-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '6484899042350030457258858034680', 'a10': 0, 'a2': -1, 'a3': -1, 'a4': 0, 'a5': 0, 'a6': 1, 'a7': 0, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.011478495290559056, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[23, [1, -1]]], 'bad_primes': [23], 'central_character': '23.22', 'coefficient_field': '1.1.1.1', 'conductor': 23, 'conductor_radical': 23, 'degree': 2, 'euler_factors': [[1, 1, 1], [1, 1, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 1, 1], [1, 0, -1], [1, 0, -1], [1, -1], [1, 1, 1], [1, 1, 1], [1, 0, -1], [1, 1, 1], [1, 0, -1], [1, 1, 1], [1, 0, -1], [1, -2, 1], [1, 0, -1], [1, 0, -1], [1, 1, 1], [1, 1, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, -2, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, -1]], 'euler_factors_factorization': [[[[1, 1, 1], 1]], [[[1, 1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, 1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1]], [[[1, 1, 1], 1]], [[[1, 1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, 1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, 1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 2]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, 1, 1], 1]], [[[1, 1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 2]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-23-23.22-c0-0-0', 'leading_term': '0.1740363269879341834995045920174800000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/23/1/b/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.109375', 'prec': 27}, 'plot_values': [0.17403632698793417, 0.17878443772623323, 0.19265734240144858, 0.21478707822854806, 0.2442750285496309, 0.28048762499088264, 0.3231139816780236, 0.3721024946751218, 0.4275723448992609, 0.4897372216814678, 0.5588472503861807, 0.6351452888481994, 0.7188326011317152, 0.8100400873355263, 0.9088026200165653, 1.0150351094569954, 1.1285096725637764, 1.2488337958636049, 1.3754297403193247, 1.5075156896754662, 1.6440893288846872, 1.7839146740157446, 1.9255130691517977, 2.0671593221633544, 2.2068839691073214, 2.342482633472524, 2.471533377732686, 2.5914228267863098, 2.699381672602213, 2.792529944724403, 2.867932151949589, 2.9226620684201547, 2.953876557132284, 2.95889740292834, 2.935299676052013, 2.8810046801522526, 2.7943750722540766, 2.674309296629689, 2.5203320721629425, 2.3326773380316568, 2.1123598206833654, 1.861231261468149, 1.5820173629687577, 1.2783316944302092, 0.9546631599873462, 0.6163341891820106, 0.2694275619217289, -0.0793192746514726, -0.4226524159053072, -0.7529709764764576, -1.0625251778478415, -1.343638922096861, -1.5889512438269333, -1.7916696000493295, -1.9458266496482197, -2.046531067402282, -2.0902021107325273, -2.0747771859028665, -1.9998816126165282, -1.8669502183330604, -1.6792913462608738, -1.4420853531094397, -1.162311698819387, -0.8486012572774095, -0.5110134412433607, -0.16074104263223513, 0.19025078237736337, 0.5296413552610516, 0.8452136191319475, 1.1253388527022754, 1.3594674998500609, 1.5386046156407813, 1.6557472416072712, 1.7062608459233668, 1.688172915210531, 1.6023639336781659, 1.4526393442250893, 1.2456706021218271, 0.9907989823932567, 0.6997021936955188, 0.38593082315804217, 0.0643288666561643, -0.24964028308756894, -0.5406344152380547, -0.7942059986278535, -0.997570613772731, -1.1403297020364696, -1.2151063951899488, -1.2180548030096432, -1.1492070976600888, -1.0126290270095326, -0.8163629610152734, -0.5721479278780152, -0.2949178910570774, -0.002092187751472333, 0.28731507837750214, 0.5537275696126652, 0.7781310498043816, 0.9432304986044175, 1.0345748878823326, 1.0415818248747917, 0.958395443429549, 0.7845161984944362, 0.5251505950011767, 0.19124210797769042, -0.20083889117341286, -0.6299492689119369, -1.0711537116625662, -1.4969930839445393, -1.878981752763772, -2.18925719754365, -2.402290925939885, -2.496560163318708, -2.4560759319563803, -2.2716656378680997, -1.9419174212902681, -1.4737091652460805, -0.8822666168640414, -0.19072154215859113, 0.5708292109971523, 1.3667311777611035, 2.157582272742739, 2.9023522570952136, 3.560694010658899, 4.095310723814183, 4.4742329006998185, 4.672858001636867, 4.67561424776887, 4.477128521071917, 4.082805689857513, 3.508761668104425, 2.7810930502322266, 1.9345097110414315, 1.0104004212336402, 0.05444222730088282, -0.8861009516831726, -1.7652191119739227, -2.5409500242547325, -3.177937549770652, -3.649576848507002, -3.9395930956221505, -4.042936426551257, -3.96592169402904, -3.7255942341893142, -3.3483585379610696, -2.8679614314615165, -2.322970892262351, -1.75393198015759, -1.2004090841628474, -0.6981361555907839, -0.27649226656556325, 0.04350157756293968, 0.2505058677293067, 0.3433987979824066, 0.3309788384341063, 0.23085375933147426, 0.06760291653283917, -0.12963889511493462, -0.32997670877694146, -0.503694564529172, -0.6250861579516279, -0.6749280859211562, -0.6423716663629603, -0.5260741277268127, -0.3344516819153589, -0.08501095724922288, 0.19720443747706437, 0.4819355427054918, 0.7366086685804023, 0.9295673044302797, 1.033348866881008, 1.0277050781252985, 0.9020763119198416, 0.6572681829282134, 0.30614073093281313, -0.1267977440510507, -0.6069052774340448, -1.091942275316205, -1.53544549499376, -1.890672403997366, -2.114784853626227, -2.172904734203565, -2.0416697249789073, -1.7119462167668922, -1.19041780111254, -0.4998572088120313, 0.32199970107836434, 1.224936554784245, 2.149930275354321, 3.0337366272343362, 3.8140148467643766, 4.434555830364681, 4.8501527929272426, 5.030668927383702, 4.963913581807696, 4.657033166002548, 4.136248078396884, 3.444911940651254, 2.6400215912877, 1.7874516955559172, 0.9563126478797579, 0.21292226183824003, -0.3850691976735217, -0.7938608491311323, -0.9875003355796136, -0.9603083020144156, -0.7274734454195277, -0.32372839124331676, 0.19980540182221693, 0.7803412509421527, 1.349303162893929, 1.8388199651559554, 2.1882339332723904, 2.350006860040961, 2.2944522803117517, 2.012824529010683, 1.5184449551962973, 0.8457294821017289, 0.047182569592641596, -0.811378882825438, -1.6569317279490055, -2.416106511156579, -3.022142918009509, -3.421264414367261, -3.577844638707284, -3.477850356879315, -3.130211321882003, -2.565970435093516, -1.835288222862541, -1.0025916174659029, -0.14034615269758946, 0.6779269546014509, 1.38468722886351, 1.9247546339914596, 2.260387186336548, 2.3745437823372457, 2.2720070003018553, 1.9782638436476492, 1.5362781221137147, 1.0015114114216697, 0.4357361578926669, -0.09968612336115187, -0.5503312650701757, -0.8743350966269816, -1.0465037650336255, -1.060470960087611, -0.9286793824439454, -0.6802086220063429, -0.35671612101768047, -0.006974525256080105, 0.319347508600117, 0.5779226174019039, 0.7352744893246516, 0.7728937301285105, 0.6894518934906275, 0.500826496244341, 0.23790863999126888], 'positive_zeros': ['5.11568332881511759855335642037843', '7.15926229054170384129282782024775', '8.881396573689177474965824491607561', '10.28202740085213205371618003800128', '11.43003635304813311896205990224263', '12.93440966771841183579118145713812', '14.66248095457465912598048536284092', '16.49823251336240134157531665335702', '17.10126330358183155194872344462881', '18.08066174344421407705280597228646'], 'prelabel': '2-23-23.22-c0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.10713773980516415, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0-0', 'trace_hash': 426797760822574538, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '5.11568332881511759855335642038', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '7.15926229054170384129282782025', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.881396573689177474965824491608', 'prec': 107}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.011478495290559056, 'bad_primes': [23], 'central_character': '23.22', 'conductor': 23, 'conductor_radical': 23, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 0, 0, 1, 0, 1, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, -1, 1, 1, 1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, -1, -1, 1, 1, -1, 0, 0, 0, -1, 0, 0, 0, 1, 2, 0, 0, 1, 0, 1, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, -1, 0, 0, -1, 0, 0, -1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, -1, 0, 0], 'euler11': [1, 0, -1], 'euler13': [1, 1, 1], 'euler17': [1, 0, -1], 'euler19': [1, 0, -1], 'euler2': [1, 1, 1], 'euler23': [1, -1, 0], 'euler29': [1, 1, 1], 'euler3': [1, 1, 1], 'euler31': [1, 1, 1], 'euler37': [1, 0, -1], 'euler41': [1, 1, 1], 'euler43': [1, 0, -1], 'euler47': [1, 1, 1], 'euler5': [1, 0, -1], 'euler53': [1, 0, -1], 'euler59': [1, -2, 1], 'euler61': [1, 0, -1], 'euler67': [1, 0, -1], 'euler7': [1, 0, -1], 'euler71': [1, 1, 1], 'euler73': [1, 1, 1], 'euler79': [1, 0, -1], 'euler83': [1, 0, -1], 'euler89': [1, 0, -1], 'euler97': [1, 0, -1], 'euler_factors': [[1, 1, 1], [1, 1, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 1, 1], [1, 0, -1], [1, 0, -1], [1, -1, 0], [1, 1, 1], [1, 1, 1], [1, 0, -1], [1, 1, 1], [1, 0, -1], [1, 1, 1], [1, 0, -1], [1, -2, 1], [1, 0, -1], [1, 0, -1], [1, 1, 1], [1, 1, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, -1]], 'index': 0, 'instance_types': ['CMF', 'CMF', 'Artin', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/23/1/b/a/22/1', 'ModularForm/GL2/Q/holomorphic/23/1/b/a', 'ArtinRepresentation/2.23.3t2.b.a', 'ArtinRepresentation/2.23.3t2.b'], 'is_instance_Artin': True, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, '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': '2-23-23.22-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-23-23.22-c0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.10713773980516415, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'trace_hash': 426797760822574538, 'z1': {'__RealLiteral__': 0, 'data': '5.11568332881511759855335642038', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 24602827
{'Lhash': '6484899042350030457258858034680', 'Lhash_array': ['6484899042350030457258858034680'], 'label': '2-23-23.22-c0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.23.3t2.b'}
-
id: 24596343
{'Lhash': '6484899042350030457258858034680', 'Lhash_array': ['6484899042350030457258858034680'], 'label': '2-23-23.22-c0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.23.3t2.b.a'}
-
id: 19812360
{'Lhash': '6484899042350030457258858034680', 'Lhash_array': ['6484899042350030457258858034680'], 'label': '2-23-23.22-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/23/1/b/a'}
-
id: 24545757
{'Lhash': '6484899042350030457258858034680', 'Lhash_array': ['6484899042350030457258858034680'], 'label': '2-23-23.22-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/23/1/b/a/22/1'}