# Zeros of 1-231-231.86-r1-0-0 downloaded from the LMFDB on 25 August 2026.
{"order_of_vanishing": 0, "positive_zeros": ["0.88718739351370152408407801263", "2.42642181806869209989756794244", "3.74081520423759104141157540810", "4.57899478183915449214368872170", "5.82102108622469074372292408737", "7.64161510013236060290418824013", "8.48069307950400372847340303478", "9.638772271294915754942552481184", "10.69717611751223313309324355046", "11.63939838199639717795504135361", "12.54208564206859879416667513280", "13.21917334913191234283173688101", "14.679417759055496179997924274057", "15.36392509437347613997981525069", "16.88153015989200667799701945823", "17.616002797051694508046793236128", "19.13866830744428622799845171959", "19.37019631126171040713756768149", "20.43930790428955083498591159287", "21.28093282820545051870693900859", "22.28276327953499334058802718270", "23.23368514972484475102349554460", "23.86976190279890474970265621835", "25.05320595119501961876727752783", "26.453140758852687204292665454578", "27.195448009001106856861970067011", "27.98322837155385037321439026200", "28.663689164686368170342898066162", "29.88494466368821821358552514898", "30.381082463155827700798463507113", "31.673193637509709576673176518926", "31.86038171698512913058041063969", "32.94646848280325081884414948061", "34.289801788610075228974620114219", "35.2675882157200425435162483584", "35.94703301302267059950610012220", "36.91479003689878476575155060697", "37.63780709625758179588321112023", "38.72191903909971920641498331484", "39.326792989362339834868967760855", "39.893403000398726431228761409622", "40.94485049524994172539485833910", "41.78907318442988580401717893605", "42.70105102020492816359991928820", "43.77950110005378487307158903780", "44.567131914348629013569803918477", "45.57503983263326328705222802465", "46.46783746197293837709988840431", "47.041726558376639744893097080461", "47.729784407218802762486485811515", "48.66979702818819310407872555634", "49.410204114158942470933763198", "50.35499659179115453343154384700", "51.02058264565542742150974082735", "51.80370896693571030683164458962", "53.08774469010540789153017813775", "54.087618525778403903582815979212", "54.64834391276245968599087789938", "55.444538124362965004815779903174", "56.1029602771784183258381792759", "57.0952666082275847131163085028", "57.76727951070433094726080173527", "58.619453095678609650086587129362", "59.39305742772809706604419602049", "59.738159885390386412787514532487", "61.26451985513707024204897185021", "62.02039748916612090410354012923", "62.98942837745522687088560557156", "63.69729075770732983552078457467", "64.21146550379714941268786151466", "65.45718154261592059769084517356", "65.99631471409659064883323442356", "66.62502837326499192114933640006", "67.41635107065829309175190349085", "68.16579125597057640995164581846", "69.01773178272760150304437970423", "69.95184012296565615037845303258", "70.88624688536904083223646522464", "71.62783254655660809376135566713", "72.588929483585203169073875314274", "73.35604895363006578335352849309", "74.17883833789233744473994310722", "74.60255137977402504929899736400", "75.514721382578869423437688033909", "76.13853743560686799742721394214", "77.26613913178374491126874785993", "77.56636420988352794719398624997", "78.80630645359345051356188080558", "79.09785141345132435781764715319", "80.71350732484252106379184412390", "81.2536947000368689312363616579", "81.9574942386611947555897220749", "82.78889624542096176286798221806", "83.373734437668312699665844120238", "84.08299664036967245189434013225", "85.10929895547138048493588737095", "85.83020052570867260791887530640", "86.150474051531806146959733651562", "87.13838881375935571300319682095", "87.90938564798513753131716606488", "89.14842018493808003225224307485", "89.868664269296371781399524676250", "90.583478216569726197003670857211", "91.1845091724642035581567723423", "92.05620058035066553035606021569", "92.92413823888712524245281360217", "93.560261616297200719720164394279", "94.11431357127931770768584792609", "94.88554698613053241140174813825", "95.67577382195092075526602068247", "96.39300391924939623545262891055", "97.52169574155352970704841232053", "98.12931610915763384447433853146", "99.07837401223594562249790974444", "99.76243926472918124012301824727", "100.71937246365362637396987692818", "101.353259001786889279038807294251", "101.79730761728515595791432199006", "102.842823439597054008801455849929", "103.17769210967963228701672372655", "104.2090447007588694225585551803", "104.987202758891342970880043736911", "105.5856946797915211387098364629", "106.32668640265997154016232138547", "107.46192673874896687829157165648", "108.44565319391362019619168527543", "108.824636607422314149920291766544", "109.81839929804963602320864273334", "110.310441542737116864007334279152", "110.90058652069391890657008305005", "111.88995492501912360158422023095", "112.75711868911000587428440915479", "113.04882737738441238215696914295", "113.9297570743986752916508579634", "114.585714975026023860820085989807", "115.54969611170365778108365581916", "116.66499652731921409350323949533", "117.40239937512304087297618968273", "117.82791238140623183980629432263", "118.59764223400555166309976913663", "119.62170634297250755342900882001", "119.99017565877380604494221564638", "121.03290396118910462700913198828", "121.47014402318345025668283963507", "122.01597842486801733944862782899", "123.04357689861723270676143845519", "123.59486853183557354546764812347", "124.65074123324741842700389406398", "125.62531424141601146498462231200", "125.92606800913654972885216579599", "127.055799981603541461180699068769", "127.8688906540672728156049681739", "128.21827693466922905138153676896", "129.21829462558989396047860991430", "129.72049178368251357649440215199", "130.29548758714042991514533608060", "131.15190061072211381194638965453", "132.07720948208799703073807951907", "132.60008537099829362539721253447", "133.193495085171964406399897473815", "134.46131099652103853438589305295", "134.98447432533192576398119088683", "136.22733827538541720142676536654", "136.395128249039407493276246701039", "137.34704446903771965640728247537", "137.76600922447218841227622290614", "138.602545072158020891924764282146", "139.523211237020188331962509015686", "139.99675907796624266094931247283", "140.74156703591999045984163989685", "141.42837950246179431762798899322", "142.001562207411336943144918017737", "143.236869936564237441108083837702", "144.04613692725529634299536579152", "144.749866235739701711299006739777", "145.36309687904655003326697676852", "145.877185436203817834186669705199", "146.93037035974733563869326053160", "147.555041466639129226532269804", "148.05836351418510385107799501818", "148.92876732472571383645216873891", "149.4709586619194527870368466000", "150.03608649993944801467025951565", "151.046586700576335361722173506636", "151.95320000168092304364982504560", "152.57668950883508450297285452192", "153.53173445877640941521720605346", "153.992356298408545235392838920491", "155.11056877962650165704664107546", "155.39324539193543918926834372012", "156.43202285456291524879327704311", "156.76777385209718206208626391741", "157.50374518848036860340530889698", "158.15193928426411111283466551817", "159.36953709944665822431266255977", "159.43200031074216535310852841435", "160.38909813444406153496443479020", "161.31365998267823941236978401363", "162.10443907799321963295572418782", "162.93189327546370786290731582748", "163.802990873613859931633226783806", "164.1644801518623110595525766443", "164.75925915358117400551065260119", "165.69877243905869954087723326102", "166.13852227763909647238716623062", "167.32061213315760656116817136503", "167.41209588840144482724606798647", "168.4703103103509694686082828003", "168.82698249219386810962906991159", "169.8213205339690173013394067489", "170.9194568853463949126291633800", "171.60630012281425408298879828806", "172.26371677209884404399156365743", "172.71254212780176209472033018833", "173.580528668335104168871801142850", "174.3598847213979357999994479435", "174.92233351907101876938953093415", "175.66534427965597013783626156566", "176.31597145028924235301145665243", "176.8472492356641662654418370600", "177.50306396235508850345427333600", "178.55324515995323621052557101105", "179.36400312208394350179045512217", "179.95208306293088013430963767911", "180.943274807663124492957827642791", "181.43553314400287527270047765604", "182.0988065464214683427595484093", "183.19018807469398681117021599960", "183.526588676113621878788402591188", "183.993023266707228170686792475131", "184.862838145707446872191912609432", "185.56519611928726803541884660645", "186.21544499801848370119593565449", "187.05525936986212463346399502626", "187.62485958625361639096953705188", "188.47769555696923852087783213992", "189.37881640524399634757147238251", "190.1321454121526271804020173812", "190.86650891388701397794296685112", "191.46100801320633483035885553034", "192.05419655137841218728789107491", "192.59053873880355837862583798685", "193.5013025839838305725366337661", "194.20636264966902529858038818921", "194.71766925334617862542076542284", "195.48759870010345599718913684299", "196.208960408851796837226497225189", "196.60337894419203236755101539033", "198.14849305832315085730520181223", "198.48512572911057853149831100151", "199.47681209665857290178983255974", "199.67762096886137369353703908246"], "negative_zeros": ["-199.686549720171945299873682099926", "-199.03654269803647999564443651086", "-198.31227736364330660225747469572", "-197.98321654278732585778069535118", "-197.13131456553210630594699144854", "-196.1636133644178152756287895485", "-195.83874156054567363480383528227", "-194.93375004931696243163179733892", "-194.630330394569274378794007136637", "-193.61757349965747250523316297492", "-193.12898399294801964658486257583", "-191.709456554227550176591946370617", "-191.35284140977171665365702668010", "-190.55999206634976165478368696277", "-190.01066816540249784862918841480", "-189.21405222820585905327518198772", "-188.40425023229480006172467222896", "-187.884926488167032907627516269667", "-187.141190468942035830845342615232", "-186.62260615160050304212018656846", "-185.899116319511719913542853935937", "-185.28299914852588696394797706979", "-184.29717018721754364630083785959", "-183.66204322144646831734236717161", "-182.743551997401870972058030101106", "-182.17337820978542837623397624677", "-181.189992631935609249311182870798", "-180.65273103930827664862677991017", "-179.87145161244027219790419350259", "-179.29777408809124631792859189755", "-178.55206379059064084248510714621", "-178.228238737429002614948030334962", "-177.12143995853284316415769313488", "-176.58849725423407257313317796628", "-175.79517157311963941226821954554", "-175.26623838059064913652188564805", "-174.45388724841025503394667552347", "-173.16410901164377314995509344694", "-172.94135118764158597386164453344", "-171.753507001136636058470295848488", "-171.30079404443301814639784045337", "-170.938913568248283646868620447804", "-170.04915036514778421548015890420", "-168.97434551115094235819451978035", "-168.8640093985154187805744169867", "-167.83972038322401065303697708534", "-167.31404525174316502774423369260", "-166.63283773165660524625335260830", "-165.94932509453546296294750968865", "-164.47433139613627079520863887937", "-164.264829438110214685723445642765", "-163.32750634808544513822245196432", "-162.74973363818707842596643085618", "-162.076086215883184200329458341091", "-161.17260658764672758592158865810", "-160.63542990974398984901293911876", "-159.79969040060329739454307535525", "-159.47646907121686531507432769755", "-158.54112118382583530903887967892", "-158.043069794949514142327306627991", "-157.00866370795180108605063849158", "-156.20914142384832563602933995639", "-155.56074907351015036074022996451", "-154.59233066239534828285630141247", "-154.05395411595212846711925884757", "-153.12191711646313997834541343131", "-152.60292757768954488909339919035", "-151.82218035174019542392720407848", "-151.1932239592770792963986078782", "-150.862106903266685166368574443284", "-149.56923968602577234596284017027", "-149.094194579892543103922043179701", "-148.628082027023977296292586850160", "-147.43449978611821181745655978410", "-147.015775957594144202133133198990", "-145.78609786450791401568691450554", "-145.05517176604927691682592436957", "-144.46534763347169070544535969157", "-143.9178519930676196964457017884", "-143.111933111355341552361877133926", "-142.520305380566498424588046067122", "-141.63537356327028493999100135859", "-140.93156138820668309154421408548", "-140.43968092804790022119237668069", "-139.57240074855092917523203277737", "-139.123488641796478666939599828056", "-137.88529525741827491267530290916", "-136.90862300564206140583118433165", "-136.40121979282114173056896783172", "-135.82274674711955753595807831503", "-134.86077853582327357208152794715", "-134.38815349914685954349094712970", "-133.39739563780172235365154816443", "-132.901922206445656435939750454461", "-132.08621753520163621446943538425", "-131.70557395507825689833125476677", "-130.82021006764091499953865312256", "-129.92448506775492868826382446110", "-129.11727614985683725365263432669", "-128.2899207187338284093306368119", "-127.45661265394525723000250955204", "-126.86212689038477032120264342577", "-125.99735506422654668637429129623", "-125.179171511179872147966497969879", "-124.64233944096982262366351261465", "-124.17028924744819430913447526544", "-123.24365707151377836295901614074", "-122.54091534952015127703859275578", "-121.759561815347325508913154436095", "-121.114224913733747276642548481810", "-120.26943838632426941153324304634", "-119.45493054995935907061999216721", "-118.42288588270514119900242640273", "-117.59977262936503019739673341507", "-117.14329339553443922492280742496", "-116.46062347149504017481302314871", "-115.64911828663811840096273661385", "-115.06170134671186902721696141373", "-114.14399326124689187405143622143", "-113.48468902485575727101062609177", "-112.78601391770525509094195487161", "-112.29682522449901419594759821424", "-111.26913570046996822424971649493", "-110.16675377401243250317367656214", "-109.26648422364643296971220917721", "-108.946246889521180724401355323839", "-108.07486303188918717922051591918", "-107.247015423182513406945230046950", "-106.692990956262912888203915365075", "-105.69445507031665038033733006144", "-105.11787902766484167376867695921", "-104.64387234489747653930757890874", "-103.85905605847186539033843844807", "-102.796137928541530326501138296020", "-102.20455142824697162052714936911", "-101.02010041376269298321896504763", "-100.33251509544574212370524303460", "-99.888270108433453944439350286335", "-98.5490971619021567693091372960", "-98.231584525768744419754232565987", "-97.46725918962637383688410092134", "-96.71916761744699469635289897979", "-96.14076284909614679603911565178", "-95.23768756859864301980569015256", "-94.49464727942434674253374636031", "-93.70163998534105543633942081272", "-92.98251007269502252784551014028", "-91.97817839340917414968157053968", "-90.97389214913525951511187840542", "-90.34968945977473554267783302486", "-89.53913918170277125775905485745", "-89.070378064353714540810533684475", "-88.24746475246311568025104202115", "-87.39595515307078385438523815579", "-86.74728366295839343925472120582", "-85.84746859224424557434861635499", "-85.260064143479511382264033270557", "-84.72756608834361914344118317094", "-83.22972680166166366184107884677", "-82.57042789954512483720761636164", "-81.734507819362902494188431245024", "-80.94457757695860904739463524687", "-80.55697334609752626326095219402", "-79.442416930130106707167151547733", "-78.754158528047868312351008374005", "-77.85439262892520668520270531781", "-77.67991718056653405756693628116", "-76.49296251237547337061370055237", "-75.96649980773179168684657808212", "-74.724186399426137050055001197781", "-73.933360307195498623477743766877", "-73.008336415248054685739410269356", "-72.54715384130678084348620075151", "-71.35830700564050833741066337263", "-70.69226559193499513502108350286", "-70.23066731621870436207835748515", "-69.2045868066880886684338966688", "-68.75392864536402741412449882107", "-67.797736039812382227957533741429", "-66.847035110874543695884421808858", "-66.286052906209726237604745278392", "-65.20049447067176510816211022651", "-64.31130147076678228420050983785", "-63.15360735674188157714753676461", "-62.85463568053534214384087200700", "-61.87609229144301923693990962724", "-61.26450523881656261796588440271", "-60.50853118939361323759175816232", "-59.53840279140413738939929346468", "-58.78999199591911904835011463683", "-58.13249502081657856970598990434", "-57.47351935589225176519765087354", "-56.070463385732143497841020083520", "-55.25497862822811209916657679788", "-54.32417598363007670581492988191", "-53.755381384620766061446959707706", "-53.09136931791910337493638424124", "-51.99359455807577508732561548061", "-51.14753036645858509120887068251", "-50.79535892844331689675123049079", "-49.68927472198500311108515019690", "-49.18249653075511442997560901453", "-48.0742441587698066073502158057", "-46.72376555397366987021751195830", "-46.36430546353026267642487070458", "-45.218075381994210012724434042208", "-44.51899728127852363067956390413", "-43.54279445710560317548816454093", "-42.75112940503928689278465294670", "-42.34606638266741566816928762977", "-41.18960184271861639910268537037", "-40.62756701138772254970850474050", "-39.4180532597486269244895113538", "-38.7644223507318975925475801880", "-37.677749121408097807379792119648", "-36.442562842473304247713609469090", "-35.92050306163210977670010473510", "-34.868596642596113588007553987535", "-34.236433159793705267031236765334", "-33.59697626932714124495554501304", "-32.35712590888165975781543860070", "-31.6749866272224822723193272581", "-30.95146859586432803930299022580", "-30.02086519779097952349932209081", "-28.73749658946508024264510642959", "-27.49924436213780742699833957597", "-27.026315736594406418839434763191", "-26.15664182220708424105735294797", "-25.211227818734967209254035448629", "-24.187448030269542019491951790988", "-23.5304239248145708384322949363", "-22.60960817352638573621558988654", "-21.91038104735060478811308199511", "-20.5880159128974676305569731087", "-19.22824031703696258923537536620", "-18.70402166507103788271687561390", "-17.50225765734099382846755060096", "-16.54603265239551600136816416569", "-15.72466943480061981829563883459", "-14.77847861005267928022973445708", "-14.12416982622342160017634899693", "-12.77908773026472907623968139339", "-11.87632171266950661286504820857", "-10.58166271731847384209999054772", "-9.27858851772314461330816620973", "-8.29234942872777675886405872634", "-7.21670892238458415064990933365", "-6.58622712823859193118404911795", "-5.00964986151435111785088720262", "-4.18150374610984625124961667447", "-2.81281861204364662791827613796", "-0.41939472037458911080833027066"], "positive_zeros_accuracy": null, "negative_zeros_accuracy": null}