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lfunc_lfunctions • Show schema
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{'Lhash': '2043845471335180383145569369368', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.41178332170387, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, -1]], [19, [1, 1]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '4560.1', 'coefficient_field': '1.1.1.1', 'conductor': 4560, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -1], [1, 2, 7], [1, 0, 11], [1, 2, 13], [1, -4, 17], [1, 1], [1, 4, 23], [1, 6, 29], [1, 10, 31], [1, 10, 37], [1, 0, 41], [1, 4, 43], [1, 4, 47], [1, -10, 53], [1, -6, 59], [1, -10, 61], [1, -4, 67], [1, 8, 71], [1, 2, 73], [1, -6, 79], [1, 6, 83], [1, -4, 89], [1, -2, 97], [1, 6, 101], [1, 0, 103], [1, 8, 107], [1, 8, 109], [1, -6, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, -1], 1]], [[[1, 2, 7], 1]], [[[1, 0, 11], 1]], [[[1, 2, 13], 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3.3995174588118044, 3.560041965790052, 3.5758863279693855, 3.451647846136718, 3.197873495639963, 2.830514752130959, 2.3701270639164878, 1.840852812267127], 'positive_zeros': ['1.61230978864933593298883413951207', '2.40137790952123960259977848437957', '3.43836804427240393836727470480500', '3.88575745120611956452812234675676', '5.19429437945824956018065244009036', '5.65175441790090956548082692201999', '6.65966705644225589840552614788915', '7.22433433977763669397425818816492', '7.957744906064071969242601726237742'], 'prelabel': '2-4560-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.034217705859134, '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': 1682025928733381214, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.61230978864933593298883413951', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.40137790952123960259977848438', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43836804427240393836727470481', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.41178332170387, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 4560, 'conductor_radical': 570, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, -2, 0, 1, 0, 0, 0, -2, 0, 1, 0, 4, 0, -1, 0, -2, 0, -4, 0, 1, 0, 1, 0, -6, 0, -10, 0, 0, 0, -2, 0, -10, 0, -2, 0, 0, 0, -4, 0, 1, 0, -4, 0, -3, 0, 4, 0, 10, 0, 0, 0, -1, 0, 6, 0, 10, 0, -2, 0, -2, 0, 4, 0, -4, 0, -8, 0, -2, 0, 1, 0, 0, 0, 6, 0, 1, 0, -6, 0, 4, 0, -6, 0, 4, 0, 4, 0, -10, 0, -1, 0, 2, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 2, 13], 'euler17': [1, -4, 17], 'euler19': [1, 1, 0], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, 6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 10, 31], 'euler37': [1, 10, 37], 'euler41': [1, 0, 41], 'euler43': [1, 4, 43], 'euler47': [1, 4, 47], 'euler5': [1, -1, 0], 'euler53': [1, -10, 53], 'euler59': [1, -6, 59], 'euler61': [1, -10, 61], 'euler67': [1, -4, 67], 'euler7': [1, 2, 7], 'euler71': [1, 8, 71], 'euler73': [1, 2, 73], 'euler79': [1, -6, 79], 'euler83': [1, 6, 83], 'euler89': [1, -4, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, -1, 0], [1, 2, 7], [1, 0, 11], [1, 2, 13], [1, -4, 17], [1, 1, 0], [1, 4, 23], [1, 6, 29], [1, 10, 31], [1, 10, 37], [1, 0, 41], [1, 4, 43], [1, 4, 47], [1, -10, 53], [1, -6, 59], [1, -10, 61], [1, -4, 67], [1, 8, 71], [1, 2, 73], [1, -6, 79], [1, 6, 83], [1, -4, 89], [1, -2, 97]], 'index': 68, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/4560/z', 'ModularForm/GL2/Q/holomorphic/4560/2/a/z/1/1', 'ModularForm/GL2/Q/holomorphic/4560/2/a/z'], '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': '2-4560-1.1-c1-0-68', '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': '2-4560-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.034217705859134, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1682025928733381214, 'z1': {'__RealLiteral__': 0, 'data': '1.61230978864933593298883413951', 'prec': 103}}
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lfunc_instances • Show schema
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id: 19991593
{'Lhash': '2043845471335180383145569369368', 'Lhash_array': ['2043845471335180383145569369368'], 'label': '2-4560-1.1-c1-0-68', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4560/2/a/z'}
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id: 24566501
{'Lhash': '2043845471335180383145569369368', 'Lhash_array': ['2043845471335180383145569369368'], 'label': '2-4560-1.1-c1-0-68', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4560/2/a/z/1/1'}
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id: 87568
{'Lhash': '1682025928733381214', 'Lhash_array': ['1682025928733381214'], 'label': '2-4560-1.1-c1-0-68', 'type': 'ECQ', 'url': 'EllipticCurve/Q/4560/z'}