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lfunc_lfunctions • Show schema
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{'Lhash': '2015596061564822592096265493106', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': -2, 'a5': 1, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.075906491948345, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -1]], [13, [1, 1]], [103, [1, -1]]], 'bad_primes': [3, 13, 103], 'central_character': '4017.1', 'coefficient_field': '1.1.1.1', 'conductor': 4017, 'conductor_radical': 4017, 'degree': 2, 'euler_factors': [[1, 0, 2], [1, -1], [1, -1, 5], [1, -2, 7], [1, 0, 11], [1, 1], [1, 3, 17], [1, 4, 19], [1, 8, 23], [1, -5, 29], [1, 1, 31], [1, -1, 37], [1, 6, 41], [1, 8, 43], [1, -3, 47], [1, 0, 53], [1, 0, 59], [1, -6, 61], [1, 12, 67], [1, 1, 71], [1, 7, 73], [1, -13, 79], [1, 6, 83], [1, -2, 89], [1, -6, 97], [1, -2, 101], [1, -1], [1, 5, 107], [1, -11, 109], [1, 12, 113]], 'euler_factors_factorization': [[[[1, 0, 2], 1]], [[[1, -1], 1]], [[[1, -1, 5], 1]], [[[1, -2, 7], 1]], [[[1, 0, 11], 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-3.299915696995772, -3.1111240205293407, -2.8124011428836013, -2.4246076874244364, -1.972834902376171, -1.4847855982639793, -0.9890336035010013, -0.5132690383145082], 'positive_zeros': ['1.59002493368593219071271688421356', '2.33128840435454651393386049364662', '3.55991169571847410774924610306144', '4.34415681869639972823357680003873', '4.86520020905111913093774715807239', '5.80653174799998452773628812101961', '6.55774121903757458544896035936076', '7.62363466505198381248563064316682', '8.289812019619759109423310079485939'], 'prelabel': '2-4017-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.66355952488789, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1768925258302969343, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.59002493368593219071271688421', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33128840435454651393386049365', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.55991169571847410774924610306', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.075906491948345, 'bad_primes': [3, 13, 103], 'central_character': '1.1', 'conductor': 4017, 'conductor_radical': 4017, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, -2, 1, 0, 2, 0, 1, 0, 0, -2, -1, 0, 1, 4, -3, 0, -4, -2, 2, 0, -8, 0, -4, 0, 1, -4, 5, 0, -1, 0, 0, 0, 2, -2, 1, 0, -1, 0, -6, 0, -8, 0, 1, 0, 3, 4, -3, 0, -3, 2, 0, 0, 0, 0, -4, 0, 0, -2, 6, 0, 2, -8, -1, 0, -12, 6, -8, 0, -1, 0, -7, 0, -4, 8, 0, 0, 13, 4, 1, 0, -6, -4, -3, 0, 5, 0, 2, 0, -2, 16, -1, 0, -4, 0, 6, 0, 0, 8], 'euler11': [1, 0, 11], 'euler13': [1, 1, 0], 'euler17': [1, 3, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 2], 'euler23': [1, 8, 23], 'euler29': [1, -5, 29], 'euler3': [1, -1, 0], 'euler31': [1, 1, 31], 'euler37': [1, -1, 37], 'euler41': [1, 6, 41], 'euler43': [1, 8, 43], 'euler47': [1, -3, 47], 'euler5': [1, -1, 5], 'euler53': [1, 0, 53], 'euler59': [1, 0, 59], 'euler61': [1, -6, 61], 'euler67': [1, 12, 67], 'euler7': [1, -2, 7], 'euler71': [1, 1, 71], 'euler73': [1, 7, 73], 'euler79': [1, -13, 79], 'euler83': [1, 6, 83], 'euler89': [1, -2, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 0, 2], [1, -1, 0], [1, -1, 5], [1, -2, 7], [1, 0, 11], [1, 1, 0], [1, 3, 17], [1, 4, 19], [1, 8, 23], [1, -5, 29], [1, 1, 31], [1, -1, 37], [1, 6, 41], [1, 8, 43], [1, -3, 47], [1, 0, 53], [1, 0, 59], [1, -6, 61], [1, 12, 67], [1, 1, 71], [1, 7, 73], [1, -13, 79], [1, 6, 83], [1, -2, 89], [1, -6, 97]], 'index': 177, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/4017/c', 'ModularForm/GL2/Q/holomorphic/4017/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/4017/2/a/c'], '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': '2-4017-1.1-c1-0-177', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-4017-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.66355952488789, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1768925258302969343, 'z1': {'__RealLiteral__': 0, 'data': '1.59002493368593219071271688421', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20145445
{'Lhash': '2015596061564822592096265493106', 'Lhash_array': ['2015596061564822592096265493106'], 'label': '2-4017-1.1-c1-0-177', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4017/2/a/c'}
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id: 24564078
{'Lhash': '2015596061564822592096265493106', 'Lhash_array': ['2015596061564822592096265493106'], 'label': '2-4017-1.1-c1-0-177', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4017/2/a/c/1/1'}
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id: 88312
{'Lhash': '1768925258302969343', 'Lhash_array': ['1768925258302969343'], 'label': '2-4017-1.1-c1-0-177', 'type': 'ECQ', 'url': 'EllipticCurve/Q/4017/c'}