Starting with polynomial:
P : 256*t^8 - 3584*t^6 + 13440*t^4 - 13440*t^2 + 1680
Extension levels are: 8 11 18
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Trying to find an order 11 Kronrod extension for:
P1 : 256*t^8 - 3584*t^6 + 13440*t^4 - 13440*t^2 + 1680
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P2 : 256*t^19 - 19308928/1347*t^17 + 418651520/1347*t^15 - 1521292480/449*t^13 + 9071700160/449*t^11 - 30031939520/449*t^9 + 52723966680/449*t^7 - 43021232100/449*t^5 + 12604959675/449*t^3 - 2144332575/898*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 256*t^37 - 361348630291589558025130458092279134914123559031960208703398831004192/6086396488736756248129170056954142823553589469301862889801776963*t^35 + 37020860223623584606917800538457650113909363235359460886538749146247760/6086396488736756248129170056954142823553589469301862889801776963*t^33 - 739745345501520955152456609998493499047636775238254484569394435193776080/2028798829578918749376390018984714274517863156433954296600592321*t^31 + 28974302201217152118437347188212643218192679047342950780176059035231107160/2028798829578918749376390018984714274517863156433954296600592321*t^29 - 8628525691603346383012225712582249824721064165448626109551009660297958159780/22316787125368106243140290208831857019696494720773497262606515531*t^27 + 166617302286983614015365184705778363564429530931876139008764403952616336591470/22316787125368106243140290208831857019696494720773497262606515531*t^25 - 2335196384712973146251174172777758462565471846367404890412550409237328260991375/22316787125368106243140290208831857019696494720773497262606515531*t^23 + 47897479796205894770471646411670141301733160150396185958195652650811802442162125/44633574250736212486280580417663714039392989441546994525213031062*t^21 - 3957852781830687342968334488967282203458176633906135224344024212990006120629324625/490969316758098337349086384594300854433322883857016939777343341682*t^19 + 10830470681390932122726779000783355376860102259575553733585176636912918871740199250/245484658379049168674543192297150427216661441928508469888671670841*t^17 - 682693149228428373282399882109892758258801975413004707314352648510240629184556146375/3927754534064786698792691076754406835466583070856135518218746733456*t^15 + 3795477602075744905884307235214320431005721314694108575561406398511069168601989520625/7855509068129573397585382153508813670933166141712271036437493466912*t^13 - 14439883570906114430421076575827521064673141678783488683542559745594097651783928108125/15711018136259146795170764307017627341866332283424542072874986933824*t^11 + 3265110533663939699935565832935589186067759658326158453511921103508392211869997200625/2856548752047117599121957146730477698521151324259007649613633987968*t^9 - 4962719609134735081201140504029663586670977523965663523058305315553319376519906228125/5713097504094235198243914293460955397042302648518015299227267975936*t^7 + 4173485951684908680097005473058900880876177418734785098285860052698911279207772640625/11426195008188470396487828586921910794084605297036030598454535951872*t^5 - 3348283196191046197741570341260572703168391386529911268849086741186441377042367596875/45704780032753881585951314347687643176338421188144122393818143807488*t^3 + 470179289136458950100707945007493694221888075272893083462419014468259838491513221875/91409560065507763171902628695375286352676842376288244787636287614976*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:
| (-5.509638199087149565 + 3.4470409872270405944e-942j)  +/-  (1.07e-247, 1.07e-247j)
| (-1.8651745430168657961 + 1.1111967473403935835e-943j)  +/-  (3.26e-248, 3.26e-248j)
| (-0.56474674797970907162 - 5.611565838819754962e-954j)  +/-  (1.92e-252, 1.92e-252j)
| (4.9726663397220773071 + 3.296097603561686126e-952j)  +/-  (2.67e-247, 2.67e-247j)
| (-6.8441577188865305408 - 5.6714030042383641855e-954j)  +/-  (3.41e-249, 3.41e-249j)
| (6.113851742267377997 + 2.4031401250933434603e-952j)  +/-  (2.97e-248, 2.97e-248j)
| (-6.113851742267377997 - 1.2680997082725988651e-951j)  +/-  (2.95e-248, 2.95e-248j)
| (-1.5169866092043167604 - 3.8562477296363990316e-952j)  +/-  (1.1e-249, 1.1e-249j)
| (3.6473028998600486888 + 3.1139415371678260883e-956j)  +/-  (6.3e-247, 6.3e-247j)
| (4.4838301627422905975 - 7.9510513861483654849e-958j)  +/-  (4.66e-247, 4.66e-247j)
| (6.8441577188865305408 + 2.377009256613117483e-960j)  +/-  (3.2e-249, 3.2e-249j)
| (3.2921703116686652561 - 3.7832720361406459608e-959j)  +/-  (4.9e-247, 4.9e-247j)
| (-3.6473028998600486888 - 7.891485088373568927e-957j)  +/-  (6.23e-247, 6.23e-247j)
| (-4.0399826837229783798 + 8.1239083435971993836e-966j)  +/-  (5.69e-247, 5.69e-247j)
| (-4.9726663397220773071 - 2.7776210244136840514e-970j)  +/-  (3e-247, 3e-247j)
| (2.5565927224498497011 - 2.59831881822026167e-976j)  +/-  (1.16e-247, 1.16e-247j)
| (1.8651745430168657961 - 5.5889947971220660358e-977j)  +/-  (3.58e-248, 3.58e-248j)
| (2.1885630273880580333 - 9.6502314939252168012e-977j)  +/-  (8.72e-248, 8.72e-248j)
| (-4.4838301627422905975 - 3.4455133413395506239e-975j)  +/-  (4.34e-247, 4.34e-247j)
| (-1.9816567566958429259 + 5.1945126041928602551e-986j)  +/-  (7.8e-248, 7.8e-248j)
| (5.509638199087149565 - 5.6875354684528976326e-995j)  +/-  (1.16e-247, 1.16e-247j)
| (0.38118699020732211685 - 3.2436958360868286282e-997j)  +/-  (2.38e-253, 2.38e-253j)
| (4.0399826837229783798 - 5.5560284723611754043e-995j)  +/-  (5.92e-247, 5.92e-247j)
| (5.919959890631998687e-997 - 4.2147063461844645238e-996j)  +/-  (1.57e-994, 1.57e-994j)
| (1.9816567566958429259 + 9.9432617891014862888e-996j)  +/-  (8.73e-248, 8.73e-248j)
| (1.5169866092043167604 + 2.4755031704750017418e-1000j)  +/-  (1.15e-249, 1.15e-249j)
| (1.1571937124467801947 - 8.9389475287250863362e-1001j)  +/-  (7.65e-251, 7.65e-251j)
| (2.9306374202572440192 - 1.3156038293482174961e-999j)  +/-  (2.36e-247, 2.36e-247j)
| (-3.2921703116686652561 - 1.7227788727759979122e-1004j)  +/-  (4.8e-247, 4.8e-247j)
| (-1.1571937124467801947 - 8.9591382967040456459e-1017j)  +/-  (7.48e-251, 7.48e-251j)
| (-0.78483006034508993587 + 3.1594261878160220433e-1023j)  +/-  (6.48e-252, 6.48e-252j)
| (-2.5565927224498497011 - 3.268706349219699447e-1036j)  +/-  (1.17e-247, 1.17e-247j)
| (0.78483006034508993587 - 2.6231245524762850613e-1053j)  +/-  (6.48e-252, 6.48e-252j)
| (-2.9306374202572440192 - 2.061527000316462802e-1055j)  +/-  (2.47e-247, 2.47e-247j)
| (-0.38118699020732211685 + 3.6909262818718052835e-1071j)  +/-  (2.52e-253, 2.52e-253j)
| (-2.1885630273880580333 - 3.8439332343360044183e-1071j)  +/-  (8.91e-248, 8.91e-248j)
| (0.56474674797970907162 + 6.0626259105992583848e-1077j)  +/-  (1.98e-252, 1.98e-252j)
-------------------------------------------------
The weights are:
| (2.0914426619232743212e-14 + 4.8492097129058425613e-955j)  +/-  (4.02e-94, 6.65e-218j)
| (0.0064618554151096942496 - 3.9802152345809056319e-945j)  +/-  (6e-78, 9.93e-202j)
| (0.017338320693152750345 + 4.2425455780285355475e-945j)  +/-  (9.15e-78, 1.52e-201j)
| (5.2613877020542302739e-12 - 9.864047874012260769e-955j)  +/-  (1.1e-93, 1.83e-217j)
| (2.1585924605424102008e-21 - 3.8657862894548938194e-960j)  +/-  (4.99e-98, 8.26e-222j)
| (2.1450167479914453611e-17 - 2.6306564383431562625e-958j)  +/-  (2.95e-97, 4.89e-221j)
| (2.1450167479914453611e-17 + 1.8663901647795320338e-957j)  +/-  (3.83e-96, 6.35e-220j)
| (0.019769595112389659961 - 1.4666566281902068077e-945j)  +/-  (3.16e-78, 5.23e-202j)
| (3.4616604622670422495e-07 + 7.4619602538177628987e-951j)  +/-  (1.87e-90, 3.09e-214j)
| (4.8895789510616602e-10 + 2.8616441282903303142e-953j)  +/-  (5.85e-93, 9.68e-217j)
| (2.1585924605424102008e-21 + 9.5505059658240098815e-961j)  +/-  (1.06e-99, 1.76e-223j)
| (3.9032406673984383266e-06 - 6.1288171000993333179e-950j)  +/-  (1.14e-89, 1.89e-213j)
| (3.4616604622670422495e-07 - 6.7243345147437029739e-951j)  +/-  (1.94e-92, 3.21e-216j)
| (1.930478607600589837e-08 + 8.3404535603985308331e-953j)  +/-  (9.89e-94, 1.64e-217j)
| (5.2613877020542302739e-12 - 4.041048520400656935e-954j)  +/-  (3.45e-96, 5.72e-220j)
| (0.00030549746410587532889 - 3.4039319207518375884e-948j)  +/-  (8.45e-90, 1.4e-213j)
| (0.0064618554151096942496 + 2.5342168267515781599e-946j)  +/-  (9.65e-88, 1.6e-211j)
| (0.0017150793934568798515 + 4.357298991431090795e-947j)  +/-  (7.6e-89, 1.26e-212j)
| (4.8895789510616602e-10 + 2.9670083764646034991e-953j)  +/-  (5.56e-96, 9.2e-220j)
| (-0.00063029282574278942552 + 5.2735911108794150831e-945j)  +/-  (7.24e-89, 1.2e-212j)
| (2.0914426619232743212e-14 + 2.2161879528380385073e-956j)  +/-  (5.43e-99, 8.98e-223j)
| (0.17925487746087733342 - 2.1980018875138283476e-945j)  +/-  (2.49e-88, 4.12e-212j)
| (1.930478607600589837e-08 - 5.7690754943747361434e-952j)  +/-  (7.27e-95, 1.2e-218j)
| (0.21737637169064897265 + 1.4601261205031095024e-945j)  +/-  (2.34e-88, 3.87e-212j)
| (-0.00063029282574278942552 - 2.1545650371424451377e-946j)  +/-  (1.87e-89, 3.1e-213j)
| (0.019769595112389659961 - 1.8630671324246268134e-946j)  +/-  (1.43e-89, 2.37e-213j)
| (0.054529751355473469128 + 3.3009332441665302666e-946j)  +/-  (1.22e-89, 2.02e-213j)
| (3.895606482384677809e-05 + 4.3148033294639082664e-949j)  +/-  (2.16e-92, 3.58e-216j)
| (3.9032406673984383266e-06 + 9.6795285661733862141e-950j)  +/-  (3.42e-96, 5.66e-220j)
| (0.054529751355473469128 + 1.2094657104808044779e-945j)  +/-  (2.45e-91, 4.06e-215j)
| (0.1125239048152888742 - 2.5198882240115843321e-945j)  +/-  (8.72e-91, 1.44e-214j)
| (0.00030549746410587532889 + 1.3833034946541906516e-947j)  +/-  (3.08e-95, 5.09e-219j)
| (0.1125239048152888742 - 1.1354879951485671492e-945j)  +/-  (5.21e-92, 8.73e-216j)
| (3.895606482384677809e-05 - 1.0622425509632548933e-948j)  +/-  (4.19e-96, 6.95e-220j)
| (0.17925487746087733342 - 3.1725778415864962743e-945j)  +/-  (2.68e-92, 4.6e-216j)
| (0.0017150793934568798515 - 3.8577199017101973851e-946j)  +/-  (3.13e-94, 5.13e-218j)
| (0.017338320693152750345 + 2.4377123554484149247e-945j)  +/-  (1.48e-92, 2.61e-216j)
