Starting with polynomial:
P : t
Extension levels are: 1 12 28
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P2 : t^13 - 78/25*t^11 + 429/115*t^9 - 1716/805*t^7 + 1287/2185*t^5 - 2574/37145*t^3 + 429/185725*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^41 - 6480388755146046950027557498984984214987525794/625410696539947778170612064609927135420169325*t^39 + 19604163731221747603332023939905435640703463266576/393883656680859110691851478291332109887622640885*t^37 - 46631687653193011739917692464603526763747660742014902/317076343628091584106940440024522348459536225912425*t^35 + 463432637994191207597638153521759232828701910901446787/1549144421725818882351051864119809188188019846600705*t^33 - 237843370507014538301637372592382911179753029762880147352/535487588443224726999346927697414042716992193641643695*t^31 + 3382778297283991978176633700697562399845481558496179880150928/6792660059402305661986715777841697131865045976344250271075*t^29 - 584647558250994347036341449659725097347088780327190346720136/1358532011880461132397343155568339426373009195268850054215*t^27 + 12474859861475566694455445907716949849231963889839998219854398/43020180376214602525915866592997415168478624516846918383475*t^25 - 11458807136922333912864419209113371740076843743161034465596/74817705002112352218984115813908548119093260029298988493*t^23 + 564557769514222642961787833495732837060702635091639352902768/8903306895251369914059109781855117226172097943486579630667*t^21 - 6855365356890830548585398615302542746313716458979052745244/334710785535765786242823676009590873164364584341600737995*t^19 + 945968559167643288159027461330192422990302372772451987622/185075375531541081804855444381773776926178064283002761009*t^17 - 142791293559429902206265850614786384345715300673594124851352/147134923547575160034860078283510152656311561104987195002155*t^15 + 404748488671076368602691930336002355447499307865513195485712/2952507465854674878032858904222437063303318659506743046376577*t^13 - 41194486601592997182518206272041659197997278433275250591256/2952507465854674878032858904222437063303318659506743046376577*t^11 + 306885471403707685175731052145198517468574830417370591799/314096538920710093407750947257706070564182836117738621954955*t^9 - 908184537307218867511056607844543353260108249316201235094/20667552260982724146230012329557059443123230616547201324636039*t^7 + 16787811237141342776279174389547353302774586022683565856/14762537329273374390164294521112185316516593297533715231882885*t^5 - 41021645768495919667335313720640341902556755070033046/2952507465854674878032858904222437063303318659506743046376577*t^3 + 149805712472470601432980486941214055728129912528551/2952507465854674878032858904222437063303318659506743046376577*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:
| (0.98418305471858814947 + 2.3638850608111522233e-843j)  +/-  (7.4e-241, 7.4e-241j)
| (-0.99938065963663877686 - 1.9401463263972704087e-858j)  +/-  (3.66e-241, 3.66e-241j)
| (-0.96775951626391108868 + 1.0105986675935229334e-864j)  +/-  (5.93e-241, 5.93e-241j)
| (0.99938065963663877686 - 7.8662217629464429108e-868j)  +/-  (3.31e-241, 3.31e-241j)
| (0.96775951626391108868 - 2.8325618843056306465e-888j)  +/-  (5.72e-241, 5.72e-241j)
| (0.94552003904703088969 + 8.405348272639129297e-907j)  +/-  (3.21e-241, 3.21e-241j)
| (-0.91759839922297796521 - 5.2896225121413478815e-915j)  +/-  (1.74e-241, 1.74e-241j)
| (-0.88416234043030430681 + 1.7227696898054105841e-916j)  +/-  (6.82e-242, 6.82e-242j)
| (-0.99469965430131955395 + 6.7273619043865918753e-915j)  +/-  (6.9e-241, 6.9e-241j)
| (0.80157809073330991279 - 3.0427974957843272465e-916j)  +/-  (5.42e-243, 5.42e-243j)
| (0.84541175979433656285 + 1.6360889006892956384e-924j)  +/-  (2.11e-242, 2.11e-242j)
| (-0.98418305471858814947 - 1.2595824350688789646e-929j)  +/-  (7.45e-241, 7.45e-241j)
| (-0.80157809073330991279 + 1.5076395089006508031e-934j)  +/-  (6.21e-243, 6.21e-243j)
| (-0.84541175979433656285 - 8.0444040168238154518e-935j)  +/-  (2.02e-242, 2.02e-242j)
| (0.99469965430131955395 - 4.291448619285560351e-931j)  +/-  (7.35e-241, 7.35e-241j)
| (0.91759839922297796521 + 7.2087843783738035031e-942j)  +/-  (1.74e-241, 1.74e-241j)
| (0.88416234043030430681 - 1.5413167176007010556e-954j)  +/-  (6.65e-242, 6.65e-242j)
| (-0.94552003904703088969 + 1.368912354316978046e-961j)  +/-  (3.75e-241, 3.75e-241j)
| (-0.7529237068328764254 + 2.1833120721028783865e-964j)  +/-  (1.34e-243, 1.34e-243j)
| (-0.23045831595513479407 - 3.009020768726232371e-970j)  +/-  (9.39e-252, 9.39e-252j)
| (0.51634640124151093842 + 2.0496323076610951963e-966j)  +/-  (4.47e-247, 4.47e-247j)
| (0.7529237068328764254 - 7.301811220394812551e-963j)  +/-  (1.31e-243, 1.31e-243j)
| (0.15441300414438573558 - 1.1662158297013458805e-975j)  +/-  (4.24e-253, 4.24e-253j)
| (-0.58109501657195363168 + 1.6220067430809454781e-967j)  +/-  (4.59e-246, 4.59e-246j)
| (-0.69974076698664806642 + 3.7177430250032388989e-966j)  +/-  (2.53e-244, 2.53e-244j)
| (0.07743926262886708714 - 2.2356742378003276296e-976j)  +/-  (2.46e-254, 2.46e-254j)
| (0.69974076698664806642 - 1.5436004399888033989e-967j)  +/-  (2.47e-244, 2.47e-244j)
| (0.44849275103644685288 + 5.8620518842509916452e-973j)  +/-  (3.98e-248, 3.98e-248j)
| (-0.15441300414438573558 + 3.1513453168070270666e-976j)  +/-  (4.45e-253, 4.45e-253j)
| (-0.64234933944034022064 + 1.5322837599032119069e-971j)  +/-  (3.44e-245, 3.44e-245j)
| (-0.07743926262886708714 - 9.79525199265414219e-982j)  +/-  (1.97e-254, 1.97e-254j)
| (0.37794181353855315337 - 5.6889693181202384366e-975j)  +/-  (2.84e-249, 2.84e-249j)
| (0.64234933944034022064 - 2.1228562837316825468e-975j)  +/-  (3.52e-245, 3.52e-245j)
| (2.5728720673277994671e-984 + 4.8786404448718581074e-984j)  +/-  (2.26e-982, 2.26e-982j)
| (-0.44849275103644685288 - 4.210828742492635648e-980j)  +/-  (3.78e-248, 3.78e-248j)
| (-0.37794181353855315337 + 3.8665068820804011281e-981j)  +/-  (2.8e-249, 2.8e-249j)
| (0.23045831595513479407 + 1.3720948270255524799e-982j)  +/-  (9.3e-252, 9.3e-252j)
| (0.58109501657195363168 - 3.1737747551259234466e-980j)  +/-  (4.57e-246, 4.57e-246j)
| (0.30511766440256551373 + 3.3825407119921527603e-985j)  +/-  (1.62e-250, 1.62e-250j)
| (-0.30511766440256551373 - 3.4515086081176238829e-982j)  +/-  (1.85e-250, 1.85e-250j)
| (-0.51634640124151093842 - 7.7069652562077014858e-982j)  +/-  (4.56e-247, 4.56e-247j)
-------------------------------------------------
The weights are:
| (0.013480498717928262033 - 3.9632261717814236393e-845j)  +/-  (1.34e-71, 4.55e-188j)
| (0.0020178294171529969062 - 4.4999786076558835037e-846j)  +/-  (3.7e-72, 1.25e-188j)
| (0.019350786653789776638 + 1.9769136770729239633e-845j)  +/-  (3.37e-72, 1.14e-188j)
| (0.0020178294171529969062 + 5.8732901201532179877e-844j)  +/-  (2.39e-72, 8.09e-189j)
| (0.019350786653789776638 + 2.3495679546067478435e-843j)  +/-  (2.88e-72, 9.75e-189j)
| (0.025105783696180226123 - 1.1425467701231424361e-843j)  +/-  (7.63e-73, 2.58e-189j)
| (0.030709514822624864969 + 2.5765860181950224592e-845j)  +/-  (1.02e-73, 3.45e-190j)
| (0.036129278601053854964 - 2.8501124369596883293e-845j)  +/-  (5.19e-74, 1.76e-190j)
| (0.0075517466327290278875 + 1.1624931582115689539e-845j)  +/-  (1.27e-73, 4.29e-190j)
| (0.046290288416953235362 - 3.3073330556989739771e-844j)  +/-  (7.21e-76, 2.44e-192j)
| (0.041333301904649676685 + 4.1092717069246558533e-844j)  +/-  (1.35e-75, 4.57e-192j)
| (0.013480498717928262033 - 1.6189239074385408375e-845j)  +/-  (5.51e-74, 1.86e-190j)
| (0.046290288416953235362 - 3.3819496804563080424e-845j)  +/-  (1.19e-76, 4.03e-193j)
| (0.041333301904649676685 + 3.1168046140168961501e-845j)  +/-  (5.89e-76, 1.99e-192j)
| (0.0075517466327290278875 - 2.18743481868015961e-843j)  +/-  (7.41e-76, 2.51e-192j)
| (0.030709514822624864969 + 7.3592083152122730714e-844j)  +/-  (4.35e-77, 1.47e-193j)
| (0.036129278601053854964 - 5.3238916409877503797e-844j)  +/-  (1.58e-77, 5.35e-194j)
| (0.025105783696180226123 - 2.2891761857808511589e-845j)  +/-  (3.02e-77, 1.02e-193j)
| (0.050969754372676086668 + 3.6499650065342259655e-845j)  +/-  (6.32e-80, 2.14e-196j)
| (0.075427993337646848653 + 6.3584996512167376314e-845j)  +/-  (5.45e-83, 1.84e-199j)
| (0.06636762012924127862 + 1.5480354435571461699e-844j)  +/-  (7.26e-83, 2.45e-199j)
| (0.050969754372676086668 + 2.7416746394226766335e-844j)  +/-  (6.83e-81, 2.31e-197j)
| (0.076586325536819268192 - 9.3793209468710504983e-845j)  +/-  (5.59e-84, 1.89e-200j)
| (0.063064698718290229004 - 4.5094427844892179505e-845j)  +/-  (3.81e-83, 1.29e-199j)
| (0.055342739833550768357 - 3.9247905402539049391e-845j)  +/-  (7.49e-82, 2.54e-198j)
| (0.077283960060534679974 + 8.6223570051967584904e-845j)  +/-  (1.63e-84, 5.52e-201j)
| (0.055342739833550768357 - 2.3235111553333098672e-844j)  +/-  (8.37e-83, 2.83e-199j)
| (0.069271686955622450818 - 1.381390395343269272e-844j)  +/-  (3e-84, 1.02e-200j)
| (0.076586325536819268192 - 6.8353298396349784669e-845j)  +/-  (3.69e-85, 1.25e-201j)
| (0.059382473883523658956 + 4.2100948438164750175e-845j)  +/-  (6.26e-84, 2.12e-200j)
| (0.077283960060534679974 + 7.3644539681287262305e-845j)  +/-  (2.13e-85, 7.21e-202j)
| (0.071759469153745021213 + 1.2424649217415939628e-844j)  +/-  (7.53e-86, 2.55e-202j)
| (0.059382473883523658956 + 2.0032709881688813602e-844j)  +/-  (4.08e-85, 1.38e-201j)
| (0.077516935224550208192 - 7.9559663895399568194e-845j)  +/-  (8.71e-86, 2.95e-202j)
| (0.069271686955622450818 - 5.1651422981561661953e-845j)  +/-  (3.25e-87, 1.1e-203j)
| (0.071759469153745021213 + 5.5298416014021739746e-845j)  +/-  (2.52e-87, 8.52e-204j)
| (0.075427993337646848653 + 1.024683990663883435e-844j)  +/-  (2.36e-87, 7.99e-204j)
| (0.063064698718290229004 - 1.751114207396197816e-844j)  +/-  (3.12e-87, 1.06e-203j)
| (0.073815781543012683883 - 1.1250688501945134329e-844j)  +/-  (1.55e-87, 5.24e-204j)
| (0.073815781543012683883 - 5.9256564939365787505e-845j)  +/-  (2.46e-88, 8.37e-205j)
| (0.06636762012924127862 + 4.826481203025028116e-845j)  +/-  (2e-88, 6.69e-205j)
