Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 4 14 20
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 14 Kronrod extension for:
P2 : 3/2*t^6 - 25/14*t^4 + 45/98*t^2 - 1/98
Solvable: 1
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P3 : 3/2*t^20 - 111542583514655/16329965371258*t^18 + 23000790623634927/1771801242781493*t^16 - 685232025857483175/51382236040663297*t^14 + 5693616311282510/710353493649723*t^12 - 271731796260106/95328823823123*t^10 + 8887675214459847/15347940635522803*t^8 - 4745531391078231/76739703177614015*t^6 + 93556582421835/30695881271045606*t^4 - 13852984108093/214871168897319242*t^2 + 69487884128/146503069702717665
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^40 - 6029485670176893560431596947825910847448930115562959175871791544695243339834374278397280249713667935278591294675852030799369426647394765477102072078950301780129445773197761445148744806695/417481397643876613666047656321566038020354418366305999593459047634794436264750553217867567894032021425507422998776443480456147819270118521534477540759213506306334799426159242059554882582*t^38 + 17396541220494521575158802576967907023986406463245979132073065954750190170987156154181676615459925551672655927651805218103888872515538570829560916568347151625954642653442885895422421901672983/271780389866163675496597024265339490751250726356465205735341840010251178008352610144831786699014845948005332372203464705776952230344847157518944879034247992605423954426429666580770228560882*t^36 - 9282495743482230624708384404920298511210670384198401920423109593103064663543316997965244878257847968983674051135310697261794469096340753903531994311188392969255458000780380601641527639669287/53616539497406439383682406147583981168614088873044156233502811974811456886001535334694706219533541037361596182271431812704296698503405221551356472734647563167056426383445308373077119920174*t^34 + 670265171456490396867269724984472358387624047840478545002229887815872339594842426640539081715781946035149274366302740693991654060710101683694017763271676985312895625182043550606702621479932290/2098356386693952014061388713321354899371669569076864478047541868650575653583969178326006457046289946962197014224350126851745429882337813443441723773842343267583435596188473204964518193239537*t^32 - 3717132937976413971399268203618587883517594284679832663713138107010143007117000029508959375059853197664378366456029512780921619261553123722655185145837772362712051971029349193504139252062538570/8731870125274832574642553032853380065127270142287597344133319388900782558462323354969510740611980747036239188223908592383069692091018643038838140865343944565105264255106872369045898287996783*t^30 + 325723697792655305057979651316045711524944734510097206764181806032974526731565658115892385963137508357693190065798557218809708731789570846903497853872251215538733979963170902604848926530773530/769475145139161491252025746190144603440334150469788271705235041933785436186335008292332364115232019853768204326244818485864378996526547087713705900011152203055253171905969595739676860628069*t^28 - 16603727839344264422471165903560519858610871929747922898793612208125008933940291681650611496465569210050426053047061368994585336104043411362538323692282468260202740894512492738290925472599642038982/51897251163910746777492876451794302779033336778434869985159577403224158743587364634276356297751823579037396540783581782779123041420732968330850894426252160335061550179198119384662505865060113705*t^26 + 5776703210654592209701958013887795667683717062665106696064646773272608608324915788847337670173417330409132533218819154233912650752986479106233600635608582125355618132093861490555928129270662654775/31138350698346448066495725871076581667420002067060921991095746441934495246152418780565813778651094147422437924470149069667473824852439780998510536655751296201036930107518871630797503519036068223*t^24 - 595677968752704303089451277032469997039787942118372263267574942925577312375121006671423832324487253707865781623436644101998721104433675668802780706193164729433885523605761680130830274886759696959637/7199276937546679507316033548134560975947120188055404181506528159249000038577819374005310539287259491794639887088004175484133477215521330815496211467669571424567277478336935639508877878828730382051*t^22 + 15493642146197297974118852403851396546335657957016341615893441589928986498433922446658191020824822720796607940121220195607863257094607143016960214507132004577632642116841942986030256572506120415605/547625889497984897588047078800588126185216934527405512878975240313931357294416687076470746031127345386976317941759130231631674519176947241995073599581544394076546153268672284266909077981406207169*t^20 - 44292729580218263006052161288301328124918679346784654200059718906874888218933709793073305880704258668904876934202434870727953890415806589696467604780858438045469006938742171219668878596439344978705/6023884784477833873468517866806469388037386279801460641668727643453244930238583557841178206342400799256739497359350432547948419710946419661945809595396988334842007685955395126935999857795468278859*t^18 + 94870987479397939703303762171021972103824556605242208601989136907162430194475275454332907505184007593903426570686020309428981241545014676607193483787480378800321094216595973137431798959157489490034/66262732629256172608153696534871163268411249077816067058356004077985694232624419136252960269766408791824134470952854758027432616820410616281403905549366871683262084545509346396295998435750151067449*t^16 - 664380080563079693678654244970025394646405948863297159187601286017088783857686352900233944014964634786579248022081380208385033609966479614964056121453066645253255970225306832556164720961641674341590/3246873898833552457799531130208687000152151204812987285859444199821299017398596537676395053218554030799382589076689883143344198224200120197788791371918976712479842142729957973418503923351757402305001*t^14 + 592740169946681030496166892578297205890226273350265053041904097482707732777183030184201845084802977095846592649576487954013318579699937202737854598288358948870435487247938118678916562691734233626/28398313983966931117780155657801927115033392461921171596438287461993868956839036772679840115614175196496057630408366324868899692923033121263458816664014373578540893376646862741269713615321493314621*t^12 - 1914124465381111120790002180597099208892446335309615133456420749952281586932773299956206754223495621382122980718047204108303534879540819730150354992679193348261833490872903023841004875245077967650/1307182998231689950542668377097003857204112822716916959242113898629354149861772632051535670776300973438712470926979043862904807077275373066642240682201146468660715667852320742545111969141616616512403*t^10 + 35698028827685397764791995574149208603156536275818314097027861483132841761388980555611358417276414462984689221484805768416520711816730983654686454913326128330428484727132742452698537148125315140115/530716297282066119920323361101383566024869806023068285452298242843517784843879688612923482335178195216117263196353491808339351673373801465056749716973665466276250561148042221473315459471496346304035618*t^8 - 6351675151861097016624228879054080044293991923001499944665843771473251881305126102345415435107341471719026171540674360390842677114952068257381363290670975194170300218411360270481263952855714449/3361327709738631301395432969678009918524861544129215038051150025046910671073129625275377439139059645985260639526517541361755218198708102171365761754231519490841840288763110480830287920649871299603322*t^6 + 6638567590133871791600169379381882845727756532011670330812279149047536065379134388933747929487433432804951727471583559487633495750080624978730799496619939999019414978816931067348147338973547307/227449841692314051394424297614878671153515631152743550908127818361507622075948437976967206715076369378335969941294353632145436431445914913595749878702999485546964526206303809202849482630641291273158122*t^4 - 42959299516887792862032641437466793790371731168634974753596034021755992864874951931413814927957217629368080151693110888059904701356755251439445014464276408559225059414336608944993396803729101/212656356053789560246819465249683310428083720183459417515729261069702248282390815994725437172632377874053955636169517623550611297693335081817164520738576754779682280599389740311607239857916654442383610*t^2 + 525208660311753700157859146382336439698103258441082568426155695140724706158353759383472500763165502022816034095596410066889999127268737505296657720693548810029840702055141930673928864182176/1664519296021025557931923268908884820714364391617805077100389943463760325192168114285987285505786157723276870934017769762518875702854195504041624112326496235139149487237041512802671213796965813408111711
-------------------------------------------------
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:
| (-0.99521824907985271661 + 7.1270970834390461903e-883j)  +/-  (1.48e-241, 1.48e-241j)
| (0.96861169018623620956 + 1.1459342153186226197e-884j)  +/-  (5.83e-242, 5.83e-242j)
| (-0.91248695683407599658 + 2.5532670606566086526e-909j)  +/-  (1.06e-242, 1.06e-242j)
| (0.99521824907985271661 + 6.0828606709715121078e-905j)  +/-  (1.43e-241, 1.43e-241j)
| (0.94425187178877033609 - 3.0041465905099213909e-927j)  +/-  (2.92e-242, 2.92e-242j)
| (0.82690885901697189971 + 1.2771577223428719791e-937j)  +/-  (8.51e-244, 8.51e-244j)
| (-0.99906219168647909054 - 3.3376905106821325406e-935j)  +/-  (7.43e-242, 7.43e-242j)
| (-0.94425187178877033609 - 5.19060515551226016e-938j)  +/-  (2.68e-242, 2.68e-242j)
| (-0.96861169018623620956 + 4.1226029696496464469e-937j)  +/-  (6.5e-242, 6.5e-242j)
| (0.13022152008293402128 - 9.5169672266007975894e-948j)  +/-  (8.06e-253, 8.06e-253j)
| (0.91248695683407599658 + 7.0504629731241121239e-937j)  +/-  (1.04e-242, 1.04e-242j)
| (-0.98559855824293156178 - 2.9471231508352466122e-942j)  +/-  (1.22e-241, 1.22e-241j)
| (-0.64864684157805656024 - 2.0433565006802999794e-946j)  +/-  (4.14e-246, 4.14e-246j)
| (-0.82690885901697189971 + 4.3302858850331624418e-944j)  +/-  (8.9e-244, 8.9e-244j)
| (0.77371124013697104157 - 8.9312447263933396747e-943j)  +/-  (1.91e-244, 1.91e-244j)
| (0.87330538424743138559 - 2.7703698611496905087e-942j)  +/-  (3.44e-243, 3.44e-243j)
| (0.41905515798203752075 + 1.5615319572727198499e-958j)  +/-  (3.6e-249, 3.6e-249j)
| (-0.33452470558410378352 - 8.6883223688908102871e-961j)  +/-  (3.55e-250, 3.55e-250j)
| (-0.77371124013697104157 - 2.2304494409294190899e-954j)  +/-  (1.77e-244, 1.77e-244j)
| (-0.25853777041146136529 + 2.7459207128429303227e-961j)  +/-  (7.16e-251, 7.16e-251j)
| (0.99906219168647909054 - 1.461416718171523212e-949j)  +/-  (7.43e-242, 7.43e-242j)
| (0.71417543668774168934 - 1.8571662912614444025e-977j)  +/-  (2.97e-245, 2.97e-245j)
| (0.98559855824293156178 - 1.3512605616021879619e-985j)  +/-  (1.1e-241, 1.1e-241j)
| (-0.87330538424743138559 - 3.3659885625217981519e-1011j)  +/-  (3.56e-243, 3.56e-243j)
| (-0.71417543668774168934 + 5.0758498089267616245e-1017j)  +/-  (2.77e-245, 2.77e-245j)
| (-0.046229710010376507347 - 1.0403201506496600223e-1025j)  +/-  (7.74e-255, 7.74e-255j)
| (0.64864684157805656024 + 2.5629982970444181649e-1018j)  +/-  (3.93e-246, 3.93e-246j)
| (0.15655801081562154215 - 2.3952826282445525491e-1025j)  +/-  (2.71e-252, 2.71e-252j)
| (-0.13022152008293402128 - 1.1524515647973398373e-1025j)  +/-  (6.97e-253, 6.97e-253j)
| (-0.57735026918962576451 + 8.0166383605589938598e-1021j)  +/-  (3.99e-247, 3.99e-247j)
| (-0.15655801081562154215 + 1.0048948343547736551e-1026j)  +/-  (3.31e-252, 3.31e-252j)
| (0.33452470558410378352 + 1.791421673880383671e-1023j)  +/-  (3.51e-250, 3.51e-250j)
| (0.57735026918962576451 - 4.1089042978480575816e-1021j)  +/-  (4.3e-247, 4.3e-247j)
| (0.046229710010376507347 - 1.0826520164475929375e-1029j)  +/-  (7.74e-255, 7.74e-255j)
| (-0.50059117102333587994 + 2.2072031151045035962e-1022j)  +/-  (3.76e-248, 3.76e-248j)
| (-0.41905515798203752075 - 5.3248673174195781138e-1023j)  +/-  (3.3e-249, 3.3e-249j)
| (0.21946217414855798398 + 2.853920883627088549e-1025j)  +/-  (2.19e-251, 2.19e-251j)
| (0.50059117102333587994 + 3.4688022545803195601e-1022j)  +/-  (3.95e-248, 3.95e-248j)
| (0.25853777041146136529 - 1.010014425152419155e-1024j)  +/-  (7.45e-251, 7.45e-251j)
| (-0.21946217414855798398 + 3.6581786825020244203e-1025j)  +/-  (2.35e-251, 2.35e-251j)
-------------------------------------------------
The weights are:
| (0.0061470851896738700564 - 1.5358952248701764234e-883j)  +/-  (1.3e-77, 8.58e-194j)
| (0.020677913369042589723 + 1.0134528618072467923e-885j)  +/-  (4.93e-78, 3.26e-194j)
| (0.035485283287040298053 + 4.3964858147002059144e-884j)  +/-  (2.21e-78, 1.46e-194j)
| (0.0061470851896738700564 + 7.2955120510425176016e-885j)  +/-  (1.38e-78, 9.09e-195j)
| (0.028050360643803668681 + 1.0949104509396363298e-884j)  +/-  (2.95e-78, 1.95e-194j)
| (0.04987692549401341074 - 3.6446077448791004985e-885j)  +/-  (5.61e-79, 3.71e-195j)
| (0.0022353735557736465943 + 5.1867909142496809573e-883j)  +/-  (6.19e-79, 4.09e-195j)
| (0.028050360643803668681 - 7.4626491356217017585e-884j)  +/-  (9.07e-80, 6e-196j)
| (0.020677913369042589723 + 1.545423440918881523e-883j)  +/-  (8.36e-80, 5.52e-196j)
| (0.058364916613419655901 + 1.2024991857691976213e-882j)  +/-  (1.91e-83, 1.27e-199j)
| (0.035485283287040298053 - 5.629960988557904699e-885j)  +/-  (8.21e-82, 5.43e-198j)
| (0.013279805368646382241 - 4.7172920557844092836e-883j)  +/-  (1.53e-79, 1.01e-195j)
| (0.068447601117500003426 - 1.909474999908579322e-884j)  +/-  (1.65e-83, 1.09e-199j)
| (0.04987692549401341074 + 2.2777830120249004034e-884j)  +/-  (2.07e-82, 1.37e-198j)
| (0.056437923675103816763 + 3.6775038984368935118e-885j)  +/-  (1.48e-83, 9.75e-200j)
| (0.042844033547546995763 + 4.1270732490743138532e-885j)  +/-  (8.93e-83, 5.9e-199j)
| (0.083511568370448526056 - 2.4682524754285625101e-884j)  +/-  (1.81e-85, 1.19e-201j)
| (0.08452395951443381127 - 1.4395590817978876085e-883j)  +/-  (2.66e-85, 1.76e-201j)
| (0.056437923675103816763 - 1.9418777291915755375e-884j)  +/-  (4.03e-84, 2.66e-200j)
| (0.055009674448135455584 + 6.333745022587471067e-883j)  +/-  (1.91e-85, 1.26e-201j)
| (0.0022353735557736465943 - 2.7767697562010171236e-885j)  +/-  (3.61e-84, 2.38e-200j)
| (0.062575917068270937344 - 4.1374701921277303663e-885j)  +/-  (3.4e-86, 2.25e-202j)
| (0.013279805368646382241 - 1.3112236864039434928e-884j)  +/-  (6.37e-84, 4.21e-200j)
| (0.042844033547546995763 - 2.9800370829211476649e-884j)  +/-  (2.97e-85, 1.96e-201j)
| (0.062575917068270937344 + 1.8312357579850962715e-884j)  +/-  (1.1e-86, 7.24e-203j)
| (0.091885755376356410986 + 3.9196920191360182607e-883j)  +/-  (2.35e-88, 1.56e-204j)
| (0.068447601117500003426 + 5.15481284033191492e-885j)  +/-  (6.2e-88, 4.09e-204j)
| (0.037507079304152947708 - 1.3742160626004833729e-882j)  +/-  (3.02e-88, 2e-204j)
| (0.058364916613419655901 - 1.5180647726104002777e-882j)  +/-  (1.31e-88, 8.68e-205j)
| (0.074099535770393634669 + 2.2386299514137810949e-884j)  +/-  (2.21e-89, 1.46e-205j)
| (0.037507079304152947708 + 1.8195705493528282298e-882j)  +/-  (1.09e-88, 7.23e-205j)
| (0.08452395951443381127 + 7.7898635574987430965e-884j)  +/-  (9.21e-91, 6.08e-207j)
| (0.074099535770393634669 - 7.2149727740216565937e-885j)  +/-  (6e-91, 3.97e-207j)
| (0.091885755376356410986 - 3.609615584918137932e-883j)  +/-  (6.67e-90, 4.4e-206j)
| (0.079311432259132644079 - 3.0792803190949715789e-884j)  +/-  (4.62e-91, 3.05e-207j)
| (0.083511568370448526056 + 5.4019868012765717299e-884j)  +/-  (4.92e-91, 3.25e-207j)
| (0.049727856027111294365 + 7.2096035546606436033e-883j)  +/-  (3.3e-91, 2.18e-207j)
| (0.079311432259132644079 + 1.1829606224163500051e-884j)  +/-  (7.59e-93, 4.97e-209j)
| (0.055009674448135455584 - 3.9633295880797110072e-883j)  +/-  (1.36e-91, 9e-208j)
| (0.049727856027111294365 - 1.0712204203631330234e-882j)  +/-  (1.79e-91, 1.14e-207j)
