Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 27
-------------------------------------------------
Trying to find an order 27 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^29 - 135166781181191/354291154925*t^27 + 22199232532727016/354291154925*t^25 - 82706779872620046/14171646197*t^23 + 4846001823106500771/14171646197*t^21 - 187353592409330912565/14171646197*t^19 + 4878490585073380593318/14171646197*t^17 - 85823844994484700611508/14171646197*t^15 + 1008860831911511339755995/14171646197*t^13 - 7724458718343561861211545/14171646197*t^11 + 36880012913997139944957900/14171646197*t^9 - 102356191234160802501552990/14171646197*t^7 + 147024777175761007252494765/14171646197*t^5 - 88404784378262007790209075/14171646197*t^3 + 13652911352920914231106950/14171646197*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:
| (5.9291598607956358936 + 7.1948336163012104763e-462j)  +/-  (1.46e-120, 1.46e-120j)
| (7.433107125360401138 - 2.8724020302809028101e-472j)  +/-  (8.45e-121, 8.45e-121j)
| (2.1332190349013850724 - 8.0854804683233007552e-480j)  +/-  (2.67e-123, 2.67e-123j)
| (-9.3362702525192777142 + 4.8434867482055252516e-479j)  +/-  (4.8e-122, 4.8e-122j)
| (-8.2991846442017581684 - 1.6095054131137307658e-477j)  +/-  (2.74e-121, 2.74e-121j)
| (9.3362702525192777142 - 2.5431591208780451541e-479j)  +/-  (4.51e-122, 4.51e-122j)
| (-7.433107125360401138 - 1.9896579405569424237e-477j)  +/-  (8.57e-121, 8.57e-121j)
| (-3.328779174831919565 + 2.7741828891271645003e-478j)  +/-  (6.24e-122, 6.24e-122j)
| (-5.9291598607956358936 + 2.3535158070841590012e-477j)  +/-  (1.53e-120, 1.53e-120j)
| (-5.242639994152478651 + 4.3666092710013041492e-479j)  +/-  (1.16e-120, 1.16e-120j)
| (2.7243262225433244902 - 1.1155207910382484376e-478j)  +/-  (1.53e-122, 1.53e-122j)
| (3.9478494441349965107 - 5.6830919239438245564e-477j)  +/-  (2.27e-121, 2.27e-121j)
| (-6.6538041176687523615 - 1.9650615877740611118e-479j)  +/-  (1.39e-120, 1.39e-120j)
| (-1.5565110156819146303 - 3.6798931844756226663e-482j)  +/-  (3.28e-124, 3.28e-124j)
| (4.5843517533437805021 - 3.8228916345013992931e-479j)  +/-  (6.11e-121, 6.11e-121j)
| (1 + 7.694828309365497069e-487j)  +/-  (3.58e-125, 3.58e-125j)
| (3.328779174831919565 - 8.536358327176356754e-483j)  +/-  (7.08e-122, 7.08e-122j)
| (3.8451605562618274823e-498 + 1.6587684302161605358e-497j)  +/-  (4.94e-496, 4.94e-496j)
| (-2.7243262225433244902 - 6.0104116245714644789e-486j)  +/-  (1.55e-122, 1.55e-122j)
| (-3.9478494441349965107 + 1.5181601330645014148e-484j)  +/-  (2.32e-121, 2.32e-121j)
| (8.2991846442017581684 - 8.0090561413716421061e-484j)  +/-  (2.95e-121, 2.95e-121j)
| (1.5565110156819146303 - 5.8944619639734223298e-496j)  +/-  (3.41e-124, 3.41e-124j)
| (-2.1332190349013850724 - 2.5501780264997855337e-494j)  +/-  (2.59e-123, 2.59e-123j)
| (-4.5843517533437805021 + 3.4660327774341595054e-491j)  +/-  (5.52e-121, 5.52e-121j)
| (-0.47812316185526106199 + 2.7042619465045527882e-498j)  +/-  (2.79e-126, 2.79e-126j)
| (6.6538041176687523615 + 2.300353967407155021e-496j)  +/-  (1.33e-120, 1.33e-120j)
| (0.47812316185526106199 + 1.0449529661154004919e-511j)  +/-  (2.32e-126, 2.32e-126j)
| (5.242639994152478651 + 1.1649346050943136334e-515j)  +/-  (1.06e-120, 1.06e-120j)
| (-1 + 8.6374720429156591414e-531j)  +/-  (3.76e-125, 3.76e-125j)
-------------------------------------------------
The weights are:
| (6.5222658223488268953e-09 - 1.4688910683776583664e-469j)  +/-  (3.41e-34, 1.23e-94j)
| (3.2699068837538161123e-13 + 1.7681174078597905221e-472j)  +/-  (5.41e-37, 1.94e-97j)
| (0.023957059914250493084 - 6.2179676782361124978e-467j)  +/-  (3.93e-23, 1.41e-83j)
| (5.618888451321894655e-20 - 5.7611892539905689303e-477j)  +/-  (3.35e-41, 1.2e-101j)
| (4.0970461862977189788e-16 + 5.931851063379004393e-475j)  +/-  (5.67e-40, 2.04e-100j)
| (5.618888451321894655e-20 + 2.5812792018708069023e-476j)  +/-  (7.89e-42, 2.84e-102j)
| (3.2699068837538161123e-13 - 1.9900480522721435711e-473j)  +/-  (4.05e-39, 1.46e-99j)
| (0.00095738092884140352565 - 3.3930223591502392272e-468j)  +/-  (9.4e-33, 3.38e-93j)
| (6.5222658223488268953e-09 - 3.957273753349379007e-471j)  +/-  (8.55e-38, 3.07e-98j)
| (2.8797187535618747883e-07 + 3.1486313835637656497e-470j)  +/-  (6.51e-37, 2.34e-97j)
| (0.0058310849299152442185 + 2.9162338109914495981e-467j)  +/-  (8.43e-33, 3.03e-93j)
| (0.00010326735376534033595 + 4.4259379020504823358e-468j)  +/-  (2.34e-36, 8.41e-97j)
| (7.2652984265858174424e-11 + 3.5139640672685360299e-472j)  +/-  (2.21e-39, 7.94e-100j)
| (0.06750048938285522502 + 6.8866884696924435061e-467j)  +/-  (5.47e-31, 1.97e-91j)
| (7.0447734908529986125e-06 - 1.4742874147972217611e-468j)  +/-  (6.51e-38, 2.34e-98j)
| (0.13124188132305454825 - 1.9907665420993500201e-466j)  +/-  (7.09e-31, 2.55e-91j)
| (0.00095738092884140352565 - 1.2079921342710899123e-467j)  +/-  (2.4e-35, 8.61e-96j)
| (0.18602797583127470059 - 3.1429333513717239047e-466j)  +/-  (2.21e-31, 7.93e-92j)
| (0.0058310849299152442185 + 1.0800322695919968946e-467j)  +/-  (3.68e-35, 1.32e-95j)
| (0.00010326735376534033595 + 8.8783523413780331976e-469j)  +/-  (3.84e-37, 1.38e-97j)
| (4.0970461862977189788e-16 - 3.561161936911625678e-474j)  +/-  (1.11e-44, 4.02e-105j)
| (0.06750048938285522502 + 1.1789531960830239828e-466j)  +/-  (1.92e-34, 6.91e-95j)
| (0.023957059914250493084 - 2.927552484106192582e-467j)  +/-  (1.31e-35, 4.68e-96j)
| (7.0447734908529986125e-06 - 1.8857958605072192761e-469j)  +/-  (2.56e-38, 9.15e-99j)
| (0.17738750891106797902 + 2.4415970612128098357e-466j)  +/-  (6.81e-35, 2.33e-95j)
| (7.2652984265858174424e-11 - 6.1017641222849237527e-471j)  +/-  (2.27e-42, 8.19e-103j)
| (0.17738750891106797902 + 2.8699134242674628165e-466j)  +/-  (2.56e-35, 8.3e-96j)
| (2.8797187535618747883e-07 + 5.1237963157834786675e-469j)  +/-  (1.87e-40, 6.85e-101j)
| (0.13124188132305454825 - 1.4161610828247967151e-466j)  +/-  (8.6e-36, 2.56e-96j)
