Starting with polynomial:
P : 32*t^5 - 160*t^3 + 120*t
Extension levels are: 5 28
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Trying to find an order 28 Kronrod extension for:
P1 : 32*t^5 - 160*t^3 + 120*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 32*t^33 - 42690952882415360/5694181252293*t^31 + 13119706753311607924/17082543756879*t^29 - 776145827343695594492/17082543756879*t^27 + 3278876910283308027057/1898060417431*t^25 - 84400838135911280269650/1898060417431*t^23 + 6039524897335551521424525/7592241669724*t^21 - 75910818399568049467595025/7592241669724*t^19 + 2681318263837747252760966925/30368966678896*t^17 - 4120115603016227895779373675/7592241669724*t^15 + 276864719577591816960878964375/121475866715584*t^13 - 772061223705703165889819789625/121475866715584*t^11 + 5485289089325937063762035320875/485903466862336*t^9 - 2923121770852644124992434831625/242951733431168*t^7 + 13658766741772306771864678806375/1943613867449344*t^5 - 3715051778800047187119041799375/1943613867449344*t^3 + 1249737051124921139803993595625/7774455469797376*t
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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:   33 out of 33
Indefinite weights: 0 out of 33
Negative weights:   0 out of 33
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (5.1400430744859207129 - 2.3547215991157258674e-450j)  +/-  (4.86e-120, 4.86e-120j)
| (-5.1400430744859207129 + 7.8298231338033510727e-455j)  +/-  (4.54e-120, 4.54e-120j)
| (-5.6797621732804364621 + 4.2476924886826577276e-464j)  +/-  (2.63e-120, 2.63e-120j)
| (-3.7099508868914665341 + 3.7576506418735153078e-469j)  +/-  (3.39e-120, 3.39e-120j)
| (4.63875697118875581 + 9.27657650394437845e-473j)  +/-  (5.82e-120, 5.82e-120j)
| (-7.0003444190824212473 - 7.321844060538496223e-475j)  +/-  (1.05e-121, 1.05e-121j)
| (6.2802996117767005113 - 1.5774437279209252076e-474j)  +/-  (7.08e-121, 7.08e-121j)
| (-4.63875697118875581 + 1.8972127266959831134e-472j)  +/-  (5.56e-120, 5.56e-120j)
| (1.245622560398127412 + 4.1665245544051395752e-478j)  +/-  (2.15e-123, 2.15e-123j)
| (-4.1643673642782892839 - 1.7065019405566734616e-475j)  +/-  (5.3e-120, 5.3e-120j)
| (2.427702020768598851 + 2.8493853919358587864e-475j)  +/-  (2.08e-121, 2.08e-121j)
| (7.0003444190824212473 + 2.1902543252495029784e-476j)  +/-  (9.95e-122, 9.95e-122j)
| (-1.245622560398127412 - 5.8628167484844963126e-479j)  +/-  (2.3e-123, 2.3e-123j)
| (5.6797621732804364621 + 6.8444323118780163723e-475j)  +/-  (2.42e-120, 2.42e-120j)
| (-6.2802996117767005113 + 2.1504182755790474202e-480j)  +/-  (8.1e-121, 8.1e-121j)
| (0.95857246461381850711 + 3.1033751985391878754e-484j)  +/-  (5.92e-124, 5.92e-124j)
| (1.6226506831658671725 - 6.7317253665163554679e-483j)  +/-  (9.7e-123, 9.7e-123j)
| (3.7099508868914665341 - 9.7368927636452875022e-480j)  +/-  (3.41e-120, 3.41e-120j)
| (-0.95857246461381850711 - 1.2693573177156240234e-490j)  +/-  (5.77e-124, 5.77e-124j)
| (-2.427702020768598851 - 1.2604559635882026883e-487j)  +/-  (2.08e-121, 2.08e-121j)
| (4.1643673642782892839 + 2.4569259270410433719e-488j)  +/-  (5.4e-120, 5.4e-120j)
| (2.8442551478028574759 + 1.5081992060562421042e-490j)  +/-  (7.29e-121, 7.29e-121j)
| (-2.8442551478028574759 - 1.0010207215360477675e-495j)  +/-  (6.21e-121, 6.21e-121j)
| (-2.0201828704560856329 - 2.4082000681876746551e-502j)  +/-  (4.39e-122, 4.39e-122j)
| (-1.6226506831658671725 + 2.8473811549330292179e-506j)  +/-  (9.81e-123, 9.81e-123j)
| (2.0201828704560856329 + 3.1090004794252009884e-505j)  +/-  (4.54e-122, 4.54e-122j)
| (0.72740555157813554438 + 2.5832637292521301127e-509j)  +/-  (1.07e-124, 1.07e-124j)
| (-0.37891433610072345678 - 5.8771024060080226638e-512j)  +/-  (3.84e-126, 3.84e-126j)
| (-7.3624353499912502694e-516 - 3.6817464336389741185e-516j)  +/-  (2.72e-514, 2.72e-514j)
| (-0.72740555157813554438 - 9.5419747554149122683e-511j)  +/-  (9.33e-125, 9.33e-125j)
| (-3.2709592315346563309 - 4.1885720737082931712e-509j)  +/-  (1.7e-120, 1.7e-120j)
| (3.2709592315346563309 - 1.1857782708151305743e-514j)  +/-  (1.69e-120, 1.69e-120j)
| (0.37891433610072345678 - 1.8678236602590992581e-523j)  +/-  (3.84e-126, 3.84e-126j)
-------------------------------------------------
The weights are:
| (9.81020583659136463e-13 + 1.2800616901849755423e-461j)  +/-  (9.35e-37, 7.73e-96j)
| (9.81020583659136463e-13 + 2.2513488173740719164e-463j)  +/-  (4.57e-37, 3.78e-96j)
| (3.1129711879453987314e-15 - 9.7876142063357980272e-465j)  +/-  (1.41e-38, 1.17e-97j)
| (2.650497688578419438e-07 - 2.6818073595884728034e-460j)  +/-  (9.36e-34, 7.74e-93j)
| (1.2395057558905017433e-10 - 6.405487586833104264e-461j)  +/-  (1.71e-37, 1.41e-96j)
| (2.4396041608201478749e-22 - 1.594344103092447702e-468j)  +/-  (1.85e-42, 1.53e-101j)
| (2.6980692923468681079e-18 - 2.2274482490115190392e-465j)  +/-  (4.24e-42, 3.51e-101j)
| (1.2395057558905017433e-10 - 3.2857397969182752614e-462j)  +/-  (1.22e-36, 1.01e-95j)
| (0.042296641535665041176 - 3.872846744682558938e-456j)  +/-  (1.33e-25, 1.1e-84j)
| (7.6904520109749781613e-09 + 3.4056391435015001488e-461j)  +/-  (1.06e-35, 8.76e-95j)
| (0.00064070496728642394788 + 1.0935310770743725365e-457j)  +/-  (6.01e-33, 4.97e-92j)
| (2.4396041608201478749e-22 + 1.0406947129221668718e-467j)  +/-  (1.76e-44, 1.45e-103j)
| (0.042296641535665041176 - 2.3620106560316039921e-456j)  +/-  (2.16e-28, 1.78e-87j)
| (3.1129711879453987314e-15 + 1.9634388313135194466e-463j)  +/-  (3.75e-41, 3.1e-100j)
| (2.6980692923468681079e-18 + 2.2232476427434449437e-466j)  +/-  (3.1e-42, 2.56e-101j)
| (0.04716735230179510522 + 8.9571908537521613144e-456j)  +/-  (1.5e-29, 1.24e-88j)
| (0.015848267480003314307 + 1.1518023187036578195e-456j)  +/-  (1.65e-31, 1.37e-90j)
| (2.650497688578419438e-07 - 1.6592792971523936648e-459j)  +/-  (3.47e-38, 2.87e-97j)
| (0.04716735230179510522 + 6.1415894392070352127e-456j)  +/-  (1.74e-31, 1.44e-90j)
| (0.00064070496728642394788 + 3.9196207341330549803e-458j)  +/-  (3.32e-36, 2.75e-95j)
| (7.6904520109749781613e-09 + 3.2467273317359057355e-460j)  +/-  (6.45e-39, 5.33e-98j)
| (7.2898113219308499692e-05 - 3.0472569340739254817e-458j)  +/-  (1.08e-36, 8.96e-96j)
| (7.2898113219308499692e-05 - 8.762946481834421212e-459j)  +/-  (2.62e-37, 2.16e-96j)
| (0.0038397783212209596385 - 1.5707754448130696295e-457j)  +/-  (6.83e-36, 5.63e-95j)
| (0.015848267480003314307 + 5.9909997308442871994e-457j)  +/-  (4.29e-35, 3.54e-94j)
| (0.0038397783212209596385 - 3.6047806801187011814e-457j)  +/-  (3.28e-36, 2.7e-95j)
| (0.10022602808090219084 - 1.0003434025867468325e-455j)  +/-  (2.75e-34, 2.26e-93j)
| (0.18230195282936115015 + 6.2587311120686469746e-456j)  +/-  (4.39e-35, 3.63e-94j)
| (0.21520119760291580236 - 6.2011132299013304425e-456j)  +/-  (3.31e-35, 2.77e-94j)
| (0.10022602808090219084 - 7.5232658989850509415e-456j)  +/-  (1.69e-35, 1.42e-94j)
| (5.5047039330243796896e-06 + 1.6838043551099911192e-459j)  +/-  (1.27e-39, 1.1e-98j)
| (5.5047039330243796896e-06 + 7.5761545544791675551e-459j)  +/-  (4.55e-40, 4.62e-99j)
| (0.18230195282936115015 + 7.2548615742219026468e-456j)  +/-  (6.9e-36, 4.68e-95j)
