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lfunc_lfunctions • Show schema
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{'Lhash': '1421033443149772331760848738875', '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': 1, 'label': '2-666-1.1-c1-0-1', '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/666/2/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.223119248779907, 1.2140783013483545, 1.1852562998312812, 1.131963173020306, 1.0476186605102598, 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3.6480950865308417, 0.8520909947016414, -2.170678970637602, -4.711555674666288, -6.1909698829141435, -6.327982413869237, -5.216991911155849, -3.2867669132188113, -1.155906353732036], 'positive_zeros': ['1.12099772831246061899779950886548', '2.59442247256705920291581006864463', '3.69526832182271691380022426077112', '5.29912923560305098381281180293784', '6.29485884015171456248050146449052', '6.87960233611251053044806376508428', '7.913878554875197130364198555005743', '9.315757253980273759687218979884396', '9.479645883044483591577807946943954', '10.11202593962156360987559406213463'], 'prelabel': '2-666-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.3060868965885213, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1724516871389907212, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.12099772831246061899779950887', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.59442247256705920291581006864', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.69526832182271691380022426077', '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': 1, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/666/c', 'ModularForm/GL2/Q/holomorphic/666/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/666/2/a/c'], '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-c1-0-1', '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': '2-666-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.3060868965885213, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1724516871389907212, 'z1': {'__RealLiteral__': 0, 'data': '1.12099772831246061899779950887', 'prec': 103}}
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lfunc_instances • Show schema
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id: 12843360
{'Lhash': '1421033443149772331760848738875', 'Lhash_array': ['1421033443149772331760848738875'], 'label': '2-666-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/666/2/a/c'}
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id: 24550119
{'Lhash': '1421033443149772331760848738875', 'Lhash_array': ['1421033443149772331760848738875'], 'label': '2-666-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/666/2/a/c/1/1'}
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id: 23234
{'Lhash': '1724516871389907212', 'Lhash_array': ['1724516871389907212'], 'label': '2-666-1.1-c1-0-1', 'type': 'ECQ', 'url': 'EllipticCurve/Q/666/c'}