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lfunc_lfunctions • Show schema
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{'Lhash': '3216896290736187068676822586367', 'a10': -2, 'a2': 1, 'a3': 0, 'a4': 1, 'a5': -2, 'a6': 0, 'a7': -3, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.318036774617276, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [37, [1, -1]]], 'bad_primes': [2, 3, 37], 'central_character': '666.1', 'coefficient_field': '1.1.1.1', 'conductor': 666, 'conductor_radical': 222, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, 2, 5], [1, 3, 7], [1, 5, 11], [1, 3, 13], [1, 3, 17], [1, -5, 19], [1, 3, 23], [1, 0, 29], [1, -4, 31], [1, -1], [1, 6, 41], [1, -4, 43], [1, -4, 47], [1, -3, 53], [1, 14, 59], [1, 14, 61], [1, -12, 67], [1, 12, 71], [1, -13, 73], [1, -6, 79], [1, -7, 83], [1, -1, 89], [1, 12, 97], [1, 10, 101], [1, 2, 103], [1, -13, 107], [1, 13, 109], [1, 2, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [1], [[[1, 2, 5], 1]], [[[1, 3, 7], 1]], [[[1, 5, 11], 1]], [[[1, 3, 13], 1]], [[[1, 3, 17], 1]], [[[1, -5, 19], 1]], [[[1, 3, 23], 1]], [[[1, 0, 29], 1]], [[[1, -4, 31], 1]], [[[1, -1], 1]], [[[1, 6, 41], 1]], [[[1, -4, 43], 1]], [[[1, -4, 47], 1]], [[[1, -3, 53], 1]], [[[1, 14, 59], 1]], [[[1, 14, 61], 1]], [[[1, -12, 67], 1]], [[[1, 12, 71], 1]], [[[1, -13, 73], 1]], [[[1, -6, 79], 1]], [[[1, -7, 83], 1]], [[[1, -1, 89], 1]], [[[1, 12, 97], 1]], [[[1, 10, 101], 1]], [[[1, 2, 103], 1]], [[[1, -13, 107], 1]], [[[1, 13, 109], 1]], [[[1, 2, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 14, 'label': '2-666-1.1-c1-0-14', '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/666/2/a/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [6.086105956378342e-120, 0.32752249632315894, 0.6628070552476608, 1.0113869092769725, 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0.18212444019502597, 0.7594009497557164, 1.005733271974734, 0.8464189407400124, 0.3870274373233697, -0.1409578405314276, -0.48377116963023636, -0.47711401649129337, -0.12159989456294422], 'positive_zeros': ['2.53768371991226370428359299532016', '3.36955088619499482554151547955088', '4.48939808970851696949242760762177', '5.42150318427562977205146477273078', '6.47610998714696152245554562179003', '7.46068180666953821854598915656765', '8.003115280121563730110945330919599', '9.388240731285929266205934536592502', '10.19101722664861990638377585527507'], 'prelabel': '2-666-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.3060868965885213, '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': 1928718393288442923, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.53768371991226370428359299532', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.36955088619499482554151547955', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.48939808970851696949242760762', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.318036774617276, 'bad_primes': [2, 3, 37], 'central_character': '1.1', 'conductor': 666, 'conductor_radical': 222, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, -2, 0, -3, 1, 0, -2, -5, 0, -3, -3, 0, 1, -3, 0, 5, -2, 0, -5, -3, 0, -1, -3, 0, -3, 0, 0, 4, 1, 0, -3, 6, 0, 1, 5, 0, -2, -6, 0, 4, -5, 0, -3, 4, 0, 2, -1, 0, -3, 3, 0, 10, -3, 0, 0, -14, 0, -14, 4, 0, 1, 6, 0, 12, -3, 0, 6, -12, 0, 13, 1, 0, 5, 15, 0, 6, -2, 0, -6, 7, 0, 6, 4, 0, -5, 1, 0, 9, -3, 0, 4, -10, 0, -12, 2, 0, -1], 'euler11': [1, 5, 11], 'euler13': [1, 3, 13], 'euler17': [1, 3, 17], 'euler19': [1, -5, 19], 'euler2': [1, -1, 0], 'euler23': [1, 3, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -1, 0], 'euler41': [1, 6, 41], 'euler43': [1, -4, 43], 'euler47': [1, -4, 47], 'euler5': [1, 2, 5], 'euler53': [1, -3, 53], 'euler59': [1, 14, 59], 'euler61': [1, 14, 61], 'euler67': [1, -12, 67], 'euler7': [1, 3, 7], 'euler71': [1, 12, 71], 'euler73': [1, -13, 73], 'euler79': [1, -6, 79], 'euler83': [1, -7, 83], 'euler89': [1, -1, 89], 'euler97': [1, 12, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, 2, 5], [1, 3, 7], [1, 5, 11], [1, 3, 13], [1, 3, 17], [1, -5, 19], [1, 3, 23], [1, 0, 29], [1, -4, 31], [1, -1, 0], [1, 6, 41], [1, -4, 43], [1, -4, 47], [1, -3, 53], [1, 14, 59], [1, 14, 61], [1, -12, 67], [1, 12, 71], [1, -13, 73], [1, -6, 79], [1, -7, 83], [1, -1, 89], [1, 12, 97]], 'index': 14, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/666/e', 'ModularForm/GL2/Q/holomorphic/666/2/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/666/2/a/e'], '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': '2-666-1.1-c1-0-14', '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': '2-666-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.3060868965885213, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1928718393288442923, 'z1': {'__RealLiteral__': 0, 'data': '2.53768371991226370428359299532', 'prec': 103}}
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lfunc_instances • Show schema
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id: 12843165
{'Lhash': '3216896290736187068676822586367', 'Lhash_array': ['3216896290736187068676822586367'], 'label': '2-666-1.1-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/666/2/a/e'}
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id: 24550121
{'Lhash': '3216896290736187068676822586367', 'Lhash_array': ['3216896290736187068676822586367'], 'label': '2-666-1.1-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/666/2/a/e/1/1'}
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id: 89514
{'Lhash': '1928718393288442923', 'Lhash_array': ['1928718393288442923'], 'label': '2-666-1.1-c1-0-14', 'type': 'ECQ', 'url': 'EllipticCurve/Q/666/e'}