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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': '1246861391864883404299605474620', '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': 5.738478032664095, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, -1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '90000.1', 'coefficient_field': '1.1.1.1', 'conductor': 90000, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1, 0, -1], [1], [1, 0, -6, 0, 49], [1, 2, 22, 22, 121], [1, 0, -4, 0, 169], [1, 0, -20, 0, 289], [1, -6, 46, -114, 361], [1, 0, 10, 0, 529], [1, -12, 78, -348, 841], [1, 8, 62, 248, 961], [1, 0, 36, 0, 1369], [1, -4, 50, -164, 1681], [1, 0, 14, 0, 1849], [1, 0, -30, 0, 2209], [1, 0, 8, 0, 2809], [1, 4, 22, 236, 3481], [1, 8, 38, 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3.92142668984557, 3.903045813104228, 3.4106942359403694, 2.5186147009982536, 1.363627037975217], 'positive_zeros': ['0.983600206271662647349506315129515', '2.13773733830389776980284506011921', '2.95663321963890379833499266268684', '3.54121389592464875097582431022680', '4.34873025801747621573057796223438', '4.97818173111463866326367880597304', '5.37046128545327580986181494415740', '6.10490391923692043188008510683769', '6.56256714616671002927373963660880', '7.31591507178608977707809656374201', '7.56769400901303834898435326102851', '8.090777049234184494344670427300735', '8.721020722425421722943335958792611', '9.188400291458291679037007918662282', '9.617923166485020541039699362690805'], 'prelabel': '4-300e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.5477441844951034, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1513289307122366082, 'z1': {'__RealLiteral__': 0, 'data': '0.983600206271662647349506315129515', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '2.13773733830389776980284506011921', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.95663321963890379833499266268684', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.738478032664095, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 90000, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0], 'euler11': [1, 2, 22, 22, 121], 'euler13': [1, 0, -4, 0, 169], 'euler17': [1, 0, -20, 0, 289], 'euler19': [1, -6, 46, -114, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 10, 0, 529], 'euler29': [1, -12, 78, -348, 841], 'euler3': [1, 0, -1, 0, 0], 'euler31': [1, 8, 62, 248, 961], 'euler37': [1, 0, 36, 0, 1369], 'euler41': [1, -4, 50, -164, 1681], 'euler43': [1, 0, 14, 0, 1849], 'euler47': [1, 0, -30, 0, 2209], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, 8, 0, 2809], 'euler59': [1, 4, 22, 236, 3481], 'euler61': [1, 8, 38, 488, 3721], 'euler67': [1, 0, 70, 0, 4489], 'euler7': [1, 0, -6, 0, 49], 'euler71': [1, -14, 190, -994, 5041], 'euler73': [1, 0, -32, 0, 5329], 'euler79': [1, 2, -10, 158, 6241], 'euler83': [1, 0, -98, 0, 6889], 'euler89': [1, -20, 214, -1780, 7921], 'euler97': [1, 0, 40, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -1, 0, 0], [1, 0, 0, 0, 0], [1, 0, -6, 0, 49], [1, 2, 22, 22, 121], [1, 0, -4, 0, 169], [1, 0, -20, 0, 289], [1, -6, 46, -114, 361], [1, 0, 10, 0, 529], [1, -12, 78, -348, 841], [1, 8, 62, 248, 961], [1, 0, 36, 0, 1369], [1, -4, 50, -164, 1681], [1, 0, 14, 0, 1849], [1, 0, -30, 0, 2209], [1, 0, 8, 0, 2809], [1, 4, 22, 236, 3481], [1, 8, 38, 488, 3721], [1, 0, 70, 0, 4489], [1, -14, 190, -994, 5041], [1, 0, -32, 0, 5329], [1, 2, -10, 158, 6241], [1, 0, -98, 0, 6889], [1, -20, 214, -1780, 7921], [1, 0, 40, 0, 9409]], 'index': 3, 'instance_types': ['ECNF', 'HMF', 'ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.5.1/3600.1/c', 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-3600.1-b', 'EllipticCurve/2.2.5.1/3600.1/b', 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-3600.1-c'], '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': '4-300e2-1.1-c1e2-0-3', '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': '4-300e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.5477441844951034, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1513289307122366082, 'z1': {'__RealLiteral__': 0, 'data': '0.983600206271662647349506315129515', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9525507
{'Lhash': '1246861391864883404299605474620', 'Lhash_array': ['1246861391864883404299605474620'], 'label': '4-300e2-1.1-c1e2-0-3', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-3600.1-c'}
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id: 9525505
{'Lhash': '1246861391864883404299605474620', 'Lhash_array': ['1246861391864883404299605474620'], 'label': '4-300e2-1.1-c1e2-0-3', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.5.1/3600.1/b'}
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id: 9525225
{'Lhash': '1246861391864883404299605474620', 'Lhash_array': ['1246861391864883404299605474620'], 'label': '4-300e2-1.1-c1e2-0-3', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.5.1/holomorphic/2.2.5.1-3600.1-b'}
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id: 9525106
{'Lhash': '1246861391864883404299605474620', 'Lhash_array': ['1246861391864883404299605474620'], 'label': '4-300e2-1.1-c1e2-0-3', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.5.1/3600.1/c'}