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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1336995866635118667760834154101', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 169.82222350744817, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, -1]], [17, [1, 0, -1]]], 'bad_primes': [2, 3, 17], 'central_character': '2663424.1', 'coefficient_field': '1.1.1.1', 'conductor': 2663424, 'conductor_radical': 102, 'degree': 4, 'euler_factors': [[1], [1, 0, -1], [1, 0, -1, 0, 25], [1, 0, 2, 0, 49], [1, 0, 21, 0, 121], [1, 0, -15, 0, 169], [1, 0, -1], [1, 2, 23, 38, 361], [1, 0, 3, 0, 529], [1, 0, -22, 0, 841], [1, 0, -26, 0, 961], [1, 0, 6, 0, 1369], [1, 16, 137, 656, 1681], [1, -22, 207, -946, 1849], [1, 0, 42, 0, 2209], [1, 0, -58, 0, 2809], [1, -16, 178, -944, 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-1.6179504557914302, -2.4383146721561397, -3.1553465270076617, -3.6810720169619575], 'positive_zeros': ['1.05470376963053088734525219746873', '1.66410651305856432119264520711461', '2.37093323908239350072883358473276', '2.82255866418502889752956409954575', '3.39628535070214125817038623917196', '4.06675786273926021118743637774708', '4.23982348710988972447801603143831', '4.79694676992625594175431971012620', '5.41747783371230540887411391057147', '5.59925972547563226148263711683413', '6.25657820354822724690977541287945', '6.51176431234695390752480750643137', '7.12308454345833641207141807395070', '7.32669361309404544253638892774907'], 'prelabel': '4-1632e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.609928754127007, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 2222863075062895893, 'z1': {'__RealLiteral__': 0, 'data': '1.05470376963053088734525219746873', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.66410651305856432119264520711461', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.37093323908239350072883358473276', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 169.82222350744817, 'bad_primes': [2, 3, 17], 'central_character': '1.1', 'conductor': 2663424, 'conductor_radical': 102, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 22, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 1, 0, -12, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0], 'euler11': [1, 0, 21, 0, 121], 'euler13': [1, 0, -15, 0, 169], 'euler17': [1, 0, -1, 0, 0], 'euler19': [1, 2, 23, 38, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 3, 0, 529], 'euler29': [1, 0, -22, 0, 841], 'euler3': [1, 0, -1, 0, 0], 'euler31': [1, 0, -26, 0, 961], 'euler37': [1, 0, 6, 0, 1369], 'euler41': [1, 16, 137, 656, 1681], 'euler43': [1, -22, 207, -946, 1849], 'euler47': [1, 0, 42, 0, 2209], 'euler5': [1, 0, -1, 0, 25], 'euler53': [1, 0, -58, 0, 2809], 'euler59': [1, -16, 178, -944, 3481], 'euler61': [1, 0, 86, 0, 3721], 'euler67': [1, 16, 182, 1072, 4489], 'euler7': [1, 0, 2, 0, 49], 'euler71': [1, 0, -110, 0, 5041], 'euler73': [1, 8, 126, 584, 5329], 'euler79': [1, 0, -34, 0, 6241], 'euler83': [1, 12, 186, 996, 6889], 'euler89': [1, 12, 178, 1068, 7921], 'euler97': [1, 8, 210, 776, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -1, 0, 0], [1, 0, -1, 0, 25], [1, 0, 2, 0, 49], [1, 0, 21, 0, 121], [1, 0, -15, 0, 169], [1, 0, -1, 0, 0], [1, 2, 23, 38, 361], [1, 0, 3, 0, 529], [1, 0, -22, 0, 841], [1, 0, -26, 0, 961], [1, 0, 6, 0, 1369], [1, 16, 137, 656, 1681], [1, -22, 207, -946, 1849], [1, 0, 42, 0, 2209], [1, 0, -58, 0, 2809], [1, -16, 178, -944, 3481], [1, 0, 86, 0, 3721], [1, 16, 182, 1072, 4489], [1, 0, -110, 0, 5041], [1, 8, 126, 584, 5329], [1, 0, -34, 0, 6241], [1, 12, 186, 996, 6889], [1, 12, 178, 1068, 7921], [1, 8, 210, 776, 9409]], 'index': 41, 'instance_types': ['BMF', 'BMF', 'ECNF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/41616.5/k', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/41616.5/o', 'EllipticCurve/2.0.8.1/41616.5/k', 'EllipticCurve/2.0.8.1/41616.5/o'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, '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': '4-1632e2-1.1-c1e2-0-41', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'prelabel': '4-1632e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.609928754127007, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2222863075062895893, 'z1': {'__RealLiteral__': 0, 'data': '1.05470376963053088734525219746873', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9866263
{'Lhash': '1336995866635118667760834154101', 'Lhash_array': ['1336995866635118667760834154101'], 'label': '4-1632e2-1.1-c1e2-0-41', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/41616.5/o'}
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id: 9866261
{'Lhash': '1336995866635118667760834154101', 'Lhash_array': ['1336995866635118667760834154101'], 'label': '4-1632e2-1.1-c1e2-0-41', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/41616.5/k'}
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id: 9865820
{'Lhash': '1336995866635118667760834154101', 'Lhash_array': ['1336995866635118667760834154101'], 'label': '4-1632e2-1.1-c1e2-0-41', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/41616.5/o'}
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id: 9865818
{'Lhash': '1336995866635118667760834154101', 'Lhash_array': ['1336995866635118667760834154101'], 'label': '4-1632e2-1.1-c1e2-0-41', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/41616.5/k'}