Starting with polynomial:
P : 256*t^8 - 3584*t^6 + 13440*t^4 - 13440*t^2 + 1680
Extension levels are: 8 22
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Trying to find an order 22 Kronrod extension for:
P1 : 256*t^8 - 3584*t^6 + 13440*t^4 - 13440*t^2 + 1680
Solvable: 1
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Ending with final polynomial:
P : 256*t^30 - 805612412622208/18480916529*t^28 + 58920743374080768/18480916529*t^26 - 2440819600664020800/18480916529*t^24 + 63620982302650892400/18480916529*t^22 - 1096825683184185616200/18480916529*t^20 + 753209077581214115400/1087112737*t^18 - 5996966544476638592400/1087112737*t^16 + 32370599322094287783375/1087112737*t^14 - 232354608261896447452125/2174225474*t^12 + 3763571335948745070750/15311447*t^10 - 1479484787563701162869625/4348450948*t^8 + 4427866251098037244121625/17393803792*t^6 - 2944702489166228915499375/34787607584*t^4 + 284137896676777816798125/34787607584*t^2 - 1526335156436577361875/34787607584
-------------------------------------------------
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
-------------------------------------------------
The nodes are:
| (4.4080960688087281449 + 8.7056638156897889528e-427j)  +/-  (6.46e-121, 6.46e-121j)
| (3.8892072772774770887 + 7.2098406639373368145e-428j)  +/-  (6.35e-121, 6.35e-121j)
| (5.5865577813387713971 + 2.8764970151524766238e-429j)  +/-  (1.42e-121, 1.42e-121j)
| (-5.5865577813387713971 - 2.5187213996602401186e-428j)  +/-  (1.24e-121, 1.24e-121j)
| (2.2310555895327321787 - 3.6449454689545441495e-433j)  +/-  (1.98e-121, 1.98e-121j)
| (4.9663143351075375476 + 3.4288917822038933536e-434j)  +/-  (4.1e-121, 4.1e-121j)
| (-4.9663143351075375476 - 1.7188797164127363347e-433j)  +/-  (3.91e-121, 3.91e-121j)
| (6.3288784135972693784 + 4.241056188414389754e-442j)  +/-  (2.18e-122, 2.18e-122j)
| (-6.3288784135972693784 - 1.4409555107487411651e-439j)  +/-  (2.33e-122, 2.33e-122j)
| (1.9816567566958429259 + 1.4628232722087106093e-444j)  +/-  (5.93e-122, 5.93e-122j)
| (1.1571937124467801947 - 1.6639362003330154736e-447j)  +/-  (5.1e-124, 5.1e-124j)
| (1.5714573612000000031 + 8.1132071665872579299e-447j)  +/-  (5.39e-123, 5.39e-123j)
| (-3.3984284068818881659 - 2.0569825526141665765e-444j)  +/-  (5.42e-121, 5.42e-121j)
| (-2.2310555895327321787 - 5.3292009281935437668e-450j)  +/-  (1.99e-121, 1.99e-121j)
| (2.9306374202572440192 - 6.2854404395004784835e-455j)  +/-  (4.15e-121, 4.15e-121j)
| (-2.4938613444442866945 + 2.886765937388564289e-463j)  +/-  (3.26e-121, 3.26e-121j)
| (-3.8892072772774770887 - 2.426236820834406793e-474j)  +/-  (6.41e-121, 6.41e-121j)
| (-4.4080960688087281449 - 3.3223503863898537703e-481j)  +/-  (5.98e-121, 5.98e-121j)
| (-1.1571937124467801947 - 1.9434803730840817728e-486j)  +/-  (4.55e-124, 4.55e-124j)
| (-2.9306374202572440192 - 3.4571496220307479236e-484j)  +/-  (4.5e-121, 4.5e-121j)
| (0.075519281818197344436 - 7.3207813034496535975e-493j)  +/-  (2.14e-127, 2.14e-127j)
| (0.38118699020732211685 - 9.9444754590828508351e-493j)  +/-  (2.89e-126, 2.89e-126j)
| (3.3984284068818881659 - 1.3584191336376467189e-487j)  +/-  (6.21e-121, 6.21e-121j)
| (-0.38118699020732211685 + 7.3305445425406299623e-495j)  +/-  (2.89e-126, 2.89e-126j)
| (-1.5714573612000000031 - 1.9889154897449932325e-489j)  +/-  (4.94e-123, 4.94e-123j)
| (2.4938613444442866945 + 2.3073645224127369243e-491j)  +/-  (3.3e-121, 3.3e-121j)
| (0.75651817558418754042 + 1.3383877628550720122e-495j)  +/-  (4.03e-125, 4.03e-125j)
| (-0.075519281818197344436 - 3.1641571702293126221e-496j)  +/-  (2.14e-127, 2.14e-127j)
| (-1.9816567566958429259 + 1.4567252122155712152e-492j)  +/-  (5.53e-122, 5.53e-122j)
| (-0.75651817558418754042 + 1.9591634069428475132e-496j)  +/-  (4.11e-125, 4.11e-125j)
-------------------------------------------------
The weights are:
| (1.1008273997595023641e-09 - 5.9370942898311537632e-435j)  +/-  (2.17e-38, 6.12e-98j)
| (7.6618628028699658849e-08 - 4.4784979188874391096e-436j)  +/-  (4.64e-37, 1.3e-96j)
| (1.0472848867557932628e-14 + 6.3771467405434779992e-439j)  +/-  (4.43e-42, 1.25e-101j)
| (1.0472848867557932628e-14 + 5.9556488649683059765e-440j)  +/-  (1.95e-44, 5.49e-104j)
| (0.00053306148617123687384 + 1.6480887143536624446e-431j)  +/-  (5.22e-33, 1.47e-92j)
| (6.4001518167242771637e-12 - 6.1048738276142759306e-437j)  +/-  (1.48e-40, 4.17e-100j)
| (6.4001518167242771637e-12 - 2.6892326376373353228e-438j)  +/-  (1.79e-43, 5.03e-103j)
| (1.9368935294110277211e-18 - 2.9599296959084625096e-441j)  +/-  (1.26e-44, 3.56e-104j)
| (1.9368935294110277211e-18 - 4.5672279814895157012e-442j)  +/-  (1.94e-46, 5.47e-106j)
| (0.004279177645236311323 - 2.3929882781388073872e-431j)  +/-  (8.77e-34, 2.47e-93j)
| (0.060488085890408312398 - 5.8525858767796626564e-431j)  +/-  (5.06e-31, 1.42e-90j)
| (0.019936564390868084308 + 3.1637402407957626163e-431j)  +/-  (8.91e-33, 2.51e-92j)
| (2.6054597639986646052e-06 + 1.2907359786075500387e-434j)  +/-  (7.6e-41, 2.14e-100j)
| (0.00053306148617123687384 - 6.3329834013588183858e-432j)  +/-  (7.24e-38, 2.04e-97j)
| (4.7926327224862004538e-05 + 4.9223806151162651957e-433j)  +/-  (2.6e-38, 7.31e-98j)
| (0.00045164986443460891584 + 1.6864737471115324326e-432j)  +/-  (8.04e-39, 2.26e-98j)
| (7.6618628028699658849e-08 - 1.0410837112153681294e-435j)  +/-  (1.22e-42, 3.45e-102j)
| (1.1008273997595023641e-09 + 6.4640732696647754864e-437j)  +/-  (8.47e-44, 2.39e-103j)
| (0.060488085890408312398 + 3.623763858344657576e-431j)  +/-  (1.43e-37, 4.04e-97j)
| (4.7926327224862004538e-05 - 1.4115227242085782524e-433j)  +/-  (9.34e-41, 2.62e-100j)
| (0.11612500485822044829 + 7.8062887250192784585e-430j)  +/-  (1.42e-36, 3.91e-96j)
| (0.17384131366758802608 - 3.0018350364001568861e-430j)  +/-  (9.74e-37, 2.69e-96j)
| (2.6054597639986646052e-06 - 3.6868272053728166639e-434j)  +/-  (4.56e-42, 1.26e-101j)
| (0.17384131366758802608 + 2.5685793464391196515e-430j)  +/-  (1.41e-37, 3.88e-97j)
| (0.019936564390868084308 - 1.6372349323053052544e-431j)  +/-  (1.93e-39, 5.51e-99j)
| (0.00045164986443460891584 - 4.946490217182343236e-432j)  +/-  (5.17e-40, 1.43e-99j)
| (0.12429453268421805608 + 1.2376857368430168853e-430j)  +/-  (6.39e-38, 1.73e-97j)
| (0.11612500485822044829 - 7.569269025622177134e-430j)  +/-  (2.31e-37, 6.29e-97j)
| (0.004279177645236311323 + 1.0305788558073239105e-431j)  +/-  (6.44e-40, 1.96e-99j)
| (0.12429453268421805608 - 9.0705301022901254665e-431j)  +/-  (1.13e-38, 2.86e-98j)
