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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': -2, 'A4': 1, 'A5': 0, 'A6': 2, 'A7': 0, 'A8': -1, 'A9': 3, 'Lhash': '1053943263762342860741910013960', 'a10': [0.0, 0], 'a2': [-0.7071067811865476, 0], 'a3': [-1.1547005383792515, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.8164965809277259, 0], 'a7': [0.0, 0], 'a8': [-0.3535533905932738, 0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.22777793843102, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 2, 1]], [17, [1, -7, 17]]], 'bad_primes': [2, 3, 17], 'central_character': '332928.1', 'coefficient_field': '1.1.1.1', 'conductor': 332928, 'conductor_radical': 102, 'degree': 4, 'euler_factors': [[1, 1], [1, 2, 1], [1, 0, 2, 0, 25], [1, 0, -10, 0, 49], [1, -2, 19, -22, 121], [1, 0, 2, 0, 169], [1, -7, 17], [1, -5, 24, -95, 361], [1, 0, 27, 0, 529], [1, 0, 28, 0, 841], [1, 0, -44, 0, 961], [1, 0, -29, 0, 1369], [1, -17, 154, -697, 1681], [1, -1, 86, -43, 1849], [1, 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-2.0463295263977357, 0.3419859718904234, 3.17387998294725, 6.175876740685503, 9.035450337587033, 11.441780496114415, 13.127883105999961], 'positive_zeros': ['0.831414637103149397570797139600808', '1.28567152849104959722738462142828', '2.37613023402199732931781555690396', '3.11034937428825338285960982931300', '3.94940104277653377776235123622125', '4.19355607099128123583116261802847', '5.25929409201904734594585140610608', '5.47821797150192998903849387984859', '5.85863707042027363997680434113832', '6.42781542175905654376957218750524', '6.99362499590386105194200362515419', '7.34593913330565877143786586932190', '7.81703780712628173921183898621548', '8.143419471126167195769331161018673', '8.899547731058799229771538395638646'], 'prelabel': '4-332928-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.1464764795303726, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1111530904488440154, 'z1': {'__RealLiteral__': 0, 'data': '0.831414637103149397570797139600808', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '1.28567152849104959722738462142828', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.37613023402199732931781555690396', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.22777793843102, 'bad_primes': [2, 3, 17], 'central_character': '1.1', 'conductor': 332928, 'conductor_radical': 102, 'degree': 4, 'dirichlet_coefficients': [1, -1, -2, 1, 0, 2, 0, -1, 3, 0, 2, -2, 0, 0, 0, 1, 7, -3, 5, 0, 0, -2, 0, 2, -2, 0, -4, 0, 0, 0, 0, -1, -4, -7, 0, 3, 0, -5, 0, 0, 17, 0, 1, 2, 0, 0, 0, -2, 10, 2, -14, 0, 0, 4, 0, 0, -10, 0, 14, 0, 0, 0, 0, 1, 0, 4, -1, 7, 0, 0, 0, -3, 14, 0, 4, 5, 0, 0, 0, 0, 5, -17, -13, 0, 0, -1, 0, -2, -17, 0, 0, 0, 0, 0, 0, 2, 4, -10, 6, -2], 'euler11': [1, -2, 19, -22, 121], 'euler13': [1, 0, 2, 0, 169], 'euler17': [1, -7, 17, 0, 0], 'euler19': [1, -5, 24, -95, 361], 'euler2': [1, 1, 0, 0, 0], 'euler23': [1, 0, 27, 0, 529], 'euler29': [1, 0, 28, 0, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, 0, -44, 0, 961], 'euler37': [1, 0, -29, 0, 1369], 'euler41': [1, -17, 154, -697, 1681], 'euler43': [1, -1, 86, -43, 1849], 'euler47': [1, 0, -9, 0, 2209], 'euler5': [1, 0, 2, 0, 25], 'euler53': [1, 0, -22, 0, 2809], 'euler59': [1, -14, 166, -826, 3481], 'euler61': [1, 0, -86, 0, 3721], 'euler67': [1, 1, 24, 67, 4489], 'euler7': [1, 0, -10, 0, 49], 'euler71': [1, 0, -125, 0, 5041], 'euler73': [1, -14, 146, -1022, 5329], 'euler79': [1, 0, -82, 0, 6241], 'euler83': [1, 13, 202, 1079, 6889], 'euler89': [1, 17, 220, 1513, 7921], 'euler97': [1, -4, 173, -388, 9409], 'euler_factors': [[1, 1, 0, 0, 0], [1, 2, 1, 0, 0], [1, 0, 2, 0, 25], [1, 0, -10, 0, 49], [1, -2, 19, -22, 121], [1, 0, 2, 0, 169], [1, -7, 17, 0, 0], [1, -5, 24, -95, 361], [1, 0, 27, 0, 529], [1, 0, 28, 0, 841], [1, 0, -44, 0, 961], [1, 0, -29, 0, 1369], [1, -17, 154, -697, 1681], [1, -1, 86, -43, 1849], [1, 0, -9, 0, 2209], [1, 0, -22, 0, 2809], [1, -14, 166, -826, 3481], [1, 0, -86, 0, 3721], [1, 1, 24, 67, 4489], [1, 0, -125, 0, 5041], [1, -14, 146, -1022, 5329], [1, 0, -82, 0, 6241], [1, 13, 202, 1079, 6889], [1, 17, 220, 1513, 7921], [1, -4, 173, -388, 9409]], 'index': 8, 'instance_types': ['ECNF', 'BMF', 'ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.8.1/5202.4/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/5202.4/a', 'EllipticCurve/2.0.8.1/5202.6/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/5202.6/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': '4-332928-1.1-c1e2-0-8', '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': '4-332928-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.1464764795303726, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1111530904488440154, 'z1': {'__RealLiteral__': 0, 'data': '0.831414637103149397570797139600808', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9881229
{'Lhash': '1053943263762342860741910013960', 'Lhash_array': ['1053943263762342860741910013960'], 'label': '4-332928-1.1-c1e2-0-8', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/5202.6/a'}
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id: 9881071
{'Lhash': '1053943263762342860741910013960', 'Lhash_array': ['1053943263762342860741910013960'], 'label': '4-332928-1.1-c1e2-0-8', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/5202.6/a'}
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id: 9881059
{'Lhash': '1053943263762342860741910013960', 'Lhash_array': ['1053943263762342860741910013960'], 'label': '4-332928-1.1-c1e2-0-8', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/5202.4/a'}
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id: 9881057
{'Lhash': '1053943263762342860741910013960', 'Lhash_array': ['1053943263762342860741910013960'], 'label': '4-332928-1.1-c1e2-0-8', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/5202.4/a'}