Starting with polynomial:
P : t
Extension levels are: 1 4 12 16
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Trying to find an order 4 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P2 : t^5 - 10/9*t^3 + 5/21*t
Solvable: 1
-------------------------------------------------
Trying to find an order 16 Kronrod extension for:
P3 : t^17 - 8857204/2038671*t^15 + 28927370/3714291*t^13 - 6039926464/813429729*t^11 + 9865688404/2440289187*t^9 - 11887949788/9490013505*t^7 + 122410578862/592447985955*t^5 - 5464102072/355468791573*t^3 + 39745277/118489597191*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^33 - 1428479311446303518095268643595248482714012045548045343102146170696165922991476/174509598479058639024614701840807754485779818263358583504082953996093835373001*t^31 + 11613326717107086196174626381367097845814628646970321033889748919739328604317304554/381303472676743126268783123522164943551428902905438504956421254481465030290007185*t^29 - 56461337206919128278965789691690898092953686350963236991535366600465326829828994024/828348923401200584652873682134358325646207616656642269388087552839044720974843195*t^27 + 740247348685601663731846893409028653487460676093662982978938681450405815928539964599786/7234755899674327948432690693778215386808416997162447441768746787151330327482650210225*t^25 - 5658587524358678395650130908499974807323524131740407271203357513452607899116327624485532/52023460115504321278422148158029813412219293914980429758195573050992796847159857050141*t^23 + 312357365649819558147991934710001853775724794773863429774499567283890372201757141470876907342646/3706630347990424783499899305392332432018340017834672927431209341721238072729302479935714888375*t^21 - 25516415992176432251232250476681864578976325459863535368247671184059717979892396863244649729539264/528989102520347765530914200869562871369474525402405464929111161768502404950939025350825596212375*t^19 + 120071013627839163944233019191567002390867867409654229268485746242418277084563666677615209070871510684/5868855677146142486057318893278921340543599083273687367354315123420603392191220623622488502820399375*t^17 - 112507634138322303938937994115200462479411407480467482680995661291358742707353735244746460398746005308/17606567031438427458171956679836764021630797249821062102062945370261810176573661870867465508461198125*t^15 + 1698557692598651179240619667989457897593571727712322439950290271967140581811587180192791698871560106/1173771135429228497211463778655784268108719816654737473470863024684120678438244124724497700564079875*t^13 - 605808688181976290993438291076514301252090654459137942266478527355524571855335240367653661015173128/2618412532880586647625573044693672598088682667922106671588848285833807667285313816693110255104485875*t^11 + 1770913225564935446929136823050612465006942288459316134531046457476085621407854778910417607455578806/70697138387775839485890472206729160148394432033896880132898903717512807016703473050713976887821118625*t^9 - 2365802670368718560734908731096415729199302173190260938135596909275340625999804092722214792441619756/1374666579762307990003425848464178113996558400659106002584145350062749025324789753763882883929855084375*t^7 + 304914911584466640366633498908244740939379377306768335772948893063671269082945006813845641396604546/4516761619219011967154113502096585231702977602165634008490763293063318226067166333795615190055238134375*t^5 - 3385326807350847971252377460872248691973800366503798409361862452311910214730555501415376582258736/2710056971531407180292468101257951139021786561299380405094457975837990935640299800277369114033142880625*t^3 + 68477498187654801489678671327112551668314595682597515383298554420922655179035898381972306633/9735504340914489776055377939856508156818669817486902570768519860261264469118112347375687874197336875*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
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (0.9962698516849579968 + 1.0108383799387778179e-310j)  +/-  (4.12e-117, 4.12e-117j)
| (-1.1428152281565795889e-311 - 1.0382778387952341387e-311j)  +/-  (5.1e-310, 5.1e-310j)
| (-0.9061798459386639928 - 1.1862124430139214935e-316j)  +/-  (5.9e-117, 5.9e-117j)
| (-0.96827060709476223499 - 2.4873771990625125111e-330j)  +/-  (2.58e-116, 2.58e-116j)
| (0.94551687263152459739 - 1.1861552472959906078e-342j)  +/-  (1.43e-116, 1.43e-116j)
| (0.9061798459386639928 + 2.0680754971945014771e-343j)  +/-  (5.8e-117, 5.8e-117j)
| (-0.98189805109989378087 - 9.1337535225982817333e-342j)  +/-  (1.9e-116, 1.9e-116j)
| (-0.85946974239072605693 - 4.138120652173789567e-353j)  +/-  (2.63e-117, 2.63e-117j)
| (-0.9962698516849579968 + 5.3528157412772156006e-354j)  +/-  (4.25e-117, 4.25e-117j)
| (0.98189805109989378087 + 3.396509785864606191e-361j)  +/-  (1.8e-116, 1.8e-116j)
| (0.85946974239072605693 - 1.1280144856208817747e-364j)  +/-  (3.04e-117, 3.04e-117j)
| (0.96827060709476223499 - 1.7671906781617611856e-366j)  +/-  (2.54e-116, 2.54e-116j)
| (-0.3701498540017078954 + 1.4251748729005137409e-372j)  +/-  (4.77e-123, 4.77e-123j)
| (-0.81141684513575577466 - 2.5089775269193013148e-367j)  +/-  (1.09e-117, 1.09e-117j)
| (-0.68735255126326749856 - 4.3807954621334616582e-370j)  +/-  (4.45e-119, 4.45e-119j)
| (0.81141684513575577466 - 2.6061715694096211943e-370j)  +/-  (1.04e-117, 1.04e-117j)
| (0.75569380316189441419 + 5.4618292964350922087e-372j)  +/-  (2.85e-118, 2.85e-118j)
| (-0.94551687263152459739 + 2.393245908614336003e-372j)  +/-  (1.57e-116, 1.57e-116j)
| (-0.75569380316189441419 + 1.0137293536640654441e-383j)  +/-  (2.5e-118, 2.5e-118j)
| (-0.27815860931240380335 + 6.7043224049432581897e-389j)  +/-  (2.8e-124, 2.8e-124j)
| (0.53846931010568309104 + 9.087294979064132676e-387j)  +/-  (7.96e-121, 7.96e-121j)
| (0.61304640697441226936 + 9.1333509199397230089e-385j)  +/-  (6.29e-120, 6.29e-120j)
| (0.27815860931240380335 + 1.0238117183053555812e-388j)  +/-  (3.02e-124, 3.02e-124j)
| (-0.53846931010568309104 - 2.7409820644600737438e-388j)  +/-  (7.74e-121, 7.74e-121j)
| (-0.45888640555451469594 + 2.3632906124895642797e-388j)  +/-  (7.43e-122, 7.43e-122j)
| (0.097048511523328935244 - 5.075315832055743869e-389j)  +/-  (1.01e-126, 1.01e-126j)
| (0.68735255126326749856 - 9.2805865220728751817e-391j)  +/-  (4.41e-119, 4.41e-119j)
| (0.18847441760531908906 + 5.653396935180908784e-395j)  +/-  (1.98e-125, 1.98e-125j)
| (-0.18847441760531908906 + 1.5613464904236528201e-395j)  +/-  (2.02e-125, 2.02e-125j)
| (-0.61304640697441226936 + 2.5652706163861716831e-392j)  +/-  (5.88e-120, 5.88e-120j)
| (-0.097048511523328935244 - 3.6668528044498638643e-396j)  +/-  (1e-126, 1e-126j)
| (0.3701498540017078954 + 1.3198097181666208792e-393j)  +/-  (4.86e-123, 4.86e-123j)
| (0.45888640555451469594 + 2.8801114147353488652e-394j)  +/-  (7.55e-122, 7.55e-122j)
-------------------------------------------------
The weights are:
| (0.0094652842925565971855 - 1.7154334092394900967e-310j)  +/-  (3.79e-19, 4.93e-75j)
| (0.09840079668658639806 - 3.3233156616043125206e-311j)  +/-  (2.36e-19, 3.07e-75j)
| (0.044303062875774274847 - 6.1153096797767509593e-312j)  +/-  (6.38e-20, 8.3e-76j)
| (0.012638785842558810292 - 5.5451811286851531674e-312j)  +/-  (4.66e-20, 6.07e-76j)
| (0.033044531003052061106 + 2.34431263930788228e-310j)  +/-  (1.23e-20, 1.61e-76j)
| (0.044303062875774274847 - 1.3850699152839901854e-310j)  +/-  (9.31e-21, 1.21e-76j)
| (0.017151000815025644917 + 2.9206251266783317791e-312j)  +/-  (7.33e-21, 9.55e-77j)
| (0.047767691838611251396 + 8.6510704047100795654e-312j)  +/-  (9.56e-22, 1.24e-77j)
| (0.0094652842925565971855 - 4.5054549121466110958e-313j)  +/-  (2.1e-21, 2.74e-77j)
| (0.017151000815025644917 + 4.2884814815526020979e-310j)  +/-  (3.09e-22, 4.03e-78j)
| (0.047767691838611251396 + 1.2634709195401751822e-310j)  +/-  (1.29e-23, 1.68e-79j)
| (0.012638785842558810292 - 4.1543452246654017995e-310j)  +/-  (3.26e-22, 4.25e-78j)
| (0.091730032337959171566 - 1.9819757301183763337e-311j)  +/-  (1.5e-25, 1.95e-81j)
| (0.049791031616470364742 - 1.1192475762481474842e-311j)  +/-  (2.12e-24, 2.76e-80j)
| (0.072725183604225670893 - 1.2804084026384969509e-311j)  +/-  (1.82e-25, 2.37e-81j)
| (0.049791031616470364742 - 1.1835672290654205485e-310j)  +/-  (5.22e-25, 6.79e-81j)
| (0.062615904449902705946 + 9.4810737531439776343e-311j)  +/-  (8.23e-26, 1.07e-81j)
| (0.033044531003052061106 + 5.7294685404701920567e-312j)  +/-  (1.8e-24, 2.34e-80j)
| (0.062615904449902705946 + 1.1970305458964128276e-311j)  +/-  (1.71e-25, 2.23e-81j)
| (0.091103651834309260159 + 2.2260625015148602905e-311j)  +/-  (7.39e-28, 9.62e-84j)
| (0.075524222479428585392 - 6.8165061551836619442e-311j)  +/-  (1.18e-28, 1.53e-84j)
| (0.074696746370028320036 + 7.182062209459680982e-311j)  +/-  (2.6e-28, 3.38e-84j)
| (0.091103651834309260159 + 4.9676186604923458286e-311j)  +/-  (9.09e-30, 1.18e-85j)
| (0.075524222479428585392 - 1.8070745166398452767e-311j)  +/-  (6.5e-29, 8.47e-85j)
| (0.084530302249126404995 + 1.8978652471759209545e-311j)  +/-  (5.81e-29, 7.57e-85j)
| (0.094538573544467666708 + 4.9067476677823553208e-311j)  +/-  (1.28e-30, 1.67e-86j)
| (0.072725183604225670893 - 7.6535610369787452672e-311j)  +/-  (5.53e-30, 7.2e-86j)
| (0.089173596503210010791 - 4.9343358181525123126e-311j)  +/-  (7.1e-31, 9.25e-87j)
| (0.089173596503210010791 - 2.3950371961056330248e-311j)  +/-  (4.37e-31, 5.69e-87j)
| (0.074696746370028320036 + 1.541971864907617969e-311j)  +/-  (9.48e-31, 1.23e-86j)
| (0.094538573544467666708 + 2.0473510959021184535e-311j)  +/-  (2.68e-31, 3.49e-87j)
| (0.091730032337959171566 - 5.1362323532059093275e-311j)  +/-  (1.86e-32, 2.44e-88j)
| (0.084530302249126404995 + 5.9024055019185770665e-311j)  +/-  (1.71e-32, 2.22e-88j)
