Starting with polynomial:
P : 4096*t^12 - 135168*t^10 + 1520640*t^8 - 7096320*t^6 + 13305600*t^4 - 7983360*t^2 + 665280
Extension levels are: 12 28
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P1 : 4096*t^12 - 135168*t^10 + 1520640*t^8 - 7096320*t^6 + 13305600*t^4 - 7983360*t^2 + 665280
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4096*t^40 - 11830521452376901066752/9396449026283357*t^38 + 1631005004112580176012288/9396449026283357*t^36 - 2540600920330923788915512320/178532531499383783*t^34 + 138469970751756794829744468480/178532531499383783*t^32 - 90329943840795383329275873269760/3035053035489524311*t^30 + 2521252356197929608962609243717760/3035053035489524311*t^28 - 52146918479145724644425470101440640/3035053035489524311*t^26 + 806724652400671297185967255717536000/3035053035489524311*t^24 - 492455918936050942983980382008496000/159739633446817069*t^22 + 81060038732864811797507731634080848000/3035053035489524311*t^20 - 581796360820051218891127184982876000/3398715605251427*t^18 + 7506479316035115741256426248979475250/9396449026283357*t^16 - 24911941860890296834672590361231410000/9396449026283357*t^14 + 113699988539685466795883627544907108125/18792898052566714*t^12 - 170042198777491480540770827920173035625/18792898052566714*t^10 + 1241840605512032198616835133456170831875/150343184420533712*t^8 - 309303659339975729837082893720368741875/75171592210266856*t^6 + 551325444213682517849984922389390784375/601372737682134848*t^4 - 35270458110888257916875217134724215625/601372737682134848*t^2 + 32511654524837328076382995958484375/300686368841067424
-------------------------------------------------
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:
| (-7.4233719654357385997 + 2.220143578837209585e-927j)  +/-  (1.61e-248, 1.61e-248j)
| (-6.1346330840143018038 - 3.1830481760861837653e-927j)  +/-  (8.42e-247, 8.42e-247j)
| (6.7198747583796350485 - 1.3062157157855385054e-925j)  +/-  (1.68e-247, 1.68e-247j)
| (-6.7198747583796350485 + 2.136378777430366208e-927j)  +/-  (1.65e-247, 1.65e-247j)
| (7.4233719654357385997 + 1.0928902273834268652e-926j)  +/-  (1.73e-248, 1.73e-248j)
| (-5.6100489615878360243 - 7.8167236804825432594e-925j)  +/-  (2.14e-246, 2.14e-246j)
| (5.1241733433664023885 - 4.5498009387957371425e-923j)  +/-  (4.17e-246, 4.17e-246j)
| (5.6100489615878360243 - 7.8201098922605979225e-937j)  +/-  (2.22e-246, 2.22e-246j)
| (-1.2716449814196364402 + 6.2772426184503642583e-952j)  +/-  (1.18e-250, 1.18e-250j)
| (1.9316737181702053946 + 6.0096101552615649052e-951j)  +/-  (5.54e-249, 5.54e-249j)
| (1.5976826351526047967 - 2.0051961695427083545e-953j)  +/-  (9.05e-250, 9.05e-250j)
| (3.8897248978697819193 + 3.0443629975576004638e-950j)  +/-  (7.58e-245, 7.58e-245j)
| (-3.8897248978697819193 + 3.4964230439780340383e-961j)  +/-  (7.55e-245, 7.55e-245j)
| (-3.8418631132345154364 - 2.4440852124493527201e-977j)  +/-  (6.16e-245, 6.16e-245j)
| (-4.2252836351715984609 + 5.3596024717388120785e-982j)  +/-  (1.53e-245, 1.53e-245j)
| (4.6655306352026868758 + 3.4398657112104798565e-983j)  +/-  (7.87e-246, 7.87e-246j)
| (3.0206370251208897717 - 3.1735931694719339172e-992j)  +/-  (6.31e-247, 6.31e-247j)
| (-4.6655306352026868758 - 7.0583004534062526227e-996j)  +/-  (7.23e-246, 7.23e-246j)
| (-0.9477883912401637437 - 2.3505048686118520545e-1002j)  +/-  (1.32e-251, 1.32e-251j)
| (6.1346330840143018038 + 1.8909717820865012996e-995j)  +/-  (8.42e-247, 8.42e-247j)
| (4.2252836351715984609 + 1.3416387915432201922e-1006j)  +/-  (1.53e-245, 1.53e-245j)
| (-5.1241733433664023885 + 1.1407709951985174868e-1025j)  +/-  (4.63e-246, 4.63e-246j)
| (3.8418631132345154364 - 8.8006929578506308154e-1034j)  +/-  (5.99e-245, 5.99e-245j)
| (2.6427540986750516832 + 4.9092304174005083497e-1046j)  +/-  (1.42e-247, 1.42e-247j)
| (-2.2795070805010599002 + 4.2149909744033208967e-1047j)  +/-  (3.02e-248, 3.02e-248j)
| (0.31424037625435911128 + 7.3964669275328229424e-1053j)  +/-  (7.43e-254, 7.43e-254j)
| (1.2716449814196364402 - 1.3997140629135815911e-1049j)  +/-  (1.2e-250, 1.2e-250j)
| (-3.4131072505221294874 - 3.1431554261718436324e-1047j)  +/-  (2.69e-246, 2.69e-246j)
| (0.04358305227879830031 + 3.3935893844077312098e-1056j)  +/-  (4.77e-255, 4.77e-255j)
| (-0.6266083650101463447 - 3.423274419796605762e-1054j)  +/-  (9.25e-253, 9.25e-253j)
| (-3.0206370251208897717 + 6.3769333815658659331e-1050j)  +/-  (6.2e-247, 6.2e-247j)
| (3.4131072505221294874 - 9.211931035099277537e-1051j)  +/-  (2.78e-246, 2.78e-246j)
| (0.6266083650101463447 + 8.8582392240229166123e-1059j)  +/-  (9.77e-253, 9.77e-253j)
| (-2.6427540986750516832 - 3.6387834842002069964e-1058j)  +/-  (1.43e-247, 1.43e-247j)
| (-1.9316737181702053946 - 4.8224455313234430301e-1057j)  +/-  (5.56e-249, 5.56e-249j)
| (-1.5976826351526047967 - 3.3268825224825280635e-1057j)  +/-  (9.32e-250, 9.32e-250j)
| (-0.04358305227879830031 - 3.4932054393637114261e-1061j)  +/-  (4.77e-255, 4.77e-255j)
| (0.9477883912401637437 - 2.0008409604152276215e-1057j)  +/-  (1.29e-251, 1.29e-251j)
| (2.2795070805010599002 - 4.2934631315560187289e-1055j)  +/-  (3.14e-248, 3.14e-248j)
| (-0.31424037625435911128 - 3.1597447340130669512e-1061j)  +/-  (7.43e-254, 7.43e-254j)
-------------------------------------------------
The weights are:
| (5.3437893896440232435e-25 - 1.7013105879161849121e-943j)  +/-  (4.54e-92, 1.56e-215j)
| (1.4043921015986882865e-17 - 3.890387527392131862e-939j)  +/-  (3.77e-89, 1.3e-212j)
| (8.6813698261182678061e-21 + 3.3341995326299312393e-940j)  +/-  (2.22e-92, 7.66e-216j)
| (8.6813698261182678061e-21 + 4.6238559207629144357e-941j)  +/-  (9.65e-91, 3.32e-214j)
| (5.3437893896440232435e-25 - 9.1133967476336633511e-943j)  +/-  (3.37e-94, 1.16e-217j)
| (6.086976875001029806e-15 + 1.2550028627352148036e-937j)  +/-  (1.34e-88, 4.63e-212j)
| (1.0493475684159776857e-12 + 3.271425671301840598e-934j)  +/-  (3.99e-89, 1.38e-212j)
| (6.086976875001029806e-15 + 3.5115239502299439841e-936j)  +/-  (2.78e-90, 9.57e-214j)
| (0.036326058962071986485 + 1.2721183480872330704e-928j)  +/-  (1.6e-71, 5.51e-195j)
| (0.0045999106841118747572 - 3.9721209567984696051e-929j)  +/-  (2.62e-77, 9.02e-201j)
| (0.014445908147351315722 + 9.7124940040214766287e-929j)  +/-  (5.61e-75, 1.93e-198j)
| (-4.2139685946706962823e-08 - 9.3274359281995044329e-931j)  +/-  (1.7e-86, 5.84e-210j)
| (-4.2139685946706962823e-08 + 1.2591806057900903626e-931j)  +/-  (1.43e-87, 4.94e-211j)
| (1.4694760573593198589e-07 - 1.5321088556791134483e-931j)  +/-  (1.72e-87, 5.91e-211j)
| (4.3457076213454410047e-09 - 3.0692752551869124323e-933j)  +/-  (2.29e-89, 7.89e-213j)
| (8.8942931776373427956e-11 - 2.3790447967752217555e-933j)  +/-  (2.22e-91, 7.65e-215j)
| (2.3673485793313387582e-05 + 1.6035584685419652777e-930j)  +/-  (1.28e-87, 4.42e-211j)
| (8.8942931776373427956e-11 + 1.0824919388454840865e-934j)  +/-  (8.39e-92, 2.89e-215j)
| (0.074261679671215358053 - 2.9567291154926297893e-928j)  +/-  (1.9e-81, 6.55e-205j)
| (1.4043921015986882865e-17 - 4.0906032904334839696e-938j)  +/-  (1.65e-95, 5.67e-219j)
| (4.3457076213454410047e-09 + 3.2528145638660030869e-932j)  +/-  (1.11e-90, 3.84e-214j)
| (1.0493475684159776857e-12 - 4.3846109433539567414e-936j)  +/-  (7e-94, 2.41e-217j)
| (1.4694760573593198589e-07 + 1.0862183059492224408e-930j)  +/-  (2.41e-89, 8.31e-213j)
| (0.000193773105087765379 - 4.8660874996884885072e-930j)  +/-  (3.35e-88, 1.15e-211j)
| (0.0011110127085065349419 - 5.5302220172002012458e-930j)  +/-  (1.82e-89, 6.27e-213j)
| (0.15582251457401545073 + 2.0816465762387189371e-927j)  +/-  (2.86e-85, 9.86e-209j)
| (0.036326058962071986485 - 2.1173285189530787363e-928j)  +/-  (1.42e-85, 4.88e-209j)
| (1.9722961049912482531e-06 + 1.172697965681170284e-931j)  +/-  (1.87e-91, 6.46e-215j)
| (0.092030046798841107606 - 7.6880431765884682247e-927j)  +/-  (7.4e-86, 2.55e-209j)
| (0.12118334032327451074 + 6.882699127409689967e-928j)  +/-  (5.24e-86, 1.81e-209j)
| (2.3673485793313387582e-05 - 4.1079322797053998386e-931j)  +/-  (2.21e-91, 7.62e-215j)
| (1.9722961049912482531e-06 - 5.9120860143105930333e-931j)  +/-  (1.12e-91, 3.84e-215j)
| (0.12118334032327451074 - 8.8111730022592036973e-928j)  +/-  (9.59e-88, 3.31e-211j)
| (0.000193773105087765379 + 1.5445918694208504064e-930j)  +/-  (4.7e-91, 1.62e-214j)
| (0.0045999106841118747572 + 1.789731952076929585e-929j)  +/-  (2.39e-90, 8.26e-214j)
| (0.014445908147351315722 - 5.0785968834632454316e-929j)  +/-  (6.2e-90, 2.13e-213j)
| (0.092030046798841107606 + 7.5577384752584035641e-927j)  +/-  (2.75e-88, 9.64e-212j)
| (0.074261679671215358053 + 4.3067347704052764926e-928j)  +/-  (8.82e-90, 2.97e-213j)
| (0.0011110127085065349419 + 1.4468461718952531664e-929j)  +/-  (8.95e-92, 2.76e-215j)
| (0.15582251457401545073 - 1.8399783838074266264e-927j)  +/-  (3.93e-89, 1.45e-212j)
