Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 5 22
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Trying to find an order 5 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P2 : t^7 - 53/3*t^5 + 215/3*t^3 - 55*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^29 - 21022351966409696216998921/62741519522400017295207*t^27 + 27126479384965994403663951001/564673675701600155656863*t^25 - 6577415154696184313923724680925/1694021027104800466970589*t^23 + 332527742873227461296995751962700/1694021027104800466970589*t^21 - 193657234134709054206107577943900/29719667142189481876677*t^19 + 1438337311102224898650518497645150/9906555714063160625559*t^17 - 21633969566245698142927540576370350/9906555714063160625559*t^15 + 72701297992704924803482530628445125/3302185238021053541853*t^13 - 481606320588024902675830554078824875/3302185238021053541853*t^11 + 2021440768050378018265307747828842375/3302185238021053541853*t^9 - 561048935798160356509022189881376625/366909470891228171317*t^7 + 2238989837817935214554822951046125750/1100728412673684513951*t^5 - 1278852524352549873095345655500071250/1100728412673684513951*t^3 + 62582832853642520232008590827932500/366909470891228171317*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
Positive weights:   29 out of 29
Indefinite weights: 0 out of 29
Negative weights:   0 out of 29
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (6.2212904095292983886 - 6.5906992246928129043e-440j)  +/-  (7.1e-121, 7.1e-121j)
| (8.9415750410609653791 - 2.2548711816805381774e-443j)  +/-  (2.51e-122, 2.51e-122j)
| (-7.0121963219552330471 + 1.0028435880366269058e-445j)  +/-  (4.69e-121, 4.69e-121j)
| (-8.9415750410609653791 + 9.7982412180605090269e-448j)  +/-  (2.51e-122, 2.51e-122j)
| (7.8906079678385033338 + 5.47403705260167525e-447j)  +/-  (1.5e-121, 1.5e-121j)
| (7.0121963219552330471 + 4.6345075747169829724e-455j)  +/-  (4.45e-121, 4.45e-121j)
| (-2.1290252659381178426 + 1.4031376025058357069e-459j)  +/-  (8.83e-123, 8.83e-123j)
| (-4.1223767869966660015 - 3.9397382239489698027e-458j)  +/-  (3.16e-121, 3.16e-121j)
| (-3.4833773961004847262 - 3.0813432802515794781e-459j)  +/-  (1.56e-121, 1.56e-121j)
| (3.4833773961004847262 + 2.1746693096726831789e-466j)  +/-  (1.76e-121, 1.76e-121j)
| (-4.7889363682180588993 + 7.0039083044537449085e-474j)  +/-  (5.18e-121, 5.18e-121j)
| (5.485626678770645773 + 1.25239033799899736e-473j)  +/-  (6.78e-121, 6.78e-121j)
| (2.8905449780873046004 - 2.4611439150657410333e-483j)  +/-  (7.81e-122, 7.81e-122j)
| (-1 + 1.9639467074245998403e-494j)  +/-  (3.65e-125, 3.65e-125j)
| (-7.8906079678385033338 + 1.8482951226410361404e-490j)  +/-  (1.65e-121, 1.65e-121j)
| (0.46560457754040928789 - 5.7487000504348685449e-495j)  +/-  (3.05e-126, 3.05e-126j)
| (2.4999232001603023459 + 2.5707272726438006468e-490j)  +/-  (3.9e-122, 3.9e-122j)
| (2.1290252659381178426 + 2.0231628749546521402e-493j)  +/-  (9.37e-123, 9.37e-123j)
| (-0.46560457754040928789 + 7.2573023875740347769e-500j)  +/-  (3.05e-126, 3.05e-126j)
| (-2.4999232001603023459 - 1.9077019604874533905e-495j)  +/-  (4.19e-122, 4.19e-122j)
| (1.57025841865997876 - 4.4508884091215781003e-496j)  +/-  (5.69e-124, 5.69e-124j)
| (1 + 1.4777883208003491947e-498j)  +/-  (3.79e-125, 3.79e-125j)
| (-2.8905449780873046004 + 3.8622225227538855128e-495j)  +/-  (8.46e-122, 8.46e-122j)
| (4.1223767869966660015 + 6.4202660743525394734e-494j)  +/-  (3.14e-121, 3.14e-121j)
| (1.0015114765715950591e-507 + 1.8593821347913683779e-507j)  +/-  (6.12e-506, 6.12e-506j)
| (-6.2212904095292983886 - 1.1416987323462709127e-498j)  +/-  (6.79e-121, 6.79e-121j)
| (4.7889363682180588993 - 1.5778831208873995766e-501j)  +/-  (5.42e-121, 5.42e-121j)
| (-5.485626678770645773 - 8.4688355499153436888e-505j)  +/-  (7.11e-121, 7.11e-121j)
| (-1.57025841865997876 - 1.2490505943636673073e-509j)  +/-  (6.59e-124, 6.59e-124j)
-------------------------------------------------
The weights are:
| (1.1939623482921377374e-09 + 2.8735327814487772414e-448j)  +/-  (1.04e-38, 1.09e-99j)
| (2.0977889772139931374e-18 + 3.7319180953682943916e-454j)  +/-  (2.25e-43, 2.36e-104j)
| (6.9363288139950005191e-12 - 3.0464862269899257627e-451j)  +/-  (9.97e-42, 1.04e-102j)
| (2.0977889772139931374e-18 - 6.6952294341417082165e-455j)  +/-  (1.25e-44, 1.31e-105j)
| (1.1345597708774496539e-14 - 6.6611003864497168e-452j)  +/-  (2.91e-42, 3.05e-103j)
| (6.9363288139950005191e-12 + 5.097446226946622603e-450j)  +/-  (6.14e-41, 6.43e-102j)
| (0.021282132163491274134 - 1.8545953651887926169e-444j)  +/-  (1.87e-31, 1.96e-92j)
| (5.3168330011745712508e-05 - 7.1991974325440497723e-447j)  +/-  (4.86e-38, 5.09e-99j)
| (0.00057639104403018923696 + 5.3354661664632859828e-446j)  +/-  (1.43e-36, 1.49e-97j)
| (0.00057639104403018923696 + 1.8911831529870349504e-445j)  +/-  (8.38e-38, 8.77e-99j)
| (2.8429905641754274291e-06 + 8.7467775765832667496e-448j)  +/-  (6.06e-40, 6.34e-101j)
| (8.3238301904414276846e-08 - 1.3747938701089214233e-447j)  +/-  (5.06e-41, 5.3e-102j)
| (0.0033019771738313267499 - 1.0999130295481118495e-444j)  +/-  (7.26e-37, 7.61e-98j)
| (0.13530957262145030918 - 3.805537652593255856e-444j)  +/-  (3.29e-33, 3.46e-94j)
| (1.1345597708774496539e-14 + 7.8795360014501846325e-453j)  +/-  (6.06e-46, 6.36e-107j)
| (0.17953834326825643284 + 7.2924148855247536774e-444j)  +/-  (9.22e-34, 9.68e-95j)
| (0.0046077907093298685951 + 2.9478626584175725714e-444j)  +/-  (2.38e-36, 2.49e-97j)
| (0.021282132163491274134 - 3.7843247421921540034e-444j)  +/-  (7.11e-36, 7.46e-97j)
| (0.17953834326825643284 + 6.2768814573921517015e-444j)  +/-  (2.31e-33, 2.42e-94j)
| (0.0046077907093298685951 + 1.2578612235251985269e-444j)  +/-  (1.26e-37, 1.32e-98j)
| (0.06689802840331371819 + 3.9603968580593542571e-444j)  +/-  (5.43e-36, 5.65e-97j)
| (0.13530957262145030918 - 5.2632382213184694061e-444j)  +/-  (3.68e-35, 3.88e-96j)
| (0.0033019771738313267499 - 4.0206269315032959102e-445j)  +/-  (1.01e-38, 1.07e-99j)
| (5.3168330011745712508e-05 - 3.5478423857148016397e-446j)  +/-  (7.03e-41, 7.28e-102j)
| (0.17685933771301806143 - 8.0960670061765331025e-444j)  +/-  (5.18e-36, 5.49e-97j)
| (1.1939623482921377374e-09 + 6.3242708029832177797e-450j)  +/-  (4.69e-45, 4.98e-106j)
| (2.8429905641754274291e-06 + 6.7234834586384560368e-447j)  +/-  (2.36e-42, 2.32e-103j)
| (8.3238301904414276846e-08 - 8.639205551665579199e-449j)  +/-  (5.85e-44, 6.32e-105j)
| (0.06689802840331371819 + 2.3640908843629764362e-444j)  +/-  (8.06e-39, 7.17e-100j)
