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lfunc_lfunctions • Show schema
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{'Lhash': '2302916189447008262032944607830', 'a10': -2, 'a2': -1, 'a3': 0, 'a4': 1, 'a5': 2, 'a6': 0, 'a7': -1, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.067265720149466, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [7, [1, 1]], [11, [1, 1]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '1386.1', 'coefficient_field': '1.1.1.1', 'conductor': 1386, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, -2, 5], [1, 1], [1, 1], [1, 4, 13], [1, -2, 17], [1, 6, 19], [1, 2, 23], [1, 2, 29], [1, 8, 31], [1, 2, 37], [1, 2, 41], [1, 2, 43], [1, -2, 47], [1, -6, 53], [1, 0, 59], [1, -4, 61], [1, 0, 67], [1, -10, 71], [1, 2, 73], [1, 12, 79], [1, 12, 83], [1, -12, 89], [1, 2, 97], [1, 6, 101], [1, 0, 103], [1, 4, 107], [1, 8, 109], [1, 4, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [1], [[[1, -2, 5], 1]], [[[1, 1], 1]], [[[1, 1], 1]], [[[1, 4, 13], 1]], 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0.02767841457992109, 0.5610814811092801, 0.9691538794709138, 1.2261949726553718, 1.3164557468333027, 1.23512145257758, 0.988587807648601, 0.5940116783169722, 0.07816490773166494], 'positive_zeros': ['1.81668054985529005187136744963698', '2.57760145046844813266140965153301', '3.88305920202674694971898012431470', '5.21358330310255541751497667931559', '5.92515700044966766081550832121533', '6.82418002670887555935696009358750', '7.55983219604555693601523262064983', '8.498661052564373095840327857912860', '9.286627858952939688643238165404444'], 'prelabel': '2-1386-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.326750023694216, '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': 1914231079442175383, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.81668054985529005187136744964', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.57760145046844813266140965153', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.88305920202674694971898012431', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.067265720149466, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 1386, 'conductor_radical': 462, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 2, 0, -1, -1, 0, -2, -1, 0, -4, 1, 0, 1, 2, 0, -6, 2, 0, 1, -2, 0, -1, 4, 0, -1, -2, 0, -8, -1, 0, -2, -2, 0, -2, 6, 0, -2, -2, 0, -2, -1, 0, 2, 2, 0, 1, 1, 0, -4, 6, 0, -2, 1, 0, 2, 0, 0, 4, 8, 0, 1, -8, 0, 0, 2, 0, 2, 10, 0, -2, 2, 0, -6, 1, 0, -12, 2, 0, 2, -12, 0, 4, 2, 0, 1, 12, 0, 4, -2, 0, -2, -12, 0, -2, -1, 0, -1], 'euler11': [1, 1, 0], 'euler13': [1, 4, 13], 'euler17': [1, -2, 17], 'euler19': [1, 6, 19], 'euler2': [1, 1, 0], 'euler23': [1, 2, 23], 'euler29': [1, 2, 29], 'euler3': [1, 0, 0], 'euler31': [1, 8, 31], 'euler37': [1, 2, 37], 'euler41': [1, 2, 41], 'euler43': [1, 2, 43], 'euler47': [1, -2, 47], 'euler5': [1, -2, 5], 'euler53': [1, -6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -4, 61], 'euler67': [1, 0, 67], 'euler7': [1, 1, 0], 'euler71': [1, -10, 71], 'euler73': [1, 2, 73], 'euler79': [1, 12, 79], 'euler83': [1, 12, 83], 'euler89': [1, -12, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, -2, 5], [1, 1, 0], [1, 1, 0], [1, 4, 13], [1, -2, 17], [1, 6, 19], [1, 2, 23], [1, 2, 29], [1, 8, 31], [1, 2, 37], [1, 2, 41], [1, 2, 43], [1, -2, 47], [1, -6, 53], [1, 0, 59], [1, -4, 61], [1, 0, 67], [1, -10, 71], [1, 2, 73], [1, 12, 79], [1, 12, 83], [1, -12, 89], [1, 2, 97]], 'index': 21, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1386/d', 'ModularForm/GL2/Q/holomorphic/1386/2/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/1386/2/a/d'], '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': '2-1386-1.1-c1-0-21', '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': '2-1386-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.326750023694216, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1914231079442175383, 'z1': {'__RealLiteral__': 0, 'data': '1.81668054985529005187136744964', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20647382
{'Lhash': '2302916189447008262032944607830', 'Lhash_array': ['2302916189447008262032944607830'], 'label': '2-1386-1.1-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1386/2/a/d'}
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id: 24552909
{'Lhash': '2302916189447008262032944607830', 'Lhash_array': ['2302916189447008262032944607830'], 'label': '2-1386-1.1-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1386/2/a/d/1/1'}
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id: 99092
{'Lhash': '1914231079442175383', 'Lhash_array': ['1914231079442175383'], 'label': '2-1386-1.1-c1-0-21', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1386/d'}