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lfunc_lfunctions • Show schema
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{'Lhash': '251645426415435182723366736215', 'a10': [66.35279315607218, -376.30538950688657], 'a2': [0.6945927106677214, 3.939231012048832], 'a3': [7.968771662821953, -6.6865933632098615], 'a4': [-15.035081932574535, 5.472322293210699], 'a5': [-89.7666058679995, -32.672372567057636], 'a6': [31.875086651287813, 26.746373452839446], 'a7': [-116.1092775575149, 201.1071679597326], 'a8': [-32.0, -55.42562584220407], 'a9': [-23.40571616379208, 132.7404125548464], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.0945851528932655, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.6945927106677214, -3.939231012048832]]], [19, [[1.0, 0], [880.6555815341064, 1304.0493651364677]]]], 'bad_primes': [2, 19], 'central_character': '38.9', 'coefficient_field': 'CDF', 'conductor': 38, 'conductor_radical': 38, 'conjugate': '3986840473901277356478990479352', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6945927106677214, 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0.08607230112329221*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.486284196675', 'prec': 47}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.19851323887680771422767506815', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.51296376658486878344653779001', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.95020936848989029498117147904', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.0945851528932655, 'bad_primes': [2, 19], 'central_character': '19.9', 'conductor': 38, 'conductor_radical': 38, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/38/6/e/b/9/4'], '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': '2-38-19.9-c5-0-0', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-38-19.9-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.468721359913521, 'root_angle': 0.486284196675094, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.19851323887680771422767506815', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '251645426415435182723366736215', 'Lhash_array': ['251645426415435182723366736215'], 'label': '2-38-19.9-c5-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/38/6/e/b/9/4'}