# Zeros of 1-231-231.116-r0-0-0 downloaded from the LMFDB on 15 July 2026.
{"order_of_vanishing": 0, "positive_zeros": ["1.047009922652531315365800007841", "2.76974582423702736201164886120", "3.67962627269968153159245383779", "4.74044698054563948521463916601", "6.28440871651602526651271089671", "7.87576091267179828637440510495", "8.51086443211071629565125545339", "9.93914777084510617242618880234", "10.823741754295152155336241284578", "11.64056924350126645902365393333", "12.577269226913103436714988536791", "13.57911166051174801550305023328", "14.71728736421148370096289040756", "15.70110215643381667663539029765", "16.95465456913321056197039260902", "18.114262849370359727051298536302", "18.80918045611406032779460139163", "19.72425333703839499919907055062", "20.47103073439953841527685723697", "21.46571243264767264672522730638", "22.585950917720843528361675387725", "23.070652620086622789178823951044", "24.10803290510051016856738390898", "25.5013966954932003977065857385", "26.667854882014913835660199812168", "27.043227746364025045317061045436", "28.27273992984239976203745546714", "28.66487066454029151915886184096", "30.27112838419154733439680612445", "30.37240237495465411395764002211", "31.37602484518627363920430935710", "32.2720335354799456853242033665", "33.20416796142233369613557455726", "34.66885117876546160700044783265", "35.20721489174362202357389455532", "36.03874310720753719783687074962", "37.16189126537413211040744460455", "37.83046432817356880222933224903", "38.60241544203041315811670544104", "39.51980300310352778096825005102", "39.94175763100437304535724017054", "41.20285034971214503567898882451", "41.88883900745718455226719862104", "42.94292680620042303814666221471", "43.831682908243773015341200564", "44.93859930654621570926688769870", "45.6350532415072234269854426441", "46.515935112854031913737619172191", "47.03603060680262583927691222915", "47.96820004505259672714506853006", "48.661063689475607568637503583143", "49.810659766698093712848090867468", "50.2738710631050327026279196694", "50.99005147082515360114110431824", "52.32921213433716466223506652519", "53.212168165262031151140491050199", "54.18335061327316987660353015800", "54.85616024312709274534916952395", "55.22573560338813146825515083849", "56.55213132520272588988117153989", "57.065232863997093450524644731267", "57.9212737802892352193101538686", "58.65032762728496991770001531440", "59.27184512692041221987600746620", "60.21657323847226375473195992540", "61.49414344150778555952787409588", "62.22465023327467480218764210813", "62.93787730629896573958932509318", "63.715536717411546414501218972145", "64.6760737800869208315169471075", "65.37012072853969946471281685664", "65.99359486880480745924972365719", "66.9583536956268640125393840711", "67.25084209948266205372724461136", "68.47098702158983781320318555915", "69.18304632561782824454586868600", "70.08751312643557676607944662773", "70.991348477896800857858626323491", "71.898187820384629492028362345269", "72.73728469811363277529156605908", "73.381866303896370352308609707753", "74.281859063610908612366860654803", "74.63583922688161311357133086103", "75.55216699302558903636899922676", "76.48448546739808464746395861251", "77.23215226498433079018422899013", "77.69950830438180740978197993562", "78.73359094204360469236763268484", "79.65194452770985232988183485303", "80.87274590474306071912254388041", "81.265701749278468441079724166332", "82.248282418980416245053853313486", "82.50155955238330967466476068263", "83.68463921168746631715897626070", "84.33812315814157315514523117408", "85.027386373192742328841254638090", "85.7972610906817644087186877980", "86.481125646847882897420149700771", "87.04937606023083998904895559059", "88.55078952276155938306597918280", "89.03750347573550868145371201020", "90.09182100399806254120205438885", "90.49383021804037281357875408828", "91.42114005205383959247379598382", "92.27959356655857098168256829413", "92.91906025651990126683017282004", "93.528474581974527130549758014054", "94.35606622240908619335746709781", "94.84621041906970313115819341007", "95.88227546433560093895947968656", "96.74809719466684314388895066150", "97.38291468004290257281185205872", "98.50568695079507279136616622566", "99.138381800120669969699353137027", "99.92492614585530583636781422713", "100.83417771936447409384437641933", "101.44072462345125624369882871753", "101.77215097377509787182690358375", "102.79989610485380875643031082685", "103.68528495362292578340696364757", "104.09823534539321589687692746964", "105.158388549995051449644474817512", "105.57667225901625114408115010836", "106.66892814584431360520711690392", "107.69842295150714534937105449240", "108.579208524175903299093540481750", "108.87053526296392729172107632847", "109.72516072132721814894838170952", "110.4798790967898144565449661254", "111.09934189366464174623487229724", "112.11060365058592091091456259467", "112.575592418099781799308007397930", "113.24905752752690174387475212649", "114.00913140405449312749776871185", "114.72126199051669012962495407181", "116.14494424885987538183906841404", "116.536203797682850301080615359574", "117.319441508296398354694877495197", "118.10848715791044182178191421473", "118.74947863334813505529002307106", "119.57843455779049910743085321341", "120.30930390002020359112633892725", "120.97246985296214998354394615240", "121.42723540512728419173838558837", "122.2271320203890005116060422315", "123.28309457250831236525733514124", "123.6980612514519458596914786571", "124.91420036445313151936852235451", "125.48025884158850139028423015224", "126.32690734311744985948173865175", "127.11172997611808484251044333407", "127.94340711814022491246613212371", "128.435773850626000116131364190646", "129.08177054681388155707239756692", "129.74488556313774855505043559505", "130.6500571336641694371830414675", "131.29675216116374446736489139408", "131.92815646256938525426532163666", "132.970494524196185439321701993718", "133.21583423811543058302023909320", "134.77704385891527281455877679739", "135.17996902917964322635372406294", "136.11634453375195812087824879568", "136.578421828894626697120891146633", "137.267407242354070076243022227783", "138.022844847556056872789169190339", "138.773774528058970758066375377138", "139.51647017883092404681726400277", "140.17829943861250036255446399037", "140.74878331325963773681332372498", "141.40045310366521573734034240944", "142.42942950438218729536070342807", "143.683266752549206154994045339331", "143.82310243671241517138704740602", "144.85332279229835565817916673891", "145.424872313626976112703061498552", "146.09774719746741220480827066507", "147.00508228873753930723149146180", "147.63117981449363478579768025464", "148.293695517379137394222056868492", "148.68211468013180226031945798056", "149.62657065534296688094398305856", "150.441235344914524946972536321495", "151.03153304475768004943248470445", "152.20242128769129433190021756283", "152.772763242704097462802977356166", "153.355486375748132015991861784876", "154.49375712494353589010935582162", "155.01711872165771656167962103571", "155.53168164185626074937409632599", "156.32773275243043646774195202182", "157.03110926780774899136872733198", "157.44334170257588638525311597644", "158.62053583563925804343021729479", "159.01344555976334768667899839667", "159.76711163441328211633939729879", "160.565012228947394524528411424707", "161.44776616893486631208298870645", "162.42270656930207393516578581216", "163.159786432489893923878940921855", "163.48232678602801883025097514794", "164.3396502322919677649856598157", "165.01193215156705103818614149973", "165.590125807420192645385705702674", "166.47232087583386743186126582547", "167.21575102365305250907622720990", "167.67488774080314565375110898584", "168.2691079499940554381260264134", "169.15203752964046901679159544065", "170.28782791491833353290653046904", "170.847581923477375229710838346042", "171.85006189534956449816910019920", "172.152811814906137885740900225703", "172.85671222657585481093256226770", "173.7493199414506045276754080071", "174.48116883153288652492800147425", "175.10863913492161498276600930093", "175.495511472309284179623763669355", "176.46058473272918611201937678678", "176.914534798087695999590531154298", "177.78392008612469422221772585020", "178.7303608279803115734729607040", "179.41651175889478460795562184887", "180.27867318380913966941948763196", "180.72037965115810130879304952380", "181.840687668154708522945411823530", "182.2857932310773058710396460423", "182.91729782355916313778208011709", "183.834122306167933454254684593260", "183.946262698827749820855757219431", "185.166008530491455951122048059681", "185.44092993378664708094858664071", "186.62121880962793703289315190094", "186.94762393262983376933719498482", "187.714106163788546983105087836126", "188.83816847568145311613461414216", "189.48334034081938203057178430087", "190.31762826064304821878655677122", "190.86479146118028375180140695929", "191.420646326215679459099805334647", "192.204340186677184231475801917972", "192.7244253847170148368029491519", "193.61051356085904826625457581340", "194.31189155040027891898494293106", "194.97490119736753773022284153884", "195.23883799375948123872687556750", "196.31250223821917356549120955171", "197.15125858583767681906966588299", "198.061507992373162720342793013193", "198.866353396849723540907682225053", "199.28158930146298290904344721643", "199.83954830396233940623444013924"], "negative_zeros": ["-199.98502199637312692707496451110", "-199.38204954778944096856503051682", "-198.7404653993239444290921767973", "-197.965480526408043939542156408203", "-197.342660593823815264905432457375", "-196.67539533937612264247715043167", "-195.78366424756741748855860379707", "-195.28562766165938142731718750131", "-194.93151658986317437176898291995", "-193.92590937365776993604739922040", "-193.148000692776319586420760744929", "-192.13215672104306620498582332833", "-191.45691730342249302842040138751", "-190.93609524930887689358586324282", "-190.12451908246606570117306856607", "-189.51499661939815448113601667321", "-188.579735090325398712964520162453", "-188.18634995466571209579832390642", "-187.33090846115623670312722162865", "-186.97047620662606312194506023662", "-186.20233193960679930987882819765", "-185.26193269677681385589391637110", "-184.73992550172445610650628547982", "-183.8501094027429170111759496516", "-183.04787721319206459195354246352", "-182.220332689291862999693212953197", "-181.72645737090339602199472492873", "-180.46227284095213023534764362042", "-180.283709794835142187100678244330", "-179.766788970972396779068338437208", "-178.82291465038302135628899569297", "-178.19592465749169340676412447460", "-177.580322086864559574216977775473", "-176.74419375339516977997664991058", "-175.97620231441099658293151857975", "-175.6289079903167853763589753275", "-174.663028372770312243911535703487", "-173.38472372312680557774979928687", "-173.0806662415136258307954109205", "-172.18706642553813647269625600514", "-171.56864917943343148779595892506", "-171.064837998206809922650279811428", "-170.29177074798948687479327204262", "-169.34927555116060825178199459196", "-168.97366072592437627089601560623", "-168.11928810970087359935422551600", "-167.477422012032936189309789381889", "-167.13295439251708422145232728849", "-165.82837948363248525198337154814", "-165.118040993586222349885037351262", "-164.22488656402521981474962049613", "-163.633954799383301637371923307988", "-163.05435253790242755656664006745", "-162.26359615962759455245033800650", "-161.4057379371373293909021899526", "-160.8422449029238992381345700815", "-160.19166928414944848194672116988", "-159.677954497806160382683689228248", "-158.86260920138481673225269992584", "-158.04686822744243241449808423506", "-157.46129163446302476619474722510", "-156.35895578827165362221205608790", "-155.774453438681808624965826223764", "-155.03271234721782607666361177702", "-154.05528385674174676692293759515", "-153.45962268622412604156780853290", "-152.82438979306122972528781530408", "-152.198964643774980921480565893396", "-151.522293730422062117308086536148", "-150.80456962936075394765499123615", "-150.13335960275463004090647237664", "-149.14785894769625525606333824020", "-148.77756051298628704517756044307", "-148.03474941738912518779631842686", "-146.97501816374386997127498904429", "-146.008342510573627400607703412427", "-145.40267161803881543921078303589", "-144.78876969903166463917383381143", "-143.93951330733720032107206373312", "-143.60544569701782343734938604722", "-142.66846493201136864648000268380", "-141.78649139056531452649299224463", "-141.32973341045171934386818627039", "-140.64448784937492768951975293708", "-139.915821852011102124909830725489", "-139.302973642551707301234853126854", "-137.923454188866004612088961162648", "-137.49074142200765187683540365364", "-136.49193572885439808493590607214", "-135.956413575118397764206074029245", "-135.447077352904906750466896642754", "-134.29651009959404869236677487530", "-133.75043004766581756107497309215", "-133.18075144293089493032391905010", "-132.57623665492866657163233254106", "-131.57133077339020626343034987912", "-131.2672804729709767787783974403", "-130.17844478316917276311582925176", "-129.237888575053025277066316125972", "-128.67408838754285955682417899053", "-127.7863037036999296342631806469", "-126.873154777510359858821536431519", "-126.36122637087916284934313341477", "-125.46531025014200679854921413494", "-124.99801382361190138481849203697", "-124.222822919232777805686573784874", "-123.69159398841590578824947770446", "-122.60449174249727172029120070032", "-122.12345081205610235823355730826", "-121.31005673919776926078529892885", "-120.65892511961922768438424821614", "-119.57875507894910307835838342022", "-118.592200267046349609909496548396", "-118.07999213587187011615333089957", "-117.272155865708151288241864091765", "-116.71005169983665362908396843062", "-116.00913704374426229309510096254", "-115.25590763038782374997747111214", "-114.30620796689608982372889867018", "-113.70359499379126576690456365290", "-113.37756704521649707894325885979", "-112.25644163357968886264047761409", "-111.6330922004947861678959890400", "-110.31934424873492361254629394635", "-109.69231024756239065129125933648", "-109.03681428480545607888296878902", "-108.51389298271698891671870870444", "-107.321418279391065561955454035932", "-106.96569742710153945164760827753", "-106.07034758040103083812828003964", "-105.3696593824243477634170416500", "-104.92145898180627499126856955466", "-103.987278619885459554148280017136", "-103.26469255351945171184358389576", "-102.1657104944780003708009908783", "-101.51967407453023439364108187889", "-100.690909173609694459928349578980", "-99.78352319172701805885342200331", "-99.17130858120456223563507083382", "-98.24863638994005974572155610554", "-97.81143512748394521318470196338", "-96.97267750719298191918670961963", "-96.469862606592774355157787911117", "-95.373440475794670926607455770188", "-94.77830631450308845352761587427", "-94.0453142724638201444165039426", "-93.25236900099147635892941284208", "-92.1192153494759227757709599450", "-91.34455337464278750013445515405", "-90.49207738231800484752593542927", "-89.987376021204170269160485624754", "-89.14474490727545866217200176463", "-88.70590791516159199933100370767", "-87.46649623198848891565214512236", "-87.00084017669039892810479089425", "-86.35755401915720931921279671216", "-85.41953023691804408082912242769", "-84.92955307991187609961871635982", "-83.60993891830066117300196547905", "-82.59443972551004724371594385510", "-82.13400870650959167008550926730", "-81.45577735792728178763030822229", "-80.53275533526668285116026530021", "-79.6971297013409168137800380158", "-79.1864368603169210001848079591", "-78.11290897254829718736758835279", "-77.79135778515681739401511105853", "-77.05683725254615966448477388811", "-75.879891025012033266529776712620", "-75.229143219970896809618315514036", "-73.99151883268726567368361293809", "-73.58561286321981638247265344152", "-72.55932785020490910992529015360", "-71.660748571945868888225122533664", "-71.16863739726474465133141006789", "-70.15996423198947422163563689710", "-69.817255750763154729703257628155", "-68.911086653277262084462683752586", "-67.97787157506246199330261731159", "-67.130439058989529676569997454208", "-66.70106968220955959944979305344", "-65.30246923019662186423415129782", "-64.69230183687101478723238382438", "-63.4751610729546148268364106070", "-62.89017043545428468312357421818", "-62.45876000816952711497850734938", "-61.43422918464718014399784881931", "-60.732695525153256414147569900160", "-59.75739275421680752251872273251", "-59.27444120444304149265146491307", "-58.19514312108582386962982636674", "-57.883297795835298723783701976746", "-56.32998308614231564803914302162", "-55.349414742938552960788314407611", "-54.927906276821618597088317658455", "-53.88983531531425927415982566734", "-53.35972743090528470303163301474", "-52.2360327678713165856089939245", "-51.62076036633765799538512698340", "-50.87623674881681692823320427918", "-50.12278598937653199950500154228", "-49.44244482955115525786167287672", "-48.16976798225137920544465533291", "-47.37274224020822043981547191216", "-46.332264587586445823377839298682", "-45.67217755896008854719906969690", "-44.69792089573918652927507453002", "-43.861515898677913049209412362205", "-43.06783898132174281418039017175", "-42.63596192260204484049477332169", "-41.570833160228261025698793151275", "-40.69499126150812589742012561860", "-39.9202854225322327058108890429", "-38.98823941476971818393943265157", "-37.927932113918671404224639209", "-36.89940103119860013853379556369", "-35.89116247598564699701868718221", "-35.42404340919691767311119463481", "-34.63828593038879591254967840191", "-33.55572411290634998195512272114", "-32.96399538158435660498007502843", "-31.74980718185536239928509578164", "-31.35119767461921898958708664593", "-30.39809095013935726042679887811", "-28.85884313409993945277788690746", "-28.06861072963237847400146323890", "-27.16164931390438223207165262707", "-26.54344455225651076370225321092", "-25.43770077898168634112137367376", "-24.60382849508336041053227837637", "-23.70063612514742385834577213866", "-23.10784025835469473787721413983", "-22.135796760709125866595695312401", "-20.86086270683372205964702680075", "-19.768273643718651873055786463137", "-18.79722612558191753021355287816", "-17.97417389847733319256303776642", "-16.781863212811659000017004733812", "-15.97055979656579515071470807728", "-15.42173652780759008944719354139", "-14.14129458882731525783624937355", "-13.34012007914034983191076450523", "-12.10055181322529707312819885695", "-11.07156130382109818488846738995", "-9.50065142637253587936518882348", "-8.74559149249816974846238388419", "-7.65326670444130027400886672499", "-6.870332246458026538963420577997", "-5.480171409263038587719593085696", "-4.50194930990587579368333288158", "-3.3879021793614595192305735356", "-0.99006661753984567568654486504"], "positive_zeros_accuracy": null, "negative_zeros_accuracy": null}