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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': -1, 'A5': 2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -4, 'Lhash': '2634775740918110559203442995848', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [-0.5, 0], 'a5': [0.894427190999916, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-1.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.2521230228448017, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, -2, 6, -5]], [101, [1, -7, 101]]], 'bad_primes': [5, 101], 'central_character': '51005.1', 'coefficient_field': '1.1.1.1', 'conductor': 51005, 'conductor_radical': 505, 'degree': 4, 'euler_factors': [[1, 0, 1, 0, 4], [1, 0, 4, 0, 9], [1, -2, 6, -5], [1, 0, -4, 0, 49], [1, 0, 13, 0, 121], [1, 3, 22, 39, 169], [1, 4, 38, 68, 289], [1, 3, 34, 57, 361], [1, 3, -8, 69, 529], [1, 0, 7, 0, 841], [1, 0, 37, 0, 961], [1, 1, 68, 37, 1369], [1, 0, 23, 0, 1681], [1, 2, 62, 86, 1849], [1, 1, 88, 47, 2209], [1, 0, -46, 0, 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-3.6464322565592084, -4.459662643463106], 'positive_zeros': ['2.07847157603502276997862052834978', '2.46604034157258189949375676810035', '3.47697954271673039561109068255481', '4.37067453180056733328480562446675', '4.86439631929958785852821223887711', '5.51864259033180555366486250250998', '6.09493305416815985505427508168912', '6.46335991685157961372547360255317', '7.20152138759499360168550782179824', '7.82578318499584537782581818851516', '8.525522793869626337956143518920948', '8.813024625233088576583383817326742', '9.291419600896184591458340969487573', '9.728700651601606822751472445507319'], 'prelabel': '4-51005-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.3428940249318722, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 628045169830482337, 'z1': {'__RealLiteral__': 0, 'data': '2.07847157603502276997862052834978', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.46604034157258189949375676810035', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.47697954271673039561109068255481', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.2521230228448017, 'bad_primes': [5, 101], 'central_character': '1.1', 'conductor': 51005, 'conductor_radical': 505, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -1, 2, 0, 0, 0, -4, 0, 0, 0, -3, 0, 0, -3, -4, 0, -3, -2, 0, 0, -3, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -1, 0, 0, 0, 0, 0, -2, 0, -8, 0, -1, 0, 4, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, -6, 0, 0, 4, 0, 0, -14, 0, 0, 0, 0, 3, 0, 0, 10, -6, 7, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 3, 0, 0, -6, 0, 29, 0, 0, 2], 'euler11': [1, 0, 13, 0, 121], 'euler13': [1, 3, 22, 39, 169], 'euler17': [1, 4, 38, 68, 289], 'euler19': [1, 3, 34, 57, 361], 'euler2': [1, 0, 1, 0, 4], 'euler23': [1, 3, -8, 69, 529], 'euler29': [1, 0, 7, 0, 841], 'euler3': [1, 0, 4, 0, 9], 'euler31': [1, 0, 37, 0, 961], 'euler37': [1, 1, 68, 37, 1369], 'euler41': [1, 0, 23, 0, 1681], 'euler43': [1, 2, 62, 86, 1849], 'euler47': [1, 1, 88, 47, 2209], 'euler5': [1, -2, 6, -5, 0], 'euler53': [1, 0, -46, 0, 2809], 'euler59': [1, 0, -58, 0, 3481], 'euler61': [1, 0, 103, 0, 3721], 'euler67': [1, 0, -84, 0, 4489], 'euler7': [1, 0, -4, 0, 49], 'euler71': [1, 14, 166, 994, 5041], 'euler73': [1, 0, 34, 0, 5329], 'euler79': [1, -10, 158, -790, 6241], 'euler83': [1, 0, -86, 0, 6889], 'euler89': [1, 0, 47, 0, 7921], 'euler97': [1, -29, 398, -2813, 9409], 'euler_factors': [[1, 0, 1, 0, 4], [1, 0, 4, 0, 9], [1, -2, 6, -5, 0], [1, 0, -4, 0, 49], [1, 0, 13, 0, 121], [1, 3, 22, 39, 169], [1, 4, 38, 68, 289], [1, 3, 34, 57, 361], [1, 3, -8, 69, 529], [1, 0, 7, 0, 841], [1, 0, 37, 0, 961], [1, 1, 68, 37, 1369], [1, 0, 23, 0, 1681], [1, 2, 62, 86, 1849], [1, 1, 88, 47, 2209], [1, 0, -46, 0, 2809], [1, 0, -58, 0, 3481], [1, 0, 103, 0, 3721], [1, 0, -84, 0, 4489], [1, 14, 166, 994, 5041], [1, 0, 34, 0, 5329], [1, -10, 158, -790, 6241], [1, 0, -86, 0, 6889], [1, 0, 47, 0, 7921], [1, -29, 398, -2813, 9409]], 'index': 0, 'instance_types': ['HMF', 'ECNF', 'ECNF', 'HMF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.101.1/holomorphic/2.2.101.1-5.1-a', 'EllipticCurve/2.2.101.1/5.2/a', 'EllipticCurve/2.2.101.1/5.1/a', 'ModularForm/GL2/TotallyReal/2.2.101.1/holomorphic/2.2.101.1-5.2-a'], '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': '4-51005-1.1-c1e2-0-0', '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': '4-51005-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.3428940249318722, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 628045169830482337, 'z1': {'__RealLiteral__': 0, 'data': '2.07847157603502276997862052834978', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9460713
{'Lhash': '2634775740918110559203442995848', 'Lhash_array': ['2634775740918110559203442995848'], 'label': '4-51005-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.101.1/holomorphic/2.2.101.1-5.2-a'}
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id: 9460711
{'Lhash': '2634775740918110559203442995848', 'Lhash_array': ['2634775740918110559203442995848'], 'label': '4-51005-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.101.1/5.1/a'}
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id: 9460679
{'Lhash': '2634775740918110559203442995848', 'Lhash_array': ['2634775740918110559203442995848'], 'label': '4-51005-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.101.1/5.2/a'}
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id: 9460639
{'Lhash': '2634775740918110559203442995848', 'Lhash_array': ['2634775740918110559203442995848'], 'label': '4-51005-1.1-c1e2-0-0', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.101.1/holomorphic/2.2.101.1-5.1-a'}