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lfunc_lfunctions • Show schema
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{'Lhash': '942528312225550185495454915095', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': -3, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 34.878655602895286, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [7, [1, 1]], [13, [1, 1]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '4368.1', 'coefficient_field': '1.1.1.1', 'conductor': 4368, 'conductor_radical': 546, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 3, 5], [1, 1], [1, -5, 11], [1, 1], [1, -3, 17], [1, -1, 19], [1, 1, 23], [1, 5, 29], [1, -8, 31], [1, -1, 37], [1, 12, 41], [1, 11, 43], [1, 8, 47], [1, -10, 53], [1, -8, 59], [1, -13, 61], [1, 2, 67], [1, 8, 71], [1, -11, 73], [1, 2, 79], [1, -18, 83], [1, -18, 89], [1, -10, 97], [1, 16, 101], [1, 5, 103], [1, -10, 107], [1, -3, 109], [1, -18, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, 3, 5], 1]], [[[1, 1], 1]], [[[1, -5, 11], 1]], [[[1, 1], 1]], [[[1, -3, 17], 1]], [[[1, -1, 19], 1]], [[[1, 1, 23], 1]], [[[1, 5, 29], 1]], [[[1, -8, 31], 1]], [[[1, -1, 37], 1]], [[[1, 12, 41], 1]], [[[1, 11, 43], 1]], [[[1, 8, 47], 1]], [[[1, -10, 53], 1]], [[[1, -8, 59], 1]], [[[1, -13, 61], 1]], [[[1, 2, 67], 1]], [[[1, 8, 71], 1]], [[[1, -11, 73], 1]], [[[1, 2, 79], 1]], [[[1, -18, 83], 1]], [[[1, -18, 89], 1]], [[[1, -10, 97], 1]], [[[1, 16, 101], 1]], [[[1, 5, 103], 1]], [[[1, -10, 107], 1]], [[[1, -3, 109], 1]], [[[1, -18, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 14, 'label': '2-4368-1.1-c1-0-14', 'leading_term': '1.802301981565069515849899926461900000000000000000000000000000000000000000000000000000000000', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/4368/2/a/n', 'plot_delta': {'__RealLiteral__': 0, 'data': 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2.13582063580644, 2.625950176519836, 3.088369219310941, 3.4945478742521527, 3.8180719752939667, 4.036362141981854, 4.132183775209441, 4.094851876189174, 3.9210522230018547, 3.6152231443280622, 3.1894685585302303, 2.6630015110233134, 2.0611464011100775, 1.4139556489720158], 'positive_zeros': ['0.74352373757867996738950068105401', '1.94123203494820510905055023907211', '3.33997612023921190589165173634530', '3.57932121815633107056850798705091', '4.39584665083835902625985252821953', '5.27675513043368811875653608734198', '6.50978895972534039318822147149039', '6.91299796740446502898825630750933', '7.75730073720067756782923916384374', '8.325893562122173473466064733160908'], 'prelabel': '2-4368-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.905815405419923, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1206658588388163161, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74352373757867996738950068105', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.94123203494820510905055023907', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33997612023921190589165173635', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 34.878655602895286, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 4368, 'conductor_radical': 546, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -3, 0, -1, 0, 1, 0, 5, 0, -1, 0, -3, 0, 3, 0, 1, 0, -1, 0, -1, 0, 4, 0, 1, 0, -5, 0, 8, 0, 5, 0, 3, 0, 1, 0, -1, 0, -12, 0, -11, 0, -3, 0, -8, 0, 1, 0, 3, 0, 10, 0, -15, 0, 1, 0, 8, 0, 13, 0, -1, 0, 3, 0, -2, 0, -1, 0, -8, 0, 11, 0, 4, 0, -5, 0, -2, 0, 1, 0, 18, 0, -9, 0, -5, 0, 18, 0, 1, 0, 8, 0, -3, 0, 10, 0, 5, 0], 'euler11': [1, -5, 11], 'euler13': [1, 1, 0], 'euler17': [1, -3, 17], 'euler19': [1, -1, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 23], 'euler29': [1, 5, 29], 'euler3': [1, -1, 0], 'euler31': [1, -8, 31], 'euler37': [1, -1, 37], 'euler41': [1, 12, 41], 'euler43': [1, 11, 43], 'euler47': [1, 8, 47], 'euler5': [1, 3, 5], 'euler53': [1, -10, 53], 'euler59': [1, -8, 59], 'euler61': [1, -13, 61], 'euler67': [1, 2, 67], 'euler7': [1, 1, 0], 'euler71': [1, 8, 71], 'euler73': [1, -11, 73], 'euler79': [1, 2, 79], 'euler83': [1, -18, 83], 'euler89': [1, -18, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 3, 5], [1, 1, 0], [1, -5, 11], [1, 1, 0], [1, -3, 17], [1, -1, 19], [1, 1, 23], [1, 5, 29], [1, -8, 31], [1, -1, 37], [1, 12, 41], [1, 11, 43], [1, 8, 47], [1, -10, 53], [1, -8, 59], [1, -13, 61], [1, 2, 67], [1, 8, 71], [1, -11, 73], [1, 2, 79], [1, -18, 83], [1, -18, 89], [1, -10, 97]], 'index': 14, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/4368/n', 'ModularForm/GL2/Q/holomorphic/4368/2/a/n/1/1', 'ModularForm/GL2/Q/holomorphic/4368/2/a/n'], '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': '2-4368-1.1-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': 0, 'prelabel': '2-4368-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.905815405419923, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1206658588388163161, 'z1': {'__RealLiteral__': 0, 'data': '0.74352373757867996738950068105', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20414239
{'Lhash': '942528312225550185495454915095', 'Lhash_array': ['942528312225550185495454915095'], 'label': '2-4368-1.1-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4368/2/a/n'}
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id: 24565653
{'Lhash': '942528312225550185495454915095', 'Lhash_array': ['942528312225550185495454915095'], 'label': '2-4368-1.1-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4368/2/a/n/1/1'}
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id: 95461
{'Lhash': '1206658588388163161', 'Lhash_array': ['1206658588388163161'], 'label': '2-4368-1.1-c1-0-14', 'type': 'ECQ', 'url': 'EllipticCurve/Q/4368/n'}