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lfunc_lfunctions • Show schema
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{'Lhash': '1863502493566173611322230031129', 'a10': -2, 'a2': -1, 'a3': 1, 'a4': 1, 'a5': 2, 'a6': -1, 'a7': 0, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 53.994841846789825, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, -1]], [7, [1]], [23, [1, 1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '6762.1', 'coefficient_field': '1.1.1.1', 'conductor': 6762, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[1, 1], [1, -1], [1, -2, 5], [1], [1, 0, 11], [1, 4, 13], [1, 0, 17], [1, 6, 19], [1, 1], [1, 6, 29], [1, -10, 31], [1, 6, 37], [1, -2, 41], [1, -12, 43], [1, 10, 47], [1, 10, 53], [1, -12, 59], [1, -14, 61], [1, 12, 67], [1, 12, 71], [1, 14, 73], [1, 0, 79], [1, 2, 83], [1, -12, 89], [1, 12, 97], [1, 0, 101], [1, -4, 103], [1, -8, 107], [1, 10, 109], [1, 14, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, -1], 1]], [[[1, -2, 5], 1]], [1], [[[1, 0, 11], 1]], 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-0.05646782535320242, -0.767604791672294, -1.3980048128591767, -1.9184467187072622, -2.304427471029458, -2.537449922495317, -2.6060274388001865, -2.506347544181836, -2.242553785954839, -1.8266245872078701, -1.277848951724351], 'positive_zeros': ['1.47004426395622444290709075383319', '2.25988769128618149359019770535904', '2.76794772888261448463062802969179', '3.94095715245293709767887032654047', '4.74849680205857491308806811466196', '5.67932025773096788829582180097196', '6.35032556384238417172028370730683', '7.02738940417009546271130138997840', '7.75307857458158543088604731601270'], 'prelabel': '2-6762-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.348118252096235, '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': 659398665086055383, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47004426395622444290709075383', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.25988769128618149359019770536', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.76794772888261448463062802969', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 53.994841846789825, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 6762, 'conductor_radical': 966, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, 1, 2, -1, 0, -1, 1, -2, 0, 1, -4, 0, 2, 1, 0, -1, -6, 2, 0, 0, -1, -1, -1, 4, 1, 0, -6, -2, 10, -1, 0, 0, 0, 1, -6, 6, -4, -2, 2, 0, 12, 0, 2, 1, -10, 1, 0, 1, 0, -4, -10, -1, 0, 0, -6, 6, 12, 2, 14, -10, 0, 1, -8, 0, -12, 0, -1, 0, -12, -1, -14, 6, -1, -6, 0, 4, 0, 2, 1, -2, -2, 0, 0, -12, -6, 0, 12, -2, 0, -1, 10, 10, -12, -1, -12, 0, 0, -1], 'euler11': [1, 0, 11], 'euler13': [1, 4, 13], 'euler17': [1, 0, 17], 'euler19': [1, 6, 19], 'euler2': [1, 1, 0], 'euler23': [1, 1, 0], 'euler29': [1, 6, 29], 'euler3': [1, -1, 0], 'euler31': [1, -10, 31], 'euler37': [1, 6, 37], 'euler41': [1, -2, 41], 'euler43': [1, -12, 43], 'euler47': [1, 10, 47], 'euler5': [1, -2, 5], 'euler53': [1, 10, 53], 'euler59': [1, -12, 59], 'euler61': [1, -14, 61], 'euler67': [1, 12, 67], 'euler7': [1, 0, 0], 'euler71': [1, 12, 71], 'euler73': [1, 14, 73], 'euler79': [1, 0, 79], 'euler83': [1, 2, 83], 'euler89': [1, -12, 89], 'euler97': [1, 12, 97], 'euler_factors': [[1, 1, 0], [1, -1, 0], [1, -2, 5], [1, 0, 0], [1, 0, 11], [1, 4, 13], [1, 0, 17], [1, 6, 19], [1, 1, 0], [1, 6, 29], [1, -10, 31], [1, 6, 37], [1, -2, 41], [1, -12, 43], [1, 10, 47], [1, 10, 53], [1, -12, 59], [1, -14, 61], [1, 12, 67], [1, 12, 71], [1, 14, 73], [1, 0, 79], [1, 2, 83], [1, -12, 89], [1, 12, 97]], 'index': 130, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6762/r', 'ModularForm/GL2/Q/holomorphic/6762/2/a/r/1/1', 'ModularForm/GL2/Q/holomorphic/6762/2/a/r'], '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': '2-6762-1.1-c1-0-130', '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': '2-6762-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.348118252096235, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 659398665086055383, 'z1': {'__RealLiteral__': 0, 'data': '1.47004426395622444290709075383', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21655297
{'Lhash': '1863502493566173611322230031129', 'Lhash_array': ['1863502493566173611322230031129'], 'label': '2-6762-1.1-c1-0-130', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6762/2/a/r'}
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id: 24576520
{'Lhash': '1863502493566173611322230031129', 'Lhash_array': ['1863502493566173611322230031129'], 'label': '2-6762-1.1-c1-0-130', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6762/2/a/r/1/1'}
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id: 31924
{'Lhash': '659398665086055383', 'Lhash_array': ['659398665086055383'], 'label': '2-6762-1.1-c1-0-130', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6762/r'}