Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 5 22
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P2 : 4*t^7 - 106/3*t^5 + 215/3*t^3 - 55/2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^29 - 42044703932819392433997842/62741519522400017295207*t^27 + 27126479384965994403663951001/564673675701600155656863*t^25 - 6577415154696184313923724680925/3388042054209600933941178*t^23 + 83131935718306865324248937990675/1694021027104800466970589*t^21 - 48414308533677263551526894485975/59439334284378963753354*t^19 + 719168655551112449325259248822575/79252445712505285004472*t^17 - 10816984783122849071463770288185175/158504891425010570008944*t^15 + 72701297992704924803482530628445125/211339855233347426678592*t^13 - 481606320588024902675830554078824875/422679710466694853357184*t^11 + 2021440768050378018265307747828842375/845359420933389706714368*t^9 - 561048935798160356509022189881376625/187857649096308823714304*t^7 + 1119494918908967607277411475523062875/563572947288926471142912*t^5 - 639426262176274936547672827750035625/1127145894577852942285824*t^3 + 15645708213410630058002147706983125/375715298192617647428608*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:
| (3.8789238236165624466 + 2.7067211995201711758e-436j)  +/-  (4.94e-121, 4.94e-121j)
| (4.3991166363090002333 + 3.9746983738683271066e-437j)  +/-  (4.67e-121, 4.67e-121j)
| (-2.9149605806913543383 - 1.498422298188246942e-436j)  +/-  (2.24e-121, 2.24e-121j)
| (-4.9583715702659123305 - 1.6935943571849540599e-440j)  +/-  (3.31e-121, 3.31e-121j)
| (6.3226483460225907422 + 7.0056804603372774509e-449j)  +/-  (1.73e-122, 1.73e-122j)
| (2.9149605806913543383 + 9.9935388941559333783e-448j)  +/-  (2.22e-121, 2.22e-121j)
| (3.3862893806378665584 + 1.1948841051709670768e-450j)  +/-  (4.26e-121, 4.26e-121j)
| (2.4631197782145911371 + 1.7706717371954309571e-451j)  +/-  (1.18e-121, 1.18e-121j)
| (-5.5795024017432090027 - 6.13334490073403848e-450j)  +/-  (1.05e-121, 1.05e-121j)
| (5.5795024017432090027 + 2.0398324902139668931e-455j)  +/-  (1.12e-121, 1.12e-121j)
| (1.76771264727892456 - 2.041786759688491875e-455j)  +/-  (2.89e-122, 2.89e-122j)
| (2.0439239553302535028 + 1.2256230217315243828e-455j)  +/-  (5.43e-122, 5.43e-122j)
| (-1.5054482028623358456 - 2.2751095412991701391e-455j)  +/-  (6.95e-123, 6.95e-123j)
| (-1.76771264727892456 - 1.7302252245063960777e-454j)  +/-  (2.72e-122, 2.72e-122j)
| (-3.8789238236165624466 - 6.2192080194967665735e-461j)  +/-  (4.96e-121, 4.96e-121j)
| (0.32923215413032109027 - 2.7510155698130946142e-476j)  +/-  (2.12e-126, 2.12e-126j)
| (1.5054482028623358456 - 9.140934969411342016e-473j)  +/-  (6.37e-123, 6.37e-123j)
| (-6.3226483460225907422 + 6.1037673504725642292e-471j)  +/-  (1.79e-122, 1.79e-122j)
| (-0.32923215413032109027 - 2.1573276398374715117e-478j)  +/-  (2.27e-126, 2.27e-126j)
| (-2.0439239553302535028 - 6.1266233728060228487e-475j)  +/-  (5.99e-122, 5.99e-122j)
| (4.9583715702659123305 + 3.7855005043801545434e-479j)  +/-  (3.26e-121, 3.26e-121j)
| (1.1103403760497357352 - 6.825243001161187711e-483j)  +/-  (4.44e-124, 4.44e-124j)
| (-4.3991166363090002333 - 5.9263535560589422782e-480j)  +/-  (5.24e-121, 5.24e-121j)
| (-0.7071067811865475244 - 7.6407958103293290249e-496j)  +/-  (2.82e-125, 2.82e-125j)
| (-1.1103403760497357352 - 3.2114914008758838397e-492j)  +/-  (4.44e-124, 4.44e-124j)
| (-3.3862893806378665584 + 4.3293048700377363719e-492j)  +/-  (3.8e-121, 3.8e-121j)
| (3.7208081705553318477e-506 - 1.8903245245153774089e-507j)  +/-  (1.08e-504, 1.08e-504j)
| (0.7071067811865475244 - 5.4055901101827861083e-501j)  +/-  (2.6e-125, 2.6e-125j)
| (-2.4631197782145911371 + 1.2961509678292909598e-500j)  +/-  (1.08e-121, 1.08e-121j)
-------------------------------------------------
The weights are:
| (8.3238301904414276846e-08 - 1.2245843222023021248e-442j)  +/-  (6.82e-37, 3.39e-97j)
| (1.1939623482921377374e-09 - 2.4638628757373578821e-444j)  +/-  (1.67e-38, 8.3e-99j)
| (5.3168330011745712508e-05 - 3.4619035563074417028e-440j)  +/-  (2.31e-35, 1.15e-95j)
| (6.9363288139950005191e-12 + 2.0117795348398028215e-445j)  +/-  (1.1e-41, 5.48e-102j)
| (2.0977889772139931374e-18 - 2.8214856549474890321e-450j)  +/-  (5.69e-44, 2.83e-104j)
| (5.3168330011745712508e-05 - 3.0571590806973665862e-441j)  +/-  (1.97e-35, 9.81e-96j)
| (2.8429905641754274291e-06 + 5.9325803029632016744e-442j)  +/-  (1.18e-36, 5.85e-97j)
| (0.00057639104403018923696 + 1.8286153505981358085e-440j)  +/-  (1.4e-34, 6.94e-95j)
| (1.1345597708774496539e-14 - 4.2095210603421601302e-447j)  +/-  (1.7e-45, 8.44e-106j)
| (1.1345597708774496539e-14 + 7.0051637612554950617e-451j)  +/-  (5.39e-43, 2.68e-103j)
| (0.0046077907093298685951 + 3.6387421382801213322e-439j)  +/-  (1.82e-33, 9.05e-94j)
| (0.0033019771738313267499 - 1.225761756198517003e-439j)  +/-  (5.33e-34, 2.65e-94j)
| (0.021282132163491274134 - 1.2379604664577171368e-438j)  +/-  (2.51e-35, 1.25e-95j)
| (0.0046077907093298685951 + 1.0652178866035089343e-438j)  +/-  (1.22e-36, 6.05e-97j)
| (8.3238301904414276846e-08 + 1.0941906288205652511e-442j)  +/-  (1.82e-43, 9.05e-104j)
| (0.17953834326825643284 + 1.6413603936635245571e-438j)  +/-  (1.1e-35, 5.49e-96j)
| (0.021282132163491274134 - 5.1693922325519055059e-439j)  +/-  (1.48e-35, 7.36e-96j)
| (2.0977889772139931374e-18 + 2.9712708276200236338e-449j)  +/-  (5.52e-49, 2.74e-109j)
| (0.17953834326825643284 + 1.9534944491042068935e-438j)  +/-  (1.25e-36, 6.2e-97j)
| (0.0033019771738313267499 - 4.6341465101841179566e-439j)  +/-  (4.24e-39, 2.1e-99j)
| (6.9363288139950005191e-12 + 2.406974403765743862e-446j)  +/-  (1.8e-44, 8.96e-105j)
| (0.06689802840331371819 + 6.3440697782420902189e-439j)  +/-  (1.91e-37, 9.53e-98j)
| (1.1939623482921377374e-09 - 5.466082394419106877e-444j)  +/-  (8.58e-45, 4.27e-105j)
| (0.13530957262145030918 - 1.4618895473495733621e-438j)  +/-  (7.82e-38, 3.88e-98j)
| (0.06689802840331371819 + 1.1722473641473641393e-438j)  +/-  (2.18e-38, 1.08e-98j)
| (2.8429905641754274291e-06 - 2.15721165161390248e-441j)  +/-  (5.21e-43, 2.62e-103j)
| (0.17685933771301806143 - 2.130989833182556645e-438j)  +/-  (1.04e-38, 5.95e-99j)
| (0.13530957262145030918 - 1.0002315057753804119e-438j)  +/-  (3.48e-39, 2.07e-99j)
| (0.00057639104403018923696 + 1.2437486049580406071e-439j)  +/-  (3.15e-41, 1.51e-101j)
