Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 27
-------------------------------------------------
Trying to find an order 27 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^29 - 270333562362382/354291154925*t^27 + 22199232532727016/354291154925*t^25 - 41353389936310023/14171646197*t^23 + 4846001823106500771/56686584788*t^21 - 187353592409330912565/113373169576*t^19 + 2439245292536690296659/113373169576*t^17 - 21455961248621175152877/113373169576*t^15 + 1008860831911511339755995/906985356608*t^13 - 7724458718343561861211545/1813970713216*t^11 + 9220003228499284986239475/906985356608*t^9 - 51178095617080401250776495/3627941426432*t^7 + 147024777175761007252494765/14511765705728*t^5 - 88404784378262007790209075/29023531411456*t^3 + 6826455676460457115553475/29023531411456*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:
| (3.2416262121338260878 + 8.4032368611993348016e-299j)  +/-  (3.84e-121, 3.84e-121j)
| (-1.9263895461247161258 - 2.2749152956453936992e-308j)  +/-  (1e-122, 1e-122j)
| (-6.6017400065466217077 + 2.7608544537722320247e-309j)  +/-  (3.4e-122, 3.4e-122j)
| (4.7049500122905473926 - 2.2356125384034513115e-307j)  +/-  (9.54e-121, 9.54e-121j)
| (5.8684097402343278829 - 5.1023223012838803655e-313j)  +/-  (1.84e-121, 1.84e-121j)
| (-3.7071062911850195143 - 1.7191903465208687748e-318j)  +/-  (6.97e-121, 6.97e-121j)
| (5.2560004536283844464 - 8.0582106836707311355e-321j)  +/-  (5.89e-121, 5.89e-121j)
| (6.6017400065466217077 - 5.7380611355404191692e-328j)  +/-  (3.23e-122, 3.23e-122j)
| (-5.8684097402343278829 + 1.7491232988867679988e-332j)  +/-  (2.13e-121, 2.13e-121j)
| (-3.8722985116382613076e-336 - 5.281728503231789522e-336j)  +/-  (1.9e-334, 1.9e-334j)
| (3.7071062911850195143 + 1.0212827034790390185e-340j)  +/-  (7.3e-121, 7.3e-121j)
| (2.353802327596210374 - 7.4576489361479194783e-359j)  +/-  (4.93e-122, 4.93e-122j)
| (-1.1006194941802424508 - 7.7444443080973629094e-372j)  +/-  (2.24e-124, 2.24e-124j)
| (-4.1925491443076802894 - 1.5502319109342047827e-366j)  +/-  (9.36e-121, 9.36e-121j)
| (-4.7049500122905473926 - 4.8779420115368244112e-368j)  +/-  (9.69e-121, 9.69e-121j)
| (1.508413645334991781 + 2.5045005509223566463e-370j)  +/-  (2.02e-123, 2.02e-123j)
| (0.7071067811865475244 + 3.0100916160907204594e-376j)  +/-  (2.44e-125, 2.44e-125j)
| (-5.2560004536283844464 - 2.8189227150269720845e-375j)  +/-  (6.23e-121, 6.23e-121j)
| (-0.7071067811865475244 + 3.8751059524269401829e-379j)  +/-  (2.44e-125, 2.44e-125j)
| (-2.353802327596210374 - 9.0540009490365949709e-375j)  +/-  (4.92e-122, 4.92e-122j)
| (2.7915511130513982526 + 7.3626920858769993383e-380j)  +/-  (1.78e-121, 1.78e-121j)
| (-1.508413645334991781 + 1.4621696463801568056e-386j)  +/-  (1.68e-123, 1.68e-123j)
| (1.1006194941802424508 - 4.225182488040752209e-388j)  +/-  (2.3e-124, 2.3e-124j)
| (-2.7915511130513982526 - 7.476081263758557733e-384j)  +/-  (1.62e-121, 1.62e-121j)
| (-3.2416262121338260878 - 4.0810663602914139474e-388j)  +/-  (3.86e-121, 3.86e-121j)
| (4.1925491443076802894 + 2.4867963053938708446e-395j)  +/-  (9.99e-121, 9.99e-121j)
| (0.33808412999020832966 - 2.6143251128181548497e-408j)  +/-  (2.31e-126, 2.31e-126j)
| (1.9263895461247161258 + 1.7636837627265096427e-408j)  +/-  (1.01e-122, 1.01e-122j)
| (-0.33808412999020832966 + 3.1417798503911611219e-418j)  +/-  (2.31e-126, 2.31e-126j)
-------------------------------------------------
The weights are:
| (7.0447734908529986125e-06 - 2.0961693501770864264e-303j)  +/-  (9.68e-34, 1.17e-93j)
| (0.0058310849299152442185 + 5.399768468438865975e-303j)  +/-  (4.41e-28, 5.34e-88j)
| (5.618888451321894655e-20 - 2.6677720034941126761e-312j)  +/-  (5.49e-43, 6.66e-103j)
| (7.2652984265858174424e-11 - 9.0221697896460875441e-307j)  +/-  (8.19e-39, 9.94e-99j)
| (4.0970461862977189788e-16 - 9.5938182970932466965e-310j)  +/-  (6.28e-42, 7.62e-102j)
| (2.8797187535618747883e-07 + 1.511508324012502924e-305j)  +/-  (1.9e-38, 2.3e-98j)
| (3.2699068837538161123e-13 + 3.9416196243266790021e-308j)  +/-  (1.34e-40, 1.63e-100j)
| (5.618888451321894655e-20 + 7.815168834063397467e-312j)  +/-  (6.91e-44, 8.38e-104j)
| (4.0970461862977189788e-16 + 2.7662771302107845433e-310j)  +/-  (3.07e-44, 3.73e-104j)
| (0.18602797583127470059 - 1.7164713329526422978e-301j)  +/-  (6.16e-31, 7.47e-91j)
| (2.8797187535618747883e-07 - 2.25639448430226219e-304j)  +/-  (4.48e-38, 5.43e-98j)
| (0.00095738092884140352565 - 1.0564413109317652318e-302j)  +/-  (2.15e-35, 2.6e-95j)
| (0.06750048938285522502 + 3.5448504901123328581e-302j)  +/-  (6.15e-31, 7.46e-91j)
| (6.5222658223488268953e-09 - 1.8847667781341425699e-306j)  +/-  (2.15e-41, 2.61e-101j)
| (7.2652984265858174424e-11 + 1.6613892041464244876e-307j)  +/-  (9.51e-43, 1.15e-102j)
| (0.023957059914250493084 - 4.0661858593577500065e-302j)  +/-  (1.84e-36, 2.23e-96j)
| (0.13124188132305454825 - 1.1560291133630245099e-301j)  +/-  (3.4e-34, 4.12e-94j)
| (3.2699068837538161123e-13 - 9.3436643415611333562e-309j)  +/-  (6.42e-44, 7.79e-104j)
| (0.13124188132305454825 - 7.4200464397503329508e-302j)  +/-  (9.51e-35, 1.15e-94j)
| (0.00095738092884140352565 - 1.6762503195155540122e-303j)  +/-  (4.6e-39, 5.58e-99j)
| (0.00010326735376534033595 + 5.8176021175308882444e-303j)  +/-  (5.39e-40, 6.53e-100j)
| (0.023957059914250493084 - 1.4836852485575372592e-302j)  +/-  (1.9e-37, 2.31e-97j)
| (0.06750048938285522502 + 7.1894273026384755976e-302j)  +/-  (1.61e-37, 1.95e-97j)
| (0.00010326735376534033595 + 4.3399320065400491568e-304j)  +/-  (2.27e-40, 2.75e-100j)
| (7.0447734908529986125e-06 - 9.1310499408097082313e-305j)  +/-  (3.64e-41, 4.41e-101j)
| (6.5222658223488268953e-09 + 1.4734828714248789152e-305j)  +/-  (1.48e-43, 1.8e-103j)
| (0.17738750891106797902 + 1.6087588028587349301e-301j)  +/-  (1.28e-38, 1.51e-98j)
| (0.0058310849299152442185 + 2.1217542712732071965e-302j)  +/-  (3.93e-40, 4.8e-100j)
| (0.17738750891106797902 + 1.3048817966029121877e-301j)  +/-  (8.48e-39, 8.48e-99j)
