# Zeros of 1-231-231.185-r0-0-0 downloaded from the LMFDB on 15 July 2026.
{"order_of_vanishing": 0, "positive_zeros": ["0.830863544630072360048487668800", "2.165589090272450151658055464600", "4.098583707243524188386476192662", "5.42560797830740625667092242260", "6.43939190156594852394730775326", "7.72680649171861803589955473189", "8.65288181007227767367065491384", "9.35605598829263964870216930496", "10.578886697132493656476759320901", "11.59623268577704080424115115472", "12.71317391084327622064491727303", "13.92890120001762138515635508421", "15.136745621311972948072112876944", "16.03343953431726646125965956691", "16.848372480966082357307977194774", "17.53094776987294608614361605648", "18.86498475465955252322030913572", "19.38324078814568110577331587646", "20.72823692784243541438186156590", "21.0311177678807293050811943483", "22.796997594658227570514203776599", "23.869740307821017140529568689708", "24.33643312315769278498935822022", "25.48487515648702328774410221351", "26.0873123020646748136380371861", "27.240545258837337366656721652654", "28.11136915196509169710503881288", "28.51676038643510430465626667991", "29.60271869762961720433094606299", "30.649973852985425083699997621090", "31.938389016886004307917448735396", "32.63648469593579805902459972189", "33.439121110604731512877970465550", "34.50212481479447936819277497033", "35.22235869116803657585249773245", "36.1568112224510819111064867443", "36.60394838806990494910707301218", "37.57493771673323127198350768539", "38.63562736399933628232171251098", "39.23796304802311603867113950707", "40.573323636746101833798013353353", "41.15976112325696625005049732289", "42.464690909136731794891731253286", "43.21494295371226260590486973719", "43.66407270082389005773025030402", "44.771941016943036557064461575642", "45.24743005617482007301377517243", "46.299725751404258756728490151963", "47.14815393243130681273847934560", "47.8224784055318327093216862502", "48.52986549048879228600460272142", "49.919214456396149232423641606936", "50.888663808415402383259626797803", "51.43053348242576619100501225585", "52.45175513380521593154614618732", "52.810652809885372019782476351171", "53.96490439960269505921889265378", "54.72695377753721685644414057632", "55.41678304070188144542600485125", "56.08386521853755615049302777262", "56.85319784975710955435197723535", "57.95157705713010415920042301996", "59.04919065067469291624057697496", "59.78210798173946570004856582325", "60.53112937359608860876683256832", "61.224362802721082302841556051602", "62.4578073121022433733515428198", "62.7295555777785132231280439471", "63.61649549436206929930990945196", "64.31942305254982015023485812569", "65.08080578246070479121349434525", "66.00909117840356376039709817705", "66.812110139944618716548119455020", "67.84584679457087726794486261377", "68.48600005004673311205365090110", "69.745281765378166580907089242631", "70.16111596396579310384627278225", "71.10017100338472643044399189108", "71.578084090293487504878843971632", "72.56648039633069124578219091209", "73.01038704662326353633786665980", "74.205561966189341147086983214341", "74.84553055666815886504526541852", "75.22769150503323970681560119612", "76.52038649644108663157290938233", "77.47311969555109021513385575965", "78.33976679576443834229897124689", "79.158506173376049593279607891741", "79.44527388521904537687253726316", "80.49636146676487754846076938790", "81.16688288738379369803787918442", "82.08891754605114474008608399757", "82.69436639460560794372382086731", "83.29916196826951909100442676504", "84.067219560925392110042479836143", "85.05023631144271749007454755652", "86.126215788085901231313863802045", "86.94258611890124141917743245095", "87.53336496876289327490267088134", "88.20553660134917261792636353426", "89.226301684096680622521662535537", "90.01212505092743849650892746389", "90.338959562804154882743700829871", "91.29862696655669810409511751775", "91.99180240261590627707132599775", "92.53582485896992648812866501153", "93.75477834973844910111880442903", "94.32684102054012580391846379103", "95.268012683565592684929402917016", "96.12164686472053179529946312410", "97.01959848598210960788886137289", "97.5531195169808488858406223453", "98.47319399440012999381678046253", "99.07923377890798605661685120177", "99.45831105157320224234481485603", "100.70604726310717370654544178627", "101.11484728023141458318872525938", "102.09284904964376680102618553864", "102.60268042615763385503834199368", "103.45179364975064327550782609687", "104.79622513152975717602452482480", "105.19541311995399668634778255491", "106.24093529556502663010621306332", "106.73986451309392038280068720068", "107.25771130045307006217383547191", "108.2221960579877406046663350228", "109.05515745551743131612295680690", "109.602358152037050047620301481487", "110.29803428034975186413493353989", "111.01515430037745692374470531455", "111.68951115938584392698102082147", "112.79341450154772102731226348617", "113.94544758629554360943994404722", "114.19974284834400846200754558751", "115.032513075322750876530291082812", "115.81686025451875693650342327307", "116.65859787705512755997123599255", "117.26059555039070257974679537037", "117.93370568702560389603700287716", "118.731355550281950634154676380100", "119.144306989716886947741699237031", "120.05549221975821940125979907916", "121.0479387590856316189805728504", "121.63031371440431848983242292682", "122.61711464368037384073885838595", "123.38052336197283562937296970428", "124.08253023861170840428013482702", "124.97766808741089935593519757407", "125.53422560656583618019844304291", "126.18784753184361135052489802268", "126.8422310715206395222091821325", "127.480849055828067105180114490121", "128.701375982615060932077208721722", "128.79604736087929015460096940570", "129.81673133022743588156222260393", "130.48919039774159789158377972458", "131.49816027325225584247605812411", "132.53681631483336880384646704023", "132.97077600513674490146462000759", "133.81555121643470166486184217636", "134.402950070769556163750349845715", "134.87516242187892755235550399340", "136.08250703691173201047379167947", "136.458581684607757049670736019884", "137.21578346544130529176677886157", "137.87129212086549515717319343114", "138.63383579707546153585029756927", "139.20610008590326112455478608843", "140.75914842336617460542256100982", "141.0845855553407613524380417487", "141.69942107410632743507444861075", "142.717050488968836215893434350368", "143.141925861068926254262236073845", "144.00044877274426964715573719489", "144.81038086364031597747963124815", "145.31116488413074053668839320350", "146.00336158801701387680644780691", "146.50834646120372841088561806988", "147.61488540745506151959556632929", "148.09711412276187357517826535170", "149.25454921885880916164245069225", "149.75615845103539723328847755126", "150.69617956792604940741076647123", "151.3414200230787274652467812185", "152.16959973654147704728027116259", "152.81951625514020899991651021161", "153.387519864724733566120664705706", "154.04371388112365722938838554948", "154.66089988486697144923265234734", "155.6485231290421435487285875638", "156.24123304048844360586997776788", "156.792356917233125386989844293367", "157.71531093669024433559826100764", "158.52202565157708138219440704165", "159.429810901467461270097320594770", "160.318291555756138557505101327842", "160.81968828091923921619835403839", "161.27992558506208331236426840958", "162.1025594935185635498121780300", "163.000138011064103537300603195675", "163.32974844588282198036919856379", "164.428151183702235668695749678423", "164.8352474968365719568980358558", "165.46439114542117138360100268848", "166.17108844508358296367602164325", "167.31144038905185657809877594850", "168.193530151332124269893076576014", "168.74192416361627502268691217478", "169.387652778570969895504068438209", "170.11870450265826819259525269669", "170.818357545470341615901067611822", "171.5310735610734615107891191382", "172.35680284502724300327986038146", "172.78299043224114522966285644612", "173.38983980093178166643806434852", "174.15918230219074540858054050785", "174.967573391298519640073745741", "175.77825224529681084464352347328", "176.56107860675635665117192800341", "177.54349361360150675319978251390", "177.8027681939904813440496128561", "178.90773273449463826875440207394", "179.53235303729367070970531763214", "180.10806197938114839624935998147", "180.89895453799556517712901634666", "181.24389901268547508543264267537", "182.06887704140183944077399489315", "183.152143730218190599385159758109", "183.25148509882774021833476874755", "184.28843796111352877556972399755", "185.01637843886593103878570906531", "185.71501583623087931606514044540", "186.842000380117352902946917758188", "187.48592348584413362586302935449", "187.93532231565498133033747592704", "188.72800208831168153066874779265", "189.23030303073689390459952028363", "190.13874947691072883927676957125", "190.56251068435652539894640637954", "191.6672263376939411564557171042", "191.92154185508907349485576659302", "192.78610451317570467356749614584", "193.14901055321469681172227652300", "194.53933405915556470796020522328", "195.087166067960520956705086334189", "196.01866101962512736068820280292", "196.6132585747808044734703236273", "196.970876248434387533310888660897", "197.98060271976808344974809880794", "198.59021775266691343713014445336", "199.28938312549420787192512623564"], "negative_zeros": ["-199.368800898719329881450758757445", "-198.802796943004319011182179449204", "-198.03037011318371444548508910790", "-197.63337548686931195933262601403", "-196.825747751198534972809258961791", "-195.99563418870394450286129994", "-194.99031787008536696004162853678", "-194.18693003881870350771932516662", "-193.76024717629514712790608400628", "-193.12730521226139363094083433178", "-191.997726319946441449023148850325", "-191.69021017062468993923891322382", "-190.99104212558349588732646644422", "-190.10548920361587452051830862136", "-189.49529502037302309853175643145", "-189.39606316441238010369330633886", "-187.930535434979426396706475003285", "-187.640305725003173470922333647236", "-186.73533533259397343645724298375", "-185.89395728022550431021151912652", "-185.086537601725497526313696138556", "-184.47243792087998034315770862709", "-183.5609075478384626745899892820", "-182.99129109463296931518517699846", "-182.33820140885384683720801192827", "-181.91558794275845645785009081135", "-180.97905403968884068186732866873", "-180.40437294426683889535354642579", "-179.503036896689140838922005425877", "-179.0286937802809743225167407155", "-178.35059062058083449970798527233", "-177.49350923683349588396086573231", "-176.543887418443291859724387455098", "-175.64662142591465810827337962326", "-175.022801202880610694370806917650", "-174.59122357519868417347074716612", "-173.74957802658063086763685901953", "-173.23936481557369794900654087955", "-172.17968344002498702013705575456", "-171.79929517120437374404354344432", "-171.07956131091274229495927560663", "-170.20559215783351038618148437048", "-169.96585517934193673901364199066", "-168.97016654146617159096748142908", "-167.66623665268828215227968044235", "-167.35195058775169664395734978748", "-166.52549521001028793845545085749", "-165.714050331565050340113882993648", "-165.29299487071762707461689035124", "-164.22643280909088113369600648056", "-163.777140410955437923973366644689", "-163.0172136572122315639207757499", "-162.40854806120654312964352996791", "-161.92273792594163367282162912783", "-160.94990335324664491407439381024", "-160.1199240057385833750501434186", "-159.62004219281354330478997450262", "-158.36082250587300369252502502163", "-158.03758786061560605600319080610", "-157.080777635357659993017709223", "-156.25018079179124203511552641447", "-155.65973290376346677072544495682", "-155.07903674197329945494659540870", "-154.50348210751731044747365102718", "-153.619970117546537008464336502199", "-153.02297845644730956144629286650", "-152.20203172599773489148271375688", "-151.47585055464354568872590514320", "-151.02942893567980071478267786120", "-149.926393530654149959667614302269", "-149.0577990848610439163541054900", "-148.186951749853886037349004236080", "-147.531125742061013410107070196780", "-147.18114269555026129158682531128", "-146.30001555911217852696658020601", "-145.546488296748135274982177643932", "-144.880806846851388202846325620778", "-144.17514697489655072756791509252", "-143.37358268645901935391541700794", "-142.945799046456886332854644144316", "-142.2871666847720449376170133164", "-140.982294216444439965505552321617", "-140.29275178286999159756357900332", "-139.54430801679343816935065012012", "-138.86201216894811201888598467437", "-138.16664186504170095268331026153", "-137.56532299287165993727254370416", "-136.41633173135183351889762545054", "-136.14341064178143864123679190707", "-135.47274806681870705856407684881", "-134.74925952296282869830159595821", "-133.938915391123087534837093076941", "-133.2719465568502087391220398254", "-132.28814839835485667425152035238", "-131.505981288490823201059748004209", "-130.80132899927266696067283417330", "-129.91256049528985088956907499322", "-129.2422173188160577643790556528", "-128.4418908067713109900401164669", "-127.72906915946982346483045384297", "-127.46811760632060065499859676544", "-126.429155107034363525853159114355", "-125.731501056470151793144549037883", "-125.03840511773521418294360320074", "-124.29060058253849736475386489557", "-123.52064258812683609647132586625", "-122.84464041428193145009082765091", "-121.38531058484363391998941909536", "-121.153850363772800065003116459792", "-120.26364868408447634977325598610", "-119.639635727434139957530225404298", "-118.95554432286846827978271293819", "-118.25455211105451469302684739541", "-117.43284458845234221694175849392", "-116.53575498479347930343874351041", "-116.26841057519877979296596488427", "-115.413124393686518930420848859189", "-114.665080583024718403538586625296", "-113.33587919858783287071533554997", "-112.886272349565757594194538431", "-111.72186842667025778877673582745", "-111.56442670307371307753040696901", "-110.67227950993958100075809104777", "-109.6325670265274126082815010124", "-109.17803802399171200045861884323", "-108.43101706560437668803520952760", "-107.752794594328784586564493266159", "-107.18833795108185945126527727099", "-106.12734229183011405485327825518", "-105.54091617879810131571716057494", "-104.26533790210189213503132021708", "-103.90291116371836027812764129279", "-102.898088188233285823614067798700", "-102.143667426453875776709725294450", "-101.1969935861574619122373654464", "-100.93040128095235460867897055990", "-99.94690923373034948678760807155", "-99.49108615388462345213793585173", "-98.49889729544138913202739565518", "-97.87844777944821674595609477295", "-96.94930629682725499394298909480", "-96.409275007064330920548212116391", "-95.447650353194334524013616464280", "-94.17747389281515008286970798648", "-93.77630885210747021948856407750", "-92.940648619436048445528438105310", "-92.24148425833358061547604800998", "-91.57061957555757462327428868497", "-90.95436715927386800264064396040", "-89.77781270661535758062458300834", "-89.291451105403779217893795338864", "-88.84714989442016006962913921653", "-87.76902018971473419801581588097", "-87.08809726267174250166109668670", "-85.61539112979242927188184182445", "-85.28011288653831272769131124072", "-84.41597646226327589909012032950", "-83.735677619798824915269191996719", "-82.968809214591829629089440657868", "-81.97260635709486369725194607110", "-81.50683785570831485070289951105", "-80.74909186692806909476625805132", "-80.09644662336405793388804441634", "-79.22982908687680720717541984422", "-78.376389272239654270150828310696", "-77.31964362051858185721264558095", "-76.487696844727510298039588464379", "-75.96493785989461611248101146059", "-74.74471740458915936829033052841", "-74.178672908388544942133571514879", "-73.604384686715584996355211117055", "-72.5178164209612367703332149120", "-72.27934723231355738825575811297", "-71.2711734958315551379081853401", "-70.318023991912464899760050363484", "-69.65617674415304765358942795099", "-68.983858168254691174343192778884", "-67.62479986125265340164498865010", "-67.0353787344022096662681215443", "-65.87324275329790220531825170752", "-65.54359306651465185309300221436", "-64.694889284288483939263153983381", "-64.02222980154602082838983801692", "-62.98871801496871459439674883890", "-62.39335011171239146869745647251", "-61.41679055607293716139785856799", "-61.1366648169740402590047679066", "-59.893932786335603034308203007047", "-58.8169404118063386409322039087", "-57.76227453972931774958550230683", "-57.3638510279145818409984119333", "-56.58048887394661797036128603311", "-55.59036833329618511107560596578", "-54.82966112694638513967731925308", "-54.07586866931045888530872031387", "-53.43536431964424132988381034805", "-52.61693082003041985310229145068", "-51.86532808435326896832518210686", "-50.67029824477763114780993387524", "-49.7106911479670714625963576577", "-49.05724203938752952315231800056", "-48.0524817928421285818770248594", "-47.150257395064507465350330441095", "-46.59090972260984811545522658945", "-45.474561913684866397455497305362", "-45.22492364517131977727798053469", "-44.211522503473427282921995970658", "-43.07506263785577344532575740350", "-42.6064165759791489146746458503", "-41.53303908216734741387556028435", "-40.4155410049988511753880905911", "-39.51338635543345810651482505468", "-38.52988276080236840599102202551", "-38.00078489693412000732235459242", "-37.24227589741229045219586011052", "-36.30042033189234046634638106210", "-35.371047323717129959849620029192", "-34.64059859386732910677388503577", "-33.8736808924564367679741090112", "-33.026143805178780167880029193", "-31.54737593528188278640672297105", "-30.725729687310359263132648805109", "-29.78483134142370695847390294153", "-29.394329302903386162313521212092", "-27.995703237261634987427867277747", "-27.4313693919650074786379874253", "-26.55753133789535115068467745200", "-25.55381935944991100708338110727", "-25.16854265853127608178588197976", "-23.54204229668309395257290054248", "-22.70270375524708798466445096560", "-21.5715313714771337961346274219", "-20.82294316142913770062090299476", "-19.71466732940575066678617603821", "-18.82751650792650461378971573012", "-18.21149717828679234153778275403", "-17.26409402005197555201140780118", "-16.144362495214930239527306921710", "-15.25632742986474690311490711849", "-14.124579880323120636349707785309", "-12.802017202515513229475545886204", "-11.74129442228963263986319735867", "-10.758165896222197905436808500654", "-10.147806793590703284978537475201", "-8.8910399323924869684877919980", "-7.80650897162909923285163690898", "-6.93954355747862867351314979648", "-5.75403385903061324056891944812", "-3.696350676612471765559888440200", "-2.90793959781575072288650053518", "-1.41564770251563377688838310047"], "positive_zeros_accuracy": null, "negative_zeros_accuracy": null}