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.264516609202524, 'bad_primes': [3, 5, 23], 'central_character': '5.4', 'conductor': 1035, 'conductor_radical': 345, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1035/2/b/e/829/1'], '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': '2-1035-5.4-c1-0-33', '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': '2-1035-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.874807229920386, 'root_angle': -0.46557876768983775, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.45920096742545616899105700241', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1849756982210492531354136975154', 'Lhash_array': ['1849756982210492531354136975154'], 'label': '2-1035-5.4-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1035/2/b/e/829/1'}