# Zeros of 1-231-231.17-r1-0-0 downloaded from the LMFDB on 11 September 2026.
{"order_of_vanishing": 0, "positive_zeros": ["0.347249048481671270279415615431", "1.8454738955755725906606566444", "2.75099466312012905307652771501", "4.394169779371788292359447981217", "5.21523775995922097343621108922", "6.67699535387250419630064494295", "8.25019106622788068381497249531", "9.302139918654275922847099438599", "9.9361079328723560848636257657", "11.07826201481309260965550986853", "12.15251950573169604323393804105", "13.033120820655526493808513441702", "13.890989570972693391882449338993", "14.82350877958249065776457966800", "16.59819591003481495805879995890", "17.20647278344928943874360309479", "18.254132592284923309997367037523", "19.08067263327226240752098254246", "20.18095052825577174631868004684", "20.946188556901346826425070421160", "21.72627390562630586474870899145", "22.51492459954599124477521250476", "23.66014333648062307379745285237", "24.74154873883035264201621011688", "25.73954496208531855501496589224", "26.7215088277344378705855615190", "27.58866202495659042494471463249", "28.61333719147684453142374358049", "29.20175002959380116831423102067", "29.91745002612099354684692133745", "30.95410523659831131296839702079", "31.91935476274063634107715804740", "32.51856135428829909319342335915", "33.66354482113569639041310900623", "34.62408473780846746811540231992", "36.04253385349442645728236226050", "36.33934769293256259048306834597", "37.2049490099126939989460913523", "38.11239031671714666226485948886", "38.85278527704083609675698544301", "39.80489128951116399436684655912", "40.69704024323672469571128904601", "41.08042001307291422818231786676", "42.17842494985935586025628738229", "43.449306144033019187930152877289", "44.471329247659778139186785588421", "44.92881483532886094534830821821", "45.84314429490029113531162440754", "46.737541493516781306438084264498", "47.50903443819235645752841448126", "48.32503602411524263443222356725", "49.13785942657992043740699748263", "49.46582379032523910124600233688", "50.86425148002699066081505436880", "51.4827772880423567728385856831", "52.74491273542266510343441060457", "53.41224056020726464909102418149", "54.1932254306639339762543990872", "55.316473557088901943914128342364", "55.81703798768775863274682129721", "56.666820672205640092205961158103", "57.13378091529473551356931470772", "58.3744439628301461698615801918", "58.723555806376191956135185264803", "59.99864481397327447278315357977", "60.38964823832571586580156443735", "61.58846872780249680038053583272", "62.6380147049278279206731965809", "63.39625553120065579681319314886", "64.08647548351443032888101622659", "64.72598568333408959083519435421", "65.52610413577196984275074995822", "66.35815495562056040087741940190", "67.152894337574575120111371514483", "67.94457282127231075814251568213", "68.49361476845481556237338037972", "69.295989371201789194419286666072", "70.67562982375728396073234950684", "71.43120264703726323344451273418", "72.08748460597463783078541857818", "73.00912958484872499443234178893", "73.40798813867676365425429269096", "74.59137714044385295004292545592", "75.18422517479632795820756308749", "75.871622588651606261341059556262", "76.55642416552326101948176510391", "77.237107495393850180945351625594", "78.32344265535414859138923577810", "79.05391168358981331255231062459", "80.31537310140656483156828630935", "80.62390229716920540111013588494", "81.532429288214863585490178480397", "82.72200228692960230099603628383", "82.979633886374659692580571744110", "83.7182943703400937257282819424", "84.719728896788827217350216797654", "85.02622823256113587796360323885", "86.15300517696940666791149327535", "86.82710728374248639338546664596", "87.62836222392311653498995108325", "88.4028557915626913163434508251", "89.57862335731574932605776173863", "90.25226375097882581205128536308", "91.04048216237541602918320577210", "91.74134505024633343628815083615", "92.198600267209612898916047908850", "93.22020254955084344049586896716", "93.774525345161445485634182741796", "94.785558051472281958110338514868", "95.30259501601179662805589695349", "95.909717672297510219660908726674", "96.82348781805533657888619933448", "98.16988114485961645825187080498", "98.609195733630784911710351799273", "99.53198316384636718371227777229", "100.22528132767328186033667800444", "100.644846069754339295766355319817", "101.7576255509160992869657937913", "102.5557995063348154092057571350", "102.92022188789842544756839164506", "103.62944340885914322892400806628", "104.68570082006565474518785769490", "104.97133107546148719508397346821", "106.326040459511447023040612201185", "107.18072339754816864260935481241", "107.631382322234330233659683268668", "108.675002705159481162406486835271", "109.25846389775003058552968088202", "110.20252081839175169426769527318", "110.72924705504338835621677353747", "111.36585867191864055048236397498", "112.11073873224192889735709765782", "112.791480974121048398019684501043", "113.69275833067507316525857802120", "114.35630363688017873079943369654", "115.19960629261090943081128663947", "115.934967410631531282141676848037", "117.17532197890958557053162075126", "117.52894265150472076102240732437", "118.558630617244430409731915697858", "118.90835595959205502230574359185", "119.8519575962472668356536248205", "120.227314439942155494122109398509", "121.318524268798939017707130536771", "121.96420855928761830758675890011", "122.60911102831496686112733369538", "123.13677133706364508216379629704", "124.139647494726010280325081471984", "125.15309064718858374641832400036", "126.00419552920270489713070344632", "126.69058075274216739006066367089", "127.23865766127427113435155448523", "127.83912203426119815700931908644", "128.899294906967232874531215723276", "129.40535886748714777007727882476", "130.2330094774287848709645850338", "130.660571804120027757296427804310", "131.594106008054325733497734417373", "132.024555858959784801587778733367", "133.16493795299988228112768148004", "134.06963780546153962874116225561", "134.822356731452760774844717495196", "135.3123727746786980374946341721", "136.27436206422078526163939505879", "137.058665614351628106430001384183", "137.49653422515595539236890143692", "138.56877215704365927007445855596", "138.768925240944583878335025602296", "139.531867540344642873210443991347", "140.51666637904244820142264093519", "141.03925092368760124348843928553", "141.995923107496177719068341558685", "142.58713276708241816330576698983", "143.55910087773437056751540673033", "144.45952186491708965913427734365", "145.08818201645425535607621305144", "145.72264998182119529178051163772", "146.600536636619306886152322266093", "146.93284374469374138779024399372", "147.62804003867057640428102731517", "148.76087526941348825481352107164", "149.18814246429855845488682655715", "149.78249743947661401778932719132", "150.59307119649995522372027730688", "151.34772232489136400465947385719", "152.31979325866114432809255391614", "153.491623787582978724505952912095", "153.68461483090549744369392312351", "154.35334164057270973609391366554", "155.225112166972327468509573057857", "155.82330210209190155032391503746", "156.6607716984003250480422416780", "157.30665125540327318065902713089", "157.89462886587938960528513903636", "158.5946286287671217551533573907", "159.15977062287850260759682707228", "160.11164797300914862985636446615", "161.19643577859793272009058561318", "161.68079395352145588528616822835", "162.68891505807526871152676345710", "162.92974330060574228150049314754", "164.051050240714728495579120029686", "164.77850654269242723103574307632", "165.040435707788096040710734468346", "166.22821283283358696881225882020", "166.409489377166755944059797308098", "167.08698670335219699644423729852", "168.22044235170198134310135948991", "168.75406198983009166782750467018", "169.377112744877475760456408894987", "170.49226607497261826947775781557", "171.08980813991835775644367168993", "171.89241523824184664050842488765", "172.71719709427624746550249487967", "173.355188488542053183236317115251", "173.75097173226297373785892421143", "174.50847933916261014929717025200", "175.275774721696455417821969890960", "176.04516633123973731282007780086", "176.606586202755544287350522838157", "177.41090564044624101056042972073", "177.87952695329264525922568687907", "178.828516266473880385066716249948", "179.859230836571398848066494403129", "180.62801416868252198010956723434", "181.23827065483188425108278568466", "181.67384614088248775633257720851", "182.49848000989575458297580891720", "183.255518542168878991462239501429", "183.840059731806851110628641604286", "184.67769565552083067649996855082", "185.23719899392455745757768464170", "185.74410789087129322870186982166", "186.52353847754847578691153509460", "187.304926947933003837105956709724", "188.50131504391868474859719403653", "188.92320762068281599451404659157", "189.693542675741214949621031613542", "190.39487231948497267352726432423", "191.09867982644248860448226230463", "191.76339261717117269276681351878", "192.67895387076181460833997659265", "192.93757947751306607016557576527", "193.768113366586492058795087415026", "194.240150376314890114394224162664", "195.21127164409201000544783288472", "195.935380067961551825127666540879", "196.45839421436735277640049842871", "197.567881334111461684265709334637", "198.13206027968745304012355561928", "198.89147112426979195276012719562", "199.78504174593256465925268690497"], "negative_zeros": ["-199.13229728553288359561576568925", "-198.89524041347080404333079396587", "-197.937851231168535076097257744856", "-197.4416700165406070906721117136", "-196.80666222152021557243346286338", "-196.095154949325653612060403943355", "-195.56010193982636566654805822350", "-194.53097956104670426812835982421", "-193.92012986287325774342956544990", "-193.53940279099353581088007642360", "-192.29964509192916035155428696150", "-191.71424390799561112846120527044", "-190.75354316397208345827497341272", "-190.12356529322483990335695064224", "-189.57326468865932542561237387138", "-188.9901495842668953294684958226", "-188.1877464917846576387249055830", "-187.644213027294193163328711784", "-186.7130272865250898690615103603", "-186.08376543366509453576656835616", "-185.634257270321111144887584466552", "-184.95098258416905233324991766251", "-183.96331474651060953250225578501", "-183.11677788589333945571174199146", "-182.16433851397700696687367834304", "-181.60255887618668702359520510249", "-181.1581809657245264260926809082", "-180.42526989327099840809854518464", "-179.415512836198019463664009976072", "-178.92944244182502256375704633370", "-178.39696871754386371449768200453", "-177.39701476952925274540727544546", "-177.12725478706555531445462089724", "-176.37827097811866251892454933006", "-175.420513492730558171843956695539", "-174.50338823147143103944955299334", "-173.876460506231319297070177871", "-173.07420927439528965341998240611", "-172.42783779442720482387345672207", "-171.6012088114864622393726338667", "-170.96911496932118607888967826154", "-170.23849543464590745330696911180", "-169.707741953705691745930514432963", "-169.09824021580795637414005554862", "-168.33823284884791186711947610668", "-167.49902898177671002223821835287", "-166.88149774601224638825140355878", "-166.12094218113728442254802549636", "-165.41457962328035497206288175631", "-164.26335028570077807156052456084", "-163.79143013636365076023244691794", "-162.8667996932021529133655791097", "-162.33731502852435474367695526820", "-161.55007131702443113193131768471", "-161.328058433561419938438462651901", "-160.09731395562504118225933881718", "-159.6132492132922614848213338370", "-158.87574510612819604193023638374", "-158.295732584447570119137647835924", "-157.50638243570896918179344794274", "-156.85079229483387877857465028440", "-155.37924419840495609052180435453", "-155.19220126577910885739029443371", "-154.042789890342278074161250288400", "-153.93318862667939543535241288674", "-152.991650088395327656578772600827", "-151.955505011858066917370509368261", "-151.76236249904093327622171311635", "-150.74844012952147089353005712419", "-150.146850866833240932301593059999", "-149.69635184393407550259982490175", "-148.84823451656017083603114947281", "-147.85786180048948201298991112702", "-146.97958324491819034755850350972", "-146.40201686733952606973384646466", "-145.39632976596975998187925486583", "-145.05923385678329959876166387838", "-144.01281468854779542900616805305", "-143.30394185266141382370832923420", "-142.90886327472480167056868187464", "-141.996963444585242310508451415863", "-141.61303864673460829680551552046", "-140.64216680502762287410713545884", "-139.87499602495941405834531819040", "-139.235564804166809762940470152925", "-138.46760205044846867239762735986", "-137.38089358935648653750779868433", "-136.843772475476898574898703376086", "-135.785327139691690786620281549510", "-135.306206340117598374474080495369", "-134.62267601612643911317147640906", "-134.09233727342273864670593378886", "-133.23868553157515653966919388044", "-132.37913719382253355651140600130", "-131.85268823199506264786024419647", "-131.178545785447149612541942513875", "-130.21467598494919704713789036127", "-129.91462413599666133106737373793", "-128.307355857429059465494445115068", "-127.75571075230606708198261102519", "-127.299221499378039578100810228612", "-126.26464925562013379370216829810", "-125.8852092514906542907210631066", "-125.01408466589211449931003538396", "-124.1682616800446221646752574995", "-123.53849721171317533344169827550", "-123.01062557776080333334887792900", "-122.25710721586437320086262639058", "-121.54641897985110132670027837987", "-120.510956854530781080969173912", "-119.57462654871222581300517839173", "-118.92355976748714958034755976403", "-118.28979559697136964680529002188", "-117.2161116757432049403047090277", "-116.93766704518872312066377536391", "-115.70115331261885930659066659953", "-115.38562074765424302291377789244", "-114.83857065083607964315152252185", "-113.91395392486421609651925194430", "-113.05986932997104175696733754914", "-112.50089348532813888429750612580", "-111.558764188112387860920378798195", "-110.721337378326332457517760784620", "-109.91324834316932827974311933075", "-109.03806155085458358104175865777", "-108.0632575662648787086593684199", "-107.89266174776450576195467762486", "-107.039250471448151851649858184301", "-106.21788155505755781172898284131", "-105.60036721530053962581708012069", "-104.73335316491703544513951906508", "-103.976615219943978753761242856431", "-103.45141058091200434998975413183", "-102.66800158361409558304384544468", "-101.40961650637670654866669534298", "-100.60386568416064595733270812453", "-99.929170606408882903241422249433", "-99.38022628929454830852426699097", "-98.47475612396605920399559924663", "-97.94293729420985235703570752223", "-96.8805408282982691670394881283", "-96.387076122037360952324415307429", "-95.59823113959815481160372982680", "-95.106520449564847296547086121871", "-94.17679234538921879251068877141", "-93.10258066062292149529729216594", "-92.30522854559247699768516573302", "-91.28140438640544169217319548258", "-91.06445600283454266685931642293", "-89.91444431148724759513689377365", "-89.2307416528065748113804693415", "-88.47678601010018390209124602748", "-87.76961823137650819431923022843", "-87.3729373110426714680102100433", "-86.26124695280133308754547906402", "-85.59639373144954923966177204340", "-84.8491197409925793600994175692", "-83.62894802633375747178997193327", "-83.279731717074686478266749768452", "-81.980219391231179047777446225677", "-81.29155464335759099163060493001", "-80.70034318929030422572596882906", "-79.975603514147333087465830563838", "-79.11468219165086209387168215274", "-78.6838044020163333704951818804", "-77.47873499866695037866436130338", "-76.971805205330290648242166437174", "-76.22311431960715203893971332568", "-75.47685000200159689617368471698", "-74.21464108537713299028780033860", "-73.325290345015620825915593711796", "-72.67761676531555588228360750291", "-71.968849522598924163717734040076", "-71.299124617707012920745518714843", "-70.40657461377163032036641294139", "-69.64675271798295171298326163965", "-68.76698401820328943638146854084", "-68.3328421559775029760012843678", "-67.57176640364804433871512896486", "-66.50847625204449026814205770334", "-65.49035508384783686277466224514", "-64.582319562635502572774568965636", "-63.7469908565403501663570983124", "-63.42019852006939724719639976852", "-61.974994358008654347010173846165", "-61.6119490162346671397959343785", "-60.88087334352163302750575548613", "-60.003185495411486371541394892443", "-59.37634035741919262823557677257", "-58.52765510133784353705797448173", "-57.4310866557790252078981539935", "-56.79037485654411337022224707585", "-55.653483973869983899210007647302", "-54.90510698241003770479823286958", "-53.84448878938622210865675913220", "-53.35674797987615597711026158586", "-52.54127291561859446008471055138", "-51.81370291726490349346384375550", "-51.02552647336965230538633482326", "-50.05511564876074537980344849354", "-49.26375694948377268416677632406", "-48.7660336956119625642497422905", "-47.47731404651773871673236256175", "-46.32896966362325343323387181782", "-45.65623644846938815427618845771", "-44.84547312001783663996204388092", "-44.15465236564005472958939351665", "-43.41390227593578888567495859357", "-42.11862724387214966062175104268", "-41.88385967426123899007387295857", "-40.86383555005476293305558993870", "-40.209689012737685351003555670037", "-39.078653865562348922030807307053", "-37.83153718915736856429564897799", "-36.971824378537643981474269283389", "-36.5245217242057105628204319620", "-35.29657295335029604053768028227", "-34.540535275088368174896382575894", "-33.7749846550689971093075084809", "-32.97539062054062969218451354575", "-32.25793491014363459423535209933", "-31.31995971869669005073681674499", "-30.18688471145105570253984085510", "-29.3336453165989697960411204361", "-28.222764803054610473882182418198", "-27.272255174642358353319738506335", "-26.43370334391496348756071619878", "-25.43710689680617638622804818813", "-25.077773767136100607461047172228", "-23.85840792153123241591652314511", "-23.08037460277107162444911486600", "-21.89955305996382014245472867868", "-21.50891764276463092787813070313", "-19.84718023145606709467289941336", "-18.86477578169101289582298548267", "-17.82730207919817254134120912373", "-17.25047135050921232518133017240", "-16.32956212108416992994737519952", "-14.88832438155688596561916850735", "-14.63582651094872716789359485831", "-13.30286758173497240354497765613", "-12.64250320448196931318701175860", "-10.7709051244638474670130449669", "-9.931034953527864311548896250458", "-8.94806991731036679634982622603", "-7.788919411245076042369859754731", "-6.71611889394128124166817594669", "-5.81157476086979037443157899242", "-4.83973225132697432978836690139", "-3.29358000174467762701344538673", "-1.59847763692419296621304958107"], "positive_zeros_accuracy": null, "negative_zeros_accuracy": null}