Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 25
-------------------------------------------------
Trying to find an order 25 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^27 - 9747712337741/29790013241*t^25 + 1355869504183650/29790013241*t^23 - 4581801244922550/1295217967*t^21 + 220084251161515125/1295217967*t^19 - 6827138644189196025/1295217967*t^17 + 138887640369503694900/1295217967*t^15 - 1845402072060784198500/1295217967*t^13 + 15673023001145376491625/1295217967*t^11 - 81603963220377320848125/1295217967*t^9 + 242742029161518427290750/1295217967*t^7 - 365991418665749862735750/1295217967*t^5 + 223805196837470455081875/1295217967*t^3 - 32911741104649851819375/1295217967*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:   27 out of 27
Indefinite weights: 0 out of 27
Negative weights:   0 out of 27
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (5.4698491162378496261 + 1.4481825914168306726e-277j)  +/-  (4.17e-121, 4.17e-121j)
| (-5.4698491162378496261 + 3.1722003698371810984e-296j)  +/-  (4.28e-121, 4.28e-121j)
| (6.2080044138619468039 - 1.7368535549050753899e-310j)  +/-  (4.56e-121, 4.56e-121j)
| (-7.0007840161112518486 - 1.0720765493423092628e-327j)  +/-  (2.66e-121, 2.66e-121j)
| (8.9330064430822511579 + 2.1719798870745276325e-337j)  +/-  (1.89e-122, 1.89e-122j)
| (7.0007840161112518486 - 1.3700629059467338709e-356j)  +/-  (2.74e-121, 2.74e-121j)
| (-8.9330064430822511579 + 3.0551579007771614135e-370j)  +/-  (2.18e-122, 2.18e-122j)
| (-3.4458349358226954319 + 5.8417323490323361335e-368j)  +/-  (3.79e-122, 3.79e-122j)
| (-2.811519163242486481 - 2.6924265671634525121e-368j)  +/-  (9.23e-123, 9.23e-123j)
| (2.1915648682895693094 + 9.4544301562768760371e-369j)  +/-  (1.64e-123, 1.64e-123j)
| (7.8807078369725818686 + 4.1871027769177160824e-366j)  +/-  (1.16e-121, 1.16e-121j)
| (-7.8807078369725818686 - 8.0931444434595556765e-371j)  +/-  (1.06e-121, 1.06e-121j)
| (-2.1915648682895693094 - 9.5560150168798258022e-373j)  +/-  (1.77e-123, 1.77e-123j)
| (2.811519163242486481 - 2.0185487409785481227e-370j)  +/-  (9.85e-123, 9.85e-123j)
| (4.7695511277097669175 - 1.2397053238457810922e-370j)  +/-  (2.4e-121, 2.4e-121j)
| (-4.7695511277097669175 - 7.5266772894772840907e-376j)  +/-  (2.8e-121, 2.8e-121j)
| (1.5858503737132226932 + 7.3660987183700680798e-378j)  +/-  (2.34e-124, 2.34e-124j)
| (-4.0970610052278795762 - 2.1221810199074039893e-376j)  +/-  (1.29e-121, 1.29e-121j)
| (-0.45778871831726016513 - 2.3509947685063676573e-386j)  +/-  (2.11e-126, 2.11e-126j)
| (-1.5858503737132226932 - 5.9452501075786679252e-379j)  +/-  (2.47e-124, 2.47e-124j)
| (-1 + 9.9958222300231469866e-379j)  +/-  (3.29e-125, 3.29e-125j)
| (0.45778871831726016513 - 7.8586215273318621576e-381j)  +/-  (2.69e-126, 2.69e-126j)
| (4.0970610052278795762 + 2.8975059787053508631e-375j)  +/-  (1.27e-121, 1.27e-121j)
| (3.4458349358226954319 + 3.0007881888403354718e-381j)  +/-  (3.72e-122, 3.72e-122j)
| (1.3072760740599472641e-393 + 8.3941804595052496115e-394j)  +/-  (4.19e-392, 4.19e-392j)
| (-6.2080044138619468039 - 7.4311578528726933542e-389j)  +/-  (4.43e-121, 4.43e-121j)
| (1 + 1.4961390174653137629e-391j)  +/-  (3.43e-125, 3.43e-125j)
-------------------------------------------------
The weights are:
| (9.112487991745658169e-08 - 3.8480270589311276189e-284j)  +/-  (1.24e-44, 6.03e-104j)
| (9.112487991745658169e-08 - 1.206298948444992423e-285j)  +/-  (1.36e-45, 6.61e-105j)
| (1.3003605024994124442e-09 - 1.8837821683101599787e-285j)  +/-  (2.74e-46, 1.33e-105j)
| (7.5288216578620036051e-12 - 7.5298195471104945929e-288j)  +/-  (7.94e-49, 3.86e-108j)
| (2.2672115233882919217e-18 + 1.1674581229336675668e-290j)  +/-  (2.14e-51, 1.04e-110j)
| (7.5288216578620036051e-12 + 6.1336126789304402827e-287j)  +/-  (3.54e-48, 1.72e-107j)
| (2.2672115233882919217e-18 - 2.8071455244202979988e-291j)  +/-  (1.79e-52, 8.72e-112j)
| (0.00067642420309115362026 + 2.0092526573606447574e-283j)  +/-  (7.35e-44, 3.57e-103j)
| (0.0048041400836838776912 - 7.0222351410263687353e-283j)  +/-  (2.13e-42, 1.04e-101j)
| (0.022156159034437525748 + 4.8306129555830392856e-282j)  +/-  (1.21e-41, 5.86e-101j)
| (1.2284959978908752608e-14 - 1.3985696454697344234e-288j)  +/-  (1.41e-50, 6.87e-110j)
| (1.2284959978908752608e-14 + 2.5255529324750608843e-289j)  +/-  (2.55e-51, 1.24e-110j)
| (0.022156159034437525748 + 2.0669973443811478584e-282j)  +/-  (3.64e-42, 1.76e-101j)
| (0.0048041400836838776912 - 2.1876033591097760416e-282j)  +/-  (2.3e-44, 1.11e-103j)
| (3.1394139409987110869e-06 + 1.2664977942247969956e-283j)  +/-  (3.19e-47, 1.54e-106j)
| (3.1394139409987110869e-06 + 8.6618926562142142719e-285j)  +/-  (1.18e-47, 5.71e-107j)
| (0.06779302693550723421 - 9.6033136817612868635e-282j)  +/-  (4.42e-43, 2.12e-102j)
| (5.9714773815022530732e-05 - 4.6961105934569995523e-284j)  +/-  (1.04e-46, 5e-106j)
| (0.18094146199790405 - 2.417750772041324855e-281j)  +/-  (9.74e-43, 4.5e-102j)
| (0.06779302693550723421 - 5.286401201915280956e-282j)  +/-  (1.36e-43, 6.38e-103j)
| (0.13808753108903958386 + 1.2109486258953413403e-281j)  +/-  (5.53e-43, 2.58e-102j)
| (0.18094146199790405 - 2.8594130583148753351e-281j)  +/-  (1.36e-43, 6.21e-103j)
| (5.9714773815022530732e-05 - 3.2727022916167949861e-283j)  +/-  (1.33e-47, 6.24e-107j)
| (0.00067642420309115362026 + 8.8506602607478681209e-283j)  +/-  (6.25e-47, 2.91e-106j)
| (0.17095662007159804957 + 3.3210626672190755826e-281j)  +/-  (5.38e-44, 2.25e-103j)
| (1.3003605024994124442e-09 + 1.1907357662295239876e-286j)  +/-  (1.47e-50, 8.96e-110j)
| (0.13808753108903958386 + 1.7527783809518448354e-281j)  +/-  (9.67e-45, 3.36e-104j)
