-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_441.310', 'a10': [0.36534102436639504, 0.9308737486442042], 'a2': [-0.2225209339563144, -0.9749279121818236], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.9009688679024191, 0.4338837391175581], 'a5': [-0.9888308262251285, 0.14904226617617444], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.6234898018587335, 0.7818314824680298], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.047995390047135, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '441.310', 'coeff_info': ['x^21 - 1', '0.955572805786141 + 0.294755174410904*I', '\\\\zeta_{21}'], 'conductor': 441, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_441.340', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^15', 0, 'a^9', 'a^10', 0, 0, 'a^3', 0, 'a^4', 'a^8', 0, 'a^8', 0, 0, 'a^18', 'a^19', 0, 'a^14', 'a^19', 0, 'a^2', 'a^16', 0, 'a^20', 'a^2', 0, 0, 'a^19', 0, 'a^0', 'a^12', 0, 'a^13', 0, 0, 'a^5', 'a^8', 0, 'a^13', 'a^17', 0, 'a^4', 'a^17', 0, 'a^10', 'a^15', 0, 0, 'a^14', 0, 'a^17', 'a^16', 0, 'a^18', 0, 0, 'a^13', 'a^18', 0, 'a^12', 'a^15', 0, 'a^6', 'a^18', 0, 'a^0', 'a^7', 0, 0, 'a^9', 0, 'a^13', 'a^20', 0, 'a^2', 0, 0, 'a^0', 'a^7', 0, 'a^11', 'a^13', 0, 'a^8', 'a^19', 0, 'a^11', 'a^20', 0, 0, 'a^4', 0, 'a^9', 'a^3', 0, 'a^7', 0, 0, 'a^8'], 'euler_factors': [[1, 'a^15'], [0], [1, 'a^10'], [0], [1, 'a^8'], [1, 'a^8'], [1, 'a^19'], [1, 'a^14'], [1, 'a^16'], [1, 'a^19'], [1, 'a^0'], [1, 'a^5'], [1, 'a^17'], [1, 'a^4'], [1, 'a^15'], [1, 'a^16'], [1, 'a^18'], [1, 'a^12'], [1, 'a^0'], [1, 'a^9'], [1, 'a^13'], [1, 'a^0'], [1, 'a^13'], [1, 'a^20'], [1, 'a^7'], [1, 'a^17']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-21e2-441.310-r0-0-0', 'leading_term': '0.414139190761651161171071802990-0.534769796601099570058585876966*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/441/310', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.6763800741310292, 0.38898855896871687, -0.17492760954583175, -1.0166052514670227, -1.7527501529651308, -1.9194316599010435, -1.32842013172911, -0.27184316100456396, 0.5905905817494546, 0.6506473549995341, -0.17892319242050697, -1.31293989537338, -1.8625622931180075, -1.3387607550973417, -0.17142533107886113, 0.4453180053881928, -0.5923122612258463, -3.3147423987273332, -6.375351829814289, -7.818966519096495, -6.478020156464691, -2.9468229178416228, 0.7148839698368199, 2.4379544639582615, 1.664484896585468, -0.3045826149099765, -1.4539378946664483, -0.7459986433883495, 1.0857504430290816, 2.3202302018628824, 1.8774281409869706, 0.28622717417016974, -0.8962833255078123, -0.6265678794572818, 0.6413659998865957, 1.4978183894258914, 1.077261271075666, -0.046857706822879173, -0.5340924631074834, 0.17236897547092553, 1.1062188296340358, 0.7626376844791777, -1.1345650546095907, -3.016204279394971, -2.878132907360377, -0.43767166368726995, 2.2449378092286176, 2.572169614573989, 0.013121484068199792, -3.1538027394973014, -3.9018632054723112, -1.4014553268164593, 2.108079812426437, 3.473298518639229, 1.6770053064405102, -1.291585485311321, -2.5707510565661096, -1.2773654954040206, 0.8758434947128614, 1.6697914941766199, 0.748447773699919, -0.3068200498758612, -0.07294552444391722, 1.01994291477673, 1.3705594576809452, 0.3443205121534069, -0.8171945379407133, -0.5045770984652348, 1.1437359287044135, 2.19552717501131, 1.183719760896552, -0.9978924709830038, -1.9995926934688015, -0.8444521034380412, 0.7057931902313661, 0.13901430783722454, -2.574386729321949, -4.397822429128204, -2.3630338515213456, 2.897637170847056, 7.321876480842277, 7.381236405446664, 3.5979759553258734, -0.21909811035939716, -1.068045001604505, 0.4359969743745691, 1.4620593957125108, 0.5534916684232317, -0.9411404330146887, -1.0183721651664037, 0.25556972135143646, 0.9346779291601983, -0.10610890470491405, -1.5925935447724142, -1.4943373650663077, 0.2726564722223957, 1.6729765641378067, 1.1877366339253028, -0.21427732236653732, -0.4468450503807929, 0.7536973437741259, 1.3554140781237047, -0.068362663985336, -1.8115115839187592, -0.5878691856797378, 4.257404114347982, 9.116287341878795, 9.601378037740492, 5.403263508609974, 0.7487867228786558, -0.24841243827713788, 2.0673847079266885, 3.8623336177880834, 2.626813753666602, -0.13796330728533063, -1.3545933219026005, -0.4243269507024198, 0.3297674110350498, -0.9257356279554156, -3.0183818341975126, -3.431331776169074, -1.7096097759556792, 0.0410013055104062, 0.08618753439356903, -0.750584800811523, -0.6433944156305562, 0.2989152544642868, 0.07555231263063479, -2.0858112372266446, -4.050938472189425, -3.3505571016814844, -0.7883854421693852, 0.09434189047852361, -2.432944728361247, -5.586337723167175, -5.175436806854202, -0.9365285107307125, 2.7893953019126254, 2.196753965929527, -1.4030613372981344, -3.356838064832897, -1.4785599374777743, 1.5215684984189548, 1.843237010523902, -0.584455192517328, -2.44620596420031, -1.6160819257116532, 0.36853719301961596, 0.9128512937969843, -0.03438031507646594, -0.4199508722576879, 0.4913419081120663, 0.9800612646401256, -0.31404554153373776, -1.959451747177975, -1.5473258969910808, 0.7198996680791023, 2.0415122674622106, 0.9415958169911255, -0.4859708505110283, 0.46327650533202597, 2.935825998238683, 3.3343779560482343, 0.48190306683035, -2.040747780559579, -0.21877438541080657, 4.780272907174066, 7.409602328266958, 4.401037578793294, -1.2112759197493257, -3.877213446263374, -2.093011639905739, 0.6340475230287276, 0.9903397780484295, -0.20428561600078418, -0.21692613249126913, 1.1962464881472317, 1.7126274507183932, 0.3375437989740357, -0.9047067527416219, -0.05059265297536056, 1.715187456460082, 1.7385013649019436, -0.13684091126372702, -1.326464017951446, -0.3999206933976984, 0.8225712127139704, 0.2698608073760493, -0.8654623578774496, 0.19138920490875985, 3.043220389816396, 3.675172448718098, -0.08629857621700242, -4.631908835608563, -4.376545842424955, 1.0796586927637626, 6.048510199195813, 5.632026168030487, 1.3995291142101014, -1.3882123249054648, -0.727475019131222, 0.4842294296306075, -0.44195101075076737, -2.0457180366392365, -1.394318882809369, 1.1758396626136118, 2.4719232153721498, 1.1455966055824034, -0.5283690457584204, -0.2744112713790716, 0.912712404290902, 0.7568567747611958, -0.47232484121324814, -0.4857692494874587, 1.0208909558582502, 1.5102553181876617, -0.3344201009156849, -1.974561121874102, -0.5477038598089883, 2.2902026557255626, 1.9443171006883002, -2.5392085951166194, -6.328402705812316, -4.862667268436496, -0.01809158501749815, 2.382037521284725, 0.386134123623697, -1.8436853777224718, -0.28574818135056035, 3.2964751754375783, 4.159943080449986, 1.3367476367587316, -1.4221962866146516, -1.2709445329955538, 0.17461352095892346, 0.1057518472875692, -1.0828502978852461, -0.9935799918987913, 0.48847840960491773, 0.9878638814982551, -0.2805525638473932, -1.028163549873633, 0.33972235682593993, 1.8034011557627045, 0.7409692127738029, -1.618856625968011, -1.638119646791682, 1.1226934251553633, 2.8909590043116196, 1.3851726769661283, -0.3386855470348529, 1.6535039979761028, 5.599834132881064, 5.559532038045637, -0.3318033629878412, -6.578560343882593, -7.076628948805757, -2.6493173553581957, 0.8813449425933092, 0.7007889770172586, -0.38612328856486494, 0.590183856090275, 2.2925659879285685, 1.9412601057644423, 0.07264966084411618, -0.5440020476710838, 0.37939956641704486, 0.2777568261695548, -1.7332862983617972, -3.033000954981959, -1.5688337457819925, 0.7528674165834475, 0.998034447857956, -0.2168743955074247, -0.02666267264801501, 1.5893103819173966, 1.5742436879237907, -0.6523854327605629, -0.9853319263222639, 3.514733231742624, 9.030282788964419, 8.978027588513537, 2.916925289373705, -2.401461198140012, -1.7768366062640322, 2.1260962519709072, 3.429705096025513, 1.2419842586195693, -0.3724908705814387, 0.6144227670605067, 1.4800439818174358, -0.1691061017532822, -2.320582099537879, -1.9271432775015802, 0.13357749787073134, 0.5968269380077152, -0.9244527618709195, -1.6100749197884818, -0.29020799309027484, 0.7618328425447083, -0.05636372553357077, -0.8909429731814799, 0.0728077429172796, 0.8508124468773022, -1.3379336988127435, -4.695865819679583, -4.494802014038591, -0.32558394874074803, 2.3607789299515796, -0.14623607132921987, -4.074495220229506, -3.3509342370380537, 1.6105968974775908, 4.591857718169435, 2.632386221711054, -0.1329512709412262, 0.8077266711218591, 3.731106697563601, 3.9458212381326736, 1.1318187212692252, -0.6766890396314904, 0.373557692467139, 1.6275444376521437, 0.8488048107109905, -0.2910629200548599, 0.37703716693855593, 1.607381694098549, 1.1305520727544338, -0.06264107471345597, 0.654522179884105, 2.5646455454258, 2.1436079184190104, -1.0881026747192204, -3.1355784548065926, -1.55545730170109, 0.6521675459967204, 0.10062710694461158, -0.8843129786254547, 2.4015568293951435, 8.778736419438093, 11.349559710946401, 6.980445766212713, 1.0891806970358044, 0.22785666450274034, 3.3374772280937304, 4.337361054982432, 1.3574373603088565, -1.4111460409431213, -0.8677318471876723, 0.8040152797954222, 0.6916113688222838, -0.12758563044160096, 0.6412295911611057, 1.8763166056479839, 0.926916753338078, -1.3781916932389509, -1.6207688516074423, 0.6102841825702862, 1.956861759862929, 0.8061731549005267, -0.2970296137007502, 0.5169029900782391, 0.876497467290278, -1.501670517689737, -3.8807982493984152, -2.307470005896023, 1.1506944546757254, 0.21171363134557575, -6.057519216600933, -10.602587635600493, -7.765519876270909, -1.1649147840987153, 1.6239168660716348, -0.6193154068419504, -2.5992802402603132, -1.3462189629502217, 0.25922418882901455, -0.4032110633937099, -1.1681940950382421, 0.6066195566785931, 2.9983322228634752, 2.5461467401481754, -0.0007649176868390876, -1.024855152625284, 0.06954749280330541, 0.5096100276651548, -0.5218284718389091, -0.5612357755586207, 1.2106260245188025, 1.949651894059708, 0.17615248888781526, -1.0089939497164506, 0.9379173708097608, 2.7743094796160443, -0.009278573710460505, -5.192047220906619, -5.835365193471845, -0.46255191682203245, 4.277726124412645, 3.1276543111402484, -0.5442357424939823, -0.6959541438052348, 2.070327395835508, 2.3341594233135874, -0.9766897459272121, -3.1017387946282278, -1.3381327249979615, 1.0262812990391077, 0.5587388287570672, -1.0866700103184428, -0.8209695559720683, 0.5137556150329919, 0.26588485012304647, -0.9416427412396557, -0.5500935635610883, 0.8384397049678654, 0.2671844609029196, -1.9531427613236507, -2.1450226818840026, 0.3746187720962186, 1.546458338186384, -0.741031255968965, -2.6890937642902064, -0.8014295345685928, 1.7489237078574964, -0.042251628112201206, -4.196971291686447, -3.8966916414944794, 1.842911419171437, 5.92018051786027, 3.433885694086114, -1.3429853468057105, -1.8384497062281306, 1.3628996552492019, 2.8019312556638036, 1.0457517122079458, -0.3419863259887782, 0.27670335074975055, 0.43394029898560615, -1.0093807665516916, -1.4299629741982083, 0.5795315775963495, 2.17342076032933, 0.9924226902234156, -0.7022413631533151, -0.05443979938028317, 1.2714248953259857, 0.1440485568583039, -2.15962155304451, -2.0096365204934212, -0.045070545449974846, -0.17992696224515362, -1.9801274116358123, -0.17836290500157845, 6.175777430459884, 9.940945693871559, 5.414140805936847, -2.7744130415023935, -5.683771585732053, -2.178748743183159, 1.0415414711891553, 0.2651746510067369, -1.0579088855523056, 0.19355784868811687, 1.5669920128763297, 0.25614574598244777, -1.510228430101991, -0.47245798732559563, 1.8265925164685481, 1.8035143410430587, 0.024152405910984612, -0.17933859833728705, 1.179840391555789, 1.0381184126401966, -0.8157277207681273, -1.268026799018802, 0.261813634133619, 0.7175195146618047, -0.42262128211896, 0.7269528385324641, 5.272090725720781, 7.585288895967683, 3.1625279983928842, -3.48613975223459, -4.644214321497563, -0.682198282265069, 1.0799964267581512, -1.9199660519602435, -4.074707177373455, -1.3829433318065703, 2.145003436070893, 1.479714093667219, -1.466215487197223, -1.8500786819423536, -0.046552963639103814, -0.09452847264466233, -2.210751127171868, -2.7342328754625984, -0.8119027015403961, 0.46610997431822043, -0.09112357550101079, -0.10974062565773261, 1.0851452026902355, 0.732597731736488, -1.816269911192826, -2.774400271658637, -0.16272398067656585, 2.170489936102537, 0.7582121270395457, -1.3464484897163744, 0.19706396699387269, 2.929793934513156, 1.2630617261441188, -3.4475046951033503, -3.920924113727824, 1.437494496281621, 5.309150328302665, 2.483680171199692, -2.438798877256265, -2.6963619816998636, 0.6080345988134798, 1.7758501130942428, 0.06880818909491498, -0.4710309732097021, 1.1395944531428337, 1.7022552768820325, 0.266684934566878, -0.4049281864415419, 0.3981896641491764, -0.2458780134195881, -3.052964181833546, -4.364540867434297, -2.2582015456383653, -0.0028619832382528855, -0.3274052707189173, -0.8209194222245988, 1.0286888523294766, 2.549217912427774, 0.7741527355849008, -1.0356756536104443, 1.7446584380553083, 5.9856620297550585, 4.105075690205422, -3.7182891491109067, -8.380063887389012, -4.779586400404005, 1.253726126792669, 2.485171880400116, 0.32140445288954017, 0.18942116651120045, 1.9996817661398039, 1.7558586964855878, -0.4357024105974966, -0.8584713115841685, 0.6197230201970967, 0.3811878317293711, -2.0026927084234156, -2.779575466295361, -0.7628262901630012, 0.6590374040267689, -0.25260814151568484, -0.8204660402009825, 0.4772124918588544, 1.055932631554665, -0.24183906309945588, 0.0007691608441132766, 3.3585440393182573, 5.034981060263691, 1.1528000034207009, -3.6286556240233248, -2.492922321743015, 2.3873714857712303, 2.7861001812637394, -2.5727254765967063, -6.150506975371614, -3.6904830938471256, -0.1352481024483298, -0.4967931554006027, -2.085172472671959, -0.5989030803584617, 1.8987578645670657, 1.0503689502912825, -1.8513394850382197, -2.2867205176865992, -0.2606882772102838, 0.5155136227223325, -0.47598058946802, -0.5401037573637184, 0.28238520602809886, -0.6468952957945497, -2.6535912018554413, -2.124162302257693, 0.6514016157563902, 1.2287120421761073, -1.1064373147634674, -1.670190516930176, 1.074149128550496, 2.0115258674932983, -1.6946132128429188, -4.5889231731035105, -1.4998114805092229, 3.2647771986978236, 2.457335723949388, -2.1995482882101864, -2.8537508644051695, 1.5999639395544727, 4.119524774479531, 1.2268528896212043, -2.16408319143511, -1.6690620216891756, 0.23256005475018512, 0.1217794260521326, -0.48820394059834615, 0.5616076385193198, 1.2164595674645948, -0.6289729895655597, -2.431085516210511, -1.3626172189982846, 0.3318685273221358, -0.5646643673269215, -2.146555196921128, -0.9461275174305995, 1.3580951242212378, 0.9982225830525486, -0.4882527815753082, 1.0977443943414826, 4.131369126279153, 3.252657714917653, -0.21221341663390403, 1.3939659399364677, 9.303603399216763, 14.415475002699983, 10.220947317772419, 2.2394420906948844, -0.9053567614357392, 0.4813398256023415, 0.7075978855590268, -0.7690376183831279, -0.1785331906262519, 2.1755310105148142, 2.319031439872483], 'positive_zeros': ['0.546957046619162597229577705359', '2.26852708290320297829477949724', '3.07389753520746535278759950284', '4.42509533206697208980962236223', '4.88864356451844404096343402101', '6.80451615382582633017728318568', '7.76314445305826481700507408337', '8.57198665205045273358044689419', '9.74314785812930320191051078543', '10.47697531640474814004290129657', '11.54828341879290011489205015809', '12.13642688953587699693121415498', '12.96010267276111818955577888125', '14.10728879605569100230047343477', '15.00120168104857327769021182496', '16.05629661507873899368438379926', '17.045641374299531243892191079752', '17.98921974355351473062301056204', '18.9399182204121960336444252783', '19.39940934915288170464307540294', '20.38856875654967991116957405926', '21.04736246261139768430001070729', '22.04421486722564172861889040442', '22.95718375993152469880778091338', '23.45894331213773546846129722709', '24.52705927604694250588887389821', '25.91207545575380900695287680958', '26.485927024521906800483284662526', '27.29203495932320456644244019568', '28.067212478370033248579371616714', '28.72955243315322109760552865176', '29.64507256189399993138755976208', '30.56947605334317347621974949979', '31.07655640918714778857957963041', '31.86492010590556244627199111349', '32.5505387504044940982958748775', '34.15275317131220303293880475922', '34.42890717645977058739918394077', '35.60739225400915951117314494328', '36.35804922316541923039642785431', '36.70684867330239461598782826999', '38.11252170293145436431208439211', '38.47217305801609485816227483940', '39.26901080859273698043872644127', '39.70457867072244748257202216469', '41.07326545704340004055723285854', '41.27726284924918064745915923308', '42.56106366477292507404614439169', '43.32122371926237799560415110234', '44.202741750404353670237434566145', '44.93491870489944217885987302601', '45.87073474599159420732965428297', '46.55199815759735970953705641936', '47.04860124039039872699510462800', '47.759996883008200941682348953113', '48.65674861184447339626006760372', '49.54191873820861523306046642650', '49.92689852453831390556473704628', '50.98032188699895708389069450557', '51.57865644014145566092206408711', '52.740269332055765658091312272805', '53.65847537650648136391521856153', '54.31593096231680738990881773861', '54.747774703431719966838931022932', '55.68483682777311542099752615058', '56.25885947488845331056937712280', '57.166557168395708843768557009858', '57.892121535184249627076663553888', '58.498382345809479902222264619542', '59.03695731359443256788155459150', '59.99477931244477785033575264892', '60.884781354490177649057110468', '61.98743428852666885055969264844', '62.64313661092509865744542012798', '63.042186569472828212188963132646', '63.9251405820308799512555456215', '64.87091798868488524672818691616', '65.38176544674492363636320017632', '66.125294029341349328861305642167', '66.678953856054482038415961601554', '67.45639254377452749081627260469', '68.18248135552081150805224895840', '68.90710107021570886448060330398', '70.001254984352961430203001302329', '70.66418344804781536256297248675', '71.27596429977366488053137476704', '72.31009121637710208314200528592', '73.07556996725303832918229183319', '73.46840279557136922390764669395', '74.27562196923745063489454130357', '74.943119879486732021397231781210', '75.5708022319168014204180291534', '76.34393447830970776664410523322', '77.074604681107885617965699477732', '78.00928561074472031416135752314', '78.259547808031700010707361421384', '79.3609210653416853450426996388', '80.50949023578703345993225595618', '81.09473260894452553807680334911', '81.45111919705825576347182988823', '82.514238484695838490415825739606', '83.00835548446590471776796211229', '83.49673318718994380723915856193', '84.56847963087923064255965881535', '85.24820699740261114427410960642', '85.63137735840864065469026932849', '86.4759412205340554747764938115', '86.97770587428398325697167327821', '88.263762536628304981318288837321', '88.89345122390660541081295678211', '89.86505537561569700126478937083', '90.18464057459113350986920040939', '90.9164986997418779553887336083', '91.85153028693034250786986157177', '92.331265881764555571665417273084', '93.18006249322552764318787225630', '93.73672540182406590655403913001', '94.35967836099296196289979963557', '94.86364216299825255883069100163', '95.96032961598985499376948120120', '96.55199866631125884574401008012', '97.40494876568003471942924428739', '98.40826780388959549813696577574', '98.635941401805296387091100346026', '99.82235929391991616764186307841', '100.24512675962060706941602528330', '101.12828320747650050454438520784', '101.47055548942668953889255844489', '102.469044837148832133395986168680', '102.661391597671052645334975287801', '103.654407227907724356871496613499', '104.5620701668306723136162943105', '105.01891019487563667223323812468', '105.459479792367967433447480075053', '106.99881177558668548049462713919', '107.14569800244433325158350136535', '108.2439412361867656291510138886', '108.89301357481558551198942671070', '109.59980149869621822427945811075', '109.83123242396489178140366534407', '110.74686329265909440791885902467', '111.48631905351628588484592916084', '112.353927322296251446826270066810', '112.67689227235955627794435261548', '113.278810311597798844487399585981', '114.25382495580519647122311697140', '114.70247976027513717169884911648', '116.008675756823138484950112286358', '116.50044259436762008426950671015', '117.40993672138263907945499964159', '117.71352553463761118202534239274', '118.36564301158013067518812027238', '119.37489607347341838039601136064', '119.98289339231821179830912807878', '120.48389317603189030925102132565', '121.05577349022528228023327111959', '121.90006014731496245045930517830', '122.39251784975896069114268789222', '123.124424937664967738966473137138', '124.08497051908940655075917276071', '124.94170152649552820376815819896', '125.39936857282132698172197677954', '126.16880986338796142123201382986', '127.021470646787802087717502782888', '127.59529060102869412164046827838', '128.300338756368189857228139264996', '128.81516178028684481331166636112', '129.488338291410106002739179368882', '130.041439987326710924127032116972', '130.89470996976907047813099759768', '131.486335231106358970219030280493', '132.26359842839702069112322727281', '132.80920842901388956775298009031', '133.66118908866114999515648304284', '134.583831423660713756973805061073', '135.188191739218406531476963611340', '136.11196628047505748865100465751', '136.4713425279483885421297038949', '136.99044382660122628129624762834', '137.7398379889179464279817594180', '138.5864688116016338580480285128', '139.072846567167173638975330600695', '139.70624712993459460318708551525', '140.6350843563987370292373393737', '140.90030921000085634801515870211', '141.574068481345940925248214806676', '142.69865390491323963908043296032', '143.60406194547980179403648377488', '144.10496333343345510796750725692', '144.65771953077577419348743711956', '145.34745769816529143072994215300', '145.99759778373877641990857776422', '146.88035298447235249514897779331', '147.23638588546150553135989906212', '147.991414468923486827863900717653', '148.69945295934831030294604687656', '149.25374567633596682099939408232', '149.60404061813910203281912175377', '150.76154907085967750210895272647', '151.61882268767086009262479950887', '152.02533861364550158624884994599', '152.9135401876367501751465824598', '153.58768079882213970774059228362', '154.38545202496418266306878946669', '154.6675207802320010573715405820', '155.760588541653981492085600459778', '156.21363946161743042701046758439', '156.59844512286276861563464325584', '157.291368545548752972019600016864', '158.139929377411240906024905183367', '158.83568321349079511993571014291', '159.35522921557539817173880177347', '160.08503823089444713583852227257', '160.86559496729849770131442740596', '161.70408282764807052845872879059', '162.44114383012760716910864439947', '163.137301185262824102383250713914', '163.55110498394917398992207912173', '164.43266467772387475565128881957', '164.85611993218496853370682238962', '165.27195771981593366447352715612', '166.563415669141376730437116508453', '166.772492452775163132451964306700', '167.36453688263900332926111328438', '168.21264610567765925223960572950', '168.61882497354233407247085624768', '169.54835878680503376400665515045', '170.54532254602335079774332680426', '171.31870242648811439975631371925', '171.51589837342210440990373310854', '172.433184746123924651055137354483', '172.995142751448112065589969817288', '173.49758752532300075213811201066', '174.4847283013291077964387359510', '174.94189360800190011609701219517', '175.530578879818127242671532379485', '176.195301015866629151243401423252', '176.56238637854870120625225462676', '177.5621743388782396261532317017', '178.28082828863648155248560988635', '178.93023670310236902797185158011', '180.02617559702786103178274787909', '180.21786683929395821618872512814', '181.00092800192169696676344788880', '181.673476100047545092821242314454', '182.544950898657489884146387306733', '182.989323780207155222553591367060', '183.61519465154699361410268702791', '183.94108732422915249473353911234', '184.92317777820372923766894240773', '185.4905803063221371907214472964', '186.14240430688411640937485037649', '186.76013004597292543574568834958', '187.584812093849557887839079435375', '188.28776489912542818805357988750', '188.962811849959560274362449557428', '189.77714107366761683623828683889', '190.56914919643863349667588163630', '190.97693840629650334616026843846', '191.44002284117560709866243340966', '192.10885127036712166344386598966', '193.02660446133090237367893781056', '193.33707958486975373631101376028', '194.17486247757116540796988958084', '194.85862048701904805869722795559', '195.18478867604674983698145894794', '196.22198407554893976560852629973', '196.462883506563311694394299052613', '197.952253241233874146417899517509', '198.35119015173436482853500913219', '198.89518081751751994651747537350', '199.40089690002076589534613033657'], 'prelabel': '1-21e2-441.310-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.047995390047135, 'root_angle': -0.5804988662131519, 'root_number': '-0.250207578003279121113896166955-0.968192216406294496552304850012*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.290249433107', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(21)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.615238903895641300944352954515-0.308067721141729325233175808333*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.546957046619', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.2685270829', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.07389753521', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.047995390047135, 'bad_primes': [3, 7], 'central_character': '441.310', 'conductor': 441, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/441/310'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-21e2-441.310-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-21e2-441.310-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.047995390047135, 'root_angle': -0.29024943310657597, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.546957046619', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_441.310', 'Lhash_array': ['dirichlet_L_441.310'], 'label': '1-21e2-441.310-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/441/310'}
Lfunction data - 1-21e2-441.310-r0-0-0