-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '576690688475882535425382238809', 'a10': [-2.1213203435596424, 1.224744871391589], 'a2': [-0.8660254037844386, -0.5], 'a3': [0, 0], 'a4': [0.5, 0.8660254037844386], 'a5': [1.224744871391589, -2.1213203435596424], 'a6': [0, 0], 'a7': [-1.0, 2.449489742783178], 'a8': [0, -1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.067265720149466, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, 0.5]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, -2.449489742783178]]], [11, [[1.0, 0], [0.8660254037844386, -0.5]]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '1386.89', 'coefficient_field': 'CDF', 'conductor': 1386, 'conductor_radical': 462, 'conjugate': '1763783557816216481386010596376', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.224744871391589, 2.1213203435596424], [-2.5, -4.330127018922194]], [[1.0, 0], [1.0, -2.449489742783178]], [[1.0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [0, -2.449489742783178], [-13.0, 0]], [[1.0, 0], [-0.8660254037844386, -1.5], [-8.5, 14.722431864335457]], [[1.0, 0], [1.5, 0.8660254037844386], [9.5, 16.454482671904334]], [[1.0, 0], [1.0761584028214513, 0.6213203435596426], [11.5, 19.91858428704209]], [[1.0, 0], [0, -7.242640687119285], [-29.0, 0]], [[1.0, 0], [7.242640687119285, -4.1815405503520555], [15.5, -26.846787517317598]], [[1.0, 0], [2.6213203435596424, -4.540260017959206], [-18.5, -32.04293994002423]], [[1.0, 0], [-8.363081100704111, 0], [41.0, 0]], [[1.0, 0], [-1.0, 0], [43.0, 0]], [[1.0, 0], [1.3733313399617268, -2.3786796564403576], [-23.5, -40.703193977868615]], [[1.0, 0], [0, 0], [26.5, -45.89934640057525]], [[1.0, 0], [2.30090327421304, 3.9852813742385704], [-29.5, 51.09549882328188]], [[1.0, 0], [-9.0, -5.196152422706632], [30.5, 52.827549630850754]], [[1.0, 0], [2.242640687119285, 3.8843676132117797], [-33.5, 58.023702053557386]], [[1.0, 0], [0, 1.2426406871192852], [-71.0, 0]], [[1.0, 0], [4.242640687119285, -2.449489742783178], [36.5, -63.21985447626402]], [[1.0, 0], [4.0, -6.928203230275509], [-39.5, -68.41600689897065]], [[1.0, 0], [7.942815102630085, 0], [83.0, 0]], [[1.0, 0], [-2.956795678960466, 5.121320343559643], [-44.5, -77.07626093681505]], [[1.0, 0], [0, -6.631030293135233], [-97.0, 0]], [[1.0, 0], [-6.9897497607423835, -12.106601717798213], [-50.5, 87.4685657822283]], [[1.0, 0], [-9.878679656440358, -5.70345835888392], [51.5, 89.20061658979718]], [[1.0, 0], [2.1523168056429025, 1.2426406871192852], [53.5, 92.66471820493493]], [[1.0, 0], [-9.121320343559642, -15.798590267156909], [-54.5, 94.39676901250381]], [[1.0, 0], [0, -10.242640687119286], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-1386-21.5-c1-0-3', 'leading_term': '0.908923277435160111959484847697896262052182433258163275', '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/1386/2/r/b/89/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.9089232774351601, 0.8180744370787789, 0.7199644264527958, 0.614328840718506, 0.5008649775660595, 0.3792919180960231, 0.24941293747245738, 0.11117666904657146, -0.03526610224755526, -0.18951253969875437, -0.3508666477598743, -0.5183083072496504, -0.690473368261765, -0.8656454030661969, -1.0417595038222447, -1.2164183503596848, -1.3869206330025576, -1.5503017624369517, -1.7033866109055986, -1.8428537947752957, -1.965310725072824, -2.0673783245203903, -2.1457839470316773, -2.197460652637419, -2.2196506042161936, -2.2100099807844895, -2.166712464955709, -2.088548079221041, -1.9750139361552677, -1.8263933495370892, -1.6438197428216472, -1.4293219019062675, -1.1858473608288893, -0.9172610880261558, -0.6283171584745509, -0.3246017496593564, -0.012446577481258516, 0.3011872232820881, 0.6088537915331275, 0.9027937825633803, 1.175129066817933, 1.418076724896495, 1.6241771585333267, 1.786530204179869, 1.8990323328705554, 1.9566073893316525, 1.9554229042749296, 1.8930838415803088, 1.7687957454520635, 1.583489652466122, 1.3399018409376167, 1.042602505483473, 0.6979687562829744, 0.31409892595800903, -0.09933301499187984, -0.5312821302974622, -0.9695933469180512, -1.401313330955791, -1.813046147828898, -2.1913434026404364, -2.52311771358989, -2.796066812551602, -2.999094373999545, -3.1227129193086376, -3.1594138890126384, -3.1039902661305527, -2.953797995725341, -2.708943884653004, -2.3723896630495127, -1.9499644033741468, -1.4502804574784232, -0.8845513977408579, -0.26631402430836726, 0.3889398013970175, 1.064212058409212, 1.7415152564613146, 2.4024407827556042, 3.028760059928067, 3.6030375667376604, 4.10923340099655, 4.533272520472881, 4.863558149438047, 5.091408119219781, 5.211395115480885, 5.221574887644137, 5.123590350899776, 4.922644053213594, 4.627336527298764, 4.249373408303587, 3.803149655650801, 3.3052245400902525, 2.7737060067143275, 2.227567368161549, 1.6859228017887327, 1.167290628958055, 0.688874689206146, 0.26589417822641576, -0.0890089590813132, -0.36625859744730616, -0.5597063527745343, -0.6668492602294166, -0.6888915796560838, -0.6306457818372218, -0.5002748855048181, -0.3088855501334124, -0.0699883494232576, 0.20115188289135957, 0.48824715526192763, 0.7747659764418631, 1.0447256926119153, 1.2834602627718508, 1.4783266106344168, 1.6193148545375229, 1.6995316198266637, 1.7155311484260543, 1.667475820702461, 1.559115700377561, 1.3975854432174584, 1.1930259629595559, 0.9580471800478063, 0.7070565363514312, 0.4554853005822839, 0.21895060861133833, 0.012395332329758773, -0.15075001945879565, -0.2593392683152767, -0.3051746843660447, -0.28352614856689656, -0.1934749210176543, -0.03806002116418425, 0.17578494246598164, 0.43750590969785186, 0.7334037698360552, 1.0472904064756823, 1.361294640610906, 1.656778557983498, 1.915317806836897, 2.1196948503921482, 2.25485217382674, 2.3087532664955575, 2.273102868328157, 2.143884372306196, 1.9216811464499393, 1.6117594678479157, 1.2239032096370128, 0.7720037490586379, 0.27342206019319565, -0.2518471248864306, -0.78216759412648, -1.2953592700413836, -1.7698430437941455, -2.1857707639942228, -2.526077747033442, -2.777398118423548, -2.93078968454229, -2.9822246091473668, -2.9328144760911954, -2.7887527346607044, -2.560973281274648, -2.2645401631498885, -1.9177991727792614, -1.5413365096267158, -1.1568018403612446, -0.7856622172241663, -0.4479587936355744, -0.16113967845161525, 0.060960607429534984, 0.20893172350666853, 0.278335860880772, 0.26995602651138406, 0.1897235491402004, 0.0483229209791825, -0.13950844531331785, -0.35594900395370255, -0.5812765627557628, -0.7951980668163444, -0.9782464277297513, -1.1131587768546027, -1.1861491562507454, -1.187992542888934, -1.1148461634863873, -0.9687479162039836, -0.7577496855942364, -0.4956644606681689, -0.20142926154160137, 0.10189039248934907, 0.3884058046772618, 0.6309508214551831, 0.8027813872491641, 0.8793299055226758, 0.8399085386265709, 0.6692549630944566, 0.35881994386987703, -0.09229174736951316, -0.6767976069303523, -1.379178599677687, -2.1761065834163094, -3.03735068692657, -3.9271263448015423, -4.8058229613579755, -5.632021469344308, -6.364692962026562, -6.965455468525568, -7.400758843788399, -7.643868287173279, -7.676525366321749, -7.49018130863617, -7.086719962688133, -6.478616020588579, -5.688506249763218, -4.748185742442696, -3.697075509548814, -2.580240023721766, -1.4460615300248332, -0.3437002718446416, 0.6795152742090735, 1.580617570228617, 2.323300547865552, 2.8798550334666406, 3.2326226886810585, 3.374879588541005, 3.3110939003772, 3.056539336637026, 2.6362848792959888, 2.0836193157696647, 1.438003994587799, 0.7426766707994277, 0.042051438031901665, -0.6209269575379, -1.2073126116683472, -1.6844165701733496, -2.0276548014875755, -2.2218726267130333, -2.2620649183009167, -2.15344945403577, -1.9108918526686924, -1.557721903468671, -1.1240201591909682, -0.6444878331387807, -0.1560400563718948, 0.30471941736757807, 0.7039761826610113, 1.0129730047728513, 1.209918448519076, 1.2814109507795268, 1.223285064241759, 1.040825027746838, 0.7483330662849654, 0.36808309087271657, -0.07126814298896288, -0.5367036511821195, -0.9931643290558722, -1.4060039987122301, -1.743413258207881, -1.9786458258754118, -2.0918942731622834, -2.071685784585977], 'positive_zeros': ['0.45492873854361321779354912077825', '2.11169663435721733875371032799060', '3.15028136939763680781396950707235', '4.24288101465527373997218789787333', '5.66768720051519828286214799695178', '6.16800769161298754043182702860693', '7.21094747845942552182034397946173', '7.57021684937986702427255611666672', '8.585408910169913929301937714097083', '9.708484705143657379454642323884131'], 'prelabel': '2-1386-21.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.326750023694216, 'root_angle': -0.36552484602631985, 'root_number': '0.4100110303924027941235994973214839026079356334125846281 - 0.9120805638519878865860376491029999747098235219142617667*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.18276242301315992', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.45492873854361321779354912078', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.11169663435721733875371032799', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.15028136939763680781396950707', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 11.067265720149466, 'bad_primes': [2, 3, 7, 11], 'central_character': '21.5', 'conductor': 1386, 'conductor_radical': 462, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1386/2/r/b/89/2'], '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': '2-1386-21.5-c1-0-3', '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': '2-1386-21.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.326750023694216, 'root_angle': -0.18276242301315992, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.45492873854361321779354912078', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '576690688475882535425382238809', 'Lhash_array': ['576690688475882535425382238809'], 'label': '2-1386-21.5-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1386/2/r/b/89/2'}