Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 12 29
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 29 Kronrod extension for:
P2 : t^14 - 124249/1555*t^12 + 3530769/1555*t^10 - 8883963/311*t^8 + 50229333/311*t^6 - 114812775/311*t^4 + 78937551/311*t^2 - 6151761/311
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^43 - 20888293171609213002444876374428885187889963853612865861683762415155608819792212869/30611954990301385588749080247211800415067230466957523419949516261492284077980480*t^41 + 6424745377939860744013626475553747570250101443679952820401616807116750115937448465763/30611954990301385588749080247211800415067230466957523419949516261492284077980480*t^39 - 393897761981906176659546105080849008931945008730461049640586268618130341725362890382401/10203984996767128529583026749070600138355743488985841139983172087164094692660160*t^37 + 920902214707019062877811721527788381932718605098216917060576053234601719909786095894946737/193875714938575442062077508232341402628759126290730981659680269656117799160543040*t^35 - 730544909197712473498117178141333092979094626780149701450219271977770028336851108769688809/1762506499441594927837068256657649114806901148097554378724366087782889083277664*t^33 + 794961308695682323048955898420073741568897665041473286116651144397785688411345030268182413637/29962610490507113773230160363180034951717319517658424438314223492309114415720288*t^31 - 38086749190576178936379992218326190871801131473200948387972887517726854671178011807360653233041/29962610490507113773230160363180034951717319517658424438314223492309114415720288*t^29 + 1381427120614593238356749520152991431201959072569799255476727795687949506563451654630587526620951/29962610490507113773230160363180034951717319517658424438314223492309114415720288*t^27 - 19061622976807417625632546419899380013755783863179760313442445351048798258534829822149289858353549/14981305245253556886615080181590017475858659758829212219157111746154557207860144*t^25 + 400180122425994306530548700543832593943573310731720770087545928326842245557468980617663530546076325/14981305245253556886615080181590017475858659758829212219157111746154557207860144*t^23 - 6360072654013990121527443538546367321970912870177293288287043676404307304057671074027829484956294375/14981305245253556886615080181590017475858659758829212219157111746154557207860144*t^21 + 75788290759797916378479177017151009905862660423280347285851107796936939289306885610725336733900202175/14981305245253556886615080181590017475858659758829212219157111746154557207860144*t^19 - 70230054615679089046592173214262544321164720928086555017007125091123737863484136070105203329891987775/1576979499500374409117376861220001839564069448297811812542853868016269179774752*t^17 + 26310165941392598172450304251945044675158110087573379210654998747829045005158867248769598341863740225/92763499970610259359845697718823637621415849899871283090756109883309951751456*t^15 - 117780699458423437600116837174419157187181168440171298975519328727717447109405054053349133162693556125/92763499970610259359845697718823637621415849899871283090756109883309951751456*t^13 + 356266195026598698354043423460127788482640948868205016031396989826561518958134033754293539352010952875/92763499970610259359845697718823637621415849899871283090756109883309951751456*t^11 - 1378204731257949605948913509266197779515247574994886451254373236033655475774405782830516878463810029875/185526999941220518719691395437647275242831699799742566181512219766619903502912*t^9 + 1573903161051848024798514244707540271721649126775496168043444174470149568969338123293902808925829146125/185526999941220518719691395437647275242831699799742566181512219766619903502912*t^7 - 938125640103756693976481797773148574253781894399659593538324166525927612618622383460722171594412767125/185526999941220518719691395437647275242831699799742566181512219766619903502912*t^5 + 234721513920989188232860963601600739203840680735451102659625659072362999844147993845168067552965699375/185526999941220518719691395437647275242831699799742566181512219766619903502912*t^3 - 3621946873720865440233249344145277261962350051959447637943940549849537352479975346647231041007126875/46381749985305129679922848859411818810707924949935641545378054941654975875728*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:
| (10.837414129389055609 + 1.038287582743092996e-745j)  +/-  (5.15e-248, 5.15e-248j)
| (-6.385329302940584864 + 1.4790520136188783067e-752j)  +/-  (3.4e-245, 3.4e-245j)
| (-3.6069468897368460303 - 1.7754737306458134546e-754j)  +/-  (4.09e-247, 4.09e-247j)
| (-7.623951426121563261 - 1.5794774437965709026e-753j)  +/-  (1.61e-245, 1.61e-245j)
| (-5.4255611644629416912 + 2.072837817755655493e-751j)  +/-  (5.3e-245, 5.3e-245j)
| (-7.1814914669695038468e-755 - 5.7706993493374180769e-755j)  +/-  (3.96e-753, 3.96e-753j)
| (-10.837414129389055609 + 3.0057943766236961501e-757j)  +/-  (4.85e-248, 4.85e-248j)
| (-2.6788642116343808239 - 7.1616340210535208927e-756j)  +/-  (2e-248, 2e-248j)
| (-9.8525533914132392217 - 3.7285298133438876175e-756j)  +/-  (5.34e-247, 5.34e-247j)
| (-8.301259812610621497 + 3.6062771300845523323e-756j)  +/-  (7.05e-246, 7.05e-246j)
| (-9.0340278148589302893 + 1.210201141081863999e-755j)  +/-  (2.56e-246, 2.56e-246j)
| (-4.1093390219292378926 - 6.6033343101127381532e-756j)  +/-  (1.62e-246, 1.62e-246j)
| (-4.6254356317132469284 - 3.4551908253199795923e-754j)  +/-  (7.2e-246, 7.2e-246j)
| (0.2983537964726121739 - 9.0373578032842133304e-757j)  +/-  (9e-254, 9e-254j)
| (-3.1287926620344167003 + 3.6181769445841954835e-756j)  +/-  (9.32e-248, 9.32e-248j)
| (-1.3822816516774470874 + 1.089678643077551613e-758j)  +/-  (5.33e-251, 5.33e-251j)
| (-5.8272369191325365786 - 2.2170419203712619231e-753j)  +/-  (4.73e-245, 4.73e-245j)
| (-1.8100151044187559318 + 1.249337036428677919e-758j)  +/-  (4.11e-250, 4.11e-250j)
| (-6.9873837872205428911 + 7.3423410117169442247e-754j)  +/-  (2.54e-245, 2.54e-245j)
| (-1 - 3.4786211258093641299e-760j)  +/-  (6.68e-252, 6.68e-252j)
| (1 - 2.4655207746246195314e-756j)  +/-  (7.06e-252, 7.06e-252j)
| (0.6584438338872697783 + 1.497083607975753405e-757j)  +/-  (8.1e-253, 8.1e-253j)
| (-5.1175907318418588229 + 5.5510635016037209809e-753j)  +/-  (3.11e-245, 3.11e-245j)
| (-0.2983537964726121739 - 8.3606000907736627776e-758j)  +/-  (6.12e-254, 6.12e-254j)
| (-0.6584438338872697783 + 1.2037098575813474119e-761j)  +/-  (8.14e-253, 8.14e-253j)
| (-2.2450487488981420889 + 1.9437880896628243057e-758j)  +/-  (3.41e-249, 3.41e-249j)
| (6.9873837872205428911 + 4.9108577118728427334e-753j)  +/-  (2.39e-245, 2.39e-245j)
| (9.8525533914132392217 - 5.9939784190898380087e-766j)  +/-  (5.17e-247, 5.17e-247j)
| (5.4255611644629416912 - 9.5912124344575103304e-778j)  +/-  (5.36e-245, 5.36e-245j)
| (4.6254356317132469284 - 2.3719925896341095438e-793j)  +/-  (7.24e-246, 7.24e-246j)
| (7.623951426121563261 + 4.3509090837689290181e-812j)  +/-  (1.47e-245, 1.47e-245j)
| (2.2450487488981420889 - 2.4679867002658468991e-827j)  +/-  (3.81e-249, 3.81e-249j)
| (8.301259812610621497 + 9.8676354611066623442e-842j)  +/-  (7.73e-246, 7.73e-246j)
| (1.3822816516774470874 - 1.6208411638338505105e-864j)  +/-  (5.48e-251, 5.48e-251j)
| (5.8272369191325365786 + 1.18218346296000677e-898j)  +/-  (4.99e-245, 4.99e-245j)
| (5.1175907318418588229 - 1.775737895997637444e-941j)  +/-  (2.98e-245, 2.98e-245j)
| (6.385329302940584864 - 3.7662888787181798378e-969j)  +/-  (3.36e-245, 3.36e-245j)
| (4.1093390219292378926 - 4.386309258093577686e-978j)  +/-  (1.67e-246, 1.67e-246j)
| (3.1287926620344167003 - 5.4571197728171390269e-982j)  +/-  (8.95e-248, 8.95e-248j)
| (3.6069468897368460303 - 1.7393890672641664873e-982j)  +/-  (4.06e-247, 4.06e-247j)
| (1.8100151044187559318 - 2.7806846480536949586e-992j)  +/-  (5.03e-250, 5.03e-250j)
| (9.0340278148589302893 + 4.2288336611884674031e-987j)  +/-  (2.64e-246, 2.64e-246j)
| (2.6788642116343808239 - 9.4851112605224039776e-995j)  +/-  (1.98e-248, 1.98e-248j)
-------------------------------------------------
The weights are:
| (1.4197521015204529973e-26 - 8.8437895687903165048e-771j)  +/-  (3.81e-72, 5.07e-194j)
| (3.2657280093639252182e-10 - 3.8258744920950827451e-761j)  +/-  (8.51e-63, 1.13e-184j)
| (0.00029341318277992769607 + 3.3328496416207186661e-757j)  +/-  (2.99e-53, 3.98e-175j)
| (6.247633641389723443e-14 - 7.0038903929116734728e-764j)  +/-  (2.49e-66, 3.32e-188j)
| (4.2569288886582680827e-08 + 4.6587789728131275398e-758j)  +/-  (1.63e-60, 2.17e-182j)
| (0.10347550059677415962 - 2.9402895746927577621e-754j)  +/-  (3.4e-50, 4.53e-172j)
| (1.4197521015204529973e-26 - 7.2245175652814355826e-772j)  +/-  (8.06e-74, 1.07e-195j)
| (0.0048346901992767964321 + 3.1218340112183897326e-756j)  +/-  (1.52e-51, 2.02e-173j)
| (2.9255249528318182299e-22 + 2.6638452980501536685e-769j)  +/-  (4.98e-72, 6.63e-194j)
| (3.0426868733047603646e-16 + 1.717468321462309052e-765j)  +/-  (4.54e-69, 6.05e-191j)
| (5.8125115767740308401e-19 - 2.9320051257891181163e-767j)  +/-  (1.26e-70, 1.67e-192j)
| (4.3939494480077838499e-05 - 1.8713414724262647009e-757j)  +/-  (5.53e-60, 7.37e-182j)
| (4.6602525789926864454e-06 + 7.2659737878760838236e-758j)  +/-  (1.17e-61, 1.56e-183j)
| (0.13342043038660690998 + 2.3558459816338207724e-754j)  +/-  (2.49e-50, 3.32e-172j)
| (0.0013849186927707134151 - 1.0291980795614713357e-756j)  +/-  (1.04e-57, 1.39e-179j)
| (0.063322317760656833646 - 4.6319601269525339467e-755j)  +/-  (3.59e-51, 4.79e-173j)
| (8.7508343933955472532e-09 + 2.4265854046367643227e-759j)  +/-  (7.7e-65, 1.03e-186j)
| (0.033782955541554016503 + 1.9139793638180058825e-755j)  +/-  (1.62e-54, 2.15e-176j)
| (6.1756040344613506825e-12 + 2.4062878254355665564e-762j)  +/-  (6.21e-68, 8.26e-190j)
| (0.084676591205865666213 + 1.0080185265726161845e-754j)  +/-  (7.79e-52, 1.04e-173j)
| (0.084676591205865666213 + 6.4520591101599063921e-755j)  +/-  (1.54e-52, 2.05e-174j)
| (0.11260224531825127737 - 1.2808405881747128871e-754j)  +/-  (1.2e-51, 1.59e-173j)
| (3.5392819968137323671e-07 - 7.6364655066647534623e-758j)  +/-  (3.67e-63, 4.89e-185j)
| (0.13342043038660690998 + 2.3729976514037468785e-754j)  +/-  (1.35e-51, 1.8e-173j)
| (0.11260224531825127737 - 1.6531301210840060571e-754j)  +/-  (5.13e-52, 6.83e-174j)
| (0.013895682085657560901 - 7.9842282653752960278e-756j)  +/-  (4.59e-57, 6.11e-179j)
| (6.1756040344613506825e-12 - 4.9506278417136705537e-764j)  +/-  (2.2e-79, 2.94e-201j)
| (2.9255249528318182299e-22 + 3.9081593432497835079e-769j)  +/-  (2.24e-84, 2.98e-206j)
| (4.2569288886582680827e-08 + 1.3738209182452173376e-760j)  +/-  (1.22e-76, 1.62e-198j)
| (4.6602525789926864454e-06 + 1.9486980792839200487e-759j)  +/-  (4.29e-75, 5.71e-197j)
| (6.247633641389723443e-14 - 9.8863364892359768696e-765j)  +/-  (3.15e-81, 4.19e-203j)
| (0.013895682085657560901 - 2.6209553261330853468e-756j)  +/-  (9.7e-70, 1.29e-191j)
| (3.0426868733047603646e-16 + 4.6087046484756606771e-766j)  +/-  (9.59e-83, 1.28e-204j)
| (0.063322317760656833646 - 2.3787461654880581576e-755j)  +/-  (2.29e-66, 3.04e-188j)
| (8.7508343933955472532e-09 - 1.0051192019504775957e-761j)  +/-  (2.59e-78, 3.44e-200j)
| (3.5392819968137323671e-07 - 4.8911430753283331259e-760j)  +/-  (3.76e-77, 5e-199j)
| (3.2657280093639252182e-10 + 1.5352887572303753789e-763j)  +/-  (1.22e-79, 1.62e-201j)
| (4.3939494480077838499e-05 - 9.5569723141367837252e-759j)  +/-  (8.83e-77, 1.17e-198j)
| (0.0013849186927707134151 - 2.1218169351149495021e-757j)  +/-  (3.8e-76, 5.04e-198j)
| (0.00029341318277992769607 + 4.7110789376851697139e-758j)  +/-  (9.38e-77, 1.25e-198j)
| (0.033782955541554016503 + 7.8695005116009198909e-756j)  +/-  (2.41e-74, 3.26e-196j)
| (5.8125115767740308401e-19 - 1.6411167967568295994e-767j)  +/-  (2.72e-87, 3.96e-209j)
| (0.0048346901992767964321 + 8.1115428014600910274e-757j)  +/-  (9.63e-76, 1.25e-197j)
