-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_441.22', 'a10': [-0.9009688679024191, 0.4338837391175581], 'a2': [0.36534102436639504, 0.9308737486442042], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.7330518718298263, 0.6801727377709194], 'a5': [0.07473009358642425, 0.9972037971811801], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9009688679024191, -0.4338837391175581], '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': '441.22', 'coeff_info': ['x^21 - 1', '0.955572805786141 + 0.294755174410904*I', '\\\\zeta_{21}'], 'conductor': 441, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_441.421', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 0, 'a^8', 'a^5', 0, 0, 'a^12', 0, 'a^9', 'a^4', 0, 'a^11', 0, 0, 'a^16', 'a^6', 0, 'a^0', 'a^13', 0, 'a^8', 'a^8', 0, 'a^10', 'a^15', 0, 0, 'a^13', 0, 'a^14', 'a^20', 0, 'a^10', 0, 0, 'a^6', 'a^4', 0, 'a^17', 'a^5', 0, 'a^16', 'a^12', 0, 'a^12', 'a^4', 0, 0, 'a^14', 0, 'a^19', 'a^15', 0, 'a^9', 0, 0, 'a^17', 'a^2', 0, 'a^13', 'a^18', 0, 'a^3', 'a^16', 0, 'a^14', 'a^14', 0, 0, 'a^15', 0, 'a^3', 'a^10', 0, 'a^8', 0, 0, 'a^7', 'a^0', 0, 'a^9', 'a^10', 0, 'a^11', 'a^20', 0, 'a^16', 'a^3', 0, 0, 'a^16', 0, 'a^8', 'a^5', 0, 'a^7', 0, 0, 'a^18'], 'euler_factors': [[1, 'a^4'], [0], [1, 'a^5'], [0], [1, 'a^4'], [1, 'a^11'], [1, 'a^6'], [1, 'a^0'], [1, 'a^8'], [1, 'a^13'], [1, 'a^14'], [1, 'a^6'], [1, 'a^5'], [1, 'a^16'], [1, 'a^4'], [1, 'a^15'], [1, 'a^2'], [1, 'a^13'], [1, 'a^14'], [1, 'a^15'], [1, 'a^3'], [1, 'a^7'], [1, 'a^10'], [1, 'a^3'], [1, 'a^7'], [1, 'a^19']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-21e2-441.22-r0-0-0', 'leading_term': '-0.174681627469400118366831426255+1.03367542018890884925353815667*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/441/22', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-1.0483313146510864, -1.9954008320057046, -3.388124272790057, -4.638533851570703, -4.986493759752902, -3.97760517801183, -1.7911261485523413, 0.735347618686695, 2.483477845460889, 2.6845764072738767, 1.4254276616661097, -0.348144427620921, -1.4120030820857563, -1.0844052464459233, 0.2946380180109671, 1.6186969249868581, 1.8617623484763905, 0.8809508027103705, -0.48123149114768604, -1.1137287892370633, -0.5928011429605333, 0.45865566359750176, 0.9678060074662591, 0.46565243609817575, -0.3826934026255968, -0.348787118019928, 1.1248659201842135, 3.1832876770616396, 4.139030772219609, 3.002984644734853, 0.5895099336943825, -0.9643165917502379, -0.029778014611357748, 2.9193269661244146, 5.502323568901817, 5.417466111345153, 2.506793333541, -1.019955535736611, -2.495495622576187, -1.1264009680157532, 1.4119378115870502, 2.647588613470564, 1.612901121027212, -0.4393849615432722, -1.5004383079231651, -0.8566046577791486, 0.38687695735483696, 0.7418980980179926, 0.06342735824923723, -0.3684764702866423, 0.5272314674014189, 2.1958407462509446, 2.923961658170183, 1.7805559013292425, -0.19349560848423097, -1.034078959161241, -0.08611527024502626, 1.1389926174743261, 0.6439532686585608, -1.5812223603535687, -3.174532109805254, -1.842665024749268, 1.8696176482801963, 4.643977132819607, 3.5475062413286818, -0.897950564793657, -5.043827247310069, -5.617865923506302, -2.7737490757842806, 0.44230677604193713, 1.4411514906758707, 0.5222540742356105, -0.10053353170220147, 0.7799848095246026, 2.0317371557334605, 1.8614258996469486, 0.24777920758899322, -0.9449617017995727, -0.28737490693233536, 1.4058752803917685, 2.0838915033134016, 1.0326684076637371, -0.2602119627994233, -0.0938986261556483, 1.1430431946400021, 1.4303911328438204, -0.07556685438944526, -1.5053975868930427, -0.3297042289158643, 3.198857377621166, 5.566082945358204, 3.593191096574614, -1.787046296055578, -6.099618834042228, -5.896159713451103, -2.248122351686587, 0.7579662860955624, 0.6492352207780966, -1.089991391528308, -1.4332773828714864, 0.2865158731117434, 1.7945814495231396, 1.0340119686631364, -1.1612752629443546, -2.2338842377969472, -1.1974306732236084, 0.292571781924455, 0.34185073344092953, -0.6724229045445635, -0.8564706695612496, 0.34499565923866704, 1.2659486597522762, 0.4518962874805509, -0.9677935491001372, -0.5206086412650843, 2.1014845982974926, 4.061988662215846, 2.736667901781175, -0.642647431447164, -2.009207718851008, 0.6529269537165856, 4.569982439208783, 5.272091523075334, 1.9236412477539582, -1.691265385406424, -1.7784411800085458, 0.9980115945606594, 2.6524682030239544, 0.9419741022393616, -2.1140590169745836, -3.145787637287807, -1.6345197411994283, -0.0005578992064171294, 0.021514932281156612, -0.49701291405353476, 0.24018327843697812, 1.7992149051569604, 2.0681978781646486, 0.4711858580324516, -0.9562572921559894, -0.3923005640235363, 1.0322196940082504, 0.7027478438376902, -1.6403447776471183, -3.198306232712305, -1.890016265958318, 0.5303492738443267, 0.6875335214599756, -1.509120102492836, -2.1057770301064407, 1.863829589040531, 7.906414933876478, 10.338866710728308, 6.855705589869216, 1.1853335364556514, -1.457622507487778, -0.2297709559898823, 1.3951921034540662, 0.7860926430209982, -0.7826914407166743, -0.7914705565179196, 0.5725194703410721, 0.8859157006080671, -0.6798274599642704, -2.039003611912881, -1.3174675216089597, 0.30586340979612126, 0.3277481478672684, -1.3297982267479918, -2.168238529672049, -0.8467266402214437, 0.7984074825563368, 0.6052721094365565, -0.43302774525942517, 0.4021437594183135, 2.9041648595414227, 3.1123285865030113, -1.565897551364771, -7.95373193138595, -10.02248522019288, -6.028428033276631, -0.6403931610132418, 0.8503108849955026, -1.309254910017685, -2.63891199414733, -0.8398874880675724, 1.5773034694879853, 1.4884734359207086, -0.3388268352839377, -0.7557111449072069, 0.9483608459821414, 2.1530420867821327, 0.9891201399340835, -0.909489603948688, -0.9857858829258577, 0.46031328147761164, 1.032222725672804, 0.12792137846725957, -0.263719831598766, 0.868276664629127, 1.421148901496867, -0.7004607525243289, -3.7470280658251323, -3.924132050022994, -0.9274792205553686, 0.9419070853485229, -1.5280219119247644, -5.651168744905912, -6.072813058815889, -2.00002377712905, 1.5944660052632775, 0.6228384029894429, -2.783030682976679, -3.522334822970728, -0.5490303631737012, 2.136934353647502, 1.4036199091207069, -0.9505208802994702, -1.3901158040386534, 0.2288336337688405, 1.101012528286533, 0.11405333882573492, -0.7334850917271314, 0.03411435261373712, 0.8660586022007147, -0.10112561212824434, -1.6274850694052816, -1.0622407687985074, 1.2705477091626352, 2.105054761333436, 0.11499731485603919, -1.836026319154161, -0.949225995319681, 1.0462424662146448, 0.4270384792359663, -2.3566120019597565, -2.44808892094311, 2.4765641220858923, 7.936238092336984, 7.827722111638824, 2.363479014664956, -2.2421812516642765, -1.858445428216821, 0.9280391345365795, 1.4492314508247222, -0.5365524825319457, -1.5927745699441476, -0.362810247482662, 0.8027917429981366, 0.1866595041866438, -0.48140223729934456, 0.8123545188809176, 2.6723492922242253, 2.2897401283892815, -0.01410474421977955, -1.1034806403018331, 0.16998511554058537, 1.3640602175998944, 0.6290862059057238, -0.20586249577870708, 1.0818299054476372, 2.730098551526014, 1.2401002708640652, -2.488906709354697, -3.0410560695214666, 2.097310731617006, 8.06147390048499, 8.344373183708676, 3.276569425981981, -0.6546089649021435, 0.40768931010233866, 3.2598466512357276, 3.1810832048521056, 0.5728192493556606, -0.7758022649897554, -0.03905696854928184, -0.17132584553729538, -2.5322047546878106, -4.371539065510022, -3.1259587607857013, -0.42714003749138235, 0.522793117371989, -0.28351833326795145, -0.40710397269927523, 0.465169692695453, 0.05243126741580758, -2.109149875995032, -3.154365418626634, -1.4403999842771376, 0.21866805471926598, -1.3059806945619195, -3.94031358473075, -2.8169243640942057, 2.1091068666795656, 4.936442362369624, 1.8055307617824525, -3.4525723559971966, -4.589898031655677, -1.548275170165598, 0.16582652504654086, -2.008967476014906, -4.212911167711119, -2.468537976092763, 1.329044871440097, 2.6030069732599173, 0.8600111731581102, -0.4007646286930576, 0.4045714056494314, 1.0214907027628117, -0.1587831201489475, -1.3103459798921602, -0.6589775435439367, 0.13541725493562656, -1.1841125447090244, -3.2030983017228145, -2.774835951996623, -0.35136944610922505, 0.37393847454458556, -1.509644006585412, -2.318383478917082, 0.2618855131305881, 2.890653864570411, 1.539748314325767, -1.6195226554190334, -0.794388674538163, 4.451222059891935, 7.586628979394706, 4.050606455873976, -2.2315340882860952, -4.333421940502535, -1.5237634461336875, 1.0571962188466464, 0.5357237040697447, -0.540393257208736, 0.3390210585277004, 1.4730507299815914, 0.5003336063603521, -1.1921575894433207, -0.89776275072382, 0.5782766573752744, 0.2198152714891486, -1.908125295138488, -2.5254283424171646, -0.5686981202702903, 1.0311758644697828, 0.34425927254984107, -0.35941385166685, 1.089939498508543, 2.3446621324583043, 0.2683708340064088, -2.811369956523768, -1.4867517456223882, 4.049913000681195, 6.733201742109118, 2.1127812019250456, -5.010806186300034, -6.936854421003117, -3.171442047725119, 0.26731873962734387, 0.17151962911640667, -0.448523658969645, 1.1826096835336655, 2.822354908946117, 1.5216560205760634, -1.0178602230612068, -1.1663088468549532, 0.7347660174845227, 1.2716872865238495, -0.20969530975885198, -0.8579863921341394, 0.44310088217897675, 1.2162897955519778, 0.050253292566240296, -0.7147444869185042, 0.7002630099574882, 1.8786341918390224, 0.3414529064874777, -1.2448413894084083, 1.4116311899317922, 6.604432271593733, 7.760336248383923, 2.962256495578481, -1.7130307253907608, -0.8700584257051699, 2.542512726339835, 2.309550687715018, -1.3905828742404531, -2.7665852798637482, 0.20615581415184342, 2.9011604547486387, 1.6122895017324992, -1.0693238953751316, -1.1474666274049017, 0.4870725658384801, 0.4506896796055127, -1.101859837369644, -1.2322387585841836, 0.2824822407725217, 0.7196814087003318, -0.4414542387811353, -0.5870121524698975, 0.8984621578536063, 0.8849313357584507, -2.05228968317146, -4.350679742447705, -2.8250496375438607, -0.10204854255868848, -0.4724669167644542, -2.5995355776512543, -1.6832620151283906, 1.8232039643314077, 1.7013540052249059, -4.282651719947966, -9.68357117999586, -8.00912969197103, -1.8737650064253006, 1.2353886293650058, -0.3516706273348113, -1.6157086231625521, 0.29530004934240633, 2.2855089526869046, 1.4946055004126524, -0.05494831927923337, 0.31188890647446715, 1.214467632693969, 0.3313386114190988, -0.8468344897363044, 0.43508119019873637, 2.8660040690133886, 2.7932710496003885, 0.3461553601982434, -0.7964131234899772, 0.2899698331546481, 0.5496658158891107, -0.9875753334862518, -0.9957936083629182, 1.7823326255533376, 2.7675335422110945, -1.551366778412497, -6.567256861010984, -5.119199924647698, 1.6426504340098704, 5.215609341099525, 1.7413587666256136, -3.1351763534780135, -3.3556026749057097, -0.6807200243091841, -0.06492584527424872, -1.363706848980616, -0.9423338455224622, 1.0989617607235782, 1.1452894837656658, -1.2388107654402127, -2.3637157691595285, -0.7698295845461509, 0.47028980459677494, -0.6538372315024448, -1.7487556475423243, -0.6532788042734244, 0.682371342886422, 0.14925017583430822, -0.30648266187224404, 1.4782826212769038, 2.7996467873977524, -0.009116192170478155, -4.41314198829502, -4.410879172676064, -0.20646504758339326, 1.2173524891910936, -3.184514322842364, -7.381081588480347, -5.373136208782089, -0.2104212626791857, 1.2645734800471828, -1.0489379022862388, -1.574169211119166, 1.1339856211085955, 2.470685730159221, 0.06024212096272882, -2.3859769415685896, -1.591806823253669, 0.22610019360711525, -0.04529202194248905, -1.1114602524117112, -0.4065843271915259, 0.9060360892003033, 0.4440038311344189, -0.4639793622101459, 0.8356632488769298, 2.7587417279438107, 1.5574832496024822, -1.8439246487722223, -2.6980495607113704, -0.3744223096554027, 0.49268114747121394, -1.617526097939299, -1.7436881843954706, 3.0560091655984247, 7.381944718964922, 5.08328162319646, -0.8031710395906796, -2.2890241818766492, 1.4985691124960612, 3.629029832458277, 0.6090235415451192, -2.8328270442912444, -2.0921096052170935, 0.5522401511913045, 1.0048056578223885, 0.017969613600615022, 0.2999916881925257, 0.846094637133491, -0.7411637364879606, -2.8672040640190826, -2.1719564273242, 0.39107774513911964, 0.95242073857091, -0.6130358032237948, -0.8234332725420638, 0.7153096149713419, 0.5039415354687475, -2.0192089100281763, -2.8098697872709795, -0.6130667422971061, -0.04806647266864898, -3.449836925805816, -5.145085393512829, 0.3600452457301644, 8.487739404255773, 9.916291614770287, 3.8185965950848813, -1.569739085698354, -1.3502033482557823, 0.5319113864152342, -0.2564781194460004, -1.6632193290276003, -0.5797550803633479, 0.9270670450648497, -0.3113503913172265, -2.415798437462159, -1.722590477933946, 0.6677560987182045, 0.9779437229002698, -0.5993012838345373, -0.8119795000014483, 0.3420373391017286, -0.11091615101744845, -1.9817625763186992, -1.905438575090916, 0.15771968287535273, 0.4999339545770479, -0.9197380119131067, 0.8855468664630418, 6.967532632443409, 10.442762708319465, 6.228462584794094, -0.49255828009965774, -1.6755844997309208, 1.674576825730322, 2.2177845016234334, -1.4627534068974115, -3.4310180783749233, -1.0847751472485958, 0.8103405728450623, -1.171582120469731, -3.494150745435818, -2.3155246069157585, 0.08408895225548885, -0.01839042746554789, -1.338127153450108, -0.7433772833165646, 0.7649866504448364, 0.43086086044830607, -0.7069314138750462, -0.025293637215737103, 1.1010781733977701, -0.37510632490908047, -2.823898867938993, -2.074077206545525, 0.8546267055650274, 0.807151881750643, -2.4443470172150215, -3.3274030381151944, -0.34002965084193826, 0.6083987448312325, -3.6954378403025654, -7.291978075471544, -4.2457759152651295, 1.338042367004616, 1.5257506338717552, -3.0828209760811833, -5.019603240418625, -1.9898624867244532, 0.7993851471750487, 0.20950046819259643, -0.685102875164452, 0.48112480897128207, 1.2816103038554383, 0.020116076597191383, -0.6672233287596515, 0.9385697889984905, 1.9928069474387944, 0.38068281837449075, -1.071383371165554, 0.20714572375259804, 1.5216125795929252, -0.18175316589072332, -2.4101897263485395, -1.5308638785382365, 0.5087119509467153, 0.16081864523495532, -0.060990556013951314, 4.4662446737687205, 10.478765624221099, 9.457849335160882, 0.9068349000744966, -5.52402890103405, -3.7387106717451286, 0.8462003263740768, 1.0632997991597275, -1.5215831932879345, -1.6198290677555303, 0.15754717848414979, -0.2706592508531255, -2.2752815069075347, -2.0324849555883646, 0.008770801092744095, 0.1025927168285416, -1.563272913194495, -1.254482448641772, 1.1555924926996786, 1.8649759616449657, 0.14061182985270657, -0.6651953355187015, 0.2739733760602841, 0.03049343119238414, -1.5384134510853376, -0.8012496340209846, 2.010597752424263, 1.3045249375152115, -4.202561820023188], 'positive_zeros': ['2.09262158218201882934393047399', '3.37250389154607994679385152155', '4.315992121815807151158520717919', '5.507281204133779648746489000265', '6.42455242543440210775413199361', '7.34631774815741734154093036173', '7.91788522631816849719678060531', '9.457959391995327752004316590555', '10.00415798875657514998778362966', '11.4619110556134249723576943573', '12.32464665141372619949809899954', '13.367040226824927157442747356515', '14.26762619486831315835534723222', '15.02452735622854038616954613943', '15.4989633473220251060131460656', '16.840655704769162575581039677348', '17.51820527063934659762559987927', '18.23100919293364002094343489075', '19.22797244439228884998893799940', '20.25659467336353323556116321937', '21.50803229074946821149432848111', '22.36538055880878941395995149387', '22.58545159626929412693549666044', '23.794723831742040784001543030649', '24.43149330654233151595052601727', '25.53800187927012600844246163456', '25.965978721560936891704385864222', '26.86293403677931931072185651900', '27.53579155072348622425673545507', '28.6533694244555786281028781143', '29.88884819778691727757818849880', '30.43187702697882650456833560071', '31.20769298937686512009373535230', '32.02545812435852805081804796080', '33.04467505883273808279010627609', '33.551423730104492916469455710223', '34.30061681254401322076981329299', '35.08846474914232029528804271738', '35.702952056828004889360547058676', '36.81311698218128576342598314235', '37.44825274703461709612869041103', '38.580793415068514093484572827476', '39.27237459504558615103798720051', '40.093178567139996088645152810099', '41.250198289270678648152474195043', '41.57330949686518002895008204037', '42.132077752001387482130543253030', '43.20183809319705835293920538166', '43.830079147718354081433963907386', '44.48558948071730083861001638527', '45.54302621774894392371029902993', '46.052123935960569598687143918812', '46.76645665464596343162973788795', '48.21196064967726516795739624417', '48.783636154220333871815499113914', '49.519331219054843872644163287084', '50.18545159304630575497369180856', '50.82658110301315064438126472266', '51.80306464400147902284924344757', '52.26467508336291501582158654249', '53.260581265066593790297328545822', '53.908109139341841994974661846158', '54.30768497380945441907837436198', '55.23372895131058035261349918807', '56.61889412649838886664051039710', '57.02788329146338613101357896905', '57.90542838397322135838334745249', '58.688667852879131779950759127578', '59.22685853362502189598710738442', '60.14651516967436421161733217833', '60.84171325418504990788774000703', '61.602477887306224748775521153664', '61.98118757106629151089935265829', '62.740825103743418717977063182513', '63.84539680030291984342985808757', '64.24411779391456897792856221195', '65.45023990533698031206604481265', '65.99709192243047382558107632604', '66.92246273323062627461737523083', '67.677908444375473902444198805292', '68.39720707589063518069812422815', '69.08881546529127026913559736011', '69.678920233539573296001186358922', '70.293927033967043687900240354578', '71.08543937773116722310742679235', '71.88851536677671073143065164094', '72.63165271401922085936428551742', '73.178286169946203908089370874051', '73.93420609845559225511663311082', '75.127825108064363860360556360859', '75.825904123399484046667956133741', '76.486461250943964459746455931571', '77.25495898713159792090670610133', '77.86430039841107620512475446308', '78.29897797414881969956502710274', '79.37301702068390038933000322172', '79.9702006222503240936071652860', '80.78902387224525860482342018251', '81.04835520708332387160501853152', '81.98059699389796561606591139980', '82.71226739077787961146622467063', '83.972291805124672769462675755880', '84.328746433751154297008746462638', '85.39005711578250694671154568698', '85.95203386352215945734974609103', '86.206137747333088239231146492773', '87.56866119658239602382831800693', '88.02957389170100765240515334683', '88.58446162505930014891876437827', '89.072775909217609773777471610676', '90.22258383020707557688246071601', '90.44062804866736995113055614359', '91.43772787723759652242767397933', '92.28787713507325389215348159895', '93.32102788505670167562187579761', '93.49837329956221241801582002780', '94.5712660825645670199031765795', '95.46010288462172713926764105139', '95.83274949934452064884320095649', '96.53242814666892256451105670486', '97.37531260406035397662099941070', '97.58746023179400027344554453759', '98.80578262394879575159662853223', '99.1512405701802933548812398409', '99.9766754719788774152389434048', '100.76350633106813857265862932849', '101.30941063925565984854046791906', '102.38008200736127251478109746252', '103.26804185565194330833948072071', '103.86373929288417905140627639862', '104.30413729135689170173181175579', '105.08052100155212616625355294160', '105.80141631051853053160200353842', '106.288495773160894020685240694433', '107.26461484509891949312447941124', '107.89841355003016026301959160634', '108.25211393787372597040535849122', '109.08619590165967890708457444636', '109.78253810867398540997176273332', '110.71206032538861191879495587989', '111.830778267870203694305986335923', '112.234088875080941144301974149813', '112.63385751531848850584485599837', '113.610043294059814512010076384882', '114.25771310183756806560157840577', '114.96012705569595886600421404147', '115.53887023861249282302330481193', '116.26032702365139318360209621396', '116.75961656303486608974681043686', '117.544034869093225246284814818358', '118.02151670901918796748420843545', '119.2260934114696439417281201297', '119.76418409546601686431352402351', '120.512064854936137405701437802208', '121.23334417047569673341541801317', '122.04487222542636654251601271023', '122.71018812218812111131904198493', '123.22148036097329004426245259226', '124.00450436116097560794843850239', '124.5784368488227652369284950969', '125.13679033366319579283835432272', '125.74462424784238955842639602564', '126.89725847093641304831429207791', '127.09917999744189885501138632993', '127.96123792395453660565873330076', '128.55186470997261479373756514217', '129.80944823518249296508518535731', '130.267112252569779604051251932920', '130.90362915647995451106250190687', '131.85394428759085566860680601058', '132.09127550061125337791278690021', '132.87640784211364820747133736799', '133.37901206677088077206704129714', '134.42318141398693360484366504043', '134.931685717444610312624119167205', '135.44101024417695012811073797712', '136.069378827055820877605419175757', '136.79171315846358572926126625010', '137.738757281503865146064804466263', '138.533596488392916772232305230232', '139.51442778506611420657933108423', '139.66253644959682979706918259893', '140.4553360712363726581444045791', '141.101126709696301200368758274035', '142.00389992075655752748075673097', '142.37455677315868155133688786935', '143.24190296429591885102951693245', '143.793487276623507419766356597850', '144.15312389690487776696072740161', '144.99938448641588010799626716379', '145.95373962292405926912407106071', '146.37325741986408283464464220020', '147.516381108609249152727465933782', '147.99841972946051432453230645625', '148.63511220128836964386748935014', '149.38066891159055718281582824103', '150.2539535804821235720672122416', '150.6132652930222588754157722628', '151.33055731269190942260208717577', '151.98445080467718679464412965691', '152.36863761275129658550030227138', '153.26713858173707746091308570386', '154.11431620181312407430376805683', '154.47370262247707668181406029292', '155.14330378372194057293968840028', '156.20101311481082993060103123845', '156.76894560226854229924090335970', '157.54319662760997404728766589481', '158.35989215557091459204429618315', '159.07260852514676161808075702508', '159.25057471606089525206751442537', '159.89978719834619073982214896825', '160.883599651517390826574147317955', '161.44634557767187625893891516513', '162.04513773837775165448813547132', '162.57450456662698370673031438451', '163.535923856324073445121167211074', '163.74097754297961934187809126564', '164.67405787869068403295655619659', '165.81060800557827290110453646212', '166.440206055296254170484338491574', '166.83014091995900337950659866479', '167.589099472158921557072864068371', '168.08309217030054708315801377051', '168.96514978682793186519425724622', '169.56936169546496124836117792434', '170.208924977156365758308458800234', '170.60298472977863568588328593128', '171.53599988123590273044081584795', '171.98263645985929688136625416987', '172.42993858119779375082485157547', '173.71969717521184831470570859928', '174.2276280280304913182552028961', '174.88948884652296806010377753172', '175.74117870510613348091039088306', '176.12271146110547952360314619266', '177.17015331947570686521476126691', '177.49569184533529723237809791445', '178.26028607269786085598164455616', '178.84874746278885880699943888228', '179.38019033144093232823349761223', '179.954989079402995510018006373557', '180.836496696155482879591980661810', '181.33968368775448849101126233065', '182.22257409216481099329094570029', '182.57150896361925871867712187987', '183.65902003251980158433768717037', '184.17872364743881518309853138712', '185.17872371508771449495788561410', '185.668611365798999950259541139226', '186.15605320070800504799527820111', '186.878944525171008064419877659471', '187.35289707976619187303247577408', '188.17828792380353030092792565306', '188.71869207381269911688733490024', '189.3544604162719732544291331630', '190.20859143460209204435135399368', '190.66537229297254348324675581187', '190.94752306029263625198232932303', '192.218257135199680743355354262575', '193.05100356811626862723536340964', '193.56442037145293923364765745657', '194.33712095077108741866115067', '194.63711153871125689454904056301', '195.62324870041192665660802121148', '195.96031405325046336486550632853', '196.729453426924505865503373717829', '197.5245398740202340793072936265', '198.03911504542132035312269984471', '198.44433219226043779222097935494', '199.15260325911822418938571358659', '199.77795511585604616947000344603'], 'prelabel': '1-21e2-441.22-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.047995390047135, 'root_angle': -0.4467120181405896, 'root_number': '-0.944470043010589208142992426336-0.328597531724716050490316223241*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.446712018141', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(21)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.646932787321362949380781214058+0.789227768555963570090200243246*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.09262158218', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.37250389155', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.31599212182', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.047995390047135, 'bad_primes': [3, 7], 'central_character': '441.22', 'conductor': 441, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/441/22'], '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': '1-21e2-441.22-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': '1-21e2-441.22-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.047995390047135, 'root_angle': -0.4467120181405896, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.09262158218', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_441.22', 'Lhash_array': ['dirichlet_L_441.22'], 'factors': ['1-21e2-441.22-r0-0-0'], 'label': '1-21e2-441.22-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/441/22'}
Lfunction data - 1-21e2-441.22-r0-0-0