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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': -1, 'A9': 2, 'Lhash': '1431711523848431133622859233013', 'a10': [0.0, 0], 'a2': [-0.7071067811865476, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [-0.3535533905932738, 0], 'a9': [0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.358641993159002, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [17, [1, -6, 17]]], 'bad_primes': [2, 17], 'central_character': '36992.1', 'coefficient_field': '1.1.1.1', 'conductor': 36992, 'conductor_radical': 34, 'degree': 4, 'euler_factors': [[1, 1], [1, 0, -2, 0, 9], [1, 0, 2, 0, 25], [1, 0, -14, 0, 49], [1, 0, 14, 0, 121], [1, 0, 22, 0, 169], [1, -6, 17], [1, 0, 22, 0, 361], [1, 0, -14, 0, 529], [1, 0, 50, 0, 841], [1, 0, -62, 0, 961], [1, 0, 2, 0, 1369], [1, 0, -50, 0, 1681], [1, 0, 70, 0, 1849], [1, 0, 94, 0, 2209], [1, 0, 70, 0, 2809], [1, 0, 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-3.9489917323764745, -3.5639942599667997, -2.866701155715336], 'positive_zeros': ['1.12942124871842761561442350611537', '2.20924692317133984874547287655693', '3.19825512904115960807108105792761', '3.90867162313150085392849000019507', '4.68351373799807119232126686211089', '5.57701141450097199376705821999342', '5.89942135419593380940820484985088', '6.79518706283797008668965856547124', '7.21242822907521813396765907095237', '7.75591260690702797156496136088023', '8.190590441387193158826838716515109', '8.835863216401317832866339248202833', '9.364746929225894270075652617229658', '9.884387289899397217041620201286301', '10.20577814736085356952207776210873'], 'prelabel': '4-36992-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.239268773266061, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 174574354579756630, 'z1': {'__RealLiteral__': 0, 'data': '1.12942124871842761561442350611537', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.20924692317133984874547287655693', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.19825512904115960807108105792761', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.358641993159002, 'bad_primes': [2, 17], 'central_character': '1.1', 'conductor': 36992, 'conductor_radical': 34, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, 1, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 1, 6, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, -6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 6, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, -2], 'euler11': [1, 0, 14, 0, 121], 'euler13': [1, 0, 22, 0, 169], 'euler17': [1, -6, 17, 0, 0], 'euler19': [1, 0, 22, 0, 361], 'euler2': [1, 1, 0, 0, 0], 'euler23': [1, 0, -14, 0, 529], 'euler29': [1, 0, 50, 0, 841], 'euler3': [1, 0, -2, 0, 9], 'euler31': [1, 0, -62, 0, 961], 'euler37': [1, 0, 2, 0, 1369], 'euler41': [1, 0, -50, 0, 1681], 'euler43': [1, 0, 70, 0, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 0, 2, 0, 25], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, 0, -26, 0, 3481], 'euler61': [1, 0, 50, 0, 3721], 'euler67': [1, 0, 118, 0, 4489], 'euler7': [1, 0, -14, 0, 49], 'euler71': [1, 0, -110, 0, 5041], 'euler73': [1, 0, -146, 0, 5329], 'euler79': [1, 0, 130, 0, 6241], 'euler83': [1, 0, 22, 0, 6889], 'euler89': [1, -12, 214, -1068, 7921], 'euler97': [1, 0, 94, 0, 9409], 'euler_factors': [[1, 1, 0, 0, 0], [1, 0, -2, 0, 9], [1, 0, 2, 0, 25], [1, 0, -14, 0, 49], [1, 0, 14, 0, 121], [1, 0, 22, 0, 169], [1, -6, 17, 0, 0], [1, 0, 22, 0, 361], [1, 0, -14, 0, 529], [1, 0, 50, 0, 841], [1, 0, -62, 0, 961], [1, 0, 2, 0, 1369], [1, 0, -50, 0, 1681], [1, 0, 70, 0, 1849], [1, 0, 94, 0, 2209], [1, 0, 70, 0, 2809], [1, 0, -26, 0, 3481], [1, 0, 50, 0, 3721], [1, 0, 118, 0, 4489], [1, 0, -110, 0, 5041], [1, 0, -146, 0, 5329], [1, 0, 130, 0, 6241], [1, 0, 22, 0, 6889], [1, -12, 214, -1068, 7921], [1, 0, 94, 0, 9409]], 'index': 2, 'instance_types': ['ECNF', 'ECNF', 'HMF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.17.1/128.5/b', 'EllipticCurve/2.2.17.1/128.6/b', 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-128.5-b', 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-128.6-b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-36992-1.1-c1e2-0-2', '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': 0, 'prelabel': '4-36992-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.239268773266061, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 174574354579756630, 'z1': {'__RealLiteral__': 0, 'data': '1.12942124871842761561442350611537', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9490087
{'Lhash': '1431711523848431133622859233013', 'Lhash_array': ['1431711523848431133622859233013'], 'label': '4-36992-1.1-c1e2-0-2', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-128.6-b'}
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id: 9489655
{'Lhash': '1431711523848431133622859233013', 'Lhash_array': ['1431711523848431133622859233013'], 'label': '4-36992-1.1-c1e2-0-2', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.17.1/holomorphic/2.2.17.1-128.5-b'}
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id: 9489542
{'Lhash': '1431711523848431133622859233013', 'Lhash_array': ['1431711523848431133622859233013'], 'label': '4-36992-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.17.1/128.6/b'}
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id: 9489530
{'Lhash': '1431711523848431133622859233013', 'Lhash_array': ['1431711523848431133622859233013'], 'label': '4-36992-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.17.1/128.5/b'}