Starting with polynomial:
P : t
Extension levels are: 1 6 22
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Trying to find an order 6 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 22 Kronrod extension for:
P2 : t^7 - 21/13*t^5 + 105/143*t^3 - 35/429*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^29 - 1278741772381889563901/183579225274692011349*t^27 + 2624601410770074272136/120817096975652007469*t^25 - 147998810268036918599083525/3696640716164024472528993*t^23 + 146579561143861505016632050/3024524222316020022978267*t^21 - 250866456954793253297997440/6193073407599469570860261*t^19 + 17013668097307799510100655/711249326923188382087593*t^17 - 1949017840539616958509849690/194171066250030428309912889*t^15 + 192123935535089937105472975/64723688750010142769970963*t^13 - 3011066929867824367109975/4978745288462318674613151*t^11 + 8521001887978712361156730/104553651057708692166876171*t^9 - 90424934073593574332862785/13324781973687985546156329793*t^7 + 41300317349981705355580/132805135950378593483285679*t^5 - 1529203909529415694219850/242293484460326431053577343787*t^3 + 249576889875869727625225/7349569028629901741958512761539*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
-------------------------------------------------
The nodes are:
| (-0.99601971622308636806 - 1.6704802542761416298e-416j)  +/-  (5.16e-119, 5.16e-119j)
| (-0.94910791234275852453 - 2.4751599765748211348e-423j)  +/-  (1.73e-118, 1.73e-118j)
| (-0.90678885812168107436 + 2.3170227747013535731e-434j)  +/-  (1.3e-118, 1.3e-118j)
| (2.7845886455544925742e-449 - 1.8670119828080831213e-449j)  +/-  (9.72e-448, 9.72e-448j)
| (0.90678885812168107436 - 4.1327416727096228606e-442j)  +/-  (1.37e-118, 1.37e-118j)
| (0.94910791234275852453 - 4.698648394134468956e-443j)  +/-  (1.67e-118, 1.67e-118j)
| (0.99601971622308636806 - 1.2320380924537792427e-443j)  +/-  (5.27e-119, 5.27e-119j)
| (-0.85393029995720000348 + 1.8818402809464215934e-444j)  +/-  (9.04e-119, 9.04e-119j)
| (-0.97911914900063586633 - 7.0171443787499195129e-452j)  +/-  (1.35e-118, 1.35e-118j)
| (0.97911914900063586633 + 1.3116758103836281816e-457j)  +/-  (1.51e-118, 1.51e-118j)
| (0.85393029995720000348 + 1.8985446413820539771e-458j)  +/-  (8.76e-119, 8.76e-119j)
| (0.79555503612646885901 + 2.6810020409949344624e-461j)  +/-  (4.76e-119, 4.76e-119j)
| (-0.68055330812198518446 - 6.4059437918834726229e-461j)  +/-  (4.48e-120, 4.48e-120j)
| (-0.79555503612646885901 + 1.8678568413569029804e-473j)  +/-  (4.78e-119, 4.78e-119j)
| (-0.19242929018355235256 + 3.7075662637651779193e-486j)  +/-  (9.86e-126, 9.86e-126j)
| (0.74153118559939443986 + 9.7140350632710044835e-479j)  +/-  (2.05e-119, 2.05e-119j)
| (0.50688844951315137419 - 2.2890320547840066143e-482j)  +/-  (4.3e-122, 4.3e-122j)
| (0.089917659063097209156 - 1.5672341079409556057e-488j)  +/-  (7.31e-127, 7.31e-127j)
| (-0.74153118559939443986 + 6.4386997840000907274e-480j)  +/-  (2e-119, 2e-119j)
| (-0.40584515137739716691 - 2.2157452498369317799e-484j)  +/-  (2.76e-123, 2.76e-123j)
| (0.40584515137739716691 + 7.3723493156443442558e-484j)  +/-  (2.68e-123, 2.68e-123j)
| (0.68055330812198518446 - 9.9576496340279276253e-481j)  +/-  (4.68e-120, 4.68e-120j)
| (-0.089917659063097209156 - 1.3838230310134878524e-490j)  +/-  (6.38e-127, 6.38e-127j)
| (-0.50688844951315137419 - 2.0906489916097840333e-486j)  +/-  (4.21e-122, 4.21e-122j)
| (-0.60000825011073864756 - 4.8302283817893791183e-486j)  +/-  (4.98e-121, 4.98e-121j)
| (0.19242929018355235256 - 1.7240364860101720266e-488j)  +/-  (1.01e-125, 1.01e-125j)
| (0.60000825011073864756 + 6.1546702636915068461e-487j)  +/-  (5.62e-121, 5.62e-121j)
| (0.29985799120056748494 - 2.2396768098023890967e-491j)  +/-  (1.72e-124, 1.72e-124j)
| (-0.29985799120056748494 - 1.046871426754249079e-491j)  +/-  (1.76e-124, 1.76e-124j)
-------------------------------------------------
The weights are:
| (0.010204483575115941791 - 2.2284587269492925659e-416j)  +/-  (3.41e-29, 4.13e-86j)
| (0.036349606179887406623 - 3.1729126884304220005e-416j)  +/-  (1.89e-29, 2.29e-86j)
| (0.048022296469789063866 + 3.3993585548257603016e-416j)  +/-  (1.28e-29, 1.55e-86j)
| (0.085607128169375507999 - 3.7210641848985770029e-416j)  +/-  (1.45e-30, 1.76e-87j)
| (0.048022296469789063866 + 1.5941049723554440656e-417j)  +/-  (3.9e-31, 4.72e-88j)
| (0.036349606179887406623 - 7.6523030242037522889e-418j)  +/-  (2.32e-31, 2.81e-88j)
| (0.010204483575115941791 - 8.5572549894800931446e-419j)  +/-  (3.21e-32, 3.89e-89j)
| (0.056973867604603677983 - 4.3698363276585828688e-416j)  +/-  (6.47e-32, 7.83e-89j)
| (0.023544982012286601843 + 3.8339987910336197591e-416j)  +/-  (1.05e-31, 1.27e-88j)
| (0.023544982012286601843 + 3.2806179685447906647e-418j)  +/-  (6.59e-32, 7.98e-89j)
| (0.056973867604603677983 - 3.3563473068016771275e-417j)  +/-  (1.28e-32, 1.55e-89j)
| (0.05757160141649796068 + 7.0935235665463601206e-417j)  +/-  (2.94e-33, 3.56e-90j)
| (0.071571529662854759502 + 5.8113209311572698043e-416j)  +/-  (1.69e-34, 2.05e-91j)
| (0.05757160141649796068 + 6.3395596346073839521e-416j)  +/-  (1.08e-33, 1.31e-90j)
| (0.10642955786777749794 - 2.8311610340970323877e-416j)  +/-  (8.78e-36, 1.06e-92j)
| (0.05279287877532335628 - 1.0782182573253616465e-416j)  +/-  (5.32e-35, 6.44e-92j)
| (0.097620325798153222288 + 9.3127466641852597632e-417j)  +/-  (2.47e-36, 2.99e-93j)
| (0.096769522873828467279 + 2.9212174420791974982e-416j)  +/-  (2.68e-36, 3.24e-93j)
| (0.05279287877532335628 - 7.36166428890083312e-416j)  +/-  (3.13e-35, 3.79e-92j)
| (0.10399833761312231923 - 2.4876698294854498042e-416j)  +/-  (4.2e-37, 5.08e-94j)
| (0.10399833761312231923 - 1.0472902834198739524e-416j)  +/-  (2.37e-37, 2.87e-94j)
| (0.071571529662854759502 + 1.0934665521198304561e-416j)  +/-  (1.01e-36, 1.23e-93j)
| (0.096769522873828467279 + 3.5009954766537329415e-416j)  +/-  (4.72e-37, 5.72e-94j)
| (0.097620325798153222288 + 2.8614410940581651525e-416j)  +/-  (1.03e-37, 1.24e-94j)
| (0.087919977989881335907 - 3.8270798640575250852e-416j)  +/-  (1.66e-37, 2.01e-94j)
| (0.10642955786777749794 - 1.9143386770805546163e-416j)  +/-  (1.46e-38, 1.78e-95j)
| (0.087919977989881335907 - 9.4958705632185641859e-417j)  +/-  (8.87e-39, 1.08e-95j)
| (0.10742746807619063478 + 1.3335126438071909069e-416j)  +/-  (5.99e-39, 7.3e-96j)
| (0.10742746807619063478 + 2.482281414200741724e-416j)  +/-  (4.98e-39, 5.57e-96j)
