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lfunc_lfunctions • Show schema
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{'Lhash': '1429112177444346038152611044612', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 68.99074734638629, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -1]]], 'bad_primes': [2, 3, 5], 'central_character': '8640.1', 'coefficient_field': '1.1.1.1', 'conductor': 8640, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1, -1], [1, 4, 7], [1, 2, 11], [1, 4, 13], [1, -1, 17], [1, -5, 19], [1, -5, 23], [1, 8, 29], [1, -7, 31], [1, -6, 37], [1, -6, 41], [1, -2, 43], [1, -8, 47], [1, 9, 53], [1, 4, 59], [1, 13, 61], [1, -10, 67], [1, 6, 71], [1, 6, 73], [1, -9, 79], [1, -17, 83], [1, 6, 89], [1, 8, 97], [1, 12, 101], [1, -4, 103], [1, 12, 107], [1, 17, 109], [1, -6, 113]], 'euler_factors_factorization': [[1], [1], [[[1, -1], 1]], [[[1, 4, 7], 1]], [[[1, 2, 11], 1]], [[[1, 4, 13], 1]], [[[1, -1, 17], 1]], [[[1, -5, 19], 1]], [[[1, -5, 23], 1]], [[[1, 8, 29], 1]], [[[1, -7, 31], 1]], [[[1, -6, 37], 1]], [[[1, -6, 41], 1]], [[[1, -2, 43], 1]], [[[1, -8, 47], 1]], [[[1, 9, 53], 1]], [[[1, 4, 59], 1]], [[[1, 13, 61], 1]], [[[1, -10, 67], 1]], [[[1, 6, 71], 1]], [[[1, 6, 73], 1]], [[[1, -9, 79], 1]], [[[1, -17, 83], 1]], [[[1, 6, 89], 1]], [[[1, 8, 97], 1]], [[[1, 12, 101], 1]], [[[1, -4, 103], 1]], [[[1, 12, 107], 1]], [[[1, 17, 109], 1]], [[[1, -6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 81, 'label': '2-8640-1.1-c1-0-81', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/8640/2/a/bf', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-5.420829714699354e-61, 0.18091664947317032, 0.3601707822066091, 0.5360627178373546, 0.7068219073492866, 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-5.339936211541261, -5.186667663217936, -4.891936555685297, -4.472899233166521, -3.952511103222889, -3.358251646479614, -2.7206066334988743, -2.0713929327752654, -1.4420207115847108], 'positive_zeros': ['1.12737072596111806526309478814964', '2.56805366284799917081919448512489', '2.85015981870912461136487956706930', '3.74003194570339284765478358434300', '4.74472917965118669238450357257207', '5.42016231751570044953010087520414', '6.05954716596321482019902208948638', '6.71401739160618710686470724247308', '7.49021375169655068173068034665104'], 'prelabel': '2-8640-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.306066899946465, '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': 1794528052930445543, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12737072596111806526309478815', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.56805366284799917081919448512', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.85015981870912461136487956707', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 68.99074734638629, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 8640, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, -4, 0, 0, 0, -2, 0, -4, 0, 0, 0, 1, 0, 5, 0, 0, 0, 5, 0, 1, 0, 0, 0, -8, 0, 7, 0, 0, 0, -4, 0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 0, 8, 0, 9, 0, 0, 0, -9, 0, -2, 0, 0, 0, -4, 0, -13, 0, 0, 0, -4, 0, 10, 0, 0, 0, -6, 0, -6, 0, 0, 0, 8, 0, 9, 0, 0, 0, 17, 0, 1, 0, 0, 0, -6, 0, 16, 0, 0, 0, 5, 0, -8, 0, 0, 0], 'euler11': [1, 2, 11], 'euler13': [1, 4, 13], 'euler17': [1, -1, 17], 'euler19': [1, -5, 19], 'euler2': [1, 0, 0], 'euler23': [1, -5, 23], 'euler29': [1, 8, 29], 'euler3': [1, 0, 0], 'euler31': [1, -7, 31], 'euler37': [1, -6, 37], 'euler41': [1, -6, 41], 'euler43': [1, -2, 43], 'euler47': [1, -8, 47], 'euler5': [1, -1, 0], 'euler53': [1, 9, 53], 'euler59': [1, 4, 59], 'euler61': [1, 13, 61], 'euler67': [1, -10, 67], 'euler7': [1, 4, 7], 'euler71': [1, 6, 71], 'euler73': [1, 6, 73], 'euler79': [1, -9, 79], 'euler83': [1, -17, 83], 'euler89': [1, 6, 89], 'euler97': [1, 8, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -1, 0], [1, 4, 7], [1, 2, 11], [1, 4, 13], [1, -1, 17], [1, -5, 19], [1, -5, 23], [1, 8, 29], [1, -7, 31], [1, -6, 37], [1, -6, 41], [1, -2, 43], [1, -8, 47], [1, 9, 53], [1, 4, 59], [1, 13, 61], [1, -10, 67], [1, 6, 71], [1, 6, 73], [1, -9, 79], [1, -17, 83], [1, 6, 89], [1, 8, 97]], 'index': 81, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/8640/bf', 'ModularForm/GL2/Q/holomorphic/8640/2/a/bf/1/1', 'ModularForm/GL2/Q/holomorphic/8640/2/a/bf'], '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': '2-8640-1.1-c1-0-81', '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': '2-8640-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.306066899946465, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1794528052930445543, 'z1': {'__RealLiteral__': 0, 'data': '1.12737072596111806526309478815', 'prec': 103}}
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lfunc_instances • Show schema
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id: 22269743
{'Lhash': '1429112177444346038152611044612', 'Lhash_array': ['1429112177444346038152611044612'], 'label': '2-8640-1.1-c1-0-81', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8640/2/a/bf'}
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id: 24584914
{'Lhash': '1429112177444346038152611044612', 'Lhash_array': ['1429112177444346038152611044612'], 'label': '2-8640-1.1-c1-0-81', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8640/2/a/bf/1/1'}
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id: 30133
{'Lhash': '1794528052930445543', 'Lhash_array': ['1794528052930445543'], 'label': '2-8640-1.1-c1-0-81', 'type': 'ECQ', 'url': 'EllipticCurve/Q/8640/bf'}