Starting with polynomial:
P : t
Extension levels are: 1 4 28
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P2 : t^5 - 10/9*t^3 + 5/21*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^33 - 12616216214138253508/1539464155910747433*t^31 + 291121411424584524407954/9536980445867080347435*t^29 - 279504537747669331539728/4087277333943034434615*t^27 + 1477643651740203905909978/14381160989799565603275*t^25 - 3332978961639791893293332/30488061298375079078943*t^23 + 2160586129074733047787814/25490018462575885787313*t^21 - 9270899287921135979071672/190951541816138653178643*t^19 + 61640481883850929993031384/2991574155119505566465407*t^17 - 356911902783568661036908972/55432109344861426672741365*t^15 + 11037441609444188388210618/7566922862949337609294853*t^13 - 651317328761057831615083744/2792194536428305577829800757*t^11 + 211549946947466486089418974/8376583609284916733489402271*t^9 - 1126844403817828682072812/649755961307215763394356151*t^7 + 315909915645181613361782/4653657560713842629716334595*t^5 - 128741214196416991586696/103311197847847306379702628009*t^3 + 1641404673570471763603/241059461644977048219306132021*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: 1
  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:
| (0.99757954096645789899 - 1.0820441316370410998e-287j)  +/-  (4.65e-117, 4.65e-117j)
| (1.1385791672708169068e-300 - 7.82722717638774577e-300j)  +/-  (2.61e-298, 2.61e-298j)
| (-0.86274586119758909118 + 5.3419133736000479825e-300j)  +/-  (3.07e-117, 3.07e-117j)
| (-0.99757954096645789899 - 2.5810588970963180064e-302j)  +/-  (4.88e-117, 4.88e-117j)
| (0.94150920098835398335 + 1.8396848093318670898e-312j)  +/-  (1.16e-116, 1.16e-116j)
| (0.9061798459386639928 + 5.0907000990641375506e-329j)  +/-  (7.08e-117, 7.08e-117j)
| (-0.98722734159271334457 - 1.6729707641382558748e-333j)  +/-  (1.23e-116, 1.23e-116j)
| (-0.9061798459386639928 + 6.02351732395805605e-336j)  +/-  (6.6e-117, 6.6e-117j)
| (0.98722734159271334457 - 4.5543665735291348478e-334j)  +/-  (1.28e-116, 1.28e-116j)
| (-0.94150920098835398335 + 4.6617236318308304565e-339j)  +/-  (1.18e-116, 1.18e-116j)
| (0.86274586119758909118 + 2.2296355298916356918e-341j)  +/-  (3.14e-117, 3.14e-117j)
| (-0.53846931010568309104 + 1.3779344488633608261e-354j)  +/-  (7.34e-121, 7.34e-121j)
| (-0.68746729056265556112 - 4.0440678316792712695e-352j)  +/-  (4.84e-119, 4.84e-119j)
| (-0.81151804022897642335 - 2.0854336474341200202e-350j)  +/-  (9.35e-118, 9.35e-118j)
| (0.9685468227028390516 + 1.1945673879566520355e-349j)  +/-  (1.63e-116, 1.63e-116j)
| (0.81151804022897642335 + 1.8676703398312601783e-356j)  +/-  (9.15e-118, 9.15e-118j)
| (0.61576219305158921375 - 4.15660950094811636e-358j)  +/-  (6.57e-120, 6.57e-120j)
| (-0.9685468227028390516 + 5.0008868665356915341e-358j)  +/-  (1.62e-116, 1.62e-116j)
| (-0.75291897471425311413 + 5.004040450436220981e-360j)  +/-  (2.46e-118, 2.46e-118j)
| (-0.094602168583405379805 - 2.0560773623683530335e-366j)  +/-  (9.18e-127, 9.18e-127j)
| (0.53846931010568309104 - 1.2924345799497868403e-359j)  +/-  (7.51e-121, 7.51e-121j)
| (0.75291897471425311413 - 4.3503306609169430607e-360j)  +/-  (2.24e-118, 2.24e-118j)
| (0.18836504932001938055 - 5.1495379361110653488e-366j)  +/-  (1.73e-125, 1.73e-125j)
| (-0.37003839199054055033 - 2.5479692376970197215e-368j)  +/-  (5.46e-123, 5.46e-123j)
| (-0.45630777317907313515 - 2.812298166596507433e-367j)  +/-  (7.11e-122, 7.11e-122j)
| (0.094602168583405379805 - 3.093158327480649362e-367j)  +/-  (9.94e-127, 9.94e-127j)
| (0.68746729056265556112 - 7.3721378470369732555e-366j)  +/-  (4.61e-119, 4.61e-119j)
| (0.2804529781475123289 - 1.1131578483765609117e-370j)  +/-  (3.7e-124, 3.7e-124j)
| (-0.18836504932001938055 + 2.4520447910430404647e-372j)  +/-  (1.78e-125, 1.78e-125j)
| (-0.61576219305158921375 + 6.8069380294598061274e-370j)  +/-  (7.66e-120, 7.66e-120j)
| (-0.2804529781475123289 + 7.84696688107444471e-375j)  +/-  (3.37e-124, 3.37e-124j)
| (0.37003839199054055033 + 5.2690909012910140066e-373j)  +/-  (4.95e-123, 4.95e-123j)
| (0.45630777317907313515 - 1.5518610866123927516e-376j)  +/-  (6.68e-122, 6.68e-122j)
-------------------------------------------------
The weights are:
| (0.0062141378831007871116 + 1.3645597394739845263e-287j)  +/-  (5.73e-25, 1.4e-80j)
| (0.09474216415935332345 + 2.1023581589698092981e-288j)  +/-  (3.38e-25, 8.24e-81j)
| (0.047392526344041457039 - 5.4426469873581274271e-289j)  +/-  (9.66e-26, 2.36e-81j)
| (0.0062141378831007871116 + 3.3701430078956751898e-290j)  +/-  (5.41e-26, 1.32e-81j)
| (0.031204098125473294222 - 1.1187410287657233061e-287j)  +/-  (3.14e-26, 7.67e-82j)
| (0.039423422292878833917 + 9.0361202538968696557e-288j)  +/-  (2.72e-26, 6.62e-82j)
| (0.014505916631671386482 - 1.1469023805512950183e-289j)  +/-  (1.3e-26, 3.17e-82j)
| (0.039423422292878833917 + 4.3382511525941599904e-289j)  +/-  (5.81e-27, 1.42e-82j)
| (0.014505916631671386482 - 2.1989334404681595002e-287j)  +/-  (1.29e-27, 3.14e-83j)
| (0.031204098125473294222 - 3.2349313609824516594e-289j)  +/-  (3.97e-27, 9.68e-83j)
| (0.047392526344041457039 - 7.5093214565912933066e-288j)  +/-  (2.64e-28, 6.44e-84j)
| (0.07985091459554632402 + 1.1319397534837237583e-288j)  +/-  (1.92e-29, 4.68e-85j)
| (0.068684243327848267816 + 8.8348944870161856349e-289j)  +/-  (4.41e-29, 1.07e-84j)
| (0.054992412323725946254 + 6.5508711418683804342e-289j)  +/-  (1.25e-28, 3.04e-84j)
| (0.022860722043461771776 + 1.4573233154699684401e-287j)  +/-  (3.81e-28, 9.3e-84j)
| (0.054992412323725946254 + 6.3694880943115861846e-288j)  +/-  (1.53e-29, 3.73e-85j)
| (0.074614798816002268187 - 4.244109184111155127e-288j)  +/-  (3.16e-31, 7.71e-87j)
| (0.022860722043461771776 + 2.1519500485361395412e-289j)  +/-  (1.99e-28, 4.84e-84j)
| (0.062119021963855817077 - 7.6760541350439443347e-289j)  +/-  (1.86e-29, 4.54e-85j)
| (0.094322233439699143097 - 1.9103695016994535961e-288j)  +/-  (4.71e-32, 1.15e-87j)
| (0.07985091459554632402 + 3.7871400830282809941e-288j)  +/-  (3.23e-32, 7.88e-88j)
| (0.062119021963855817077 - 5.4920666519951686492e-288j)  +/-  (2.22e-31, 5.4e-87j)
| (0.093064177584311372377 + 2.5387865998224937645e-288j)  +/-  (5.06e-33, 1.23e-88j)
| (0.088061459074787891245 + 1.4119187714135424253e-288j)  +/-  (5.23e-33, 1.27e-88j)
| (0.084345179080420329013 - 1.2673879846012682476e-288j)  +/-  (1.1e-32, 2.67e-88j)
| (0.094322233439699143097 - 2.3106566034055826857e-288j)  +/-  (1.69e-33, 4.11e-89j)
| (0.068684243327848267816 + 4.8005878332364232793e-288j)  +/-  (3.16e-33, 7.7e-89j)
| (0.090973654393498448642 - 2.7918481464380773016e-288j)  +/-  (4e-34, 9.75e-90j)
| (0.093064177584311372377 + 1.7323093545922450298e-288j)  +/-  (4.2e-34, 1.02e-89j)
| (0.074614798816002268187 - 1.0044211209375623376e-288j)  +/-  (5.27e-34, 1.28e-89j)
| (0.090973654393498448642 - 1.5665551816786655545e-288j)  +/-  (2.76e-34, 6.74e-90j)
| (0.088061459074787891245 + 3.0770339679116370169e-288j)  +/-  (1.61e-35, 3.95e-91j)
| (0.084345179080420329013 - 3.4042775229959476692e-288j)  +/-  (1.44e-35, 3.48e-91j)
