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lfunc_lfunctions • Show schema
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{'Lhash': '2601818451004245389089509321139', 'a10': 8, 'a2': -2, 'a3': -3, 'a4': 2, 'a5': -4, 'a6': 6, 'a7': -4, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 40.54004910620407, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5077, [1, None]]], 'bad_primes': [5077], 'central_character': '5077.1', 'coefficient_field': '1.1.1.1', 'conductor': 5077, 'conductor_radical': 5077, 'degree': 2, 'euler_factors': [[1, 2, 2], [1, 3, 3], [1, 4, 5], [1, 4, 7], [1, 6, 11], [1, 4, 13], [1, 4, 17], [1, 7, 19], [1, 6, 23], [1, 6, 29], [1, 2, 31], [1, 0, 37], [1, 0, 41], [1, 8, 43], [1, 9, 47], [1, 9, 53], [1, 11, 59], [1, 2, 61], [1, 12, 67], [1, 8, 71], [1, 14, 73], [1, -9, 79], [1, 2, 83], [1, -11, 89], [1, -6, 97], [1, -4, 101], [1, 0, 103], [1, -12, 107], [1, -7, 109], [1, 5, 113]], 'euler_factors_factorization': [[[[1, 2, 2], 1]], [[[1, 3, 3], 1]], [[[1, 4, 5], 1]], [[[1, 4, 7], 1]], [[[1, 6, 11], 1]], [[[1, 4, 13], 1]], [[[1, 4, 17], 1]], [[[1, 7, 19], 1]], [[[1, 6, 23], 1]], [[[1, 6, 29], 1]], [[[1, 2, 31], 1]], [[[1, 0, 37], 1]], [[[1, 0, 41], 1]], [[[1, 8, 43], 1]], [[[1, 9, 47], 1]], [[[1, 9, 53], 1]], [[[1, 11, 59], 1]], [[[1, 2, 61], 1]], [[[1, 12, 67], 1]], [[[1, 8, 71], 1]], [[[1, 14, 73], 1]], [[[1, -9, 79], 1]], [[[1, 2, 83], 1]], [[[1, -11, 89], 1]], [[[1, -6, 97], 1]], [[[1, -4, 101], 1]], [[[1, 0, 103], 1]], [[[1, -12, 107], 1]], [[[1, -7, 109], 1]], [[[1, 5, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 410, 'label': '2-5077-1.1-c1-0-410', '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': 3, 'origin': 'ModularForm/GL2/Q/holomorphic/5077/2/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.5071365126069953e-61, 0.0001784126237692164, 0.001428178067205937, 0.004824757328073271, 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-0.38964107347107513, -0.098020042385026, 0.20978059214979738, 0.516380943055781, 0.8036324084168227, 1.053667493519831, 1.2499795179600144, 1.3784698917394167, 1.4283998089671794], 'positive_zeros': ['2.05247285847993976968922276314351', '3.26244355597875746635580364385534', '4.47055151331009795091782387950043', '4.75443151596340586415163559396894', '6.01192275298639519014642522248824', '6.62250461340770678139848771792466', '7.34281497953964814691434021056175'], 'prelabel': '2-5077-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.367106808135393, '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': 129556073554127214, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.05247285847993976968922276314', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.26244355597875746635580364386', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.47055151331009795091782387950', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 40.54004910620407, 'bad_primes': [5077], 'central_character': '1.1', 'conductor': 5077, 'conductor_radical': 5077, 'degree': 2, 'dirichlet_coefficients': [1, -2, -3, 2, -4, 6, -4, 0, 6, 8, -6, -6, -4, 8, 12, -4, -4, -12, -7, -8, 12, 12, -6, 0, 11, 8, -9, -8, -6, -24, -2, 8, 18, 8, 16, 12, 0, 14, 12, 0, 0, -24, -8, -12, -24, 12, -9, 12, 9, -22, 12, -8, -9, 18, 24, 0, 21, 12, -11, 24, -2, 4, -24, -8, 16, -36, -12, -8, 18, -32, -8, 0, -14, 0, -33, -14, 24, -24, 9, 16, 9, 0, -2, 24, 16, 16, 18, 0, 11, 48, 16, -12, 6, 18, 28, -24, 6, -18, -36, 22], 'euler11': [1, 6, 11], 'euler13': [1, 4, 13], 'euler17': [1, 4, 17], 'euler19': [1, 7, 19], 'euler2': [1, 2, 2], 'euler23': [1, 6, 23], 'euler29': [1, 6, 29], 'euler3': [1, 3, 3], 'euler31': [1, 2, 31], 'euler37': [1, 0, 37], 'euler41': [1, 0, 41], 'euler43': [1, 8, 43], 'euler47': [1, 9, 47], 'euler5': [1, 4, 5], 'euler53': [1, 9, 53], 'euler59': [1, 11, 59], 'euler61': [1, 2, 61], 'euler67': [1, 12, 67], 'euler7': [1, 4, 7], 'euler71': [1, 8, 71], 'euler73': [1, 14, 73], 'euler79': [1, -9, 79], 'euler83': [1, 2, 83], 'euler89': [1, -11, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 2, 2], [1, 3, 3], [1, 4, 5], [1, 4, 7], [1, 6, 11], [1, 4, 13], [1, 4, 17], [1, 7, 19], [1, 6, 23], [1, 6, 29], [1, 2, 31], [1, 0, 37], [1, 0, 41], [1, 8, 43], [1, 9, 47], [1, 9, 53], [1, 11, 59], [1, 2, 61], [1, 12, 67], [1, 8, 71], [1, 14, 73], [1, -9, 79], [1, 2, 83], [1, -11, 89], [1, -6, 97]], 'index': 410, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/5077/a', 'ModularForm/GL2/Q/holomorphic/5077/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/5077/2/a/a'], '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': '2-5077-1.1-c1-0-410', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 3, 'prelabel': '2-5077-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.367106808135393, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 129556073554127214, 'z1': {'__RealLiteral__': 0, 'data': '2.05247285847993976968922276314', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21374097
{'Lhash': '2601818451004245389089509321139', 'Lhash_array': ['2601818451004245389089509321139'], 'label': '2-5077-1.1-c1-0-410', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5077/2/a/a'}
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id: 24568785
{'Lhash': '2601818451004245389089509321139', 'Lhash_array': ['2601818451004245389089509321139'], 'label': '2-5077-1.1-c1-0-410', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5077/2/a/a/1/1'}
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id: 101585
{'Lhash': '129556073554127214', 'Lhash_array': ['129556073554127214'], 'label': '2-5077-1.1-c1-0-410', 'type': 'ECQ', 'url': 'EllipticCurve/Q/5077/a'}