Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 7 48
-------------------------------------------------
Trying to find an order 7 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 48 Kronrod extension for:
P2 : t^9 - 173/5*t^7 + 1743/5*t^5 - 1113*t^3 + 798*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^57 - 7989549274047306224572874421092123129254354781305484429880089202604453109280180291362563794023/5722700202290391004250024117545855759647687160213004148198159743606260084540019009579058455*t^55 + 1555134489846222707090378676821682345782712963400531289411631649101435747739296927454651363494595101/1722532760889407692279257259381302583653953835224114248607646082825484285446545721883296594955*t^53 - 619230516699504533408485354659881603752325858556925139848487164945063087847633851003619386277136898551/1722532760889407692279257259381302583653953835224114248607646082825484285446545721883296594955*t^51 + 170255587927586748509986325105183961379984160051351111076180194326421098166585008827347887387067097255996/1722532760889407692279257259381302583653953835224114248607646082825484285446545721883296594955*t^49 - 4908386419183452375726056262934419718136572118294140074368555292962517958518115372094888979932385768963078/246076108698486813182751037054471797664850547889159178372520868975069183635220817411899513565*t^47 + 754491595496100176098330942238431291339393324523902415150049291219525415094388005183025721890719496445731234/246076108698486813182751037054471797664850547889159178372520868975069183635220817411899513565*t^45 - 38262586983166041062943892970387801394663572191711991154953205742832329663992127326898252189362748083640158/104049094587098018259091347591742831993594312003872802694511995338295637900727618355982881*t^43 + 3638921195852902563138159063996551677850321987546218484827848034347690931916197320270841600706061915280587951/104049094587098018259091347591742831993594312003872802694511995338295637900727618355982881*t^41 - 277413856568938417725553881180645850718267557754282532512576637792787574330174803709742552487397600441625215019/104049094587098018259091347591742831993594312003872802694511995338295637900727618355982881*t^39 + 17072328426805924913189104925699061943453922395489981945139143599461409540309634988881515115268670991136859849909/104049094587098018259091347591742831993594312003872802694511995338295637900727618355982881*t^37 - 851612650946159481634536283519175310661053325841754278116891718696617669107816645700164317871453677240389484375967/104049094587098018259091347591742831993594312003872802694511995338295637900727618355982881*t^35 + 34491005690572215538807050545712197723103444994409318783985570014132621731057981120341586547292169568186875452695430/104049094587098018259091347591742831993594312003872802694511995338295637900727618355982881*t^33 - 1133712386409007266289110068314389203944342228769660001075311693912992960898508526255892941873850051662308435100848660/104049094587098018259091347591742831993594312003872802694511995338295637900727618355982881*t^31 + 30172473438629040970064108374358523019320802958186075720045999215608322998171128112867146825669863935180602214923561340/104049094587098018259091347591742831993594312003872802694511995338295637900727618355982881*t^29 - 647419430139337277107837066113521812931115339835259893002294369648367264575899757798115814159582786951669321579750065140/104049094587098018259091347591742831993594312003872802694511995338295637900727618355982881*t^27 + 11131056814336957985196561610348411054152999579359260788456111020783573202853605797853228793291901059319293436603851252095/104049094587098018259091347591742831993594312003872802694511995338295637900727618355982881*t^25 - 152074255656297785162056061077288848386226105861099686499906688662154976244574845023909013519438927950111119614269937156375/104049094587098018259091347591742831993594312003872802694511995338295637900727618355982881*t^23 + 1633421612760735446969976189128790120658677244186051836191764128227375838893257266624560936215840792771405923560615097644625/104049094587098018259091347591742831993594312003872802694511995338295637900727618355982881*t^21 - 13607856849626730141571463596741950512788077145484194398505106541358857236803743939116409433498425107738391108863396774017875/104049094587098018259091347591742831993594312003872802694511995338295637900727618355982881*t^19 + 86443872563972949392475567403718126893783297278854759887134660547480067258176784687804237663204547341351736730488275591901000/104049094587098018259091347591742831993594312003872802694511995338295637900727618355982881*t^17 - 409791144260492346393366244490268382839606262333333806793304119745565483941046750409595566051559609971258939489509959329476750/104049094587098018259091347591742831993594312003872802694511995338295637900727618355982881*t^15 + 1409974491379133629246164494782837995902543362957469842646489605693205478121634850716833264800868021545287892762248278647236250/104049094587098018259091347591742831993594312003872802694511995338295637900727618355982881*t^13 - 3394094501943970882244028258090539507888046282547212617281351759745601740817674030007867122980243027796826712255352031741228750/104049094587098018259091347591742831993594312003872802694511995338295637900727618355982881*t^11 + 5434468964093910101027671558859596329469321168939946387583476105457321483864629816109677424429680757640200933930773055587180625/104049094587098018259091347591742831993594312003872802694511995338295637900727618355982881*t^9 - 5378696555967918366603296926520110569604240006248420942326726358684654223070915178354348222510236401057965984373943068673218125/104049094587098018259091347591742831993594312003872802694511995338295637900727618355982881*t^7 + 2934485228732405373846218252604244499207908706611736028421904023942358513868833951727784567155684786970754441405776333297591875/104049094587098018259091347591742831993594312003872802694511995338295637900727618355982881*t^5 - 721581190455284816832258146674977881274627426093539714159296292046955445065526038113263877386310228605099902867873033275215625/104049094587098018259091347591742831993594312003872802694511995338295637900727618355982881*t^3 + 50906832640965209644269592431532828191557708774040614688349477125257519437313463777024916480509159220525759781154826371318750/104049094587098018259091347591742831993594312003872802694511995338295637900727618355982881*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: 0
  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:
| (11.066977271421312444 - 2.2316367689894443342e-511j)  +/-  (4.29e-243, 4.29e-243j)
| (-8.7376227702162173171 - 1.698948611718741131e-523j)  +/-  (5.88e-242, 5.88e-242j)
| (10.436910210693572853 + 4.6679560328191168545e-532j)  +/-  (1.31e-242, 1.31e-242j)
| (11.749323207028642275 + 6.8698442162560470936e-534j)  +/-  (1.1e-243, 1.1e-243j)
| (-13.434562379705019779 + 3.798000762298286155e-534j)  +/-  (8.13e-246, 8.13e-246j)
| (13.434562379705019779 + 1.5487854198792828746e-535j)  +/-  (8.3e-246, 8.3e-246j)
| (-12.513066466060153164 - 4.4616092538746335379e-531j)  +/-  (1.48e-244, 1.48e-244j)
| (-2.7348934856989767145 - 1.5363096574494458698e-537j)  +/-  (4.02e-247, 4.02e-247j)
| (-11.749323207028642275 - 4.9837102496161807594e-532j)  +/-  (1.07e-243, 1.07e-243j)
| (8.7376227702162173171 + 1.3001296044821125575e-536j)  +/-  (6.04e-242, 6.04e-242j)
| (2.3605545667757946951 - 2.9280960128491305108e-544j)  +/-  (8.96e-248, 8.96e-248j)
| (-6.7249929201527825481 + 7.8665065128630155471e-538j)  +/-  (2.13e-242, 2.13e-242j)
| (-5.7837874438545169067 + 6.1909903464204976588e-550j)  +/-  (4.36e-243, 4.36e-243j)
| (-4.4288667337963182986 - 4.7167669329806455117e-556j)  +/-  (1.75e-244, 1.75e-244j)
| (7.2095673337107825348 + 8.9309535127540075031e-553j)  +/-  (3.32e-242, 3.32e-242j)
| (7.7052462206312233047 + 1.3348743651551540919e-559j)  +/-  (4.83e-242, 4.83e-242j)
| (-9.2796772689056521681 + 6.59111224610108919e-573j)  +/-  (4.61e-242, 4.61e-242j)
| (9.8441365689327272731 - 2.1202246695746983334e-585j)  +/-  (2.64e-242, 2.64e-242j)
| (-2.0314545988278380851 + 6.5551079974125085724e-592j)  +/-  (1.97e-248, 1.97e-248j)
| (12.513066466060153164 - 2.4690453392047437119e-589j)  +/-  (1.49e-244, 1.49e-244j)
| (5.3251742654880700245 - 1.904658556497736843e-587j)  +/-  (1.78e-243, 1.78e-243j)
| (-5.3251742654880700245 + 1.3963693273978491399e-585j)  +/-  (1.73e-243, 1.73e-243j)
| (4.4288667337963182986 + 2.1579014806988936208e-595j)  +/-  (1.62e-244, 1.62e-244j)
| (3.5604533861266068972 - 2.273485526857732374e-597j)  +/-  (9.44e-246, 9.44e-246j)
| (-1.3562801033676776566 - 5.2041459063197102256e-601j)  +/-  (2.69e-250, 2.69e-250j)
| (-9.8441365689327272731 + 3.4702682189402341871e-593j)  +/-  (2.68e-242, 2.68e-242j)
| (1 - 5.0891956480714354075e-609j)  +/-  (2.35e-251, 2.35e-251j)
| (1.3562801033676776566 - 3.8194284260904413427e-608j)  +/-  (2.67e-250, 2.67e-250j)
| (-4.8736472514172613604 + 1.2309843689655157002e-600j)  +/-  (5.77e-244, 5.77e-244j)
| (-0.66229763968787951317 - 1.5516922349583482137e-616j)  +/-  (1.63e-252, 1.63e-252j)
| (-6.250105750086328354 + 2.3597387901504443174e-606j)  +/-  (1.24e-242, 1.24e-242j)
| (3.1397980296785904718 - 1.3757111019362068539e-625j)  +/-  (2.06e-246, 2.06e-246j)
| (1.7082536203896324893 - 3.6698777302239807227e-628j)  +/-  (2.69e-249, 2.69e-249j)
| (-11.066977271421312444 + 3.4839833988712850792e-620j)  +/-  (4.5e-243, 4.5e-243j)
| (6.250105750086328354 - 2.1865179629504407622e-624j)  +/-  (1.02e-242, 1.02e-242j)
| (9.2796772689056521681 - 1.8448944541575821727e-623j)  +/-  (4.27e-242, 4.27e-242j)
| (5.7837874438545169067 - 5.6935235584027602737e-630j)  +/-  (4.42e-243, 4.42e-243j)
| (4.8736472514172613604 + 1.43017269775175845e-634j)  +/-  (5.3e-244, 5.3e-244j)
| (8.2138273209382866991 - 4.0561697172475117348e-635j)  +/-  (6.18e-242, 6.18e-242j)
| (-8.2138273209382866991 - 1.7990253516596304867e-657j)  +/-  (5.9e-242, 5.9e-242j)
| (-1.7082536203896324893 + 1.2138497251192675583e-689j)  +/-  (2.78e-249, 2.78e-249j)
| (-7.7052462206312233047 - 2.7220331232140001178e-687j)  +/-  (4.72e-242, 4.72e-242j)
| (-10.436910210693572853 - 1.3883048185597003427e-710j)  +/-  (1.39e-242, 1.39e-242j)
| (2.7348934856989767145 + 1.9776703810832912971e-725j)  +/-  (4.37e-247, 4.37e-247j)
| (-3.9908868563553459072 + 5.2493507597618903957e-724j)  +/-  (4.12e-245, 4.12e-245j)
| (-7.2095673337107825348 - 3.5629686413607180329e-722j)  +/-  (3.45e-242, 3.45e-242j)
| (-2.3605545667757946951 - 3.0577033786542781832e-734j)  +/-  (8.53e-248, 8.53e-248j)
| (6.7249929201527825481 + 2.8521839573432647653e-732j)  +/-  (1.98e-242, 1.98e-242j)
| (0.66229763968787951317 - 1.0668986768577743804e-743j)  +/-  (1.72e-252, 1.72e-252j)
| (-3.1397980296785904718 - 1.4230175797383248664e-737j)  +/-  (1.99e-246, 1.99e-246j)
| (-3.5604533861266068972 + 1.9595704463073680972e-737j)  +/-  (9.64e-246, 9.64e-246j)
| (0.33555035021659491682 - 1.7550406989074637939e-745j)  +/-  (1.26e-253, 1.26e-253j)
| (2.5795069586484380554e-768 - 1.2425436355680753819e-768j)  +/-  (1.63e-766, 1.63e-766j)
| (2.0314545988278380851 + 3.3565059335489122408e-740j)  +/-  (1.92e-248, 1.92e-248j)
| (3.9908868563553459072 - 2.0575402691784593427e-740j)  +/-  (4.36e-245, 4.36e-245j)
| (-1 + 1.2132579538329615742e-748j)  +/-  (2.24e-251, 2.24e-251j)
| (-0.33555035021659491682 - 1.4383579229333906865e-749j)  +/-  (1.26e-253, 1.26e-253j)
-------------------------------------------------
The weights are:
| (6.6075069973556659281e-28 + 8.700834626383003494e-538j)  +/-  (1.71e-66, 1.27e-187j)
| (5.6074565492681933781e-18 + 1.7995830792209475352e-534j)  +/-  (2.8e-62, 2.09e-183j)
| (5.3985600650345382976e-25 - 8.4905615835265658045e-537j)  +/-  (2.23e-65, 1.67e-186j)
| (3.0166107265834206036e-31 + 3.6217004407980123406e-540j)  +/-  (2.73e-68, 2.04e-189j)
| (2.7258537627825036821e-40 - 1.7620449685330808274e-546j)  +/-  (5.72e-74, 4.27e-195j)
| (2.7258537627825036821e-40 + 1.8234955362646647145e-545j)  +/-  (7.01e-73, 5.23e-194j)
| (3.2772792990230364277e-35 + 8.4630536176273585442e-544j)  +/-  (2.1e-72, 1.57e-193j)
| (0.0037260708843277379825 - 1.1862792788212595256e-524j)  +/-  (3.14e-41, 2.35e-162j)
| (3.0166107265834206036e-31 - 1.0831085768467420533e-541j)  +/-  (3.5e-71, 2.61e-192j)
| (5.6074565492681933781e-18 + 1.5300425190003774566e-533j)  +/-  (4.06e-65, 3.03e-186j)
| (0.0086496541059686098053 + 6.0667201136329942629e-524j)  +/-  (7.33e-40, 5.47e-161j)
| (2.891473150416685356e-11 + 1.3436712675801110036e-530j)  +/-  (1.45e-60, 1.08e-181j)
| (1.004201806466585988e-08 + 4.9882612748287366694e-529j)  +/-  (8.29e-58, 6.19e-179j)
| (9.6930661312579959337e-06 - 5.3601347168355141876e-527j)  +/-  (4.73e-53, 3.53e-174j)
| (1.0095662797165126904e-12 - 8.6665606960149572471e-531j)  +/-  (2.29e-63, 1.71e-184j)
| (2.5658136309934443409e-14 + 1.2035529160467931405e-531j)  +/-  (2.01e-64, 1.5e-185j)
| (4.4068601353167667433e-20 - 1.2134923752837858601e-535j)  +/-  (7.79e-69, 5.81e-190j)
| (2.0860297816144037314e-22 + 1.0913886636359068409e-535j)  +/-  (9.05e-69, 6.76e-190j)
| (0.015937412891545179579 - 9.6346251922568159752e-524j)  +/-  (4.61e-44, 3.44e-165j)
| (3.2772792990230364277e-35 - 1.3799919274893039604e-542j)  +/-  (1.96e-74, 1.46e-195j)
| (1.2622964754687608599e-07 - 7.385651169781038763e-528j)  +/-  (1.2e-60, 8.95e-182j)
| (1.2622964754687608599e-07 - 2.5870276399998221943e-528j)  +/-  (4.06e-60, 3.03e-181j)
| (9.6930661312579959337e-06 - 1.2512569324302933729e-526j)  +/-  (2.83e-58, 2.12e-179j)
| (0.00030039722805832716828 - 1.6716599293976981135e-525j)  +/-  (2.25e-55, 1.68e-176j)
| (0.057168070125590309085 - 2.7817175695752051442e-523j)  +/-  (1.22e-42, 9.1e-164j)
| (2.0860297816144037314e-22 + 6.38222892786392684e-537j)  +/-  (5.09e-72, 3.8e-193j)
| (0.084415806197662339242 + 5.3328240475008480185e-523j)  +/-  (8.43e-41, 6.29e-162j)
| (0.057168070125590309085 - 3.5587551932464921815e-523j)  +/-  (7.28e-45, 5.44e-166j)
| (1.2431748485950262549e-06 + 1.2248026243703786727e-527j)  +/-  (9.36e-60, 6.99e-181j)
| (0.1050800876315221905 - 6.5545707971669491612e-523j)  +/-  (5.74e-45, 4.29e-166j)
| (6.1774858577561860696e-10 - 8.6745545061157256025e-530j)  +/-  (1.8e-63, 1.34e-184j)
| (0.0011953901031833674187 + 5.8019106531614624775e-525j)  +/-  (1.14e-55, 8.48e-177j)
| (0.031426326010953361031 + 2.3692327578967608466e-523j)  +/-  (6.52e-49, 4.87e-170j)
| (6.6075069973556659281e-28 + 6.6619633122746684241e-540j)  +/-  (4.07e-75, 3.04e-196j)
| (6.1774858577561860696e-10 - 3.1185803182573974549e-529j)  +/-  (2.45e-65, 1.83e-186j)
| (4.4068601353167667433e-20 - 1.381440456192706001e-534j)  +/-  (7.35e-71, 5.49e-192j)
| (1.004201806466585988e-08 + 1.5910090650555901867e-528j)  +/-  (1.61e-64, 1.2e-185j)
| (1.2431748485950262549e-06 + 3.1524431286841877378e-527j)  +/-  (9.23e-63, 6.89e-184j)
| (4.6034781771615080644e-16 - 1.4592101980736653345e-532j)  +/-  (4.02e-69, 3e-190j)
| (4.6034781771615080644e-16 - 2.1593193409881325812e-533j)  +/-  (1.23e-72, 9.18e-194j)
| (0.031426326010953361031 + 1.7356237462746878335e-523j)  +/-  (6.31e-58, 4.71e-179j)
| (2.5658136309934443409e-14 + 2.1553223390839171409e-532j)  +/-  (5.44e-72, 4.06e-193j)
| (5.3985600650345382976e-25 - 2.4877478547074470995e-538j)  +/-  (1.32e-77, 9.84e-199j)
| (0.0037260708843277379825 - 1.9650395264422369532e-524j)  +/-  (1.37e-62, 1.02e-183j)
| (6.0293680047198324334e-05 + 2.1981705921801913871e-526j)  +/-  (1.4e-66, 1.04e-187j)
| (1.0095662797165126904e-12 - 1.8291459137819608602e-531j)  +/-  (3.26e-71, 2.43e-192j)
| (0.0086496541059686098053 + 3.9336661801504328371e-524j)  +/-  (1.19e-63, 8.9e-185j)
| (2.891473150416685356e-11 + 5.505907593332944452e-530j)  +/-  (5.47e-71, 4.08e-192j)
| (0.1050800876315221905 - 7.3890178492408065133e-523j)  +/-  (5.11e-62, 3.81e-183j)
| (0.0011953901031833674187 + 3.2373837424614018595e-525j)  +/-  (5.93e-66, 4.42e-187j)
| (0.00030039722805832716828 - 8.5786456548186171726e-526j)  +/-  (1.38e-66, 1.03e-187j)
| (0.12443733761029824237 + 8.650531373328294523e-523j)  +/-  (3.54e-63, 2.64e-184j)
| (0.13518416074099733046 - 8.7897976524641964954e-523j)  +/-  (1.85e-63, 1.38e-184j)
| (0.015937412891545179579 - 1.3966926984469893772e-523j)  +/-  (3.97e-65, 2.97e-186j)
| (6.0293680047198324334e-05 + 4.6776898654530763696e-526j)  +/-  (4.66e-68, 3.49e-189j)
| (0.084415806197662339242 + 4.4489532479214954552e-523j)  +/-  (5.51e-65, 4.15e-186j)
| (0.12443733761029824237 + 8.1414005657543459331e-523j)  +/-  (1.47e-64, 1.06e-185j)
