Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 14 25
-------------------------------------------------
Trying to find an order 14 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 25 Kronrod extension for:
P2 : t^16 - 935281/8628*t^14 + 38001691/8628*t^12 - 245286041/2876*t^10 + 2383796415/2876*t^8 - 11245499265/2876*t^6 + 22854346515/2876*t^4 - 15081381315/2876*t^2 + 1321665345/2876
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^41 - 36536974694389094843212509710635785995330102214740239325090121926765779672113742201/64301487709824112838067284787501520085949280303299554228708846592950350801461588*t^39 + 9259868215363355243689200919527550291020978495319500146757339170835263350661422092211/64301487709824112838067284787501520085949280303299554228708846592950350801461588*t^37 - 462447457979799083176873521359164470440448877604339894829759851482460578030562407789761/21433829236608037612689094929167173361983093434433184742902948864316783600487196*t^35 + 45776370905664007030888923307200637701903101647584989044325966540055022169509708078786815/21433829236608037612689094929167173361983093434433184742902948864316783600487196*t^33 - 1585060310564307642449504145356768830143045303709391703025508134739337644151986286839537745/10716914618304018806344547464583586680991546717216592371451474432158391800243598*t^31 + 79344071084585707551349204790445447298870654935203233221698944389279793299512748223447250595/10716914618304018806344547464583586680991546717216592371451474432158391800243598*t^29 - 2925793443979718949426878216714613608478811977771785032966552336865135452340379067292746590495/10716914618304018806344547464583586680991546717216592371451474432158391800243598*t^27 + 80281085711114562781916785777749715513638845987368173667567923015839624344272543221373847982685/10716914618304018806344547464583586680991546717216592371451474432158391800243598*t^25 - 822517117131973093575453843981528899409735126145122214808579161654995212162177744687990210564250/5358457309152009403172273732291793340495773358608296185725737216079195900121799*t^23 + 12563001340685421993405876705085807730240618459665696894420304087185289946581136258309774858000750/5358457309152009403172273732291793340495773358608296185725737216079195900121799*t^21 - 512766718926058925654129113334834623970920941580242154612740726746772587454904828323084064203000/19344611224375485210008208419825968738251889381257386952078473704257024910187*t^19 + 1174008566692170361745506321679800311816345909456451595250633377259257722096116188778131575809523500/5358457309152009403172273732291793340495773358608296185725737216079195900121799*t^17 - 13923079053948846574541063772965381323253813158842071921198789895356176603125019422978502097706015375/10716914618304018806344547464583586680991546717216592371451474432158391800243598*t^15 + 57622461937705910509286910269435145645319700012068398739825145576742213945310441671822355955342038125/10716914618304018806344547464583586680991546717216592371451474432158391800243598*t^13 - 159851360409156031359691484202767240696102148670238048347000480298567777184255792734375894116842440625/10716914618304018806344547464583586680991546717216592371451474432158391800243598*t^11 + 279115522286207473254642472688860495358158390460184385152389053203937935276283302125512878363975493125/10716914618304018806344547464583586680991546717216592371451474432158391800243598*t^9 - 549813201564225037357668732207353973154889250840852886075156979588195840435793169846466307860055733125/21433829236608037612689094929167173361983093434433184742902948864316783600487196*t^7 + 242433021364848837771831353767583860301010189797732276229929339664139216885174211745279768171974724375/21433829236608037612689094929167173361983093434433184742902948864316783600487196*t^5 - 23068971148632182727388035650359331397703705095394716608431201336821784563630846612371768430774909375/21433829236608037612689094929167173361983093434433184742902948864316783600487196*t^3 + 347056281150675885231842479960558287667080986292315542772540052936826878495315072540110649501040625/21433829236608037612689094929167173361983093434433184742902948864316783600487196*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:
| (-9.3055232824374250241 + 3.1464933467433341933e-620j)  +/-  (1.45e-247, 1.45e-247j)
| (-1 + 5.9802746141449528062e-628j)  +/-  (2.91e-252, 2.91e-252j)
| (7.0456330792702966482 + 3.2990891961104828678e-633j)  +/-  (2.43e-246, 2.43e-246j)
| (-8.4746227067863760837 - 2.1802112273251795888e-647j)  +/-  (6.77e-247, 6.77e-247j)
| (-7.731326482147013726 - 8.5601283051743712293e-647j)  +/-  (1.49e-246, 1.49e-246j)
| (9.3055232824374250241 + 3.0100732290967948356e-646j)  +/-  (1.48e-247, 1.48e-247j)
| (-5.80060616930244861 - 1.3327497508897682697e-650j)  +/-  (3.43e-246, 3.43e-246j)
| (-1.7404508708598477666 + 2.6560868978194976802e-653j)  +/-  (1.79e-249, 1.79e-249j)
| (-10.305267714382455555 + 6.745392155305904017e-653j)  +/-  (1.58e-248, 1.58e-248j)
| (-7.0456330792702966482 + 2.9173036024609936705e-650j)  +/-  (2.62e-246, 2.62e-246j)
| (3.7994677775414471755 + 2.0187380286618779731e-649j)  +/-  (6.67e-247, 6.67e-247j)
| (4.7254766412651289193 + 3.1032157493739989485e-662j)  +/-  (2.43e-246, 2.43e-246j)
| (7.731326482147013726 + 9.6084430197060340781e-682j)  +/-  (1.49e-246, 1.49e-246j)
| (10.305267714382455555 + 2.77303209346313113e-694j)  +/-  (1.48e-248, 1.48e-248j)
| (3.3633245069953754209 + 5.667905273134212678e-699j)  +/-  (2.2e-247, 2.2e-247j)
| (1.7404508708598477666 - 8.1449361072195837977e-707j)  +/-  (1.66e-249, 1.66e-249j)
| (-2.0081114997377229069 - 6.9683038813384838446e-708j)  +/-  (3.21e-249, 3.21e-249j)
| (8.4746227067863760837 - 3.8493188753298091448e-713j)  +/-  (7.56e-247, 7.56e-247j)
| (4.2555162521877678015 + 2.8891627751598746381e-726j)  +/-  (1.43e-246, 1.43e-246j)
| (-4.7254766412651289193 + 2.4276989793381845321e-731j)  +/-  (2.53e-246, 2.53e-246j)
| (1 - 1.5552881991644701144e-739j)  +/-  (3.01e-252, 3.01e-252j)
| (-1.1106599509075738012e-742 - 2.4228725416201192951e-743j)  +/-  (4.66e-741, 4.66e-741j)
| (5.80060616930244861 - 1.3923503667057349187e-738j)  +/-  (3.5e-246, 3.5e-246j)
| (6.4037654380415055938 - 1.4251066428243827081e-762j)  +/-  (3.71e-246, 3.71e-246j)
| (-5.2385718534747252466 - 1.1302989974407766699e-774j)  +/-  (3.1e-246, 3.1e-246j)
| (-6.4037654380415055938 - 2.5950240174458560092e-775j)  +/-  (3.34e-246, 3.34e-246j)
| (2.5291115060537482634 + 1.3778202049872638284e-776j)  +/-  (1.27e-248, 1.27e-248j)
| (2.9658396624571211144 + 3.9210852042295500163e-777j)  +/-  (6.56e-248, 6.56e-248j)
| (-2.5291115060537482634 - 2.532587572308011814e-779j)  +/-  (1.29e-248, 1.29e-248j)
| (-2.9658396624571211144 + 3.3928144992428820672e-778j)  +/-  (7.05e-248, 7.05e-248j)
| (-3.3633245069953754209 - 2.755723792525865459e-779j)  +/-  (2.5e-247, 2.5e-247j)
| (2.0081114997377229069 - 5.4503455822257963918e-782j)  +/-  (2.96e-249, 2.96e-249j)
| (0.32075040850526950902 - 2.8251281633660469395e-786j)  +/-  (6.42e-254, 6.42e-254j)
| (-4.2555162521877678015 - 5.8188213278492005427e-780j)  +/-  (1.4e-246, 1.4e-246j)
| (-1.5898537181939983695 + 1.8167802061646447087e-788j)  +/-  (5.15e-250, 5.15e-250j)
| (-0.32075040850526950902 - 9.8908933104245069942e-792j)  +/-  (6.1e-254, 6.1e-254j)
| (5.2385718534747252466 - 2.1257730829072116568e-791j)  +/-  (3.25e-246, 3.25e-246j)
| (1.5898537181939983695 - 1.5043450154675869156e-802j)  +/-  (4.94e-250, 4.94e-250j)
| (-3.7994677775414471755 - 3.7310080350805978655e-802j)  +/-  (6.25e-247, 6.25e-247j)
| (0.13597367915093623848 - 2.2065043343608101736e-811j)  +/-  (1.91e-254, 1.91e-254j)
| (-0.13597367915093623848 + 2.5804896272245816452e-811j)  +/-  (1.91e-254, 1.91e-254j)
-------------------------------------------------
The weights are:
| (5.6037118534230192748e-20 + 9.8714985909252444092e-639j)  +/-  (1.26e-89, 5.67e-212j)
| (0.13790527431104653446 + 3.7777493614747651162e-626j)  +/-  (1.56e-67, 7e-190j)
| (4.3911040230351340374e-12 - 1.208440656993427478e-635j)  +/-  (4.68e-86, 2.1e-208j)
| (7.8998105726106707675e-17 - 1.8304886252034179746e-637j)  +/-  (3.47e-88, 1.56e-210j)
| (2.9738471652862228044e-14 + 4.3240346083535996716e-636j)  +/-  (4.57e-87, 2.06e-209j)
| (5.6037118534230192748e-20 + 9.4784758134957278655e-641j)  +/-  (1.02e-92, 4.6e-215j)
| (1.1500137251158809738e-08 - 1.9792249024235136117e-632j)  +/-  (6.36e-84, 2.86e-206j)
| (-0.034892465180015623787 + 7.056448851115247012e-626j)  +/-  (1.56e-67, 7e-190j)
| (3.9973512683931943787e-24 + 6.1200945556326618224e-642j)  +/-  (7.04e-93, 3.17e-215j)
| (4.3911040230351340374e-12 - 8.7379805390104129879e-635j)  +/-  (2.99e-86, 1.34e-208j)
| (0.00013235558257958567268 - 2.8273340723954284618e-629j)  +/-  (3.37e-81, 1.52e-203j)
| (2.7553712295180985679e-06 - 6.4171349659205959057e-631j)  +/-  (2.53e-84, 1.14e-206j)
| (2.9738471652862228044e-14 + 3.9976887631278799157e-637j)  +/-  (2.28e-91, 1.03e-213j)
| (3.9973512683931943787e-24 - 3.1213196725701724246e-643j)  +/-  (7.2e-97, 3.24e-219j)
| (0.00057552495047236780741 + 1.4096926129953332321e-628j)  +/-  (1.69e-81, 7.62e-204j)
| (-0.034892465180015623787 + 4.8509591959121486886e-626j)  +/-  (3.88e-75, 1.75e-197j)
| (0.032556954856817928255 - 1.9901401493841464046e-626j)  +/-  (5.52e-77, 2.48e-199j)
| (7.8998105726106707675e-17 - 8.5587092535672624511e-639j)  +/-  (3.65e-93, 1.64e-215j)
| (2.137867598649383275e-05 + 4.7176251874697501392e-630j)  +/-  (2.04e-84, 9.2e-207j)
| (2.7553712295180985679e-06 - 1.9639873421867838349e-630j)  +/-  (2.25e-88, 1.01e-210j)
| (0.13790527431104653446 + 3.040085867613636862e-626j)  +/-  (1.11e-77, 5.02e-200j)
| (2.6514011883836249926 - 4.6154020679122241934e-624j)  +/-  (3.91e-78, 1.76e-200j)
| (1.1500137251158809738e-08 - 4.5957616632897845439e-633j)  +/-  (6.42e-89, 2.89e-211j)
| (3.0908042592430573608e-10 + 2.6665808028568396034e-634j)  +/-  (6.04e-90, 2.72e-212j)
| (2.3619008353003960801e-07 + 2.2433878270612400593e-631j)  +/-  (6.38e-90, 2.87e-212j)
| (3.0908042592430573608e-10 + 1.4425995573214404537e-633j)  +/-  (8.88e-92, 4e-214j)
| (0.0077543868508825780875 + 1.6190078269475747908e-627j)  +/-  (8.63e-84, 3.88e-206j)
| (0.0019680208917356157187 - 4.9281764419887167832e-628j)  +/-  (1.89e-84, 8.52e-207j)
| (0.0077543868508825780875 + 2.8217119832506217827e-627j)  +/-  (6.49e-86, 2.92e-208j)
| (0.0019680208917356157187 - 9.5233127529102873196e-628j)  +/-  (1.81e-87, 8.15e-210j)
| (0.00057552495047236780741 + 3.0011947619899562121e-628j)  +/-  (9.37e-89, 4.22e-211j)
| (0.032556954856817928255 - 1.2873900845854388399e-626j)  +/-  (5.56e-86, 2.5e-208j)
| (0.66322112383268938438 - 6.4749065223178741588e-625j)  +/-  (3.56e-84, 1.6e-206j)
| (2.137867598649383275e-05 + 1.2654690457379491409e-629j)  +/-  (8.19e-91, 3.69e-213j)
| (0.08875978463075811655 - 6.6426689339745146813e-626j)  +/-  (7.87e-86, 3.56e-208j)
| (0.66322112383268938438 - 6.948045510830139507e-625j)  +/-  (2.6e-85, 1.18e-207j)
| (2.3619008353003960801e-07 + 6.2786069397261357205e-632j)  +/-  (7.51e-93, 3.4e-215j)
| (0.08875978463075811655 - 4.7255822458382727967e-626j)  +/-  (1.21e-86, 5.49e-209j)
| (0.00013235558257958567268 - 6.7210261686068201479e-629j)  +/-  (3.81e-90, 1.71e-212j)
| (-1.723705936969717124 + 2.9126740740646014118e-624j)  +/-  (1.66e-85, 7.45e-208j)
| (-1.723705936969717124 + 3.0008723715473100161e-624j)  +/-  (1.24e-85, 5.73e-208j)
