Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 7 48
-------------------------------------------------
Trying to find an order 7 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 48 Kronrod extension for:
P2 : 4*t^9 - 346/5*t^7 + 1743/5*t^5 - 1113/2*t^3 + 399/2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^57 - 15979098548094612449145748842184246258508709562610968859760178405208906218560360582725127588046/5722700202290391004250024117545855759647687160213004148198159743606260084540019009579058455*t^55 + 1555134489846222707090378676821682345782712963400531289411631649101435747739296927454651363494595101/1722532760889407692279257259381302583653953835224114248607646082825484285446545721883296594955*t^53 - 619230516699504533408485354659881603752325858556925139848487164945063087847633851003619386277136898551/3445065521778815384558514518762605167307907670448228497215292165650968570893091443766593189910*t^51 + 42563896981896687127496581276295990344996040012837777769045048581605274541646252206836971846766774313999/1722532760889407692279257259381302583653953835224114248607646082825484285446545721883296594955*t^49 - 2454193209591726187863028131467209859068286059147070037184277646481258979259057686047444489966192884481539/984304434793947252731004148217887190659402191556636713490083475900276734540883269647598054260*t^47 + 377245797748050088049165471119215645669696662261951207575024645609762707547194002591512860945359748222865617/1968608869587894505462008296435774381318804383113273426980166951800553469081766539295196108520*t^45 - 19131293491583020531471946485193900697331786095855995577476602871416164831996063663449126094681374041820079/1664785513393568292145461561467885311897508992061964843112191925412730206411641893695726096*t^43 + 3638921195852902563138159063996551677850321987546218484827848034347690931916197320270841600706061915280587951/6659142053574273168581846245871541247590035968247859372448767701650920825646567574782904384*t^41 - 277413856568938417725553881180645850718267557754282532512576637792787574330174803709742552487397600441625215019/13318284107148546337163692491743082495180071936495718744897535403301841651293135149565808768*t^39 + 17072328426805924913189104925699061943453922395489981945139143599461409540309634988881515115268670991136859849909/26636568214297092674327384983486164990360143872991437489795070806603683302586270299131617536*t^37 - 851612650946159481634536283519175310661053325841754278116891718696617669107816645700164317871453677240389484375967/53273136428594185348654769966972329980720287745982874979590141613207366605172540598263235072*t^35 + 17245502845286107769403525272856098861551722497204659391992785007066310865528990560170793273646084784093437726347715/53273136428594185348654769966972329980720287745982874979590141613207366605172540598263235072*t^33 - 283428096602251816572277517078597300986085557192415000268827923478248240224627131563973235468462512915577108775212165/53273136428594185348654769966972329980720287745982874979590141613207366605172540598263235072*t^31 + 7543118359657260242516027093589630754830200739546518930011499803902080749542782028216786706417465983795150553730890335/106546272857188370697309539933944659961440575491965749959180283226414733210345081196526470144*t^29 - 161854857534834319276959266528380453232778834958814973250573592412091816143974939449528953539895696737917330394937516285/213092545714376741394619079867889319922881150983931499918360566452829466420690162393052940288*t^27 + 11131056814336957985196561610348411054152999579359260788456111020783573202853605797853228793291901059319293436603851252095/1704740365715013931156952638943114559383049207871451999346884531622635731365521299144423522304*t^25 - 152074255656297785162056061077288848386226105861099686499906688662154976244574845023909013519438927950111119614269937156375/3409480731430027862313905277886229118766098415742903998693769063245271462731042598288847044608*t^23 + 1633421612760735446969976189128790120658677244186051836191764128227375838893257266624560936215840792771405923560615097644625/6818961462860055724627810555772458237532196831485807997387538126490542925462085196577694089216*t^21 - 13607856849626730141571463596741950512788077145484194398505106541358857236803743939116409433498425107738391108863396774017875/13637922925720111449255621111544916475064393662971615994775076252981085850924170393155388178432*t^19 + 10805484070496618674059445925464765861722912159856844985891832568435008407272098085975529707900568417668967091311034448987625/3409480731430027862313905277886229118766098415742903998693769063245271462731042598288847044608*t^17 - 204895572130246173196683122245134191419803131166666903396652059872782741970523375204797783025779804985629469744754979664738375/27275845851440222898511242223089832950128787325943231989550152505962171701848340786310776356864*t^15 + 704987245689566814623082247391418997951271681478734921323244802846602739060817425358416632400434010772643946381124139323618125/54551691702880445797022484446179665900257574651886463979100305011924343403696681572621552713728*t^13 - 1697047250971985441122014129045269753944023141273606308640675879872800870408837015003933561490121513898413356127676015870614375/109103383405760891594044968892359331800515149303772927958200610023848686807393363145243105427456*t^11 + 5434468964093910101027671558859596329469321168939946387583476105457321483864629816109677424429680757640200933930773055587180625/436413533623043566376179875569437327202060597215091711832802440095394747229573452580972421709824*t^9 - 5378696555967918366603296926520110569604240006248420942326726358684654223070915178354348222510236401057965984373943068673218125/872827067246087132752359751138874654404121194430183423665604880190789494459146905161944843419648*t^7 + 2934485228732405373846218252604244499207908706611736028421904023942358513868833951727784567155684786970754441405776333297591875/1745654134492174265504719502277749308808242388860366847331209760381578988918293810323889686839296*t^5 - 721581190455284816832258146674977881274627426093539714159296292046955445065526038113263877386310228605099902867873033275215625/3491308268984348531009439004555498617616484777720733694662419520763157977836587620647779373678592*t^3 + 25453416320482604822134796215766414095778854387020307344174738562628759718656731888512458240254579610262879890577413185659375/3491308268984348531009439004555498617616484777720733694662419520763157977836587620647779373678592*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
Positive weights:   57 out of 57
Indefinite weights: 0 out of 57
Negative weights:   0 out of 57
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-9.4996701609631006187 + 1.4249511103028322031e-860j)  +/-  (6.26e-246, 6.26e-246j)
| (-6.9608557228188046944 - 2.8461267658606961744e-870j)  +/-  (1.92e-242, 1.92e-242j)
| (-6.1784323122698739981 - 1.7027538449082612938e-884j)  +/-  (4.24e-242, 4.24e-242j)
| (5.4484318533203547065 + 1.3180319880677282628e-889j)  +/-  (3.45e-242, 3.45e-242j)
| (8.8480741515891222277 + 4.4353572765082157874e-894j)  +/-  (1.15e-244, 1.15e-244j)
| (7.8255346758594047496 + 7.3910207405016268174e-892j)  +/-  (3.52e-243, 3.52e-243j)
| (8.3080261140424269718 + 1.83759467407474079e-892j)  +/-  (7.61e-244, 7.61e-244j)
| (-8.8480741515891222277 + 7.8969533059536925079e-893j)  +/-  (1.06e-244, 1.06e-244j)
| (-2.8219831590771280998 + 1.9494339772470977088e-901j)  +/-  (2.72e-245, 2.72e-245j)
| (-7.8255346758594047496 - 7.8119267048057669897e-898j)  +/-  (3.63e-243, 3.63e-243j)
| (5.80805299813079496 - 7.8538105135807267527e-904j)  +/-  (4.21e-242, 4.21e-242j)
| (4.7552880972715548766 - 3.236505259616432356e-906j)  +/-  (1.55e-242, 1.55e-242j)
| (9.4996701609631006187 + 2.9862592389142233589e-917j)  +/-  (6.5e-246, 6.5e-246j)
| (-1.9338617295606605688 - 1.351076358565274753e-919j)  +/-  (2.95e-247, 2.95e-247j)
| (-5.4484318533203547065 + 3.5678415305477266292e-914j)  +/-  (3.45e-242, 3.45e-242j)
| (6.1784323122698739981 - 1.0942226230421523132e-924j)  +/-  (3.92e-242, 3.92e-242j)
| (-6.5617227240658479191 + 1.6956610789684950046e-936j)  +/-  (2.98e-242, 2.98e-242j)
| (6.9608557228188046944 + 2.9082003448739182364e-948j)  +/-  (1.88e-242, 1.88e-242j)
| (-1.2079177189639794792 - 3.4264542952032804172e-954j)  +/-  (1.9e-249, 1.9e-249j)
| (1.6691641415280373462 - 2.3803575065785921422e-953j)  +/-  (6.02e-248, 6.02e-248j)
| (4.0897553224911369115 - 3.0865051413811590443e-948j)  +/-  (3.23e-243, 3.23e-243j)
| (1.4364553225037617879 - 2.9929735482455189555e-953j)  +/-  (1.33e-248, 1.33e-248j)
| (5.0979339510879111613 - 1.7574088842014668679e-947j)  +/-  (2.51e-242, 2.51e-242j)
| (0.95903485827967650288 + 3.6178482186367088762e-956j)  +/-  (1.71e-250, 1.71e-250j)
| (-2.2201724783418921227 + 1.3270068226141605454e-951j)  +/-  (1.34e-246, 1.34e-246j)
| (7.3800099846165438394 + 1.9053859901921998416e-948j)  +/-  (9.35e-243, 9.35e-243j)
| (3.7654668341267066651 + 1.5470233998803450276e-948j)  +/-  (1.32e-243, 1.32e-243j)
| (3.1316817004388926669 - 1.0839024587252308409e-949j)  +/-  (1.03e-244, 1.03e-244j)
| (-7.3800099846165438394 + 5.3074094257941123498e-946j)  +/-  (9.2e-243, 9.2e-243j)
| (-0.7071067811865475244 - 5.8153394013043672407e-961j)  +/-  (1.66e-251, 1.66e-251j)
| (1.2079177189639794792 + 8.9750462670918034516e-960j)  +/-  (1.92e-249, 1.92e-249j)
| (-3.4461890205883241979 - 2.6386433149253730589e-953j)  +/-  (4.16e-244, 4.16e-244j)
| (-8.3080261140424269718 - 1.381859366360088756e-953j)  +/-  (7.55e-244, 7.55e-244j)
| (-5.0979339510879111613 - 1.4177772866557135573e-951j)  +/-  (2.49e-242, 2.49e-242j)
| (-3.7654668341267066651 - 3.828269844677308459e-960j)  +/-  (1.21e-243, 1.21e-243j)
| (-1.4364553225037617879 + 6.4160923174916912576e-967j)  +/-  (1.39e-248, 1.39e-248j)
| (-1.6691641415280373462 - 1.839666291808783097e-966j)  +/-  (6.45e-248, 6.45e-248j)
| (0.7071067811865475244 + 2.992150664732952721e-970j)  +/-  (1.65e-251, 1.65e-251j)
| (-0.95903485827967650288 + 3.4419086994965764251e-969j)  +/-  (1.66e-250, 1.66e-250j)
| (2.5176207334287288265 + 1.4675490292688718848e-965j)  +/-  (6.55e-246, 6.55e-246j)
| (-5.80805299813079496 + 5.0502915142416462687e-960j)  +/-  (4.19e-242, 4.19e-242j)
| (4.4194921590190758694 - 2.7036338534734994788e-970j)  +/-  (7.31e-243, 7.31e-243j)
| (2.8219831590771280998 - 3.0657303903640924955e-972j)  +/-  (2.65e-245, 2.65e-245j)
| (-4.0897553224911369115 - 1.9748390499043678881e-968j)  +/-  (3.42e-243, 3.42e-243j)
| (1.9338617295606605688 - 1.7791013360061359901e-974j)  +/-  (2.74e-247, 2.74e-247j)
| (-2.5176207334287288265 + 1.5269567270381504603e-971j)  +/-  (6.4e-246, 6.4e-246j)
| (6.5617227240658479191 + 4.7336949185839030144e-969j)  +/-  (3.07e-242, 3.07e-242j)
| (0.23726992806767517156 - 1.6998382862016886412e-980j)  +/-  (8.54e-254, 8.54e-254j)
| (0.46831515218714431237 + 1.5095697792657398305e-980j)  +/-  (1.29e-252, 1.29e-252j)
| (3.4461890205883241979 + 1.2802072693202858078e-971j)  +/-  (4.1e-244, 4.1e-244j)
| (-3.1316817004388926669 + 1.8213832402948609739e-970j)  +/-  (1.13e-244, 1.13e-244j)
| (-0.46831515218714431237 + 5.4787313854991378917e-979j)  +/-  (1.35e-252, 1.35e-252j)
| (-4.7552880972715548766 + 4.03292161780657569e-974j)  +/-  (1.49e-242, 1.49e-242j)
| (2.2201724783418921227 + 2.0655087648030142769e-986j)  +/-  (1.28e-246, 1.28e-246j)
| (-7.592300756030817433e-1015 + 1.295612935352675508e-1014j)  +/-  (8.56e-1013, 8.56e-1013j)
| (-4.4194921590190758694 - 1.7611075902510821662e-989j)  +/-  (8.18e-243, 8.18e-243j)
| (-0.23726992806767517156 - 1.2010823035442434732e-1001j)  +/-  (7.87e-254, 7.87e-254j)
-------------------------------------------------
The weights are:
| (2.7258537627825036821e-40 + 3.8476010315074856186e-899j)  +/-  (1.75e-79, 4.13e-199j)
| (2.0860297816144037314e-22 - 9.2102248239130434488e-891j)  +/-  (3.89e-72, 9.14e-192j)
| (5.6074565492681933781e-18 - 1.1680922510524995577e-888j)  +/-  (1.97e-69, 4.63e-189j)
| (2.5658136309934443409e-14 - 2.5802445484749353404e-887j)  +/-  (1.1e-68, 2.58e-188j)
| (3.2772792990230364277e-35 - 1.0347016022564790554e-898j)  +/-  (1.73e-80, 4.07e-200j)
| (6.6075069973556659281e-28 - 8.1009214595959528467e-895j)  +/-  (6.07e-78, 1.43e-197j)
| (3.0166107265834206036e-31 + 1.3205380194956085386e-896j)  +/-  (3.94e-79, 9.27e-199j)
| (3.2772792990230364277e-35 - 2.7083640681778369129e-897j)  +/-  (1.78e-81, 4.2e-201j)
| (6.0293680047198324334e-05 - 4.8153182528035094714e-881j)  +/-  (6.57e-59, 1.55e-178j)
| (6.6075069973556659281e-28 - 7.1657007412581772211e-894j)  +/-  (1.17e-78, 2.76e-198j)
| (4.6034781771615080644e-16 + 2.5919930068830722754e-888j)  +/-  (2.95e-73, 6.95e-193j)
| (2.891473150416685356e-11 - 1.5996141242309179313e-885j)  +/-  (3.67e-70, 8.63e-190j)
| (2.7258537627825036821e-40 + 2.1610699797080554366e-901j)  +/-  (1.09e-84, 2.55e-204j)
| (0.0037260708843277379825 + 2.0918725827279763167e-879j)  +/-  (3.66e-55, 8.62e-175j)
| (2.5658136309934443409e-14 - 1.0175390657456139204e-886j)  +/-  (6.1e-74, 1.44e-193j)
| (5.6074565492681933781e-18 - 2.165877672730483982e-889j)  +/-  (3.93e-75, 9.24e-195j)
| (4.4068601353167667433e-20 + 1.0312905495599625565e-889j)  +/-  (5.78e-77, 1.36e-196j)
| (2.0860297816144037314e-22 - 7.7210024516967803358e-892j)  +/-  (6.78e-78, 1.6e-197j)
| (0.031426326010953361031 - 2.5773183546628071192e-878j)  +/-  (3.23e-51, 7.61e-171j)
| (0.0086496541059686098053 - 4.527064277461667503e-879j)  +/-  (6.45e-57, 1.52e-176j)
| (1.004201806466585988e-08 - 5.9033162392860509527e-884j)  +/-  (2.29e-70, 5.39e-190j)
| (0.015937412891545179579 + 1.1050602770858220062e-878j)  +/-  (1.62e-55, 3.82e-175j)
| (1.0095662797165126904e-12 + 2.1837366692784652877e-886j)  +/-  (1.43e-72, 3.36e-192j)
| (0.057168070125590309085 + 3.1668935137954787414e-878j)  +/-  (4.99e-55, 1.17e-174j)
| (0.0011953901031833674187 - 6.1159390654748130174e-880j)  +/-  (2.07e-63, 4.86e-183j)
| (5.3985600650345382976e-25 + 3.0173028250512621558e-893j)  +/-  (2.02e-79, 4.75e-199j)
| (1.2622964754687608599e-07 + 3.0520679702160309152e-883j)  +/-  (6.21e-70, 1.46e-189j)
| (9.6930661312579959337e-06 + 6.2821845545292765472e-882j)  +/-  (2.05e-68, 4.83e-188j)
| (5.3985600650345382976e-25 + 1.7028716251703449752e-892j)  +/-  (2.18e-83, 5.14e-203j)
| (0.084415806197662339242 - 5.8751894394840938461e-878j)  +/-  (2.39e-59, 5.63e-179j)
| (0.031426326010953361031 - 1.9838034060507704724e-878j)  +/-  (5.69e-59, 1.34e-178j)
| (1.2431748485950262549e-06 - 3.1488628504739862813e-882j)  +/-  (2.53e-73, 5.95e-193j)
| (3.0166107265834206036e-31 + 1.7841845596693044499e-895j)  +/-  (1.55e-86, 3.64e-206j)
| (1.0095662797165126904e-12 + 7.6313032895926870404e-886j)  +/-  (8.36e-79, 1.97e-198j)
| (1.2622964754687608599e-07 + 7.2439823922606726656e-883j)  +/-  (4.22e-75, 9.94e-195j)
| (0.015937412891545179579 + 1.5097385979108437936e-878j)  +/-  (7.67e-65, 1.8e-184j)
| (0.0086496541059686098053 - 6.5127486450557995831e-879j)  +/-  (3.72e-66, 8.75e-186j)
| (0.084415806197662339242 - 5.0436253699624622428e-878j)  +/-  (2.89e-63, 6.81e-183j)
| (0.057168070125590309085 + 3.8965602704342021124e-878j)  +/-  (1.68e-63, 3.95e-183j)
| (0.00030039722805832716828 + 9.9834171828528037049e-881j)  +/-  (6.27e-72, 1.48e-191j)
| (4.6034781771615080644e-16 + 1.1753159890843544268e-887j)  +/-  (1.09e-80, 2.55e-200j)
| (6.1774858577561860696e-10 + 1.029680287607633858e-884j)  +/-  (1.51e-76, 3.55e-196j)
| (6.0293680047198324334e-05 - 2.5673576592391919757e-881j)  +/-  (4.81e-73, 1.13e-192j)
| (1.004201806466585988e-08 - 1.5281229291271585612e-883j)  +/-  (8.75e-78, 2.06e-197j)
| (0.0037260708843277379825 + 1.3702461296787728879e-879j)  +/-  (5.41e-71, 1.27e-190j)
| (0.00030039722805832716828 + 1.7425838592388006965e-880j)  +/-  (5.12e-73, 1.2e-192j)
| (4.4068601353167667433e-20 + 1.4642784920220163772e-890j)  +/-  (4.18e-83, 9.84e-203j)
| (0.12443733761029824237 - 9.1514112091485234265e-878j)  +/-  (2e-69, 4.69e-189j)
| (0.1050800876315221905 + 7.3994170824864645524e-878j)  +/-  (3.9e-69, 9.16e-189j)
| (1.2431748485950262549e-06 - 1.4403113674118100202e-882j)  +/-  (4.71e-75, 1.11e-194j)
| (9.6930661312579959337e-06 + 1.2699905911162310944e-881j)  +/-  (1.85e-75, 4.34e-195j)
| (0.1050800876315221905 + 8.1854706611755517062e-878j)  +/-  (5.68e-71, 1.32e-190j)
| (2.891473150416685356e-11 - 5.0156538956947768762e-885j)  +/-  (2.77e-80, 6.49e-200j)
| (0.0011953901031833674187 - 3.7535503598374972258e-880j)  +/-  (3.45e-74, 7.91e-194j)
| (0.13518416074099733046 + 9.8344844793214685944e-878j)  +/-  (1.01e-71, 2.25e-191j)
| (6.1774858577561860696e-10 + 2.923283115139625957e-884j)  +/-  (1.61e-79, 3.8e-199j)
| (0.12443733761029824237 - 9.6313638132212630511e-878j)  +/-  (7.92e-72, 1.74e-191j)
