Starting with polynomial:
P : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Extension levels are: 8 11 18
-------------------------------------------------
Trying to find an order 11 Kronrod extension for:
P1 : t^8 - 28*t^6 + 210*t^4 - 420*t^2 + 105
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P2 : t^19 - 150851/1347*t^17 + 6541430/1347*t^15 - 47540390/449*t^13 + 566981260/449*t^11 - 3753992440/449*t^9 + 13180991670/449*t^7 - 21510616050/449*t^5 + 12604959675/449*t^3 - 2144332575/449*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^37 - 11292144696612173688285326815383722966066361219748756521981213468881/24345585954947024992516680227816571294214357877207451559207107852*t^35 + 2313803763976474037932362533653603132119335202209966305408671821640485/24345585954947024992516680227816571294214357877207451559207107852*t^33 - 46234084093845059697028538124905843690477298452390905285587152199611005/4057597659157837498752780037969428549035726312867908593201184642*t^31 + 3621787775152144014804668398526580402274084880917868847522007379403888395/4057597659157837498752780037969428549035726312867908593201184642*t^29 - 2157131422900836595753056428145562456180266041362156527387752415074489539945/44633574250736212486280580417663714039392989441546994525213031062*t^27 + 83308651143491807007682592352889181782214765465938069504382201976308168295735/44633574250736212486280580417663714039392989441546994525213031062*t^25 - 2335196384712973146251174172777758462565471846367404890412550409237328260991375/44633574250736212486280580417663714039392989441546994525213031062*t^23 + 47897479796205894770471646411670141301733160150396185958195652650811802442162125/44633574250736212486280580417663714039392989441546994525213031062*t^21 - 3957852781830687342968334488967282203458176633906135224344024212990006120629324625/245484658379049168674543192297150427216661441928508469888671670841*t^19 + 43321882725563728490907116003133421507440409038302214934340706547651675486960797000/245484658379049168674543192297150427216661441928508469888671670841*t^17 - 682693149228428373282399882109892758258801975413004707314352648510240629184556146375/490969316758098337349086384594300854433322883857016939777343341682*t^15 + 3795477602075744905884307235214320431005721314694108575561406398511069168601989520625/490969316758098337349086384594300854433322883857016939777343341682*t^13 - 14439883570906114430421076575827521064673141678783488683542559745594097651783928108125/490969316758098337349086384594300854433322883857016939777343341682*t^11 + 3265110533663939699935565832935589186067759658326158453511921103508392211869997200625/44633574250736212486280580417663714039392989441546994525213031062*t^9 - 4962719609134735081201140504029663586670977523965663523058305315553319376519906228125/44633574250736212486280580417663714039392989441546994525213031062*t^7 + 4173485951684908680097005473058900880876177418734785098285860052698911279207772640625/44633574250736212486280580417663714039392989441546994525213031062*t^5 - 3348283196191046197741570341260572703168391386529911268849086741186441377042367596875/89267148501472424972561160835327428078785978883093989050426062124*t^3 + 470179289136458950100707945007493694221888075272893083462419014468259838491513221875/89267148501472424972561160835327428078785978883093989050426062124*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:
| (-9.6791006690698363881 + 5.3922003510302923575e-748j)  +/-  (4.4e-249, 4.4e-249j)
| (9.6791006690698363881 - 4.3996293432303297909e-745j)  +/-  (4.54e-249, 4.54e-249j)
| (-8.6462920522529024076 + 1.0114276420055603224e-749j)  +/-  (4.49e-248, 4.49e-248j)
| (6.3410934275277093073 - 4.3007716272503817182e-747j)  +/-  (6.49e-247, 6.49e-247j)
| (-7.7918050649179216675 + 4.5832172348366755852e-758j)  +/-  (1.47e-247, 1.47e-247j)
| (-7.0324121787911382292 + 2.788009530471036511e-758j)  +/-  (3.91e-247, 3.91e-247j)
| (-5.1580652270647994111 + 6.8277203467480360443e-757j)  +/-  (9.09e-247, 9.09e-247j)
| (-4.6558319044038856986 + 1.5377455166606833117e-757j)  +/-  (5.95e-247, 5.95e-247j)
| (-2.8024858612875416991 + 4.9726992634341714422e-760j)  +/-  (1.16e-247, 1.16e-247j)
| (5.1580652270647994111 + 5.6388802545231187697e-765j)  +/-  (8.16e-247, 8.16e-247j)
| (2.1453430366751189845 - 1.7566123115671629949e-780j)  +/-  (1.47e-249, 1.47e-249j)
| (1.1099173154981207971 + 2.8565698234450808553e-784j)  +/-  (9.4e-252, 9.4e-252j)
| (-2.6377551349274913907 + 1.3431633055480558359e-779j)  +/-  (4.95e-248, 4.95e-248j)
| (-4.1445471861258943321 + 1.4941422487319191104e-778j)  +/-  (3.29e-247, 3.29e-247j)
| (5.7133983030734902123 + 7.2886535372655226467e-783j)  +/-  (8.97e-247, 8.97e-247j)
| (3.0950955154405111371 + 1.4185327224408289028e-798j)  +/-  (1.14e-247, 1.14e-247j)
| (4.6558319044038856986 + 2.4704061731824863318e-809j)  +/-  (5.94e-247, 5.94e-247j)
| (2.6377551349274913907 - 5.8032561088999111993e-813j)  +/-  (4.71e-248, 4.71e-248j)
| (-0.79867251029900488539 + 8.2445361752333602293e-826j)  +/-  (2.28e-252, 2.28e-252j)
| (8.6462920522529024076 - 9.8928657855083564548e-819j)  +/-  (4.33e-248, 4.33e-248j)
| (7.7918050649179216675 - 5.8715888513819736292e-828j)  +/-  (1.53e-247, 1.53e-247j)
| (0.79867251029900488539 - 5.5045365797143151687e-840j)  +/-  (2.41e-252, 2.41e-252j)
| (-1.6365190424351079992 - 4.491059439918443181e-839j)  +/-  (9.81e-251, 9.81e-251j)
| (-6.3410934275277093073 - 2.6649339574947487588e-834j)  +/-  (6.1e-247, 6.1e-247j)
| (-3.6155681015529313987 - 1.2317163803381429959e-835j)  +/-  (1.62e-247, 1.62e-247j)
| (-1.1099173154981207971 + 2.4506935099882399053e-843j)  +/-  (8.39e-252, 8.39e-252j)
| (0.53907981135137510807 + 1.0967142707913583211e-844j)  +/-  (3.61e-253, 3.61e-253j)
| (3.6155681015529313987 + 1.2387672617759383698e-837j)  +/-  (1.52e-247, 1.52e-247j)
| (-5.7133983030734902123 - 2.3505514253758883823e-847j)  +/-  (7.89e-247, 7.89e-247j)
| (-0.53907981135137510807 + 4.8342816558277964584e-854j)  +/-  (3.83e-253, 3.83e-253j)
| (6.9405212233706257073e-869 + 1.6561875635348639997e-868j)  +/-  (6.64e-867, 6.64e-867j)
| (1.6365190424351079992 - 3.2040322874600716781e-850j)  +/-  (9.98e-251, 9.98e-251j)
| (2.8024858612875416991 + 7.8806115109787080033e-848j)  +/-  (1.01e-247, 1.01e-247j)
| (-3.0950955154405111371 - 7.1033063800540439779e-856j)  +/-  (1.16e-247, 1.16e-247j)
| (7.0324121787911382292 + 9.7676276197614679873e-857j)  +/-  (3.57e-247, 3.57e-247j)
| (-2.1453430366751189845 + 1.8353150730507606946e-867j)  +/-  (1.54e-249, 1.54e-249j)
| (4.1445471861258943321 + 2.6049747383520228319e-872j)  +/-  (3.4e-247, 3.4e-247j)
-------------------------------------------------
The weights are:
| (2.1585924605424102008e-21 + 5.8841702043104917698e-765j)  +/-  (1.53e-96, 3.09e-221j)
| (2.1585924605424102008e-21 - 2.2588089610073671265e-764j)  +/-  (1.27e-97, 2.56e-222j)
| (2.1450167479914453611e-17 - 1.5970313706898756036e-762j)  +/-  (5.84e-95, 1.18e-219j)
| (4.8895789510616602e-10 + 1.009544242894041971e-755j)  +/-  (4.7e-92, 9.49e-217j)
| (2.0914426619232743212e-14 + 1.3292432025528234032e-760j)  +/-  (7.72e-94, 1.56e-218j)
| (5.2613877020542302739e-12 - 5.8404475145949779379e-759j)  +/-  (7.21e-93, 1.46e-217j)
| (3.4616604622670422495e-07 + 4.2361314169545653541e-755j)  +/-  (6.61e-90, 1.34e-214j)
| (3.9032406673984383266e-06 - 3.4285847755012544942e-754j)  +/-  (6.88e-89, 1.39e-213j)
| (-0.00063029282574278942552 - 1.117964849069071655e-750j)  +/-  (5.12e-84, 1.03e-208j)
| (3.4616604622670422495e-07 + 4.0962248159127823306e-754j)  +/-  (1.92e-93, 3.89e-218j)
| (0.019769595112389659961 - 1.8775517972913771027e-750j)  +/-  (1.91e-83, 3.85e-208j)
| (0.1125239048152888742 - 7.410236553151066825e-750j)  +/-  (4.19e-76, 8.46e-201j)
| (0.0064618554151096942496 + 1.303232785873012896e-750j)  +/-  (4.54e-84, 9.16e-209j)
| (3.895606482384677809e-05 + 2.3730970386476917675e-753j)  +/-  (1.09e-88, 2.2e-213j)
| (1.930478607600589837e-08 - 6.3400574764908314799e-755j)  +/-  (6.35e-95, 1.28e-219j)
| (0.0017150793934568798515 + 6.653843826554733659e-751j)  +/-  (3.94e-89, 7.96e-214j)
| (3.9032406673984383266e-06 - 2.2275207751890799399e-753j)  +/-  (4.42e-93, 8.92e-218j)
| (0.0064618554151096942496 + 3.1532418368221293335e-750j)  +/-  (7.96e-88, 1.61e-212j)
| (0.017338320693152750345 + 1.0807892731061687759e-749j)  +/-  (3.2e-82, 6.46e-207j)
| (2.1450167479914453611e-17 + 1.0069183366841701334e-761j)  +/-  (2.79e-102, 5.63e-227j)
| (2.0914426619232743212e-14 - 1.274415521041989355e-759j)  +/-  (1.12e-100, 2.26e-225j)
| (0.017338320693152750345 + 1.3914698544651878117e-749j)  +/-  (9.96e-85, 2.01e-209j)
| (0.054529751355473469128 + 1.587182969164420933e-750j)  +/-  (2.99e-87, 6.04e-212j)
| (4.8895789510616602e-10 + 1.671497562925199037e-757j)  +/-  (7.68e-98, 1.55e-222j)
| (0.00030549746410587532889 - 1.8346008390436198744e-752j)  +/-  (7.41e-93, 1.49e-217j)
| (0.1125239048152888742 - 5.2067683312179491374e-750j)  +/-  (2.16e-87, 4.33e-212j)
| (0.17925487746087733342 - 1.1185558645664701889e-749j)  +/-  (5.62e-87, 1.13e-211j)
| (0.00030549746410587532889 - 6.6817390117749356368e-752j)  +/-  (6.54e-94, 1.31e-218j)
| (1.930478607600589837e-08 - 3.3223127438328802197e-756j)  +/-  (9.98e-97, 2.02e-221j)
| (0.17925487746087733342 - 9.4363991185835906528e-750j)  +/-  (2.59e-88, 5.24e-213j)
| (0.21737637169064897265 + 5.7711091422283450869e-750j)  +/-  (1.75e-88, 3.55e-213j)
| (0.054529751355473469128 + 2.6881423970145056563e-750j)  +/-  (2.28e-90, 4.61e-215j)
| (-0.00063029282574278942552 - 2.8824008749704818145e-750j)  +/-  (7.67e-92, 1.56e-216j)
| (0.0017150793934568798515 + 2.2945818170499425011e-751j)  +/-  (5.83e-93, 1.25e-217j)
| (5.2613877020542302739e-12 + 1.117742931405679505e-757j)  +/-  (3.91e-101, 7.92e-226j)
| (0.019769595112389659961 - 9.297848108701086878e-751j)  +/-  (1.49e-92, 3.64e-217j)
| (3.895606482384677809e-05 + 1.128706206293024635e-752j)  +/-  (1.99e-95, 3.83e-220j)
