Starting with polynomial:
P : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Extension levels are: 8 40
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P1 : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^48 - 911482131494893539006537177845526565971616/947397510533097832003392609306155659087*t^46 + 6798195690026501725016335724232682059442211100/16105757679062663144057674358204646204479*t^44 - 19862645329230318955479624296418311683910550339840/177163334469689294584634417940251108249269*t^42 + 3576463550867792036434055918950525505242656874689555/177163334469689294584634417940251108249269*t^40 - 27250536266687872250243013799204190125069333016581740/10421372615864076152037318702367712249957*t^38 + 44709993956122182236766831522211726233937228845550509390/177163334469689294584634417940251108249269*t^36 - 3286182825639792546419050096576158760824053237028678340500/177163334469689294584634417940251108249269*t^34 + 997124310869871746738357969768965794161172876188818066200/947397510533097832003392609306155659087*t^32 - 44023601516343704440726545390955358662824649228902280400400/947397510533097832003392609306155659087*t^30 + 1517770976182710018100586571154554838360170824452562787458400/947397510533097832003392609306155659087*t^28 - 40860958444742597978569404054661946163448720763623465960393200/947397510533097832003392609306155659087*t^26 + 856242228681188608156353816777796222371505551102842780759906250/947397510533097832003392609306155659087*t^24 - 13877620190364431128585182918001589864443278197851344339422355000/947397510533097832003392609306155659087*t^22 + 172294862513073155256711022112742900203620941295457978538099547500/947397510533097832003392609306155659087*t^20 - 1616759897796846080743667748697187215233621802189291674056386485000/947397510533097832003392609306155659087*t^18 + 11262269130152386726031375567264209134435722638830546359945960664375/947397510533097832003392609306155659087*t^16 - 56863105452286156000766359758728494699802735575565771190245634750000/947397510533097832003392609306155659087*t^14 + 201528319728119226257854161033223093965144600334859748934203949012500/947397510533097832003392609306155659087*t^12 - 479812904312580375532562353664550829840995006671830482535142385150000/947397510533097832003392609306155659087*t^10 + 721238334279968779743512967357714511872101366322596950294966294978125/947397510533097832003392609306155659087*t^8 - 624610483741772547519781907577192611871477260160925056851171091262500/947397510533097832003392609306155659087*t^6 + 270020529531609689990719298095787857604109977134098572526612057656250/947397510533097832003392609306155659087*t^4 - 45089021412810599911814209738234209597934675837293212298214401937500/947397510533097832003392609306155659087*t^2 + 1367263188133790621263854499799567347125076268446172813975392781250/947397510533097832003392609306155659087
-------------------------------------------------
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:
| (-11.154965943933032491 + 2.6903272057819519619e-862j)  +/-  (5.36e-246, 5.36e-246j)
| (11.154965943933032491 + 7.4930583311467676117e-859j)  +/-  (5.67e-246, 5.67e-246j)
| (9.6556096304376860266 + 2.2476973970284005093e-862j)  +/-  (8.91e-245, 8.91e-245j)
| (-9.0008037896200085203 - 3.7685691444093945963e-870j)  +/-  (2.1e-244, 2.1e-244j)
| (-9.6556096304376860266 + 6.7676752750911849138e-873j)  +/-  (9.59e-245, 9.59e-245j)
| (-10.363681654149252798 - 5.5417616111638944444e-875j)  +/-  (2.88e-245, 2.88e-245j)
| (6.6826821729763901398 + 4.241239093609072831e-871j)  +/-  (2.97e-244, 2.97e-244j)
| (-5.1253418285995348211 + 5.9074842794305981277e-879j)  +/-  (3.73e-245, 3.73e-245j)
| (12.108033555472363855 - 7.6432478780367070288e-880j)  +/-  (4.23e-247, 4.23e-247j)
| (-7.7955843222988379167 - 4.3869063711798819725e-881j)  +/-  (4.19e-244, 4.19e-244j)
| (3.2207462804438175412 + 3.6996155924667075872e-885j)  +/-  (3.93e-247, 3.93e-247j)
| (-5.6322313272630486331 + 8.2177111727400036269e-882j)  +/-  (9.03e-245, 9.03e-245j)
| (-2.4251467285733674753 - 8.5349394744651038624e-892j)  +/-  (2.14e-248, 2.14e-248j)
| (-12.108033555472363855 - 1.0295860461059601759e-890j)  +/-  (4.16e-247, 4.16e-247j)
| (-4.1445471861258943321 + 9.7960973764008055432e-889j)  +/-  (4.68e-246, 4.68e-246j)
| (9.0008037896200085203 + 6.0953834760092731702e-895j)  +/-  (2.07e-244, 2.07e-244j)
| (-3.6728902171689409957 + 1.736081322037695728e-911j)  +/-  (1.33e-246, 1.33e-246j)
| (-8.3838655653020856623 - 5.2634591002753089226e-912j)  +/-  (3.27e-244, 3.27e-244j)
| (8.3838655653020856623 - 4.9451402113299367318e-926j)  +/-  (3.33e-244, 3.33e-244j)
| (-6.6826821729763901398 + 4.8323217315640701813e-939j)  +/-  (3.05e-244, 3.05e-244j)
| (2.8024858612875416991 + 3.6811593436070602901e-950j)  +/-  (9.83e-248, 9.83e-248j)
| (1.2182528067518898659 - 8.2047565443973681201e-957j)  +/-  (3.62e-251, 3.62e-251j)
| (7.7955843222988379167 + 2.0081575169507319153e-949j)  +/-  (4.51e-244, 4.51e-244j)
| (4.1445471861258943321 - 1.4903066267900374441e-959j)  +/-  (4.5e-246, 4.5e-246j)
| (-0.83776494241009525348 + 2.2410543902848414627e-966j)  +/-  (4.42e-252, 4.42e-252j)
| (7.2299222267002983679 - 2.2953618282728572834e-957j)  +/-  (4e-244, 4e-244j)
| (-6.1508458217519374301 - 2.6925471901897326125e-961j)  +/-  (1.65e-244, 1.65e-244j)
| (-4.6293837392862982468 - 1.1434594771578120871e-963j)  +/-  (1.39e-245, 1.39e-245j)
| (2.0461937435529887607 - 2.5584056660241330545e-966j)  +/-  (3.03e-249, 3.03e-249j)
| (-3.2207462804438175412 - 1.5501796166172739229e-965j)  +/-  (3.82e-247, 3.82e-247j)
| (10.363681654149252798 - 4.7616961152925789641e-962j)  +/-  (2.86e-245, 2.86e-245j)
| (-1.6365190424351079992 + 7.4634527176612715375e-969j)  +/-  (3.42e-250, 3.42e-250j)
| (5.1253418285995348211 - 1.3437580182661473086e-960j)  +/-  (3.91e-245, 3.91e-245j)
| (4.6293837392862982468 + 2.3804034691011891398e-965j)  +/-  (1.39e-245, 1.39e-245j)
| (-1.2182528067518898659 + 1.5122270478721091358e-977j)  +/-  (3.27e-251, 3.27e-251j)
| (-2.8024858612875416991 - 8.4884955919433024436e-973j)  +/-  (9.99e-248, 9.99e-248j)
| (2.4251467285733674753 - 8.1430981956921711899e-973j)  +/-  (2.08e-248, 2.08e-248j)
| (0.83776494241009525348 - 3.907593086815224844e-977j)  +/-  (4.45e-252, 4.45e-252j)
| (3.6728902171689409957 + 2.0177290007479784847e-970j)  +/-  (1.35e-246, 1.35e-246j)
| (-0.19597504745192230607 - 5.289258456373764835e-979j)  +/-  (3.2e-254, 3.2e-254j)
| (-0.53907981135137510807 - 4.7425283932463670851e-978j)  +/-  (4.88e-253, 4.88e-253j)
| (-7.2299222267002983679 + 2.1231215132414816449e-970j)  +/-  (3.71e-244, 3.71e-244j)
| (0.19597504745192230607 - 5.7816418911692490255e-980j)  +/-  (3.2e-254, 3.2e-254j)
| (0.53907981135137510807 + 3.1547838820617286328e-978j)  +/-  (4.88e-253, 4.88e-253j)
| (5.6322313272630486331 + 9.5896960600741187829e-974j)  +/-  (9.39e-245, 9.39e-245j)
| (-2.0461937435529887607 + 4.8575788894951171936e-985j)  +/-  (3.19e-249, 3.19e-249j)
| (6.1508458217519374301 + 1.7251509200037376443e-986j)  +/-  (1.82e-244, 1.82e-244j)
| (1.6365190424351079992 - 6.965350637518088729e-995j)  +/-  (3.61e-250, 3.61e-250j)
-------------------------------------------------
The weights are:
| (3.2391796336337123716e-28 + 1.5607881482409622553e-887j)  +/-  (1.17e-85, 6.16e-208j)
| (3.2391796336337123716e-28 - 1.3844761828609152884e-885j)  +/-  (4.32e-86, 2.27e-208j)
| (1.5395438856907315814e-21 - 2.4580112154079859339e-882j)  +/-  (3.31e-83, 1.74e-205j)
| (6.4700626827117350311e-19 - 1.8170680500442304675e-882j)  +/-  (2.74e-82, 1.44e-204j)
| (1.5395438856907315814e-21 + 6.4201777996427491555e-884j)  +/-  (1.11e-83, 5.85e-206j)
| (1.4086554727824250923e-24 - 1.4065333483037627699e-885j)  +/-  (3.89e-85, 2.04e-207j)
| (4.3169372369670838629e-11 + 2.598727895821772759e-877j)  +/-  (4.67e-80, 2.45e-202j)
| (3.9517466939711400265e-07 + 1.9867458248135971678e-875j)  +/-  (7e-75, 3.68e-197j)
| (6.4170609362046219564e-33 - 9.2421724883914719895e-889j)  +/-  (6.14e-91, 3.22e-213j)
| (1.4627161168302265007e-14 - 5.3024280401808180233e-880j)  +/-  (1.93e-81, 1.01e-203j)
| (0.00097763600695314210618 - 2.0162042944013501132e-872j)  +/-  (8.43e-70, 4.42e-192j)
| (2.6442425515977441681e-08 - 3.2671797732951279445e-876j)  +/-  (9.16e-77, 4.81e-199j)
| (0.0077540237884846337095 + 1.0800258536461912719e-871j)  +/-  (1.1e-65, 5.8e-188j)
| (6.4170609362046219564e-33 - 4.5728938572138931601e-890j)  +/-  (3.37e-90, 1.77e-212j)
| (3.5570619351867947324e-05 + 5.4117948529792733621e-874j)  +/-  (2.92e-73, 1.53e-195j)
| (6.4700626827117350311e-19 + 2.6695060373464253197e-881j)  +/-  (2.41e-87, 1.27e-209j)
| (0.00021758743765439903896 - 2.5114137982256667062e-873j)  +/-  (2.83e-72, 1.48e-194j)
| (1.3090837219998670622e-16 + 3.5845672190706920031e-881j)  +/-  (9.23e-83, 4.84e-205j)
| (1.3090837219998670622e-16 - 3.2406798216336397523e-880j)  +/-  (9.68e-87, 5.08e-209j)
| (4.3169372369670838629e-11 - 5.893849383402375936e-878j)  +/-  (1.17e-80, 6.14e-203j)
| (0.0031099758043847626491 + 6.8257244262590280805e-872j)  +/-  (8.61e-74, 4.52e-196j)
| (0.077941676887309103446 + 1.2372302513050754727e-870j)  +/-  (1e-64, 5.27e-187j)
| (1.4627161168302265007e-14 + 3.5450683412963624236e-879j)  +/-  (3.34e-86, 1.76e-208j)
| (3.5570619351867947324e-05 - 1.2302569802479881077e-873j)  +/-  (6.07e-80, 3.19e-202j)
| (0.094347146990260458916 + 2.2027637272666583985e-870j)  +/-  (1.91e-67, 1e-189j)
| (9.8902593146266296958e-13 - 3.2897297349889281802e-878j)  +/-  (1.81e-85, 9.51e-208j)
| (1.2755380957011637016e-09 + 4.7274913879550210905e-877j)  +/-  (1.21e-81, 6.33e-204j)
| (4.3436941195235048756e-06 - 1.084171995906262586e-874j)  +/-  (7.98e-79, 4.19e-201j)
| (0.019443088729668503373 + 3.3378617357472949717e-871j)  +/-  (1.29e-74, 6.79e-197j)
| (0.00097763600695314210618 + 1.0807420151580597022e-872j)  +/-  (7.28e-77, 3.82e-199j)
| (1.4086554727824250923e-24 + 1.6323486065076496912e-884j)  +/-  (4.74e-92, 2.49e-214j)
| (0.043850189931083866459 + 4.4901584016690487174e-871j)  +/-  (6.39e-74, 3.36e-196j)
| (3.9517466939711400265e-07 - 5.6787270427412001892e-875j)  +/-  (5.49e-84, 2.88e-206j)
| (4.3436941195235048756e-06 + 2.7517931848881423596e-874j)  +/-  (6.22e-83, 3.27e-205j)
| (0.077941676887309103446 - 9.836917044491898671e-871j)  +/-  (6.66e-75, 3.5e-197j)
| (0.0031099758043847626491 - 3.9850238514062097155e-872j)  +/-  (2.43e-78, 1.27e-200j)
| (0.0077540237884846337095 - 1.7155908501595003673e-871j)  +/-  (1.31e-78, 6.86e-201j)
| (0.094347146990260458916 - 2.5780553819103949947e-870j)  +/-  (1.1e-75, 5.79e-198j)
| (0.00021758743765439903896 + 5.1520975737783831098e-873j)  +/-  (3.68e-81, 1.93e-203j)
| (0.15022389155687210798 + 3.2206406801608750693e-870j)  +/-  (9.21e-76, 4.84e-198j)
| (0.10209444561705146506 - 3.1947745247811207448e-870j)  +/-  (8.85e-76, 4.65e-198j)
| (9.8902593146266296958e-13 + 6.1824162345306583137e-879j)  +/-  (2.22e-86, 1.16e-208j)
| (0.15022389155687210798 - 3.341128178561454013e-870j)  +/-  (2.24e-76, 1.17e-198j)
| (0.10209444561705146506 + 3.5346834515998040241e-870j)  +/-  (1.46e-76, 7.65e-199j)
| (2.6442425515977441681e-08 + 1.062801467437226589e-875j)  +/-  (8.5e-86, 4.46e-208j)
| (0.019443088729668503373 - 2.2635696940641028199e-871j)  +/-  (4.01e-80, 2.09e-202j)
| (1.2755380957011637016e-09 - 1.7740864135224263425e-876j)  +/-  (1.14e-86, 6e-209j)
| (0.043850189931083866459 - 6.116969333237053098e-871j)  +/-  (2.17e-80, 1.1e-202j)
