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lfunc_lfunctions • Show schema
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{'Lhash': '2155414478846353891416934201401', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.587658166755635, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1]], [5, [1]], [11, [1, 1]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': '1.1.1.1', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[1, 0, 2], [1, 1], [1], [1, -1, 7], [1, 1], [1, -1, 13], [1, -6, 17], [1, 7, 19], [1, 6, 23], [1, 6, 29], [1, 7, 31], [1, 2, 37], [1, 6, 41], [1, -1, 43], [1, 0, 47], [1, -6, 53], [1, 0, 59], [1, -5, 61], [1, 5, 67], [1, 12, 71], [1, 14, 73], [1, 4, 79], [1, -6, 83], [1, -6, 89], [1, 17, 97], [1, 0, 101], [1, 8, 103], [1, -6, 107], [1, -11, 109], [1, -18, 113]], 'euler_factors_factorization': [[[[1, 0, 2], 1]], [[[1, 1], 1]], [1], [[[1, -1, 7], 1]], [[[1, 1], 1]], [[[1, -1, 13], 1]], [[[1, -6, 17], 1]], [[[1, 7, 19], 1]], [[[1, 6, 23], 1]], [[[1, 6, 29], 1]], [[[1, 7, 31], 1]], [[[1, 2, 37], 1]], [[[1, 6, 41], 1]], [[[1, -1, 43], 1]], [[[1, 0, 47], 1]], [[[1, -6, 53], 1]], [[[1, 0, 59], 1]], [[[1, -5, 61], 1]], [[[1, 5, 67], 1]], [[[1, 12, 71], 1]], [[[1, 14, 73], 1]], [[[1, 4, 79], 1]], [[[1, -6, 83], 1]], [[[1, -6, 89], 1]], [[[1, 17, 97], 1]], [[[1, 0, 101], 1]], [[[1, 8, 103], 1]], [[[1, -6, 107], 1]], [[[1, -11, 109], 1]], [[[1, -18, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-825-1.1-c1-0-19', '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/825/2/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-5.337746588653895e-121, 0.22575551146304482, 0.45259358287616425, 0.6795676914740405, 0.9021336627686852, 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-2.532708327273679, -2.5187368625773257, -1.748823435284377, -0.5334812687899814, 0.6787904129409553, 1.4705095413417282, 1.6107568103100487, 1.1387737049911701], 'positive_zeros': ['1.70032221690921013211384714861863', '3.55718547289049389773277815437995', '4.39119879142282475890989547542366', '5.41932401993915498989382893014877', '5.99232217815539757223706684674547', '7.35087717315634547606388680691182', '8.166540824143412625936193267718054', '8.914517223015984535585916849605376', '9.974328952037568305037681431369153'], 'prelabel': '2-825-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.566643365712431, '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': 735916545652299001, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70032221690921013211384714862', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.55718547289049389773277815438', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.39119879142282475890989547542', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.587658166755635, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, -2, 0, 0, 1, 0, 1, 0, -1, 2, 1, 0, 0, 4, 6, 0, -7, 0, -1, 0, -6, 0, 0, 0, -1, -2, -6, 0, -7, 0, 1, 0, 0, -2, -2, 0, -1, 0, -6, 0, 1, 2, 0, 0, 0, -4, -6, 0, -6, -2, 6, 0, 0, 0, 7, 0, 0, 0, 5, 0, 1, -8, 0, 0, -5, -12, 6, 0, -12, 0, -14, 0, 0, 14, -1, 0, -4, 0, 1, 0, 6, 2, 0, 0, 6, 0, 6, 0, 1, 12, 7, 0, 0, 0, -17, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, -1, 13], 'euler17': [1, -6, 17], 'euler19': [1, 7, 19], 'euler2': [1, 0, 2], 'euler23': [1, 6, 23], 'euler29': [1, 6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 7, 31], 'euler37': [1, 2, 37], 'euler41': [1, 6, 41], 'euler43': [1, -1, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, -6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -5, 61], 'euler67': [1, 5, 67], 'euler7': [1, -1, 7], 'euler71': [1, 12, 71], 'euler73': [1, 14, 73], 'euler79': [1, 4, 79], 'euler83': [1, -6, 83], 'euler89': [1, -6, 89], 'euler97': [1, 17, 97], 'euler_factors': [[1, 0, 2], [1, 1, 0], [1, 0, 0], [1, -1, 7], [1, 1, 0], [1, -1, 13], [1, -6, 17], [1, 7, 19], [1, 6, 23], [1, 6, 29], [1, 7, 31], [1, 2, 37], [1, 6, 41], [1, -1, 43], [1, 0, 47], [1, -6, 53], [1, 0, 59], [1, -5, 61], [1, 5, 67], [1, 12, 71], [1, 14, 73], [1, 4, 79], [1, -6, 83], [1, -6, 89], [1, 17, 97]], 'index': 19, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/825/b', 'ModularForm/GL2/Q/holomorphic/825/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/825/2/a/b'], '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': '2-825-1.1-c1-0-19', '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': '2-825-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.566643365712431, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 735916545652299001, 'z1': {'__RealLiteral__': 0, 'data': '1.70032221690921013211384714862', 'prec': 103}}
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lfunc_instances • Show schema
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id: 15456229
{'Lhash': '2155414478846353891416934201401', 'Lhash_array': ['2155414478846353891416934201401'], 'label': '2-825-1.1-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/2/a/b'}
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id: 24550682
{'Lhash': '2155414478846353891416934201401', 'Lhash_array': ['2155414478846353891416934201401'], 'label': '2-825-1.1-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/2/a/b/1/1'}
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id: 89918
{'Lhash': '735916545652299001', 'Lhash_array': ['735916545652299001'], 'label': '2-825-1.1-c1-0-19', 'type': 'ECQ', 'url': 'EllipticCurve/Q/825/b'}