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lfunc_lfunctions • Show schema
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{'Lhash': '1739702823240640870785449489787', 'a10': -1, 'a2': 1, 'a3': -1, 'a4': 1, 'a5': -1, 'a6': -1, 'a7': 0, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 40.484153824789175, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, 1]], [5, [1, 1]], [13, [1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '5070.1', 'coefficient_field': '1.1.1.1', 'conductor': 5070, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1, -1], [1, 1], [1, 1], [1, 0, 7], [1, 6, 11], [1], [1, -6, 17], [1, -6, 19], [1, 6, 23], [1, 6, 29], [1, 0, 31], [1, -6, 37], [1, -12, 41], [1, 8, 43], [1, 0, 47], [1, 12, 53], [1, 6, 59], [1, -10, 61], [1, 0, 67], [1, 12, 71], [1, -6, 73], [1, 8, 79], [1, 0, 83], [1, 0, 89], [1, 6, 97], [1, 18, 101], [1, 14, 103], [1, 0, 107], [1, 6, 109], [1, 18, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, 1], 1]], [[[1, 1], 1]], [[[1, 0, 7], 1]], [[[1, 6, 11], 1]], [1], [[[1, -6, 17], 1]], [[[1, -6, 19], 1]], [[[1, 6, 23], 1]], [[[1, 6, 29], 1]], [[[1, 0, 31], 1]], [[[1, -6, 37], 1]], [[[1, -12, 41], 1]], [[[1, 8, 43], 1]], [[[1, 0, 47], 1]], [[[1, 12, 53], 1]], [[[1, 6, 59], 1]], [[[1, -10, 61], 1]], [[[1, 0, 67], 1]], [[[1, 12, 71], 1]], [[[1, -6, 73], 1]], [[[1, 8, 79], 1]], [[[1, 0, 83], 1]], [[[1, 0, 89], 1]], [[[1, 6, 97], 1]], [[[1, 18, 101], 1]], [[[1, 14, 103], 1]], [[[1, 0, 107], 1]], [[[1, 6, 109], 1]], [[[1, 18, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 78, 'label': '2-5070-1.1-c1-0-78', '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/5070/2/a/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.2397413248863993e-60, 0.20725987309086066, 0.413565815498046, 0.6179203409016526, 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1.7976040723629017, 1.6749290867272542, 1.487550178810194, 1.246477177678999, 0.9657468661847908, 0.6615901378217559, 0.35147738814893653, 0.05309591442792094], 'positive_zeros': ['1.37238354395716185195209308098551', '2.64244932660467667002330355008921', '3.33427348565644673024134151745903', '4.21675435150430547913884022182354', '5.12596459372855700664543977641244', '5.53300865905222736088367810362201', '6.15716794561398460837617323259521', '7.27825133601096414587290414694092', '7.79691102918406998688326032731522'], 'prelabel': '2-5070-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.3627159157697095, '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': 131014251800624117, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37238354395716185195209308099', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.64244932660467667002330355009', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33427348565644673024134151746', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 40.484153824789175, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 5070, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, 1, -1, -1, 0, 1, 1, -1, -6, -1, 0, 0, 1, 1, 6, 1, 6, -1, 0, -6, -6, -1, 1, 0, -1, 0, -6, 1, 0, 1, 6, 6, 0, 1, 6, 6, 0, -1, 12, 0, -8, -6, -1, -6, 0, -1, -7, 1, -6, 0, -12, -1, 6, 0, -6, -6, -6, 1, 10, 0, 0, 1, 0, 6, 0, 6, 6, 0, -12, 1, 6, 6, -1, 6, 0, 0, -8, -1, 1, 12, 0, 0, -6, -8, 6, -6, 0, -1, 0, -6, 0, 0, -6, -1, -6, -7, -6, 1], 'euler11': [1, 6, 11], 'euler13': [1, 0, 0], 'euler17': [1, -6, 17], 'euler19': [1, -6, 19], 'euler2': [1, -1, 0], 'euler23': [1, 6, 23], 'euler29': [1, 6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 31], 'euler37': [1, -6, 37], 'euler41': [1, -12, 41], 'euler43': [1, 8, 43], 'euler47': [1, 0, 47], 'euler5': [1, 1, 0], 'euler53': [1, 12, 53], 'euler59': [1, 6, 59], 'euler61': [1, -10, 61], 'euler67': [1, 0, 67], 'euler7': [1, 0, 7], 'euler71': [1, 12, 71], 'euler73': [1, -6, 73], 'euler79': [1, 8, 79], 'euler83': [1, 0, 83], 'euler89': [1, 0, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, -1, 0], [1, 1, 0], [1, 1, 0], [1, 0, 7], [1, 6, 11], [1, 0, 0], [1, -6, 17], [1, -6, 19], [1, 6, 23], [1, 6, 29], [1, 0, 31], [1, -6, 37], [1, -12, 41], [1, 8, 43], [1, 0, 47], [1, 12, 53], [1, 6, 59], [1, -10, 61], [1, 0, 67], [1, 12, 71], [1, -6, 73], [1, 8, 79], [1, 0, 83], [1, 0, 89], [1, 6, 97]], 'index': 78, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/5070/l', 'ModularForm/GL2/Q/holomorphic/5070/2/a/l/1/1', 'ModularForm/GL2/Q/holomorphic/5070/2/a/l'], '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': '2-5070-1.1-c1-0-78', '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': '2-5070-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.3627159157697095, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 131014251800624117, 'z1': {'__RealLiteral__': 0, 'data': '1.37238354395716185195209308099', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21314076
{'Lhash': '1739702823240640870785449489787', 'Lhash_array': ['1739702823240640870785449489787'], 'label': '2-5070-1.1-c1-0-78', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5070/2/a/l'}
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id: 24568743
{'Lhash': '1739702823240640870785449489787', 'Lhash_array': ['1739702823240640870785449489787'], 'label': '2-5070-1.1-c1-0-78', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5070/2/a/l/1/1'}
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id: 30982
{'Lhash': '131014251800624117', 'Lhash_array': ['131014251800624117'], 'label': '2-5070-1.1-c1-0-78', 'type': 'ECQ', 'url': 'EllipticCurve/Q/5070/l'}