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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1051244124434186844972647605387', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896257, 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': 13.662168500166677, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [31, [1, -5, 35, -31]]], 'bad_primes': [2, 3, 31], 'central_character': '214272.1', 'coefficient_field': '1.1.1.1', 'conductor': 214272, 'conductor_radical': 186, 'degree': 4, 'euler_factors': [[1], [1, 1], [1, 0, 6, 0, 25], [1, 0, 14, 0, 49], [1, 0, -10, 0, 121], [1, 0, -10, 0, 169], [1, 0, 2, 0, 289], [1, -12, 70, -228, 361], [1, 0, -34, 0, 529], [1, 0, 10, 0, 841], [1, -5, 35, -31], [1, -4, 62, -148, 1369], [1, 0, 30, 0, 1681], [1, -12, 118, -516, 1849], [1, 0, -34, 0, 2209], [1, 0, -22, 0, 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0.15674918296938326, 0.49203920689050856, 0.5941365877687343, 0.3723995492548958, -0.20569417311274207], 'positive_zeros': ['0.829285391609422609333888963661578', '1.68775166527744861991585850622588', '2.75436860305933135872352463064462', '3.26085305245353197687960137611313', '4.00423209001720156661471362856396', '4.57024261949286174732621188593672', '5.19183088818837598274241663429152', '5.59300252499016180443370297334166', '6.08128156063897742710474004613970', '6.56947839218317451637377764575964', '7.24102921467505772339821362992377', '7.64708463579025774976884144695002', '7.899973351433242250186053370125232', '8.530484615407473322321301773176759', '9.321039659323861061097159872571030'], 'prelabel': '4-214272-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.9225600310645568, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1465714159227790594, 'z1': {'__RealLiteral__': 0, 'data': '0.829285391609422609333888963661578', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '1.68775166527744861991585850622588', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.75436860305933135872352463064462', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.662168500166677, 'bad_primes': [2, 3, 31], 'central_character': '1.1', 'conductor': 214272, 'conductor_radical': 186, 'degree': 4, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, -6, 0, -1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 4, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, -8, 0, 6, 0, 0, 0, 20, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, -4, 0, 0, 0], 'euler11': [1, 0, -10, 0, 121], 'euler13': [1, 0, -10, 0, 169], 'euler17': [1, 0, 2, 0, 289], 'euler19': [1, -12, 70, -228, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -34, 0, 529], 'euler29': [1, 0, 10, 0, 841], 'euler3': [1, 1, 0, 0, 0], 'euler31': [1, -5, 35, -31, 0], 'euler37': [1, -4, 62, -148, 1369], 'euler41': [1, 0, 30, 0, 1681], 'euler43': [1, -12, 118, -516, 1849], 'euler47': [1, 0, -34, 0, 2209], 'euler5': [1, 0, 6, 0, 25], 'euler53': [1, 0, -22, 0, 2809], 'euler59': [1, 0, -50, 0, 3481], 'euler61': [1, -4, 110, -244, 3721], 'euler67': [1, 12, 166, 804, 4489], 'euler7': [1, 0, 14, 0, 49], 'euler71': [1, 0, 62, 0, 5041], 'euler73': [1, 8, 126, 584, 5329], 'euler79': [1, -20, 222, -1580, 6241], 'euler83': [1, 0, -106, 0, 6889], 'euler89': [1, 0, -54, 0, 7921], 'euler97': [1, 4, 134, 388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 1, 0, 0, 0], [1, 0, 6, 0, 25], [1, 0, 14, 0, 49], [1, 0, -10, 0, 121], [1, 0, -10, 0, 169], [1, 0, 2, 0, 289], [1, -12, 70, -228, 361], [1, 0, -34, 0, 529], [1, 0, 10, 0, 841], [1, -5, 35, -31, 0], [1, -4, 62, -148, 1369], [1, 0, 30, 0, 1681], [1, -12, 118, -516, 1849], [1, 0, -34, 0, 2209], [1, 0, -22, 0, 2809], [1, 0, -50, 0, 3481], [1, -4, 110, -244, 3721], [1, 12, 166, 804, 4489], [1, 0, 62, 0, 5041], [1, 8, 126, 584, 5329], [1, -20, 222, -1580, 6241], [1, 0, -106, 0, 6889], [1, 0, -54, 0, 7921], [1, 4, 134, 388, 9409]], 'index': 1, 'instance_types': ['ECNF', 'BMF', 'BMF', 'ECNF'], 'instance_urls': ['EllipticCurve/2.0.3.1/23808.1/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/23808.2/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/23808.1/a', 'EllipticCurve/2.0.3.1/23808.2/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': '4-214272-1.1-c1e2-0-1', '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': '4-214272-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.9225600310645568, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1465714159227790594, 'z1': {'__RealLiteral__': 0, 'data': '0.829285391609422609333888963661578', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9745051
{'Lhash': '1051244124434186844972647605387', 'Lhash_array': ['1051244124434186844972647605387'], 'label': '4-214272-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/23808.2/a'}
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id: 9745049
{'Lhash': '1051244124434186844972647605387', 'Lhash_array': ['1051244124434186844972647605387'], 'label': '4-214272-1.1-c1e2-0-1', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/23808.1/a'}
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id: 9744648
{'Lhash': '1051244124434186844972647605387', 'Lhash_array': ['1051244124434186844972647605387'], 'label': '4-214272-1.1-c1e2-0-1', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/23808.2/a'}
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id: 9744272
{'Lhash': '1051244124434186844972647605387', 'Lhash_array': ['1051244124434186844972647605387'], 'label': '4-214272-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/23808.1/a'}