Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 4 8 24
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P2 : 4*t^5 - 14*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P3 : 4*t^9 - 142/3*t^7 + 1399/9*t^5 - 2965/18*t^3 + 295/6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 24 Kronrod extension for:
P4 : 4*t^17 - 3059628507938/16753860777*t^15 + 159113012962007/50261582331*t^13 - 8081473967104151/301569493986*t^11 + 71537082906692561/603138987972*t^9 - 36627085158415339/134030886216*t^7 + 83781328830792607/268061772432*t^5 - 88756606077394045/536123544864*t^3 + 5750035763152135/178707848288*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^41 - 34539237527908905260857316469972740706664708066042839012136810786436119513149091462037632540019554963429980130112561582853828661922560205452081541845777488452674775273250880905162587167926303420095820254/29608085965386344001760983259998076955241787125225105880009980353549861538895780581813907218145201888145245294686407194901458402548258529479395531949748039368587482465275150240064487256826251441343719*t^39 + 229767368157832384706340281745950422999771601149948508546384500415028381000369168747389155248615658478634729677607262246774431483040299395655638910850054517172905701019645905910025706365364121390151900869113/1510012384234703544089810146259901924717331143386480399880508998031042938483684809672509268125405296295407510029006766939974378529961185003449172129437150007797961605729032662243288850098138823508529669*t^37 - 106660736974093957418392994882216086451629318132755378045245078307945811128511657286797223872617848446387293440438152167550125946557434435896063076540257277356805603341398113572009120589128931115490671732963685/9060074305408221264538860877559411548303986860318882399283053988186257630902108858035055608752431777772445060174040601639846271179767110020695032776622900046787769634374195973459733100588832941051178014*t^35 + 2737221881200349494278707118977052102699989834449358508017041253180992911608754703791894451521393894507686021355804985372601226734483744599739481461663094571913287818232057481843360450732894804942826277586074345/4530037152704110632269430438779705774151993430159441199641526994093128815451054429017527804376215888886222530087020300819923135589883555010347516388311450023393884817187097986729866550294416470525589007*t^33 - 307317139916168226842979150807132788344633318997821041855335579990193491082665086554510789971576821143307698096482746694946799196103693247009075415044738024719641041051236582321192307587827471087896489238201375515/14093448919523899744838228031759084630695090671607150398884750648289734092514391556943419835837116098757136760270729824773094199612971060032192273208080066739447641653470971514270695934249295686079610244*t^31 + 145186158891219740183894458580878843134574446456624505460313038671226048197742296667309011258327035903751746604819084688332984351650924914304201792307870716769764969028784741534579223404456250151412578176371329968323/253682080551430195407088104571663523352511632088928707179925511669215213665259048024981557045068089777628461684873136845915695593033479080579460917745441201310057549762477487256872526816487322349432984392*t^29 - 5656786938521774388108901443381870966415574477804537774312531179232988053728661106701667522023722652177057001695428032012267026680887180380731116954643334892735399647483243858296865058037206871301234191314068458363169/507364161102860390814176209143327046705023264177857414359851023338430427330518096049963114090136179555256923369746273691831391186066958161158921835490882402620115099524954974513745053632974644698865968784*t^27 + 3065504039308461159574504603617890163756916111685468370607678825594216258784358791974181638727839914514895822102057569468880320483417979292062269510701967832486720130220195882756714934114777381393027299694246064949649/18791265226031866326450970709012112840926787562142867198513000864386312123352522075924559781116154798342849013694306433030792266150628080042923030944106755652596855537961295352360927912332394248106146992*t^25 - 33879315072085252889809293135619043773527084997769237855480873636828070826528935488149173993116593749329529873952378298645413088103990161054321399672510747741018387549762610413522057333583179099658603934787017105863325/18791265226031866326450970709012112840926787562142867198513000864386312123352522075924559781116154798342849013694306433030792266150628080042923030944106755652596855537961295352360927912332394248106146992*t^23 + 2526708208938617055486028966431067257927525077653725450020885904307988684950830023289375787049375449099621878447031538033572139612255657195294405149808816534283575504039980639994583694320897682529002255788585692764325/167779153803855949343312238473322436079703460376275599986723222003449215387076089963612140902822810699489723336556307437774930947773465000383241347715238889755329067303225851360365427788682091500947741*t^21 - 53514777304401883338839011509763787850724947198854913557316579013492823990979422794823865773236078450492665725373318610057369287148028869716705105131078131664012255020233357038386062435920776005583433335509676654107525/565150833865620039893262276962770311005316919162191494692120326748460514988045776719535632514771572882491699659979140843031346350394829474975128750198699418123213700389813394055967756761876518740034496*t^19 + 118146428341858116632293677541044325010188060277460882285301484553010856344033016876723807355002737210886821627339261370742242221121375757539974943093534881543758664380827587113053922938297539560643679209770146764909275/265953333583821195243888130335421322826031491370443056325703683175746124700256836103310885889304269591760799839990183926132398282538743282341237058917035020293277035477559244261631885535000714701192704*t^17 - 815389571721305598012457522034284198383967879234156316541433496496704394813313468838476275426673124579071673014904920704070720501580473655003890646672689301820578201231989508202579325046969604016562435346894192304718475/531906667167642390487776260670842645652062982740886112651407366351492249400513672206621771778608539183521599679980367852264796565077486564682474117834070040586554070955118488523263771070001429402385408*t^15 + 4053554066099503643804096921858808693018635900385620957683846612792800701721367261666061531460866559590216953539678052432596980245210661055513943656317039383451801716980574128125967581305584379555829613140157967978222875/1063813334335284780975552521341685291304125965481772225302814732702984498801027344413243543557217078367043199359960735704529593130154973129364948235668140081173108141910236977046527542140002858804770816*t^13 - 14093942727452016864258853811061451151131346282198052187961759159231045749001988649101384070514695058289946549366181633541317808123711944057649259869297390202818132512231731308658099807803360391717988815516152195426659625/2127626668670569561951105042683370582608251930963544450605629465405968997602054688826487087114434156734086398719921471409059186260309946258729896471336280162346216283820473954093055084280005717609541632*t^11 + 65780395591159009861455405891270254873047371833500210526337104919503430853030892751780013471023016326354619872961022888976739328777558945385149154815109436698643351644076089335960359415314092132346066023604164546716446125/8510506674682278247804420170733482330433007723854177802422517861623875990408218755305948348457736626936345594879685885636236745041239785034919585885345120649384865135281895816372220337120022870438166528*t^9 - 97175262821511308207923024578473451059701010794046423754803940377676858818432053879687894215501245197544836649788347287071585235377329827993948214673111204885133053527504072324837748752769046347666121163761245169414864625/17021013349364556495608840341466964660866015447708355604845035723247751980816437510611896696915473253872691189759371771272473490082479570069839171770690241298769730270563791632744440674240045740876333056*t^7 + 83176064662009030819824040149620817593149792864056983239965806362817887495221383817311871231771087858909683163134962875049144432138762284355381663421451193223720251449551775114910984204543367786594372579322058591219729125/34042026698729112991217680682933929321732030895416711209690071446495503961632875021223793393830946507745382379518743542544946980164959140139678343541380482597539460541127583265488881348480091481752666112*t^5 - 35188495094096836950914934201933419313990150127375989656972802118290941885820435797451577462948521348673287981575211428169315756628439446505346663308525335868926014979468309016839582978643761061532739056243922359669091875/68084053397458225982435361365867858643464061790833422419380142892991007923265750042447586787661893015490764759037487085089893960329918280279356687082760965195078921082255166530977762696960182963505332224*t^3 + 2452928367689004633434457778873185406224267565660637400253903349566313649635937447506893271226055567760982457310382118529323092053534804708776100041714510754305551045987643741217523468743404939770439910895454915885261875/68084053397458225982435361365867858643464061790833422419380142892991007923265750042447586787661893015490764759037487085089893960329918280279356687082760965195078921082255166530977762696960182963505332224*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-6.6233613935604471635 - 4.9915733100731231424e-953j)  +/-  (1.31e-247, 1.31e-247j)
| (-1.0672470719421885588 - 7.5609393101224352787e-956j)  +/-  (1.44e-250, 1.44e-250j)
| (-7.3273227656192850919 + 3.9053595071798507031e-955j)  +/-  (1.26e-248, 1.26e-248j)
| (-5.5140955513625837945 + 4.1984392331354203696e-952j)  +/-  (1.35e-246, 1.35e-246j)
| (5.5140955513625837945 - 3.5250732008559840421e-952j)  +/-  (1.41e-246, 1.41e-246j)
| (-6.0381599529455616724 - 2.2587105728026615931e-952j)  +/-  (5.72e-247, 5.72e-247j)
| (6.6233613935604471635 - 5.6955723672092371325e-954j)  +/-  (1.24e-247, 1.24e-247j)
| (-1.4130206485936689977 + 1.7391554172150213915e-954j)  +/-  (1.36e-249, 1.36e-249j)
| (2.885756962383750957 + 1.4786827218536230622e-951j)  +/-  (5.41e-246, 5.41e-246j)
| (-4.5726189987872107779 - 4.1199525693697903649e-951j)  +/-  (3.42e-246, 3.42e-246j)
| (1.9710861567584257974 - 1.7087571240287254378e-953j)  +/-  (7.9e-248, 7.9e-248j)
| (7.3273227656192850919 + 9.8859726341839116819e-957j)  +/-  (1.35e-248, 1.35e-248j)
| (4.5726189987872107779 + 3.1917237830124238852e-952j)  +/-  (3.2e-246, 3.2e-246j)
| (-2.885756962383750957 - 1.840043980591218963e-948j)  +/-  (5.83e-246, 5.83e-246j)
| (6.0381599529455616724 + 2.3862903405867982664e-954j)  +/-  (5.38e-247, 5.38e-247j)
| (2.6813849084694901771 - 6.0477314036017382505e-948j)  +/-  (7.78e-244, 7.78e-244j)
| (1.7320508075688772935 + 3.3061324319015343823e-976j)  +/-  (1.38e-248, 1.38e-248j)
| (-1.7320508075688772935 + 5.6210638051106120759e-973j)  +/-  (1.38e-248, 1.38e-248j)
| (-5.0293053396298155133 + 7.5871777333548667929e-973j)  +/-  (2.49e-246, 2.49e-246j)
| (4.1373536398299946158 - 1.694949738548117694e-973j)  +/-  (3.7e-246, 3.7e-246j)
| (-4.1373536398299946158 - 8.7622171510617183281e-971j)  +/-  (3.55e-246, 3.55e-246j)
| (1.0672470719421885588 - 2.0119421037406901384e-986j)  +/-  (1.4e-250, 1.4e-250j)
| (5.0293053396298155133 + 1.0620713360496024348e-980j)  +/-  (2.65e-246, 2.65e-246j)
| (-2.6822224032999497583 + 3.7857754566877580371e-981j)  +/-  (7.78e-244, 7.78e-244j)
| (-3.7188530770715567898 + 1.785166079124954876e-1023j)  +/-  (3.24e-246, 3.24e-246j)
| (2.2456732555148681046 - 1.921524810421108497e-1029j)  +/-  (2.61e-247, 2.61e-247j)
| (3.3121706201791718697 + 8.0186656312148410991e-1030j)  +/-  (2.78e-246, 2.78e-246j)
| (0.7071067811865475244 + 1.9462991201948246521e-1035j)  +/-  (1.25e-251, 1.25e-251j)
| (1.4130206485936689977 + 3.7163352696204977913e-1033j)  +/-  (1.3e-249, 1.3e-249j)
| (-0.7071067811865475244 + 8.0128028432355502852e-1035j)  +/-  (1.11e-251, 1.11e-251j)
| (-2.6813849084694901771 - 1.1108930332731340888e-1027j)  +/-  (8.4e-244, 8.4e-244j)
| (0.83127776868067864513 + 3.9637333952352407312e-1061j)  +/-  (3.56e-251, 3.56e-251j)
| (2.6822224032999497583 + 2.6096461175877625407e-1055j)  +/-  (7.7e-244, 7.7e-244j)
| (3.7188530770715567898 - 2.194290212858789335e-1079j)  +/-  (3.28e-246, 3.28e-246j)
| (-0.35530271467948512259 - 4.2564790081469848605e-1086j)  +/-  (1.23e-253, 1.23e-253j)
| (-2.2456732555148681046 + 4.4531400839523413018e-1078j)  +/-  (2.62e-247, 2.62e-247j)
| (0.35530271467948512259 + 1.6605227355190515657e-1086j)  +/-  (1.23e-253, 1.23e-253j)
| (-1.9710861567584257974 - 1.0280655981385437068e-1078j)  +/-  (7.59e-248, 7.59e-248j)
| (6.1976350215342857197e-1104 - 6.9154622701528508526e-1104j)  +/-  (3.81e-1102, 3.81e-1102j)
| (-3.3121706201791718697 - 1.4905524958910867107e-1081j)  +/-  (2.87e-246, 2.87e-246j)
| (-0.83127776868067864513 + 4.9776269976605702742e-1089j)  +/-  (3.77e-251, 3.77e-251j)
-------------------------------------------------
The weights are:
| (3.1478049967536503238e-20 + 1.5654067541664601261e-964j)  +/-  (7.24e-95, 4.42e-216j)
| (0.062865385851119754654 + 9.8679639903935068524e-952j)  +/-  (2.25e-65, 1.37e-186j)
| (2.2058300074305174674e-24 - 4.8951645436090873628e-967j)  +/-  (7.36e-97, 4.49e-218j)
| (1.7672343021965541717e-14 + 7.4501286982804857591e-961j)  +/-  (1.62e-92, 9.91e-214j)
| (1.7672343021965541717e-14 - 9.5707024221886230601e-961j)  +/-  (4.27e-95, 2.61e-216j)
| (4.5423914948513287371e-17 - 1.49359804335148369e-962j)  +/-  (7.85e-94, 4.79e-215j)
| (3.1478049967536503238e-20 - 1.9431847968456970336e-964j)  +/-  (1.79e-98, 1.09e-219j)
| (0.026021299450872424593 - 1.6780313813813963365e-951j)  +/-  (7.86e-76, 4.8e-197j)
| (7.6388400545988245403e-05 - 1.3279980559718261972e-951j)  +/-  (2.11e-86, 1.29e-207j)
| (2.0858209325143881287e-10 + 6.0618459421787449046e-958j)  +/-  (1.11e-91, 6.77e-213j)
| (0.0025783750724716461324 + 7.3762598767937750497e-951j)  +/-  (1.51e-81, 9.22e-203j)
| (2.2058300074305174674e-24 + 5.9654590283189212078e-967j)  +/-  (1.16e-100, 7.05e-222j)
| (2.0858209325143881287e-10 - 8.1377866281853410722e-958j)  +/-  (9.6e-94, 5.86e-215j)
| (7.6388400545988245403e-05 - 1.8205900835751597834e-951j)  +/-  (1.28e-88, 7.83e-210j)
| (4.5423914948513287371e-17 + 1.8866957352049766712e-962j)  +/-  (2.76e-97, 1.69e-218j)
| (0.029610257326886374604 - 2.1355131718057423028e-946j)  +/-  (2.97e-87, 1.81e-208j)
| (0.0079871053792400478543 - 8.7389424922760563993e-951j)  +/-  (2.29e-83, 1.4e-204j)
| (0.0079871053792400478543 + 2.156145746175230834e-951j)  +/-  (1.58e-83, 9.63e-205j)
| (2.7411054315676529835e-12 - 2.4558832646544060755e-959j)  +/-  (3.92e-95, 2.39e-216j)
| (8.8492481523497740569e-09 + 1.74769724587074099e-956j)  +/-  (3.19e-93, 1.95e-214j)
| (8.8492481523497740569e-09 - 1.3009876725469938298e-956j)  +/-  (1.35e-93, 8.21e-215j)
| (0.062865385851119754654 - 1.9990462547850839557e-950j)  +/-  (8.21e-83, 5.01e-204j)
| (2.7411054315676529835e-12 + 3.2039385271617219951e-959j)  +/-  (2e-95, 1.22e-216j)
| (-0.029421730657189159034 + 4.3082342905257132386e-949j)  +/-  (1.02e-89, 6.22e-211j)
| (2.2887361125862154989e-07 + 2.7279076528309431375e-955j)  +/-  (1.3e-93, 7.92e-215j)
| (0.0012035222795035881094 - 4.6637792408275378817e-951j)  +/-  (3.64e-89, 2.22e-210j)
| (3.9193547925002855935e-06 + 9.0961603795311916517e-954j)  +/-  (6.52e-93, 3.98e-214j)
| (0.11694104276064291717 - 3.6304991201674875794e-950j)  +/-  (2.9e-87, 1.77e-208j)
| (0.026021299450872424593 + 9.7306373719656041067e-951j)  +/-  (7.18e-88, 4.38e-209j)
| (0.11694104276064291717 - 5.2960837750046346845e-951j)  +/-  (1.42e-88, 8.72e-210j)
| (0.029610257326886374604 - 4.2948880340746321168e-949j)  +/-  (9.16e-90, 5.59e-211j)
| (0.0054191585516878333917 + 4.4457282980049969422e-950j)  +/-  (1.15e-87, 7.04e-209j)
| (-0.029421730657189159034 + 2.1355446335273346241e-946j)  +/-  (2.27e-88, 1.39e-209j)
| (2.2887361125862154989e-07 - 3.6057680062607966527e-955j)  +/-  (2.52e-94, 1.54e-215j)
| (0.17641970626659349236 + 4.3582400004922803994e-951j)  +/-  (1.18e-89, 7.32e-211j)
| (0.0012035222795035881094 + 1.325016513735218711e-951j)  +/-  (1.96e-92, 1.19e-213j)
| (0.17641970626659349236 + 9.6605752933359392707e-951j)  +/-  (5.2e-90, 3.32e-211j)
| (0.0025783750724716461324 - 2.0611752856389940527e-951j)  +/-  (5.38e-92, 3.3e-213j)
| (0.20059066405726452837 - 5.7012148170750122041e-951j)  +/-  (1.33e-90, 8.8e-212j)
| (3.9193547925002855935e-06 - 7.6539296568287720652e-954j)  +/-  (3.16e-95, 1.86e-216j)
| (0.0054191585516878333917 + 3.0501581838873113117e-951j)  +/-  (1.44e-90, 9.7e-212j)
