5
$s = 2 + {1\over 2}\sqrt 2 = \Nn{2.70710678118654}$
10
$s = 3 + {1\over 2}\sqrt 2 = \Nn{3.70710678118654}$
11
$s = {}^{8}🔒 = \Nn{3.87708359002281}$
$s^8 - 20s^7 + 178s^6 - 842s^5 + 1923s^4 - 496s^3 - 6754s^2 + 12420s - 6865 = 0$
17
$s = {}^{18}🔒 = \Nn{4.67553009360455}$
$4775s^{18}-190430s^{17}+3501307s^{16}-39318012s^{15}+300416928s^{14}-1640654808s^{13}+6502333062s^{12}-18310153596s^{11}+32970034584s^{10}-18522084588s^9-93528282146s^8+350268230564s^7-662986732745s^6+808819596154s^5-660388959899s^4+358189195800s^3-126167814419s^2+26662976550s-2631254953=0$
18
$s = {7\over 2} + {1\over 2}\sqrt 7 = \Nn{4.82287565553229}$
19
$s = 3 + {4\over 3}\sqrt 2 = \Nn{4.88561808316412}$
26
$s = {7\over 2} + {3\over 2}\sqrt 2 = \Nn{5.62132034355964}$
27
$s = 5 + {1\over 2}\sqrt 2 = \Nn{5.70710678118654}$
28
$s = {}^{6}🔒 = \Nn{5.82444461667405}$
$s^6-24s^5+212s^4-812s^3+1025s^2+882s-1615=0$
29
$s = \Nn{5.93383346267692}$
37
$s = {}^{8}🔒 = \Nn{6.59861960924436}$
$6s^4-(208+64\sqrt{2})s^3+(2058+850\sqrt{2})s^2-(7936+3658\sqrt{2})s+11163+5502\sqrt{2}=0$
$36s^8-2496s^7+59768s^6-733760s^5+5289248s^4-23462672s^3+63458276s^2-96673872s+64068561=0$
38
$s = 6 + {1\over 2}\sqrt 2 = \Nn{6.70710678118654}$
39
$s = {}^{5}🔒 = \Nn{6.81072208306864}$
$9s^5-171s^4+999s^3-1959s^2+1636s+166=0$
40
$s = 4 + 2 \sqrt 2 = \Nn{6.82842712474619}$
41
$s = {}^{42}🔒 = \Nn{6.92669309446880}$
$144s^{42}-33248s^{41}+3740531s^{40}-273229120s^{39}+14568177368s^{38}-604345329616s^{37}+20303247278518s^{36}-567715628580628s^{35}+13476130642163772s^{34}-275622556171657148s^{33}+4913118839607229315s^{32}-77021965442580593792s^{31}+1069597207525632250760s^{30}-13234280063158548374864s^{29}+146588403144234109714492s^{28}-1459056537531761947694412s^{27}+13090219490685085049164304s^{26}-106115059640167069135194108s^{25}+778709778173545540562913112s^{24}-5180160724110239826615572336s^{23}+31267085211757278545052994144s^{22}-171331300125735569491450805184s^{21}+852412555299622931388971786184s^{20}-3849639590878015114188275848896s^{19}+15771592794879254264477226832440s^{18}-58556476540137831140983424890112s^{17}+196742347065286547712609208667628s^{16}-597075318553361988026330293830592s^{15}+1632807555219691500831155576662224s^{14}-4011703707846363075271797958908992s^{13}+8823126218415607049547609565313808s^{12}-17292499393880618294971765830702496s^{11}+30033784585675389426408059928238624s^{10}-45904080196423917967770013765165584s^9+61200148145342575539111090507985440s^8-70370773645277985938951580858638528s^7+68756165329665893470887878785349152s^6-55949600498940958320310297578555360s^5+36867848125763978702951438802849616s^4-18873332426700882570902855047275200s^3+7023595398126017089078028623797120s^2-1682258751137636203725622554061120s+192930128676231207430057837613968=0$
50
$s = 7 + {4\over 7} = \Nn{7.57142857142857}$
51
$s = {}^{12}🔒 = \Nn{7.70079923541701}$
$s^{12}-52s^{11}+1168s^{10}-14808s^9+116250s^8-584196s^7+1885642s^6-3878332s^5+5185145s^4-4669592s^3-1070690s^2+14600744s-1119939=0$
52
$s = 7 + {1\over 2}\sqrt 2 = \Nn{7.70710678118654}$
53
$s = {13\over 2} + {1\over 2}\sqrt 7 = \Nn{7.82287565553229}$
54
$\begin{aligned}s &= 7-{1\over 2}\sqrt 2+\sqrt{1+\sqrt 2} \\ &= \Nn{7.84666719284348}\end{aligned}$
55
$s = \Nn{7.94577100750391}$
65
$s = 5 + {5\over 2}\sqrt 2 = \Nn{8.53553390593273}$
66
$s = 3 + 4 \sqrt 2 = \Nn{8.65685424949238}$
67
$s = 8 + {1\over 2}\sqrt 2 = \Nn{8.70710678118654}$
68
$s = \Nn{8.80345993651653}$
69
$s = {}^{82}🔒 = \Nn{8.82721205592900}$
$52389094428262881s^{82}-28863139436366651460s^{81}+7840436786580754561842s^{80}-1399864630898909951672184s^{79}+184777024966383679131379203s^{78}-19229480097533386652981194668s^{77}+1643178003450476327369002864080s^{76}-118561352785653984081132853368864s^{75}+7372351836836707441183744339971015s^{74}-401254176764396680092337021141946484s^{73}+19350157008010415954432078062713291394s^{72}-834969623551779032213936610875479861512s^{71}+32500264420943843392373991413578392058093s^{70}-1148852629892528066579108553164478473663708s^{69}+37092466248098270905023679715303792737820304s^{68}-1099206042418214352026228628885408398048015000s^{67}+30025320958251433175557289720600502032769753340s^{66}-758792087058505752402362438963674625699826919880s^{65}+17799410748369850870306914205805242294037335637896s^{64}-388686829570450651667791276249653981802721222714056s^{63}+7922061683854685568474881816199072307645318622376904s^{62}-151058341641411022199807974673871019724902497364765552s^{61}+2700552785792713834768094889293145620129036537676224092s^{60}-45354522344129825814676420288826173471599912259984496632s^{59}+716878712470410740335863321139824820808423827153710652804s^{58}-10682567284888720343007934969631240418818071811270135320816s^{57}+150320784390672934545124162608853418121767017935787301000808s^{56}-2000572646236355172723818796429406996345627284039771483014960s^{55}+25219559033013693277083797294746787502373277261234753716013214s^{54}-301583920452466921147984771117351156297618201001262096981290160s^{53}+3426054385349213936246735756144263675017479361589187104582644952s^{52}-37026637210515130032012648558266141117178874708570301177143938096s^{51}+381221915869963598518466209504441332617716678547088629463788058492s^{50}-3744411601889467025365599805308355961072225438102130448464025588920s^{49}+35132927721859555152174976560750433704133787706160759119646097007600s^{48}-315304729246464792403348347852665200866883662496880642068223778829192s^{47}+2709948932058311309971179409319475857433539061059204130543172912232550s^{46}-22330292252239325190451014020603871952094854771701615927312762869972264s^{45}+176590827377409087722261448341442541695845580235159787543827412635270192s^{44}-1341409274447219282944440341226557560736584173610170808364041163179628592s^{43}+9794628200723929363909228342085371052888507149267241738990749330177446536s^{42}-68784984456991565723134237317800008579678347641360227701542986898597128624s^{41}+464787351026639375955250101748280481985644641368851374515808386357693042884s^{40}-3022573184259078701450135458529957385309345186803651626114551783083378175032s^{39}+18919089267049873225236080915564725310548628869115830052258169804904606332284s^{38}-113971460035925598073276330819280830203445312638283436481301177127978414813080s^{37}+660644243129473954993233623574173921633210380878554917654203983937559606764892s^{36}-3683382377823441838082957327165940185883796561462208003223994363396807558829680s^{35}+19741959358629662296400872197474154929765830845655143211973252362263291667066932s^{34}-101642479500862445314955859849362422289005748345703180795721307378605167190176216s^{33}+502223128747819353777858875489650546509178956355195996750910607953412777650946008s^{32}-2378848650747301593887480639497480434456215486100674152450449358032767827357494504s^{31}+10787427200018965953466228877088228967021423580833924967176436387993308084517771520s^{30}-46763657666979111364440110538290788706620901509781273614839323079790048897674112936s^{29}+193478197292846750318686197125966160724659499210376202873234094610563436453287357712s^{28}-762652613846301377253090541691216290609269954386886415663741638905969508874033669080s^{27}+2858810541382820711701247202901545177530055188476676694775559880120687456958481517369s^{26}-10170991995607092582144907594501215089484328088609684391404365725870234777077196212052s^{25}+34275552245333382898966081848057394622466895493701655338137448625314981168202736100870s^{24}-109180149865199065847120380278545633781677317125880517882096621147002464901674366232896s^{23}+328024240104468595897778174882791456088805151159650666727391352426213891813001741009597s^{22}-927474305514792318700089933609615567301057834087731929460292201817254239263791481291308s^{21}+2462182229902610406598305774365812710170450400050717006211185019057179425643813174021924s^{20}-6122044755330252945719750665463174625835643677192302695331089860574738738324123064544448s^{19}+14219984970544731850691516928796082391054234525105419850802193862381157708451060567522208s^{18}-30768851545907889218776308829677014260927583947632211969217096923859242673238301283472512s^{17}+61831404131179569857993652298053425544232611206764320680249716948926268397092525417269376s^{16}-115009817315259102016058959098678198023224949369106956091463566410698079424438533154919424s^{15}+197271311091301472792347653205833439690067290927728227908502214395626223917618164276099328s^{14}-310715226079337036201755817142663826462822486357621041087800464785427130883680776524049408s^{13}+447233873751878497967377512304289813779839139617400585441961124659571901207054515474723840s^{12}-584994487650569941937265070878539829783049696806373201094322271724763322754772388187897856s^{11}+690809670769485727048919721008636863534640513613632064766742686036251506800827979919523840s^{10}-730705950216779945965312115026670309649787853302475272108288646183442394632173792483868672s^9+685727465494402560587060223400049402456139486767982657035415974606333680206469376237371392s^8-564182795837916615774045743559109089033591178820776604035503312959295256878380021673099264s^7+400823651584041532933559377617252554932923674966442340917105411238495035002689607404879872s^6-241020915379745770711663822572215144075000506186967983082373034574012538132391946971250688s^5+119331539747892530196375157797097038574572404727228577993084411405965584791382011108392960s^4-46729898398085553837033675288544422050050908921747303951054359523991662277479822073528320s^3+13577207271788496430462938959054088460341797225685886738526659498529340720805243256832000s^2-2603186344462167626779756466825247201285474002427939337103647694067437869176377573376000s+247160402287431680471138762403368003391572385877539215982119721342810263983667281920000=0$
70
$s = {}^{4}🔒 = \Nn{8.88166675700900}$
$23s^4-742s^3+8848s^2-45876s+86229=0$
71
$s = \Nn{8.94407155757031}$
82
$s = 6 + {5\over 2}\sqrt 2 = \Nn{9.53553390593273}$
83
$s = {}^{24}🔒 = \Nn{9.63482562092335}$
$46438209s^{24}+1718447880s^{23}-1304818741864s^{22}+154362940868008s^{21}-10223870917986092s^{20}+463012769729234068s^{19}-15608677475881443482s^{18}+410530364971106359132s^{17}-8675319117762080311978s^{16}+150196459602374087471728s^{15}-2158879193002672091253360s^{14}+25993038455067669296355532s^{13}-263613888105247221344935027s^{12}+2258335015809616506745502008s^{11}-16347943921555337654669478150s^{10}+99786776593815833271369617220s^9-511154425074511891757096094175s^8+2180187656593439512672814134216s^7-7652314463979073976449593048904s^6+21727853135387976484209118127392s^5-48671720700899577518293563957136s^4+82801528406446840092722047620736s^3-100540002112755895115349929950336s^2+77621257841393908308227797286912s-28634116465193128516311336597248=0$
84
$s = 9 + {1\over 2}\sqrt 2 = \Nn{9.70710678118654}$
85
$s = {11\over 2} + 3 \sqrt 2 = \Nn{9.74264068711928}$
86
$s = {17\over 2} + {1\over 2}\sqrt 7 = \Nn{9.82287565553229}$
87
$s = {}^{44}🔒 = \Nn{9.83881743996618}$
$629407744s^{44}-222450679808s^{43}+38325385756672s^{42}-4288660082065408s^{41}+350399070882492416s^{40}-22278553803273224192s^{39}+1147211537906515146752s^{38}-49165134066758334425088s^{37}+1788289659043280951068608s^{36}-56019383059428524897963904s^{35}+1528333582392710799260183056s^{34}-36630930585616880256564390736s^{33}+776543722002840046363087727297s^{32}-14636706341423531247516707219912s^{31}+246257253722069243863014484299360s^{30}-3708577084615935587358116609301672s^{29}+50074372636267901037924496964125186s^{28}-606479613834953151228303026322056904s^{27}+6582752938907446459101615245660789892s^{26}-63854390288109107749984304630348881800s^{25}+550526226273592526694018724167940975017s^{24}-4175960161221920130654884897696082820472s^{23}+27333308361495923310409348740175473961584s^{22}-148034863695064180910459529146184056115272s^{21}+589148297042380492962295030591016626388382s^{20}-802163371353907808165482957048549332378608s^{19}-13170004747477877616293633845629891862121520s^{18}+167392797210322735047434221678453545578017040s^{17}-1289394300288384411131628488173364706102979582s^{16}+7787489258551633023583289334261547248712408216s^{15}-39385778676485241094858686353246027501471904572s^{14}+170965915920626557796308089870520546518118278944s^{13}-643154540172295005723535558458606455031058629500s^{12}+2101724893624280757011728452832803445528481662064s^{11}-5952381674143195979828863351096699278368526615456s^{10}+14521989109696597926922222011586158834006883331752s^9-30220186517608350885252195687799573775025255492983s^8+52871604435569645714797351939274760286735693270688s^7-76162701057186797152957613136211362895325167372620s^6+87583595303336820271204366145801190135485625910672s^5-76547308527338366706545567730043731458801541686452s^4+46512363388633322446129276907281520687047667820792s^3-15838102486745813882030359867355235545830428100484s^2+479096262707743168168387643797274914963482844224s+1204779998286697546929705082841769576290141607076=0$
88
$s = {}^{20}🔒 = \Nn{9.88815305375857}$
$3528s^{10}-(300552+15456\sqrt{2})s^9+(11614660+1180832\sqrt{2})s^8-(268405824+40209136\sqrt{2})s^7+(4111948776+801750848\sqrt{2})s^6-(43682208312+10328732976\sqrt{2})s^5+(326223055436+89277369408\sqrt{2})s^4-(1692962073984+518553084040\sqrt{2})s^3+(5849274524474+1954912407552\sqrt{2})s^2-(12163170266098+4347871933856\sqrt{2})s+11572065260145+4353477802040\sqrt{2}=0$
$254016s^{20}-43279488s^{19}+3506260608s^{18}-179642577984s^{17}+6530192527760s^{16}-179088304328704s^{15}+3846118270819200s^{14}-66261902137415296s^{13}+930479746642904384s^{12}-10759858027891736896s^{11}+103070340120029179008s^{10}-819709665351861223904s^9+5405590814889373243192s^8-29412949608198679086720s^7+130831566348158107359392s^6-468664620024162429231904s^5+1321046745485882223459068s^4-2825402176181244872057384s^3+4315682289270565775115128s^2-4199847844458434080013540s+1959329723251932809573425=0$
89
$s = 5 + {7\over 2}\sqrt 2 = \Nn{9.94974746830583}$
101
$s = 7 + {5\over 2}\sqrt 2 = \Nn{10.53553390593273}$
102
$s = {}^{8}🔒 = \Nn{10.61138823373863}$
$24s^4-(1400+352\sqrt{2})s^3+(27061+10102\sqrt{2})s^2-(218629+97462\sqrt{2})s+641430+317240\sqrt{2}=0$
$576s^8-67200s^7+3011120s^6-72041376s^5+1033920257s^4-9243724322s^3+50697397293s^2-156795019420s+210150009700=0$
103
$s = \Nn{10.70383477210707}$
104
$s = 10 + {1\over 2}\sqrt 2 = \Nn{10.70710678118654}$
105
$s = \Nn{10.80789399144854}$
106
$s = {}^{32}🔒 = \Nn{10.82297973416944}$
$2401s^{32}-701092s^{31}+96532058s^{30}-8317521660s^{29}+501462496833s^{28}-22376320364004s^{27}+760407348527794s^{26}-19848555869936524s^{25}+391901782318184024s^{24}-5471444559723346548s^{23}+39629249963743971218s^{22}+353696512578770314160s^{21}-16715802829777049603255s^{20}+292780863461637719269068s^{19}-3146950297418725382386108s^{18}+17996731060753457271434416s^{17}+58068494391477930003466013s^{16}-2710032149344351718373370304s^{15}+35897708426171881544444261010s^{14}-321777454480517334707593455472s^{13}+2318288875965343221612347387046s^{12}-15552954072951813301922897418028s^{11}+110324583017828739076547861980256s^{10}-814314195444111054964406531808040s^9+5535691601850017528577776913992458s^8-31551366481166818299554205010301876s^7+144126073330457054877480503221027356s^6-514883701839008702934553147517634876s^5+1404879821405123399570947930851054697s^4-2828245713344639081326540531975430356s^3+3961424449372054137804580730689208222s^2-3448216591537867586914544066365388952s+1404226509074988020217588819457924033=0$
107
$\begin{aligned}s &= 10-{1\over 2}\sqrt 2+\sqrt{1+\sqrt 2} \\ &= \Nn{10.84666719284348}\end{aligned}$
108
$s = {}^{144}🔒 = \Nn{10.92591939016138}$
$827055562171106304s^{144}-1028746038533781676032s^{143}+614161678485829473038592s^{142}-236434676228380170030685824s^{141}+66980317656649750618706949945s^{140}-15177024487481458274595256127868s^{139}+2918547306910189530506516307375692s^{138}-495729497699611401035280356277680196s^{137}+76089742722234909946196429571333895452s^{136}-10671270893794158877895712177505617523828s^{135}+1375524471618065793880112212598599154653012s^{134}-163680131457973276468171788500327444221444244s^{133}+18041122005484577974071987969780608673747943250s^{132}-1845193374227011301793607038733620442135422735440s^{131}+175195858247481457503205356072668634514707875635464s^{130}-15447131106769150898435521166852265757689347117679048s^{129}+1266589004665859543076277348204652895182867619945255898s^{128}-96872971664861242811412554825190666410176955662558075472s^{127}+6939847565941400486198515625279425362463969118244043805152s^{126}-467586251641955795650527642523133741785627313804139361021412s^{125}+29712916686346155911816329503684280580564307321782343390920945s^{124}-1781869546071794107416303074386560117711940471499978105624204512s^{123}+100692141845407597467752420973765886037444159069768871392617305440s^{122}-5345881769519666404549787030353246578976419001556791199058788111868s^{121}+265745153241256297998761893367366891336827254195720886433343716673314s^{120}-12331900216784265711374361173174853992773142985602439082869045995043620s^{119}+533124642048160878797787516816371559269658695957365696289239653586152536s^{118}-21454346119467121162152752804366671634925654995122131901651080854842653908s^{117}+804137509033612105675830501719617753487476429965727315635094765154608429509s^{116}-28127107800477454224608783588306926887609791011395988349691834833987158467700s^{115}+921246416930684576450726414356413649291858434685374246183966749784918747685898s^{114}-28390357852514647575635304153251006733509079472468682793162434720668520497597508s^{113}+828166533055942389980323072853474773741844516945352000111380951692338661814562750s^{112}-23019859946745245564619050854509564382765776816954463496160143457200568875655263500s^{111}+613584341652374269884917793377224034449208943707706722281248832851205212434542935116s^{110}-15759013359756201601425954086600815916125169227043330927990424168462555090123951648000s^{109}+390943459868126235255883761901077907242607987729337591414340253957672403607173215398650s^{108}-9366575279423493930590320245377238666248026521863698157365356790349162864711782205289356s^{107}+216352869031916941103974168883097076410229240427531516289660856895884573411040138391989008s^{106}-4808372152188842416685049720889157609648589700259906966073914535288536332426660045281665576s^{105}+102730532296869024506560636386673680062422941215075875113492165335062102679114067711595589286s^{104}-2111527924549381695924838025670328572466346746690319171877130768902470515781848199414410720936s^{103}+41831905131678357252471218884771916619975870088217821433418140699364041647672903374550946065106s^{102}-799937696943205886362309315869391648647226626812787165601913537214769018438999347145254423256568s^{101}+14750154008419083794676619125813636103060922241286812273744920967608624399426277671233689970750816s^{100}-260975431069180213161379096976636911786047810516915330900553443161331183641061936532309426166815268s^{99}+4392344885718180821788009252695595386788391929454071852322904840485213772415318679286843092164107326s^{98}-69572449764366603777509810702402733716637668631656846420562636123468612787624389077681592721918843488s^{97}+1027097836001128208475480477047724529415634205788396193786255672967383685469857620307489972997358673526s^{96}-14074624684738338344020983555256300931561811169605846968675883195494170910423934868009815189998913131444s^{95}+180660626905403779319995260410889237792268816586814685932269189175254703565979443977412180365929218465280s^{94}-2245499788361448111606620260028829428953487326596025966685205057335044673291677551140402757171317681417428s^{93}+28671416193365649478884844283419050835810755858475230587266033381784144945601933009018387101662354025540734s^{92}-394217288266871322892333222337975011689661831536401018523536110370589489067761042286000949956400639666042316s^{91}+5703863195259166781025704560694159480317740632678599117279192239656528808349240434327194661001025914590969266s^{90}-80059468446622758198796944179244414275773216304886340967166998450686606958848716898739757721312778409184831024s^{89}+1004138763079804275697043916259570490495614067448884056635127265173895325706519305292407648765439933024547087131s^{88}-10573856961381771762913436897417012389280833263671551808955616987901353562852378162633710797010666619591470102324s^{87}+89592018192513343122608501728306468444080160150570013764942281507872879104525037337900571968575192851768883617072s^{86}-646389054343915846566881857708086454471929561189842086401340461316692430061948367583499858586482550023315255624968s^{85}+6456718039810642099097859415092985378580884294959550540027954767107746733301451637312622694638748754500860323625379s^{84}-121023800920367114740456394384550822251050056535699652844407560836793153142889879029201912725542299088040282912816412s^{83}+2214141842312360842088957869209457033301720300938782561853379834542254228530730720572869711076120400759476676641522398s^{82}-28356343598793509512104101813100331277565377324628374155113333362320620691129713431589660642515885646665728949957477120s^{81}+193326276149342220348774592944517638189290015659976291135487116422639964326276855218454081728375249402566358883373624790s^{80}+888472476272455806191699350838019983663121907875952247282463449324543968737416517836134506583328478952629369845934328836s^{79}-42516537162213569430575995651576954679361212816157294187330310652158106528978951354541798233606533231648621660546804630396s^{78}+522112618129065489804870961459261921170565607990283944017017884543960537160124898069342739174661088356952862568709664565256s^{77}-1342618545725336778489199000787373760761785986907874651237799425060724070361802064472627862822500854916814272826188325433077s^{76}-66040491223199134845147045618672350098757682287069730480920474397277038810690315296551503606743808182508641787706942512705164s^{75}+1364262952834996451203530234946071828185078314277787225442019945572575873923452401856807517021112062607955301736792258600115700s^{74}-13304705641978749958134178788470551595129945699827963361846668354324907739991418713157631994431710893854072722431832213527803176s^{73}+29334976001373298587903081051887382593307649378454900368649597243942243317945696771258177340101688123405963487826199934571536171s^{72}+1254835871470570051042488556794782792117588418222127787554947339513820049704381358376331547707331981952512919464228495319707041300s^{71}-22523027530891505503424966569441421955488549575814604109969927454345802854713294070383275569698336985041069676914510298701111648094s^{70}+181702127965464358789961366947986371165479372958138984901788782694017267869197239482254324417848441510234082919323692280372069142108s^{69}-20768799131995511726547789169370726272427918594867720419390177503737878025976344057907990000958397962055809328439860608970578006384s^{68}-19948075295156435836109416656894226436859162335547613453893980458285069023524724410930500311563593776277707912623104756442308900616644s^{67}+277563091444976350615905331060373322634535062447019073345119343068602535806279410217354898329020266936906113467046714692076787190517266s^{66}-1657529682697455583606917948661907761885472383877503556662422214348275381728884400911364454542824541263535122772441870701633036499017088s^{65}-6744849600069427808638230749843403124653230671460065700956906542840940661429701435668241660784144332366731173866842139099059890338659144s^{64}+265900908796658414004729928138936373412886667531854755436897064634621860471087269993031566692511491887334178739574983962544285302951587764s^{63}-3004424004466380868565336932403529322000477743347609526493919992842453474623296242097283235139283222055685673533785844596271002087966265990s^{62}+15952510880649934170232238691799370484761013335755266838626867339458538348381802226217665035418121984733265851053463965786729252377141707484s^{61}+52844709700436977087393341276324793709660968031613386057626302877464564408156691999020204826101726918451918753716514518653939104902807275846s^{60}-2020674089621228236630508895214379255893304051445553669408570930712697328955808462321802474775318116468031697138899887932815900530503253464264s^{59}+21720276987169510823339394441454329063158033536388122857300531947339919803132580158062195710710999281720948054195728928689471455915236910094206s^{58}-123945160342402108837609034409811687164199656966421494063861646481080781267519604556573384186075344164833138333164907325588762460786498271453432s^{57}+44574107425540990846180840471846706825213839713246484550404991612829013903850846881816303942148266438023306269815814368306169446552675801486280s^{56}+7043824362903877815158421706864485471583470853784370070351861510447554792631018438464382842061566827841356061186149033035612189381569305181720468s^{55}-81447656430069729921479002912373965713913127744698469344092991559439127831727673470354817001585796935419290598861809384864800164216802662432493556s^{54}+533786590466670491383481539626347909344170840135127462433041660886116923842185053958885929953494389188325696209406443838826387220390453673109992580s^{53}-2116541960302835675553353594145351449238728301921812240573560280248684228744585149488550970171793164825050327781031643128574796472867560653613243218s^{52}+3042948170495903945999235284887334737132580532798221389547657620543666641117412190765416637977694675305654793730888039091363799987012594343648945396s^{51}+27609636724094973670928771835738395933166262752744105922531913364700416781961563130557283449015792394218419389495653106570930294501237967490057857688s^{50}-535856184735292315076747519233736512106709191330577252771971066879179545865400124497410606516639892462944920430659191994031842122665106072584000073636s^{49}+9289760837849638287332599480903824722673077825932368112447806423033624772888996178571334220536824361538601511617850978270439889143126658707691731998777s^{48}-125129969873038500048560769292164746322306013461715802450003503070735762748866018193205570046002447761511851032903958622437752743022735149313171238461164s^{47}+1154266720416345119930570232789769471910935131428139622638819161420476818306399798289250749604001284385593060534517914816939127528100655286722806489234910s^{46}-6155347508487510778452873045039556496803779369931409811342652196446647965553605479183191821479797982092607592983786041364255694567667823119856341961712472s^{45}-4705422442445264170641209404732464062403033481594279957892352081275879344131352868908690345518278712304175540521346934310220488715133097556158203021623739s^{44}+477385330622194871540714901817427073853555309007756566201664841051909755035981063889138411055134053075555822017382567204366073006837470654518830743613855476s^{43}-5403260090768220329374696002698538354445091405687249641474961424473160437583176018901238856933269109499580687477379252201433759844969136766502615033267738828s^{42}+34451778414145911680605100571033521479002635696448024736687434353108072694302586432634391199625488570949880833320558761154462651347736880634415001947468462908s^{41}-92660486844670382931588007576780584402517646773957137488811089611022685042394577843905835574559044478128074621397249100727736631324086822318220614389564790495s^{40}-714837448921436203054323898911243391574481889808766987694135879991605974536153865109307552237003127199748961600046894863223133503309353095230663403511397016552s^{39}+11624931431528951864555130312736667723124390283627750589959434390824814621800245892414834253984498708902238309739842056980100464935276494645694231533839396867092s^{38}-85293747080268269354524075835268403276092870355177474696023961949203931609974572195599369454884506107469067558455674553867342759877723432880683167025116068819292s^{37}+358645306233043821827940333667537139341688112496886694316963414605039414990090759181422176355634044342983398977107716662291522271104225587784602869161778857395391s^{36}-161164684912919635858970720976866669205248284715434300850403045047818580246097782203661094143075430492329918283741612712665054876928834644222003125249567196633384s^{35}-11227055124267903211621520916429103872085299888922884348729542525094319574836867374279887831739685527592712417087738353722821736942796810188521562456948716290709886s^{34}+106058435278834292310521849175463437522966582442814895102735941183736660230881366472497604610357510746154132942479325143387006531136395736670537095805273415267943036s^{33}-580307236978343287105572620276111732536942254983767146119698194948133646717836148420334319960235070684225157655205317554630292393920094393130497171519298601710916302s^{32}+1895965112509067834727522941595462769928567205552389310091026742896088653434660773656397874749862386646285205492529606799569173990082446003203312235521334234911264228s^{31}-281228032600096281089868042758579945018243705945322660215888748527926367173006657940355889752566137071873239467832433366604962565666390252821472992809230279920184806s^{30}-44370178598006247883241212367125685693645039954533752691057674122752010052943927229286879476778404562372618472667375889606221709538973089695857043181941006466970567812s^{29}+356780592051133411708292097468496866244738889560021416852681435298411619340498593328899884705703658268404288954199963136286199506575948646119627812290750900427642515204s^{28}-1837235013992137325629183502195335421318243919884136182988997070894350439954964889249677762821374283823478667972709846567336867172113658868492884727500950279184583187304s^{27}+7221443124847617781788373300390715937367304972348443165964134453723086586523312206085175493975063487214169292227524792882577227236483318533352753443957834328956507082102s^{26}-23004142126115830327884318402481747926884526942550526331897592784708122149286447714491516144450112895857396842298757664425762006626073805111277369462328010158070433929140s^{25}+63248233072340143485879460633240457174944459516567045044304775863303051601456220250833321266627636440431199372300482606780539701988410847709147317949613132511096126263640s^{24}-171792426938194278256340007554072402096680026124332348937317565710800458765157824740924477939386045204049012299190186335048662579240473048757779539597014454849162664683144s^{23}+548334836715901681726239120510252375427013853169543572101101236438092091480058359854429398295940122197477634838681870185975893385898825039815833867898091219617598247907692s^{22}-2006589451553807610243512714559840481006248089198126276522240015853630028079932462157270295169192462828944247862031127588841964412159322619332737288964112376102921561219712s^{21}+6933713881648100376185966690672246844126416150779644410368495867065371129821375557694909369247222849964995116624472482518698600845587148973207257593680351464491045229428107s^{20}-19695243579981274034590191760844403328170456749484062381584594548563510620839502849756230599165415677492877065999984120421121195269944252386063215867997965556261291940242624s^{19}+42752995719342109007073309801937950993946012490989905499470499598761505754958006442284368075680722988266742026913595643083746178164761177947674928064813297676111642120740038s^{18}-68167563372601798627962470120790124268417203473654245147270025380241431674642862246671331641912593258603637937727858298544647183907862025244415205968110028368947677405397512s^{17}+97201533763344833630341912129547600738095679277559467385191778767666752213631521110574371288562099229486126334426926682980655974177980671246942592721868111969458401695847364s^{16}-292573372532404131374570807719548824093907880963159842783439061192915000299191518408204438739039929820491098873917431912585982998625385344102162425806314176538541953609748448s^{15}+1352344471409892828406009898696886993798976750469549197301203714928479068387437476563549150636619708693819178171876860597957082066601945828348783341513137117818820599292950318s^{14}-4765006940401980572867838345160123961396857616001999537417101227138867695691837798024799045080269456915472104599371497476941621069092489384167249308920549675167569267067014800s^{13}+11774676999751576070246611443864097525774364549952040070784832034865148639198006486736951575186651415699464142976442486367303797786928601361815737965466921442529456858527132576s^{12}-20210794953938272942815068887702471174367132058620513293741801597357673933292027108341390836224527293415981368992658432115658354192696156302004299816007066531539418482508830532s^{11}+22171352349337531536597312065758748175832632583803828430349681416959036553555786743423142098066151758763844680607737146194564464973883569249728651926269976556748136337882499406s^{10}-9943960762789370037254626665006877388393334592958720666605598736359636792158775722578859081204709334484642965371264421550076367368887366620805231603314367704140177459551097680s^9-9462716588537317106131462908640911916705712103371241914890068172586018699479161859600939147226891554937983417487288999428383308413046674175776128064758907121217795201115093447s^8+11431053062959721130240889258059223317315414518602769644295431657582693425240878832248905249990310277644373202717612341549319886351126633890293721891803604311831673218004504444s^7+17558091838082441388110992143714629127288968995601274846612664935375838849238641584069301684580301822863944741929769773837019831763597679038920396258877545677847619029702809940s^6-50440638984549886742637830912455530766636840591072562194030433527100104166298043389833811696896722899898034604329334118866561969607722402639610109325432393439209845130929914972s^5+48930578540733176411513407390498053524393255749074829767557713134959917857430696895303323727831137789951428980453693870767210127585212376990630100035399454322999956445059944130s^4-22320488662021778559207851456079654919254368275171557750633145536225253890317389730027964253263436511511301937825491617364584677942304741733684712696623911405226759624255189892s^3+9809848611512309887530438813580672200291292895031877405876831664622893955736777649125794892479814871907974142553340442624693513888227928720409331749232412680625032354120747656s^2-12245808929872592520229364020264603387335790904082081958870409334270114802521925962664690621258649164318004605903688101265373061250569391487984736455840517923227405045435648996s+7018617870467530988657249433449716369158334159306648717130983519959047765679033813906095771794142994002693361846522958564789607366846150713328341711092969276808661035566901585=0$
109
$s = 6 + {7\over 2}\sqrt 2 = \Nn{10.94974746830583}$
110
$s = \Nn{10.99683777797875}$
122
$s = 8 + {5\over 2}\sqrt 2 = \Nn{11.53553390593273}$
123
$s = {}^{12}🔒 = \Nn{11.60139979378801}$
$196s^{12}-26488s^{11}+1651440s^{10}-62766716s^9+1618595997s^8-29815750560s^7+402059235258s^6-3996945599928s^5+29059125001479s^4-150620866376828s^3+528127756018414s^2-1124357849826920s+1098765914618225=0$
124
$s = 6 + 4 \sqrt 2 = \Nn{11.65685424949238}$
125
$s = 11 + {1\over 2}\sqrt 2 = \Nn{11.70710678118654}$
126
$s = {}^{59}🔒 = \Nn{11.77617894651987}$
$103727375923893369330209296s^{59}-66459520111369498843387398048s^{58}+20984329777930027658962486463944s^{57}-4351984463195143798965010730184216s^{56}+666687597816139249593148784451810689s^{55}-80437601187195761145119711505429371872s^{54}+7958851957658374209199569980591594814596s^{53}-663970184693824249587042395525558012303624s^{52}+47656218937812393681498721763550477091389692s^{51}-2988182303866249333810381839547924169756480176s^{50}+165654430357465514192443072787971581861849937032s^{49}-8197124382146014341147836594827868966674867968640s^{48}+364894874922743341692547213648315564575454126270264s^{47}-14706889078955847476754230966169066617800637472971200s^{46}+539587226078608281436460559285520668919736259659279616s^{45}-18103632741105160954207882647980809072466693499707260480s^{44}+557585345861528934437763964865981218857543916416201779248s^{43}-15817262947846928633382408483301037584257527948351500326912s^{42}+414431320216485974680637436345665342303734151662538663236704s^{41}-10053720706600678001976425846862433637452130993583771993589760s^{40}+226284569647540177334064359603411274762166518842198552714789200s^{39}-4733759152517412405655786220989299972751266809408192403262333952s^{38}+92179303857101690590943463901100886562361422006241927175500288192s^{37}-1672960880610675687561599553613456404353499890450249160517926849152s^{36}+28328155965071830750649114297222577573737263041261615183323834187456s^{35}-447919533736344610230445733776110830046882845020254305668342798162176s^{34}+6617899464680638705931910964826771950378130327080957719202859033233408s^{33}-91409906287902988999275876436122248409672350798530677686891645769950208s^{32}+1180762818586624946451420285182606032560987685384480825492161016877865728s^{31}-14266035758552976658869792803314865573221372493976743630736058442671376384s^{30}+161221645021528693481600237931024869745295739849234342018943309786459454464s^{29}-1703981869218340104518205680834638338093845417894482077716237293956551886848s^{28}+16838533218881790259245529284324114444679442816984936069651292036750863016960s^{27}-155507096005148562687360644397398099803664438720968695334519092641261137022976s^{26}+1341352207710179476924096858857901812229831030179784620098151738073888619790336s^{25}-10798171511029759592830752371596870956414204206741621062504417333405685159886848s^{24}+81052170118119047525304211048570354210314271885674274312331023002336366706393088s^{23}-566627077124483750134722356793280904558159317087277285384745996320116490200023040s^{22}+3684442919811890828463311011580309432000999223341205429086714471473151446435495936s^{21}-22249274396690493322552083876993000099081166687059558607644004406914233102047379456s^{20}+124552050122653107194057662720770265183766531498214018152534598663746678264316035072s^{19}-645029361671781299599296494361306865872819321944021774312439765584515217495396712448s^{18}+3082971153505608860762253281131318317152697408173385645293686789199851377994502242304s^{17}-13562323036880913892655449542328326722966446788097216930557569549306753603730726191104s^{16}+54740314326884958907759200874363245537500276472385155660821578429631150980435833520128s^{15}-201981782442364856363618820987120260153075419046198318261369689063877557069555018235904s^{14}+678454620619581023501502437862982780835374672007458222016728490158146019922598795673600s^{13}-2064436047222561869480414730777110273397659211723851059092229157758529074339050325803008s^{12}+5657822692000862951856502458470034351072956359376976212464506914883038250278596768694272s^{11}-13870526150873954065582070659971088194709355013075244287120899726399280664638800391045120s^{10}+30169237202060583946794207604883117238012283183329248484260467345739886960763300156014592s^9-57638821146611472988664430990500393055759650090200986958760477435746210148744278438838272s^8+95531208027292543052966021814412362080198304100349288922028438203568859274024955521531904s^7-135203344761287990105966704145072151250652183716897669760569045084963600901666937270960128s^6+160041814214673878562014258437703372584550901902947932679906068352094502186763966417469440s^5-154016683298825557276438882149337620795791870685777351688672777397378372447441511881113600s^4+115651046550947142095553287942602374474866214498930249064530890702755579234634640130048000s^3-63504407975087039964592928651896133586911076368041736628455664161047965497809019338752000s^2+22656559274302339443118663917820262176712502445618848038990511314458453343489281228800000s-3936908799940438911888396204756925415661006746097453884053057654812145020629208268800000=0$
127
$s = {21\over 2} + {1\over 2}\sqrt 7 = \Nn{11.82287565553229}$
128
$s = {}^{40}🔒 = \Nn{11.82509196821368}$
$6765201s^{40}-2845098648s^{39}+580218189444s^{38}-76444672534332s^{37}+7313700827489408s^{36}-541478198967270496s^{35}+32282461276159060998s^{34}-1592401650332728651212s^{33}+66264078654438595433370s^{32}-2360056578357132809629748s^{31}+72739322148379315505619294s^{30}-1956653332398832550681084364s^{29}+46240556849238042597672084213s^{28}-964953122823176982192672366676s^{27}+17849625763191276058228284471146s^{26}-293485855211047587757484370460572s^{25}+4296830596115061642805514450068373s^{24}-56062026207183424768909339152161084s^{23}+651753580603034236066787916795623964s^{22}-6743132871649823544913588155645442656s^{21}+61932541245281919280766873166108057833s^{20}-502864388097908644186877008296638914520s^{19}+3586164305875893817104519150255679222830s^{18}-22233865523258917656574596200774765950936s^{17}+117836973554812356574280571124747241305248s^{16}-517669550834165752088850944695261707233564s^{15}+1760771073593491738800908345083273891209716s^{14}-3688451224681060758343247748983014976447272s^{13}-3038946790141535208034747244682683990472658s^{12}+71735791138334020614589956733651574834185892s^{11}-381139020218879456095819418101710611273627456s^{10}+1267518021830549968006069595148713683301836788s^9-2664006348624383405491809555245054393205103691s^8+1793492920161456183420660943446317121911023248s^7+10946284003184957815907569175715318463243584102s^6-52105146308542520023979647560364421311730107464s^5+129236789770564934710391555764344704402747982753s^4-211311873022032856645395618371922980818558351272s^3+230091479010044538699295485926277667974383569488s^2-153189145317923709976188931598288062177638461184s+47601488782509082091988946077133401472942285824=0$
129
$s = {}^{20}🔒 = \Nn{11.88130621809000}$
$512s^{20}-102912s^{19}+9795328s^{18}-586977280s^{17}+24833686144s^{16}-788425574784s^{15}+19488070063424s^{14}-383997272257792s^{13}+6125462923505760s^{12}-79879749327995680s^{11}+856196296518997712s^{10}-7556258973091735104s^9+54814239105846342840s^8-325093619883814992744s^7+1561244435270252784700s^6-5979678235068566487856s^5+17845354889140483660018s^4-40018900764845892469246s^3+63498519812052276506109s^2-63640403941763504944184s+30347196858954912683392=0$
130
$s = {}^{8}🔒 = \Nn{11.91119052015898}$
$5617s^4-(259504+12612\sqrt{2})s^3+(4502202+422478\sqrt{2})s^2-(34773984+4731588\sqrt{2})s+100926915+17726970\sqrt{2}=0$
$5617s^8-519008s^7+20936788s^6-481754784s^5+6917560482s^4-63487737120s^3+363767813964s^2-1189915431840s+1701575795025=0$
131
$s = \Nn{11.95654869347733}$
132
$s = \Nn{11.99143643966336}$
145
$s = 9 + {5\over 2}\sqrt 2 = \Nn{12.53553390593273}$
146
$s = {}^{16}🔒 = \Nn{12.60090777851301}$
$4s^{16}-664s^{15}+51488s^{14}-2476628s^{13}+82758797s^{12}-2038683388s^{11}+38335080074s^{10}-561971068668s^9+6500206337793s^8-59622322943944s^7+433020664362230s^6-2468567342450368s^5+10847755732088938s^4-35571513994776316s^3+82161582314776868s^2-119456945705052640s+82323170428761425=0$
147, 148
$s = 7 + 4 \sqrt 2 = \Nn{12.65685424949238}$
149
$s = 12 + {1\over 2}\sqrt 2 = \Nn{12.70710678118654}$
150
$s = 5 + {11\over 2}\sqrt 2 = \Nn{12.77817459305202}$
151
$s = {23\over 2} + {1\over 2}\sqrt 7 = \Nn{12.82287565553229}$
152
$s = {}^{84}🔒 = \Nn{12.83100282216725}$
$15197358585941502961s^{84}-14964876021186235227298s^{83}+7272595222812913346894003s^{82}-2325304163405568837985711872s^{81}+550199014011902976417247729787s^{80}-102744907802613577303858434436162s^{79}+15770698108244892301462590278910373s^{78}-2046188803886728893706559592846166940s^{77}+229043365901827791271124033850409760904s^{76}-22465861798723536733581343377318969312880s^{75}+1954663063042408634836851737534542472988316s^{74}-152349951255709169941326823887066293346193624s^{73}+10723829667261655134952521210622665945643784968s^{72}-686326223380322052977518105478585500875790507640s^{71}+40166977336061074256998638756973363193038422762460s^{70}-2160190971013429916138221567315873809290109191227128s^{69}+107210371553542169414048201729669662441830314197024226s^{68}-4928367697648782759676964001463807238961374648608591036s^{67}+210520282427005491506665365123774698375707578804045991166s^{66}-8380048643861127985429658865920308979713621168800528636888s^{65}+311642979584387473990467919553614272825113220053872893167686s^{64}-10851807764621222577237269161423835499294065873227886719724876s^{63}+354529200442735318891489329639289130837080983716609686105844682s^{62}-10886472654344044554989820001276664684754352275834326626073676952s^{61}+314707830740258412075262705001018514633277114685570369659228230886s^{60}-8577131365576184973326383639361903919077060020501484349486798462044s^{59}+220676659864024529834222826550027169451751436159279143212643304100750s^{58}-5366108560854773099323062782542881689148622349128272868132841503304592s^{57}+123455035085747414638373053783111838415779807885794670228653620606756656s^{56}-2689771757042576617382266796760465801989789910549251473683839639432673824s^{55}+55545344660722669971771487790593823603421739027747117357084896573560148132s^{54}-1088014439077084998878807873686497414222608555337013172037085789785737027128s^{53}+20228760646280093419477169754640747236777672568049390223893488286064642987733s^{52}-357199319350132942687604624139422297924839641572382189922202437482576762356002s^{51}+5993578492259294457183648659781874954535555138522882079496926437004560861449475s^{50}-95607888374734158621452463758465962667527766889151119870233929745815458197870464s^{49}+1450449889734808340651325100183427866248693256913059099309145940155004921623663049s^{48}-20934174377970907243549394685205967930306737373954662348822439943609230423042271998s^{47}+287521214531466154844493934641558475944025274728304204144868014752283863593850841071s^{46}-3758693037139824522492196965950225707948971038134502497610180651441239588793706153212s^{45}+46776156166368620484370637225042926774946526631884418623684508412824264790410695322622s^{44}-554213498552523069017939780278197270272937025886205771218096298876624373232634030307268s^{43}+6251950732475223994427997225766260343105672057938693543298710223719438546214455983422174s^{42}-67148743958288503662262110524028512420572740818205612649788782970039163837877122850002224s^{41}+686624504976838308996418090639964921283797740974390943510927597462462930108635451388956672s^{40}-6683624210795197215545578694769827454378481281503786991205805051093122539577000607518492112s^{39}+61922038451063372274525115664711614781745351857035675107097735737909228871958371309771201252s^{38}-545914626236899516397451030889695660434986026741727925639735898323422010790358226899471142192s^{37}+4578596394614695256434177101284715486045596223316501591974779425322438106683698243945133312657s^{36}-36519557390596147521078972913970989194289986313602140505586138261168362886227188120613809866274s^{35}+276908452084060463131678792053749272309227620650243616383774652462199807972600272617027105313715s^{34}-1995125618573564239441569968811948768877908975264805329921557835273555692406902924736432832072656s^{33}+13652302794929101077954196396097847995447641729570461853834329101037063785834852682999232389861183s^{32}-88673260640330913380557229503418078388290914029958962882747927428883329136607168216172985057506786s^{31}+546323078740762777551499851151749299500660383154079131025685851053212263193896570529297338202937057s^{30}-3190532419019051137207920527310810985363082905053938554402580063971581164010258646801817355978728172s^{29}+17647597956569345600264156757559024534779396494222803173516820647844865659043181903919579547455993405s^{28}-92370185046480996167766003031798069104355227778256861958172638341670501748986559657158143287384201746s^{27}+457063596008246343843246947652497192740604188316726144667941077879214729203288916667939807194976754475s^{26}-2135754321030318339803946148640432723925062036840170746475770465651607920747496502359936750118636877936s^{25}+9413245107777963706229663058434971410824508757077884118452667020417078901491483099639931354293862639251s^{24}-39081567129013269416348118385885630160005422872090989882489179092615712699596245833330552131314742641914s^{23}+152623748753623567775238681507133061671421661548557325363509181608802271715863896420772452309156580126893s^{22}-559755021749304754461642532733408124950018980895075585999339578832360136778923426307553163340902938629628s^{21}+1924575434803718372008270042897715699164358183917612079945858652072146738653167981508516336683663859061599s^{20}-6191354447775618609836439234314634277309179603333612701552040527406315440826478331716065451128871996534670s^{19}+18595526459860121841165340574719138895821326772209658546058960991768583728860803392397281925779742313102481s^{18}-52017877357788563455349165010925854251068156661668439408177886419332674892024542973348383001969034647203800s^{17}+135157501868692938192366500327069236098923290104122566272833032709737094637647438296644161923551840062478047s^{16}-325194345405021237494009612258086437235941593129725154570748027251348017358438973985857832818544091573466890s^{15}+722027337085845458293091421627894365163696335388182663348454109292879460761558869358682885259404296739097605s^{14}-1473490515445565711145580914132319537412939207599828450536062468067653025235732598973121176466499270242277300s^{13}+2751263110572258451275788319799047606274296134838009812884081346353904687815554600474281715625532788431857500s^{12}-4675004465981033004681427309219791294001064124937869088877001968417898773888626422941020050924220157893424000s^{11}+7183663179262068580520363661753568724897226652642552988417888182903983412500744464905921688273238836620034000s^{10}-9906503785168325598131719638667321753622423751680769939351178446313898592975073862661742325684296198395800000s^9+12146944042621050502155105222176120253288451344101362562568904240946898405180038535485859612413971290688600000s^8-13090089533045063828551500666675702412696959576885680069538751766268511536417556308969034651288724717832000000s^7+12214708422409722054795434067910885386456675508392415014637505990855532116097110284775444747515260212130400000s^6-9676741582044228838733364917804914719594151753924645775721115515700953860674142281619525345349780994608000000s^5+6333689917226114819893572648325901156172023728019394254226767788794528703035140896587138185275926267216000000s^4-3291213620680948097795240144789699630837845626207176614176801595943955328302192020992095429065402069760000000s^3+1274139733072931259621243156734865080962818490295409701367431118912261529814385684303575896038896856000000000s^2-326961724135799194553082826640306328403985650565477078726674395723377915426470127881664726913341548800000000s+41749176420191321903553288073015514269407918838782863228971623490248342604054718097305744082801772800000000=0$
153
$s = {}^{4}🔒 = \Nn{12.88166675700900}$
$23s^4-1110s^3+19960s^2-158164s+464677=0$
154
$s = \Nn{12.93171183926903}$
155
$s = \Nn{12.95851388606690}$
156
$s = \Nn{12.98219172354800}$
170
$s = 10 + {5\over 2}\sqrt 2 = \Nn{13.53553390593273}$
171
$s = 13 + {4\over 7} = \Nn{13.57142857142857}$
172
$s = {}^{8}🔒 = \Nn{13.61898898660160}$
$54s^4-(3936+864\sqrt{2})s^3+(98658+33466\sqrt{2})s^2-(1047336+434398\sqrt{2})s+4049739+1891234\sqrt{2}=0$
$2916s^8-425088s^7+24654168s^6-774089568s^5+14674175968s^4-173849337008s^3+1265419604436s^2-5196681822080s+9246853882609=0$
173
$s = 8 + 4 \sqrt 2 = \Nn{13.65685424949238}$
174
$s = 13 + {1\over 2}\sqrt 2 = \Nn{13.70710678118654}$
175
$s = 6 + {11\over 2}\sqrt 2 = \Nn{13.77817459305202}$
176
$s = {25\over 2} + {1\over 2}\sqrt 7 = \Nn{13.82287565553229}$
177
$s = {}^{32}🔒 = \Nn{13.82302875075647}$
$2401s^{32}-931588s^{31}+169658874s^{30}-19231837912s^{29}+1515206475113s^{28}-87554613482844s^{27}+3800602014647796s^{26}-123749571598485028s^{25}+2895774212866682688s^{24}-40503170127651197920s^{23}-85797782465034115616s^{22}+22358489056150565928884s^{21}-670371983793922205889766s^{20}+11585516453329663611601440s^{19}-107946265554474207035275274s^{18}-325416702082583543878844088s^{17}+31678001381593454789856242308s^{16}-627531463707625262161828471384s^{15}+7738051841906036676459384893372s^{14}-65825971528188631650991553430380s^{13}+390859965437244296776723867974104s^{12}-1981263185614787515387345660456708s^{11}+20697660792797450992561898119685608s^{10}-341458570720939415832614447938585072s^9+4331777593881436240458282284914909233s^8-39425956807257141453494313251818730308s^7+265332233224572263186725591178500406376s^6-1341713349412185465951061216890867086592s^5+5078477010422928472451310243101300746580s^4-14041240100101609173845558593200611383568s^3+26892648324465918884312724426364749628480s^2-31980711702815550619890642368200074811200s+17821422876028786503270705680802036472000=0$
178
$\begin{aligned}s &= 13-{1\over 2}\sqrt 2+\sqrt{1+\sqrt 2} \\ &= \Nn{13.84666719284348}\end{aligned}$
179
$s = {25\over 2} + \sqrt 2 = \Nn{13.89540982243640}$
180
$s = \Nn{13.93513929847193}$
181
$s = \Nn{13.95698416446504}$
182
$s = \Nn{13.97442960739443}$
197
$s = 11 + {5\over 2}\sqrt 2 = \Nn{14.53553390593273}$
198
$s = 14 + {4\over 7} = \Nn{14.57142857142857}$
199
$s = {}^{8}🔒 = \Nn{14.61898898660160}$
$54s^4-(4152+864\sqrt{2})s^3+(110790+36058\sqrt{2})s^2-(1256676+503922\sqrt{2})s+5199723+2359962\sqrt{2}=0$
$2916s^8-448416s^7+27711432s^6-931104720s^5+18929518528s^4-240795061296s^3+1883132387964s^2-8311787117640s+15898277993841=0$
200
$s = 9 + 4 \sqrt 2 = \Nn{14.65685424949238}$
201
$s = 14 + {1\over 2}\sqrt 2 = \Nn{14.70710678118654}$
202
$s = 2 + 9 \sqrt 2 = \Nn{14.72792206135785}$
203
$s = 7 + {11\over 2}\sqrt 2 = \Nn{14.77817459305202}$
204
$s = {27\over 2} + {1\over 2}\sqrt 7 = \Nn{14.82287565553229}$
205
$s = {}^{40}🔒 = \Nn{14.82445114612408}$
$6765201s^{40}-3656922768s^{39}+958435862652s^{38}-162258762163956s^{37}+19944495118895680s^{36}-1896817614997924732s^{35}+145244607337067116310s^{34}-9200231755130148537584s^{33}+491532552940826676421598s^{32}-22471266124455622725351620s^{31}+888775367178021320983990528s^{30}-30670374642432504931208393536s^{29}+929494097506723220926745638527s^{28}-24862568075564651560878275579812s^{27}+589158528037990588430776578667278s^{26}-12400310845434669601706739856078348s^{25}+232178750736807601084495428509773447s^{24}-3869279274647141302600286447060842028s^{23}+57359828211423634121225283370282978472s^{22}-755020486735335189866154838905984601284s^{21}+8794114159490040759213225924279409129174s^{20}-90126731671943479290165241436087360926864s^{19}+805381183069421598181526905692816890290502s^{18}-6181562346162193722542638238059633411805108s^{17}+39656170956144484959733239448754004343189341s^{16}-200557184022962853819962178120475887680432104s^{15}+668299828757988666056469128930860611880478162s^{14}+47787548247188382784775375655144589392168024s^{13}-20274687460176342070123115001595419340631113986s^{12}+171806640590364466782586102889249290168160938968s^{11}-887645374096288133345472520371583078066772417438s^{10}+2995081869452847889056141420143309758645762048480s^9-4490901292932914262604076259256067123710050815195s^8-18138284909745955939878418372807115317752603411176s^7+165869320264318841451647718375161237581492991097810s^6-695527958949195756061996697585676748194320009594040s^5+1948735509481744597514888658808885791132097191929625s^4-3838064311683628303762259793886602147590339042385000s^3+5169742707762800848775847149992971475362078199650000s^2-4315559969700226767159393981391684637349630444000000s+1694040395896101772224866098180283214283057728000000=0$
206
$s = \Nn{14.87253189075152}$
207
$s = \Nn{14.89397859563780}$
208
$s = \Nn{14.93783044811097}$
209
$s = \Nn{14.95868244078260}$
210
$s = \Nn{14.97421396826961}$
226
$s = 12 + {5\over 2}\sqrt 2 = \Nn{15.53553390593273}$
227
$s = {17\over 2} + 5 \sqrt 2 = \Nn{15.57106781186547}$
228
$s = {}^{12}🔒 = \Nn{15.60902282132495}$
$24s^6-(3008+632\sqrt{2})s^5+(143990+46836\sqrt{2})s^4-(3498934+1393560\sqrt{2})s^3+(46342192+20798868\sqrt{2})s^2-(320302448+155625644\sqrt{2})s+907787225+466763736\sqrt{2}=0$
$576s^{12}-144384s^{11}+15160736s^{10}-915791264s^9+36096990788s^8-988137514952s^7+19384693200660s^6-275725098032832s^5+2830331680270636s^4-20490408263563724s^3+99460046477154240s^2-290971312817869664s+388340875383845233=0$
229
$s = 10 + 4 \sqrt 2 = \Nn{15.65685424949238}$
230
$s = 15 + {28\over 41} = \Nn{15.68292682926829}$
231
$s = 15 + {1\over 2}\sqrt 2 = \Nn{15.70710678118654}$
232, 233
$s = 8 + {11\over 2}\sqrt 2 = \Nn{15.77817459305202}$
234
$s = {29\over 2} + {1\over 2}\sqrt 7 = \Nn{15.82287565553229}$
235
$s = {}^{83}🔒 = \Nn{15.82660563342856}$
$15197358585941502961s^{83}-19054029395700781380870s^{82}+11796924216629042649354579s^{81}-4808108614769876120043468180s^{80}+1451030856404178122570781430789s^{79}-345799767275884788306353984453266s^{78}+67774498813564804634645374167057335s^{77}-11234508000945633407554425804213908384s^{76}+1607532344825153174801872971520978793189s^{75}-201668659118682967539387133057113450996510s^{74}+22454296891522560058771023859593458711158383s^{73}-2240889622579706580689718577985790904704763388s^{72}+202076916434677863681321953179975198173682882349s^{71}-16577690712578589166013893731214562354253387341274s^{70}+1244306501679531491606992301185434118328699167129267s^{69}-85872410283218882421430889383517071885115187773104056s^{68}+5471931933759042230241340087362460711039430660491160647s^{67}-323138905823957289824620179077427648515971541643473332874s^{66}+17742026808852576915081042170482522649963659530339729297241s^{65}-908282679855850349803743965878897364257354889699334907097884s^{64}+43465080817124537825282652035527867092782838207883438915180955s^{63}-1948672651714009470065517948906139063310384408556369781794367782s^{62}+82014228252452305308486172380001566000442685829960411231106701149s^{61}-3246186057482410594749950508613065532781882056581161088848208781448s^{60}+121030129123359970782879324721925653713348068894577966308153780376769s^{59}-4256774383890838346683359771242014391309685520375828879287765027421558s^{58}+141417395891604974478673542444206052527574423688874097457316926184111667s^{57}-4442950325166710767652318494176477005346284036871039689545149858425019188s^{56}+132143761554097136892656409949813501644806291750873673851743056646810847307s^{55}-3724278121653142074595785794031359776637918996855481246500264411247627583870s^{54}+99547162759226989443922275915301342990394148481013546431915854939056693130149s^{53}-2525451166316636919882169794346033300450573261760214407544561168810183261623712s^{52}+60851054822925884393362872088231784921476592249704525359339306693211978978637574s^{51}-1393407983201463082750103812667205031231534119903960161407503385026149533812640388s^{50}+30338905815230015350337507443629547938133322986372599251613731735431147148807587298s^{49}-628396204847897965060061083685759495211044889335692127791727849670706521484518435856s^{48}+12386583193977551660461241876390719826604576164873235895959785437607584760441587730192s^{47}-232433724444205471983096462597776075369365835330568989261391110164425311728212391035632s^{46}+4153323734217430140145070137613411920743170003732119525339537946385437046481746033523872s^{45}-70686380467717783902448903568646078963423628086622300763415121270383317250590261969131336s^{44}+1146011275499749445486974909121594149473099806147735475740109750306258973873693081841338630s^{43}-17701136698331714953844021503637463123650314086731790857767064280112784186506532020777615276s^{42}+260492277459372683985340515012561460001230750454462824800331349575718851511822995239394574714s^{41}-3652320068116991521691903234094675077664783199210342925565230028260558957233172085378428693648s^{40}+48786365568085939831648565613081789083584480449521988080326278540514634832953535303132015187720s^{39}-620776840486987337546656613456515581406101803594950169186131730819070047268868384631491241542280s^{38}+7523288801124157164696453440451668126537802179655932385275366967957982556047497857359919983352588s^{37}-86819738273128010242526385979967991470567862056150689620462183702554367768947413111616038233016416s^{36}+953774954925025648253304474733609592484747994431472390301868754639755982678716269084529930641443023s^{35}-9971081293651892380457737953978637874233272651346699205006125992828217866601482502757629011345866570s^{34}+99159113935527095843791193320314995744620431737333925602216138254954437828859473360567133620147394445s^{33}-937591882456243116942831217151994956616595933093755511723294563972551195048414611565248985607152821236s^{32}+8424667140126948167633953265193969962679276499025327494839034104790577492192909219817624591386758730279s^{31}-71892659494830178227616871456048478350079377496302951700870381917053589308972575388983039596535479420278s^{30}+582251421494115025057046976615977029976720394400712813199098003690123303907349827395875756580289035731733s^{29}-4471937667537034121585882112126200967254037591271575148365797097846048547850509627026833861786334101222136s^{28}+32543614650180016207874244187164028503629361855235911764700956406683943044733068359145297584031071397155994s^{27}-224183523933854882502864682078640188285826762871716486751957673723635189271192115484721934301078509843540820s^{26}+1460312333249097739412739848153412311136035088888884922686424538738960526601793346522957489286185673762602902s^{25}-8984148217876593612167877570397820635649870435669726928588777366245474742877218816201439836639845502892953560s^{24}+52134501077125370653590265849501908514957010403776225078820415168994018070692909692704843148671899014807836538s^{23}-284941297083362220078712187212822093342654560298933781771361807935255252780142074341846765908056419933065354916s^{22}+1464404571156043076914637252120097347255977567642248877431122565189765063022644175773142656036823662408630919410s^{21}-7064080779433205483997411627458329256081928935674885720573960927817446941144054662390438254917264293853571028424s^{20}+31919881457624033726193536951838036401111886302890312451699329606929040067283389942070240214272698940267541956493s^{19}-134801722329859078816742606094646334228067206837309021726684217834848607820988762454709381034223562103046457675998s^{18}+530707012396024913429576740380121941086737225273466472672403349930854389215481675641529836588022052334151834279003s^{17}-1942205476550803484882315247161577147422888428395169781637047795709098197490266699760943181834041758117906367397268s^{16}+6585767384476720675187977121595259536735035857996075281802198937005198489937485851461054520341053364378881846325263s^{15}-20614892940117095331097736607876870976314189060882921080291907574510740821764737500291921914248821586266401315666942s^{14}+59316353011229384909666880954476222015479423693489595098884075044567497728679992849404330173399583652230381335502305s^{13}-156117670782437502269990886042735284992957692699464203987769629925609348266900609376317045942894365095896351357414520s^{12}+373698270769972479755939957244422481116455737532015818487606025512111631824244935754777237146223432771503247544608560s^{11}-808048121315624822538485230387020159879703732818682364581834764813478780649668941927219429385916131623619099840318128s^{10}+1565583417239292630942979288694634658573835168674069318551077876822765011658251873382962913367365429573513955164437064s^9-2691230551310123431856658453025381333299196967548104418289076204697729928184484894708129837595375747556018998818512192s^8+4054542066273187475893579325962915065845321084583224373643180486702374676704731329107411831884877578115801740253541904s^7-5270878662724145249388262906951781140123258747428763886318687210813398134336463475140327838867254422860035408448158432s^6+5792836201656880167367652921094881746142782983189532980946755918671194010952081295188183352763611672876752443571623568s^5-5233614558124453824846563012926178182173958634839557295689659286203290796724301748107667652717293231008062406343836800s^4+3732102862328364130585244845143109502510706215299361787475517662634187688740089578345011212002758654232473965037848832s^3-1969628432244786328367806409266293170003496844663625159204453312874075246094750590119459796978694116823499446641506304s^2+683920819913111461189983402245349089127449075173547013376466597761071475636877690918573610486424418270329963001143296s-117203977757280124647356183279343983773836101226288348510440504667964165618210763520372674407323269025478320565518336=0$
236
$s = {}^{12}🔒 = \Nn{15.87607676541001}$
$6596s^6-(619856+19000\sqrt{2})s^5+(24226944+1444540\sqrt{2})s^4-(504036792+43818500\sqrt{2})s^3+(5886496273+662906450\sqrt{2})s^2-(36585732598+5001593450\sqrt{2})s+94529982167+15055629320\sqrt{2}=0$
$26384s^{12}-4958848s^{11}+426380416s^{10}-22179443008s^9+777414394344s^8-19344554351312s^7+350411708641272s^6-4655972006018640s^5+45039272938487593s^4-309348405383979564s^3+1432057511182322314s^2-4011939813305628468s+5144071303851334561=0$
237
$s = {29\over 2} + \sqrt 2 = \Nn{15.91421356237309}$
238
$s = \Nn{15.93984676308969}$
239
$s = \Nn{15.95643304058435}$
240
$s = \Nn{15.97559404379946}$
241
$s = \Nn{15.99091684780193}$
257
$s = 13 + {5\over 2}\sqrt 2 = \Nn{16.53553390593273}$
258
$s = {19\over 2} + 5 \sqrt 2 = \Nn{16.57106781186547}$
259
$s = {}^{8}🔒 = \Nn{16.60257141234448}$
$150s^4-(11600+1720\sqrt{2})s^3+(324554+80686\sqrt{2})s^2-(3938328+1264082\sqrt{2})s+6617328\sqrt{2}+17614577=0$
$22500s^8-3480000s^7+226009400s^6-8156031520s^5+180271536264s^4-2511556300176s^3+21612680769420s^2-105284582762928s+222695263169761=0$
260
$s = 11 + 4 \sqrt 2 = \Nn{16.65685424949238}$
261
$s = 16 + {28\over 41} = \Nn{16.68292682926829}$
262
$s = 16 + {1\over 2}\sqrt 2 = \Nn{16.70710678118654}$
263
$s = {25\over 2} + 3 \sqrt 2 = \Nn{16.74264068711928}$
264, 265
$s = 9 + {11\over 2}\sqrt 2 = \Nn{16.77817459305202}$
266
$s = {}^{32}🔒 = \Nn{16.82306208283780}$
$2401s^{32}-1162084s^{31}+263199482s^{30}-36971795756s^{29}+3593304360857s^{28}-254523535144036s^{27}+13408548240776810s^{26}-519901936408593644s^{25}+13805430523268790240s^{24}-171760035794017558004s^{23}-4426818799267672804198s^{22}+326745541238344524670064s^{21}-10052823560617182774582207s^{20}+181074087488548519346667052s^{19}-1180165534713863709787052484s^{18}-39814767996810201813233201880s^{17}+1608559573416436468095371051805s^{16}-32123383071505854643466513964696s^{15}+412614513240021198536387912093202s^{14}-3166929683248511957762311522115552s^{13}+4864413227687588362660593637481982s^{12}+178773674416065677195226856423404204s^{11}-1078437021027255344046160578887057944s^{10}-30113420634289372798330615891075770272s^9+791230647693671970529285145442783714082s^8-10342818482011428376427887130138935213892s^7+91890490062472897914498395018088233984940s^6-595883639785360944056309451122760067196636s^5+2858083210066295032341927117330041150532457s^4-9961121615142990990156112009477337084333564s^3+23996879793794528190240708983850819688279982s^2-35874639749283350605126520242841070953510704s+25142156270060598069723106950936800398659193=0$
267
$\begin{aligned}s &= 16-{1\over 2}\sqrt 2+\sqrt{1+\sqrt 2} \\ &= \Nn{16.84666719284348}\end{aligned}$
268
$s = {}^{6}🔒 = \Nn{16.87933209237563}$
$2s^6-176s^5+6280s^4-115238s^3+1129107s^2-5432722s+9316447=0$
269
$s = {}^{8}🔒 = \Nn{16.90596764828402}$
$1338s^4-(92136+4180\sqrt{2})s^3+(2378600+206890\sqrt{2})s^2-(27290208+3419060\sqrt{2})s+18867680\sqrt{2}+117431679=0$
$8028s^8-1105632s^7+66453952s^6-2277483296s^5+48690729660s^4-665109430256s^3+5669988144368s^2-27584892248768s+58646728859167=0$
270
$s = \Nn{16.94073593015457}$
271
$s = \Nn{16.95509447506437}$
272
$s = \Nn{16.96980702828259}$
273
$s = \Nn{16.98832058897683}$
290, 291
$s = 14 + {5\over 2}\sqrt 2 = \Nn{17.53553390593273}$
292
$s = {}^{8}🔒 = \Nn{17.60257141234448}$
$150s^4-(12200+1720\sqrt{2})s^3+(360254+85846\sqrt{2})s^2-(4622836+1430614\sqrt{2})s+21889209+7963816\sqrt{2}=0$
$22500s^8-3660000s^7+250999400s^6-9586427920s^5+224565209864s^4-3318846008432s^3+30314003053732s^2-156807860101352s+352292740081969=0$
293
$s = 17 + {26\over 41} = \Nn{17.63414634146341}$
294
$s = 12 + 4 \sqrt 2 = \Nn{17.65685424949238}$
295, 296
$s = 17 + {1\over 2}\sqrt 2 = \Nn{17.70710678118654}$
297
$s = \Nn{17.74116992948972}$
298
$s = 10 + {11\over 2}\sqrt 2 = \Nn{17.77817459305202}$
299
$s = {33\over 2} + {1\over 2}\sqrt 7 = \Nn{17.82287565553229}$
300
$s = {}^{40}🔒 = \Nn{17.82412338847854}$
$6765201s^{40}-4468746888s^{39}+1431055332684s^{38}-295991953326108s^{37}+44445603736025352s^{36}-5163220519287531048s^{35}+482878985597614632366s^{34}-37353497397438488815260s^{33}+2436831832955268577880066s^{32}-136013384348919954233715980s^{31}+6566863009941672632548971230s^{30}-276576685299846988827282188436s^{29}+10227647719730769459718165452749s^{28}-333724070621087598910090605855348s^{27}+9643524705514237911246918698322714s^{26}-247404094366714093683897197709917204s^{25}+5643119674396861410915876260884036989s^{24}-114477712300768469604781612467804162660s^{23}+2063707000134940629708077092426963028132s^{22}-32985932723685807897922726019150035754248s^{21}+465583759504110006491405487605416144111553s^{20}-5764247971291523576624473899585978835759824s^{19}+61914526137823063569936032519366359362310830s^{18}-566147126795280425805190165571461577530656336s^{17}+4248816809091624736372842695988910574840203032s^{16}-23948399126640716409385371068745856498999580804s^{15}+69800847299887214247772249238723707512987918380s^{14}+394782152673201159198736947784032596106016880136s^{13}-7828936745814934561867828618761111333890039348250s^{12}+67387777391090638044324068706351575262477706086740s^{11}-381562083381768156325668597682082463480074995868360s^{10}+1336650893593888696724108652818662244745263296865588s^9-614601349329475752238933120184261110575651083354603s^8-28305247058854021955410328849850580588215220244356248s^7+224981301926271768349655651977718726650378985178322646s^6-1055948455747248748890178989019952798681204013121554736s^5+3473810396018259264801879879806884179343515176608754025s^4-8177313821139351944992551555783250987371382184946020000s^3+13278518858240943321872383441026571982205038824476375000s^2-13426397690512873291977824583646716429736153596450000000s+6401405918124622124119207874790462553248468260156250000=0$
301
$s = \Nn{17.86899185179999}$
302
$s = {}^{4}🔒 = \Nn{17.88674602860566}$
$s^4-66s^3+1631s^2-17882s+73369=0$
303
$s = \Nn{17.93127894394689}$
304
$s = \Nn{17.94917201919110}$
305
$s = \Nn{17.96075558628675}$
306
$s = \Nn{17.96926975248972}$
307
$s = \Nn{17.98281564631754}$
626
$s = {27\over 2} + {17\over 2}\sqrt 2 = \Nn{25.52081528017130}$
1453
$s = {}^{62}🔒 = \Nn{38.62811880681648}$
$14057529258938368s^{62}-16144332707905069056s^{61}+4126908192850362814464s^{60}-114048398674982625548288s^{59}-52812457965071023131108736s^{58}+3123757315293716451259828736s^{57}+395914808055074354598655919872s^{56}-25655581919693099977675345288928s^{55}-2342138210856135887439487492867911s^{54}+130614558810433031715467943008591574s^{53}+9582864850318173225492635922395708673s^{52}-400208116572281336325713849443556893320s^{51}-19278076716042492939533753042312495338866s^{50}+155639463279626013183461774071774170428332s^{49}-22682951311029575205053841559156685327668694s^{48}+4481148848166715045575771589473008085986195508s^{47}+339908983431725009307125627170625587965064721641s^{46}-21836898654237099253200945764943586503872843975282s^{45}-1733607911337837421674786648905767199367409287630091s^{44}+65577710215566787889219323647412546993333020408126340s^{43}+6575020048126915878362134657166967660162756051625767082s^{42}-189919577494849234065185357103567819076518682190184112052s^{41}-18786350786500438406048733796469585237988085985102482357718s^{40}+577860661366947067720361099304613584329095511092740182446472s^{39}+38560113418007612161265092791117116831719699647020808115500290s^{38}-1509778230715804736044763817572589857709434302255396595167198724s^{37}-53691061034745282967831861830008396823011099992793727965608258808s^{36}+2981962876446433126961251394849875590796626863624033992874793421944s^{35}+42946650830136738474116255305854244294539529383743966678795990596614s^{34}-4305207796096057376307480627217176796778265873544269426186757603548600s^{33}+847984922128592247433827812551628892707545393068784907659271398018534s^{32}+4472381287851045675238737659317271974769806475510817553632400089733850984s^{31}-54024990039620679626108375115227820285123938297900797999074130495666406019s^{30}-3193681274533744120801748520386719645289103551859824962842504952991692546322s^{29}+80917624554132100648898693934599191301469617060018407110555412748900902279137s^{28}+1304198975666560613729453090086267184069864122474264569263280366382519245805416s^{27}-69287844982281380279236661128207636125050487817999177431635188503445709265641520s^{26}+68996038980379916684164096301103219794837210102541034822026299278384997449217692s^{25}+37867353091715263710849645403683336968945849908862704327076999773411927727397591158s^{24}-509915867359895925422359611092573447179100380327510553509286921447269433977643865508s^{23}-11683211944540307067146210206410836570815757425407896484941417171550422135445264863064s^{22}+368827309307507537219147042570180764187110525313995270219698774784754026548995528531660s^{21}+185724218102520508187862654139453737315454289351002925523872644784163316111213102216680s^{20}-136830853415425229763805282272266732584005552776626700663010740658119017917916268390287556s^{19}+1547848085441210529100258771205521079963814294017010309696882835752388457232036205727597039s^{18}+21914646855044175829856156796290016500376182741174287509692603427850292470216693384112852346s^{17}-642013029716693421472434447425253341135587415866685406570588222982341705951674252923582041795s^{16}+2430889433553432642414397495285152141337085610751304554696488205951846350369700845506363822732s^{15}+92064055623459052561344041325712052237179537558423822365643138628075940784085506754380742599882s^{14}-1436706418001841492955377568562805242864121009591891493210031742373552154899343547291316137557908s^{13}+4993033976064547466127206717163229131723638752386640105025500484333917749253388698555336828511242s^{12}+96031442149539838915450548148896134358831811633526781603086096632377321989140256994318562339417100s^{11}-1733048273294974846832844855482169873194419439395735002201619922770668316679232678681162587124552260s^{10}+15770820434262396395851079386321352123276831933189279029980483538751595421431357063482729417803984580s^9-97278075882540976992627527924963133628721769353102052957581703613903792317825205295534444102067365466s^8+463911493164648755268346400550691149594031202366680322675918086734493393306092169030187572680145939860s^7-2090656957701197789966258215824701051567847005345271229373699635289968414443018273787166250135969126875s^6+9442609168926974312630527590013048294221786119093364465176592130998930554703600095438263441086719047690s^5-39415054084443633566696762271703899900300756149352769966371040153484310767724118279361770290440553743801s^4+156031640636394568927996748174625458407871841132601217731374082667948155491740616882144255248507174778908s^3-496791378964789968261213028274305514593846288225401594028735451597189456726232160601931666507937957449457s^2+1305836137839118688998085219859481571482741756188636214545184411851028521415422566589743034644001594557270s-3410485277066865875954124600874980278861680322256497845789816598547317193010330644022088333312859866677675=0$
1765
$s = {}^{4}🔒 = \Nn{42.48797851186022}$
$2s^4-212s^3+8129s^2-148140s+1362276=0$
1850
$s = {}^{4}🔒 = \Nn{43.48878088476276}$
$2s^4-224s^3+9311s^2-185004s+1705932=0$
2043
$s = {}^{12}🔒 = \Nn{45.69644276992823}$
$4s^{12}-1608s^{11}+293084s^{10}-31920420s^9+2301941449s^8-114905182392s^7+4022452365218s^6-97595016541596s^5+1574653827588509s^4-15396232508703888s^3+72639007870740216s^2-58090491554723760s+46014771089277232=0$