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lfunc_lfunctions • Show schema
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{'Lhash': '1426378898681151137753547944789', 'a10': [-3.7853188626880683, 6.556364593024573], 'a2': [2.309566616655817, 0.840613502517618], 'a3': [0.0, 0.0], 'a4': [3.0953780099181034, 2.5973305464765435], 'a5': [-0.5348820423888605, 3.0334668026399334], 'a6': [0.0, 0.0], 'a7': [-2.0366571837960015, 1.7089582917577828], 'a8': [2.507841132270207, 4.34370825840306], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.568', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '3384648648324474064182695172653', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.309566616655817, -0.840613502517618], [1.532088886237956, 1.2855752193730787]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.5348820423888605, -3.0334668026399334], [-4.698463103929542, -1.7101007166283437]], 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'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.89536409788632413610039585663', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '27.4', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/u/568/2'], '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': '2-3e6-27.4-c1-0-15', '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': '2-3e6-27.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.3148148148148148, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.12521454920176276856875776862', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1426378898681151137753547944789', 'Lhash_array': ['1426378898681151137753547944789'], 'label': '2-3e6-27.4-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/u/568/2'}