Starting with polynomial:
P : t
Extension levels are: 1 28
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^29 - 29/4*t^27 + 377/16*t^25 - 725/16*t^23 + 7337/128*t^21 - 51359/1024*t^19 + 127281/4096*t^17 - 28101/2048*t^15 + 140505/32768*t^13 - 121771/131072*t^11 + 70499/524288*t^9 - 6409/524288*t^7 + 2639/4194304*t^5 - 1015/67108864*t^3 + 29/268435456*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:
| (-0.99853341385112386457 - 7.614368686620260531e-430j)  +/-  (1.28e-118, 1.28e-118j)
| (-0.96354999251922296004 - 2.1121495989809149394e-430j)  +/-  (3.03e-118, 3.03e-118j)
| (-0.92897671981679144179 - 2.6007703481391678987e-431j)  +/-  (2.02e-118, 2.02e-118j)
| (-7.4584007669222494777e-441 + 7.2775196644322363361e-441j)  +/-  (3.02e-439, 3.02e-439j)
| (0.92897671981679144179 + 4.7569625596276820665e-430j)  +/-  (1.9e-118, 1.9e-118j)
| (0.76216205512763646326 - 4.628361604036034197e-437j)  +/-  (1.07e-119, 1.07e-119j)
| (0.99853341385112386457 + 7.3576521864206347406e-440j)  +/-  (1.28e-118, 1.28e-118j)
| (-0.88351204444602292283 - 7.9104151252109297637e-452j)  +/-  (1.25e-118, 1.25e-118j)
| (-0.98682652254152615177 + 8.2035350743548284122e-452j)  +/-  (3.2e-118, 3.2e-118j)
| (0.98682652254152615177 - 1.0596658160198246642e-450j)  +/-  (2.72e-118, 2.72e-118j)
| (0.88351204444602292283 + 1.1148593063009821363e-462j)  +/-  (1.1e-118, 1.1e-118j)
| (0.96354999251922296004 - 1.0151098236698866857e-474j)  +/-  (3.18e-118, 3.18e-118j)
| (-0.68769945885342329308 - 1.6990314253111268113e-486j)  +/-  (1.75e-120, 1.75e-120j)
| (-0.82768899815689055614 - 1.1753004053436848536e-486j)  +/-  (3.54e-119, 3.54e-119j)
| (-0.21497044021102406718 + 2.4011313698002604985e-490j)  +/-  (8.93e-126, 8.93e-126j)
| (0.82768899815689055614 + 5.8697849901372048614e-489j)  +/-  (3.51e-119, 3.51e-119j)
| (0.51555385717702173971 - 6.4881829486562416932e-495j)  +/-  (3.87e-122, 3.87e-122j)
| (0.10811901842394176303 + 7.11393232342145206e-501j)  +/-  (5.99e-127, 5.99e-127j)
| (-0.76216205512763646326 + 1.6702418452326853115e-495j)  +/-  (8.96e-120, 8.96e-120j)
| (-0.41988910156026457697 + 1.1528359297785405431e-498j)  +/-  (2.86e-123, 2.86e-123j)
| (0.41988910156026457697 + 1.5934899525294582134e-496j)  +/-  (2.91e-123, 2.91e-123j)
| (0.68769945885342329308 + 2.7037956607779118669e-496j)  +/-  (1.67e-120, 1.67e-120j)
| (-0.10811901842394176303 - 2.587742427258329108e-504j)  +/-  (5.99e-127, 5.99e-127j)
| (-0.51555385717702173971 + 6.4923414357895641024e-500j)  +/-  (3.05e-122, 3.05e-122j)
| (-0.60517421519376516592 - 9.9187443806578758729e-502j)  +/-  (2.71e-121, 2.71e-121j)
| (0.21497044021102406718 + 3.4104746238323826885e-503j)  +/-  (9.83e-126, 9.83e-126j)
| (0.60517421519376516592 + 1.951921850457330043e-499j)  +/-  (2.82e-121, 2.82e-121j)
| (0.3193015301359799732 - 3.6336964298030048301e-503j)  +/-  (1.47e-124, 1.47e-124j)
| (-0.3193015301359799732 + 1.3195291825510694996e-503j)  +/-  (1.97e-124, 1.97e-124j)
-------------------------------------------------
The weights are:
| (0.034482758620689655172 - 4.4310013267415145771e-429j)  +/-  (1.59e-30, 1.2e-86j)
| (0.034482758620689655172 - 3.7703148543067086067e-429j)  +/-  (8.55e-31, 6.44e-87j)
| (0.034482758620689655172 + 2.8603736792409220021e-429j)  +/-  (4.44e-31, 3.34e-87j)
| (0.034482758620689655172 - 4.6363629169095662047e-430j)  +/-  (5.56e-32, 4.18e-88j)
| (0.034482758620689655172 + 4.2359344583249263838e-431j)  +/-  (1.22e-32, 9.15e-89j)
| (0.034482758620689655172 - 1.5620141111928359902e-431j)  +/-  (6.99e-33, 5.27e-89j)
| (0.034482758620689655172 - 4.832423307998810759e-431j)  +/-  (2.02e-33, 1.52e-89j)
| (0.034482758620689655172 - 2.0979349771818943158e-429j)  +/-  (3.1e-32, 2.33e-88j)
| (0.034482758620689655172 + 6.5159761632658766498e-429j)  +/-  (1.77e-31, 1.33e-87j)
| (0.034482758620689655172 + 1.6550929789393677811e-430j)  +/-  (2.11e-33, 1.59e-89j)
| (0.034482758620689655172 + 3.2960004425703310508e-430j)  +/-  (3.85e-34, 2.9e-90j)
| (0.034482758620689655172 - 4.1248732744564652286e-430j)  +/-  (1.59e-33, 1.2e-89j)
| (0.034482758620689655172 + 1.1772027225723133054e-429j)  +/-  (5.32e-36, 4e-92j)
| (0.034482758620689655172 + 1.6779350660789501483e-429j)  +/-  (4.01e-35, 3.02e-91j)
| (0.034482758620689655172 - 5.9884415126097831056e-430j)  +/-  (6.6e-37, 4.97e-93j)
| (0.034482758620689655172 - 8.8750470110160376374e-431j)  +/-  (2.02e-35, 1.52e-91j)
| (0.034482758620689655172 + 1.969465645627078311e-430j)  +/-  (1.76e-37, 1.33e-93j)
| (0.034482758620689655172 + 4.0493448521623571393e-430j)  +/-  (1.67e-37, 1.26e-93j)
| (0.034482758620689655172 - 1.3894444609032738432e-429j)  +/-  (1.69e-36, 1.27e-92j)
| (0.034482758620689655172 - 7.7198198214896155915e-430j)  +/-  (3.57e-38, 2.69e-94j)
| (0.034482758620689655172 - 2.4753956454635523671e-430j)  +/-  (1.89e-38, 1.43e-94j)
| (0.034482758620689655172 + 8.6339722389298027726e-431j)  +/-  (5.5e-38, 4.14e-94j)
| (0.034482758620689655172 + 5.2770129469176832344e-430j)  +/-  (2.81e-38, 2.11e-94j)
| (0.034482758620689655172 + 8.8117244227713329057e-430j)  +/-  (8.07e-39, 6.08e-95j)
| (0.034482758620689655172 - 1.0130463468535089243e-429j)  +/-  (1.14e-38, 8.62e-95j)
| (0.034482758620689655172 - 3.5018647965998543519e-430j)  +/-  (8.81e-40, 6.67e-96j)
| (0.034482758620689655172 - 1.4435165495668213459e-430j)  +/-  (5.7e-40, 4.35e-96j)
| (0.034482758620689655172 + 2.9813782136937729071e-430j)  +/-  (4.72e-40, 3.57e-96j)
| (0.034482758620689655172 + 6.7927561359974120052e-430j)  +/-  (4.02e-40, 2.84e-96j)
