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lfunc_lfunctions • Show schema
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{'Lhash': '4365351560504951123894134469019', 'a10': -2, 'a2': 1, 'a3': 1, 'a4': -1, 'a5': -2, 'a6': 1, 'a7': 0, 'a8': -3, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.4551472915212984, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -1]], [19, [1, 1]]], 'bad_primes': [3, 19], 'central_character': '57.1', 'coefficient_field': '1.1.1.1', 'conductor': 57, 'conductor_radical': 57, 'degree': 2, 'euler_factors': [[1, -1, 2], [1, -1], [1, 2, 5], [1, 0, 7], [1, 0, 11], [1, -6, 13], [1, 6, 17], [1, 1], [1, -4, 23], [1, -2, 29], [1, -8, 31], [1, 10, 37], [1, 2, 41], [1, 4, 43], [1, -12, 47], [1, 6, 53], [1, 12, 59], [1, 2, 61], [1, 4, 67], [1, 0, 71], [1, -10, 73], [1, 0, 79], [1, -16, 83], [1, 2, 89], [1, -10, 97], [1, 10, 101], [1, -8, 103], [1, -4, 107], [1, 10, 109], [1, -6, 113]], 'euler_factors_factorization': [[[[1, -1, 2], 1]], [[[1, -1], 1]], [[[1, 2, 5], 1]], [[[1, 0, 7], 1]], [[[1, 0, 11], 1]], [[[1, -6, 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0.18957017249303867, -0.021722479535975725, -0.3252206098801572, -0.6213779996218272, -0.807945743903379, -0.8068762116450594, -0.585546036837008, -0.16728064526567626], 'positive_zeros': ['3.44365518362789223021999993571232', '4.56991321080597356703354311171678', '6.46787589567348650226556085188865', '8.263513432862467471567669978548273', '9.032116632714081125535639739797092', '10.84155613367776600825623791063400', '12.07987440084703696834915246162358', '13.30135307533368428997273937211662', '13.89424674132429450373973021658182', '15.35090650815041953121172131081091'], 'prelabel': '2-57-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.6746460490666928, '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': 75089547396961172, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.44365518362789223021999993571', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.56991321080597356703354311172', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.46787589567348650226556085189', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.4551472915212984, 'bad_primes': [3, 19], 'central_character': '1.1', 'conductor': 57, 'conductor_radical': 57, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, -1, -2, 1, 0, -3, 1, -2, 0, -1, 6, 0, -2, -1, -6, 1, -1, 2, 0, 0, 4, -3, -1, 6, 1, 0, 2, -2, 8, 5, 0, -6, 0, -1, -10, -1, 6, 6, -2, 0, -4, 0, -2, 4, 12, -1, -7, -1, -6, -6, -6, 1, 0, 0, -1, 2, -12, 2, -2, 8, 0, 7, -12, 0, -4, 6, 4, 0, 0, -3, 10, -10, -1, 1, 0, 6, 0, 2, 1, -2, 16, 0, 12, -4, 2, 0, -2, -2, 0, -4, 8, 12, 2, 5, 10, -7, 0, 1], 'euler11': [1, 0, 11], 'euler13': [1, -6, 13], 'euler17': [1, 6, 17], 'euler19': [1, 1, 0], 'euler2': [1, -1, 2], 'euler23': [1, -4, 23], 'euler29': [1, -2, 29], 'euler3': [1, -1, 0], 'euler31': [1, -8, 31], 'euler37': [1, 10, 37], 'euler41': [1, 2, 41], 'euler43': [1, 4, 43], 'euler47': [1, -12, 47], 'euler5': [1, 2, 5], 'euler53': [1, 6, 53], 'euler59': [1, 12, 59], 'euler61': [1, 2, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, -10, 73], 'euler79': [1, 0, 79], 'euler83': [1, -16, 83], 'euler89': [1, 2, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, -1, 2], [1, -1, 0], [1, 2, 5], [1, 0, 7], [1, 0, 11], [1, -6, 13], [1, 6, 17], [1, 1, 0], [1, -4, 23], [1, -2, 29], [1, -8, 31], [1, 10, 37], [1, 2, 41], [1, 4, 43], [1, -12, 47], [1, 6, 53], [1, 12, 59], [1, 2, 61], [1, 4, 67], [1, 0, 71], [1, -10, 73], [1, 0, 79], [1, -16, 83], [1, 2, 89], [1, -10, 97]], 'index': 1, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/57/c', 'ModularForm/GL2/Q/holomorphic/57/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/57/2/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': '2-57-1.1-c1-0-1', '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': '2-57-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.6746460490666928, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 75089547396961172, 'z1': {'__RealLiteral__': 0, 'data': '3.44365518362789223021999993571', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9957054
{'Lhash': '4365351560504951123894134469019', 'Lhash_array': ['4365351560504951123894134469019'], 'label': '2-57-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/57/2/a/c'}
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id: 24546206
{'Lhash': '4365351560504951123894134469019', 'Lhash_array': ['4365351560504951123894134469019'], 'label': '2-57-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/57/2/a/c/1/1'}
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id: 21862
{'Lhash': '75089547396961172', 'Lhash_array': ['75089547396961172'], 'label': '2-57-1.1-c1-0-1', 'type': 'ECQ', 'url': 'EllipticCurve/Q/57/c'}