Starting with polynomial:
P : t
Extension levels are: 1 4 6 22
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P2 : t^5 - 10/9*t^3 + 5/21*t
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P3 : t^11 - 319/117*t^9 + 15994/5915*t^7 - 219098/186745*t^5 + 23263/112047*t^3 - 383/37349*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^33 - 2624182172905840234342452169007117406597471632012633961824101780693/320964008380396297833034189556816696741341027588693344741661573125*t^31 + 20160004965559767902614016275124775410165605754945389304891457750971627/663432605322279147620881669813940112164351904025829143581014471649375*t^29 - 1045894445447386975782404446087190001316131168871276242319633214683032815728/15394953606503487620542559148032480302773785932919365276797440814623746875*t^27 + 31281734989750335137254084671877388665770139882418220444818595660533737754/307021866796365849982330239419451174129391742251953153668325030491071875*t^25 - 20821159283308240295068905865644121648631241783221250269637714009847638997/192400369859055932655593616702856069121085491811223976298817019107738375*t^23 + 13909779682952518623135204835753949028420275218524024715449049530898949299/166044154809870188456197230853149758282580629919275486394869482243664625*t^21 - 1189108088430127628440627679704078413291421145664488594919487764277134794354/24819647711818215312571576554668432916620028443647892942547395464898250375*t^19 + 2519421496155756156454915778993812159428812042075626492182781741386072829358/124098238559091076562857882773342164583100142218239464712736977324491251875*t^17 - 1803300682177929279651385323719772144970949067512875276431527236805726427379/284695959047326587408909260480020259925935620383019948458631889156185813125*t^15 + 335311542030313031636269645581770744267770286949040397029066462148169670527/234083344105579638536214280839127769272435954537149735399319553306197224125*t^13 - 1518820913846981199370344158597368239640932624856445662081532031072869822996/6644365690381452816912543817664472835502220555708327104796070397691290438625*t^11 + 491908956908616265515426116385441094343479725325620189925148084354303662378/19933097071144358450737631452993418506506661667124981314388211193073871315875*t^9 - 130806188020909765211810108983888807000256221359454154803633839444692349877/77517599721116949530646344539418849747525906483263816222620821306398388450625*t^7 + 5151658112273244621819634409619746030754980434347673083371931964765159/78538601541151924549793662147334194273075893093479043791915725741031801875*t^5 - 7902885805108670682979730525669711453296196676429337118899911923806334/6644365690381452816912543817664472835502220555708327104796070397691290438625*t^3 + 182827717558847373546972924241739764321803148462342086678132076619287/28792251324986295539954356543212715620509622408069417454116305056662258567375*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:
| (0.9969315800359169849 - 4.3186372980910955371e-391j)  +/-  (3.39e-117, 3.39e-117j)
| (0.093075825090466195759 + 3.4150456438708569341e-400j)  +/-  (8.76e-127, 8.76e-127j)
| (-0.9061798459386639928 - 1.5557771123072907623e-391j)  +/-  (1.08e-116, 1.08e-116j)
| (-0.96237269896445671097 + 3.8745212443771757753e-401j)  +/-  (1.54e-116, 1.54e-116j)
| (0.9061798459386639928 + 8.2518963824466991823e-412j)  +/-  (1.07e-116, 1.07e-116j)
| (0.86626616425555031402 - 2.4494188750904845953e-413j)  +/-  (3.93e-117, 3.93e-117j)
| (-0.9969315800359169849 - 1.7013246980328259243e-413j)  +/-  (3.22e-117, 3.22e-117j)
| (-0.93570636509895242351 - 3.7893901635192108108e-422j)  +/-  (1.58e-116, 1.58e-116j)
| (-0.093075825090466195759 + 5.4100884941540442388e-440j)  +/-  (8.76e-127, 8.76e-127j)
| (0.96237269896445671097 - 1.8300155730927495214e-428j)  +/-  (1.64e-116, 1.64e-116j)
| (0.81464754019601538171 - 7.6678433327023939561e-431j)  +/-  (1.06e-117, 1.06e-117j)
| (-0.9840853600948424645 - 1.0682372217882857766e-428j)  +/-  (9.95e-117, 9.95e-117j)
| (-0.86626616425555031402 + 1.9370756665177189957e-437j)  +/-  (3.92e-117, 3.92e-117j)
| (-0.68706602399851241633 - 5.6624827159679874987e-445j)  +/-  (4.52e-119, 4.52e-119j)
| (-0.37039985093866279814 - 1.5133779533691245992e-448j)  +/-  (4.99e-123, 4.99e-123j)
| (0.75416672657084922044 + 5.9752941493812295149e-443j)  +/-  (2.65e-118, 2.65e-118j)
| (0.93570636509895242351 + 3.0543583397238403256e-442j)  +/-  (1.78e-116, 1.78e-116j)
| (0.9840853600948424645 + 6.2740755758682648103e-445j)  +/-  (9.61e-117, 9.61e-117j)
| (-0.75416672657084922044 - 6.5576276514627124232e-446j)  +/-  (2.36e-118, 2.36e-118j)
| (-0.81464754019601538171 + 3.3045109926162068778e-452j)  +/-  (1.09e-117, 1.09e-117j)
| (0.18657478545145848384 + 2.2692373201625390207e-462j)  +/-  (1.76e-125, 1.76e-125j)
| (0.68706602399851241633 + 3.7888415254804621258e-456j)  +/-  (4.7e-119, 4.7e-119j)
| (0.45701852487852261096 - 1.0698184547059155238e-459j)  +/-  (7.79e-122, 7.79e-122j)
| (-0.53846931010568309104 - 3.7684837072987260101e-457j)  +/-  (7.98e-121, 7.98e-121j)
| (-0.45701852487852261096 + 9.0942492367487131508e-459j)  +/-  (7.21e-122, 7.21e-122j)
| (-7.1583834954748429596e-466 + 4.064141263405691826e-466j)  +/-  (2.72e-464, 2.72e-464j)
| (0.53846931010568309104 + 1.9764078029383239404e-457j)  +/-  (7.34e-121, 7.34e-121j)
| (0.27963041316178319341 + 1.1494076331547897307e-462j)  +/-  (3.48e-124, 3.48e-124j)
| (-0.27963041316178319341 + 8.3171417152083371338e-462j)  +/-  (3.16e-124, 3.16e-124j)
| (-0.61498008079408840393 + 5.3242400873740466841e-459j)  +/-  (6.15e-120, 6.15e-120j)
| (-0.18657478545145848384 - 7.7438892365653649374e-465j)  +/-  (1.99e-125, 1.99e-125j)
| (0.37039985093866279814 - 1.7077301367091744369e-461j)  +/-  (5.23e-123, 5.23e-123j)
| (0.61498008079408840393 + 2.2445946998950166665e-460j)  +/-  (6.46e-120, 6.46e-120j)
-------------------------------------------------
The weights are:
| (0.0078483991319272960013 + 6.020474258913827181e-391j)  +/-  (2.41e-20, 3.06e-77j)
| (0.09330899921904648469 - 1.7301473212199085517e-391j)  +/-  (1.48e-20, 1.88e-77j)
| (0.033528941409181692716 + 6.2373274435196495062e-392j)  +/-  (4.29e-21, 5.45e-78j)
| (0.025120648825990407398 + 5.4108957612912855915e-392j)  +/-  (3.03e-21, 3.85e-78j)
| (0.033528941409181692716 + 1.0702946759742678833e-390j)  +/-  (6.75e-22, 8.57e-79j)
| (0.046249948792911328949 - 7.3656155254293152295e-391j)  +/-  (6.25e-22, 7.94e-79j)
| (0.0078483991319272960013 + 3.7003292615507773897e-393j)  +/-  (1.07e-22, 1.35e-79j)
| (0.027443339251889059864 - 1.7173229419888774658e-391j)  +/-  (3.19e-22, 4.05e-79j)
| (0.09330899921904648469 - 1.3994620928802791654e-391j)  +/-  (6.43e-24, 8.17e-81j)
| (0.025120648825990407398 + 1.0687489832677871864e-390j)  +/-  (1.14e-23, 1.44e-80j)
| (0.056475998657526608593 + 5.1188784289837050973e-391j)  +/-  (1.73e-23, 2.2e-80j)
| (0.017654414166876723291 - 1.6795749264168591273e-392j)  +/-  (1.6e-22, 2.03e-79j)
| (0.046249948792911328949 + 7.7801227771993298525e-392j)  +/-  (1.77e-23, 2.25e-80j)
| (0.069798398692060461785 + 3.8435760304360134004e-392j)  +/-  (3.3e-25, 4.19e-82j)
| (0.088961169100297091248 + 9.0528756088007675106e-392j)  +/-  (1.01e-25, 1.28e-82j)
| (0.064119124121383169141 - 4.0398328340918652923e-391j)  +/-  (1.33e-25, 1.69e-82j)
| (0.027443339251889059864 - 1.2009674744615110513e-390j)  +/-  (6.5e-25, 8.26e-82j)
| (0.017654414166876723291 - 1.0961818054334633167e-390j)  +/-  (2.29e-25, 2.91e-82j)
| (0.064119124121383169141 - 2.1620862720152342234e-392j)  +/-  (8.28e-27, 1.05e-83j)
| (0.056475998657526608593 - 3.1105353018126254531e-393j)  +/-  (2.22e-26, 2.83e-83j)
| (0.093534482080885522313 + 1.8496689446479652791e-391j)  +/-  (2.5e-29, 3.17e-86j)
| (0.069798398692060461785 + 3.5132619687835614727e-391j)  +/-  (5.86e-29, 7.44e-86j)
| (0.084096171564014467318 - 2.5370412277966866119e-391j)  +/-  (4.67e-30, 5.93e-87j)
| (0.0788617557660591658 + 6.7812361213254324105e-392j)  +/-  (9.71e-30, 1.23e-86j)
| (0.084096171564014467318 - 7.9564918407894638255e-392j)  +/-  (7.38e-30, 9.37e-87j)
| (0.092940332616874747575 + 1.5860871521920172957e-391j)  +/-  (1.49e-30, 1.9e-87j)
| (0.0788617557660591658 + 2.8755510952718423328e-391j)  +/-  (2.55e-31, 3.24e-88j)
| (0.092252445357798846086 - 2.0003312356041767698e-391j)  +/-  (2.16e-31, 2.75e-88j)
| (0.092252445357798846086 - 1.0348593240640982363e-391j)  +/-  (1.69e-31, 2.15e-88j)
| (0.074275597553714301019 - 5.3858963400187043916e-392j)  +/-  (2.84e-31, 3.6e-88j)
| (0.093534482080885522313 + 1.2026907707053703753e-391j)  +/-  (1.21e-31, 1.53e-88j)
| (0.088961169100297091248 + 2.2283350006197866597e-391j)  +/-  (1.68e-32, 2.15e-89j)
| (0.074275597553714301019 - 3.187375286444278578e-391j)  +/-  (1.19e-32, 1.49e-89j)
