Starting with polynomial:
P : t
Extension levels are: 1 4 34
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P2 : t^5 - 10/9*t^3 + 5/21*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^39 - 4696539289052255393081411/478845736116280070379327*t^37 + 6500272104608694611183578795903/146361593472621584911793194185*t^35 - 35532475210662846327761084210261/288541427131739695968963725679*t^33 + 48606233886251649701390728424708/207873931374479135805597522801*t^31 - 66961270847523487539383704962548/207873931374479135805597522801*t^29 + 622621863464105641250932811465516/1870865382370312222250377705209*t^27 - 5555181727379865587677697033597876/21133849689738712140235748151435*t^25 + 39987376516432680679870536522765110/249379426338916803254781828186933*t^23 - 17260475879746190687757959225346490/227694258831184907319583408344591*t^21 + 300442062581150341589963762120870/10842583753865947967599209921171*t^19 - 4465085390384590871885993021306630/574656938954895242282758125822063*t^17 + 2841541116537161600130976102441252/1723970816864685726848274377466189*t^15 - 1041586482220855684058959223552260/4022598572684266695979306880754441*t^13 + 5521017439930535963980604965546340/189062132916160534711027423395458727*t^11 - 3844642954612801964926193173640500/1701559196245444812399246810559128543*t^9 + 6375801715863764995558743492657875/56907702007764320948019254442033076827*t^7 - 1063823885373812792574498709790377/333316540331191022695541347446193735701*t^5 + 42878778841145746046086618720465/999949620993573068086624042338581207103*t^3 - 57370736999979889022542071935/333316540331191022695541347446193735701*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:
| (0.93698031044656696524 - 2.5906092289764417902e-406j)  +/-  (2.66e-114, 2.66e-114j)
| (0.9799843714180220558 - 4.5620002487557923726e-405j)  +/-  (5.89e-114, 5.89e-114j)
| (-0.9061798459386639928 + 4.3951758075188107756e-404j)  +/-  (1.16e-114, 1.16e-114j)
| (0.96161046718947345305 - 1.640010590685753384e-408j)  +/-  (4.61e-114, 4.61e-114j)
| (0.86938170144517454387 + 2.0945662970507666374e-409j)  +/-  (4.64e-115, 4.64e-115j)
| (0.8268162198400882461 + 1.372608828174608159e-411j)  +/-  (1.43e-115, 1.43e-115j)
| (-0.9985693331177160735 + 4.4391465452060713383e-406j)  +/-  (1.76e-114, 1.76e-114j)
| (-0.93698031044656696524 + 3.6933900558738037886e-412j)  +/-  (2.51e-114, 2.51e-114j)
| (-0.96161046718947345305 + 1.4671214729972087029e-416j)  +/-  (4.45e-114, 4.45e-114j)
| (0.9985693331177160735 + 1.7987184846278432697e-426j)  +/-  (1.86e-114, 1.86e-114j)
| (0.9061798459386639928 - 1.3618241510047664807e-432j)  +/-  (1.15e-114, 1.15e-114j)
| (-0.9799843714180220558 - 5.6820532295866549711e-431j)  +/-  (5.29e-114, 5.29e-114j)
| (-0.86938170144517454387 - 1.7805369680124626606e-443j)  +/-  (4.71e-115, 4.71e-115j)
| (-0.66747413107963908498 + 1.9041373907153716885e-453j)  +/-  (1.18e-117, 1.18e-117j)
| (-0.99217752912855004168 - 1.33417371384002587e-451j)  +/-  (4.64e-114, 4.64e-114j)
| (0.77875963802025331087 + 2.8972787785229510217e-461j)  +/-  (3.36e-116, 3.36e-116j)
| (0.31933412895747678459 - 2.9816327075101090324e-469j)  +/-  (6.38e-123, 6.38e-123j)
| (-0.31933412895747678459 - 9.9419553857251547822e-470j)  +/-  (7.12e-123, 7.12e-123j)
| (-0.77875963802025331087 - 5.8179171110357122534e-460j)  +/-  (3.54e-116, 3.54e-116j)
| (-0.8268162198400882461 + 7.9907514922901496278e-462j)  +/-  (1.34e-115, 1.34e-115j)
| (0.24137678724948259861 - 1.7087557153554774103e-471j)  +/-  (4.3e-124, 4.3e-124j)
| (0.72552816857966140365 - 4.0685210005010517718e-462j)  +/-  (7.01e-117, 7.01e-117j)
| (0.16181484548141075381 + 2.2446733846869611415e-472j)  +/-  (1.59e-125, 1.59e-125j)
| (-0.46837588960743087055 + 1.3573514353351854237e-467j)  +/-  (1.53e-120, 1.53e-120j)
| (-0.72552816857966140365 + 4.9640766207934955397e-464j)  +/-  (6.9e-117, 6.9e-117j)
| (-0.081177233065810326431 - 6.6885253870791469819e-474j)  +/-  (9.5e-127, 9.5e-127j)
| (0.66747413107963908498 + 2.0842109679820237588e-463j)  +/-  (1.03e-117, 1.03e-117j)
| (0.46837588960743087055 + 1.4763739423938182858e-467j)  +/-  (1.35e-120, 1.35e-120j)
| (-0.16181484548141075381 - 1.4733291548604429065e-472j)  +/-  (1.83e-125, 1.83e-125j)
| (-0.60498277782820558087 + 1.3513189895170111701e-465j)  +/-  (1.35e-118, 1.35e-118j)
| (-0.24137678724948259861 - 1.0868989596898418482e-471j)  +/-  (4.46e-124, 4.46e-124j)
| (0.39516857059230187317 - 1.9595982292740762213e-469j)  +/-  (1.04e-121, 1.04e-121j)
| (0.60498277782820558087 - 9.0257558134192629843e-465j)  +/-  (1.38e-118, 1.38e-118j)
| (-2.6114911608277461833e-485 + 7.3326497349219068872e-486j)  +/-  (1.06e-483, 1.06e-483j)
| (-0.53846931010568309104 - 1.280420616568900557e-466j)  +/-  (1.47e-119, 1.47e-119j)
| (-0.39516857059230187317 - 8.1737254394139146756e-469j)  +/-  (1.19e-121, 1.19e-121j)
| (0.081177233065810326431 + 8.2111543924862844248e-474j)  +/-  (9.5e-127, 9.5e-127j)
| (0.53846931010568309104 + 5.8524744685139576037e-466j)  +/-  (1.52e-119, 1.52e-119j)
| (0.99217752912855004168 - 4.2315359643479425818e-469j)  +/-  (4.73e-114, 4.73e-114j)
-------------------------------------------------
The weights are:
| (0.027738296946279573715 + 1.8636432998213784296e-405j)  +/-  (5.27e-18, 2.07e-70j)
| (0.015251159956707671987 + 1.5428474564745057218e-406j)  +/-  (1.59e-18, 6.24e-71j)
| (0.033833442167292616702 + 7.6038951437250184204e-406j)  +/-  (2.7e-19, 1.06e-71j)
| (0.021506572427284575327 - 4.1763933784320358778e-405j)  +/-  (2.84e-18, 1.12e-70j)
| (0.039724281584093670202 + 4.6583014174090307922e-406j)  +/-  (2.4e-19, 9.43e-72j)
| (0.045360551066908064578 - 4.8559246896684330961e-407j)  +/-  (6.83e-20, 2.69e-72j)
| (0.0037110885013641118585 + 2.3037196504018714353e-405j)  +/-  (3.87e-20, 1.52e-72j)
| (0.027738296946279573715 + 4.2713862340212748156e-404j)  +/-  (1.17e-19, 4.6e-72j)
| (0.021506572427284575327 - 2.0039027512075873732e-404j)  +/-  (4.9e-20, 1.93e-72j)
| (0.0037110885013641118585 - 8.430350632873859879e-406j)  +/-  (8.07e-21, 3.18e-73j)
| (0.033833442167292616702 - 1.1474831432110337091e-405j)  +/-  (1.97e-20, 7.77e-73j)
| (0.015251159956707671987 + 1.1687588296649373227e-404j)  +/-  (2.07e-20, 8.15e-73j)
| (0.039724281584093670202 - 4.4377359415726406035e-404j)  +/-  (9.27e-22, 3.65e-74j)
| (0.060339498579809790007 - 8.5526955277713645291e-405j)  +/-  (7.28e-24, 2.87e-76j)
| (0.0091965858163615091179 - 6.679005004267099854e-405j)  +/-  (1.23e-20, 4.86e-73j)
| (0.050699848701744643597 - 2.5555383645023215923e-406j)  +/-  (3.99e-23, 1.57e-75j)
| (0.076981215627788368823 + 1.5991892436610250985e-405j)  +/-  (1.11e-25, 4.36e-78j)
| (0.076981215627788368823 + 3.8546099065197646943e-405j)  +/-  (5.97e-26, 2.35e-78j)
| (0.050699848701744643597 - 1.4655338208878803731e-404j)  +/-  (9.17e-24, 3.61e-76j)
| (0.045360551066908064578 + 2.2159850918376903238e-404j)  +/-  (3.98e-23, 1.57e-75j)
| (0.078847026941230403289 - 1.7871673677557554357e-405j)  +/-  (7.58e-27, 2.98e-79j)
| (0.055704318376033511545 + 4.9938663031597347236e-406j)  +/-  (4.63e-26, 1.82e-78j)
| (0.080188643165569679436 + 1.9888876423876280904e-405j)  +/-  (2.34e-27, 9.2e-80j)
| (0.071729879745151528464 + 5.0456066622162344963e-405j)  +/-  (2.69e-27, 1.06e-79j)
| (0.055704318376033511545 + 1.0856392069317406333e-404j)  +/-  (1.97e-25, 7.74e-78j)
| (0.080997180785153977572 - 2.7300651658529255744e-405j)  +/-  (3.4e-28, 1.34e-80j)
| (0.060339498579809790007 - 7.0830688428866696862e-406j)  +/-  (1.08e-27, 4.24e-80j)
| (0.071729879745151528464 + 1.2470565056438716077e-405j)  +/-  (1.81e-28, 7.13e-81j)
| (0.080188643165569679436 + 3.0467482616819489769e-405j)  +/-  (9.27e-29, 3.65e-81j)
| (0.064573958054359595361 + 7.0031458179134973125e-405j)  +/-  (2.24e-28, 8.8e-81j)
| (0.078847026941230403289 - 3.4160576132570802948e-405j)  +/-  (6.97e-29, 2.74e-81j)
| (0.074603574360335335292 - 1.4205662258080263371e-405j)  +/-  (1.86e-29, 7.31e-82j)
| (0.064573958054359595361 + 8.968103789065990408e-406j)  +/-  (8.39e-30, 3.3e-82j)
| (0.081267289011093234426 + 2.4539223133155179925e-405j)  +/-  (4.49e-30, 1.77e-82j)
| (0.068379232690984755913 - 5.8878543398232899875e-405j)  +/-  (9.74e-30, 3.83e-82j)
| (0.074603574360335335292 - 4.3860833426195380195e-405j)  +/-  (6.03e-30, 2.37e-82j)
| (0.080997180785153977572 - 2.2092253179513513694e-405j)  +/-  (2.38e-30, 9.35e-83j)
| (0.068379232690984755913 - 1.0741940308276688251e-405j)  +/-  (6.76e-31, 2.67e-83j)
| (0.0091965858163615091179 + 3.7930462860786256636e-405j)  +/-  (9.43e-32, 3.63e-84j)
