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lfunc_lfunctions • Show schema
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{'A10': 4, 'A2': -2, 'A3': 0, 'A4': 2, 'A5': -2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -1, 'Lhash': '1851591068201092288371585969694', 'a10': [1.264911064067352, 0], 'a2': [-1.4142135623730951, 0], 'a3': [0.0, 0], 'a4': [1.0, 0], 'a5': [-0.894427190999916, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 76.03253854158619, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 2]], [3, [1, 0, 1]], [7, [1, 0, -1]], [13, [1, -2, 1]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '1192464.1', 'coefficient_field': '1.1.1.1', 'conductor': 1192464, 'conductor_radical': 546, 'degree': 4, 'euler_factors': [[1, 2, 2], [1, 0, 1], [1, 2, 7, 10, 25], [1, 0, -1], [1, 0, -10, 0, 121], [1, -2, 1], [1, 8, 46, 136, 289], [1, 0, 25, 0, 361], [1, 0, 5, 0, 529], [1, 10, 67, 290, 841], [1, 0, -7, 0, 961], [1, 8, 54, 296, 1369], [1, 4, 70, 164, 1681], [1, 0, -67, 0, 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-1.3127573405464004, -0.6592242955217462, 0.1975719397501564, 1.1507829319115572, 2.0633235141047144, 2.7851042813475155, 3.1738058734191665], 'positive_zeros': ['1.46064780616025386946068472796355', '1.90904621969199088972348353023539', '2.59576257942983043796575068903974', '3.37609454946844954285086937314904', '3.87042173203129843101493213742047', '4.32524747834379556749989773299695', '4.82256444477867172068844542845934', '5.39727176441123470831132457411865', '6.08438128655268018804505437264215', '6.37880564536158778802948162237330', '7.03092845601429042649054713264475', '7.23966685543565994596268384950945', '7.69519394202618448007204550633138'], 'prelabel': '4-1092e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.9529077027099615, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 2162089271061822212, 'z1': {'__RealLiteral__': 0, 'data': '1.46064780616025386946068472796355', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.90904621969199088972348353023539', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.59576257942983043796575068903974', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 76.03253854158619, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 1192464, 'conductor_radical': 546, 'degree': 4, 'dirichlet_coefficients': [1, -2, 0, 2, -2, 0, 0, 0, -1, 4, 0, 0, 2, 0, 0, -4, -8, 2, 0, -4, 0, 0, 0, 0, -3, -4, 0, 0, -10, 0, 0, 8, 0, 16, 0, -2, -8, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 1, 6, 0, 4, -10, 0, 0, 0, 0, 20, 0, 0, -12, 0, 0, -8, -4, 0, 0, -16, 0, 0, 0, 0, -6, 16, 0, 0, 0, 0, 0, 8, 1, 8, 0, 0, 16, 0, 0, 0, -6, -4, 0, 0, 0, 0, 0, 0, -14, -2, 0, -6], 'euler11': [1, 0, -10, 0, 121], 'euler13': [1, -2, 1, 0, 0], 'euler17': [1, 8, 46, 136, 289], 'euler19': [1, 0, 25, 0, 361], 'euler2': [1, 2, 2, 0, 0], 'euler23': [1, 0, 5, 0, 529], 'euler29': [1, 10, 67, 290, 841], 'euler3': [1, 0, 1, 0, 0], 'euler31': [1, 0, -7, 0, 961], 'euler37': [1, 8, 54, 296, 1369], 'euler41': [1, 4, 70, 164, 1681], 'euler43': [1, 0, -67, 0, 1849], 'euler47': [1, 0, 73, 0, 2209], 'euler5': [1, 2, 7, 10, 25], 'euler53': [1, 10, 67, 530, 2809], 'euler59': [1, 0, -26, 0, 3481], 'euler61': [1, 12, 142, 732, 3721], 'euler67': [1, 0, 34, 0, 4489], 'euler7': [1, 0, -1, 0, 0], 'euler71': [1, 0, -110, 0, 5041], 'euler73': [1, 6, 151, 438, 5329], 'euler79': [1, 0, -51, 0, 6241], 'euler83': [1, 0, -151, 0, 6889], 'euler89': [1, 6, 87, 534, 7921], 'euler97': [1, 14, 239, 1358, 9409], 'euler_factors': [[1, 2, 2, 0, 0], [1, 0, 1, 0, 0], [1, 2, 7, 10, 25], [1, 0, -1, 0, 0], [1, 0, -10, 0, 121], [1, -2, 1, 0, 0], [1, 8, 46, 136, 289], [1, 0, 25, 0, 361], [1, 0, 5, 0, 529], [1, 10, 67, 290, 841], [1, 0, -7, 0, 961], [1, 8, 54, 296, 1369], [1, 4, 70, 164, 1681], [1, 0, -67, 0, 1849], [1, 0, 73, 0, 2209], [1, 10, 67, 530, 2809], [1, 0, -26, 0, 3481], [1, 12, 142, 732, 3721], [1, 0, 34, 0, 4489], [1, 0, -110, 0, 5041], [1, 6, 151, 438, 5329], [1, 0, -51, 0, 6241], [1, 0, -151, 0, 6889], [1, 6, 87, 534, 7921], [1, 14, 239, 1358, 9409]], 'index': 46, 'instance_types': ['ECNF', 'BMF', 'ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.4.1/74529.2/c', 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/74529.2/c', 'EllipticCurve/2.0.4.1/74529.2/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/74529.2/a'], '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': '4-1092e2-1.1-c1e2-0-46', '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': 2, 'prelabel': '4-1092e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.9529077027099615, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2162089271061822212, 'z1': {'__RealLiteral__': 0, 'data': '1.46064780616025386946068472796355', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9742048
{'Lhash': '1851591068201092288371585969694', 'Lhash_array': ['1851591068201092288371585969694'], 'label': '4-1092e2-1.1-c1e2-0-46', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/74529.2/a'}
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id: 9741703
{'Lhash': '1851591068201092288371585969694', 'Lhash_array': ['1851591068201092288371585969694'], 'label': '4-1092e2-1.1-c1e2-0-46', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/74529.2/a'}
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id: 9741577
{'Lhash': '1851591068201092288371585969694', 'Lhash_array': ['1851591068201092288371585969694'], 'label': '4-1092e2-1.1-c1e2-0-46', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/74529.2/c'}
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id: 9741454
{'Lhash': '1851591068201092288371585969694', 'Lhash_array': ['1851591068201092288371585969694'], 'label': '4-1092e2-1.1-c1e2-0-46', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/74529.2/c'}