Starting with polynomial:
P : 2*t
Extension levels are: 1 26
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^27 - 351*t^25 + 26325*t^23 - 2220075/2*t^21 + 233107875/8*t^19 - 7972289325/16*t^17 + 45176306175/8*t^15 - 677644592625/16*t^13 + 26428139112375/128*t^11 - 161505294575625/256*t^9 + 290709530236125/256*t^7 - 554990921359875/512*t^5 + 924984868933125/2048*t^3 - 213458046676875/4096*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:
| (4.5369066633724417512 + 2.5327599890840782886e-352j)  +/-  (2.76e-121, 2.76e-121j)
| (6.4519401407534719686 - 1.6855981722146894005e-360j)  +/-  (1.18e-122, 1.18e-122j)
| (-4.0183186704087389185 + 5.2038549992124129447e-364j)  +/-  (3.2e-121, 3.2e-121j)
| (-4.5369066633724417512 + 1.0140607760824891225e-364j)  +/-  (2.27e-121, 2.27e-121j)
| (-3.0535824198222552775 - 4.3901944617568965757e-365j)  +/-  (8.22e-122, 8.22e-122j)
| (5.7122555528165366544 + 1.0965453810271656801e-363j)  +/-  (7.15e-122, 7.15e-122j)
| (-5.7122555528165366544 + 7.5294469465308511561e-372j)  +/-  (8.26e-122, 8.26e-122j)
| (-2.1482966453616273647 + 1.2379112719659146626e-372j)  +/-  (6.52e-123, 6.52e-123j)
| (4.0183186704087389185 - 2.4617816893688723916e-371j)  +/-  (2.62e-121, 2.62e-121j)
| (-6.4519401407534719686 - 5.2767445994848624523e-382j)  +/-  (9.71e-123, 9.71e-123j)
| (1.2770668173398579882 - 3.9790114381443046951e-383j)  +/-  (2.13e-124, 2.13e-124j)
| (-1.2770668173398579882 - 7.0379013458169369015e-383j)  +/-  (1.83e-124, 1.83e-124j)
| (5.0939100031131838921 - 5.9494315337434454419e-379j)  +/-  (1.48e-121, 1.48e-121j)
| (-0.84901134206010306228 + 6.5242399001325947866e-389j)  +/-  (2.6e-125, 2.6e-125j)
| (1.7095607392603373503 - 1.8883021089025951251e-384j)  +/-  (1.31e-123, 1.31e-123j)
| (3.5262753401343531784 + 1.2901442980079842469e-385j)  +/-  (1.43e-121, 1.43e-121j)
| (2.5954163389108182612 - 9.4339193391573135504e-392j)  +/-  (2.78e-122, 2.78e-122j)
| (-0.42380790054385304107 - 1.8029602953940112358e-404j)  +/-  (1.61e-126, 1.61e-126j)
| (4.1782112286848907981e-405 + 1.2552858521753862154e-407j)  +/-  (1.13e-403, 1.13e-403j)
| (-3.5262753401343531784 - 1.5138094364831117418e-399j)  +/-  (1.76e-121, 1.76e-121j)
| (3.0535824198222552775 + 1.4934831175804302679e-401j)  +/-  (7.63e-122, 7.63e-122j)
| (0.84901134206010306228 + 3.6634369132899445637e-411j)  +/-  (1.91e-125, 1.91e-125j)
| (-2.5954163389108182612 + 4.3466337144338481079e-409j)  +/-  (2.74e-122, 2.74e-122j)
| (-5.0939100031131838921 - 4.885572928613575592e-410j)  +/-  (1.77e-121, 1.77e-121j)
| (-1.7095607392603373503 - 1.3473307448972054097e-413j)  +/-  (1.3e-123, 1.3e-123j)
| (0.42380790054385304107 + 2.5746620233993522658e-416j)  +/-  (1.61e-126, 1.61e-126j)
| (2.1482966453616273647 + 2.3283026434995753238e-420j)  +/-  (7.51e-123, 7.51e-123j)
-------------------------------------------------
The weights are:
| (3.4726047028458830923e-10 - 3.9903338347683335767e-361j)  +/-  (1.82e-42, 3.1e-102j)
| (4.0033647665501902082e-19 - 1.559401409011927031e-366j)  +/-  (1.64e-46, 2.79e-106j)
| (2.7619339184479042377e-08 + 9.1684706867170363617e-362j)  +/-  (2.41e-42, 4.11e-102j)
| (3.4726047028458830923e-10 - 9.6930297461673823699e-363j)  +/-  (8.74e-44, 1.49e-103j)
| (2.3395576715668111184e-05 + 3.0075913608138925856e-360j)  +/-  (2.58e-40, 4.39e-100j)
| (2.5223632508734059723e-15 + 2.0167809260693622088e-364j)  +/-  (9.56e-47, 1.63e-106j)
| (2.5223632508734059723e-15 - 2.3127951064258049336e-365j)  +/-  (3.82e-47, 6.51e-107j)
| (0.0024718724459619764701 + 3.5101050975129632172e-359j)  +/-  (1.17e-38, 2e-98j)
| (2.7619339184479042377e-08 + 1.5125366123961805228e-360j)  +/-  (2.3e-44, 3.92e-104j)
| (4.0033647665501902082e-19 + 2.7175789747087548905e-367j)  +/-  (5.78e-49, 9.84e-109j)
| (0.047489575562742793953 + 3.1551832772838957032e-358j)  +/-  (2.37e-37, 4.04e-97j)
| (0.047489575562742793953 + 1.7690813695762589217e-358j)  +/-  (3.34e-37, 5.69e-97j)
| (1.7682365112196694161e-12 - 1.1267669220537850092e-362j)  +/-  (3.52e-46, 6.01e-106j)
| (0.11699626517501002799 - 2.9974225688107519504e-358j)  +/-  (1.5e-38, 2.55e-98j)
| (0.01321102584046355634 - 1.9187174927584419082e-358j)  +/-  (3.49e-40, 5.95e-100j)
| (1.0805815336838314678e-06 - 4.8546477987469756256e-360j)  +/-  (2.75e-44, 4.68e-104j)
| (0.00030283982593616503115 - 4.2305124237985796988e-359j)  +/-  (3.21e-43, 5.47e-103j)
| (0.2000149701605134941 + 4.2550897369282342231e-358j)  +/-  (2.84e-39, 4.84e-99j)
| (0.23897789372550444027 - 5.0855828186887844705e-358j)  +/-  (1.8e-39, 3.06e-99j)
| (1.0805815336838314678e-06 - 6.0847679387793396882e-361j)  +/-  (2.57e-45, 4.38e-105j)
| (2.3395576715668111184e-05 + 1.5390491668042898105e-359j)  +/-  (3.5e-44, 5.97e-104j)
| (0.11699626517501002799 - 4.3775299398457835035e-358j)  +/-  (5.94e-42, 1.01e-101j)
| (0.00030283982593616503115 - 1.151588189537156537e-359j)  +/-  (4.88e-44, 8.32e-104j)
| (1.7682365112196694161e-12 + 6.5167156686825709215e-364j)  +/-  (1.58e-48, 2.69e-108j)
| (0.01321102584046355634 - 8.684713666501305247e-359j)  +/-  (4.05e-43, 6.9e-103j)
| (0.2000149701605134941 + 5.1319666379053627184e-358j)  +/-  (1.12e-42, 1.78e-102j)
| (0.0024718724459619764701 + 9.8240257057125216494e-359j)  +/-  (6.28e-44, 1.09e-103j)
