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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 2, 'Lhash': '1397598705995969446805163582972', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-0.447213595499958, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.7927507558433, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 1, 3, -5]], [13, [1, -2, 13]]], 'bad_primes': [2, 5, 13], 'central_character': '216320.1', 'coefficient_field': '1.1.1.1', 'conductor': 216320, 'conductor_radical': 130, 'degree': 4, 'euler_factors': [[1], [1, 0, -2, 0, 9], [1, 1, 3, -5], [1, 0, -2, 0, 49], [1, -4, 22, -44, 121], [1, -2, 13], [1, -4, 38, -68, 289], [1, -12, 70, -228, 361], [1, 0, 46, 0, 529], [1, 0, 6, 0, 841], [1, 0, 38, 0, 961], [1, -4, 78, -148, 1369], [1, 0, -18, 0, 1681], [1, 0, -50, 0, 1849], [1, 0, 30, 0, 2209], [1, 0, -10, 0, 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-0.29483735356429563, 0.3835387596362748, 0.8344651120786069, 0.9993950117089399], 'positive_zeros': ['1.10251098034769519741233554296039', '1.49671912923580168401035638668141', '2.88997843750678363405458694623974', '3.29290533862603305121610232408319', '4.05031802431707437226167480446015', '4.24177323828206065139649065134294', '5.22099424574918792536697068746845', '5.54688175679406757253645675591303', '6.09878835919971051546496417989286', '6.77235450050653575886759107610204', '7.19426798589639996540396316685351', '7.60623590010481518643358407853118', '7.966426079446993756000846373600031', '8.593631180839430835377838256285053', '9.117421653671586813266405213339134'], 'prelabel': '4-216320-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.927137587346998, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 23192469493134396, 'z1': {'__RealLiteral__': 0, 'data': '1.10251098034769519741233554296039', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.49671912923580168401035638668141', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.88997843750678363405458694623974', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.7927507558433, 'bad_primes': [2, 5, 13], 'central_character': '1.1', 'conductor': 216320, 'conductor_radical': 130, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 4, 0, 12, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, -5, 0, -12, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 8, 0], 'euler11': [1, -4, 22, -44, 121], 'euler13': [1, -2, 13, 0, 0], 'euler17': [1, -4, 38, -68, 289], 'euler19': [1, -12, 70, -228, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 6, 0, 841], 'euler3': [1, 0, -2, 0, 9], 'euler31': [1, 0, 38, 0, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, 0, -18, 0, 1681], 'euler43': [1, 0, -50, 0, 1849], 'euler47': [1, 0, 30, 0, 2209], 'euler5': [1, 1, 3, -5, 0], 'euler53': [1, 0, -10, 0, 2809], 'euler59': [1, 4, 22, 236, 3481], 'euler61': [1, 0, 86, 0, 3721], 'euler67': [1, -4, -58, -268, 4489], 'euler7': [1, 0, -2, 0, 49], 'euler71': [1, 0, 86, 0, 5041], 'euler73': [1, 0, 30, 0, 5329], 'euler79': [1, 24, 286, 1896, 6241], 'euler83': [1, 12, 102, 996, 6889], 'euler89': [1, 0, -130, 0, 7921], 'euler97': [1, 0, -50, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -2, 0, 9], [1, 1, 3, -5, 0], [1, 0, -2, 0, 49], [1, -4, 22, -44, 121], [1, -2, 13, 0, 0], [1, -4, 38, -68, 289], [1, -12, 70, -228, 361], [1, 0, 46, 0, 529], [1, 0, 6, 0, 841], [1, 0, 38, 0, 961], [1, -4, 78, -148, 1369], [1, 0, -18, 0, 1681], [1, 0, -50, 0, 1849], [1, 0, 30, 0, 2209], [1, 0, -10, 0, 2809], [1, 4, 22, 236, 3481], [1, 0, 86, 0, 3721], [1, -4, -58, -268, 4489], [1, 0, 86, 0, 5041], [1, 0, 30, 0, 5329], [1, 24, 286, 1896, 6241], [1, 12, 102, 996, 6889], [1, 0, -130, 0, 7921], [1, 0, -50, 0, 9409]], 'index': 4, 'instance_types': ['HMF', 'HMF', 'ECNF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.104.1/holomorphic/2.2.104.1-20.2-b', 'ModularForm/GL2/TotallyReal/2.2.104.1/holomorphic/2.2.104.1-20.1-b', 'EllipticCurve/2.2.104.1/20.1/b', 'EllipticCurve/2.2.104.1/20.2/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': '4-216320-1.1-c1e2-0-4', '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': '4-216320-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.927137587346998, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 23192469493134396, 'z1': {'__RealLiteral__': 0, 'data': '1.10251098034769519741233554296039', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9463297
{'Lhash': '1397598705995969446805163582972', 'Lhash_array': ['1397598705995969446805163582972'], 'label': '4-216320-1.1-c1e2-0-4', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.104.1/20.2/b'}
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id: 9463296
{'Lhash': '1397598705995969446805163582972', 'Lhash_array': ['1397598705995969446805163582972'], 'label': '4-216320-1.1-c1e2-0-4', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.104.1/20.1/b'}
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id: 9463280
{'Lhash': '1397598705995969446805163582972', 'Lhash_array': ['1397598705995969446805163582972'], 'label': '4-216320-1.1-c1e2-0-4', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.104.1/holomorphic/2.2.104.1-20.1-b'}
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id: 9463223
{'Lhash': '1397598705995969446805163582972', 'Lhash_array': ['1397598705995969446805163582972'], 'label': '4-216320-1.1-c1e2-0-4', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.104.1/holomorphic/2.2.104.1-20.2-b'}