-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1653597920668694732294420894365', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -1.0], 'a4': [0, 0], 'a5': [1.8538428603401482, 1.250306622059508], 'a6': [0, 0], 'a7': [0, 1.1237733237277931], 'a8': [0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.144741006170603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [-1.8538428603401482, -1.250306622059508]]], [17, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3, 5, 17], 'central_character': '1020.409', 'coefficient_field': 'CDF', 'conductor': 1020, 'conductor_radical': 510, 'conjugate': '1290096186952579683105592378387', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [-1.8538428603401482, -1.250306622059508]], [[1.0, 0], [0, -1.1237733237277931], [-7.0, 0]], [[1.0, 0], [0.781901148741906, 0], [11.0, 0]], [[1.0, 0], [0, 6.906900960707731], [-13.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [-4.990200113541219, 0], [19.0, 0]], [[1.0, 0], [0, 2.6986019959084184], [-23.0, 0]], [[1.0, 0], [-4.489586869422203, 0], [29.0, 0]], [[1.0, 0], [-5.36581354569441, 0], [31.0, 0]], [[1.0, 0], [0, 1.877453164510239], [-37.0, 0]], [[1.0, 0], [-12.197272590102498, 0], [41.0, 0]], [[1.0, 0], [0, -4.103663224259101], [-43.0, 0]], [[1.0, 0], [0, -12.102947062572198], [-47.0, 0]], [[1.0, 0], [0, 7.123773323727793], [-53.0, 0]], [[1.0, 0], [8.612133704911964, 0], [59.0, 0]], [[1.0, 0], [13.010564184966833, 0], [61.0, 0]], [[1.0, 0], [0, 8.612133704911964], [-67.0, 0]], [[1.0, 0], [-13.813801921415463, 0], [71.0, 0]], [[1.0, 0], [0, 7.290371629394768], [-73.0, 0]], [[1.0, 0], [12.73162709138882, 0], [79.0, 0]], [[1.0, 0], [0, -13.060122080633016], [-83.0, 0]], [[1.0, 0], [10.763017537511246, 0], [89.0, 0]], [[1.0, 0], [0, 18.227946874538024], [-97.0, 0]], [[1.0, 0], [-5.248773135693618, 0], [101.0, 0]], [[1.0, 0], [0, 4.103663224259101], [-103.0, 0]], [[1.0, 0], [0, -2.25306659666343], [-107.0, 0]], [[1.0, 0], [-11.980400227082438, 0], [109.0, 0]], [[1.0, 0], [0, -8.280571742935987], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-1020-5.4-c1-0-9', 'leading_term': '1.867593728396304677877173573000175056140976519793849872', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1020/2/g/d/409/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.8675937283963047, 1.8992744488972588, 1.9251982960681984, 1.9450457906018113, 1.9582573378940646, 1.964053730576902, 1.961468947379011, 1.9493929561942407, 1.9266219581964863, 1.89191354580514, 1.8440444946408494, 1.7818692571996224, 1.7043775779492698, 1.6107499418919218, 1.5004097718865808, 1.3730714029210929, 1.2287829010136166, 1.0679627861543965, 0.8914296899189119, 0.700423953650331, 0.49662017227063376, 0.28212972646128476, 0.05949243185192128, -0.16834342665491467, -0.3980532125150281, -0.6259804955838221, -0.8481940406694779, -1.0605568751799224, -1.2588067084664092, -1.4386465756898141, -1.5958441678555237, -1.7263379009501172, -1.826347385903456, -1.8924856032141057, -1.921869777671476, -1.91222770566333, -1.861996125301555, -1.7704076518998773, -1.6375628400668405, -1.4644840880806582, -1.2531483763023217, -1.0064962313910941, -0.7284148299975454, -0.4236937928101532, -0.09795296089707575, 0.24245772507159133, 0.5905852269285805, 0.9390253402903919, 1.2800966546287569, 1.6060327140335033, 1.9091876779614496, 2.1822499994286373, 2.4184579825098407, 2.6118105855718388, 2.7572665322891408, 2.8509247056060874, 2.890178950960278, 2.8738408176042616, 2.802224425734185, 2.6771885580597767, 2.50213222323125, 2.2819413007899567, 2.0228854185597505, 1.7324658896073517, 1.4192172944205046, 1.0924670749002, 0.7620592448225004, 0.43804994801795777, 0.13038404128513634, -0.15143692341530607, -0.39868405625691183, -0.6037160441764551, -0.7602677298994576, -0.8637007930877034, -0.9112057593690779, -0.9019458072071848, -0.8371345233687807, -0.7200418367186404, -0.5559247801382365, -0.35188241684320076, -0.11663712983306183, 0.13975259186962158, 0.406239842324879, 0.6711867005329671, 0.9227981269502177, 1.1495770760355035, 1.3407839872149965, 1.4868828515180355, 1.579955753015939, 1.6140682027587356, 1.585568740700183, 1.493308170867948, 1.338766378143302, 1.1260778811798002, 0.8619510043687666, 0.5554796734587066, 0.2178512014333708, -0.13804213836516963, -0.4980756405115086, -0.847432676960863, -1.1711935507250293, -1.4549502073090956, -1.6854222907151422, -1.8510489544475577, -1.942530804547047, -1.9532974127008071, -1.8798779986936713, -1.7221561002099723, -1.4834932324784904, -1.1707115510971542, -0.7939311854306467, -0.36626398636624324, 0.09662831953455231, 0.5770974274665168, 1.0561732880330583, 1.514305439298473, 1.9321515850513502, 2.2913810882816064, 2.5754592913247163, 2.770378271123098, 2.865300861747181, 2.853087531466681, 2.730679922271474, 2.4993204089121903, 2.164593707696883, 1.7362840968529072, 1.2280498835343605, 0.6569250125443228, 0.04266578060155361, -0.5930318862574723, -1.2274125871639294, -1.837601767329551, -2.401565258250718, -2.8990452142807173, -3.3124297012955464, -3.6275152858241655, -3.8341260437454885, -3.9265583230626366, -3.9038281271948363, -3.7697068183857025, -3.5325405850846336, -3.20485932413407, -2.8027907718670546, -2.3453053762927074, -1.853326043527685, -1.348744058405212, -0.8533877738398234, -0.3879937696713474, 0.028769116428474836, 0.38117428641937795, 0.6571660922302494, 0.8489050572506318, 0.9531005752428705, 0.9711123855059183, 0.9088136328290872, 0.7762204444805125, 0.5869050822220755, 0.35722122482265684, 0.10538018965624399, -0.14957465817668494, -0.388841924194435, -0.5949277945706262, -0.752645888276947, -0.8499965269796328, -0.8788761053440849, -0.8355755145064663, -0.7210372311945964, -0.5408532212807277, -0.3049995901799804, -0.027318228528404605, 0.27523021440906953, 0.5835046187818586, 0.8772642009206513, 1.136334176928474, 1.3417926674995144, 1.477112645317404, 1.529193744591705, 1.4892234096349932, 1.3533149929616604, 1.122881662430137, 0.8047187968899722, 0.4107832371396116, -0.042325514068677565, -0.5341601921256232, -1.0414587748671575, -1.5393632851519883, -2.002760361651203, -2.4076711580570738, -2.732613596746345, -2.9598597012842154, -3.0765147894780007, -3.0753536069671172, -2.955360657727422, -2.7219374484126853, -2.386757310510809, -1.967267936559198, -1.4858616898937937, -0.968752993177014, -0.4446195503479305, 0.05692123471241327, 0.5069184188319502, 0.8786876364670126, 1.1493150855943464, 1.3009789646435248, 1.3220106508930614, 1.2076312678346959, 0.9603166240022598, 0.5897638993705792, 0.11245578753293034, -0.44915918763070767, -1.0678291024067907, -1.7129423450762464, -2.3521739635823553, -2.9532431048428363, -3.4856822280331783, -3.9225166845682096, -4.241757084913084, -4.427616502638057, -4.471379536580428, -4.371869770950691, -4.135485160188968, -3.775796009468167, -3.3127260557141676, -2.7713621395885153, -2.180460578472154, -1.5707371999295654, -0.9730418716860338, -0.4165263443050294, 0.07308427528185146, 0.4750112745796631, 0.7746398066967914, 0.9643580778050631, 1.0439646259095912, 1.020616025762843, 0.908315352181425, 0.7269700720321962, 0.5010749652562277, 0.25809950546404675, 0.026678332077057176, -0.1652832479407214, -0.29247029995415197, -0.33386824751630223, -0.274212423092699, -0.10508299204294783, 0.17442763032949413, 0.5575215699772536, 1.0299937323324466, 1.5710077987210174, 2.154305841440976, 2.7497793878601757, 3.3253059754147434, 3.848737272055193, 4.289913922570562, 4.622579219373021, 4.826068793408106, 4.886666562448183, 4.798537429145552], 'positive_zeros': ['1.30445875257028939355857812238959', '2.59519455053895040382739056238584', '4.01070555226233830347381057344413', '4.71460746623800598662832313814182', '5.66107777184493740711690035981682', '6.55052543829634552243760601657761', '7.50397179181763375031125998044270', '8.667544914260807429953378420835048', '9.281867785265370326489583635159061', '9.907782797180915955844132660634089'], 'prelabel': '2-1020-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.853899263493826, 'root_angle': 0.09443699907012097, 'root_number': '0.82906373106464409283993986002457716451727544173971830844 + 0.5591541199286396149569165155862722710751522894394880793*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.09443699907012096', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30445875257028939355857812239', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.59519455053895040382739056239', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.01070555226233830347381057344', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 8.144741006170603, 'bad_primes': [2, 3, 5, 17], 'central_character': '5.4', 'conductor': 1020, 'conductor_radical': 510, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1020/2/g/d/409/4'], 'is_instance_Artin': False, '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': '2-1020-5.4-c1-0-9', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1020-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.853899263493826, 'root_angle': 0.09443699907012097, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30445875257028939355857812239', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1653597920668694732294420894365', 'Lhash_array': ['1653597920668694732294420894365'], 'factors': ['2-1020-5.4-c1-0-9'], 'label': '2-1020-5.4-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1020/2/g/d/409/4'}