History of Roots of the cuckoo hashing threshold equation

   number-header: $\xi_{k,\ell}$ Numbers:-  '2':-    '2':-      number: '2.687999345499491341463796937790041489618073899549236397935209599334514422260144214209251869745312739'-      comment: The associated cuckoo hashing threshold is HREF{T274#2,2}[$c^*_{2,2}$].-    '3':-      number: '5.071469708158110598648643546349746111224536523134635041837351018367446479545269819843879943093996070'-      comment: The associated cuckoo hashing threshold is HREF{T274#2,3}[$c^*_{2,3}$].-    '4':-      number: '7.321703358983259836814496629523591100449318121409982457321275056792696725897271000383910518926918359'-      comment: The associated cuckoo hashing threshold is HREF{T274#2,4}[$c^*_{2,4}$].-    '5':-      number: '9.496116339631318678686127155202154774263071948634199710067456727225709958713336937514852230633003440'-      comment: The associated cuckoo hashing threshold is HREF{T274#2,5}[$c^*_{2,5}$].-    '6':-      number: '11.62201083475983117017772549639697906479047433129974127980306614609092022913414759542897782318128499'-      comment: The associated cuckoo hashing threshold is HREF{T274#2,6}[$c^*_{2,6}$].-  '3':-    '1':-      number: '2.149125799907062542079080149425149925528828496714285459034660801183768221524370129087681616217046728'-      comment: The associated cuckoo hashing threshold is HREF{T274#3,1}[$c^*_{3,1}$].-        This is also HREF{T287#3}[$\xi_{3}$].-    '2':-      number: '5.656576349425156386746617941568588192659141691293506742008009681442341139286464459237741396129083249'-      comment: The associated cuckoo hashing threshold is HREF{T274#3,2}[$c^*_{3,2}$].-    '3':-      number: '8.849851652473190362812087757716704933249004939448022043446615039577597636956590060258950889502471470'-      comment: The associated cuckoo hashing threshold is HREF{T274#3,3}[$c^*_{3,3}$].-    '4':-      number: '11.93324063021001784506567092268224882890651379335616698876346069366242440532751486950076095207023045'-      comment: The associated cuckoo hashing threshold is HREF{T274#3,4}[$c^*_{3,4}$].-    '5':-      number: '14.97035798828812027443562587311940396807103878054315654978741750621682886826142355899362774443783528'-      comment: The associated cuckoo hashing threshold is HREF{T274#3,5}[$c^*_{3,5}$].-    '6':-      number: '17.98693229671281992725192590653386429471971042695500411009746368493209696294996668806395227602097357'-      comment: The associated cuckoo hashing threshold is HREF{T274#3,6}[$c^*_{3,6}$].-  '4':-    '1':-      number: '3.593511969447426082272169884555315798860946340951301392760865045230967927293167350976509334752600022'-      comment: The associated cuckoo hashing threshold is HREF{T274#4,1}[$c^*_{4,1}$].-        This is also HREF{T287#4}[$\xi_{4}$].-    '2':-      number: '7.907674019123758850790566789844419922995108412022415004802350765389662552216371593154538151656605121'-      comment: The associated cuckoo hashing threshold is HREF{T274#4,2}[$c^*_{4,2}$].-    '3':-      number: '11.97840754548836518417183962921129418652192059426167092339410984246940990181779382295840160771130815'-      comment: The associated cuckoo hashing threshold is HREF{T274#4,3}[$c^*_{4,3}$].-    '4':-      number: '15.99506456917725118329956899417052588708356806076354172978753823547047795118689779120004162634038769'-      comment: The associated cuckoo hashing threshold is HREF{T274#4,4}[$c^*_{4,4}$].-    '5':-      number: '19.99889979196351691674775775685275577102351928181638457324870251227217088836762137643885395177578993'-      comment: The associated cuckoo hashing threshold is HREF{T274#4,5}[$c^*_{4,5}$].-    '6':-      number: '23.99975947604794575691841460248553012829750258139642040533729634692718122214453372206287303646511694'-      comment: The associated cuckoo hashing threshold is HREF{T274#4,6}[$c^*_{4,6}$].-  '5':-    '1':-      number: '4.801007549722517843402554184936876206309580045670987737307642940448096932959992199826971793616174495'-      comment: The associated cuckoo hashing threshold is HREF{T274#5,1}[$c^*_{5,1}$].-        This is also HREF{T287#5}[$\xi_{5}$].-    '2':-      number: '9.976864303760496064518075863793575319292786047595390211066663963569991540942269856056674145453186667'-      comment: The associated cuckoo hashing threshold is HREF{T274#5,2}[$c^*_{5,2}$].-    '3':-      number: '14.99741350114707424427436529215687505875158666319175852037547329980901221594064290374107937980231339'-      comment: The associated cuckoo hashing threshold is HREF{T274#5,3}[$c^*_{5,3}$].-    '4':-      number: '19.99972511819509434997149501618076756231262856417056906108861824236177909822971068355118859476119916'-      comment: The associated cuckoo hashing threshold is HREF{T274#5,4}[$c^*_{5,4}$].-    '5':-      number: '24.99997174425962980488681204119343855489405198561699586682058895464280942938737404120353105180800265'-      comment: The associated cuckoo hashing threshold is HREF{T274#5,5}[$c^*_{5,5}$].-    '6':-      number: '29.99999715761549573994778634148325126494830338224240111896361395105934488672352627555997411293020102'-      comment: The associated cuckoo hashing threshold is HREF{T274#5,6}[$c^*_{5,6}$].-  '6':-    '1':-      number: '5.903000058948943810458175385422799724242893481515842146827627134583507853576375177519654679441566068'-      comment: The associated cuckoo hashing threshold is HREF{T274#6,1}[$c^*_{6,1}$].-        This is also HREF{T287#6}[$\xi_{6}$].-    '2':-      number: '11.99466733019710920890189533055350295714134739551676260854413064936109585534197475883076176045683468'-      comment: The associated cuckoo hashing threshold is HREF{T274#6,2}[$c^*_{6,2}$].-    '3':-      number: '17.99973347635061616803411249948014909629259883939838752321236504416573051808206817338186269012884600'-      comment: The associated cuckoo hashing threshold is HREF{T274#6,3}[$c^*_{6,3}$].-    '4':-      number: '23.99998747487764539641451256705490343509005188952388808136197333588086708276694929140893017510583906'-      comment: The associated cuckoo hashing threshold is HREF{T274#6,4}[$c^*_{6,4}$].-    '5':-      number: '29.99999943152413327868681837784491101013451684606105198098041990967162124172322669914399673273473956'-      comment: The associated cuckoo hashing threshold is HREF{T274#6,5}[$c^*_{6,5}$].-    '6':-      number: '35.99999997475451784136341288345456857119692422196366712451810528566280859222197757374080216380199990'-      comment: The associated cuckoo hashing threshold is HREF{T274#6,6}[$c^*_{6,6}$].-  '7':-    '1':-      number: '6.953455713353474571757750459668776777157703675694193843415968941936946472738479953900380174362202268'-      comment: The associated cuckoo hashing threshold is HREF{T274#7,1}[$c^*_{7,1}$].-        This is also HREF{T287#7}[$\xi_{7}$].-    '2':-      number: '13.99885801107353040821026786739382027366723850806829945798703162739514390358101431148202137692247181'-      comment: The associated cuckoo hashing threshold is HREF{T274#7,2}[$c^*_{7,2}$].-    '3':-      number: '20.99997542174545116865984920724717820919492653448481645717520596822045513748851642102679476382231719'-      comment: The associated cuckoo hashing threshold is HREF{T274#7,3}[$c^*_{7,3}$].-    '4':-      number: '27.99999950416907812559837246489148384069148256876607111079228415555129553225681370701807267652350603'-      comment: The associated cuckoo hashing threshold is HREF{T274#7,4}[$c^*_{7,4}$].-    '5':-      number: '34.99999999034126708478328429759287181356009191496219282981587565655646617784379490803056882062904127'-      comment: The associated cuckoo hashing threshold is HREF{T274#7,5}[$c^*_{7,5}$].-    '6':-      number: '41.99999999981590402367849092443096959604956068083312186280042756840973653364740468966946712440564761'-      comment: The associated cuckoo hashing threshold is HREF{T274#7,6}[$c^*_{7,6}$].+- comment: The associated cuckoo hashing threshold is HREF{T274#2,2}[$c^*_{2,2}$].+  params:+    k: '2'+    ell: '2'+  number: '2.687999345499491341463796937790041489618073899549236397935209599334514422260144214209251869745312739'+- comment: The associated cuckoo hashing threshold is HREF{T274#2,3}[$c^*_{2,3}$].+  params:+    k: '2'+    ell: '3'+  number: '5.071469708158110598648643546349746111224536523134635041837351018367446479545269819843879943093996070'+- comment: The associated cuckoo hashing threshold is HREF{T274#2,4}[$c^*_{2,4}$].+  params:+    k: '2'+    ell: '4'+  number: '7.321703358983259836814496629523591100449318121409982457321275056792696725897271000383910518926918359'+- comment: The associated cuckoo hashing threshold is HREF{T274#2,5}[$c^*_{2,5}$].+  params:+    k: '2'+    ell: '5'+  number: '9.496116339631318678686127155202154774263071948634199710067456727225709958713336937514852230633003440'+- comment: The associated cuckoo hashing threshold is HREF{T274#2,6}[$c^*_{2,6}$].+  params:+    k: '2'+    ell: '6'+  number: '11.62201083475983117017772549639697906479047433129974127980306614609092022913414759542897782318128499'+- comment: The associated cuckoo hashing threshold is HREF{T274#3,1}[$c^*_{3,1}$].+    This is also HREF{T287#3}[$\xi_{3}$].+  params:+    k: '3'+    ell: '1'+  number: '2.149125799907062542079080149425149925528828496714285459034660801183768221524370129087681616217046728'+- comment: The associated cuckoo hashing threshold is HREF{T274#3,2}[$c^*_{3,2}$].+  params:+    k: '3'+    ell: '2'+  number: '5.656576349425156386746617941568588192659141691293506742008009681442341139286464459237741396129083249'+- comment: The associated cuckoo hashing threshold is HREF{T274#3,3}[$c^*_{3,3}$].+  params:+    k: '3'+    ell: '3'+  number: '8.849851652473190362812087757716704933249004939448022043446615039577597636956590060258950889502471470'+- comment: The associated cuckoo hashing threshold is HREF{T274#3,4}[$c^*_{3,4}$].+  params:+    k: '3'+    ell: '4'+  number: '11.93324063021001784506567092268224882890651379335616698876346069366242440532751486950076095207023045'+- comment: The associated cuckoo hashing threshold is HREF{T274#3,5}[$c^*_{3,5}$].+  params:+    k: '3'+    ell: '5'+  number: '14.97035798828812027443562587311940396807103878054315654978741750621682886826142355899362774443783528'+- comment: The associated cuckoo hashing threshold is HREF{T274#3,6}[$c^*_{3,6}$].+  params:+    k: '3'+    ell: '6'+  number: '17.98693229671281992725192590653386429471971042695500411009746368493209696294996668806395227602097357'+- comment: The associated cuckoo hashing threshold is HREF{T274#4,1}[$c^*_{4,1}$].+    This is also HREF{T287#4}[$\xi_{4}$].+  params:+    k: '4'+    ell: '1'+  number: '3.593511969447426082272169884555315798860946340951301392760865045230967927293167350976509334752600022'+- comment: The associated cuckoo hashing threshold is HREF{T274#4,2}[$c^*_{4,2}$].+  params:+    k: '4'+    ell: '2'+  number: '7.907674019123758850790566789844419922995108412022415004802350765389662552216371593154538151656605121'+- comment: The associated cuckoo hashing threshold is HREF{T274#4,3}[$c^*_{4,3}$].+  params:+    k: '4'+    ell: '3'+  number: '11.97840754548836518417183962921129418652192059426167092339410984246940990181779382295840160771130815'+- comment: The associated cuckoo hashing threshold is HREF{T274#4,4}[$c^*_{4,4}$].+  params:+    k: '4'+    ell: '4'+  number: '15.99506456917725118329956899417052588708356806076354172978753823547047795118689779120004162634038769'+- comment: The associated cuckoo hashing threshold is HREF{T274#4,5}[$c^*_{4,5}$].+  params:+    k: '4'+    ell: '5'+  number: '19.99889979196351691674775775685275577102351928181638457324870251227217088836762137643885395177578993'+- comment: The associated cuckoo hashing threshold is HREF{T274#4,6}[$c^*_{4,6}$].+  params:+    k: '4'+    ell: '6'+  number: '23.99975947604794575691841460248553012829750258139642040533729634692718122214453372206287303646511694'+- comment: The associated cuckoo hashing threshold is HREF{T274#5,1}[$c^*_{5,1}$].+    This is also HREF{T287#5}[$\xi_{5}$].+  params:+    k: '5'+    ell: '1'+  number: '4.801007549722517843402554184936876206309580045670987737307642940448096932959992199826971793616174495'+- comment: The associated cuckoo hashing threshold is HREF{T274#5,2}[$c^*_{5,2}$].+  params:+    k: '5'+    ell: '2'+  number: '9.976864303760496064518075863793575319292786047595390211066663963569991540942269856056674145453186667'+- comment: The associated cuckoo hashing threshold is HREF{T274#5,3}[$c^*_{5,3}$].+  params:+    k: '5'+    ell: '3'+  number: '14.99741350114707424427436529215687505875158666319175852037547329980901221594064290374107937980231339'+- comment: The associated cuckoo hashing threshold is HREF{T274#5,4}[$c^*_{5,4}$].+  params:+    k: '5'+    ell: '4'+  number: '19.99972511819509434997149501618076756231262856417056906108861824236177909822971068355118859476119916'+- comment: The associated cuckoo hashing threshold is HREF{T274#5,5}[$c^*_{5,5}$].+  params:+    k: '5'+    ell: '5'+  number: '24.99997174425962980488681204119343855489405198561699586682058895464280942938737404120353105180800265'+- comment: The associated cuckoo hashing threshold is HREF{T274#5,6}[$c^*_{5,6}$].+  params:+    k: '5'+    ell: '6'+  number: '29.99999715761549573994778634148325126494830338224240111896361395105934488672352627555997411293020102'+- comment: The associated cuckoo hashing threshold is HREF{T274#6,1}[$c^*_{6,1}$].+    This is also HREF{T287#6}[$\xi_{6}$].+  params:+    k: '6'+    ell: '1'+  number: '5.903000058948943810458175385422799724242893481515842146827627134583507853576375177519654679441566068'+- comment: The associated cuckoo hashing threshold is HREF{T274#6,2}[$c^*_{6,2}$].+  params:+    k: '6'+    ell: '2'+  number: '11.99466733019710920890189533055350295714134739551676260854413064936109585534197475883076176045683468'+- comment: The associated cuckoo hashing threshold is HREF{T274#6,3}[$c^*_{6,3}$].+  params:+    k: '6'+    ell: '3'+  number: '17.99973347635061616803411249948014909629259883939838752321236504416573051808206817338186269012884600'+- comment: The associated cuckoo hashing threshold is HREF{T274#6,4}[$c^*_{6,4}$].+  params:+    k: '6'+    ell: '4'+  number: '23.99998747487764539641451256705490343509005188952388808136197333588086708276694929140893017510583906'+- comment: The associated cuckoo hashing threshold is HREF{T274#6,5}[$c^*_{6,5}$].+  params:+    k: '6'+    ell: '5'+  number: '29.99999943152413327868681837784491101013451684606105198098041990967162124172322669914399673273473956'+- comment: The associated cuckoo hashing threshold is HREF{T274#6,6}[$c^*_{6,6}$].+  params:+    k: '6'+    ell: '6'+  number: '35.99999997475451784136341288345456857119692422196366712451810528566280859222197757374080216380199990'+- comment: The associated cuckoo hashing threshold is HREF{T274#7,1}[$c^*_{7,1}$].+    This is also HREF{T287#7}[$\xi_{7}$].+  params:+    k: '7'+    ell: '1'+  number: '6.953455713353474571757750459668776777157703675694193843415968941936946472738479953900380174362202268'+- comment: The associated cuckoo hashing threshold is HREF{T274#7,2}[$c^*_{7,2}$].+  params:+    k: '7'+    ell: '2'+  number: '13.99885801107353040821026786739382027366723850806829945798703162739514390358101431148202137692247181'+- comment: The associated cuckoo hashing threshold is HREF{T274#7,3}[$c^*_{7,3}$].+  params:+    k: '7'+    ell: '3'+  number: '20.99997542174545116865984920724717820919492653448481645717520596822045513748851642102679476382231719'+- comment: The associated cuckoo hashing threshold is HREF{T274#7,4}[$c^*_{7,4}$].+  params:+    k: '7'+    ell: '4'+  number: '27.99999950416907812559837246489148384069148256876607111079228415555129553225681370701807267652350603'+- comment: The associated cuckoo hashing threshold is HREF{T274#7,5}[$c^*_{7,5}$].+  params:+    k: '7'+    ell: '5'+  number: '34.99999999034126708478328429759287181356009191496219282981587565655646617784379490803056882062904127'+- comment: The associated cuckoo hashing threshold is HREF{T274#7,6}[$c^*_{7,6}$].+  params:+    k: '7'+    ell: '6'+  number: '41.99999999981590402367849092443096959604956068083312186280042756840973653364740468966946712440564761'+- params:+    k: '2'+    ell: '7'+  number: '13.71478188066531187419592663386781404667256909748779267691699334062513889841987887243770904218501949'+- params:+    k: '2'+    ell: '8'+  number: '15.78402951575241749514337877292627806948039669526522457278218532643843899662344975085249937108013643'+- params:+    k: '3'+    ell: '7'+  number: '20.99428721963569996390356939647821605540269988019492846111677264277639899563812999474020204223244644'+- params:+    k: '3'+    ell: '8'+  number: '23.99752228639355428601762208898877869365731075533340009984939339959751647474711325899830231566627929'+- params:+    k: '4'+    ell: '7'+  number: '27.99994816711800378712866883725114403620723445488544625643687745996149027919522284745023750300229475'+- params:+    k: '4'+    ell: '8'+  number: '31.99998894879824441417761862037158295979322617563944053294099209179496582008077917131009191700694329'+- params:+    k: '5'+    ell: '7'+  number: '34.99999971828689495073763165197240517066200863512164923396388731330097929439240393661829966466206228'+- params:+    k: '5'+    ell: '8'+  number: '39.99999997237895330621788962981778883738297516823892960097598945470307781177261883554921351313680319'+- params:+    k: '6'+    ell: '7'+  number: '41.99999999889542414122366233303485143320654681741093711561127695504527103766420273066250232144793028'+- params:+    k: '6'+    ell: '8'+  number: '47.99999999995219035911121073083261956776388908486262174893059213350857113390914160633563926285687229'+- params:+    k: '7'+    ell: '7'+  number: '48.99999999999654292747548744500679934181770500628007276070831287944725977561733647959273498745564802'+- params:+    k: '7'+    ell: '8'+  number: '55.99999999999993577845740933717347678095367153698328337540863073043813488092281488750741802432689143'+- params:+    k: '8'+    ell: '1'+  number: '7.978107736977070325801043211904953879262698393828180241246253405412112875926606187603354958634672340'+  comment: This is also HREF{T287#8}[$\xi_{8}$].+- params:+    k: '8'+    ell: '2'+  number: '15.99976948102927827986542124541488713267127746399729766072612805128795102265768110760940453279424376'+- params:+    k: '8'+    ell: '3'+  number: '23.99999791249776477526583476080506216234102397159993337514112341684209297104091256244852792327457149'+- params:+    k: '8'+    ell: '4'+  number: '31.99999998229421298460254326745152221550730148833673533729524296426543935216880675395508263187643527'+- params:+    k: '8'+    ell: '5'+  number: '39.99999999985498950806757475620303349980850606530853798231452429691164904454209053823396541671456058'+- params:+    k: '8'+    ell: '6'+  number: '47.99999999999883796011733170868052057137582534802368310535910608098338588451248045651064858878746216'+- params:+    k: '8'+    ell: '7'+  number: '55.99999999999999082549391562002909328701108769779675895602517556708034266361241800416573464377913288'+- params:+    k: '8'+    ell: '8'+  number: '63.99999999999999992834402649754375760190095303136801320458170026394134384645740733675987984543584298'+- params:+    k: '9'+    ell: '1'+  number: '8.989912519269479737859486962678439859820876867181214191191759058921700750894868987723157685967200046'+  comment: This is also HREF{T287#9}[$\xi_{9}$].+- params:+    k: '9'+    ell: '2'+  number: '17.99995558761294977966818068289267088363733341183405815612510976231904637506443052969637856628689981'+- params:+    k: '9'+    ell: '3'+  number: '26.99999983352352961042941034339633686304220206518353674195280425530683901186238491867268566768515694'+- params:+    k: '9'+    ell: '4'+  number: '35.99999999941561385098893372788096996561690281820301749212947615290516804614045183422834008690123778'+- params:+    k: '9'+    ell: '5'+  number: '44.99999999999801919305082234770327569019046986214351730820829668360886856474366257676088334662390077'+- params:+    k: '9'+    ell: '6'+  number: '53.99999999999999343065909329240090609003008758610857626415549884626998582815644147538220664394674172'+- params:+    k: '9'+    ell: '7'+  number: '62.99999999999999997853447576929085008477958958894807023008980265237111984961160627932241566256965976'+- params:+    k: '9'+    ell: '8'+  number: 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