Starting with polynomial:
P : 256*t^8 - 3584*t^6 + 13440*t^4 - 13440*t^2 + 1680
Extension levels are: 8 42
-------------------------------------------------
Trying to find an order 42 Kronrod extension for:
P1 : 256*t^8 - 3584*t^6 + 13440*t^4 - 13440*t^2 + 1680
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 256*t^50 - 16766945183542805182237063185789097259337019017344/122749103214213163428429988486872850615280185*t^48 + 4099367213082069252238778413820796367583217047300736/122749103214213163428429988486872850615280185*t^46 - 121992254138438564955734342519076081016022868812585920/24549820642842632685685997697374570123056037*t^44 + 210380645722731274834764580122430090656228296315669819392/417346950928324755656661960855367692091952629*t^42 - 15448583876841928964284785466397935464888860543538701590752/417346950928324755656661960855367692091952629*t^40 + 851040238556253743826075728060822167497703343342711925312696/417346950928324755656661960855367692091952629*t^38 - 972265978374583068341956810558382191668096775781661371068212/11279647322387155558288161104199126813296017*t^36 + 603632567865176765548011767193611077876796983379604098189925/212823534384663312420531341588662770062189*t^34 - 97262501074086957743856442519329959886267632105279207017411605/1327017332045547712739783659317544330976002*t^32 + 991515611845239828951823564722652515466094640496730561231540865/663508666022773856369891829658772165488001*t^30 - 31939911596126360408618439956797990313943710397248565115157436015/1327017332045547712739783659317544330976002*t^28 + 405721813347607767373944322238274758340117367986023699064561432885/1327017332045547712739783659317544330976002*t^26 - 2023226166698865731114336301377487741558331181463732602104992841875/663508666022773856369891829658772165488001*t^24 + 251649754000317525232455150479802998696012773505734715381610678694875/10616138656364381701918269274540354647808016*t^22 - 3018223810813388403272626082475660181898063933068418065211183884594125/21232277312728763403836538549080709295616032*t^20 + 110164004769635428767904641812725099839702642424260161366629334351995875/169858218501830107230692308392645674364928256*t^18 - 751046361658732995204816423996874505270101364211310885979169523548013875/339716437003660214461384616785291348729856512*t^16 + 1868124668485641163561957324198358869094686035178585892198961481315640625/339716437003660214461384616785291348729856512*t^14 - 6573817254083714368047823941108098106251419584461321072011877886264099375/679432874007320428922769233570582697459713024*t^12 + 3922773484873680253918808850431997636604878388945910438086445336283466875/339716437003660214461384616785291348729856512*t^10 - 11973460391254338646785694322003954817325920096205257407205074961108118125/1358865748014640857845538467141165394919426048*t^8 + 21377599443097339270014081258542417286966191790923160149235452804765949375/5435462992058563431382153868564661579677704192*t^6 - 9620973961140072820845284833201637966537637019142853833596012648243265625/10870925984117126862764307737129323159355408384*t^4 + 3247398975199601167248431400156602164593303084321037179212261548160071875/43483703936468507451057230948517292637421633536*t^2 - 84159669392864016658268201230066290441059327904791805855537630959409375/86967407872937014902114461897034585274843267072
-------------------------------------------------
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:
| (-5.7964856109598455846 + 8.6936197427799931901e-957j)  +/-  (1.01e-243, 1.01e-243j)
| (-8.1393678872348312096 - 8.1696366138458474134e-968j)  +/-  (1.1e-245, 1.1e-245j)
| (7.5866075967427463775 - 5.4186377021332902953e-971j)  +/-  (5.69e-245, 5.69e-245j)
| (-6.2059598311030961436 + 2.6895641061700276232e-972j)  +/-  (7.29e-244, 7.29e-244j)
| (6.6357842758298765948 - 1.7580698179560945152e-978j)  +/-  (4.6e-244, 4.6e-244j)
| (8.1393678872348312096 + 2.1940370028406005086e-980j)  +/-  (9.84e-246, 9.84e-246j)
| (3.5986647090675758523 - 1.659066967669477571e-980j)  +/-  (6.92e-245, 6.92e-245j)
| (-7.0924059001110117924 - 2.515110474717793661e-978j)  +/-  (1.97e-244, 1.97e-244j)
| (2.6064468456120341991 + 2.1274553838798648758e-989j)  +/-  (1.76e-246, 1.76e-246j)
| (5.0229615048159853714 - 2.286551110982211216e-986j)  +/-  (8.82e-244, 8.82e-244j)
| (-7.5866075967427463775 + 2.5752446281885752059e-988j)  +/-  (5.62e-245, 5.62e-245j)
| (-1.9816567566958429259 - 2.4884444382004344847e-997j)  +/-  (8.21e-248, 8.21e-248j)
| (8.8057393751253944508 + 1.9419447098294914642e-996j)  +/-  (6.51e-247, 6.51e-247j)
| (3.9427129052972516563 - 5.3020190644321421048e-992j)  +/-  (1.74e-244, 1.74e-244j)
| (-8.8057393751253944508 - 1.7784945792275873358e-993j)  +/-  (6.93e-247, 6.93e-247j)
| (7.0924059001110117924 + 1.7687383220285062002e-995j)  +/-  (1.92e-244, 1.92e-244j)
| (1.9816567566958429259 + 3.5179444534039960208e-1000j)  +/-  (8.46e-248, 8.46e-248j)
| (-1.6868264033671747669 - 1.1913401920719382772e-1001j)  +/-  (1.63e-248, 1.63e-248j)
| (-1.1571937124467801947 - 3.0690408932459055976e-1001j)  +/-  (4.21e-250, 4.21e-250j)
| (-5.4031347164055713348 - 7.8494064674286332116e-994j)  +/-  (1.07e-243, 1.07e-243j)
| (-3.9427129052972516563 - 3.7008875846353918945e-1004j)  +/-  (1.75e-244, 1.75e-244j)
| (1.6868264033671747669 + 4.7312736763693301549e-1013j)  +/-  (1.52e-248, 1.52e-248j)
| (4.2941421169836359642 + 1.5314390123249185671e-1007j)  +/-  (3.51e-244, 3.51e-244j)
| (5.7964856109598455846 - 6.4112643582996902546e-1008j)  +/-  (1.03e-243, 1.03e-243j)
| (-1.411638634796749597 - 1.5616556634097720329e-1014j)  +/-  (2.97e-249, 2.97e-249j)
| (-2.9306374202572440192 + 1.0003509410888173173e-1010j)  +/-  (6.78e-246, 6.78e-246j)
| (0.64463068828497589319 + 3.5179387818582512442e-1017j)  +/-  (4.18e-252, 4.18e-252j)
| (3.2614049039658069018 - 1.4748837744397848195e-1010j)  +/-  (2.18e-245, 2.18e-245j)
| (1.1571937124467801947 - 4.6930504979955647809e-1015j)  +/-  (4.46e-250, 4.46e-250j)
| (-0.64463068828497589319 - 4.5016072946842568525e-1017j)  +/-  (4.18e-252, 4.18e-252j)
| (-5.0229615048159853714 - 2.7728169366876056145e-1010j)  +/-  (8.75e-244, 8.75e-244j)
| (1.411638634796749597 + 2.1743194296876179235e-1021j)  +/-  (2.8e-249, 2.8e-249j)
| (6.2059598311030961436 - 2.2249676745910208315e-1015j)  +/-  (7.98e-244, 7.98e-244j)
| (-3.5986647090675758523 - 1.0889242073346401826e-1016j)  +/-  (6.57e-245, 6.57e-245j)
| (-2.2895188248127165401 + 2.2033273343303169123e-1020j)  +/-  (4.46e-247, 4.46e-247j)
| (-3.2614049039658069018 + 1.6409710709820076113e-1018j)  +/-  (2.4e-245, 2.4e-245j)
| (-2.6064468456120341991 - 4.4188900727565208445e-1021j)  +/-  (1.9e-246, 1.9e-246j)
| (-0.38118699020732211685 + 9.8490300912739676722e-1028j)  +/-  (2.65e-253, 2.65e-253j)
| (4.6538276316716293928 + 8.7399797591295352857e-1019j)  +/-  (6.62e-244, 6.62e-244j)
| (-4.2941421169836359642 + 9.9228139562714172619e-1018j)  +/-  (3.67e-244, 3.67e-244j)
| (-0.90582047809227711214 - 1.0733385041259752648e-1041j)  +/-  (5.45e-251, 5.45e-251j)
| (-4.6538276316716293928 - 7.137104843806810589e-1034j)  +/-  (5.8e-244, 5.8e-244j)
| (0.90582047809227711214 - 6.3641427949960001951e-1056j)  +/-  (5.52e-251, 5.52e-251j)
| (2.9306374202572440192 + 6.3057751844142043265e-1050j)  +/-  (7.03e-246, 7.03e-246j)
| (-6.6357842758298765948 - 1.325865179688049153e-1060j)  +/-  (4.16e-244, 4.16e-244j)
| (-0.1251934691979292294 - 7.1958561222336376754e-1084j)  +/-  (1.57e-254, 1.57e-254j)
| (0.1251934691979292294 + 9.025524083140071046e-1084j)  +/-  (1.57e-254, 1.57e-254j)
| (2.2895188248127165401 - 1.0349295153672341369e-1081j)  +/-  (3.81e-247, 3.81e-247j)
| (0.38118699020732211685 - 3.2937167417415316634e-1089j)  +/-  (2.65e-253, 2.65e-253j)
| (5.4031347164055713348 - 1.8963757053407118768e-1085j)  +/-  (1.05e-243, 1.05e-243j)
-------------------------------------------------
The weights are:
| (5.7866155594665462081e-16 + 3.2566848957571341886e-971j)  +/-  (1.08e-83, 1.4e-203j)
| (5.6750472010489540615e-30 + 5.5771689959523213605e-980j)  +/-  (3.72e-91, 4.81e-211j)
| (2.9492126766511512868e-26 - 9.2953777289131872884e-979j)  +/-  (8.34e-91, 1.08e-210j)
| (4.4365380739013591032e-18 + 8.2268347518355840604e-973j)  +/-  (1.26e-85, 1.63e-205j)
| (1.8757502407213474686e-20 - 1.3536038329985078347e-975j)  +/-  (1.7e-88, 2.2e-208j)
| (5.6750472010489540615e-30 + 9.3762828334122298194e-981j)  +/-  (1.35e-92, 1.74e-212j)
| (4.5641559187500385847e-07 - 9.6271283334535129434e-968j)  +/-  (4.16e-78, 5.39e-198j)
| (3.8051762651812559463e-23 + 4.4988967567937682938e-976j)  +/-  (4.22e-90, 5.46e-210j)
| (0.00020284920416327232747 + 7.8444555744906186067e-966j)  +/-  (5.26e-73, 6.81e-193j)
| (2.3301844922793745216e-12 - 5.1705758910366419331e-971j)  +/-  (1.63e-84, 2.11e-204j)
| (2.9492126766511512868e-26 - 6.9492977313745416862e-978j)  +/-  (1.07e-91, 1.39e-211j)
| (0.0033600259224627139357 - 1.9970678321960591432e-964j)  +/-  (8.08e-71, 1.05e-190j)
| (9.1568834223350436502e-35 - 2.6320216196499086766e-983j)  +/-  (2.05e-95, 2.66e-215j)
| (3.4787607596833944254e-08 + 1.8008926376331373444e-968j)  +/-  (5.21e-81, 6.75e-201j)
| (9.1568834223350436502e-35 - 1.2771728431824632817e-982j)  +/-  (3.45e-96, 4.47e-216j)
| (3.8051762651812559463e-23 + 4.5234391032910699044e-977j)  +/-  (2.37e-90, 3.07e-210j)
| (0.0033600259224627139357 + 9.794719137392409382e-965j)  +/-  (1.8e-72, 2.33e-192j)
| (0.0093836970148778189131 + 5.6076720012353624317e-964j)  +/-  (2.78e-71, 3.6e-191j)
| (0.036803971371404488365 + 2.6852012981726263934e-963j)  +/-  (1.08e-66, 1.4e-186j)
| (4.5674219644248845079e-14 - 1.4967098902048735889e-970j)  +/-  (1.14e-87, 1.47e-207j)
| (3.4787607596833944254e-08 - 9.4613815657113840142e-968j)  +/-  (2.4e-84, 3.1e-204j)
| (0.0093836970148778189131 - 3.0796017630849828235e-964j)  +/-  (6.49e-73, 8.4e-193j)
| (1.9673674300850110069e-09 - 2.9676677853913756503e-969j)  +/-  (6.62e-84, 8.57e-204j)
| (5.7866155594665462081e-16 - 4.3394082766752470617e-973j)  +/-  (7.06e-89, 9.15e-209j)
| (0.020269537834162212408 - 1.3782905639369410096e-963j)  +/-  (7.6e-73, 9.84e-193j)
| (3.4409822861989880078e-05 + 6.0428781232120683765e-966j)  +/-  (3.03e-82, 3.92e-202j)
| (0.098436480249617272465 - 4.4119156203097097859e-963j)  +/-  (5.74e-72, 7.43e-192j)
| (4.5255737919822916923e-06 + 4.5958654538577136796e-967j)  +/-  (1.93e-81, 2.51e-201j)
| (0.036803971371404488365 - 1.7914879374083794654e-963j)  +/-  (6.71e-73, 8.69e-193j)
| (0.098436480249617272465 + 5.5160057958532539813e-963j)  +/-  (1.72e-72, 2.23e-192j)
| (2.3301844922793745216e-12 + 7.2321950882772090384e-970j)  +/-  (1.71e-88, 2.21e-208j)
| (0.020269537834162212408 + 8.3844187551440617722e-964j)  +/-  (9.99e-75, 1.29e-194j)
| (4.4365380739013591032e-18 + 2.8066586601174087584e-974j)  +/-  (5.66e-90, 7.32e-210j)
| (4.5641559187500385847e-07 + 4.1153634386276448701e-967j)  +/-  (3.68e-85, 4.76e-205j)
| (0.0009337011368799464257 + 6.6197362704623360338e-965j)  +/-  (5.4e-81, 7e-201j)
| (4.5255737919822916923e-06 - 1.6421112743086390152e-966j)  +/-  (1.92e-84, 2.49e-204j)
| (0.00020284920416327232747 - 2.0663206687971558833e-965j)  +/-  (1.68e-82, 2.17e-202j)
| (0.12719115806190937931 - 6.8453592792205293794e-963j)  +/-  (4.84e-79, 6.26e-199j)
| (8.0676022158143127239e-11 + 4.2429174769130523363e-970j)  +/-  (5.28e-89, 6.85e-209j)
| (1.9673674300850110069e-09 + 1.9932612590039974608e-968j)  +/-  (3.26e-88, 4.22e-208j)
| (0.063655950379407154906 - 4.1333700819049310736e-963j)  +/-  (1.4e-80, 1.8e-200j)
| (8.0676022158143127239e-11 - 3.8804101927330108059e-969j)  +/-  (2.83e-89, 3.67e-209j)
| (0.063655950379407154906 + 3.0161154492526794574e-963j)  +/-  (4.49e-82, 5.76e-202j)
| (3.4409822861989880078e-05 - 1.9843849197607180376e-966j)  +/-  (1.36e-86, 1.77e-206j)
| (1.8757502407213474686e-20 - 2.0050512262206966797e-974j)  +/-  (2.61e-95, 3.35e-215j)
| (0.13972320017484240286 + 7.691660050173537889e-963j)  +/-  (2.95e-82, 3.64e-202j)
| (0.13972320017484240286 - 7.3664328325085484257e-963j)  +/-  (9.33e-83, 1.16e-202j)
| (0.0009337011368799464257 - 2.8710341946957921119e-965j)  +/-  (1.22e-85, 1.59e-205j)
| (0.12719115806190937931 + 6.000587447174641314e-963j)  +/-  (4.63e-83, 5.41e-203j)
| (4.5674219644248845079e-14 + 5.2567154688431223665e-972j)  +/-  (1.1e-92, 1.53e-212j)
