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lfunc_lfunctions • Show schema
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{'Lhash': '1245457616230705526906524844980', 'a10': [2.867072470708733, 2.405759452730231], 'a2': [-0.6862416378687336, -0.7273736415730487], 'a3': [0.8626290886680674, 1.5019557434837085], 'a4': [-0.05814482891047583, 0.9983081582712682], 'a5': [-3.7173905220686905, 0.4345006365134674], 'a6': [0.5005110199385132, -1.6581582309659442], 'a7': [3.1135466792499003, 1.5636819136972355], 'a8': [0.766044443118978, -0.6427876096865394], 'a9': [-1.5117421107673987, 2.5912614284422424], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.293576512744743, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.6862416378687336, 0.7273736415730487]]], [3, [[1.0, 0], [-0.8626290886680674, -1.5019557434837085]]]], 'bad_primes': [2, 3], 'central_character': '162.103', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '3165466286646443817663317477636', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'root_angle': -0.39218072598395, 'root_number': '0.33228409160098515 - 0.9431793479868545*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.196090362992', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.982492822554157887070919041992', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.47807418872303349428991798637', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.95889364808430003764707759411', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.293576512744743, 'bad_primes': [2, 3], 'central_character': '81.22', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/g/b/103/4'], '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': '2-162-81.22-c1-0-1', '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': '2-162-81.22-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': -0.196090362991975, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.982492822554157887070919041992', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1245457616230705526906524844980', 'Lhash_array': ['1245457616230705526906524844980'], 'label': '2-162-81.22-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/g/b/103/4'}