Starting with polynomial:
P : t
Extension levels are: 1 10 18
-------------------------------------------------
Trying to find an order 10 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 18 Kronrod extension for:
P2 : t^11 - 55*t^9 + 990*t^7 - 6930*t^5 + 17325*t^3 - 10395*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^29 - 12380943233/40529468*t^27 + 1615566477339/40529468*t^25 - 59326255051605/20264734*t^23 + 2721315373896825/20264734*t^21 - 23381025270609285/5789924*t^19 + 470995616550501135/5789924*t^17 - 1596425847858783945/1447481*t^15 + 14439167887952579850/1447481*t^13 - 340758017553554982225/5789924*t^11 + 1260875025129864476475/5789924*t^9 - 1371849782210823447675/2894962*t^7 + 224891447290917875325/413566*t^5 - 221182651456612399125/827132*t^3 + 28114295564123715375/827132*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:
| (2.3496302641852602357 + 5.1149440809209726128e-462j)  +/-  (1.55e-122, 1.55e-122j)
| (7.5569695503790077613 + 7.9516727420614684541e-462j)  +/-  (1.3e-121, 1.3e-121j)
| (-3.9361666071299769287 - 2.3068197250688462647e-460j)  +/-  (3.8e-121, 3.8e-121j)
| (3.3913760609641391637 - 5.7922072245913747724e-464j)  +/-  (1.74e-121, 1.74e-121j)
| (8.6087502749587156592 - 1.6212340225396987629e-465j)  +/-  (2.18e-122, 2.18e-122j)
| (-7.5569695503790077613 - 1.0173555076987006324e-463j)  +/-  (1.46e-121, 1.46e-121j)
| (-5.1880012243748709482 - 1.0225988495575648393e-462j)  +/-  (7.1e-121, 7.1e-121j)
| (-5.9020871503339242124 + 1.0718068136613396424e-463j)  +/-  (6.3e-121, 6.3e-121j)
| (-4.5321442980336152115 + 1.0550385652476160467e-465j)  +/-  (5.81e-121, 5.81e-121j)
| (5.1880012243748709482 - 2.6271484055759799775e-467j)  +/-  (7.07e-121, 7.07e-121j)
| (-6.6824496114902561952 - 8.5905544638846801599e-470j)  +/-  (3.79e-121, 3.79e-121j)
| (-1.8760350201548458453 - 1.2662824484360945443e-473j)  +/-  (2.81e-123, 2.81e-123j)
| (5.9020871503339242124 + 1.8279483311904764086e-479j)  +/-  (6.77e-121, 6.77e-121j)
| (-8.6087502749587156592 + 1.0350428847295928267e-483j)  +/-  (2.08e-122, 2.08e-122j)
| (-2.3496302641852602357 + 3.3936228354285281198e-481j)  +/-  (1.43e-122, 1.43e-122j)
| (6.6824496114902561952 + 2.4604112977014434298e-484j)  +/-  (3.66e-121, 3.66e-121j)
| (1.8760350201548458453 + 2.0517098424723971129e-486j)  +/-  (2.9e-123, 2.9e-123j)
| (4.5321442980336152115 + 1.9475690884749467146e-484j)  +/-  (6.55e-121, 6.55e-121j)
| (-0.92886899738106394014 - 1.2977482108423582764e-486j)  +/-  (3.38e-125, 3.38e-125j)
| (3.9361666071299769287 - 3.3173478849493405204e-491j)  +/-  (3.92e-121, 3.92e-121j)
| (-2.8651231606436449977 + 1.021180267378715492e-499j)  +/-  (5.99e-122, 5.99e-122j)
| (1.4215970522813950237 + 5.6014330365488539026e-509j)  +/-  (3.84e-124, 3.84e-124j)
| (2.8651231606436449977 + 1.6876021936744787916e-507j)  +/-  (5.92e-122, 5.92e-122j)
| (-1.4215970522813950237 - 1.2129320575842913519e-511j)  +/-  (4.11e-124, 4.11e-124j)
| (-7.9955751796064702495e-513 + 1.745901819370289383e-513j)  +/-  (2.37e-511, 2.37e-511j)
| (0.92886899738106394014 + 4.1899165373125568506e-517j)  +/-  (3.24e-125, 3.24e-125j)
| (-3.3913760609641391637 + 2.3497991435866299486e-524j)  +/-  (1.86e-121, 1.86e-121j)
| (-0.43408935016079658403 - 2.6061054661890888153e-531j)  +/-  (2.35e-126, 2.35e-126j)
| (0.43408935016079658403 + 2.9430664378502450481e-531j)  +/-  (2.35e-126, 2.35e-126j)
-------------------------------------------------
The weights are:
| (0.01260795274669886874 + 8.5853718423579881016e-464j)  +/-  (1.09e-22, 4.36e-84j)
| (1.4905511425843755446e-13 + 2.0557364059986980835e-471j)  +/-  (3.49e-37, 1.39e-98j)
| (9.7662677584387606183e-05 - 7.3488989976927038035e-464j)  +/-  (1.42e-30, 5.67e-92j)
| (0.00067226557261078963588 + 2.0650451154955483185e-464j)  +/-  (3.07e-28, 1.22e-89j)
| (3.9017391292513226965e-17 - 1.496509199865533323e-473j)  +/-  (6.48e-39, 2.58e-100j)
| (1.4905511425843755446e-13 - 6.0630147584108080582e-471j)  +/-  (5.79e-39, 2.31e-100j)
| (3.9071277513451324357e-07 + 2.3625521790431225806e-466j)  +/-  (8.31e-35, 3.31e-96j)
| (8.1023969611801284182e-09 - 1.0364252584259766795e-467j)  +/-  (2.04e-36, 8.12e-98j)
| (8.6588668849196037974e-06 - 5.1729777628549889513e-465j)  +/-  (8.43e-34, 3.36e-95j)
| (3.9071277513451324357e-07 - 3.7008100653277882255e-467j)  +/-  (4.36e-37, 1.74e-98j)
| (6.5791523259871790566e-11 + 3.3111261398944321346e-469j)  +/-  (3.24e-38, 1.29e-99j)
| (0.0309578352911785763 - 1.6967360437090570731e-462j)  +/-  (1.81e-29, 7.2e-91j)
| (8.1023969611801284182e-09 + 2.2942737056356834757e-468j)  +/-  (1.29e-38, 5.12e-100j)
| (3.9017391292513226965e-17 + 3.760765406707066448e-473j)  +/-  (1.92e-42, 7.65e-104j)
| (0.01260795274669886874 + 8.9713325024538616731e-463j)  +/-  (7.13e-32, 2.84e-93j)
| (6.5791523259871790566e-11 - 9.3456254804633405095e-470j)  +/-  (5.93e-40, 2.36e-101j)
| (0.0309578352911785763 - 2.7899136274438733192e-463j)  +/-  (1.87e-32, 7.42e-94j)
| (8.6588668849196037974e-06 + 4.2551666062115617426e-466j)  +/-  (2.88e-37, 1.15e-98j)
| (0.13106687350525354275 - 3.0907722616376441201e-462j)  +/-  (3.63e-33, 1.44e-94j)
| (9.7662677584387606183e-05 - 3.4850656920033697316e-465j)  +/-  (1.63e-36, 6.51e-98j)
| (0.0034513728820546081675 - 4.1128444577078131909e-463j)  +/-  (6.81e-36, 2.72e-97j)
| (0.068489766485317710109 + 8.8450448795840874498e-463j)  +/-  (1.1e-33, 4.38e-95j)
| (0.0034513728820546081675 - 1.0417387565802721402e-463j)  +/-  (2.78e-35, 1.1e-96j)
| (0.068489766485317710109 + 2.4599006891166197746e-462j)  +/-  (2.3e-34, 9.12e-96j)
| (0.16379999512949740125 - 4.0169178190532851761e-462j)  +/-  (2.59e-34, 1.03e-95j)
| (0.13106687350525354275 - 1.6888326356439624893e-462j)  +/-  (7.09e-35, 2.84e-96j)
| (0.00067226557261078963588 + 2.0926677918648609764e-463j)  +/-  (3.52e-37, 1.42e-98j)
| (0.17074721552655518337 + 3.8642887332328056913e-462j)  +/-  (6.2e-35, 2.64e-96j)
| (0.17074721552655518337 + 2.9476404408599713193e-462j)  +/-  (4.2e-35, 1.45e-96j)
