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lfunc_lfunctions • Show schema
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{'Lhash': '1452086316881955715817930208347', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -3.0], 'a4': [0, 0], 'a5': [15.689129409653287, 0], 'a6': [0, 0], 'a7': [10.836094376377146, 15.019289552646876], 'a8': [0, 0], 'a9': [-9.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 79.29856704771542, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 3.0]]], [7, [[1.0, 0], [-10.836094376377146, -15.019289552646876]]]], 'bad_primes': [2, 3, 7], 'central_character': '1344.223', 'coefficient_field': 'CDF', 'conductor': 1344, 'conductor_radical': 42, 'conjugate': '1114348543165267438065410474488', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.0]], [[1.0, 0], [-15.689129409653287, 0], [125.0, 0]], [[1.0, 0], [-10.836094376377146, -15.019289552646876]], [[1.0, 0], [-41.32374052074464, 0], [1331.0, 0]], [[1.0, 0], [-8.029948109131618, 0], [2197.0, 0]], [[1.0, 0], [0, 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'1.89210774623465044352414027704', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33958031795393944455269544911', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 79.29856704771542, 'bad_primes': [2, 3, 7], 'central_character': '56.27', 'conductor': 1344, 'conductor_radical': 42, 'degree': 2, 'index': 72, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1344/4/p/c/223/21'], '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': '2-1344-56.27-c3-0-72', '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': '2-1344-56.27-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.904974286752063, 'root_angle': 0.10886211659051509, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.14549412639454458265780365998', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1452086316881955715817930208347', 'Lhash_array': ['1452086316881955715817930208347'], 'label': '2-1344-56.27-c3-0-72', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1344/4/p/c/223/21'}