Starting with polynomial:
P : 2*t
Extension levels are: 1 12 28
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P2 : 2*t^13 - 6*t^11 + 55/8*t^9 - 15/4*t^7 + 63/64*t^5 - 7/64*t^3 + 7/2048*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^41 - 20*t^39 + 741/8*t^37 - 2109/8*t^35 + 66045/128*t^33 - 11781/16*t^31 + 202895/256*t^29 - 168113/256*t^27 + 3471039/8192*t^25 - 876525/4096*t^23 + 44352165/524288*t^21 - 13656825/524288*t^19 + 51895935/8388608*t^17 - 2340135/2097152*t^15 + 5014575/33554432*t^13 - 482885/33554432*t^11 + 2042975/2147483648*t^9 - 43263/1073741824*t^7 + 33649/34359738368*t^5 - 385/34359738368*t^3 + 21/549755813888*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: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (0.97492791218182360702 - 9.5736413712752250364e-855j)  +/-  (8.85e-242, 8.85e-242j)
| (-0.99720379718118014823 + 2.9443188947274682997e-871j)  +/-  (2.03e-242, 2.03e-242j)
| (-0.93087374864420425564 - 4.3589125037015478042e-874j)  +/-  (6.35e-242, 6.35e-242j)
| (0.99720379718118014823 - 2.2727273024724904347e-874j)  +/-  (2.1e-242, 2.1e-242j)
| (0.93087374864420425564 - 6.8849148991134403069e-899j)  +/-  (7.6e-242, 7.6e-242j)
| (0.95557280578614073281 + 2.907279038695633104e-924j)  +/-  (8.21e-242, 8.21e-242j)
| (-0.86602540378443864676 + 4.093138135689657539e-938j)  +/-  (1.54e-242, 1.54e-242j)
| (-0.90096886790241912624 + 9.1876115994201336064e-938j)  +/-  (3.38e-242, 3.38e-242j)
| (-0.97492791218182360702 + 4.7889133667191855188e-937j)  +/-  (8.18e-242, 8.18e-242j)
| (0.5 + 1.2160705906433073754e-940j)  +/-  (1.59e-247, 1.59e-247j)
| (0.90096886790241912624 + 2.1770451187952814836e-939j)  +/-  (3.71e-242, 3.71e-242j)
| (-0.98883082622512854507 - 9.0609945273719685948e-949j)  +/-  (7.08e-242, 7.08e-242j)
| (-0.95557280578614073281 + 1.5584522726715557412e-951j)  +/-  (8.83e-242, 8.83e-242j)
| (-0.78183148246802980871 + 1.3312922987698539622e-958j)  +/-  (1.64e-243, 1.64e-243j)
| (0.98883082622512854507 - 1.0848172763755052467e-956j)  +/-  (6.24e-242, 6.24e-242j)
| (0.78183148246802980871 - 6.9221578126524188298e-964j)  +/-  (1.53e-243, 1.53e-243j)
| (0.82623877431599487195 + 2.3119485574215635963e-964j)  +/-  (6.49e-243, 6.49e-243j)
| (-0.82623877431599487195 + 5.9077952615452452864e-969j)  +/-  (6.45e-243, 6.45e-243j)
| (-0.73305187182982632852 + 4.2506929363663706121e-970j)  +/-  (4.12e-244, 4.12e-244j)
| (-0.22252093395631440429 - 1.0979360126914111044e-978j)  +/-  (5.31e-252, 5.31e-252j)
| (0.86602540378443864676 + 5.9016731559074094549e-970j)  +/-  (1.55e-242, 1.55e-242j)
| (0.73305187182982632852 - 2.3487081344606139023e-976j)  +/-  (4.55e-244, 4.55e-244j)
| (0.14904226617617444693 + 1.952088005810014651e-985j)  +/-  (2.43e-253, 2.43e-253j)
| (-0.62348980185873353053 + 7.2492714913876403882e-981j)  +/-  (1.19e-245, 1.19e-245j)
| (-0.56332005806362202775 + 1.5208661303503832387e-982j)  +/-  (1.78e-246, 1.78e-246j)
| (0.074730093586424254291 - 2.6989008533770668309e-985j)  +/-  (1.08e-254, 1.08e-254j)
| (0.68017273777091939019 + 1.2398693533714217206e-980j)  +/-  (7.96e-245, 7.96e-245j)
| (0.36534102436639501454 + 9.0916816191934287799e-985j)  +/-  (1.24e-249, 1.24e-249j)
| (-0.14904226617617444693 - 1.2234008735199736842e-989j)  +/-  (2.18e-253, 2.18e-253j)
| (-0.68017273777091939019 - 1.8265914416722915913e-985j)  +/-  (8.87e-245, 8.87e-245j)
| (-0.074730093586424254291 + 4.3005513271500058013e-990j)  +/-  (1.08e-254, 1.08e-254j)
| (0.43388373911755812048 + 2.7271913339103180431e-984j)  +/-  (1.68e-248, 1.68e-248j)
| (0.62348980185873353053 + 3.5147987903515574463e-985j)  +/-  (1.33e-245, 1.33e-245j)
| (4.5995896321354865406e-993 - 2.40757747290173102e-993j)  +/-  (2.13e-991, 2.13e-991j)
| (-0.43388373911755812048 - 3.3588667031465093766e-991j)  +/-  (1.36e-248, 1.36e-248j)
| (-0.36534102436639501454 - 1.0425806219134446904e-992j)  +/-  (1.28e-249, 1.28e-249j)
| (0.22252093395631440429 + 3.5206059803542321269e-992j)  +/-  (5.35e-252, 5.35e-252j)
| (0.56332005806362202775 + 3.6263272927304297936e-991j)  +/-  (1.71e-246, 1.71e-246j)
| (0.29475517441090421683 + 3.1639038212178279222e-993j)  +/-  (7.28e-251, 7.28e-251j)
| (-0.29475517441090421683 + 2.6183303732724541321e-993j)  +/-  (7.87e-251, 7.87e-251j)
| (-0.5 - 1.2997298864666639094e-991j)  +/-  (1.88e-247, 1.88e-247j)
-------------------------------------------------
The weights are:
| (0.0011789420487807246877 + 3.3334322121696021192e-856j)  +/-  (7.23e-73, 3.13e-190j)
| (0.00013296635446275541584 + 6.4548031251090760777e-859j)  +/-  (1.92e-73, 8.3e-191j)
| (0.0031779539067877818033 + 1.5964195867497772216e-857j)  +/-  (1.66e-73, 7.17e-191j)
| (0.00013296635446275541584 - 5.7145751655166667148e-857j)  +/-  (1.04e-73, 4.49e-191j)
| (0.0031779539067877818033 + 6.906178339318290115e-856j)  +/-  (8.22e-74, 3.55e-191j)
| (0.0020685860200476800959 - 1.0231873851123474516e-855j)  +/-  (1.51e-73, 6.51e-191j)
| (0.005952380952380952381 + 3.0954592954137286584e-857j)  +/-  (9.66e-75, 4.17e-192j)
| (0.004482264263586505589 - 2.2875240816252801971e-857j)  +/-  (1.48e-74, 6.38e-192j)
| (0.0011789420487807246877 + 5.7885143257844143273e-858j)  +/-  (1.68e-75, 7.28e-193j)
| (0.017857142857142857143 - 3.599659595590676197e-856j)  +/-  (2.62e-78, 1.13e-195j)
| (0.004482264263586505589 - 5.8020747846264320122e-856j)  +/-  (1.34e-76, 5.79e-194j)
| (0.00052889516921261032367 - 2.5784494673460176617e-858j)  +/-  (1.16e-75, 5e-193j)
| (0.0020685860200476800959 - 1.0258427006655325169e-857j)  +/-  (1.32e-75, 5.69e-193j)
| (0.0092557031671867332823 + 5.0439908294489823667e-857j)  +/-  (3.25e-78, 1.41e-195j)
| (0.00052889516921261032367 + 3.6420081842337246712e-856j)  +/-  (3.58e-77, 1.55e-194j)
| (0.0092557031671867332823 + 4.5889394688943930496e-856j)  +/-  (9.16e-80, 3.96e-197j)
| (0.0075554639956381545888 - 4.8647334785875615062e-856j)  +/-  (2.23e-79, 9.65e-197j)
| (0.0075554639956381545888 - 4.0159138646110799339e-857j)  +/-  (6.84e-79, 2.96e-196j)
| (0.011015117933494949354 - 6.1742410387255283706e-857j)  +/-  (2.06e-80, 8.92e-198j)
| (0.022630581760743084836 - 1.8093221643614404311e-856j)  +/-  (1.45e-83, 6.26e-201j)
| (0.005952380952380952381 + 5.2327500423923473161e-856j)  +/-  (1.16e-79, 5.01e-197j)
| (0.011015117933494949354 - 4.3598691546346096429e-856j)  +/-  (2.32e-81, 1e-198j)
| (0.0232806286403111992 + 2.6986834143216682363e-856j)  +/-  (2.21e-84, 9.55e-202j)
| (0.014553820642337076242 - 8.7169366422613533025e-857j)  +/-  (4.89e-83, 2.11e-200j)
| (0.016254059813885654935 + 1.0116089375405989173e-856j)  +/-  (1.27e-83, 5.47e-201j)
| (0.023676557455061054108 - 2.5180117669561504153e-856j)  +/-  (3.34e-85, 1.44e-202j)
| (0.01279440587602886017 + 4.1556201230544150241e-856j)  +/-  (7.08e-84, 3.06e-201j)
| (0.020631569902736027721 - 3.2402148918103945618e-856j)  +/-  (1.2e-85, 5.2e-203j)
| (0.0232806286403111992 + 1.9829742264673156169e-856j)  +/-  (5.03e-86, 2.17e-203j)
| (0.01279440587602886017 + 7.4007011850991722429e-857j)  +/-  (1.89e-84, 8.18e-202j)
| (0.023676557455061054108 - 2.159473549818221761e-856j)  +/-  (2.89e-86, 1.25e-203j)
| (0.019327259545937303935 + 3.4199102549133483809e-856j)  +/-  (2.05e-86, 8.86e-204j)
| (0.014553820642337076242 - 3.9646542397892920554e-856j)  +/-  (4.72e-86, 2.04e-203j)
| (0.023809523809523809524 + 2.3380584279620894564e-856j)  +/-  (1.09e-86, 4.69e-204j)
| (0.019327259545937303935 + 1.3133923999826350051e-856j)  +/-  (3.93e-88, 1.7e-205j)
| (0.020631569902736027721 - 1.4737284867907874764e-856j)  +/-  (3.33e-88, 1.44e-205j)
| (0.022630581760743084836 - 2.8795197289589824572e-856j)  +/-  (3.46e-88, 1.49e-205j)
| (0.016254059813885654935 + 3.7805532117157088019e-856j)  +/-  (3.6e-88, 1.56e-205j)
| (0.021740937789476129428 + 3.0601041458052478906e-856j)  +/-  (2.28e-88, 9.85e-206j)
| (0.021740937789476129428 + 1.6393062463343185833e-856j)  +/-  (3.42e-89, 1.49e-206j)
| (0.017857142857142857143 - 1.1590931340977951397e-856j)  +/-  (2.44e-89, 1.04e-206j)
