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lfunc_lfunctions • Show schema
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{'Lhash': '2091938956743106948137633529946', 'a10': 0, 'a2': -1, 'a3': -2, 'a4': -1, 'a5': 0, 'a6': 2, 'a7': 1, 'a8': 3, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5373728095427226, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[443, [1, 1]]], 'bad_primes': [443], 'central_character': '443.1', 'coefficient_field': '1.1.1.1', 'conductor': 443, 'conductor_radical': 443, 'degree': 2, 'euler_factors': [[1, 1, 2], [1, 2, 3], [1, 0, 5], [1, -1, 7], [1, -3, 11], [1, -3, 13], [1, 5, 17], [1, 7, 19], [1, 3, 23], [1, 0, 29], [1, -7, 31], [1, 3, 37], [1, 6, 41], [1, 8, 43], [1, 2, 47], [1, -4, 53], [1, -6, 59], [1, 13, 61], [1, 8, 67], [1, -16, 71], [1, 8, 73], [1, 2, 79], [1, 7, 83], [1, 1, 89], [1, 10, 97], [1, -4, 101], [1, -6, 103], [1, 20, 107], [1, -2, 109], [1, -9, 113]], 'euler_factors_factorization': [[[[1, 1, 2], 1]], [[[1, 2, 3], 1]], [[[1, 0, 5], 1]], [[[1, -1, 7], 1]], [[[1, -3, 11], 1]], [[[1, -3, 13], 1]], [[[1, 5, 17], 1]], [[[1, 7, 19], 1]], [[[1, 3, 23], 1]], [[[1, 0, 29], 1]], [[[1, -7, 31], 1]], [[[1, 3, 37], 1]], [[[1, 6, 41], 1]], [[[1, 8, 43], 1]], [[[1, 2, 47], 1]], [[[1, -4, 53], 1]], [[[1, -6, 59], 1]], [[[1, 13, 61], 1]], [[[1, 8, 67], 1]], [[[1, -16, 71], 1]], [[[1, 8, 73], 1]], [[[1, 2, 79], 1]], [[[1, 7, 83], 1]], [[[1, 1, 89], 1]], [[[1, 10, 97], 1]], [[[1, -4, 101], 1]], [[[1, -6, 103], 1]], [[[1, 20, 107], 1]], [[[1, -2, 109], 1]], [[[1, -9, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-443-1.1-c1-0-16', '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/443/2/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-2.3427820064017076e-120, 0.12788928238353958, 0.25693650399230383, 0.38713345679892386, 0.5163612826944624, 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2.4807171556140934, 4.25210209372073, 5.218627763944451, 5.095935434311232, 3.90111787065726, 1.9546918350562683, -0.20741439307666504, -1.9868652187561902, -2.8956162333037057, -2.696459783832927], 'positive_zeros': ['1.65024885908346640526056366422649', '4.03480921686296141905054645464888', '4.80628065334994799877239926768816', '6.09630380700586307112961369058031', '6.74959768754122577112491189066627', '8.285292308235240080848380600808473', '8.701661060815549683587536680742682', '9.881781756372744287873890056581008', '10.69819795490158406782422490461942'], 'prelabel': '2-443-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.880790474652273, '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': 1339622243522997787, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.65024885908346640526056366423', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.03480921686296141905054645465', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.80628065334994799877239926769', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.5373728095427226, 'bad_primes': [443], 'central_character': '1.1', 'conductor': 443, 'conductor_radical': 443, 'degree': 2, 'dirichlet_coefficients': [1, -1, -2, -1, 0, 2, 1, 3, 1, 0, 3, 2, 3, -1, 0, -1, -5, -1, -7, 0, -2, -3, -3, -6, -5, -3, 4, -1, 0, 0, 7, -5, -6, 5, 0, -1, -3, 7, -6, 0, -6, 2, -8, -3, 0, 3, -2, 2, -6, 5, 10, -3, 4, -4, 0, 3, 14, 0, 6, 0, -13, -7, 1, 7, 0, 6, -8, 5, 6, 0, 16, 3, -8, 3, 10, 7, 3, 6, -2, 0, -11, 6, -7, 2, 0, 8, 0, 9, -1, 0, 3, 3, -14, 2, 0, 10, -10, 6, 3, 5], 'euler11': [1, -3, 11], 'euler13': [1, -3, 13], 'euler17': [1, 5, 17], 'euler19': [1, 7, 19], 'euler2': [1, 1, 2], 'euler23': [1, 3, 23], 'euler29': [1, 0, 29], 'euler3': [1, 2, 3], 'euler31': [1, -7, 31], 'euler37': [1, 3, 37], 'euler41': [1, 6, 41], 'euler43': [1, 8, 43], 'euler47': [1, 2, 47], 'euler5': [1, 0, 5], 'euler53': [1, -4, 53], 'euler59': [1, -6, 59], 'euler61': [1, 13, 61], 'euler67': [1, 8, 67], 'euler7': [1, -1, 7], 'euler71': [1, -16, 71], 'euler73': [1, 8, 73], 'euler79': [1, 2, 79], 'euler83': [1, 7, 83], 'euler89': [1, 1, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 1, 2], [1, 2, 3], [1, 0, 5], [1, -1, 7], [1, -3, 11], [1, -3, 13], [1, 5, 17], [1, 7, 19], [1, 3, 23], [1, 0, 29], [1, -7, 31], [1, 3, 37], [1, 6, 41], [1, 8, 43], [1, 2, 47], [1, -4, 53], [1, -6, 59], [1, 13, 61], [1, 8, 67], [1, -16, 71], [1, 8, 73], [1, 2, 79], [1, 7, 83], [1, 1, 89], [1, 10, 97]], 'index': 16, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/443/a', 'ModularForm/GL2/Q/holomorphic/443/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/443/2/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': '2-443-1.1-c1-0-16', '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': '2-443-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.880790474652273, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1339622243522997787, 'z1': {'__RealLiteral__': 0, 'data': '1.65024885908346640526056366423', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10799080
{'Lhash': '2091938956743106948137633529946', 'Lhash_array': ['2091938956743106948137633529946'], 'label': '2-443-1.1-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/443/2/a/a'}
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id: 24549368
{'Lhash': '2091938956743106948137633529946', 'Lhash_array': ['2091938956743106948137633529946'], 'label': '2-443-1.1-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/443/2/a/a/1/1'}
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id: 42142
{'Lhash': '1339622243522997787', 'Lhash_array': ['1339622243522997787'], 'label': '2-443-1.1-c1-0-16', 'type': 'ECQ', 'url': 'EllipticCurve/Q/443/a'}