-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_847.837', 'a10': [-0.32706796331742166, 0.9450008187146685], 'a2': [-0.9954719225730846, -0.09505604330418266], 'a3': [-0.5, -0.8660254037844386], 'a4': [0.9819286972627067, 0.18925124436041021], 'a5': [0.23575893550942723, -0.9718115683235417], 'a6': [0.41541501300188644, 0.9096319953545183], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9594929736144974, -0.28173255684142967], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 3.933451463423862, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '847.837', 'coeff_info': ['x^33 - 1', '0.981928697262707 + 0.189251244360410*I', '\\\\zeta_{33}'], 'conductor': 847, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_847.254', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^17', 'a^22', 'a^1', 'a^26', 'a^6', 0, 'a^18', 'a^11', 'a^10', 0, 'a^23', 'a^12', 0, 'a^15', 'a^2', 'a^19', 'a^28', 'a^14', 'a^27', 0, 0, 'a^2', 'a^7', 'a^19', 'a^29', 'a^0', 0, 'a^3', 'a^32', 'a^10', 'a^19', 0, 'a^3', 0, 'a^12', 'a^32', 'a^31', 'a^1', 'a^11', 'a^6', 0, 'a^18', 0, 'a^4', 'a^19', 'a^5', 'a^24', 0, 'a^3', 'a^8', 'a^13', 'a^31', 'a^17', 0, 0, 'a^3', 'a^20', 'a^16', 'a^16', 'a^5', 'a^27', 0, 'a^3', 'a^5', 0, 'a^28', 'a^20', 'a^24', 0, 'a^3', 'a^29', 'a^13', 'a^16', 'a^8', 'a^15', 0, 'a^18', 'a^26', 'a^28', 'a^22', 'a^23', 'a^9', 0, 'a^12', 'a^2', 'a^25', 0, 'a^8', 'a^21', 0, 'a^3', 'a^32', 'a^22', 'a^7', 'a^8', 'a^18', 0, 0, 'a^20'], 'euler_factors': [[1, 'a^17'], [1, 'a^22'], [1, 'a^26'], [0], [0], [1, 'a^12'], [1, 'a^19'], [1, 'a^14'], [1, 'a^2'], [1, 'a^3'], [1, 'a^10'], [1, 'a^32'], [1, 'a^6'], [1, 'a^18'], [1, 'a^5'], [1, 'a^31'], [1, 'a^16'], [1, 'a^5'], [1, 'a^28'], [1, 'a^3'], [1, 'a^13'], [1, 'a^26'], [1, 'a^9'], [1, 'a^8'], [1, 'a^18'], [1, 'a^16']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-847-847.837-r0-0-0', 'leading_term': '0.535520662015681683616553677469+0.0166373936698746018215539558962*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/847/837', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.53577904243619, 0.670943937520952, 0.5426624387302638, 0.03868776071965967, -0.5092073420806459, -0.5424466344375308, 0.15678285506142497, 1.0379658996008465, 0.9668562771880214, -0.919368502683088, -4.2638223099378605, -7.32495715704605, -8.005595449933974, -5.472644649014319, -1.0521587776215324, 2.537894361358186, 3.199699777697383, 1.08928137549288, -1.5965319702092815, -2.571667423919845, -1.413026217030506, 0.29142982824108205, 0.6957876174392306, -0.43197290468142524, -1.6207755234857006, -1.426358780287925, -0.0657673402973825, 0.8690046000040531, 0.3107811105090577, -0.9486846736639454, -1.1091567673961114, 0.48364429336766923, 2.386836808132816, 2.56512536806464, 0.739442044643348, -1.1805274112554545, -1.2290565501430013, 0.3396584667176837, 1.3957403082375304, 0.6130682757417993, -0.7494724444763216, -0.3428657123924675, 2.081575451065097, 3.747058017085548, 1.7698857230228175, -3.168399094073107, -6.8368574857730815, -5.618392331579308, -0.37517386977360423, 4.366454798256027, 5.063698150844583, 2.4505759702026406, 0.004134042908960422, -0.20339214131495076, 0.7234875673120669, 0.755690240826218, -0.18046802498541487, -0.46005076633885167, 0.5756390535640772, 1.4989271614680435, 0.842400701434775, -0.655279103467908, -0.9808935962392374, 0.1691731248624477, 0.6578722459266063, -1.1448102033934158, -3.6299269140084176, -3.5954187455219784, -0.6515563022854566, 1.4930895360495655, -0.7664567952681782, -6.14435595224415, -9.37165509252775, -7.142604673072632, -1.892857787583535, 1.2506990050168358, 0.41617505092889173, -1.584448913438367, -1.6240570408166546, -0.22217771514097523, 0.008310983959997784, -1.3125221895891996, -1.6275925000819338, 0.6840252070639393, 3.565584945312922, 3.790146587754231, 1.2998039507665164, -0.724394795752066, -0.13958409504485206, 1.5539827872968557, 1.7438218114504835, 0.4222503760953841, -0.31437116363954515, 0.1333744081826543, -0.0342450817166868, -1.7082196950782855, -2.6849718746275455, -0.6607219059055223, 2.608920724495698, 2.726975201988945, -1.2645395063576808, -4.543606470841312, -2.0978151654620345, 4.570599066693996, 8.75513342066609, 6.5876427601859335, 1.4150587780637667, -0.963576288440056, 0.5394233764064189, 2.098209181805677, 0.9881262599184414, -1.0809670372671447, -1.3247702764365104, -0.08240008766414227, 0.3244906754552236, -0.4854645755982609, -0.7451050618619341, -0.0236569028633819, -0.2311263958304294, -2.14237549248003, -3.215382944403501, -0.999705778752968, 2.6059257033623084, 3.252790736226906, 0.19191113296147716, -2.404966480041861, -1.2620182796866117, 1.3955771061621716, 1.373781460581026, -1.0139563867048758, -1.3679432116980703, 1.9288420613458241, 4.800715861395339, 3.2338014018450836, -0.7058387450341452, -1.659616746326951, 1.4136898881808286, 3.9733257779292868, 2.632311613291289, -0.23188876499680272, -0.5013027883584612, 1.597277921943875, 2.455560541888101, 0.9382855455475958, -0.21675224498482593, 0.8323907444350306, 2.1186368004798553, 1.3127064693838053, -0.460145371838957, -0.7079612935012904, 0.19432136853344534, -0.098814433762419, -1.487741826788291, -1.3908211109874666, 0.39835243588804226, 0.5158424496017214, -2.1836798969826803, -2.794450237097294, 3.772776158344894, 14.362162496421035, 19.48930970128687, 14.50993333616469, 5.121717123343964, -0.2220558312767214, -0.15322822688504353, 0.5115931946264539, -0.88183068210656, -2.008959565797716, -0.9061183104595674, 0.5196156948864994, 0.20630933934889853, -0.3295499908057948, 1.0800414053290042, 2.904736599787981, 2.0305417791828764, -0.9078591055268909, -2.1059644687110524, -0.5119337817818901, 0.6270449689384551, -0.7555636501058617, -2.172259213830782, -1.030753090503573, 0.6456061436635395, -0.47626823638384863, -3.0146677099581036, -2.6395177538427017, 0.61151141029041, 1.6503395946943866, -1.7365874549940779, -4.8657433088646895, -3.0918622482028226, 0.854716716986226, 0.954399206211661, -2.7017893241402566, -3.9620136792214433, -0.10125727503440966, 4.040040729183229, 3.4135564767050783, -0.12290975005368321, -1.4496302397937904, 0.15595555291181912, 1.250978205178057, 0.4473325987688568, -0.18894683131992285, 0.2885902486211608, 0.16504969231961739, -1.0127256545641015, -1.0502162503624601, 0.583091131161817, 0.8489831714227958, -1.713186253006937, -3.3494539706386677, -0.553610717198749, 3.365731179533507, 2.3050624060424005, -3.0315800362692022, -5.313482424998804, -1.3099432911347462, 3.226122978911492, 2.2952974351028175, -1.5687679081584913, -1.882391780666387, 1.720690982404455, 3.7519771040806384, 1.8946243745389533, -0.22494555043754227, 0.12521393382538715, 0.772227011779633, -0.37868904700083506, -1.169389800742401, 0.5873145392592354, 2.4261025242200134, 1.0067489479835745, -1.9506615997512644, -2.158917594021104, 0.2601676487817279, 1.1943744971980341, -0.49485065003625484, -1.4943685584778523, -0.1810643340103325, 0.8251570580283796, 0.00048231325744001993, -0.18059233859751406, 1.317370630332809, 0.5377269145267805, -4.854887713150237, -9.155575374481232, -5.179026920427127, 4.407046995957514, 9.17965069618918, 4.836717048598675, -1.6036645472498638, -2.561452425720765, 0.3551385310645826, 1.2895179873565465, -0.32139525242881484, -0.7661168143514044, 0.505893425763266, 0.6204206734261402, -0.7203207392185222, -0.7220359006446222, 0.9743716803173255, 1.4769813175172901, 0.0802483807705811, -0.4548523656233323, 0.6598828536354323, 0.5616850042507124, -1.3829404574435578, -1.1715722477096109, 2.933040238940635, 5.896189463835724, 3.1823981329359334, -1.3273848253602765, -0.7975050923962645, 3.687106188394952, 4.747300485471289, 0.46536262505463405, -2.941489736903996, -1.4217908741995426, 1.1709675833530062, 0.7326128847010243, -0.2002716927431068, 1.9682960154418458, 4.591819490907678, 3.139268541277947, -0.5474152779366394, -0.8934144553767578, 2.2965936546104464, 3.857556116697272, 1.865716685068463, -0.09752311412457351, 0.16790503094645787, 0.3971016519657763, -0.7915270587038208, -1.1275340041377717, 0.3724334061885637, 0.9013077204149417, -0.7800906620327868, -1.4752430470063236, 0.40064255652914693, 0.9594790405560214, -2.2258924217474623, -4.15305338430761, 0.1842203209552285, 6.073728962978462, 4.767500758637639, -2.746503521144654, -6.2777076199947075, -1.3580810499990688, 4.780564686431714, 4.784695118416107, 1.0464297956131439, -0.40732573300847297, 0.5520065982149793, 0.4886557192666284, -0.43405253125852067, 0.1366245450789115, 1.2592411422164471, 0.5723841997394032, -0.6072166893083547, 0.20964559987240283, 1.0262548758613126, -1.7103807104958617, -5.882120093376624, -5.931065432267204, -1.8428095545407268, 0.8228990299801682, 0.1638849399523163, 0.11804700105575663, 2.172056836557046, 2.4344408093367313, -0.20673604545954108, -0.4893927432168924, 4.126921942246591, 7.550015248061084, 4.263734183627481, -1.2346553242170748, -1.4034278924207948, 2.3309168650253964, 2.7067790751234018, -1.0287183095917058, -2.727534409859921, -0.408036114063164, 1.0567429536484316, -0.7572824044317172, -1.942157271797388, 0.040178626464818255, 1.9139410451586578, 0.9364173889100457, -0.4943806143066425, 0.012039617438671196, 0.6151244391060735, -0.3066508392640181, -0.7048860879270316, 0.5322064528901772, 0.8456458106143044, -0.19864639136574602, 1.7520032939644268, 7.58730820200522, 9.863420738143136, 3.212030532465012, -5.413996408955535, -5.428952459164238, 1.863385715181467, 5.7675515218314155, 2.4264569342178177, -1.3681952096909225, -0.7444035533621289, 0.8637054173942198, 0.2171962374511434, 0.05924524908557077, 2.445145244190334, 3.902544341965202, 1.8695279355782708, -0.39638772684196233, 0.027133087411765393, 0.47727033529167967, -1.5982004314596612, -3.22604617040065, -1.449188036279159, 0.785302620970455, -0.09438947161433421, -1.7832667465346, -0.8341525326078727, 0.5383107466440704, -1.0931801496601292, -3.1976439630689484, -1.7193523030271032, 0.9452565562193824, 0.213396531712642, -1.6584259839565618, 0.3674083756995843, 3.45696810667625, 0.4058958061850977, -6.918944113615941, -8.38318614038592, -1.3024636823897808, 5.001403532256161, 3.582725995801874, -0.7680432303826906, -1.1622456381913502, 0.9944006003843149, 1.115830284184995, -0.14772158077784195, 0.006562632601554113, 0.5339501798554267, -0.4045664554032632, -1.0398850665646429, 0.05588597534548162, 0.24760299133121505, -1.9232453248213466, -2.7789125615122447, -0.040901091071975815, 2.0710636638486353, 0.19014058344914536, -1.4516057070298394, 1.3347331050039908, 3.9719470912622192, 0.5975761022105844, -4.595213195085895, -3.4319277744105525, 2.23180539140151, 3.298291784717799, -1.5094447293093616, -4.330473766371921, -1.789292782791339, 0.8062628209856844, 0.18684801940404913, -0.15394940943603158, 1.6179296963226069, 1.965923426741211, -0.12475277292315808, -0.2062253017332995, 3.068943821124975, 4.483515159194413, 1.2500323606667212, -2.0476700469452505, -1.5423157051251886, 0.041103906276979546, -0.29850555916679333, -0.611054365570443, 0.708834708247548, 1.2064965768716944, 0.07237085355169091, 0.5686256677883549, 2.7384227094067435, 1.5778212671714067, -2.790747650951359, -1.984233621647569, 7.068579155991992, 14.196052662271688, 10.06700108891464, 0.5180439503876971, -2.8314261166299555, 0.25023157243061234, 1.4924272129461518, -0.8762025732692891, -1.482560181351292, 0.6919516595335152, 1.1709079387821504, -0.7606826504008586, -1.263015208250059, 0.1759469464236451, 0.47765031359617155, -0.23009626224132299, 0.6351512187053137, 1.8458405767786075, 0.5279641379467054, -1.2024729495353368, 0.2619281637142685, 2.0915812428795815, -0.6849790723439246, -5.1517437666647075, -4.3761296821558, 0.42132969893042677, 1.8393111271928226, -0.7398884512198155, -1.1007000078137141, 1.3115630166774157, 0.4757967843779696, -3.814967118806277, -4.468997167412826, -0.08625675521534634, 2.1077138084915896, -0.6444980212901834, -1.8575271172773071, 1.8725226936133366, 4.540895828657933, 1.7252849481627064, -1.8906729027538247, -1.4430996207866136, 0.4294085374010835, 0.24225328377223734, -0.030738255975752388, 1.4680347755273448, 2.01424941201799, 0.18311407759724635, -0.8124420692492663, 0.3466717475561297, 0.4107157449652571, -1.3060961369946407, -1.0345481061723891, 1.315113247148254, 1.1758673716916266, -0.5160273300203243, 3.220788580525816, 11.543256604130733, 12.999560424752058, 3.0075593915183156, -7.100626900641537, -6.489336413784345, -0.005645385451254725, 1.9861441749525692, -0.4303003906683622, -0.9138411107811014, 0.753741012997143, 0.7257956079752843, -0.3528835644255135, 0.004886575310811205, 0.0007602685263728069, -2.1062061022423983, -2.84071568461726, 0.1975687393269126, 2.655169674800325, 0.8342205732420741, -1.454526577553644, -0.1646784187962847, 1.5493251482953114, 0.027821038483083146, -1.731572596149641, -0.5657565013449312, 0.45812268330767436, -0.8937775320543038, -0.44267491989824265, 3.5612000381787587, 4.539551257667587, -1.2205009074305104, -6.16087836793672, -3.386863792661423, 1.5788328396824365, 0.9750485156832563, -1.6372271327043422, 0.882478154964798, 5.412961903696141, 4.395432790178708, -0.41530846114358055, -1.7125892806684868, 0.5407617511855976, 0.9464567166565034, -0.6891844349084952, -0.5602193352921885, 0.8641991986541763, 0.6101884124698675, -0.353878035535859, 0.07344445288241963, 0.27231944307196077, -0.677625915152451, 0.45684437133725936, 3.914345447960776, 3.7311435816985328, -1.6315395516450977, -4.1193639449151735, 0.723540160039423, 4.826112670680639, 0.9149961651349281, -4.823496997600368, -3.817878744243275, 0.27802757999810973, -0.46337043356429436, -3.8305506530267857, -3.0327735276295043, 0.23979432039904894, 0.1333367472866018, -1.8831742015857054, -0.9173323935051881, 1.3432202900995722, 0.7068160005959467, -0.7491826899288264, 0.6609390457700395, 2.3214313346997004, 0.7505624278072639, -0.9571450329109968, 0.7009541653534487, 2.345740660537526, 0.357346822176433, -1.8970040910009107, -0.776840337653072, 0.8268844099294914, 0.1032458949238119, -0.12024558572174315, 1.4206982788498996, 0.6051511082608912, -2.834545291152378, -2.643950653341678, 1.169137441402174, -1.174417936988319, -12.263455041928191, -19.483878026289148, -13.373340086511716, -2.3056829719851506, 1.3417945314113138, -1.1635286331066472, -1.702288924951112, 0.14457795281796984, 0.2556289125492039, -0.42467567992484256, 0.6760451109892266, 1.4556555743591153, 0.06375938540077956, -0.5684320427252334, 0.9923730196469669, 1.3080067281936982, -0.5370422683134821, -0.6104510322288385, 1.32245539896734, 0.498469057630303, -2.8034390827157343, -2.6235261429834758, 0.9572663625744384, 1.3677935570031943, -1.0591780734437022, 1.4944409015584121, 8.893467892561928, 11.116365756959203, 5.206219040524268, 0.08381528357047088, 0.6681527004070833, 1.2063156545191882, -1.5960047887429374, -2.6968606130745365, -0.20530458442271804, 0.5327573082251758, -1.6465576156654738, -0.8833688916778603, 3.65627935146311, 5.16559683875758, 1.6337432645588454, -0.8378287551042064, 0.5036010943027562, 1.4478059042091322, 0.1742857375343021], 'positive_zeros': ['0.95706431683791001027030981604', '1.82202938815002544534909984221', '2.69704756458643645941623104150', '4.45066903969528325950894883964', '5.430073324771657639984676447014', '6.497899006802276318254499190138', '7.09348725032819503681824169460', '8.13937428496593919699779394571', '8.82643915747370004744774388938', '9.61405151534417527949025868444', '10.72710211915319740624333962097', '11.50163087959395311427577092651', '12.31155665260050215587671193137', '12.86982663222571949219724948090', '13.87252157030352645351996646950', '15.02015855274589368213961474154', '16.2509320198457778271657156830', '16.63617365222408739937478258695', '17.44068682879837570958375708405', '17.98381957341576866050738694747', '18.919519464144892183057339841569', '19.647047471196837005113800013416', '20.16024934861180617785788054640', '21.312761367277231610799964471263', '21.81756809311725622966900029678', '23.26370602797343928709276373181', '23.80925352301406259399591670781', '24.7558882126395170780792922288', '25.0031899095921169644280495792', '25.86839351135639467138388246297', '27.033617293068392036273499526158', '27.52591943762047723723410525854', '28.54801579052081513707888992935', '28.989039753779334083987396502537', '29.36440228091145719902077138787', '30.372339526127401759480378584072', '31.16677808886159724485606896238', '31.98167364851090921762870455781', '33.24104991466078829556377629002', '33.675445840366442224892094813218', '34.51127963142056849637032418346', '35.33562965840113834478472682414', '35.77267763113639890193910952157', '36.57459370858585599529388229242', '36.80094073099243628581405171045', '37.8950548471518717309618079489', '38.76625894125709621970745740285', '39.511487830800692093898116960519', '40.18313452525920720996259776931', '40.7830531562394886137213545904', '41.81212240576090368362335348472', '42.38152694567925612164285228160', '43.40411654699060815577632011619', '43.83937722246086666162289059023', '44.87466741339379327142987808896', '45.13285381060339303614336951093', '46.15557715934579197069096479443', '46.79672725727180447979637760402', '47.16006152359064208012931012026', '48.05421383326942203385516876284', '48.516526158291808196405726665028', '49.23904801601376127176765665842', '50.908462372717614379949168201251', '51.287883690639358800593507550733', '51.719266093275868572050798441795', '52.6639204881380092012821505981', '53.19395167755658269999838034866', '53.56509521374012774625062019446', '54.59026026576066372328829132849', '55.396164443249923819353554495233', '55.816314838611368681302929004938', '56.717529710842261481701418088420', '57.12356495231492952459301794809', '58.06641570352066776497696134670', '58.622131832373287344800086911175', '59.606088677388427670158906905076', '60.095431778547488731418269400137', '60.94359404422931280986617288751', '61.86279305572269935683576724010', '62.47529491620348290140808342060', '63.2674533396669615741984954142', '63.59960369495125025836477990214', '64.11511539941575328029588742618', '64.89534697478689916791308667965', '65.44388134425439529878846012909', '66.28802046092311347979825055514', '67.01815441062505429578725276236', '67.88466295716632788367018179571', '68.61467094600972586686944931170', '69.2398579716185285955433759877', '70.252765622576510841373820522325', '70.588962967817257659213701552316', '71.17536580252186655250698566888', '71.80085510748193475568597563151', '72.60011747489901408342553696633', '73.40400331150415715583046408612', '73.98734631812184718491359346641', '74.72055198129103813625478572153', '75.312642481949042377436285051714', '75.674995652596552222767534077098', '76.2951222969994055131176207425', '77.35819143135607237102973731652', '78.34135877320089934815264069949', '79.02299483551199319501584241427', '79.62859260004917277892974558334', '80.194250358342588845981281802750', '80.774937631411412479397545877799', '81.39384514286976255989813113860', '82.204936624539203037836249398888', '82.64662392191609420643762698637', '83.22596045215557584505078225592', '83.86245607090607940327432257366', '84.88660142423310582853771447546', '85.375203175799423330806120945667', '86.27876246063487591831523743631', '87.017373911739428366867846833', '87.65662082409819960226015532430', '87.88279003917842261227597582243', '89.00661064710556299696410695601', '89.47954400798949059125646005070', '90.59150701121621339075854496105', '90.869761538589365008012515603926', '91.37910213677908525725001419770', '92.11857216737281701761360409463', '92.68924070995605215935935107680', '93.38065147729176401499938454113', '93.875497281036677601586989421474', '94.678903906440020075203306939529', '95.515425537382200784264290994263', '96.30783725530768086936238563638', '97.31470152204839879695912675169', '97.65428119173555720314948520546', '98.26885276161729166159359023388', '98.71694166562109046178621336872', '99.4928530886710336415582980868', '99.957129950406593566413374198562', '100.48399496626184188733207641101', '101.72214615087754447913475942804', '102.23714253785178307870642060357', '102.4696190130946781332320096807', '103.41290491519321643242390608973', '103.80105025217250308541226886121', '104.91205415979049588368288241369', '105.43434495894563477288537043753', '106.16973021834827683111223179620', '106.92132558293157691242198356353', '107.40148799092582151622857013284', '108.12041914874411802682470716603', '108.91337429113106031932300215246', '109.371530592353057269746863415202', '109.92009732999066358825323860764', '110.507739595109919339001146934922', '111.16612322592905193945453609349', '111.38036063750421139781430150888', '112.60182181203269088649101992741', '113.36191238138389414055088743126', '114.22445390509503151363942685706', '114.79794040787412968556375850449', '115.37729764746178866222598370589', '115.60963452261822823847032775184', '116.78611447810539115265941024200', '117.180403441686295427367212170155', '117.608191597542636202482192848797', '118.60182166438260341777919360081', '119.04828257450333728739561048859', '119.82344000695833724616876065355', '120.17209671507480417506043182393', '121.1114672993929548966984911999', '121.59056174292709675746946053030', '122.1568924979349121112484751008', '122.83126383422761544832557518959', '123.79769307056986899402107161123', '124.61774254912670889996923850304', '125.16283617765368353692884834752', '125.887122338556785157926514020726', '126.24750667384167750667164535806', '126.77725431447480833762143962272', '127.486435440987925801035660304835', '127.86518161136817727755382424048', '128.753698556848128346622279689935', '129.39541205614932725906786309618', '129.89360669842041389452893196054', '130.65638873225772118352404250717', '131.4359100205090254519562798798', '132.10093465898177339159291995092', '132.98114480335177345066623388263', '133.48519539200535489961761956904', '133.79118129268121670094296770392', '134.66793148645951700320553238265', '135.028618878948474044257029236290', '136.02936089476006272407560568812', '136.85796774430933989987799486433', '137.0759456353451338063714740672', '137.66892517514523988376911531897', '138.4658037637861844274003151307', '138.622539942350102924630048960564', '139.48933675478432305486800479153', '140.08921438075564772600491859452', '141.27152362210670821438473387703', '141.85255164638356374411362810185', '142.395846991756050258065031757588', '143.03057335709553259785069443563', '143.634263969274246554036963956838', '144.335426693422981391701127708693', '144.8660248775813955651441774686', '145.16969671928797638779814389682', '146.00752481925778490804864234926', '146.53165689745113114361078080708', '147.14189434789013543847067218171', '148.0946023031470632462165895684', '148.66519037200790218050869361074', '149.20566001468089346013548281709', '149.72750407865467838076229755508', '150.63086229885509442464336484629', '151.19168013265641776884662122105', '151.74727052988507703797626165393', '152.621861662838600942831759447993', '153.339318784340549916127807770600', '153.843628288757872024803893128602', '154.07477151190896572626645841573', '155.02825877210782627783342869354', '155.54512713642184934400199361388', '156.021140579490670531929636530096', '156.69949494988048499688449504313', '157.357776325102930267416017283632', '157.61949982726488859213062506455', '158.82480040397213456169926228685', '159.68782935612080378018104438235', '160.25766068721223079869221957722', '160.793507104234224339331892589140', '161.43190876997274556028897646554', '161.87304903230310334159178773309', '162.18769575995384676644448326182', '163.10894722173737003576602510697', '163.833661403949871024567430925830', '164.3956414928510978036817236668', '165.00340902922044200951264095880', '165.72292113385764591245200761500', '166.077804471604480652381178586307', '166.60774048492404052435008059351', '167.44721659633767432897456152095', '168.31196894618469828162985116626', '168.84183569393659827883090404141', '169.31613434016565262709391710828', '170.2813040855403760156419779610', '170.863726899119387552427194486633', '171.427103226369859695644371126702', '171.989140378701437933824378479208', '172.661761158188114568251687264460', '173.09657464697639743792656381642', '173.53471414146209628885719807762', '174.00878588749001202016892669624', '174.9134741747483561436675209509', '175.59013306096813893154785609161', '176.2916309546009064265575861117', '177.15512139687135314989441305738', '177.45312607556345820681802468902', '178.40577761508148509569445877307', '178.76994454768229271746916123094', '179.48317932702831724219422235011', '180.11231442520416270923244398600', '180.5354045785472975711439602204', '181.34272639477553915182662271485', '181.78960173919051034308724569650', '182.53584534874943911334496870804', '183.23643197750403243101076866896', '183.77828068036465077911820170346', '184.09473831951498692555514860122', '184.747047487642225195685412062403', '185.51790413768607102812197873963', '185.88407397426707928951520129335', '187.291597758891078876931359052275', '187.68614279641584504420998348791', '188.40742331770112337408973153544', '188.830901949158097214253589138859', '189.23574103761730059875324038243', '190.01193056846370340462412448945', '190.451335651025777550760933602519', '191.16040748538377667555255610567', '191.66311126668635698997986240258', '192.237370779562198790885306134505', '193.03723236963496968194688968440', '193.59714167532727282983754365601', '193.97421693991915134486886059938', '195.32689480342135016481204845706', '195.50301854904793731047426118609', '196.09471144157282836149594607415', '196.900695043791857002309645553165', '197.2773606410707851188432347463', '197.88305921269158673129751048353', '198.89223576995295465150897876725', '199.29704062104513339269564437361'], 'prelabel': '1-847-847.837-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': 0.019771950527321096, 'root_number': '0.998071457837403324801612340330+0.0620754786555886118684443692508*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00988597526366', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(33)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.528606585885009747671738049005-0.158064567533993179090382447802*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.957064316838', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.82202938815', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.69704756459', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.933451463423862, 'bad_primes': [7, 11], 'central_character': '847.837', 'conductor': 847, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/847/837'], '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': '1-847-847.837-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': '1-847-847.837-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': 0.009885975263660548, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.957064316838', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_847.837', 'Lhash_array': ['dirichlet_L_847.837'], 'label': '1-847-847.837-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/847/837'}