-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '545542994408729679239586621019,929132489490284020739939518583,1361965867310964095530041544925,1499520156164306099120928254115,1635398034848565202161496416872,1661122794022982020094979517517,1795365084858313655970281694608,2489925223314341094404343164843,2549594226034223515056396518856,3072934461757244896046819728155,3519393914514563562319222212690,3715569342840108790885901342514,4003113693730225160412010204997,4301684411811287390143147574448,4514864795499172070821551382899,4938549153448677919643650176905', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 12, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -4, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20155316.23850961, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [1, 0, 4, 0, 90, 0, -944, 0, -2381, 0, -76464, 0, 590490, 0, 2125764, 0, 43046721]], [5, [1, 0, 0, 0, 250, 0, 0, 0, -328125, 0, 0, 0, 97656250, 0, 0, 0, 152587890625]], [7, [1, 0, 104, 0, 11230, 0, 693056, 0, 42687379, 0, 1664027456, 0, 64738715230, 0, 1439493868904, 0, 33232930569601]]], 'bad_primes': [3, 5, 7], 'central_character': '105.1', 'coefficient_field': '1.1.1.1', 'conductor': 218287458838193562060699462890625, 'conductor_radical': 105, 'degree': 32, 'euler_factors': [[1, 0, -12, 0, 56, 0, -48, 0, -644, 0, 3744, 0, -3616, 0, -79584, 0, 542992, 0, -1273344, 0, -925696, 0, 15335424, 0, -42205184, 0, -50331648, 0, 939524096, 0, -3221225472, 0, 4294967296], [1, 0, 4, 0, 90, 0, -944, 0, -2381, 0, -76464, 0, 590490, 0, 2125764, 0, 43046721], [1, 0, 0, 0, 250, 0, 0, 0, -328125, 0, 0, 0, 97656250, 0, 0, 0, 152587890625], [1, 0, 104, 0, 11230, 0, 693056, 0, 42687379, 0, 1664027456, 0, 64738715230, 0, 1439493868904, 0, 33232930569601], [1, 0, 668, 0, 227076, 0, 54959032, 0, 10898303846, 0, 1884559898604, 0, 292753217618464, 0, 41349775413708356, 0, 5280291937987187427, 0, 605402061832104040196, 0, 62754252137843427978784, 0, 5914556263409244073997484, 0, 500774117694829537524831206, 0, 36973688499498403387598053432, 0, 2236637897091689096942786006916, 0, 96332237319141488337167610806108, 0, 2111377674535255285545615254209921], [1, 0, -752, 0, 294396, 0, -94491808, 0, 27897426986, 0, -6946713193296, 0, 1486545931814704, 0, -295772053309921424, 0, 53570281236296108787, 0, -8447545614584665790864, 0, 1212621184758825332321584, 0, -161845115298872016788087376, 0, 18563411269959456713604589226, 0, -1795813388062991723457691842208, 0, 159798375595133181477906587896956, 0, -11658205467602121953882690399351792, 0, 442779263776840698304313192148785281], [1, 0, -1812, 0, 1746836, 0, -1184674728, 0, 632617771366, 0, -284097553986276, 0, 111128236807771424, 0, -38432090155534531404, 0, 11793543729578919124387, 0, -3209886601880399597393484, 0, 775203624817021597595165984, 0, -165521552494986928520852760036, 0, 30783934756397679703494449715046, 0, -4814792236199270369836390571439528, 0, 592961159204531401059840157935179156, 0, -51372179568084274008566954547306230292, 0, 2367911594760467245844106297320951247361], [1, -48, -1532, 78336, 2653734, -99758160, -2908984696, 79073899248, 2758377278513, -50151488370768, -1975770167526888, 22031645624013456, 1185999145130228470, -7147818937900046784, -566860592607956328356, 949992618446762430096, 227741761450133276567076, 342947335259281237264656, -73873839289261476667682276, -336275439161991990894496704, 20142491247891343374977977270, 135077479089217957140388970256, -4373001588433109474095818436968, -40071374510206194474070427774928, 795630241367097590603288011338353, 8233755606418236297814462317203568, -109348657511047398101127252194882296, -1353716277753077868634994512304951760, 13000013747830451868965535133058407014, 138533566958469351568857158187730223616, -978046699774246729777619345512160126012, -11062397659065370322184456931484798083248, 83198449060887472631428936505541918917761], [1, 0, -2132, 0, 1767156, 0, -1229468968, 0, 1248595253606, 0, -923539261736676, 0, 468287785415244064, 0, -303211874716399935884, 0, 198161384670708543891747, 0, -84851114232512074457714444, 0, 36672077870925264368926621984, 0, -20239016069184569861405782992996, 0, 7657148257234013587294803163403366, 0, -2109960338878115933741535535313622568, 0, 848678019101002447296602158376436561396, 0, -286527696829366173852549205555103147777492, 0, 37608910510519071039902074217516707306379521], [1, 0, -9576, 0, 45402440, 0, -140765141160, 0, 318379322605540, 0, -555757542808824888, 0, 773262795811472582168, 0, -873860179983381108476280, 0, 810135983840573705163240070, 0, -618064701958825773784211794680, 0, 386821939880883334440742332679448, 0, -196635234523708557582165000074292408, 0, 79673302774774083303865991625557466340, 0, -24914666496465333899539197835608924005160, 0, 5683699948146868752417299089857524599021640, 0, -847867675954198545674622999457386566455368936, 0, 62623297589448778360828428329074752308805325441], [1, -344, 59116, -6962560, 644966390, -50363052712, 3435919762968, -209372772204072, 11579483269444545, -587768400942165480, 27595302421736225256, -1205497742639776491864, 49224919456418007325926, -1884863496224161633689600, 67835803472994372228786900, -2298558197729668914265384728, 73394137708506951686592058692, -2208914428018211826609034723608, 62647789059183235635101506674900, -1672823291081473051038493611417600, 41983492623134020053962964355995366, -988060049759062512928418688100703064, 21735792724991664006438669078660963816, -444907726407597545981352127517468719080, 8423183868078654122002349098293021086145, -146362794338491967412238023042843601421352, 2308218354544208567448911612101954777311768, -32513918363578622034467092012770359426827432, 400145314253230307495853782486508969234163190, -4151193622039590826706112197613098011458559360, 33871346981028995902427806159775450676994411756, -189412770998993328056840683935367879873528665944, 529144398052420314716929933900838757437386767361], [1, 0, 4936, 0, 9651186, 0, 11563577072, 0, 17334945323297, 0, 28195141563554256, 0, 40294960676450729842, 0, 82774213735327269675832, 0, 147723512473845461234622276, 0, 155132203188414691062926976952, 0, 141535221472587828319890058610482, 0, 185607263710743238127658358797705936, 0, 213870094458479886276541276075920292577, 0, 267378621975497465844861878826625219826672, 0, 418236626737949643944388431136878650625917746, 0, 400888340090478784358010451625778534517883814856, 0, 152214200233450528559804138174517974884637692126081], [1, 0, -12216, 0, 83224040, 0, -398236530360, 0, 1476742426794340, 0, -4443292746221574888, 0, 11154007950540985616888, 0, -23716326153822879285813480, 0, 43083733638609157921580222470, 0, -67016669508752693193559585058280, 0, 89063919490090935212830578926995448, 0, -100256192781057938593586192465884733928, 0, 94155666042960099040606289905472370051940, 0, -71749392767218614048972765004371249963858360, 0, 42370282096001232296678454057725525000326206440, 0, -17574258582772624620923546269598769238449105354936, 0, 4065214023175683899921868126254722311886802750234881], [1, 0, -16496, 0, 146336700, 0, -884936332960, 0, 4029319118940650, 0, -14503865770472138448, 0, 42481960034335372232368, 0, -102908562118417781386883600, 0, 208027477131765359105845167795, 0, -351823895079008829423259038563600, 0, 496537657066353285217897324677589168, 0, -579569121321120969631746249240449565648, 0, 550461505786567094478586872646639511820650, 0, -413314972399281023976220518939444609578572960, 0, 233666358808082027517040058435597842392326096700, 0, -90052423308752701157127077481243234779295406730096, 0, 18663392025969146670022260524972832947786731075670401], [1, 0, -14672, 0, 116061396, 0, -646412138848, 0, 2818120883606186, 0, -10187086332486400176, 0, 31511435695414691713744, 0, -84790042597275507436071344, 0, 199917465627374108064901115667, 0, -413748359851115945401156051961264, 0, 750327828467167310231110317962943184, 0, -1183652669530494486123617317643372170416, 0, 1597810773942166771537209548272203091854506, 0, -1788408239583414733805079394125323994081694048, 0, 1566882320946647917393026239935666164269561957076, 0, -966561162069943227376428543726663285364769984378192, 0, 321463340914028260476243062478235279920395730789296641], [1, 0, -15272, 0, 115608996, 0, -649480499248, 0, 3153703513389386, 0, -13200443109519730776, 0, 48037620613154020278544, 0, -158372269876092022445673944, 0, 472097770717226134401351928467, 0, -1249633386384176457359163787327064, 0, 2990807387473382877843514027162138384, 0, -6484835217685913906457114806440062931416, 0, 12224603322201304542030396621825259584584906, 0, -19864768482673345830742578380052261119744646448, 0, 27900533005389483167610169474567618231768610173476, 0, -29081731751119261005959471198655763725003024005373992, 0, 15025461748906708859452861070130993269553796873817927041], [1, 0, 948, 0, 25945076, 0, -22761523608, 0, 169024123159846, 0, -863462355580598076, 0, 4141075811916101091104, 0, -2323175168914222669865364, 0, 99988912175376285054299118307, 0, -28150752187969614125142436984404, 0, 608035973616310006275927259925060384, 0, -1536269993796025471671656517315161320956, 0, 3644021057278651181763752429363510697419686, 0, -5946228063949536799135721954040584966653546008, 0, 82130265471209257686098618717091266131832917125236, 0, 36363415077372401702134485906972924307480749332478708, 0, 464798130469793589516643498190087912509935907396786423681], [1, 392, 58168, 4718896, 501756764, 73806620440, 6607252863504, 417358734799608, 43016457989400138, 4408106367429180192, 266826572912162614632, 16833003484353437962056, 1690706907543180554609520, 116953244901619219770905256, 5550722508787024887997468104, 419490434896474956704599514976, 33169619643915883937630392693971, 1560923908249783313897814795225696, 76854421291786249462255751770555464, 6025474960065136817669771444982541416, 324120878311045543516430935491776715120, 12007703717560129521061204344595820587656, 708250840124738923040495261432375663152872, 43538128380341707089597319658445278689968672, 1580927694823340635418583018816189376661628618, 57075081113515054682432611871565252052757310648, 3362154201901857259663243620683839862627997164304, 139749959256152437078187509867711988292402337105240, 3535161639737875312379508137569695728252855095823324, 123713221553421082930097853030150816920239371828116656, 5674394317649610902748817659030866780274864321492282808, 142292207611433902666385528119026118715546106020267697992, 1350687001332003958728623852374735172807518011483204347521], [1, 0, 25096, 0, 320737746, 0, 2939997955952, 0, 22183328725900097, 0, 145120466564960354256, 0, 844167542922670703605522, 0, 4435418621494949553910291192, 0, 21021350810484141392366845910916, 0, 89378657327397929349742300955226232, 0, 342789153623304948509068186038075371602, 0, 1187479985210241558868768937434623163601616, 0, 3657830342018599313549439593358271828348579457, 0, 9768841933571799947865059051492025642214371735152, 0, 21475601551905889926077011797230560254296737389886866, 0, 33860937746524001500602073375656809913083918914319328136, 0, 27189028279553414235049966267283185807800188603627566700161], [1, 0, -54696, 0, 1473645320, 0, -26047422376680, 0, 338289093213534820, 0, -3420795296041945606008, 0, 27834490970292132211947608, 0, -185763895284534489022543706040, 0, 1027168473043198821594367598639110, 0, -4720572848287994668538882466446253240, 0, 17974220834494392812733972957544304089688, 0, -56134165528724788840591234443618412584119928, 0, 141065747796236162659230730913434825302268293220, 0, -276014391444461852732565958712431453495634902408680, 0, 396819804183611611012908865714884317797988599281990920, 0, -374273717637273598549311934277252161930322763763542118056, 0, 173887017684702179246328390437079448141248104062408434512641], [1, 0, 21656, 0, 234439266, 0, 1309085752912, 0, 2475221846446577, 0, -11590633136358955344, 0, 25640523813063653119042, 0, 1558159667579488643235006632, 0, 12716944684257376935794514951396, 0, 44248993756402205147350737972134312, 0, 20678059190495685854482809197148190402, 0, -265449236978134873657800406368299017318224, 0, 1609829536570648552546749371128109108695747697, 0, 24178274214659866893540715999265340857068663519312, 0, 122964286993642878418068463083346069105440777878094306, 0, 322565804947687814735941678488730231626547034459859197336, 0, 422991386556309150149363832086603107763045099853453376062721], [1, -608, 158548, -26562304, 4208789174, -690629020960, 95475474742824, -11336959661249952, 1376670495367192833, -162662283177219304608, 16722605184638925760152, -1644117179385679907376864, 165877293353502354158645670, -15349309823384966777148536064, 1292631712250469302658943264044, -110863174585305092058196189333344, 9261032587932971440635568922777796, -691897072586889079535202417629399904, 50348109895324471626579355508918187564, -3731224668970141477100157479667864409344, 251653903110053457436163577155123007240870, -15566955366613346772338265120787974450557664, 988164008746422474139739098188552232134139032, -59988242989117511828566876785054929253988978848, 3168571163119383415292636111680718124092032750593, -162848680718321920772974691721441427612583410733472, 8559209417353452425421225496866907673525698463888424, -386403304924201094815390855640907310644917958270595360, 14696278135676948774881029479920070945201773018754656694, -578855436359272389028496351875318532299516192187956489984, 21563503524724247671792384317477725749805697182921317356628, -516079155225325138567191087111979461954478848803618213453408, 5297450670659957549009604563595170759963655420038456036451841], [1, 0, 29544, 0, 661846280, 0, 10426300509480, 0, 139767629955703780, 0, 1535588514048427501752, 0, 14862680365368504632892248, 0, 123277233839667783008490962040, 0, 912480700116526498364181668166790, 0, 5850530535555016179375309802093134840, 0, 33475099535684926742800424116079507054168, 0, 164139068150035552419603561651261361794102072, 0, 709016070375966252043880381648939305711322494180, 0, 2510106137683402058349967141364105449356354154797480, 0, 7561907301568103296381576243621974782426590197443023880, 0, 16019755417098992878840489611931244962520119677450496489704, 0, 25733505785478367615107164358252046214490685371339768616901761], [1, 0, -3172, 0, -240595644, 0, 390057940792, 0, 37366996704615206, 0, -36104713523503280916, 0, -3704425195681976827921376, 0, 750860105615056098352170116, 0, 276240220801708620001282489833507, 0, 47110645703785302951331560291069956, 0, -14582798756882410866874298155119547583456, 0, -8917517763778252966605992768966559566905236, 0, 579066312096968222533740721988980404086751510566, 0, 379253202350665347031142094459749906366690357083192, 0, -14677359089917273601214046454887112396018285170535747004, 0, -12140969405109633464981527413511679490919426355718203951332, 0, 240148684864128390378794468324923219083866317778128398613374721], [1, 0, -149792, 0, 10524668616, 0, -460430092223968, 0, 14037362496246878876, 0, -316246112482341563469216, 0, 5446093182088385543580162424, 0, -73129983228930169756375130532704, 0, 773831593196422564367688817701285702, 0, -6474144834799246327739835472341432105824, 0, 42683393663406836668492335916727593463513464, 0, -219424949340376726534073307319331973835520957856, 0, 862250119829973109479566664110174706318107447114396, 0, -2503792794646343204050568311244321014300467037447411168, 0, 5066756726656225986875509900438120945471408067989188983496, 0, -6384063217261844376233042195663415252762626323373109480986912, 0, 3773075507922571775273744352333525624409237957166570157859261441], [1, 0, 36788, 0, 445549716, 0, 4790475749992, 0, 124790350505724326, 0, 1733319344220241683204, 0, 12297948091889502443839264, 0, 177280065018366002141010349676, 0, 2700158258659274465372718836289507, 0, 18447834655117238547560395532434780076, 0, 133169155567686003077740008485419293170464, 0, 1953147622279299830956999193102528604056168004, 0, 14632650009555560655603222735892120158663415845926, 0, 58452907967525048141695320818212266107395461840533992, 0, 565729912048754308556340996348833003177376576273765028116, 0, 4860765209025285077319889840210184814284609493810486649683188, 0, 13749406785310970541622913505711040449564178320493809360964963201], [1, 0, 26056, 0, 406179186, 0, -1442798314768, 0, -103188429345672223, 0, -1802567460127341096624, 0, -5407261420732640172693518, 0, 147693528734655959185857316792, 0, 3158310478118634136881208388653956, 0, 16623036777084343438268283745235693752, 0, -68497569900256032544916669114777459424398, 0, -2570030180551222147255992517571327945733188784, 0, -16558713701149050184652915501141755646939581748383, 0, -26058542456645820231978748247782941397518249748445968, 0, 825678655467683702878522954701104543299587960095145697266, 0, 5961424351901007614635541116777808559120642531426014716745416, 0, 25750827556851106532658069028441289322166445432839581773436522241], [1, 0, -35292, 0, 636267716, 0, -1737146847288, 0, -115752144410667674, 0, 2436842310893124656724, 0, -11304468523242595979816416, 0, -236014200832788614724722289924, 0, 5228948371797383650503005245107427, 0, -30936647275495799335459322599044240324, 0, -194231815869803832609043617003029347803616, 0, 5488235756217351081555908610654822064365867924, 0, -34171928454788103648234588517753169155662981109274, 0, -67222101640072249007177261373628487405262127028271288, 0, 3227383336144711203253619832081030514623883341841551829316, 0, -23465080353360846777974125958205458249938657071322145681857692, 0, 87152707983437572386914428735274683878049343856532228222877116801], [1, -208, -60572, 11804416, 2761459334, -424978863920, -92226195099576, 10474380369103248, 2501531226621582993, -197676819045627415728, -54790910891877124858728, 2764378038445121095725936, 1002197973279372736263953430, -27561537036978087769498052544, -15310194391463680826249002640196, 125992915170466371009976392877296, 198177642598759423653830639957444196, 1496921825140310953969529523775153776, -2161158884851527283724269740774212039556, -46223456819664277713913410380476042029504, 19969422411341034939869336751065728021539030, 654428815105519100243477209042960565733828336, -154108465427387590074909266872477842559460558568, -6605819688628640013890946489919626358315355823408, 993184414070939784026154943259573361303404337071313, 49408913497523611663010417180032972901248787634286608, -5168734808872852756015480365796112851825431843728216376, -282976444739744608195841336840766087837908641892190169520, 21846134474775457294235303905772237918867775185953586187974, 1109515701354797254588931776283870670363340632437585811494656, -67641597528172531442660015908113069197815011049283611235080412, -2759677121579299213871271858167017863517168830904048499264841808, 157633287891748336346175869936934323252151359999860577979642238081], [1, 0, 202864, 0, 19309089720, 0, 1144654106096720, 0, 47301303247389841820, 0, 1444805289641627550356592, 0, 33743102351866746129166699528, 0, 614653471112949974369450889918160, 0, 8825417360726993430313764480765674310, 0, 100217626394456226245956606620257493975760, 0, 897041544979675227303392077740481840792340488, 0, 6262541903230775352076993327504498161557877309552, 0, 33429370789108810612498766724695827305340692871134620, 0, 131899497248034857070097211700916008453782898558457712720, 0, 362780925249675343009307531494324203227101499475807138004920, 0, 621443145369110561274770801501078806394522770280531255963538544, 0, 499470901017296553026067587470451820114248277410727635080006663681]], 'euler_factors_factorization': [[[[1, 0, -6, 0, 10, 0, 36, 0, -156, 0, 576, 0, 2560, 0, -24576, 0, 65536], 2]], [[[1, 0, 4, 0, 90, 0, -944, 0, -2381, 0, -76464, 0, 590490, 0, 2125764, 0, 43046721], 1]], [[[1, 0, 0, 0, 250, 0, 0, 0, -328125, 0, 0, 0, 97656250, 0, 0, 0, 152587890625], 1]], [[[1, 0, 52, 0, 4263, 0, 124852, 0, 5764801], 2]], [[[1, 0, 334, 0, 57760, 0, 8187676, 0, 1046359339, 0, 119875764316, 0, 12381368966560, 0, 1048235077824814, 0, 45949729863572161], 2]], [[[1, 0, -188, 0, 20583, 0, -5369468, 0, 815730721], 4]], [[[1, 0, -906, 0, 463000, 0, -172859364, 0, 52513801899, 0, -14437386940644, 0, 3229775695183000, 0, -527855746930163466, 0, 48661191875666868481], 2]], [[[1, -12, -599, -252, 369744, -90972, -78062279, -564550572, 16983563041], 4]], [[[1, 0, -1066, 0, 315400, 0, -278518084, 0, 277658769259, 0, -77940779144644, 0, 24699284757627400, 0, -23360989644533662186, 0, 6132610415680998648961], 2]], [[[1, 0, -2394, 0, 2753756, 0, -1693230714, 0, 500246412961], 4]], [[[1, -86, 3685, -153854, 5740444, -147853694, 3403174885, -76325316566, 852891037441], 4]], [[[1, 0, 2468, 0, 1780081, 0, 1388548628, 0, 3656190464464, 0, 2602363685201108, 0, 6252497938815147601, 0, 16246725550413207073508, 0, 12337511914217166362274241], 2]], [[[1, 0, -3054, 0, 6815636, 0, -8629874094, 0, 7984925229121], 4]], [[[1, 0, -4124, 0, 11073111, 0, -14099135324, 0, 11688200277601], 4]], [[[1, 0, -7336, 0, 31122250, 0, -94893243424, 0, 228626385513379, 0, -463048756964467744, 0, 741060816308991282250, 0, -852380720087246769975976, 0, 566977372488557307219621121], 2]], [[[1, 0, -7636, 0, 28650250, 0, -105966940624, 0, 357269785558579, 0, -836130131621800144, 0, 1783755695208095490250, 0, -3751252992904360916838676, 0, 3876269050118516845397872321], 2]], [[[1, 0, 474, 0, 12860200, 0, -17476496604, 0, 10103548950219, 0, -211769018365942044, 0, 1888268793679088924200, 0, 843339576245538507801594, 0, 21559177407076402401757871041], 2]], [[[1, 98, 136, 198548, 40060699, 738797108, 1883034376, 5048996687378, 191707312997281], 4]], [[[1, 0, 12548, 0, 81642721, 0, 445546114868, 0, 2168184767444464, 0, 8978253671784967028, 0, 33152470105874802860161, 0, 102676756815333091449951428, 0, 164890958756244164895763202881], 2]], [[[1, 0, -13674, 0, 87943916, 0, -347479325994, 0, 645753531245761], 4]], [[[1, 0, 10828, 0, 58596841, 0, 20056282108, 0, -696353387031776, 0, 569563132866972028, 0, 47256013777562853198121, 0, 247983376247396521328349388, 0, 650377879817809571042122834561], 2]], [[[1, -152, 4981, -857432, 145300984, -5351233112, 194010353461, -36949293239192, 1517108809906561], 4]], [[[1, 0, 7386, 0, 83632076, 0, 350527158906, 0, 2252292232139041], 4]], [[[1, 0, -1586, 0, -121555520, 0, 2241915676, 0, 11299181809334539, 0, 140662813645269916, 0, -478514099303295421037120, 0, -391726780054505754521384306, 0, 15496731425178936435099327730561], 2]], [[[1, 0, -37448, 0, 527638098, 0, -3315244514888, 0, 7837433594376961], 4]], [[[1, 0, 18394, 0, 53605240, 0, 1409223090436, 0, 35037164849653579, 0, 146644319889229424836, 0, 580467935908025844997240, 0, 20726819604247451041842131194, 0, 117257864492369852051862561201601], 2]], [[[1, 0, 13028, 0, 118225201, 0, -2261637076012, 0, -29118205922296976, 0, -254549245407414566572, 0, 1497641474928372723333361, 0, 18574812833832019301294472548, 0, 160470643909878751793805444097921], 2]], [[[1, 0, -17646, 0, 162443200, 0, 1997899283556, 0, -35815038060824661, 0, 261883840926706341156, 0, 2791076612476725631883200, 0, -39742172778802688617385962446, 0, 295216374856540727739668685278401], 2]], [[[1, -52, -19199, 96668, 306457024, 1148512508, -2710095533039, -87209205763732, 19925626416901921], 4]], [[[1, 0, 50716, 0, 969103446, 0, 8269109960476, 0, 26584441929064321], 4]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 3, 'label': '32-105e16-1.1-c2e16-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/105/3/o/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0078125', 'prec': 30}, 'plot_values': [32.38714423380734, 32.41083685798766, 32.38917909649252, 32.3229955597032, 32.21321769496532, 32.0608767480719, 31.867096678264705, 31.633087059364176, 31.360135997416226, 31.04960309303783, 30.70291247446592, 30.32154592517667, 29.907036127854827, 29.46096004446157, 28.98493245018582, 28.480599637170265, 27.949633302085488, 27.393567492473117, 26.813338016122543, 26.2097795710358, 25.58378635289934, 24.936311487319596, 24.26836628379056, 23.58101930472576, 22.875395243117104, 22.152673602658954, 21.41408717449813, 20.66092030514598, 19.894506950515115, 19.116228511527243, 18.32751144728123, 17.52982466237253, 16.724676665622507, 15.913642116089822, 15.098441906118644, 14.28084075040809, 13.462611526247953, 12.645530416631235, 11.831371936965231, 11.021903858206292, 10.218882040207488, 9.424045190027005, 8.639109560892512, 7.865763608447844, 7.105662621817892, 6.360423347909509, 5.631618628214817, 4.920772068191665, 4.22935276005837, 3.5587675337612663, 2.910350233031674, 2.285367664825326, 1.6850172785356512, 1.1104219048095234, 0.5626246612074833, 0.042584054419197354, -0.44883069090021566, -0.9108440464010582, -1.3427783070980641, -1.7440574010209933, -2.1142103515622725, -2.452874363118435, -2.7597975013115286, -3.0348409399727356, -3.277980748180694, -3.4893077680948372, -3.6690252737094933, -3.817455484705121, -3.9350409311952155, -4.022343482599219, -4.080042733863199, -4.108933738247937, -4.109924079655698, -4.084030281452467, -4.032373552945923, -3.9561748790823885, -3.8567494635065307, -3.735500539862077, -3.5939125710727047, -3.4335438612999276, -3.256018610296809, -3.0630190856704895, -2.8562790899707378, -2.637573364186584, -2.4087069578863884, -2.171504748248962, -1.9278006739572284, -1.6794267550963, -1.4282019744590697, -1.1759210994753813, -0.9243435272876241, -0.675182238239121, -0.4300929451671053, -0.19066352734673483, 0.04159616133278912, 0.2652640204098428, 0.4790148783968757, 0.6816280176606594, 0.8719923616121734, 1.0491173368304416, 1.212140305148609, 1.36033188149672, 1.4931001689257708, 1.6099938511073983, 1.7107040919902927, 1.7950652025866567, 1.8630540459926082, 1.9147881636354944, 1.9505226182953446, 1.9706455625610224, 1.9756725549354923, 1.9662396596684377, 1.943095380426467, 1.907091600766577, 1.8591741243264572, 1.800371811823055, 1.7317843482402, 1.6545692730662678, 1.5699284182731323, 1.4790939044563325, 1.383313854977686, 1.283837995694586, 1.1819033137430153, 1.078719952696343, 0.9754575230994494, 0.873232006748563, 0.7730934300462852, 0.6760144762299785, 0.5828801982010816, 0.4944793574696382, 0.4114976896039782, 0.33451022344629483, 0.26397625544585457, 0.20023650172775342, 0.14351206898952953, 0.09390527851308193, 0.05140234948249732, 0.015877918440006772, -0.012898658515942745, -0.035255304857358664, -0.05160763879990603, -0.062447949398911184, -0.06833290759375946, -0.06987021385223185, -0.06770440964441661, -0.06250214102849325, -0.054937247253740926, -0.04567556551815169, -0.0353599108749708, -0.024595669759516485, -0.013937313194760574, -0.0038761449880371276, 0.005170409677828834, 0.012867685866471558, 0.018970563503292844, 0.023327916055592743, 0.025884518605359657, 0.02668025059698851, 0.02584647381106226, 0.0235995161977797, 0.020231246482799645, 0.01609680183864566, 0.011599592278490492, 0.007173542910936143, 0.0032629534534397713, 0.0003003054966321707, -0.0013176272502033993, -0.0012549367917482558, 0.0007374766649548863, 0.004795709371591826, 0.010916978630657355, 0.018934672418932555, 0.02849495163837143, 0.03903554420880845, 0.049767370043319395, 0.05965962323214217, 0.06742891194569851, 0.07153301306181563, 0.07016993221082965, 0.06128289887413248, 0.04257127687341432, 0.011507731958838235, -0.03463815763247691, -0.09876981217098305, -0.18392717451875404, -0.2932440723418649, -0.4298997812519435, -0.5970652912457597, -0.7978449175419657, -1.0352140320135657, -1.3119538199869591, -1.6305840862752095, -1.993295240989481, -2.4018797775892247, -2.857662976584542, -3.361441691304622, -3.9134268812064255, -4.5131913770493215, -5.159624988662855, -5.850898265595249, -6.584436135019579, -7.35690252615055, -8.164196946705042, -9.001463805862313, -9.863115081615407, -10.742866710855996, -11.633788841118225, -12.528369827330378, -13.418593589437222, -14.296031977244473, -15.151955804588683, -15.977444604956016, -16.7635068128574, -17.501208794830887, -18.181808966719217, -18.79689481100869, -19.33852044962363, -19.79934230852766, -20.17275033518851, -20.452992202117223, -20.63528795217164, -20.71593261607595, -20.69238446058679, -20.563336706784757, -20.328770790789722, -19.99000110208825, -19.549721466579218, -19.011958304215455, -18.382022365644637, -17.666448889353916, -16.872915226738485, -16.010136866497437, -15.087743250507442, -14.116135221135178, -13.106326364647837, -12.06977090688593, -11.018181165907661, -9.9633378626937, -8.916896826797085, -7.890195801635664, -6.894065147785573, -5.938653705050882, -5.033274502700867, -4.1862164343563135, -3.4046000034825807, -2.6942644621877654, -2.0596797874956576, -1.5038855425412994, -1.0284581215179982, -0.6335072829909263, -0.31770224886305526, -0.07832699948255945, 0.08863625635140196, 0.18839709929713486, 0.22722268419199046, 0.21228214590848538, 0.15147300075819609, 0.053233694726570274, -0.07365336745897577, -0.22026779959642614, -0.37775823906596784, -0.5375443975948031, -0.6915096202607027, -0.8321794361809948, -0.9528819099163355, -1.0478860349880528, -1.1125149408567154, -1.1432313003567156, -1.1376930116093351, -1.0947779703980665, -1.0145775276799398, -0.8983590227912085, -0.7484985755975336, -0.5683888583603794, -0.3623270276190324, -0.13536285688255192, 0.1068662746761792, 0.3583107983985652, 0.6126925241195573, 0.8636912124211374, 1.1051289488375342, 1.3311472071240928, 1.5363717207618817, 1.7160606509400684, 1.8662320358032118, 1.9837671165214579, 2.066486844088138, 2.113199657035866, 2.123719462378451, 2.0988546442874023, 2.0403713590164205, 1.9509230427489936, 1.8339529470758849, 1.6935748969333166, 1.534435743517207, 1.3615640291190676, 1.1802097629286346, 0.9956804343700821, 0.813178456455587, 0.6376451339309607, 0.4736159927454296, 0.3250918967585715, 0.19542982761695318, 0.0872565319035622, 0.0024074674869886824, -0.05810704457204816, -0.09410863428273152, -0.10623260719845622, -0.09588021681422425, -0.06514579632606028, -0.01672239330182755, 0.04621041673872596, 0.12011229972395239, 0.2012168685530653, 0.2856704360469985, 0.36966985942427916, 0.4495946294211416, 0.5221286378238522, 0.584367498771774, 0.6339078852951565, 0.6689160515439708, 0.6881741906058778, 0.6911049017972254, 0.6777675834312971, 0.6488309049573768, 0.605523473725332, 0.549564739421781, 0.48307936032550686, 0.4084988414619225, 0.3284546824087918, 0.24566752604690548, 0.1628368699499938, 0.08253578760124616, 0.007114812793966274, -0.06138131981868838, -0.12128099253491857, -0.17133472436619962, -0.2107442016393354, -0.23917120606876577, -0.25672749291452385, -0.26394378199470475, -0.2617210548800127, -0.2512672908054254, -0.23402303583683168, -0.21157964953524533, -0.1855943422432506, -0.15770619218453097, -0.12945721135586438, -0.10222221801725889, -0.07715078541648271, -0.05512389333597969, -0.036727140528975244, -0.022241517618678163, -0.011651875352565379, -0.0046721400805015325, -0.0007854150275108711, 0.0007027705851273604, 0.0006016769949162336, -0.00023309071361331385, -0.0009695869610041841, -0.0008668790646102185, 0.0006643485432270247, 0.004011703654354303, 0.009324730915701544, 0.01649478522528978, 0.02515274656554706, 0.03468519722872009, 0.04426862818006037, 0.05292017769969297, 0.05956238528380008, 0.06309867045590456, 0.06249536790099757, 0.056865125470133344, 0.04554661281685183, 0.028175393444177393, 0.004741034664197043, -0.02437393313818104, -0.058376789669765436, -0.09607166591240901, -0.1358921479923817, -0.1759593593116015, -0.21416398569621856, -0.24826925914801823, -0.2760305452242356, -0.2953259639692865, -0.3042919707945114, -0.3014577776758999, -0.2858668227373491, -0.2571799012937816, -0.21575317755411236, -0.16268456469740708, -0.09982357382905059, -0.02974137221372957, 0.044340291686484304, 0.11866052871489972, 0.1890681433524712, 0.25120270185183025, 0.30070061688739896, 0.33341722067694196, 0.3456543439929566, 0.33438191828095376, 0.2974416488803016, 0.23372167534220448, 0.1432905012341017, 0.027478474021971164, -0.11109959485560383, -0.26858543592865974, -0.43998393680059145, -0.6193340470342613, -0.7999392095537168, -0.9746491404755976, -1.1361815732017904, -1.277469765630087, -1.3920193134116776, -1.4742562715341232, -1.5198478886771059, -1.5259774964007, -1.4915580875245469, -1.417371903052673, -1.3061088123259181, -1.1623082154448128, -0.9922014045948557, -0.8034552784400479, -0.6048252881380263, -0.40573090160709596, -0.21577194225211713, -0.04420859994557898, 0.10056855135517721, 0.21154981302939532, 0.2835691623295928, 0.31368935318745633, 0.30148217153781753, 0.24918040379076778, 0.1616832635669509, 0.046402773968444, -0.08705360862764447, -0.22735758707504417, -0.36207678494057177, -0.47841024323261216, -0.5640108267895648, -0.6078553274537069, -0.6011171491937833, -0.5379924629359336, -0.4164289797711644, -0.2387072763805461, -0.01182807453490266, 0.25233493710232413, 0.5371483442473634, 0.82161872751337, 1.0810840124389247, 1.2881906068918707, 1.41414965425694, 1.4302066243966256, 1.3092738777015713, 1.0276605830584291, 0.5668205302452197, -0.08496959230700214, -0.9310931573289378, -1.9653295829032267, -3.1709306950764713, -4.520115742215918, -5.974049689623905, -7.48335152431186, -8.98915768527024, -10.424741159913303, -11.717676645929714, -12.792539002991466, -13.573919208868052, -13.989724004036512, -13.974637652451177, -13.473587885842647, -12.445057424335895, -10.864077452639195, -8.724741664437564, -6.042089358355444, -2.8532236375630777, 0.7824442609028399, 4.783901756416038, 9.050232617850558, 13.463303474471212, 17.891392417856043, 22.193629673679208, 26.22509223060182, 29.84267347842822, 32.91116865480674, 35.30938558051499, 36.93606178393081, 37.71532055083073, 37.601402611191375, 36.58242624603959, 34.682956498783, 31.96520330695854, 28.528717597556838, 24.50851206661125, 20.071597382827598, 15.411992414389895, 10.744335975900269, 6.296252816492488, 2.2996982811219944, -1.0180393392038767, -3.4436623028365503, -4.7871048031866446, -4.890261845162715, -3.6348214349328565, -0.9488378332149695, 3.18827803833961, 8.742621233599383, 15.624711317134723, 23.690591100073306, 32.745143102206264, 42.54756972770965, 52.818890635867675, 63.251221286757506, 73.51875117853908, 83.29046225859379, 92.24213373337608, 100.06856203671951, 106.49553015652792, 111.29084902744549, 114.27400589633928, 115.32400272645768, 114.38503444966649, 111.46973968723645, 106.65985217101364, 100.1041856203589, 92.01399391657418, 82.65585743818343, 72.34235067113102, 61.42084110944295, 50.26103792377545, 39.24170545020256, 28.735663753883046, 19.095791491140996, 10.642092102998662, 3.6500873935450366, -1.6590023982547635, -5.125909362732097, -6.658509356039645, -6.234368420469284, -3.9005703136275525, 0.22913452526470582, 5.979706694871661, 13.12246637529604, 21.384664965417645, 30.46055631809498, 40.023528404433236, 49.73900732756011, 59.27725810515058, 68.32542757488042, 76.5984796247888, 83.84860779277263, 89.872790234957, 94.51824468421837, 97.68564168323586, 99.33003817617664, 99.45959554207327, 98.13224162010565, 95.45052091274448, 91.5549472891625, 86.61622627844584, 80.82674749184683, 74.39196889040223, 67.52219035265732, 60.42342571483984, 53.289665417424615, 46.296515053802544, 39.59618329371885, 33.31394409562337, 27.546116773576763, 22.359528972108798, 17.792355904935913, 13.856167764853483, 10.5389687366941, 7.808977435512617, 5.618880836115599, 3.910291920353998, 2.618154513595228, 1.6748727436549056, 1.0139598103365484, 0.5730268546034314, 0.2961139800126714, 0.13526182673952683, 0.051320471931358365, 0.014055107094115568, 0.0016472750491030364, -0.000280309493394572, 3.059645794661177e-05, -0.0010101942555105236, -0.0038565757363559763, -0.007241128202239773, -0.009382030138686999, -0.00890418694383187, -0.005430529742782129, 0.00016594685242092604, 0.005826362389056626, 0.008635416368199226, 0.005340695893404255, -0.007027267297412114, -0.03052851160403689, -0.06577137302737926, -0.1115328155489512, -0.16460027146177128, -0.2198690009923754, -0.27070089698049254, -0.3095218580786484, -0.3286078501504402, -0.32098694602153094, -0.2813680312007326, -0.20699805867498863, -0.09834978271227734, 0.040451076821924274, 0.20153350256963823, 0.3735651063266586, 0.5424270272143173, 0.6922600884057525, 0.8068273940324892, 0.8711061321588981, 0.8729940518383337, 0.8049963664369312, 0.6657486788570812, 0.4612322523104474, 0.2055501140064302, -0.07884421425251374, -0.36154026261648625, -0.6052199955000784, -0.7673487357323021, -0.8024531430039603, -0.6648847690599142, -0.31188505445988984, 0.29322789671582555, 1.177958410154679, 2.357837637542823, 3.8341465155650436, 5.592349009768382, 7.60139118335822, 9.813972589419079, 12.167837356089848, 14.58806672670378, 16.99028696137872, 19.28464098833689, 21.3803136496433, 23.190360542080835, 24.63656043227784, 25.65392120922254, 26.19459524693255, 26.230937498679356, 25.757478074815108, 24.791649399182745, 23.3731833458774, 21.562177608749874, 19.435917647126992, 17.08462514376855, 14.606380198303164, 12.101526974428397, 9.666916437806453, 7.390361434585503, 5.34567629084736, 3.5886403943881273, 2.1541848539317607, 1.0550519140544388, 0.28197659332588637, -0.1945858413894756, -0.4212709385138618, -0.45734852318019364, -0.3692861586361168, -0.22469788114640118, -0.086099289303107, -0.004919431086688914, -0.016219825057866368, -0.13454016590226722, -0.35122955634428155, -0.6335342339434811, -0.9256023849044251, -1.1514486508264514, -1.2197531507499109, -1.03011347391311, -0.480489231527101, 0.5246054218913738, 2.0656907209915247, 4.200250509985189, 6.9555651239356004, 10.322979937203367, 14.254075023464338, 18.65910253927958, 23.407932365000615, 28.333600093052667, 33.238393015230905, 37.90224872294578, 42.09308717466368, 45.57904918911576, 48.14270277896312, 49.59232175940835, 49.772864867645346, 48.57589396825935, 45.947399853467886, 41.89302836945545, 36.48033707837198, 29.83787439634182, 22.151049962021347, 13.654946713067993, 4.624401188767968, -4.638161450350106, -13.816516858934737, -22.595334050095392, -30.674989278276616, -37.785848725912125, -43.7019236998733, -48.251695723438715, -51.325398792224824, -52.879024307841064, -52.93487400086562, -51.5786791688826, -48.95349695656831, -45.25077220338841, -40.69910640734454, -35.55139502187963, -30.071074118837288, -24.518253350235607, -19.13650270519448, -14.141007055961897, -9.708708767742786, -5.971064312449442, -3.0096270955155475, -0.8537182933298136, 0.5181104877287662, 1.1735497253712008, 1.2195369530261773, 0.7933175460369217, 0.05217885039855651, -0.8374717607637415, -1.7110040366233357, -2.4157877930888203, -2.820161854341366, -2.820671159942144, -2.34722093863673, -1.3659395168371362, 0.12030954913081045, 2.0736257985121385, 4.424679560310207, 7.078378771572849, 9.920813021941994, 12.826951986290034, 15.668613733256736, 18.322190404423047, 20.675665030171533, 22.634526919841395, 24.126287691011115, 25.103408110471808, 25.544559559601137, 25.45425524915867, 24.860988046456953, 23.81409776559366, 22.3796562643294, 20.635710573486715, 18.66724749412922, 16.561121479006335, 14.401326820735997, 12.264898435114944, 10.21863651141741, 8.316783090355079, 6.599702566547776, 5.093545087693464, 3.810806846379511, 2.751648371073394, 1.9057939557417398, 1.254813828023366, 0.7745856999264469, 0.43774286370214766, 0.2159397902741622, 0.08179846645883745, 0.010442854578729944, -0.019417592607374468, -0.024886302375572187, -0.018721874829660274, -0.009558535849602331, -0.002419402057716692, 0.0005750628831720425, -0.0005966894388090632, -0.004663221480328124, -0.009789483966002443, -0.014170650323869853, -0.016454210593694975, -0.01597747659326221, -0.012829286044767291, -0.007762691291089923, -0.0019983729368686334, 0.0030345960226444983, 0.005972383062768596, 0.005760102408543276, 0.001831681011311672, -0.005795889211425348, -0.016522049951627656, -0.02925062190082764, -0.04254921931718875, -0.05485446737678259, -0.06469246806294296, -0.07088322356929679, -0.07270101006641694, -0.06996942278620513, -0.06307904225280166, -0.05292620491300954, -0.04078199557346025, -0.02810930335261525, -0.016352591174568065, -0.006731494984829634, -6.58570822618122e-05, 0.003343703771707953, 0.0037623493055373818, 0.0019866297125593836, -0.0007685138626022458, -0.003048663189407484, -0.003383028709479923, -0.0005234012797704816, 0.006332755713585761, 0.01736638216757783, 0.032035137153382354, 0.0490653019515517, 0.0665471707078231, 0.08213392746087352, 0.09331938599345392, 0.09776929135705349, 0.09367124198686096, 0.08006199751089002, 0.057091125342922065, 0.026184224444231876, -0.009922398759638965, -0.0472914675577176, -0.08104001209649991, -0.10572555315050094, -0.11583340678061793, -0.10632242006461692, -0.07317727468685628, -0.013911216943952635, 0.0720352534950874, 0.18304781449498034, 0.3152852749297378, 0.46283406271689154, 0.6180650337307437, 0.7721689796572994, 0.9158281606558835, 1.0399657879834947, 1.136505198210579, 1.1990667475868355, 1.223533860135545, 1.2084301373855355, 1.1550662105354823, 1.0674366394746018, 0.951871626813246, 0.8164732211435568, 0.6703916976982098, 0.5230111959828924, 0.38310189516721344, 0.25806295829617326, 0.15332796345386557, 0.07199170714033339, 0.014698353071257542, -0.020197645900042225, -0.036217568003779614, -0.038141628834399956, -0.03126619294605517, -0.020631294774316033, -0.010324560043481038, -0.0029659285262044798, 0.0005363059017946255, 0.0008932081266830658, -2.2725415631360136e-05, 1.1995477640811385e-05, 0.0024674385672997334, 0.0067647280821382895, 0.008929202053772995, 0.0003568942572641522, -0.03313057181117126, -0.1117743386399814, -0.2617665418865494, -0.5144375006335751, -0.904698508032068, -1.468765411945676, -2.2412622808858558, -3.2518776659795687, -4.521811370444071, -6.060300406955988, -7.861595211237474, -9.902865453071888, -12.142928407796923, -14.52221890627985, -16.964180245669404, -19.378089502345425, -21.663248088014747, -23.71435074050497, -25.42773431525688, -26.708111529448157, -27.47532332770845, -27.670604436764645, -27.261855414775294, -26.247453766812153, -24.658216023447135, -22.557238296942412, -20.037669182862405, -17.218493709330716, -14.237055420029943, -11.240500245040886, -8.37642600439135, -5.783177575948872, -3.580490076816751, -1.86118628304331, -0.6845840569614647, -0.0721665219877297, -0.00591806981355561, -0.4295428196224112, -1.2525719152511536, -2.3571474004323685, -3.6070599029200747, -4.858431475935855, -5.9712937549762355, -6.821267237784264, -7.3103979498192775, -7.37618965970539, -6.9981311672554245, -6.201165907739262, -5.055763705548649, -3.6745024518708496, -2.2053265160531215, -0.8218993243582912, 0.288309320118878, 0.9373821157069605, 0.9508203744935836, 0.1809266818493336, -1.481265628964334, -4.0963932685507265, -7.6702150339445, -12.150724211747548, -17.429232128296732, -23.345190955174857, -29.694463572846267, -36.24048551496482, -42.72755143841618, -48.895317268489535, -54.49353619832101, -59.29604632395901, -63.11309849647213, -65.8012481859454, -67.27022321805661, -67.48640482279244, -66.4728046856058, -64.30566672002264, -61.10833004558627, -57.043063541600944, -52.29927803052987, -47.08144639765983, -41.59724735959976, -36.04641869743669, -30.61100156756417, -25.447511516246678, -20.681395332829847, -16.403941481626866, -12.67162149371187, -9.507665325505409, -6.90552806942486, -4.833798169969693, -3.242034320074234, -2.067001287864702, -1.2388084099796879, -0.6864975700705973, -0.3427163614727554, -0.14733537976289143, -0.04983202134925373, -0.010440856539425556, -0.0001904160359050492, -2.640546158325658e-05, 0.0007269292885600917, 0.006294079580260264, 0.016498446439807996, 0.02870209592736761, 0.039453149710832094, 0.04572178024302202, 0.045672393846241145, 0.03898239685167119, 0.026770534353021305, 0.011234736263698189, -0.004879054584110717, -0.01885133761043104, -0.02849809332189478, -0.03253262442131711, -0.030733209111595335, -0.023906844160374287, -0.013673761825795902, -0.002124526632843431, 0.008581791021623422, 0.016605158130766816, 0.020731747626993757, 0.020551812756214566, 0.01648349606618041, 0.009644980951642602, 0.0016034834188913434, -0.005949956570211291, -0.011539486102299538, -0.014191811328031967, -0.01361777109402051, -0.010252310622485066, -0.005141761945373363, 0.0003049409176487044, 0.004658206463487405, 0.006839382474688414, 0.006447171100875776, 0.003964416309273518, 0.0007838002023735548, -0.0009843331862344267, 0.0010749081820985728, 0.00908239541847344, 0.02415503060748726, 0.045692616813564485, 0.07078260833784288, 0.09384755802786911, 0.1066468554351299, 0.09871006302503582, 0.05822992464593433, -0.026617586619280882, -0.16602442733701395, -0.36673380186041843, -0.6302680610879062, -0.9514459258605104, -1.3174404411428695, -1.7076058480356873, -2.094247254598289, -2.444423852374869, -2.7228030224532644, -2.8954823859271483, -2.93422086433873, -2.820908878227005, -2.5518500619966566, -2.1413536728134295, -1.6241689308415017, -1.0563479985806414, -0.5142275516544076, -0.09136417679512226, 0.10656429375677223, -0.03131458217459998, -0.6127130608057891, -1.732974729266171, -3.465723967328872, -5.854168347259302, -8.903901007332552, -12.578184586611137, -16.79615781142797, -21.4342199158169, -26.33075989542702, -31.29405809888708, -36.11291375585627, -40.56930014345251, -44.45214683993743, -47.57121619278448, -49.769993401289604, -50.93655394453209, -51.01150777261831, -49.99233762255106, -47.933732062626966, -44.943838894856256, -41.177054424628174, -36.824065461314056, -32.097128464088826, -27.21503911382732, -22.388551933259976, -17.80704064261027, -13.627446247600941, -9.96633499265719, -6.895591408520527, -4.441931208929945, -2.5900674747236114, -1.289035249433078, -0.4609060163952423, -0.010930868942983502, 0.1619421312252165, 0.1552164535437435, 0.054581009408557916, -0.07206850787230237, -0.17788830541974002, -0.23749229638317357, -0.24472773290262073, -0.2083547776501716, -0.146386400615049, -0.07997048311721837, -0.027712305279040044, -0.001241149133307392, -0.0026305483704896783, -0.024010279059703557, -0.04939134133798637, -0.05840077141961148, -0.031330961230660426, 0.04531435258934578, 0.1737174181391793, 0.34103644718947757, 0.5179122629410867, 0.6597350404096963, 0.7108771290519409, 0.6116971246349341, 0.3077083101047283, -0.2400663385152078, -1.044812699521989, -2.085130303434674, -3.2991298736482753, -4.582652099347147, -5.79249180692107, -6.755025645532259, -7.280055963917105, -7.179055481351112, -6.286443217931733, -4.48196024773828, -1.7113110012458037, 1.996882096568412, 6.520054479094366, 11.638512309379106, 17.041325038218535, 22.341741040090298, 27.101653934058003, 30.86369910081852, 33.18867298367803, 33.695236001655054, 32.0983684466375, 28.242864822167462, 22.128317206476577, 13.922562343479955, 3.9614275505467025, -7.266893331157488, -19.152584181116968, -31.006706903060767, -42.11281186999679, -51.78362124817604, -59.41790043856646, -64.55233219819269, -66.90337750796395, -66.39475718819891, -63.16728422507964, -57.56924065913291, -50.12720796691592, -41.49907967533976, -32.41274538630199, -23.595469055309167, -15.70038120530721, -9.236532535184205, -4.507883453276584, -1.571054362090031, -0.21553375784750498, 0.031072354998542155, -0.12809771898041597, 0.1852899534428965, 1.9485789220694942, 6.147129096504559, 13.675971668403154, 25.24259898004081, 41.27969773842006, 61.87618874857601, 86.73373280413028, 115.15397634656603, 146.05984900380096, 178.05245354944321, 209.4967481932263, 238.6314025063682, 263.69514301140856, 283.0595901817009, 295.35800004273756, 299.59935839238796, 295.25819224417074, 282.3321997838601, 261.36222514588553, 233.4120260947904, 200.00846534356515, 163.04593891327917, 124.66177354786363, 87.09173462108157, 52.516472897805876, 22.909546758969192, -0.09995474789220515, -15.336995416141693, -22.156311586419093, -20.47926835805951, -10.789585835009245, 5.911121136035089, 28.18396432091545, 54.26283169013087, 82.18501071702099, 109.93215412375035, 135.57081999506462, 157.38214542626295, 173.97135699071458, 184.34966914400496, 187.98469047372862, 184.81735537223526, 175.23534342972906, 160.01780115387962, 140.25647364950692, 117.25950680120089, 92.44630437756553, 67.24198561213981, 42.97945195563531, 20.815923016090863, 1.6691738253815114, -13.823236298943023, -25.32052701303771, -32.77186013036395, -36.38871823263754, -36.60056805523074, -33.999754017604396, -29.281189827544033, -23.175326740759846, -16.388853335382255, -9.555942116668728, -3.201842504245366, 2.2797390925086827, 6.635394696953804, 9.748044892860205, 11.622357027871473, 12.362332768992193, 12.14417923430356, 11.187581825742527, 9.728208495623567, 7.993755665274005, 6.185172700706976, 4.4640143491369475, 2.9460330213171795, 1.7001408703314418, 0.7524930305852596, 0.0941537574260138, -0.30925821078898963, -0.5074065465806602, -0.5558021986844807, -0.5080200806605527, -0.4101167005222779, -0.2974225592679775, -0.19355271184333825, -0.11122723749204395, -0.054340194313699935, -0.02066558111013241, -0.004632606207869745, 0.0002803533611629494, -0.0001785460062802811, -0.0019795166462332563, -0.0030274596946379853, -0.0028248324950466215, -0.0018303068081788887, -0.0007736694272961187, -0.0001435735863047128, 1.9662226154026386e-05, -9.7078145392711e-07, 1.9770216783357757e-05, -0.0002306481221818897, -0.0019822310928701726, -0.007467795047345977, -0.019572982249612566, -0.04100241608015742, -0.07302957142947765, -0.11401773635706224, -0.15799686308100025, -0.193636070864026, -0.20395264755534268, -0.16703581975939252, -0.05794116686458776, 0.14825803691357384, 0.47247185058089725, 0.927050686023626, 1.5112652335633734, 2.2074802291691924, 2.978715127433268, 3.768211561964149, 4.501457357977461, 5.090861187735253, 5.442989673808498, 5.467932304626103, 5.089654356750955, 4.256531729473028, 2.950863222206335, 1.1960931968505353, -0.9393787325091553, -3.342668483411677, -5.861645230542411, -8.314949155239674, -10.506282382429815, -12.241954220837208, -13.350215010334512, -13.700585373426872, -13.221224024541097, -11.912407074386955, -9.854455841246075, -7.208670538255525, -4.210360710102602, -1.1548409465279825, 1.622954473371704, 3.7738335693988656, 4.962668229385286, 4.8972884897221105, 3.355407285231236, 0.2071142386563357, -4.569207138166775, -10.879158151426367, -18.513727810209577, -27.1599552121913, -36.42016584878541, -45.83832521419468, -54.93191876857947, -63.22791379825868, -70.29543960260436, -75.77493583300917, -79.40179260305264, -81.02235102712898, -80.60117492325709, -78.21928493524176, -74.06383076102033, -68.41039231456027, -61.599682085219825, -54.010819136345994, -46.03352984257151, -38.041593028355535, -30.369600909726934, -23.29468523193006, -17.02443916639892, -11.691256836475661, -7.3522652713015475, -3.9960916640349855, -1.5543670511000307, 0.08383445545647945, 1.056267854913597, 1.5120766069040228, 1.5979954159436243, 1.4472214574356181, 1.1715811687131616, 0.8572036661658239, 0.5635238026543399, 0.3251169111941196, 0.15564152950623464, 0.05305075006161065, 0.005229032415393137, -0.004700678043509173, 0.006028774449437508, 0.022982972512134794, 0.03627401424534653, 0.040991740622827615, 0.03658214553865216, 0.02554242018443917, 0.01183641697909441, -0.0005981840845711172, -0.008965913232773957, -0.01218802114040005, -0.010902601697772242, -0.006978477421397147, -0.002722260064864486, -6.655280857046134e-06, 0.00045115969239192946, -0.0005236153062996393, -0.0006167505351444232, 0.0034780771421107372, 0.015214455810876874, 0.03717559034747113, 0.07010542811592625, 0.11221443516065831, 0.15894628513186124, 0.20331401533170826, 0.2368107977982217, 0.2507884916701363, 0.23809583735960638, 0.1946959279188265, 0.12095407850574338, 0.02231080434839151, -0.0908676575595032, -0.20435566816641584, -0.3019985394110905, -0.3682486564629052, -0.3909535584447737, -0.36394683327990385, -0.2889588875933984, -0.17640593982797498, -0.04472992487489827, 0.08186003082117936, 0.17717157982095288, 0.21802606902659433, 0.18993109721547718, 0.09271401880658738, -0.054699115893331436, -0.21117739697773047, -0.31266877309269864, -0.27438976905441675, 0.003960753527784397, 0.6301680080110889, 1.7091863040752202, 3.3314290984436217, 5.560806336261376, 8.42379560042538, 11.900840945833977, 15.921233640476155, 20.362348938415845, 25.053715757842703, 29.785919786606694, 34.32383416080141, 38.42319036231016, 41.84910002626649, 44.39529548775752, 45.90288568807968, 46.27317960534141, 45.476206119918494, 43.553941850942536, 40.61749232975316, 36.838435106292984, 32.435109157660854, 27.65513371807544, 22.755807632479325, 17.9842377405559, 13.559050282536283, 9.655352508688628, 6.3942533197751334, 3.8377615125609323, 1.989312219688782, 0.799607037133113, 0.17682879999799292, -6.395453741833115e-05, 0.13377315787124452, 0.44403005509139143, 0.8104338892875501, 1.1369053989557687, 1.3578349556678977, 1.4401313038587802, 1.3812088771001725, 1.2035466292663441, 0.9468187745002834, 0.6588251417354211, 0.3865133117475179, 0.16828390838172622, 0.028522269760803298, -0.025061015868170226, -0.0011136034726136699, 0.07839128579940485, 0.18322680852919165, 0.281105752570174, 0.3439417793296456, 0.3531401927224669, 0.3030430035827476, 0.2019388861526103, 0.07041784653785886, -0.06274680719806085, -0.1666244975961705, -0.21518703363053, -0.1943330322941013, -0.10775733302348339, 0.019351506281580073, 0.13955794109864073, 0.18574772250771615, 0.07687387900634818, -0.2735789964824225, -0.9472695855198466, -2.0099676771863177, -3.501117457511896, -5.4252967338220435, -7.746713940831545, -10.387585228063239, -13.230826060187031, -16.127021278342486, -18.90515800638307, -21.386172308569208, -23.398023514290088, -24.790809387453287, -25.450882215253998, -25.313007763437927, -24.365241025728466, -22.64982129027416, -20.259759002890572, -17.331038621736365, -14.031254547344627, -10.545832224197218, -7.063192601546119, -3.7602771701764306, -0.7897612499242753, 1.7299401349052017, 3.7210976888299347, 5.149142263510146, 6.021220196800619, 6.381250696690361, 6.302291433633544, 5.877224926925811, 5.208261080787384, 4.396927630404388, 3.53554291354875, 2.700795059971544, 1.9498040523549465, 1.3187331009197403, 0.8237308895498876, 0.46375679049400126, 0.22468836151916186, 0.0840447258479833, 0.01567991421457759, -0.00610425853535526, -0.0034250388461933633, 0.007117788687828504, 0.01515269874212658, 0.016160909464697972, 0.010270715461421772, 0.0005698505543576715, -0.00869240512229833, -0.013690098967001204, -0.012154484133028123, -0.003928565317671021, 0.009070615196459934, 0.02339155092387391, 0.03492240350072336, 0.03989103502901085, 0.03577948493213876, 0.02197418329041953, 3.3333196053633717e-05, -0.026471282708257333, -0.052504416185843096, -0.07241159091828459, -0.08088854996590107, -0.07390732001264501, -0.049442933919708394, -0.007880768982503648, 0.04795780148215401, 0.11316913789157153, 0.18143671696737443, 0.24590398460579702, 0.3001102008988819, 0.3388442580812116, 0.35879028175906347, 0.3588769149185835, 0.3402925200192582, 0.30618244894839003, 0.2610966200345018, 0.21028742218757873, 0.15894751405708435, 0.11154288795537706, 0.07133092933625355, 0.040115869545834244, 0.018254081203114166, 0.004878910234962081, -0.00171948694833328, -0.00364406907353163, -0.0029588775637603365, -0.001350481319539461, 6.755323108934549e-05, 0.0007909723261020006, 0.0008197745303410908, 0.0004576571421587308, 7.847273547898054e-05, -7.556864293578831e-05, -1.1905143798858438e-05, 5.988059001626059e-06, -0.0004384134191916816, -0.0017347169802203086, -0.004043689062234146, -0.007138147269636121, -0.010345416056644649, -0.012628579120211359, -0.012810436749408186, -0.009905506466364133, -0.0034899508424379045, 0.005984400865963152, 0.017030595146881766, 0.02720218236767395, 0.033443824438948395, 0.032697983964619884, 0.022678114808656693, 0.0026639798553649355, -0.025866583800216773, -0.05896796423392099, -0.09049169830708573, -0.11299281355121482, -0.11928338663600045, -0.10451467541897065, -0.06853920722655102, -0.01819061758438205, 0.030955318211125203, 0.05379000791497969, 0.016245227214678325, -0.1225113718317517, -0.40622283193639713, -0.8763743269655928, -1.5661432944976559, -2.494084960822928, -3.658408106288518, -5.032719774427417, -6.564054208932086, -8.173813082854323, -9.761942561661504, -11.21428575595086, -12.412619959173245, -13.246471156132532, -13.625452840342904, -13.490658454655035, -12.823591880566388, -11.65127471354545, -10.04692329439638, -8.125759034441248, -6.03281052048165, -3.9277700092687646, -1.9680035070359536, -0.2912821134768851, 0.9995775477082066, 1.8480920115880375, 2.2498407446963817, 2.2515385656592, 1.9432885170951457, 1.444785611995794, 0.8871400982431126, 0.39272576067985226, 0.055917639644897835, -0.07232535519630084, 0.006591259219295626, 0.23829350347965295, 0.5241005841302214, 0.738321691411063, 0.7520480683284931, 0.4601871396368407, -0.19231768777187772, -1.1894284769811398, -2.4321476622480738, -3.7389454888640943, -4.860097167373043, -5.505666486286658, -5.384812273651021, -4.252118599122902, -1.9550400244060768, 1.5244277773552415, 6.0405572635800775, 11.273466342698248, 16.745059981655917, 21.859419418128592, 25.9658170909365, 28.439233019329574, 28.769744341570643, 26.6497549964865, 22.046760170194162, 15.24948435118683, 6.876930759480527, -2.156903274393331, -10.725377939893653, -17.61595181779032, -21.69286657679069, -22.081840787611323, -18.35859952159569, -10.720363654258618, -0.11404185397819434, 11.698361881783269, 22.15209803691444, 27.979068089713504, 25.3952169521961, 10.36783188716693, -21.054306875777122, -72.37292327008139, -146.2654182852292, -244.23761321486185, -366.33865184709225, -510.969460766054, -674.8097185127858, -852.8790384261407, -1038.7430774045906, -1224.8751767187152, -1403.101403221567, -1565.117157221919, -1703.0399938733785, -1809.950447292274, -1880.3762773814622, -1910.679714240678, -1899.3151782349632, -1846.935880203927, -1756.3406319709081, -1632.2659017671822, -1481.0413377376294, -1310.1384160697917, -1127.6504881224362, -941.7475264090061, -760.1579869383025, -589.7148234782796, -435.94081320957486, -302.79383319468303, -192.56063490436483, -105.88663033215973, -41.92850149732285, 1.393547674720218, 27.07426333478081, 38.66674103071178, 39.92527007416191, 34.479123232454185, 25.562963013610823, 15.82167331197022, 7.198470318467587, 0.9060954499244745, -2.5271596612902782, -3.151955355393686, -1.4526865725149467, 1.818490599853983, 5.805872592785528, 9.694334242391522, 12.82012287218915, 14.740727448409691, 15.262071577560185, 14.426617138913976, 12.47022752775251, 9.758433361039236, 6.71388771227436, 3.7463267428405085, 1.1944933447518469, -0.7133847387010571, -1.8773626497708122, -2.3220210187295516, -2.174478188548038, -1.62974369094334, -0.9103071536443916, -0.22678258573728896, 0.25453362412858843, 0.4330180739067798, 0.28193548031222204, -0.15633012909832075, -0.785897444559688, -1.4802591118726716, -2.107999356703813, -2.556894510023368, -2.7525630606200906, -2.669008244384754, -2.3299602361838057, -1.8014391974114232, -1.1769147262838797, -0.5586717673627024, -0.038765716358404825, 0.31720350776151524, 0.48084910064898034, 0.4646706594216803, 0.3182683514906565, 0.11797007832081098, -0.048197220334004864, -0.09754629185707031, 0.03113961272793076, 0.36510343369064396, 0.8908333388122225, 1.5541547419595798, 2.267237262542347, 2.921487426729009, 3.4042628623153965, 3.6166816191886255, 3.4897872879714895, 2.9965914004826653, 2.1581591773536566, 1.0428159830718948, -0.2414192600274921, -1.56007630692751, -2.7692452685840765, -3.7339382630330666, -4.345230422020742, -4.533832476870743, -4.278301203625771, -3.6068897703053127, -2.5929675994820593, -1.3446445842608392, 0.009896758413800461, 1.3386274310690884, 2.5213389168073057, 3.4627451202226043, 4.101451282433266, 4.413904781039163, 4.4132078591882635, 4.143402013325711, 3.670422496582076, 3.071290997063661, 2.4232245392158718, 1.7941903775178276, 1.236070896828705, 0.7810912326391048, 0.44160940538087173, 0.2127924623517363, 0.07728523335110303, 0.010994943494192557, -0.011269376590435908, -0.011278163080943407, -0.00459022083665776, 0.00031325771315269445, 0.0011732923192937712, -0.00010144058147659732, 1.4739792038630558e-05, 0.0043378102435327505, 0.013450873171466973, 0.02530328748675224, 0.03592986664190536, 0.040978508091300346, 0.03750662854493706, 0.025412080355878167, 0.00792849097544725, -0.009148104865709505, -0.019493963567968384, -0.019161976170159346, -0.009620137561918518, 3.0025398066103163e-05, -0.007362883018587308, -0.05482941136789028, -0.1661517921372248, -0.35799296806245123, -0.6301566923612538, -0.9554769882227553, -1.2712964606064772, -1.4746789324791583, -1.4233231716857428, -0.9435478671531667, 0.1541403502347005, 2.0525999082143715, 4.9006223130251625, 8.783528548921714, 13.695649741431565, 19.518931141833395, 26.01171251302227, 32.81094037450226, 39.449701550967205, 45.39016356284198, 50.06997219624302, 52.95814972814363, 53.61483892526838, 51.74811082122104, 47.26111080332938, 40.28271304866203, 31.172922304216225, 20.50508608373148, 9.024563877431314, -2.4135389367285858, -12.921796971588938, -21.665170562614176, -27.943867665892135, -31.265051771967148, -31.395025485926407, -28.385512519055283, -22.57049618913993, -14.53342330398561, -5.048044308897712, 5.000697650111313, 14.706463149100003, 23.23217257802533, 29.89428493404368, 34.225855084198336, 36.0130286603989, 35.30222299963457, 32.378212240785, 27.716847501833072, 21.919120866722388, 15.635348408941665, 9.489147092847453, 4.010512422683275, -0.4142637955270178, -3.5706350024458673, -5.4197520060258535, -6.079601816378047, -5.787615155219031, -4.851285142159163, -3.595146075302508, -2.312078064273638, -1.2256057790875368, -0.4679194585789561, -0.07561730920303918, -0.002231742823443603, -0.14390567491982348, -0.3725399820133613, -0.5696532658576678, -0.6542511680558534, -0.5991951542151335, -0.43271657636044664, -0.22451479055662069, -0.05887284535962232, 6.281361173914271e-05, -0.05627038946935278, -0.15258344026503862, -0.11585252674506098, 0.31886111562118924, 1.4803642875079932, 3.7120271913863863, 7.305866692466742, 12.427983265908765, 19.045768796474704, 26.868464759453744, 35.31225738154822, 43.499079111302756, 50.29479135134407, 54.387806968565975, 54.40399964259884, 49.04983304236915, 37.26969997380203, 18.38767772074183, -7.771603393982471, -40.79915383252321, -79.6684733903599, -122.7604370100989, -167.94764099244995, -212.73327104018307, -254.433508605746, -290.38745889409694, -318.17515214986116, -335.82275394403604, -341.9749100256312, -336.0170891166024, -318.135572662581, -289.31393049798464, -251.2673714151601, -206.27973615384673, -157.0083220274832, -106.26923291567944, -56.818168322426125, -11.146859754098905, 28.687079186793582, 61.183268616332576, 85.46635108643237, 101.29604144891985, 109.02280469603959, 109.49759423436534, 103.94793804216705, 93.83496958541673, 80.70662087812735, 66.06202957013095, 51.238747830427826, 37.32455493098401, 25.107883550169547, 15.065056310969839, 7.3792837722093765, 1.9846114011413802, -1.3737157702563554, -3.071541815919097, -3.539251795693552, -3.2034355682987297, -2.4417374819894824, -1.5535054789408558, -0.7465316902344856, -0.13817503847717225, 0.23231874792006832, 0.3843376113140169, 0.37341340812468043, 0.26943703030455984, 0.13883445091597926, 0.03233309896614843, -0.021145434782890014, -0.014931711178551773, 0.03936043203374814, 0.11852303858029353, 0.19536366057955729, 0.24563496660749712, 0.253107483162264, 0.21215385446589868, 0.12777284134170835, 0.013461466333687843, -0.11232414397372266, -0.2302360769021862, -0.32379497130076595, -0.3820902124056441, -0.40105261157178484, -0.3832834432200327, -0.33667486993805495, -0.2722532899448434, -0.2017653697185313, -0.1355048242005687, -0.08076407500817057, -0.04112122148011668, -0.016579208944193003, -0.004400097159946506, -0.00035472951494218674, -5.5901728044807356e-05, -6.508953726471792e-05, 0.001452312516171818, 0.004624300572465706, 0.008281760261204573, 0.01071757957600454, 0.010564519553762143, 0.007547852051169289, 0.0029106336328968085, -0.0006053614850283888, 0.0007683483808063113, 0.011001175865696794, 0.033267516833257, 0.06900796918704971, 0.11726946521449086, 0.17449261347775855, 0.234824356770873, 0.2909255886162699, 0.3351468526253456, 0.3608720630942781, 0.36369682465582787, 0.34224846030652456, 0.2984926422069922, 0.2374582922067234, 0.1664292978034758, 0.09375331911785766, 0.027490143589862986, -0.025849252389371247, -0.06224200862281002, -0.08060525321484915, -0.0826919767680813, -0.07247256128024594, -0.055144970713583395, -0.03598872590026342, -0.019306611930784947, -0.007672050974104514, -0.0016315727382229842, 7.568797103053385e-05, -0.00013550968957746652, 0.0003936507597673673, 0.0036364554132729916, 0.010176663897178334, 0.01892820602479069, 0.027381030463290705, 0.03234949112886608, 0.031068447472010464, 0.022373967277610405, 0.0076456538252818425, -0.008806037162783028, -0.020145529765881045, -0.018306506859710615, 0.003911825047087208, 0.05025597130024617, 0.11841711487694977, 0.19796502690944678, 0.2693631688239639, 0.3045002849534653, 0.268964716720319, 0.12600844159231153, -0.1581596703316724, -0.6083969988376902, -1.2348235490528137, -2.0281420741569223, -2.9569807340022454, -3.9679537114967403, -4.988798317627272, -5.934517784537219, -6.71604461165026, -7.250422014382736, -7.471066564163541, -7.3367668093634455, -6.838119811273086, -6.000381269764055, -4.882157261067059, -3.5699234177694215, -2.1689416637347994, -0.791669239047779, 0.4548606416734005, 1.4810246537283371, 2.2243532418053995, 2.6557124329865816, 2.781090741464491, 2.6388435481769212, 2.2928247679354556, 1.8219056070927542, 1.308178397040945, 0.825502854641147, 0.42997852252934626, 0.15367959854177002, 0.0024619502524942925, -0.0419925197387703, -0.016391546026334473, 0.03261725545218155, 0.05808564272610532, 0.02195510873632615, -0.09773770707279904, -0.30282536717320874, -0.5747841047767788, -0.8783228371233286, -1.1681836306987747, -1.3978011602170508, -1.5282430986860749, -1.5358438377087966, -1.417142713771984, -1.190207045046596, -0.8920459934135325, -0.5725043630711335, -0.28565208599328773, -0.08014931251149639, 0.009712227407470965, -0.029343999557210215, -0.18653283608681082, -0.42827059416976826, -0.7037360145401641, -0.9539856966450292, -1.1232573469295275, -1.170424977164549, -1.0786444599787757, -0.8614594853962209, -0.5641147494975625, -0.25955967010972986, -0.039462714776880306, -0.001370009890538183, -0.23380310120519296, -0.8014918479571568, -1.7330103224686044, -3.01280705741636, -4.579030577037767, -6.327730708333268, -8.123086703746738, -9.812665229852715, -11.246211466186967, -12.293264016179952, -12.858441500597783, -12.892450994186147, -12.397210048041607, -11.424503838282428, -10.068519119842831, -8.453445992761546, -6.71799193356249, -4.999017178594512, -3.4165293179543506, -2.0619731998495068, -0.9911760037589857, -0.22255383748630056, 0.2596220626148011, 0.4978383143721972, 0.5513497459699799, 0.4852472490484795, 0.3603571914161159, 0.22558642307092064, 0.11359146044164646, 0.039972911845754584, 0.00556732108127065, 0.0009145157413790382, 0.011697188384416742, 0.023917124451420375, 0.02777890500301053, 0.019643255519097798, 0.001901908015711636, -0.018889025951152223, -0.03489951024097143, -0.040026697297766825, -0.03212262950223883, -0.013762806686672267, 0.008669028127783111, 0.02729737972527379, 0.035757241748027954, 0.031880689996338876, 0.01901728405930487, 0.005158002173123671, -0.0004996209849984374, 0.006731941469100297, 0.019999993118489733, 0.014134075545489773, -0.05895005268314016, -0.27072406662730764, -0.7108578773864523, -1.475643060911016, -2.6505124559661546, -4.288367192400513, -6.386602966249652, -8.86662550464486, -11.56000585157742, -14.205160637132197, -16.457491864946604, -17.91434930029402, -18.1541541804548, -16.786802317101557, -13.510361217975687, -8.16741720998745, -0.7935083661255187, 8.349889316217144, 18.76427634751424, 29.729808902493904, 40.351042613039084, 49.62639512329025, 56.536109027968045, 60.14103990895263, 59.68168071272943, 54.66631583833468, 44.93784126220029, 30.710743895595183, 12.572804523269882, -8.550076120260284, -31.463387181004624, -54.80137219430158, -77.14251895877977, -97.13129990242614, -113.59352014298028, -125.63515567695515, -132.7176478746217, -134.686415990185, -131.76219231798842, -124.49873969755974, -113.71186624829812, -100.38885833086822, -85.58907048649108, -70.34667643544546, -55.58553941188055, -42.054009125305036, -30.284532315429765, -20.579689317701433, -13.023075679598943, -7.510732406707815, -3.7968981484370814, -1.546909779795735, -0.3899861278173133, 0.034090083469472524, 0.03878083414781366, -0.13177614902896495, -0.31144851493098447, -0.40863186577508714, -0.3936970299366833, -0.28114364981815576, -0.11027485841004332, 0.07233302360241316, 0.22623945508695825, 0.3252464110151485, 0.3601520108255138, 0.3370319817788854, 0.2725376283519054, 0.1879313359868827, 0.10343771753259294, 0.03407425922755352, -0.012366077007556103, -0.03519420434067946, -0.03906298483128745, -0.03134324350494509, -0.01947500302131092, -0.00898039151915794, -0.0025291420792894876, -9.672375869959618e-05, 5.8030554208351606e-05, 6.851500028910819e-05, 0.0013051950480096294, 0.0037915637697354654, 0.006360484743323709, 0.007438754047596978, 0.006100072415028454, 0.0028851260365251987, -8.623080168860323e-05, 9.682858692068058e-06, 0.004881677586712056, 0.012783947753994995, 0.016411200211434687, 0.001974284663527541, -0.049629750208365644, -0.1589278279401531, -0.3411619524613478, -0.5973487777021164, -0.904417895113996, -1.2063448177589655, -1.4085302318124446, -1.377679388842732, -0.9489647506968366, 0.0594602167769039, 1.8249729533423082, 4.493954978066831, 8.153466624791427, 12.805183957316988, 18.345962352739765, 24.559019288005093, 31.11866363070549, 37.609837797577384, 43.56168881460021, 48.49223447722243, 51.95927379856034, 53.611330156680005, 53.23187170677961, 50.77122533458787, 46.36158918674978, 40.30584821719149, 33.047424172259376, 25.124057869885046, 17.110533400880552, 9.557731874240332, 2.935962570569773, -2.4100839546981803, -6.2891105127073, -8.670604124978299, -9.671729248349454, -9.526599739211289, -8.543314583372412, -7.055765497334745, -5.3776966354277915, -3.7657966981828426, -2.3965632326902035, -1.3589237927243545, -0.6627779451124591, -0.25944493577909095, -0.06834590267127318, -0.003635915471673711, 0.0049228060639175016, 0.0007699269330157237, 0.00029428727435056, 0.0017361071375260654, -0.0013387997048240692, -0.008526570290560555, -0.01017467271232741, -0.00019069540257544867, -0.007533765070892365, -0.14586472232834408, -0.6760737213140012, -2.0719339299472384, -5.075805052841725, -10.729716706694928, -20.367967863417885, -35.560738140284094, -58.00391705190977, -89.35781101349725, -131.04563769623306, -184.03059461212993, -248.59656322371887, -324.16106950523795, -409.14914790753875, -500.9528657407541, -595.9936024088445, -689.9046339588898, -777.8520076694085, -854.8787247246258, -916.296215062478, -958.0877815100081, -977.2738114613194, -972.1988030644761, -942.7074792502698, -890.1886195574245, -817.479409234795, -728.6383820211356, -628.6095437037402, -522.8122117083227, -416.69901000178675, -315.32734877983404, -222.98726641842092, -142.9265077937155, -77.19191299005315, -26.561237354677857, 9.370986010824264, 31.995914941288838, 43.42071407716453, 46.16342257019371, 42.84979710106774, 35.9455906977733, 27.54992799898189, 19.265107168445272, 12.146861436013943, 6.728439928511806, 3.10321183589144, 1.0448714868543545, 0.14223197566672707, -0.07299896587907055, -0.022690215180553266, -0.01405133507738304, -0.21038752307583508, -0.6373179890786215, -1.215708633023593, -1.809480545488752, -2.2758195373300074, -2.506962803624054, -2.4561230439676645, -2.144429819204958, -1.6501346597669342, -1.0849223285265672, -0.5643859397081789, -0.18025214123346323, 0.019180977185601286, 0.03635299647426545, -0.0814201902614725, -0.25876301903015025, -0.415145404954926, -0.48770674595525304, -0.44815987623643894, -0.30954080057892847, -0.12114065758382711, 0.04707269292825174, 0.12652592730166368, 0.07275198016698366, -0.11762614362870048, -0.4010258280407284, -0.695186243433703, -0.9013469496060695, -0.9364922064709332, -0.7686960814354591, -0.446738626003521, -0.11544775692551151, -0.00954923553555912, -0.4226517112361757, -1.65282444343698, -3.931374285492554, -7.346025788721664, -11.77278948587426, -16.831622725203246, -21.879135095514776, -26.047090142297808, -28.328793960491126, -27.70754465719586, -23.313349783559527, -14.58743074773894, -1.430221859751826, 15.694167079017586, 35.722328480867134, 57.030600731815056, 77.55333231628883, 94.97321662928519, 106.96501271041875, 111.46505757861722, 106.93340969632311, 92.57422356241113, 68.48343753454454, 35.70078776175289, -3.8453843191347494, -47.49854994021093, -92.12389362215049, -134.41984995889138, -171.25954621032358, -200.02970240613814, -218.88339808622013, -226.9039349279151, -224.16365980489869, -211.66980270701507, -191.20751395948028, -165.10318194824427, -135.94061516321707, -106.26753942755236, -78.3295228650564, -53.863071403388226, -33.970119014994324, -19.08392429511434, -9.023288108048941, -3.119924210336759, -0.3944205944489004, 0.24905654105107955, -0.16049805635931483, -0.8050811949817768, -1.1639126436061, -1.0340991818009748, -0.4891337590813555, 0.21148809971510088, 0.7409980578668894, 0.8282808893984963, 0.36129998188717954, -0.548364675416635, -1.5518858136639104, -2.103310258766277, -1.5467959787948307, 0.7639393893969142, 5.334730099454457, 12.413025903432317, 21.9044177953923, 33.33767373607364, 45.886209313225834, 58.444997609118616, 69.75332561576856, 78.54677779500429, 83.71734164134425, 84.45920556143045, 80.37979319108457, 71.5604988646573, 58.55868184485638, 42.350670131242374, 24.22361369086144, 5.6308541545942274, -11.970354539290035, -27.28057241640359, -39.29307823199373, -47.383248488971724, -51.34754719521477, -51.39097689615098, -48.06828576324448, -42.18980113969854, -34.706470983424566, -26.59017143937817, -18.724550143908466, -11.81890820711834, -6.353421256169272, -2.5590625735128127, -0.4306675753537151, 0.23264644550559166, -0.23156767447648272, -1.4168294237712347, -2.9135608129658297, -4.3638791798814465, -5.499478664126103, -6.1601753073200225, -6.293851820540482, -5.94109252529854, -5.209481742822094, -4.243223575079095, -3.193469345960457, -2.1936931779796645, -1.3429129670490265, -0.6978293532741416, -0.27334958614757354, -0.049715441243817285, 0.016293301510299264, -0.02121833329833216, -0.10884060172268417, -0.20253648544355723, -0.2725159739907727, -0.30432770315938773, -0.296871802285999, -0.2584535012629618, -0.20211626035163735, -0.14135013877550076, -0.08694368568548697, -0.045335583884201405, -0.018424579045326503, -0.0044918152939859, 0.0002751839248628128, 0.0001838698499619351, -0.0012178155370951274, -0.001817242314657864, -0.0010030040675925792, 0.0007356309176195257, 0.0024334985457904012, 0.0032467479607693485, 0.002834367164519536, 0.001442787308194553, -0.00027465901953586177, -0.0015863642358285475, -0.0020067293499119454, -0.001483911172988031, -0.0003835638787245725, 0.0007135089681397118, 0.0013051542513077205, 0.0012167623903264176, 0.0006779560544580355, 0.0001596898467184631, -2.485506199232846e-07, -5.1359391073838054e-05, -0.0011617252533579559, -0.005411986487501845, -0.015296456708864255, -0.03270076636659364, -0.057491230606379715, -0.08601772347115227, -0.10995276273565514, -0.11592304659716854, -0.08630986015257609, -0.0013997966420677874, 0.15721679981478914, 0.40242375204154385, 0.7372394151403633, 1.1512802980662595, 1.6190517108793137, 2.100669649507672, 2.545350560067277, 2.8975068201826173, 3.104732106606778, 3.126485567264527, 2.9419813753059247, 2.55574282456518, 1.9995275620716833, 1.3298583539963753, 0.6211303114340245, -0.04490975094622291, -0.5917539490927419, -0.960691111798215, -1.1210440895801663, -1.076013086920496, -0.86252560919159, -0.544832620985052, -0.20269549647864718, 0.0839396355193046, 0.25103789157682965, 0.26420978641379017, 0.12712225145556783, -0.11762359378437258, -0.39611246528034266, -0.6186417167529458, -0.7009562645407322, -0.5876246088087267, -0.27313527135147603, 0.18383701115587128, 0.6568837308603828, 0.9615525132099237, 0.8781389269948598, 0.18525815194462297, -1.300009237854981, -3.68129994948354, -6.948150549039838, -10.953596175388206, -15.409286571335022, -19.900978978144156, -23.924389830858615, -26.93828382607123, -28.42882084679508, -27.97702882635227, -25.320200316516217, -20.398250938204516, -13.377461278816615, -4.644804312648268, 5.226323366243917, 15.532225948145038, 25.51145459497472, 34.42492264580684, 41.63348292487132, 46.66321585353486, 49.2503869989822, 49.36084513845421, 47.182134631667275, 43.09027801036678, 37.59651328946822, 31.28177037402443, 24.72799554393996, 18.455415821762312, 12.873900101300768, 8.253035600332423, 4.711351179080035, 2.2294147286749624, 0.6797485349750061, -0.13362514253656993, -0.43317461525348333, -0.43012038806408687, -0.29625161158775287, -0.14841623131953238, -0.04632612556009802, -0.001955633293012713, 0.0030522585217768114, -0.003357613221597013, -0.0028943967055678034, -0.0005447183748976519, -0.02989875750857557, -0.14936772877310428, -0.430499018550242, -0.941270940737462, -1.7281821910264221, -2.801104243037785, -4.124241475639697, -5.615295987862243, -7.153320479582308, -8.594075146964128, -9.790291426499126, -10.613337127505051, -10.972525251462091, -10.828741726371762, -10.200091439159904, -9.158680619087846, -7.819471802203685, -6.323213404143182, -4.814389808574017, -3.4208476869469977, -2.2379604119192855, -1.3193705527618003, -0.6753810835420758, -0.27864393235613694, -0.07551083946621034, -0.0004931506165984684, 0.00912485775195974, 0.0013093025560835564, 0.002048797960017366, 0.013942726061916582, 0.02046994747596288, -0.0053284279602825654, -0.08985935998481212, -0.24818703024735025, -0.47596657594479785, -0.7459678176443365, -1.0100422184358437, -1.2062628779547233, -1.2699018114654064, -1.1461205122977658, -0.8018815684481023, -0.2347030790350471, 0.5235554341625921, 1.4087795869631556, 2.332388446827109, 3.193612190071076, 3.8942284778128515, 4.353278447694511, 4.519327134033104, 4.378267820289624, 3.9549619471268707, 3.30887278319354, 2.524587417472606, 1.6988852986731129, 0.9265580089984378, 0.2872947492628069, -0.16434297502538836, -0.40445553977824555, -0.4402731139776166, -0.30585873582153567, -0.05411824975643192, 0.25327604013983585, 0.5562206753936619, 0.8050607550218224, 0.9667355315725786, 1.0275151555745277, 0.991975908622712, 0.8790790053508659, 0.7164643248425723, 0.534205084703601, 0.3592257311206164, 0.2112991065220408, 0.10111277696933134, 0.030425486388717095, -0.006080292005381495, -0.017927668345694633, -0.015743508628015775, -0.008642369696833694, -0.002597185492101279, 2.7632464792491008e-06, -0.0002834292744013429, -0.0013010075496224514, -0.0008726107179536241, 0.0019023269715874854, 0.005987094497957623, 0.008539928788776945, 0.005757062686746472, -0.005854337503698105, -0.02816885454296673, -0.06050155894738849, -0.09933093495021185, -0.1388031440231796, -0.17192243693807105, -0.19214335309433997, -0.19496296585394732, -0.1790968560941826, -0.1469251336526286, -0.10406342639048947, -0.05806981919590215, -0.01669457224684022, 0.013899734618864075, 0.030500991518867655, 0.0334334869201558, 0.026201331473223063, 0.014269574716799438, 0.0033006002984194314, -0.00266889549059849, -0.002574658680100902, 0.0012514634497997248, 0.0038105817317065434, -0.000753870369236381, -0.016657235959719414, -0.043934319037758275, -0.07664367398241652, -0.10248877786665903, -0.10425881493447962, -0.06309560842099315, 0.03687520059993594, 0.20342784722132617, 0.4317831601666013, 0.7020073339136685, 0.9792274211630442, 1.2171556482925483, 1.364766439833976, 1.3752641176204632, 1.2158586616638396, 0.8764726207694201, 0.37544389058241673, -0.2393517527615431, -0.8949682589265392, -1.5036306857753654, -1.9769408124907752, -2.241927992076106, -2.256224220546204, -2.019488238662773, -1.578629691420987, -1.025299016905274, -0.4853746743867514, -0.1015853004626671, -0.01170078486054119, -0.3256697540319598, -1.1054800965362057, -2.3512724818414705, -3.9963559381003075, -5.912462081624584, -7.925191134019701, -9.836967078776098, -11.453822679471129, -12.611839793710642, -13.19901243326005, -13.169121418529448, -12.545600460711407, -11.415098591354063, -9.912185782102378, -8.198089099390314, -6.437227227103106, -4.7754822070496195, -3.323596993058139, -2.1479434491378804, -1.269408795804766, -0.6696228673419568, -0.3023959740570135, -0.1074869017305565, -0.023969334706440724, -0.00047126064544283984, -0.0007927192133118363, -0.004715586056161223, -0.004977242278128553, -0.0021602365353000745, 0.0005229447985339438, 0.0009261714356298729, -0.0006680559974806823, -0.0023334130070111134, -0.0023796196305257054, -0.0008628269498706879, 0.00048700700182586674, 0.0001889329887607353, -0.000404042011807057, 0.0033829702031214315, 0.01402184558021967, 0.016125417724995737, -0.05228580962076444, -0.3418274363606571, -1.143275507815226, -2.939914892275943, -6.4474087234453625, -12.6245944669305, -22.6378802163691, -37.76472651026613, -59.228559949791986, -87.96818584016846, -124.35833836377823, -167.9155524037173, -217.04181625783838, -268.83265132690536, -319.0108212731372, -362.032302521985, -391.39217124055796, -400.1369858358618, -381.561686489612, -330.0380102281614, -241.8921452403176, -116.22646013066166, 44.431934445648565, 233.7707902239896, 441.7169733293517, 654.9071720016298, 857.6184875001295, 1033.157891449369, 1165.677794951295, 1241.8666431152442, 1252.577064714208, 1194.2120204169437, 1069.654773374649, 888.5985010283488, 667.1889037601325, 426.96503230757844, 193.16192808353125, -7.485521444853717, -149.23410457487935, -209.87183000165717, -173.0404504156768, -30.087766206089235, 218.76228349388455, 564.0665074000502, 987.7585137363401, 1464.6838447570155, 1964.7941414939467, 2455.7751653897863, 2905.8433083509544, 3286.4274259641643, 3574.473737675894, 3754.160571313535, 3817.8802376127414, 3766.4283830515974, 3608.4267598047386, 3359.0835922721776, 3038.458067055585, 2669.4356899882473, 2275.636052957235, 1879.496586147938, 1500.693070099651, 1154.7852416327576, 852.542632579783, 599.8518829805988, 398.09305026666607, 244.87501624047943, 134.99608644944493, 61.491013743584034, 16.63804400079374, -7.17471318829335, -16.790360518321286, -17.861876407863523, -14.664293706009387, -10.108612801920895, -5.907087333138912, -2.831110170632582, -1.0037303833068645, -0.17809253128910485, 0.032642785168638555, -0.005886797724530711, -0.038360663179195696, 0.053801524689190326, 0.271433628871021, 0.5417541752210384, 0.7686678496718446, 0.8747099403983286, 0.8261763601908111, 0.6391936170363997, 0.36961649672205393, 0.09291748801195675, -0.11862020966157404, -0.214879824753596, -0.17868010982488672, -0.026661935583896783, 0.1984788918831652, 0.44119130378931626, 0.6476831476945507, 0.7781811344560987, 0.8141850195138033, 0.7596591133556715, 0.636730644728357, 0.4777306708166733, 0.3160621958024573, 0.17833217316736916, 0.07953452119163845, 0.02204952867783852, -0.0018731313934438657, -0.005369666394875027, -0.001647525219820587, 0.00023582589157184226, -0.0026775681479513473, -0.007947015179604569, -0.010637066303396116, -0.007329406460237274, 0.0001630704031320671, 0.0026906686210852546, -0.015882862583513298, -0.07572802191398076, -0.19610015317502233, -0.3896015885929493, -0.6571615777105316, -0.9851507186331775, -1.3455859395513639, -1.699741421057655, -2.0047571726223805, -2.221181982439593, -2.3201757440556956, -2.2888601242832896, -2.1326099201011677, -1.8738175265232861, -1.5474499909982786, -1.1944199081696067, -0.854244499548039, -0.5585689433683836, -0.3268625130476873, -0.16503043781916707, -0.06696364304337456, -0.01835312845159072, -0.0015993924431398532, -0.0004734219321989511, -0.00337760752001633, -0.004538021012436416, -0.003123241272998902, -0.0009606953446219065, 8.047078081737497e-05, -5.556324221181985e-05, 0.0007338227432058783, 0.005423744424423024, 0.015543392033864675, 0.02900407942748209, 0.039475504653692435, 0.03843635847503679, 0.020238711509558676, -0.010632414689294769, -0.03217139371994488, -0.0003730631949275438, 0.14899042791171418, 0.489777873520107, 1.0853136811552837, 1.960417047427382, 3.0703167895394, 4.273753367414127, 5.319146501478892, 5.852602799509646, 5.454341752178712, 3.7057900756232574, 0.2835427901077795, -4.93052726185458, -11.740294667821837, -19.54963753438725, -27.323736754997633, -33.61898037139882, -36.69726254196834, -34.72525758852498, -26.043468092885956, -9.47875569910593, 15.339401037720085, 47.70703777509512, 85.66814474967684, 125.97552964478619, 164.22069173742958, 195.14317728000918, 213.1054704036514, 212.69398313768514, 189.3838685328002, 140.1888869638954, 64.2104954259609, -36.99388632529419, -159.3007677853007, -296.2251771074226, -439.3977167032196, -579.2811634029936, -706.056836769436, -810.582303528351, -885.3090882406871, -925.0505538181557, -927.5062048810252, -893.4774858772312, -826.747984315441, -733.6427585349027, -622.3216123168195, -501.89404416448224, -381.4647975974607, -269.22976159575586, -171.72246653441923, -93.27052753403018, -35.77277518074934, 1.2173647354907315, 20.142501091907043, 24.891160253444568, 20.133791920205088, 10.64022857849996, 0.6687645585630033, -6.500240469996554, -8.839482830654152, -5.642529406097263, 2.6011757866908374, 14.483718359868828, 28.050359304192135, 41.20105645075401, 52.06170918425037, 59.25994053934494, 62.08153876381025, 60.50153166549051, 55.10184562390108, 46.90447784119954, 37.15869391557012, 27.12302264981399, 17.878196266792045, 10.197193147136552, 4.4854320770808656, 0.7904898005707096, -1.1311392996916358, -1.7109053758017918, -1.45283595033045, -0.8287661331398094, -0.20159610581422752, 0.2136009338709686, 0.3498058125294241, 0.2571190646043548, 0.053194231691046694, -0.13063283672012393, -0.19453818143093082, -0.09760309148359009, 0.13642335873601336, 0.43333571434687873, 0.6964865706204723, 0.8397560349913527, 0.8162037255338267, 0.6348749502604211, 0.3616113299686477, 0.1038807649825707, -0.016385701021458116, 0.1052747513781417, 0.5274014426088522, 1.244404712642575, 2.1829419756300426, 3.213788270575181, 4.176569995438492, 4.911866002690396, 5.2935987062377965, 5.254646447790925, 4.800165791108781, 4.005849137467606, 3.0016474522225147, 1.9446390666913682, 0.9870454281478142, 0.2464486902376233, -0.21558041691573362, -0.401989636948724, -0.37313895667668073, -0.22690726637850275, -0.07117035940852667, 0.0047457686535759625, -0.047080383004283584, -0.22133283820445887, -0.4614075304447431, -0.6747199628861625, -0.7578409432827014, -0.6255799384772374, -0.2370608596782419, 0.3877099070274722, 1.1653643078065978, 1.962354100271435, 2.6219853232086567, 3.000124676210709, 3.0017442898760707, 2.6102079704769507, 1.9023055045307469, 1.0446780737186927, 0.2709479497868601, -0.1571828038796581, 0.0018345470029200635, 0.9207407232247236, 2.663817191593914, 5.164337437963176, 8.224269031900555, 11.537336876415994, 14.732191962894735, 17.428891890832077, 19.299631540573447, 20.120094023055838, 19.803650998336813, 18.41267389450201, 16.144986981789103, 13.298259181140144, 10.219127066937286, 7.246520220898705, 4.65952592368601, 2.639036509366051, 1.2495977293631717, 0.4438772909421031, 0.08777741278638772, 0.0002733462657739801, -0.0006701639994470835, -0.05575075682901116, -0.23431083664900046, -0.5227339800602568, -0.83326618710747, -1.0309557668094835, -0.9726674962025019, -0.5496278940550825, 0.2758211868740602, 1.4474995254055956, 2.812200968105536, 4.1376906158587525, 5.149300614670062, 5.578738170440876, 5.216089169211548, 3.9550572502311083, 1.822422726413146, -1.0145643588869513, -4.265687265320357, -7.558358671476612, -10.493151060971066, -12.705352480300839, -13.922288322439357, -14.006688128415268, -12.978749793949463, -11.013180571958317, -8.41172778829464, -5.555812100228777, -2.847140073891408, -0.6460572203368173, 0.7823870778705693, 1.3061554538786104, 0.9420637915081629, -0.1523211736889907, -1.7092954708088992, -3.397214360777758, -4.873896105256516, -5.838736377017315, -6.075567007020277, -5.480318971182416, -4.070342536732185, -1.975318549530931, 0.5874565785824954, 3.348454536832542, 6.02580280411653, 8.36338391124887, 10.161729320149737, 11.297935293936805, 11.732901082873044, 11.50674581987339, 10.724792124563358, 9.533897545278087, 8.097593033618773, 6.573635818692652, 5.096439191121631, 3.7660335905551916, 2.6439009630790684, 1.75488925833574, 1.0936181815714963, 0.6334069059999468, 0.33577923299112206, 0.158950916333214, 0.06425243932180158, 0.020049528855843882, 0.0032688555842235343, -0.0009706091076333257, -0.0009208701109510882, -0.00025062811780206815, 1.3957269068461645e-06, -7.292153737094232e-05, -0.00016437162314908202, -0.00013206206697602554, -3.136434311699569e-05, 1.8382103765978318e-05, -3.281210499199868e-05, -0.00011711811136931221, -9.510512214008532e-05, 0.00014716429244277104, 0.0006129596160384785, 0.0011703839903548603, 0.0016026379877090084, 0.0017094680815302847, 0.0014112899092135738, 0.000803454498556169, 0.0001318444702708087, -0.0003054355879727965, -0.0002926362392043536, 0.00018941611196155188, 0.0009226884559549684, 0.0015126333755578086, 0.0015387060015959618, 0.0007441509863523237, -0.0008095296700765352, -0.002696307836917714, -0.004230367732190768, -0.004713306037194539, -0.0037579743852568137, -0.0015795214537276706, 0.0008690508592178654, 0.0020113128687455416, 3.287464034870347e-05, -0.006527411819273908, -0.018128702352044643, -0.033721042438297134, -0.050576235753250355, -0.064588611916113, -0.07106096051008436, -0.06584843037456108, -0.04660290846436644, -0.013782587212638111, 0.028902535876395172, 0.0748364388039694, 0.11567666541497337, 0.14318276736488358, 0.15129649245049226, 0.13791965871729828, 0.10585017081425095, 0.06251046560285346, 0.0183809732870106, -0.01559521957168653, -0.031034985809866054, -0.024744411923980286, -0.00011314615472079995, 0.03334804621059319, 0.06250353761549383, 0.07470912517220384, 0.06253208185180303, 0.027609220488180368, -0.017960633196023586, -0.05401343589542281, -0.059107091561176814, -0.021123408797380783, 0.05006979885509938, 0.11068785760172657, 0.07527051796427048, -0.1834971902270491, -0.8248167232891404, -2.018720817582415, -3.915211909004092, -6.607323957841817, -10.094035507753148, -14.250393281060672, -18.812422091336035, -23.383121731939575, -27.46306606394961, -30.50592744687875, -31.99481488396888, -31.521851784369538, -28.86358879211308, -24.039058836141926, -17.33772179763451, -9.30888011525802, -0.709769749208866, 7.583694970508946, 14.69270599517328, 19.8613746850938, 22.572683157047702, 22.634440395142434, 20.218388409650096, 15.842187208409815, 10.293061254631928, 4.5019902251712525, -0.6149360178712767, -4.319564987463105, -6.1854214091655955, -6.179908247030582, -4.678156745044604, -2.402129155336902, -0.2912391365538287, 0.6768993225133724, -0.31291926597394276, -3.7256669449507895, -9.535323513246615, -17.159763707678295, -25.488932389913273, -33.009299806337076, -38.011463292839466, -38.854552792754326, -34.25128827403707, -23.5097845591331, -6.697595340531693, 15.300316320811062, 40.84465483580482, 67.72077197624836, 93.40983052125408, 115.41333198667539, 131.58305547916999, 140.40683289937905, 141.20681484253436, 134.22003378706893, 120.54909389286054, 101.99085763164317, 80.7698627400078, 59.22002448245456, 39.46162495557106, 23.108054867163013, 11.075058199097988, 3.511999516337623, -0.14244152787012324, -0.9947877026855722, -0.45334161202766265, 0.04988330946388213, -0.6754072244615118, -3.368407746702943, -8.196443309314294, -14.73956019038024, -22.079213325186736, -28.972606394485457, -34.08069100988371, -36.2091190802477, -34.519344004236494, -28.68193320175108, -18.943971727528986, -6.102450327425515, 8.608038345648714, 23.69217518261732, 37.604978063701836, 48.96286769387953, 56.7224913215801, 60.302058237480445, 59.63052060323652, 55.122125803300676, 47.5855732657914, 38.086360007890214, 27.78655220543372, 17.787939450070976, 9.000040077554694, 2.048223212557727, -2.7628955339555317, -5.435897823018778, -6.2267517985801915, -5.564657040282786, -3.9615156875659068, -1.9262084286799268, 0.10427804231654293, 1.8094525210424304, 3.0033602543243747, 3.6284608591973875, 3.731245920792807, 3.4273969680658554, 2.8644989066760194, 2.1891271757139603, 1.522790988838957, 0.9486126215827612, 0.5088547337325721, 0.21060008341781786, 0.036151594206111845, -0.04523055646158548, -0.06697810691462038, -0.05791969973602573, -0.03857802882940409, -0.02064788067254111, -0.008649208522923411, -0.0025584336937358163, -0.0003783046791960911, 1.6459651633311814e-05, -2.04809007895411e-05, -5.980550359127284e-06, 2.3221315674386794e-05, -6.438847662157009e-05, -0.00025052410581084713, -0.00037429933643556206, -0.000301628172666204, -9.031741587919254e-05, -1.003140454718234e-05, -0.00037973879843505913, -0.0013105031489307655, -0.0025238357922180354, -0.0034066131287314927, -0.003349846621233676, -0.0022315120201968726, -0.0007121252264865502, 9.732500354878771e-05, -1.420395643186193e-05, 0.002157301913226974, 0.016655725717003817, 0.06399885827602518, 0.17794495538480984, 0.4061400372217194, 0.807527818575169, 1.4458836479759287, 2.3796116950194617, 3.648887076876179, 5.262132077932812, 7.184462164517723, 9.330921670198807, 11.566925201211477, 13.717319184742578, 15.584002719358368, 16.971418034704932, 17.718275856172625, 17.721266230545158, 16.95254954918037, 15.467664357969769, 13.401052731892783, 10.949389628484978, 8.345126082038282, 5.8245069825878435, 3.595418699473484, 1.8105168329416916, 0.5501337764396789, -0.18236278869926278, -0.45244228941155024, -0.3756026961324128, -0.09193660348742043, 0.2607436649436393, 0.5700526447793061, 0.7644141340778746, 0.818019829214729, 0.7454458880901123, 0.5885218754571765, 0.39956739527954294, 0.22553623459348826, 0.09688127022271736, 0.023303701678322478, -0.00356163070854533, -0.002465109475465678, 0.006878107517876011, 0.011433026705040275, 0.00809406952105918, 0.0017258983303876847, -0.0006370116465963542, 0.003764883520436025, 0.010278975444865833, 0.010102929487464841, 0.00046732407206473826, -0.0015711381341619985, 0.05076215482625554, 0.22908035691025447, 0.5980926069890355, 1.146871804243825, 1.6786660578481594, 1.6638658040722258, 0.07207784458262176, -4.789107582223569, -15.391647988665936, -35.019284050583515, -67.67562365954181, -117.84562438710321, -190.10888956753746, -288.6182930772279, -416.48793078198435, -575.157430712528, -763.8160116717598, -978.9759466186189, -1214.278508687315, -1460.5954126566076, -1706.456696032208, -1938.795483365539, -2143.9564166554683, -2308.873981270384, -2422.295849307677, -2475.910101872701, -2465.3173193672637, -2390.8032131877194, -2257.1444978556638, -2073.0808401557833, -1850.4662872158383, -1603.1268312480424, -1345.5620409908797, -1091.6447855285119, -853.4680800853745, -640.4631681017187, -458.87222412216806, -311.60887484788014, -198.48767671559108, -116.75737137885989, -61.83862525673335, -28.149377590961635, -9.902686276091856, -1.7732378193973253, 0.6341100468180171, 0.528971791466776, -0.09112235726466954, -0.2802310885478955, 0.13540603375320312, 0.8805495553530286, 1.52993018247263, 1.7331758458306599, 1.3402108347756958, 0.4267765931932769, -0.759305451408166, -1.8972985486723453, -2.700531085255518, -2.9988062941133196, -2.775874463778944, -2.1567155894954846, -1.3538033395635687, -0.5931782160135222, -0.044509210719964415, 0.22344124321713732, 0.24913768819797324, 0.1454943735556586, 0.03902503194298969, 0.0006579029922769433, -0.008843799512444453, -0.1591394954937468, -0.7254733164285883, -2.020458642765436, -4.297106612662089, -7.647663297891186, -11.927089035983881, -16.727102838866596, -21.415149781108518, -25.23806623882272, -27.473663708860506, -27.59907828907888, -25.43656642618671, -21.23773888751151, -15.676792768205178, -9.74084669470849, -4.5278437730907966, -0.985159790466344, 0.35993294791694047, -0.38213022974028005, -2.3545468307201425, -3.9957454464557807, -3.246132742372848, 2.100675068797039, 13.958751437502858, 33.495937630535416, 60.74987606867093, 94.39486806865006, 131.7202522755212, 168.8481623262378, 201.17811429071494, 224.00477481125364, 233.22082385192255, 225.99556988523022, 201.316375459856, 160.29555642003132, 106.1784594753206, 44.03399762612919, -19.842037674102635, -78.75126139903368, -126.50114576546804, -158.2253748379608, -171.0134137810912, -164.26017057763542, -139.68818852471165, -101.04618693811983, -53.537443512912084, -3.0714073810815936, 44.54421132398308, 84.34923880065496, 112.80824824788583, 128.14424763623157, 130.39600052998793, 121.21138752771368, 103.4334184887799, 80.56153644334627, 56.15501959130102, 33.31314168215989, 14.30539094547703, 0.38888237451816754, -8.182927760491845, -11.989646278923713, -12.165570027835887, -10.079831473452591, -7.039997749977223, -4.070670853397216, -1.7968809013744966, -0.4369005198054398, 0.11421980094753992, 0.14607852213663342, -0.01732466546173367, -0.13870246442920192, -0.1297855835029477, -0.0429168083848237, 0.0002614140972922366, -0.08089489473087394, -0.21049968532658464, -0.07069071739541705, 0.9251857493152342, 3.5856258968204298, 8.822138534075117, 17.477340054048057, 30.13200720851321, 46.92987487688226, 67.45782152082828, 90.71022288581172, 115.154947745092, 138.90586798874344, 159.94852724283476, 176.39660680997054, 186.73999932952128, 190.04252912454933, 186.05861608988192, 175.25236493352654, 158.71910406548216, 138.0252357433643, 114.99461483597413, 91.47655556809778, 69.13108871981927, 49.26157537265674, 32.71461838464833, 19.854536767540843, 10.607443097841507, 4.557618935110317, 1.0717637095385666, -0.5661278753121461, -1.0370050778308972, -0.9028943265070878, -0.5637351521764697, -0.2531424265626341, -0.06449599333534849, 0.005234750711411333, 0.007322558893053054, 9.264551638987028e-05, 0.02197014124429315, 0.0811394962509748, 0.15968218012047866, 0.22688314440761095, 0.25509132624987535, 0.23212119687612467, 0.1662767079609037, 0.08300266403060144, 0.014947242184474657, -0.010825153690754775, 0.015958894040323544, 0.08292743002889712, 0.1566085230673319, 0.19116157168362785, 0.1419270482303031, -0.020035612756103497, -0.29664267544500783, -0.6581600293549816, -1.0469766395209992, -1.3892743417669258, -1.6120125853521423, -1.6611240671536722, -1.5156993405379924, -1.19490402769059, -0.7556957554162621, -0.28154547256109497, 0.1353910022445783, 0.41458098426953854, 0.5051663115838874, 0.39748018669970214, 0.12523447259931486, -0.2422512891160183, -0.6160627186539401, -0.9082561308344755, -1.0521579455016832, -1.017572738383484, -0.8171803522241925, -0.5023471408135081, -0.1495544181914929, 0.15928861032351094, 0.3580332863766244, 0.413952874736298, 0.3376371398928364, 0.18262474511834048, 0.034597282539534285, -0.00766430563378018, 0.14454632588651295, 0.5476756403278918, 1.2097213894369583, 2.083830529895531, 3.0734086037684802, 4.047995760728541, 4.86708591024963, 5.4075601013544325, 5.586717398733474, 5.377457002479057, 4.812796730845597, 3.978826048715505, 2.997758472712856, 2.0047265623322983, 1.1231299481004724, 0.44348362791116536, 0.009823302206467823, -0.18397499933021744, -0.18773138540537945, -0.08022179711206746, 0.05034452710112383, 0.1263033583446072, 0.09674309500801129, -0.05335010862521686, -0.30255614184363816, -0.6005861213460946, -0.8816942885755319, -1.08063349702034, -1.1475496787864727, -1.0586873465401607, -0.8208875366921936, -0.4693229718536292, -0.05939657780187296, 0.3450894521609584, 0.68473964958825, 0.9155823281673582, 1.0161209569163854, 0.9892591536315333, 0.8591656766563943, 0.6641965465986434, 0.4474733689359863, 0.2477486457849637, 0.09248299573039111, -0.005693852718291564, -0.04882319769796509, -0.050304631743024616, -0.029615069020379147, -0.006538424054836198, 0.003695895527088124, -0.006636079335152652, -0.037129549263829977, -0.08075855315508236, -0.1268259667241075, -0.16440396568693078, -0.18532550373742745, -0.18602590083443743, -0.16785658858431435, -0.13607238882682032, -0.09797406358414086, -0.06083176658656267, -0.030181586350525945, -0.008890055289787738, 0.0028976858808980196, 0.007081216665524422, 0.00653953283375046, 0.004071544121765587, 0.0016609557832384927, 0.00021807155786152173, -0.00023979845348165348, -0.00015516392886526136, 1.377949333562592e-05, 5.4526222311138234e-05, 9.291483545522778e-06, 5.071117636770908e-06, 7.232310480440821e-05, 0.00011101382824335776, 4.3711723722564695e-05, 5.8812955628181946e-06, 0.00024236175167985727, 0.0003014640097017654, -0.0027768814476202583, -0.01726552998384954, -0.060048136862185575, -0.1593782928850864, -0.35566423871688607, -0.698765438469017, -1.2407367614344176, -2.0241402904181776, -3.066970972916229, -4.346842203101753, -5.788327802476879, -7.257871624315934, -8.570319079266124, -9.509638787623645, -9.863869582586702, -9.471083069374373, -8.269772665983048, -6.344302464836255, -3.9546313483913442, -1.54008422280546, 0.31021837888944376, 0.9226601588220044, -0.36417925386664585, -4.083549911048747, -10.523193908344641, -19.628266581257876, -30.944266426268204, -43.61612260811399, -56.45222818272792, -68.05209968573315, -76.98518147505239, -81.99799198710467, -82.21927619861532, -77.32972864279763, -67.66519438385937, -54.23017151244792, -38.61107203963924, -22.794271784885225, -8.909815780525786, 1.0668463800195847, 5.603968837948698, 3.8424130898035727, -4.266567563218664, -17.936863708926982, -35.64217066837789, -55.31719784059564, -74.63620075581865, -91.32743974521112, -103.47652010102865, -109.77342416573012, -109.66714862918452, -103.4067387753234, -91.96571331575686, -76.86537150122177, -59.93042876750279, -43.014716462333325, -27.727558846422248, -15.235645047807665, -6.156809904000335, -0.55055353390606, 2.0028738603204768, 2.2571461455976625, 1.1198843733653097, -0.5272894045774649, -1.9772069377208328, -2.7912119985152013, -2.8279378246474116, -2.2090192883247624, -1.23567767922006, -0.27837941088413465, 0.3347657355497537, 0.40742546617373754, -0.07614156814491872, -0.9523490948781586, -1.9248479729833716, -2.642738851469894, -2.791041072424124, -2.1725239753729957, -0.7628980940779692, 1.272218546228782, 3.6016975139137872, 5.789121827071308, 7.376119236316914, 7.971761186363224, 7.330204939048596, 5.401521014663413, 2.3461517519379185, -1.4901631259809967, -5.6351979387270115, -9.56965261069319, -12.81187115889697, -14.992330557807014, -15.905227919201918, -15.529581055223952, -14.01838817466628, -11.660306242406302, -8.822892153363911, -5.888947170090416, -3.19762473836012, -0.9999023688507059, 0.5656187683921676, 1.474986516835265, 1.8018267834653423, 1.6868970746526595, 1.301386313631691, 0.8113738822788452, 0.35033579131608605, 0.0034534936609736523, -0.1955228666806792, -0.25671747697510594, -0.2195542121773083, -0.13560191093893992, -0.052985442953852345, -0.0053878211578465025, -0.007089670654661203, -0.05387215782112552, -0.12831369806889142, -0.20727912376001292, -0.2693236225863667, -0.30019883509163037, -0.29531065162704334, -0.25919302764810026, -0.2027408419122791, -0.13934962679086704, -0.08117989286390355, -0.03649697582392737, -0.008569797843656517, 0.003899219383162781, 0.005251547342300297, 0.0009108969707972679, -0.004371463940624009, -0.007610037272167241, -0.007852733239249081, -0.005744822650402414, -0.002706585209654615, -9.942999777277486e-05, 0.0013187565949762618, 0.0015238473986514851, 0.0010017673174493142, 0.0003583110919358353, -1.7376385568518212e-05, -7.992758697745873e-05, -1.6270368157303033e-05, 2.6347869655422423e-06, 2.8482838838067468e-05, 0.0003390559112498986, 0.0011893401362403878, 0.0024326338735283816, 0.003296386816490207, 0.0026738823319368225, 0.00022372347626190402, -0.0016693316108411468, 0.00462339714107032, 0.034412139006666856, 0.1121603730800847, 0.27107087091859355, 0.5501067439702958, 0.9882719955010071, 1.6166585553595827, 2.4494780099494093, 3.4758531359537583, 4.654374450938124, 5.9122148277168725, 7.1499195329669885, 8.25194063903194, 9.101758306056446, 9.599782062193869, 9.681605190827339, 9.328802163818608, 8.572995194936038, 7.492135106862845, 6.199048928380192, 4.824268841828434, 3.496330623668805, 2.323243535368797, 1.3785601444408744, 0.6944644305133625, 0.2627719969889549, 0.04304332341109348, -0.024459553302946715, -0.004148372973731862, 0.04787665119309871, 0.09253239657415337, 0.11082971603177488, 0.10142906006208749, 0.07427643677681077, 0.042904998731112545, 0.01800345976682633, 0.0040565988617956815, -0.00045975722067422345, -0.0002439479071633758, 0.00041935559842028414, -3.975676709747585e-05, -0.0006835441298114869, -0.0003855611351137405, 5.7246657360360814e-05, -0.00015766357890174468, 0.008247379379999796, 0.06555434609981779, 0.2740350491382592, 0.8332137272220054, 2.068123751103858, 4.434742970022425, 8.484871849736338, 14.774839390111415, 23.709392449397342, 35.323799643215956, 49.02230438713811, 63.30722635283468, 75.54706970195879, 81.84049505140649, 77.0328694879698, 54.93131632516602, 8.742403615526637, -68.27191950013889, -181.97486511284066, -336.49142969623466, -533.3669524323525, -770.8695664192302, -1043.555348904984, -1342.1898679289125, -1654.0823920170876, -1963.8394927539061, -2254.4895754198806, -2508.876866041038, -2711.180626102348, -2848.389848676225, -2911.560146182376, -2896.6995764384383, -2805.1718470937976, -2643.640177189807, -2423.59503055404, -2159.9075709532644, -1869.2845661552599, -1568.7179694797023, -1274.0251003153917, -998.6359116084261, -752.7418308826097, -542.8664426395558, -371.8603420720004, -239.2693385100755, -141.98401783858833, -75.05433642278187, -32.547320560425575, -8.337961726598904, 3.2507077211546638, 7.00855347572833, 6.613862249091427, 4.599524521660911, 2.4738435847677245, 0.9401771236616444, 0.15387310437388424, -0.03479273500998541, 0.11356192285824562, 0.35659474288112736, 0.5348085200756103, 0.5840330958878918, 0.514592917968966, 0.37652022360130544, 0.22638893112887146, 0.10514935321403795, 0.029806447106693692, -0.003410535953520965, -0.009607347169067745, -0.005101210416585707, -0.0006936622367430413, 0.00013478888113005463, -0.0009837033009989537, -0.0011784077566299738, 0.0005989483732434558, 0.0028181821126571755, 0.0028909066893987416, -0.00038407708177791785, -0.005319047149924877, -0.008102787884385542, -0.005738637824645411, 0.0006431769747444378, 0.005094986630607331, 0.001751833853620477, -0.003326440613655653, 0.025015188520891952, 0.16845502593792333, 0.5649781869459144, 1.4021464206989396, 2.8868028585191343, 5.189007225000901, 8.365249248264526, 12.274160206848608, 16.504936158654278, 20.34224400211055, 22.789658854812206, 22.665808092967193, 18.77388598829981, 10.128081152653657, -3.796611179585512, -22.843016366269374, -46.038060662085584, -71.57963134220924, -96.97236812701246, -119.31452426312532, -135.7071550077793, -143.7282956968652, -141.8935610715039, -130.01599862507908, -109.38538203367183, -82.71092463113187, -53.808886051611026, -27.06198148387223, -6.722949973331043, 3.8286632049789513, 2.748495436787885, -9.81785928080188, -31.60582966897409, -58.46959700079517, -84.9597092926581, -105.15914869764735, -113.64643949238051, -106.42593512655523, -81.66452690024919, -40.10183748419976, 14.946595792915547, 78.0053296658384, 142.21412329318284, 200.33876822066335, 245.8515819581973, 273.90153718523356, 282.02231817536716, 270.4650766201474, 242.01493561020695, 201.43234123139638, 154.61865984827918, 107.64513598554602, 65.81364385839387, 32.90634690532183, 10.743093715826259, -0.8925275406447543, -3.964457177537962, -1.6026557612422283, 2.651555015498644, 5.626641367637056, 5.181811330964769, 0.6275308470308306, -7.165666102681416, -15.979349311294472, -22.756426465701487, -24.306410466430904, -18.050831471734185, -2.6516615553569327, 21.6084982253785, 52.772879246095286, 87.4936178237377, 121.59199294663213, 150.7806768207645, 171.4023443645714, 181.03957419586075, 178.88170611986442, 165.7877519876289, 144.04840424555601, 116.92041000138467, 88.00852742092094, 60.58543319158332, 37.16010129925829, 19.266210839038283, 7.441023698267879, 1.3564385056349888, 0.04776363739462391, 2.18298537968602, 6.322803034967503, 11.135394048686212, 15.545773943190628, 18.814506010008987, 20.55226726792674, 20.684393243418736], 'positive_zeros': ['0.43035754040625187678929390223673', '0.73295629672955769027688904651650', '1.07440162696704758806588195137249', '1.18291282778892749501470561703060', '1.29010157416730295557730040311229', '1.31039483097622593488844790063028', '1.41629332604352798620029223162306', '1.96420466559638108415540453246523', '2.01127520909562254602281258747800', '2.15285452680164303372314334841315', '2.37525987648620775742984734512454', '2.42411786118666289230701219657389', '2.60233703092335750155863565304203', '2.77631226923327885045307993238219', '2.79490619265118629517914206702208', '2.81785623249694407595296026733848', '2.93106739520428817967027018980263', '3.06567165373098373285659821318814', '3.15789989213865363061611904672566', '3.33034808235857770858893882388292', '3.39343065907656789796931377177127', '3.47693574817576494567709102313683', '3.56160032952795522618213981749220', '3.71714283654786154020038916265284', '3.89582835566798559926186319546872', '3.93955515206484403126615733110414', '4.17694861864766202407557029634872', '4.21838962604927604741199973367265', '4.56648693633757129722320938162176', '4.57604767841661733329410062350866', '4.57929378827655541886262267346642', '4.63259861610294059997721965220927', '4.66043885518469251328931631185257', '4.76349425342028937981427854927952', '4.85724531781899137546224360925781', '4.91070254173855271553061816542186', '5.16030903799092380079405817564106', '5.21214245427719241148173530381476', '5.21589323808236746022929174105030', '5.28545959070592479532940261541230', '5.47266329689364508350105926223701', '5.65277560934353916903710308901161', '5.68798096355925937048737711678161', '5.74945110533179800718143638109042', '6.01753740944115514801361611160786', '6.05965397058580468844998127186679', '6.06847833375334732573277113318762', '6.13566457337216143461270132953443', '6.16631111493728511359034507637755', '6.28915922781058128025933060222275', '6.31817898138447284050839006441291', '6.34456871111593429967385413816908', '6.44325709288695662724206857525407', '6.50144573010741809890631306500197', '6.68243821555956572934211585010066', '6.74021071239464131260439894144126', '6.75759102266963141958811377299276', '6.76554116892735239336987602159599', '6.79701704217695333894765841362552', '7.08033293609686930239329640554417', '7.08569245479341663557123681822555', '7.20862959857878013758417634384670', '7.23549341094272282220702658124524', '7.55529609885061713888156305304225', '7.56221770698715395506484219204890', '7.56745688170960270638956304564357', '7.64601609501665248199071735756906', '7.70458771512267212686758844268652', '7.75937685225043497752060951502559', '7.81203832222291642951465760049933', '7.85388994338428776072481899305048', '7.86505545594025237726275066162157', '7.935493895259607451763781282216637', '8.080575220413170025047194022141610', '8.092993992637788550907315660998278', '8.359671971759394315902958347417550', '8.386174204869634771199511797586881', '8.454066324349724163971269599171731', '8.459049333606020536469756839244175', '8.496059418621094033095261776281999', '8.559513105344879870623651014746433', '8.652278555509174814751863966716429', '8.760648430083083091223570387324651', '8.917739261213827738375796858061675', '8.923702187855605920211719955211887', '8.935403867504325639425948300881464', '9.148394052084886835809520833453722', '9.185048959912938487050451993530692', '9.336677702026518450960967786562427', '9.426276524239064325509204181875102', '9.540538735255650760804338577522119', '9.631606402218720516539494485603319', '9.639733379280096770405190840021647', '9.692469078275023998189277361088826', '9.702491102282185084344136448413563', '9.705201900068705781317915807841059', '9.713955128787968756634597051046205', '9.807338245713085225655631679219289', '9.926395844275869713160444256222905', '10.03434086809809346945417870513669', '10.07853361687672396767601649392942', '10.29636145045679541905188775360929', '10.38471660148772282607581433004518', '10.39514138283385652267938396628429', '10.45268037358876074268260773378791', '10.50003293382558076326892445497307', '10.51193130920715806099691352197429', '10.52575641627043076853862152982765', '10.62659268394346211997657992055752', '10.69795011249530405961849400593621', '10.73948074619044327129819949442023', '10.77336552881020736414244053663497', '11.02323627907760955705111989130561', '11.02357280358997804789363196785948', '11.12774368309150977021652462925411', '11.14077700598523973265567564167247', '11.20714950510746589802439614341604', '11.24886786923054780358080296291342', '11.27579618155883065122624219971928', '11.46323756020399423084868263622253', '11.60563829238976187422780273701595', '11.61989767861221298591911879829697', '11.65669330262901645573390673265719', '11.69010874451277854180289454170192', '11.74219736099284712466402143254269', '11.79810998289235855083692166130560', '11.94250645481440231414314660165365', '11.97611255592199752823536106097780', '12.01029205699301472642634227513022', '12.02436128550017373463593354466924', '12.03154352453234952119835446548535', '12.10469722204224496515358732501005', '12.15707085791459067347999284560126', '12.22143803587962925307108151871417', '12.24359348529869502530921793816484', '12.42347219136206638447681138995121', '12.49428940699124724658264499466619', '12.50750136490351815408188587820571', '12.55276599409250943508595487615979', '12.62188429176543034758636366079760', '12.71689826608742135378780622002410', '12.77351771987372641513906068705329', '12.81562549890636148630459233432702', '13.06217815851365842833293305018422', '13.12653478650076918130324539776528', '13.15224556485278910839330784815975', '13.24671973272882658539376204196708', '13.30001749042499868209278809422029', '13.32578692855648074343058059853022', '13.45822235443613584012598511926319', '13.56887088055867753175093409216369', '13.64837468107979046892903831828569', '13.82747724458106950609773236836856', '13.90185712049079237408430589940353', '14.02258822270382910314901644492275', '14.17018405571802995392582491277282', '14.43417205947112842229622651175272', '14.43712974584529651728306993022568', '14.50792262025026553528266296101561', '14.53450347137685401429978577380268'], 'prelabel': '32-105e16-1.1-c2e16-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.6914617275549328, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c2e16-0', 'trace_hash': 118576819474984765, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.43035754040625187678929390224', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.73295629672955769027688904652', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.07440162696704758806588195137', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 20155316.23850961, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 218287458838193562060699462890625, 'conductor_radical': 105, 'degree': 32, 'dirichlet_coefficients': [1, 0, 0, 12, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 88, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 344, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -392, 0, 0, 432, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 576, 0, 0, 608, 0, -74, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, 668, 0, 227076, 0, 54959032, 0, 10898303846, 0, 1884559898604, 0, 292753217618464, 0, 41349775413708356, 0, 5280291937987187427, 0, 605402061832104040196, 0, 62754252137843427978784, 0, 5914556263409244073997484, 0, 500774117694829537524831206, 0, 36973688499498403387598053432, 0, 2236637897091689096942786006916, 0, 96332237319141488337167610806108, 0, 2111377674535255285545615254209921], 'euler13': [1, 0, -752, 0, 294396, 0, -94491808, 0, 27897426986, 0, -6946713193296, 0, 1486545931814704, 0, -295772053309921424, 0, 53570281236296108787, 0, -8447545614584665790864, 0, 1212621184758825332321584, 0, -161845115298872016788087376, 0, 18563411269959456713604589226, 0, -1795813388062991723457691842208, 0, 159798375595133181477906587896956, 0, -11658205467602121953882690399351792, 0, 442779263776840698304313192148785281], 'euler17': [1, 0, -1812, 0, 1746836, 0, -1184674728, 0, 632617771366, 0, -284097553986276, 0, 111128236807771424, 0, -38432090155534531404, 0, 11793543729578919124387, 0, -3209886601880399597393484, 0, 775203624817021597595165984, 0, -165521552494986928520852760036, 0, 30783934756397679703494449715046, 0, -4814792236199270369836390571439528, 0, 592961159204531401059840157935179156, 0, -51372179568084274008566954547306230292, 0, 2367911594760467245844106297320951247361], 'euler19': [1, -48, -1532, 78336, 2653734, -99758160, -2908984696, 79073899248, 2758377278513, -50151488370768, -1975770167526888, 22031645624013456, 1185999145130228470, -7147818937900046784, -566860592607956328356, 949992618446762430096, 227741761450133276567076, 342947335259281237264656, -73873839289261476667682276, -336275439161991990894496704, 20142491247891343374977977270, 135077479089217957140388970256, -4373001588433109474095818436968, -40071374510206194474070427774928, 795630241367097590603288011338353, 8233755606418236297814462317203568, -109348657511047398101127252194882296, -1353716277753077868634994512304951760, 13000013747830451868965535133058407014, 138533566958469351568857158187730223616, -978046699774246729777619345512160126012, -11062397659065370322184456931484798083248, 83198449060887472631428936505541918917761], 'euler2': [1, 0, -12, 0, 56, 0, -48, 0, -644, 0, 3744, 0, -3616, 0, -79584, 0, 542992, 0, -1273344, 0, -925696, 0, 15335424, 0, -42205184, 0, -50331648, 0, 939524096, 0, -3221225472, 0, 4294967296], 'euler23': [1, 0, -2132, 0, 1767156, 0, -1229468968, 0, 1248595253606, 0, -923539261736676, 0, 468287785415244064, 0, -303211874716399935884, 0, 198161384670708543891747, 0, -84851114232512074457714444, 0, 36672077870925264368926621984, 0, -20239016069184569861405782992996, 0, 7657148257234013587294803163403366, 0, -2109960338878115933741535535313622568, 0, 848678019101002447296602158376436561396, 0, -286527696829366173852549205555103147777492, 0, 37608910510519071039902074217516707306379521], 'euler29': [1, 0, -9576, 0, 45402440, 0, -140765141160, 0, 318379322605540, 0, -555757542808824888, 0, 773262795811472582168, 0, -873860179983381108476280, 0, 810135983840573705163240070, 0, -618064701958825773784211794680, 0, 386821939880883334440742332679448, 0, -196635234523708557582165000074292408, 0, 79673302774774083303865991625557466340, 0, -24914666496465333899539197835608924005160, 0, 5683699948146868752417299089857524599021640, 0, -847867675954198545674622999457386566455368936, 0, 62623297589448778360828428329074752308805325441], 'euler3': [1, 0, 4, 0, 90, 0, -944, 0, -2381, 0, -76464, 0, 590490, 0, 2125764, 0, 43046721, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, -344, 59116, -6962560, 644966390, -50363052712, 3435919762968, -209372772204072, 11579483269444545, -587768400942165480, 27595302421736225256, -1205497742639776491864, 49224919456418007325926, -1884863496224161633689600, 67835803472994372228786900, -2298558197729668914265384728, 73394137708506951686592058692, -2208914428018211826609034723608, 62647789059183235635101506674900, -1672823291081473051038493611417600, 41983492623134020053962964355995366, -988060049759062512928418688100703064, 21735792724991664006438669078660963816, -444907726407597545981352127517468719080, 8423183868078654122002349098293021086145, -146362794338491967412238023042843601421352, 2308218354544208567448911612101954777311768, -32513918363578622034467092012770359426827432, 400145314253230307495853782486508969234163190, -4151193622039590826706112197613098011458559360, 33871346981028995902427806159775450676994411756, -189412770998993328056840683935367879873528665944, 529144398052420314716929933900838757437386767361], 'euler37': [1, 0, 4936, 0, 9651186, 0, 11563577072, 0, 17334945323297, 0, 28195141563554256, 0, 40294960676450729842, 0, 82774213735327269675832, 0, 147723512473845461234622276, 0, 155132203188414691062926976952, 0, 141535221472587828319890058610482, 0, 185607263710743238127658358797705936, 0, 213870094458479886276541276075920292577, 0, 267378621975497465844861878826625219826672, 0, 418236626737949643944388431136878650625917746, 0, 400888340090478784358010451625778534517883814856, 0, 152214200233450528559804138174517974884637692126081], 'euler41': [1, 0, -12216, 0, 83224040, 0, -398236530360, 0, 1476742426794340, 0, -4443292746221574888, 0, 11154007950540985616888, 0, -23716326153822879285813480, 0, 43083733638609157921580222470, 0, -67016669508752693193559585058280, 0, 89063919490090935212830578926995448, 0, -100256192781057938593586192465884733928, 0, 94155666042960099040606289905472370051940, 0, -71749392767218614048972765004371249963858360, 0, 42370282096001232296678454057725525000326206440, 0, -17574258582772624620923546269598769238449105354936, 0, 4065214023175683899921868126254722311886802750234881], 'euler43': [1, 0, -16496, 0, 146336700, 0, -884936332960, 0, 4029319118940650, 0, -14503865770472138448, 0, 42481960034335372232368, 0, -102908562118417781386883600, 0, 208027477131765359105845167795, 0, -351823895079008829423259038563600, 0, 496537657066353285217897324677589168, 0, -579569121321120969631746249240449565648, 0, 550461505786567094478586872646639511820650, 0, -413314972399281023976220518939444609578572960, 0, 233666358808082027517040058435597842392326096700, 0, -90052423308752701157127077481243234779295406730096, 0, 18663392025969146670022260524972832947786731075670401], 'euler47': [1, 0, -14672, 0, 116061396, 0, -646412138848, 0, 2818120883606186, 0, -10187086332486400176, 0, 31511435695414691713744, 0, -84790042597275507436071344, 0, 199917465627374108064901115667, 0, -413748359851115945401156051961264, 0, 750327828467167310231110317962943184, 0, -1183652669530494486123617317643372170416, 0, 1597810773942166771537209548272203091854506, 0, -1788408239583414733805079394125323994081694048, 0, 1566882320946647917393026239935666164269561957076, 0, -966561162069943227376428543726663285364769984378192, 0, 321463340914028260476243062478235279920395730789296641], 'euler5': [1, 0, 0, 0, 250, 0, 0, 0, -328125, 0, 0, 0, 97656250, 0, 0, 0, 152587890625, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, -15272, 0, 115608996, 0, -649480499248, 0, 3153703513389386, 0, -13200443109519730776, 0, 48037620613154020278544, 0, -158372269876092022445673944, 0, 472097770717226134401351928467, 0, -1249633386384176457359163787327064, 0, 2990807387473382877843514027162138384, 0, -6484835217685913906457114806440062931416, 0, 12224603322201304542030396621825259584584906, 0, -19864768482673345830742578380052261119744646448, 0, 27900533005389483167610169474567618231768610173476, 0, -29081731751119261005959471198655763725003024005373992, 0, 15025461748906708859452861070130993269553796873817927041], 'euler59': [1, 0, 948, 0, 25945076, 0, -22761523608, 0, 169024123159846, 0, -863462355580598076, 0, 4141075811916101091104, 0, -2323175168914222669865364, 0, 99988912175376285054299118307, 0, -28150752187969614125142436984404, 0, 608035973616310006275927259925060384, 0, -1536269993796025471671656517315161320956, 0, 3644021057278651181763752429363510697419686, 0, -5946228063949536799135721954040584966653546008, 0, 82130265471209257686098618717091266131832917125236, 0, 36363415077372401702134485906972924307480749332478708, 0, 464798130469793589516643498190087912509935907396786423681], 'euler61': [1, 392, 58168, 4718896, 501756764, 73806620440, 6607252863504, 417358734799608, 43016457989400138, 4408106367429180192, 266826572912162614632, 16833003484353437962056, 1690706907543180554609520, 116953244901619219770905256, 5550722508787024887997468104, 419490434896474956704599514976, 33169619643915883937630392693971, 1560923908249783313897814795225696, 76854421291786249462255751770555464, 6025474960065136817669771444982541416, 324120878311045543516430935491776715120, 12007703717560129521061204344595820587656, 708250840124738923040495261432375663152872, 43538128380341707089597319658445278689968672, 1580927694823340635418583018816189376661628618, 57075081113515054682432611871565252052757310648, 3362154201901857259663243620683839862627997164304, 139749959256152437078187509867711988292402337105240, 3535161639737875312379508137569695728252855095823324, 123713221553421082930097853030150816920239371828116656, 5674394317649610902748817659030866780274864321492282808, 142292207611433902666385528119026118715546106020267697992, 1350687001332003958728623852374735172807518011483204347521], 'euler67': [1, 0, 25096, 0, 320737746, 0, 2939997955952, 0, 22183328725900097, 0, 145120466564960354256, 0, 844167542922670703605522, 0, 4435418621494949553910291192, 0, 21021350810484141392366845910916, 0, 89378657327397929349742300955226232, 0, 342789153623304948509068186038075371602, 0, 1187479985210241558868768937434623163601616, 0, 3657830342018599313549439593358271828348579457, 0, 9768841933571799947865059051492025642214371735152, 0, 21475601551905889926077011797230560254296737389886866, 0, 33860937746524001500602073375656809913083918914319328136, 0, 27189028279553414235049966267283185807800188603627566700161], 'euler7': [1, 0, 104, 0, 11230, 0, 693056, 0, 42687379, 0, 1664027456, 0, 64738715230, 0, 1439493868904, 0, 33232930569601, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 0, -54696, 0, 1473645320, 0, -26047422376680, 0, 338289093213534820, 0, -3420795296041945606008, 0, 27834490970292132211947608, 0, -185763895284534489022543706040, 0, 1027168473043198821594367598639110, 0, -4720572848287994668538882466446253240, 0, 17974220834494392812733972957544304089688, 0, -56134165528724788840591234443618412584119928, 0, 141065747796236162659230730913434825302268293220, 0, -276014391444461852732565958712431453495634902408680, 0, 396819804183611611012908865714884317797988599281990920, 0, -374273717637273598549311934277252161930322763763542118056, 0, 173887017684702179246328390437079448141248104062408434512641], 'euler73': [1, 0, 21656, 0, 234439266, 0, 1309085752912, 0, 2475221846446577, 0, -11590633136358955344, 0, 25640523813063653119042, 0, 1558159667579488643235006632, 0, 12716944684257376935794514951396, 0, 44248993756402205147350737972134312, 0, 20678059190495685854482809197148190402, 0, -265449236978134873657800406368299017318224, 0, 1609829536570648552546749371128109108695747697, 0, 24178274214659866893540715999265340857068663519312, 0, 122964286993642878418068463083346069105440777878094306, 0, 322565804947687814735941678488730231626547034459859197336, 0, 422991386556309150149363832086603107763045099853453376062721], 'euler79': [1, -608, 158548, -26562304, 4208789174, -690629020960, 95475474742824, -11336959661249952, 1376670495367192833, -162662283177219304608, 16722605184638925760152, -1644117179385679907376864, 165877293353502354158645670, -15349309823384966777148536064, 1292631712250469302658943264044, -110863174585305092058196189333344, 9261032587932971440635568922777796, -691897072586889079535202417629399904, 50348109895324471626579355508918187564, -3731224668970141477100157479667864409344, 251653903110053457436163577155123007240870, -15566955366613346772338265120787974450557664, 988164008746422474139739098188552232134139032, -59988242989117511828566876785054929253988978848, 3168571163119383415292636111680718124092032750593, -162848680718321920772974691721441427612583410733472, 8559209417353452425421225496866907673525698463888424, -386403304924201094815390855640907310644917958270595360, 14696278135676948774881029479920070945201773018754656694, -578855436359272389028496351875318532299516192187956489984, 21563503524724247671792384317477725749805697182921317356628, -516079155225325138567191087111979461954478848803618213453408, 5297450670659957549009604563595170759963655420038456036451841], 'euler83': [1, 0, 29544, 0, 661846280, 0, 10426300509480, 0, 139767629955703780, 0, 1535588514048427501752, 0, 14862680365368504632892248, 0, 123277233839667783008490962040, 0, 912480700116526498364181668166790, 0, 5850530535555016179375309802093134840, 0, 33475099535684926742800424116079507054168, 0, 164139068150035552419603561651261361794102072, 0, 709016070375966252043880381648939305711322494180, 0, 2510106137683402058349967141364105449356354154797480, 0, 7561907301568103296381576243621974782426590197443023880, 0, 16019755417098992878840489611931244962520119677450496489704, 0, 25733505785478367615107164358252046214490685371339768616901761], 'euler89': [1, 0, -3172, 0, -240595644, 0, 390057940792, 0, 37366996704615206, 0, -36104713523503280916, 0, -3704425195681976827921376, 0, 750860105615056098352170116, 0, 276240220801708620001282489833507, 0, 47110645703785302951331560291069956, 0, -14582798756882410866874298155119547583456, 0, -8917517763778252966605992768966559566905236, 0, 579066312096968222533740721988980404086751510566, 0, 379253202350665347031142094459749906366690357083192, 0, -14677359089917273601214046454887112396018285170535747004, 0, -12140969405109633464981527413511679490919426355718203951332, 0, 240148684864128390378794468324923219083866317778128398613374721], 'euler97': [1, 0, -149792, 0, 10524668616, 0, -460430092223968, 0, 14037362496246878876, 0, -316246112482341563469216, 0, 5446093182088385543580162424, 0, -73129983228930169756375130532704, 0, 773831593196422564367688817701285702, 0, -6474144834799246327739835472341432105824, 0, 42683393663406836668492335916727593463513464, 0, -219424949340376726534073307319331973835520957856, 0, 862250119829973109479566664110174706318107447114396, 0, -2503792794646343204050568311244321014300467037447411168, 0, 5066756726656225986875509900438120945471408067989188983496, 0, -6384063217261844376233042195663415252762626323373109480986912, 0, 3773075507922571775273744352333525624409237957166570157859261441], 'euler_factors': [[1, 0, -12, 0, 56, 0, -48, 0, -644, 0, 3744, 0, -3616, 0, -79584, 0, 542992, 0, -1273344, 0, -925696, 0, 15335424, 0, -42205184, 0, -50331648, 0, 939524096, 0, -3221225472, 0, 4294967296], [1, 0, 4, 0, 90, 0, -944, 0, -2381, 0, -76464, 0, 590490, 0, 2125764, 0, 43046721, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 250, 0, 0, 0, -328125, 0, 0, 0, 97656250, 0, 0, 0, 152587890625, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 104, 0, 11230, 0, 693056, 0, 42687379, 0, 1664027456, 0, 64738715230, 0, 1439493868904, 0, 33232930569601, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 668, 0, 227076, 0, 54959032, 0, 10898303846, 0, 1884559898604, 0, 292753217618464, 0, 41349775413708356, 0, 5280291937987187427, 0, 605402061832104040196, 0, 62754252137843427978784, 0, 5914556263409244073997484, 0, 500774117694829537524831206, 0, 36973688499498403387598053432, 0, 2236637897091689096942786006916, 0, 96332237319141488337167610806108, 0, 2111377674535255285545615254209921], [1, 0, -752, 0, 294396, 0, -94491808, 0, 27897426986, 0, -6946713193296, 0, 1486545931814704, 0, -295772053309921424, 0, 53570281236296108787, 0, -8447545614584665790864, 0, 1212621184758825332321584, 0, -161845115298872016788087376, 0, 18563411269959456713604589226, 0, -1795813388062991723457691842208, 0, 159798375595133181477906587896956, 0, -11658205467602121953882690399351792, 0, 442779263776840698304313192148785281], [1, 0, -1812, 0, 1746836, 0, -1184674728, 0, 632617771366, 0, -284097553986276, 0, 111128236807771424, 0, -38432090155534531404, 0, 11793543729578919124387, 0, -3209886601880399597393484, 0, 775203624817021597595165984, 0, -165521552494986928520852760036, 0, 30783934756397679703494449715046, 0, -4814792236199270369836390571439528, 0, 592961159204531401059840157935179156, 0, -51372179568084274008566954547306230292, 0, 2367911594760467245844106297320951247361], [1, -48, -1532, 78336, 2653734, -99758160, -2908984696, 79073899248, 2758377278513, -50151488370768, -1975770167526888, 22031645624013456, 1185999145130228470, -7147818937900046784, -566860592607956328356, 949992618446762430096, 227741761450133276567076, 342947335259281237264656, -73873839289261476667682276, -336275439161991990894496704, 20142491247891343374977977270, 135077479089217957140388970256, -4373001588433109474095818436968, -40071374510206194474070427774928, 795630241367097590603288011338353, 8233755606418236297814462317203568, -109348657511047398101127252194882296, -1353716277753077868634994512304951760, 13000013747830451868965535133058407014, 138533566958469351568857158187730223616, -978046699774246729777619345512160126012, -11062397659065370322184456931484798083248, 83198449060887472631428936505541918917761], [1, 0, -2132, 0, 1767156, 0, -1229468968, 0, 1248595253606, 0, -923539261736676, 0, 468287785415244064, 0, -303211874716399935884, 0, 198161384670708543891747, 0, -84851114232512074457714444, 0, 36672077870925264368926621984, 0, -20239016069184569861405782992996, 0, 7657148257234013587294803163403366, 0, -2109960338878115933741535535313622568, 0, 848678019101002447296602158376436561396, 0, -286527696829366173852549205555103147777492, 0, 37608910510519071039902074217516707306379521], [1, 0, -9576, 0, 45402440, 0, -140765141160, 0, 318379322605540, 0, -555757542808824888, 0, 773262795811472582168, 0, -873860179983381108476280, 0, 810135983840573705163240070, 0, -618064701958825773784211794680, 0, 386821939880883334440742332679448, 0, -196635234523708557582165000074292408, 0, 79673302774774083303865991625557466340, 0, -24914666496465333899539197835608924005160, 0, 5683699948146868752417299089857524599021640, 0, -847867675954198545674622999457386566455368936, 0, 62623297589448778360828428329074752308805325441], [1, -344, 59116, -6962560, 644966390, -50363052712, 3435919762968, -209372772204072, 11579483269444545, -587768400942165480, 27595302421736225256, -1205497742639776491864, 49224919456418007325926, -1884863496224161633689600, 67835803472994372228786900, -2298558197729668914265384728, 73394137708506951686592058692, -2208914428018211826609034723608, 62647789059183235635101506674900, -1672823291081473051038493611417600, 41983492623134020053962964355995366, -988060049759062512928418688100703064, 21735792724991664006438669078660963816, -444907726407597545981352127517468719080, 8423183868078654122002349098293021086145, -146362794338491967412238023042843601421352, 2308218354544208567448911612101954777311768, -32513918363578622034467092012770359426827432, 400145314253230307495853782486508969234163190, -4151193622039590826706112197613098011458559360, 33871346981028995902427806159775450676994411756, -189412770998993328056840683935367879873528665944, 529144398052420314716929933900838757437386767361], [1, 0, 4936, 0, 9651186, 0, 11563577072, 0, 17334945323297, 0, 28195141563554256, 0, 40294960676450729842, 0, 82774213735327269675832, 0, 147723512473845461234622276, 0, 155132203188414691062926976952, 0, 141535221472587828319890058610482, 0, 185607263710743238127658358797705936, 0, 213870094458479886276541276075920292577, 0, 267378621975497465844861878826625219826672, 0, 418236626737949643944388431136878650625917746, 0, 400888340090478784358010451625778534517883814856, 0, 152214200233450528559804138174517974884637692126081], [1, 0, -12216, 0, 83224040, 0, -398236530360, 0, 1476742426794340, 0, -4443292746221574888, 0, 11154007950540985616888, 0, -23716326153822879285813480, 0, 43083733638609157921580222470, 0, -67016669508752693193559585058280, 0, 89063919490090935212830578926995448, 0, -100256192781057938593586192465884733928, 0, 94155666042960099040606289905472370051940, 0, -71749392767218614048972765004371249963858360, 0, 42370282096001232296678454057725525000326206440, 0, -17574258582772624620923546269598769238449105354936, 0, 4065214023175683899921868126254722311886802750234881], [1, 0, -16496, 0, 146336700, 0, -884936332960, 0, 4029319118940650, 0, -14503865770472138448, 0, 42481960034335372232368, 0, -102908562118417781386883600, 0, 208027477131765359105845167795, 0, -351823895079008829423259038563600, 0, 496537657066353285217897324677589168, 0, -579569121321120969631746249240449565648, 0, 550461505786567094478586872646639511820650, 0, -413314972399281023976220518939444609578572960, 0, 233666358808082027517040058435597842392326096700, 0, -90052423308752701157127077481243234779295406730096, 0, 18663392025969146670022260524972832947786731075670401], [1, 0, -14672, 0, 116061396, 0, -646412138848, 0, 2818120883606186, 0, -10187086332486400176, 0, 31511435695414691713744, 0, -84790042597275507436071344, 0, 199917465627374108064901115667, 0, -413748359851115945401156051961264, 0, 750327828467167310231110317962943184, 0, -1183652669530494486123617317643372170416, 0, 1597810773942166771537209548272203091854506, 0, -1788408239583414733805079394125323994081694048, 0, 1566882320946647917393026239935666164269561957076, 0, -966561162069943227376428543726663285364769984378192, 0, 321463340914028260476243062478235279920395730789296641], [1, 0, -15272, 0, 115608996, 0, -649480499248, 0, 3153703513389386, 0, -13200443109519730776, 0, 48037620613154020278544, 0, -158372269876092022445673944, 0, 472097770717226134401351928467, 0, -1249633386384176457359163787327064, 0, 2990807387473382877843514027162138384, 0, -6484835217685913906457114806440062931416, 0, 12224603322201304542030396621825259584584906, 0, -19864768482673345830742578380052261119744646448, 0, 27900533005389483167610169474567618231768610173476, 0, -29081731751119261005959471198655763725003024005373992, 0, 15025461748906708859452861070130993269553796873817927041], [1, 0, 948, 0, 25945076, 0, -22761523608, 0, 169024123159846, 0, -863462355580598076, 0, 4141075811916101091104, 0, -2323175168914222669865364, 0, 99988912175376285054299118307, 0, -28150752187969614125142436984404, 0, 608035973616310006275927259925060384, 0, -1536269993796025471671656517315161320956, 0, 3644021057278651181763752429363510697419686, 0, -5946228063949536799135721954040584966653546008, 0, 82130265471209257686098618717091266131832917125236, 0, 36363415077372401702134485906972924307480749332478708, 0, 464798130469793589516643498190087912509935907396786423681], [1, 392, 58168, 4718896, 501756764, 73806620440, 6607252863504, 417358734799608, 43016457989400138, 4408106367429180192, 266826572912162614632, 16833003484353437962056, 1690706907543180554609520, 116953244901619219770905256, 5550722508787024887997468104, 419490434896474956704599514976, 33169619643915883937630392693971, 1560923908249783313897814795225696, 76854421291786249462255751770555464, 6025474960065136817669771444982541416, 324120878311045543516430935491776715120, 12007703717560129521061204344595820587656, 708250840124738923040495261432375663152872, 43538128380341707089597319658445278689968672, 1580927694823340635418583018816189376661628618, 57075081113515054682432611871565252052757310648, 3362154201901857259663243620683839862627997164304, 139749959256152437078187509867711988292402337105240, 3535161639737875312379508137569695728252855095823324, 123713221553421082930097853030150816920239371828116656, 5674394317649610902748817659030866780274864321492282808, 142292207611433902666385528119026118715546106020267697992, 1350687001332003958728623852374735172807518011483204347521], [1, 0, 25096, 0, 320737746, 0, 2939997955952, 0, 22183328725900097, 0, 145120466564960354256, 0, 844167542922670703605522, 0, 4435418621494949553910291192, 0, 21021350810484141392366845910916, 0, 89378657327397929349742300955226232, 0, 342789153623304948509068186038075371602, 0, 1187479985210241558868768937434623163601616, 0, 3657830342018599313549439593358271828348579457, 0, 9768841933571799947865059051492025642214371735152, 0, 21475601551905889926077011797230560254296737389886866, 0, 33860937746524001500602073375656809913083918914319328136, 0, 27189028279553414235049966267283185807800188603627566700161], [1, 0, -54696, 0, 1473645320, 0, -26047422376680, 0, 338289093213534820, 0, -3420795296041945606008, 0, 27834490970292132211947608, 0, -185763895284534489022543706040, 0, 1027168473043198821594367598639110, 0, -4720572848287994668538882466446253240, 0, 17974220834494392812733972957544304089688, 0, -56134165528724788840591234443618412584119928, 0, 141065747796236162659230730913434825302268293220, 0, -276014391444461852732565958712431453495634902408680, 0, 396819804183611611012908865714884317797988599281990920, 0, -374273717637273598549311934277252161930322763763542118056, 0, 173887017684702179246328390437079448141248104062408434512641], [1, 0, 21656, 0, 234439266, 0, 1309085752912, 0, 2475221846446577, 0, -11590633136358955344, 0, 25640523813063653119042, 0, 1558159667579488643235006632, 0, 12716944684257376935794514951396, 0, 44248993756402205147350737972134312, 0, 20678059190495685854482809197148190402, 0, -265449236978134873657800406368299017318224, 0, 1609829536570648552546749371128109108695747697, 0, 24178274214659866893540715999265340857068663519312, 0, 122964286993642878418068463083346069105440777878094306, 0, 322565804947687814735941678488730231626547034459859197336, 0, 422991386556309150149363832086603107763045099853453376062721], [1, -608, 158548, -26562304, 4208789174, -690629020960, 95475474742824, -11336959661249952, 1376670495367192833, -162662283177219304608, 16722605184638925760152, -1644117179385679907376864, 165877293353502354158645670, -15349309823384966777148536064, 1292631712250469302658943264044, -110863174585305092058196189333344, 9261032587932971440635568922777796, -691897072586889079535202417629399904, 50348109895324471626579355508918187564, -3731224668970141477100157479667864409344, 251653903110053457436163577155123007240870, -15566955366613346772338265120787974450557664, 988164008746422474139739098188552232134139032, -59988242989117511828566876785054929253988978848, 3168571163119383415292636111680718124092032750593, -162848680718321920772974691721441427612583410733472, 8559209417353452425421225496866907673525698463888424, -386403304924201094815390855640907310644917958270595360, 14696278135676948774881029479920070945201773018754656694, -578855436359272389028496351875318532299516192187956489984, 21563503524724247671792384317477725749805697182921317356628, -516079155225325138567191087111979461954478848803618213453408, 5297450670659957549009604563595170759963655420038456036451841], [1, 0, 29544, 0, 661846280, 0, 10426300509480, 0, 139767629955703780, 0, 1535588514048427501752, 0, 14862680365368504632892248, 0, 123277233839667783008490962040, 0, 912480700116526498364181668166790, 0, 5850530535555016179375309802093134840, 0, 33475099535684926742800424116079507054168, 0, 164139068150035552419603561651261361794102072, 0, 709016070375966252043880381648939305711322494180, 0, 2510106137683402058349967141364105449356354154797480, 0, 7561907301568103296381576243621974782426590197443023880, 0, 16019755417098992878840489611931244962520119677450496489704, 0, 25733505785478367615107164358252046214490685371339768616901761], [1, 0, -3172, 0, -240595644, 0, 390057940792, 0, 37366996704615206, 0, -36104713523503280916, 0, -3704425195681976827921376, 0, 750860105615056098352170116, 0, 276240220801708620001282489833507, 0, 47110645703785302951331560291069956, 0, -14582798756882410866874298155119547583456, 0, -8917517763778252966605992768966559566905236, 0, 579066312096968222533740721988980404086751510566, 0, 379253202350665347031142094459749906366690357083192, 0, -14677359089917273601214046454887112396018285170535747004, 0, -12140969405109633464981527413511679490919426355718203951332, 0, 240148684864128390378794468324923219083866317778128398613374721], [1, 0, -149792, 0, 10524668616, 0, -460430092223968, 0, 14037362496246878876, 0, -316246112482341563469216, 0, 5446093182088385543580162424, 0, -73129983228930169756375130532704, 0, 773831593196422564367688817701285702, 0, -6474144834799246327739835472341432105824, 0, 42683393663406836668492335916727593463513464, 0, -219424949340376726534073307319331973835520957856, 0, 862250119829973109479566664110174706318107447114396, 0, -2503792794646343204050568311244321014300467037447411168, 0, 5066756726656225986875509900438120945471408067989188983496, 0, -6384063217261844376233042195663415252762626323373109480986912, 0, 3773075507922571775273744352333525624409237957166570157859261441]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/105/3/o/a'], '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': '32-105e16-1.1-c2e16-0-3', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'order_of_vanishing': 0, 'prelabel': '32-105e16-1.1-c2e16-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.6914617275549328, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e16-0', 'trace_hash': 118576819474984765, 'z1': {'__RealLiteral__': 0, 'data': '0.43035754040625187678929390224', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '545542994408729679239586621019,929132489490284020739939518583,1361965867310964095530041544925,1499520156164306099120928254115,1635398034848565202161496416872,1661122794022982020094979517517,1795365084858313655970281694608,2489925223314341094404343164843,2549594226034223515056396518856,3072934461757244896046819728155,3519393914514563562319222212690,3715569342840108790885901342514,4003113693730225160412010204997,4301684411811287390143147574448,4514864795499172070821551382899,4938549153448677919643650176905', 'Lhash_array': ['545542994408729679239586621019', '929132489490284020739939518583', '1361965867310964095530041544925', '1499520156164306099120928254115', '1635398034848565202161496416872', '1661122794022982020094979517517', '1795365084858313655970281694608', '2489925223314341094404343164843', '2549594226034223515056396518856', '3072934461757244896046819728155', '3519393914514563562319222212690', '3715569342840108790885901342514', '4003113693730225160412010204997', '4301684411811287390143147574448', '4514864795499172070821551382899', '4938549153448677919643650176905'], 'label': '32-105e16-1.1-c2e16-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/105/3/o/a'}