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lfunc_lfunctions • Show schema
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{'Lhash': '2339570176709773583331289180966', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': 3, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.621468302298142, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [11, [1, -1]]], 'bad_primes': [2, 11], 'central_character': '704.1', 'coefficient_field': '1.1.1.1', 'conductor': 704, 'conductor_radical': 22, 'degree': 2, 'euler_factors': [[1], [1, -3, 3], [1, -3, 5], [1, 2, 7], [1, -1], [1, 0, 13], [1, 6, 17], [1, 4, 19], [1, -1, 23], [1, -8, 29], [1, 7, 31], [1, -1, 37], [1, -4, 41], [1, 6, 43], [1, 8, 47], [1, 2, 53], [1, -1, 59], [1, 4, 61], [1, -5, 67], [1, -3, 71], [1, -16, 73], [1, -2, 79], [1, -2, 83], [1, -15, 89], [1, 7, 97], [1, -10, 101], [1, 16, 103], [1, 2, 107], [1, -14, 109], [1, 7, 113]], 'euler_factors_factorization': [[1], [[[1, -3, 3], 1]], [[[1, -3, 5], 1]], [[[1, 2, 7], 1]], [[[1, -1], 1]], [[[1, 0, 13], 1]], [[[1, 6, 17], 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-0.7870431106282703, -1.0255538973144716, -0.7233110121885344, -0.00921410688574351, 0.8342555354636506, 1.4835219843527234, 1.700263671121378], 'positive_zeros': ['1.84559544742735453993387759114202', '2.58128943528283843865888199294026', '3.63547474808138538276796488469708', '4.78987665155787865457700111620721', '6.33216658844039512399715167893476', '6.80526418655862410599202441775921', '8.118360153173760371978857071616207', '8.911534990908679817989792101964592', '9.424260651660627252011971923444274', '10.05533835255727124496621603450147'], 'prelabel': '2-704-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.3709635809725427, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 71051827741580723, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.84559544742735453993387759114', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.58128943528283843865888199294', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.63547474808138538276796488470', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.621468302298142, 'bad_primes': [2, 11], 'central_character': '1.1', 'conductor': 704, 'conductor_radical': 22, 'degree': 2, 'dirichlet_coefficients': [1, 0, 3, 0, 3, 0, -2, 0, 6, 0, 1, 0, 0, 0, 9, 0, -6, 0, -4, 0, -6, 0, 1, 0, 4, 0, 9, 0, 8, 0, -7, 0, 3, 0, -6, 0, 1, 0, 0, 0, 4, 0, -6, 0, 18, 0, -8, 0, -3, 0, -18, 0, -2, 0, 3, 0, -12, 0, 1, 0, -4, 0, -12, 0, 0, 0, 5, 0, 3, 0, 3, 0, 16, 0, 12, 0, -2, 0, 2, 0, 9, 0, 2, 0, -18, 0, 24, 0, 15, 0, 0, 0, -21, 0, -12, 0, -7, 0, 6, 0], 'euler11': [1, -1, 0], 'euler13': [1, 0, 13], 'euler17': [1, 6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 23], 'euler29': [1, -8, 29], 'euler3': [1, -3, 3], 'euler31': [1, 7, 31], 'euler37': [1, -1, 37], 'euler41': [1, -4, 41], 'euler43': [1, 6, 43], 'euler47': [1, 8, 47], 'euler5': [1, -3, 5], 'euler53': [1, 2, 53], 'euler59': [1, -1, 59], 'euler61': [1, 4, 61], 'euler67': [1, -5, 67], 'euler7': [1, 2, 7], 'euler71': [1, -3, 71], 'euler73': [1, -16, 73], 'euler79': [1, -2, 79], 'euler83': [1, -2, 83], 'euler89': [1, -15, 89], 'euler97': [1, 7, 97], 'euler_factors': [[1, 0, 0], [1, -3, 3], [1, -3, 5], [1, 2, 7], [1, -1, 0], [1, 0, 13], [1, 6, 17], [1, 4, 19], [1, -1, 23], [1, -8, 29], [1, 7, 31], [1, -1, 37], [1, -4, 41], [1, 6, 43], [1, 8, 47], [1, 2, 53], [1, -1, 59], [1, 4, 61], [1, -5, 67], [1, -3, 71], [1, -16, 73], [1, -2, 79], [1, -2, 83], [1, -15, 89], [1, 7, 97]], 'index': 14, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/704/l', 'ModularForm/GL2/Q/holomorphic/704/2/a/l/1/1', 'ModularForm/GL2/Q/holomorphic/704/2/a/l'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-704-1.1-c1-0-14', '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': '2-704-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.3709635809725427, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 71051827741580723, 'z1': {'__RealLiteral__': 0, 'data': '1.84559544742735453993387759114', 'prec': 103}}
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lfunc_instances • Show schema
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id: 13367793
{'Lhash': '2339570176709773583331289180966', 'Lhash_array': ['2339570176709773583331289180966'], 'label': '2-704-1.1-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/704/2/a/l'}
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id: 24550258
{'Lhash': '2339570176709773583331289180966', 'Lhash_array': ['2339570176709773583331289180966'], 'label': '2-704-1.1-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/704/2/a/l/1/1'}
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id: 38108
{'Lhash': '71051827741580723', 'Lhash_array': ['71051827741580723'], 'label': '2-704-1.1-c1-0-14', 'type': 'ECQ', 'url': 'EllipticCurve/Q/704/l'}