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lfunc_lfunctions • Show schema
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{'Lhash': '1914543212952188498778994679948', 'a10': [1.7057370639048863, -2.9544232590366244], 'a2': [-0.1527036446661393, -0.8660254037844386], 'a3': [0.0, 0.0], 'a4': [1.1527036446661394, -0.41954981558864], 'a5': [2.9717815070238642, 2.493620766483186], 'a6': [0.0, 0.0], 'a7': [2.053033419238747, 0.7472430545566693], 'a8': [-1.4187480877851173, -2.457343771185013], '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': '729.82', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '2032113536977349225265750018812', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.1527036446661393, 0.8660254037844386], [-1.8793852415718169, 0.6840402866513374]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.9717815070238642, -2.493620766483186], [0.8682408883346517, 4.924038765061041]], 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{'__RealLiteral__': 0, 'data': '4.33162500712435502897221860025', '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': '27.13', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/e/c/82/1'], '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': '2-3e6-27.13-c1-0-17', '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': '2-3e6-27.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.07407407407407408, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51030829205420779291072382727', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1914543212952188498778994679948', 'Lhash_array': ['1914543212952188498778994679948'], 'label': '2-3e6-27.13-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/e/c/82/1'}