Starting with polynomial:
P : 4096*t^13 - 13312*t^11 + 16640*t^9 - 9984*t^7 + 2912*t^5 - 364*t^3 + 13*t
Extension levels are: 13 66
-------------------------------------------------
Trying to find an order 66 Kronrod extension for:
P1 : 4096*t^13 - 13312*t^11 + 16640*t^9 - 9984*t^7 + 2912*t^5 - 364*t^3 + 13*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4096*t^79 - 81920*t^77 + 788224*t^75 - 4859136*t^73 + 21563616*t^71 - 73381056*t^69 + 199185175*t^67 - 442912679*t^65 + 1644569069/2*t^63 - 1292591872*t^61 + 55639367641/32*t^59 - 64564422455/32*t^57 + 520258854297/256*t^55 - 228500787123/128*t^53 + 89934700841721/65536*t^51 - 60650453072805/65536*t^49 + 575013464726925/1048576*t^47 - 74901971179455/262144*t^45 + 2196407410747935/16777216*t^43 - 884348069228085/16777216*t^41 + 2499753756530415/134217728*t^39 - 386740267088175/67108864*t^37 + 6687918051923745/4294967296*t^35 - 1572336121450185/4294967296*t^33 + 1280743811157265/17179869184*t^31 - 28082597092459/2147483648*t^29 + 539540996494465/274877906944*t^27 - 68742519953863/274877906944*t^25 + 58902866522353/2199023255552*t^23 - 2620961293159/1099511627776*t^21 + 24454290230667/140737488355328*t^19 - 1434561782775/140737488355328*t^17 + 2119961251221/4503599627370496*t^15 - 18730885957/1125899906842624*t^13 + 31241278523/72057594037927936*t^11 - 570666577/72057594037927936*t^9 + 54331355/576460752303423488*t^7 - 187967/288230376151711744*t^5 + 39559/18446744073709551616*t^3 - 39/18446744073709551616*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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: 0
  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
Positive weights:   79 out of 79
Indefinite weights: 0 out of 79
Negative weights:   0 out of 79
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.97094181742605202716 + 4.1070304001473956104e-810j)  +/-  (8.38e-227, 8.38e-227j)
| (-0.94853644194714552616 + 5.7870623942588928577e-807j)  +/-  (2.37e-227, 2.37e-227j)
| (-0.93501624268541482344 - 5.0231211193797289329e-810j)  +/-  (1.07e-227, 1.07e-227j)
| (-0.9927088740980539928 - 1.8110839525637448771e-813j)  +/-  (3.23e-226, 3.23e-226j)
| (0.91997944365882420313 + 5.221147417044773998e-827j)  +/-  (4.54e-228, 4.54e-228j)
| (0.90345043461038227502 + 2.5726626736821058068e-827j)  +/-  (1.88e-228, 1.88e-228j)
| (0.9927088740980539928 + 2.9606274261648454427e-825j)  +/-  (2.82e-226, 2.82e-226j)
| (-0.91997944365882420313 + 9.3089948825869009961e-826j)  +/-  (4.16e-228, 4.16e-228j)
| (-0.9991889981715696377 + 6.7304086884354055746e-822j)  +/-  (3.82e-226, 3.82e-226j)
| (-0.98705026263791286379 - 3.9330764048691517744e-842j)  +/-  (2.05e-226, 2.05e-226j)
| (0.86602540378443864676 - 1.7292962878507284353e-861j)  +/-  (1.94e-229, 1.94e-229j)
| (1 - 2.6298805823827340654e-856j)  +/-  (2.07e-226, 2.07e-226j)
| (-0.8854560256532098959 + 7.6029717058753597067e-861j)  +/-  (6.53e-229, 6.53e-229j)
| (-0.86602540378443864676 - 1.9261391761956087464e-861j)  +/-  (2.24e-229, 2.24e-229j)
| (0.9991889981715696377 + 1.6086476489534840233e-857j)  +/-  (4.02e-226, 4.02e-226j)
| (0.84519008554379475254 + 3.1388772067103093277e-862j)  +/-  (5.81e-230, 5.81e-230j)
| (0.82298386589365639458 + 2.5272798823144525983e-863j)  +/-  (1.51e-230, 1.51e-230j)
| (0.98705026263791286379 + 3.3146280723867765702e-858j)  +/-  (2.02e-226, 2.02e-226j)
| (-0.79944276340350114978 - 3.6421374293124450965e-863j)  +/-  (3.32e-231, 3.32e-231j)
| (-1 - 1.9547972585495729213e-855j)  +/-  (2.17e-226, 2.17e-226j)
| (0.8854560256532098959 - 7.4970331506505753764e-880j)  +/-  (7.35e-229, 7.35e-229j)
| (0.77460496182765458307 + 7.8239626348259898564e-883j)  +/-  (7.71e-232, 7.71e-232j)
| (0.99675730813420998559 - 3.1351177909110929826e-877j)  +/-  (3.6e-226, 3.6e-226j)
| (-0.84519008554379475254 - 4.2858504834305522663e-879j)  +/-  (5.82e-230, 5.82e-230j)
| (-0.82298386589365639458 + 9.8681997444712358639e-881j)  +/-  (1.7e-230, 1.7e-230j)
| (0.27821746391645263455 + 3.4627916166723800388e-897j)  +/-  (9.93e-247, 9.93e-247j)
| (0.74851074817110109863 - 3.9894428107746323529e-883j)  +/-  (1.51e-232, 1.51e-232j)
| (0.96051811163137229844 + 1.0863401775215629635e-877j)  +/-  (4.68e-227, 4.68e-227j)
| (0.72120244734381453129 - 3.8784628585112516147e-884j)  +/-  (2.59e-233, 2.59e-233j)
| (-0.63244537559537723782 + 1.3286106747916304175e-885j)  +/-  (8.96e-236, 8.96e-236j)
| (-0.97979065204226770147 - 1.5910073780728233246e-874j)  +/-  (1.21e-226, 1.21e-226j)
| (0.79944276340350114978 + 5.7114466716862140284e-899j)  +/-  (3.42e-231, 3.42e-231j)
| (0.66312265824079520238 + 2.8436817192563412213e-903j)  +/-  (6.47e-235, 6.47e-235j)
| (-0.99675730813420998559 + 3.8523796714436632962e-891j)  +/-  (3.36e-226, 3.36e-226j)
| (-0.6927243535095993926 - 1.8176764397301928184e-912j)  +/-  (4.14e-234, 4.14e-234j)
| (-0.77460496182765458307 - 5.5583184056197354256e-910j)  +/-  (7.44e-232, 7.44e-232j)
| (-0.39196660986007507588 + 6.9088504961437222355e-923j)  +/-  (4.44e-243, 4.44e-243j)
| (0.63244537559537723782 + 2.4758549773610973954e-916j)  +/-  (7.7e-236, 7.7e-236j)
| (0.93501624268541482344 + 1.3194595571164861e-906j)  +/-  (1.03e-227, 1.03e-227j)
| (-0.97094181742605202716 - 6.7992646268988054883e-905j)  +/-  (8.28e-227, 8.28e-227j)
| (-0.56806474673115580251 - 2.0329074527127019269e-922j)  +/-  (1.06e-237, 1.06e-237j)
| (-0.96051811163137229844 + 8.0951649665582570747e-912j)  +/-  (4.74e-227, 4.74e-227j)
| (0.6927243535095993926 + 1.1527868985347791744e-920j)  +/-  (4.93e-234, 4.93e-234j)
| (0.60074226423797891692 - 5.3932691621613256128e-925j)  +/-  (9.2e-237, 9.2e-237j)
| (0.080466568716725880436 + 1.4389134207552549406e-940j)  +/-  (2.47e-253, 2.47e-253j)
| (-0.66312265824079520238 - 3.5352145217972088131e-921j)  +/-  (7.16e-235, 7.16e-235j)
| (-0.72120244734381453129 - 1.8526196133410604404e-919j)  +/-  (2.82e-233, 2.82e-233j)
| (0.94853644194714552616 - 1.8769613695860388372e-912j)  +/-  (2.47e-227, 2.47e-227j)
| (0.5 - 6.3504687610934978572e-929j)  +/-  (1.07e-239, 1.07e-239j)
| (0.040265940109415143362 + 1.6224316943534528931e-945j)  +/-  (1.14e-254, 1.14e-254j)
| (-0.53446582612780109204 - 4.585009408713676717e-927j)  +/-  (1.19e-238, 1.19e-238j)
| (-0.5 - 3.5287784676992075989e-928j)  +/-  (1.07e-239, 1.07e-239j)
| (-0.90345043461038227502 - 1.0220369756096080964e-917j)  +/-  (1.93e-228, 1.93e-228j)
| (0.56806474673115580251 + 5.1836332563284090079e-927j)  +/-  (1.03e-237, 1.03e-237j)
| (0.53446582612780109204 + 2.7035377929919412557e-928j)  +/-  (1.06e-238, 1.06e-238j)
| (-0.12053668025532305335 + 3.0497746746030118881e-941j)  +/-  (7.4e-252, 7.4e-252j)
| (-0.46472317204376854566 + 1.7258897063923961912e-931j)  +/-  (8.15e-241, 8.15e-241j)
| (-0.60074226423797891692 - 7.0052985709671840844e-927j)  +/-  (9.48e-237, 9.48e-237j)
| (0.23931566428755776715 - 1.4394779243274392935e-938j)  +/-  (5.14e-248, 5.14e-248j)
| (0.39196660986007507588 + 1.1252933665680096452e-933j)  +/-  (4.41e-243, 4.41e-243j)
| (0.97979065204226770147 - 7.2107706825022136242e-925j)  +/-  (1.24e-226, 1.24e-226j)
| (-0.20002569377604442753 - 2.4426237102388483369e-947j)  +/-  (2.45e-249, 2.45e-249j)
| (-0.42869256140305418307 + 3.8113153177724539013e-939j)  +/-  (6.28e-242, 6.28e-242j)
| (-0.080466568716725880436 - 3.104486965742766454e-951j)  +/-  (2.71e-253, 2.71e-253j)
| (0.42869256140305418307 - 9.9251206012671997514e-942j)  +/-  (6.36e-242, 6.36e-242j)
| (0.46472317204376854566 + 1.1332788391218702719e-940j)  +/-  (8.72e-241, 8.72e-241j)
| (-0.74851074817110109863 + 2.5576993455431430918e-944j)  +/-  (1.57e-232, 1.57e-232j)
| (-0.35460488704253562597 + 2.1978195266073389885e-957j)  +/-  (2.78e-244, 2.78e-244j)
| (-0.23931566428755776715 + 5.3332096802716346907e-962j)  +/-  (5.32e-248, 5.32e-248j)
| (0.12053668025532305335 - 1.4923532282224101809e-965j)  +/-  (7.92e-252, 7.92e-252j)
| (0.35460488704253562597 - 9.851274590003061598e-959j)  +/-  (3.12e-244, 3.12e-244j)
| (0.16041128085776024037 + 7.7693034300941978715e-965j)  +/-  (1.4e-250, 1.4e-250j)
| (-0.27821746391645263455 + 1.0139826224487130808e-959j)  +/-  (1.04e-246, 1.04e-246j)
| (-0.31666799380147249909 - 5.5868804021661470297e-959j)  +/-  (1.77e-245, 1.77e-245j)
| (4.8985024190723243029e-1017 + 3.8202000311099486257e-1017j)  +/-  (4.91e-1015, 4.91e-1015j)
| (0.31666799380147249909 - 3.5821222640396458192e-960j)  +/-  (1.88e-245, 1.88e-245j)
| (0.20002569377604442753 + 7.5264739614229789512e-963j)  +/-  (2.41e-249, 2.41e-249j)
| (-0.040265940109415143362 - 9.5213423271908110272e-970j)  +/-  (2.11e-254, 2.11e-254j)
| (-0.16041128085776024037 - 3.1510739634095729603e-964j)  +/-  (1.27e-250, 1.27e-250j)
-------------------------------------------------
The weights are:
| (0.012820512820512820513 + 3.9132875264693216203e-809j)  +/-  (1.53e-21, 1.61e-126j)
| (0.012820512820512820513 - 3.5568674375894756713e-808j)  +/-  (7.2e-22, 7.56e-127j)
| (0.012820512820512820513 - 5.487308357686019169e-807j)  +/-  (6.52e-22, 6.85e-127j)
| (0.012820512820512820513 + 1.6807685396726997753e-807j)  +/-  (3.67e-23, 3.86e-128j)
| (0.012820512820512820513 + 3.8708502218205686334e-809j)  +/-  (4.83e-23, 5.08e-128j)
| (0.012820512820512820513 - 3.9316235641573096151e-809j)  +/-  (3.93e-23, 4.13e-128j)
| (0.012820512820512820513 - 4.0671742148901375584e-809j)  +/-  (1.75e-24, 1.84e-129j)
| (0.012820512820512820513 + 2.6023261807279606207e-807j)  +/-  (2.71e-23, 2.84e-128j)
| (0.012820512820512820513 + 1.4657794102800551668e-807j)  +/-  (1.47e-24, 1.55e-129j)
| (0.012820512820512820513 - 1.927662587537390022e-807j)  +/-  (3.71e-24, 3.9e-129j)
| (0.012820512820512820513 - 4.04215163986046809e-809j)  +/-  (3.28e-25, 3.45e-130j)
| (0.0064102564102564102564 + 1.9960822873865411518e-809j)  +/-  (9.74e-26, 1.02e-130j)
| (0.012820512820512820513 + 1.1774383192681046788e-807j)  +/-  (5.5e-26, 5.78e-131j)
| (0.012820512820512820513 - 9.0009504963682896423e-808j)  +/-  (1.73e-26, 1.82e-131j)
| (0.012820512820512820513 - 3.9989539022330061986e-809j)  +/-  (1.02e-25, 1.08e-130j)
| (0.012820512820512820513 + 4.0980024331022846232e-809j)  +/-  (3.33e-27, 3.5e-132j)
| (0.012820512820512820513 - 4.1561808809466053051e-809j)  +/-  (6.59e-28, 6.92e-133j)
| (0.012820512820512820513 + 4.1633320681505801334e-809j)  +/-  (1.08e-26, 1.14e-131j)
| (0.012820512820512820513 + 4.9807284386051070548e-808j)  +/-  (3.13e-30, 3.29e-135j)
| (0.0064102564102564102564 - 7.2134195178844155215e-808j)  +/-  (1.82e-27, 1.91e-132j)
| (0.012820512820512820513 + 3.9873869173589907571e-809j)  +/-  (4.07e-27, 4.28e-132j)
| (0.012820512820512820513 - 4.282638725169456308e-809j)  +/-  (5.16e-30, 5.42e-135j)
| (0.012820512820512820513 + 4.0212782042887601589e-809j)  +/-  (1.53e-26, 1.61e-131j)
| (0.012820512820512820513 + 7.1859543202119591408e-808j)  +/-  (7.64e-30, 8.03e-135j)
| (0.012820512820512820513 - 5.9147818961057503647e-808j)  +/-  (2.18e-30, 2.29e-135j)
| (0.012820512820512820513 + 6.0456298775388040724e-809j)  +/-  (4.84e-35, 5.09e-140j)
| (0.012820512820512820513 + 4.3520486137552906514e-809j)  +/-  (6.27e-31, 6.59e-136j)
| (0.012820512820512820513 - 3.3846389276135358059e-809j)  +/-  (1.07e-28, 1.12e-133j)
| (0.012820512820512820513 - 4.4262017910323076743e-809j)  +/-  (6.21e-32, 6.53e-137j)
| (0.012820512820512820513 + 2.34900736782699496e-808j)  +/-  (3.39e-36, 3.56e-141j)
| (0.012820512820512820513 + 2.3753231238625022158e-807j)  +/-  (1.74e-31, 1.83e-136j)
| (0.012820512820512820513 + 4.2175193142068310107e-809j)  +/-  (3.72e-30, 3.91e-135j)
| (0.012820512820512820513 - 4.590449088269162654e-809j)  +/-  (6.07e-34, 6.38e-139j)
| (0.012820512820512820513 - 1.5396855585279929505e-807j)  +/-  (1.26e-30, 1.33e-135j)
| (0.012820512820512820513 + 2.9026393583511728108e-808j)  +/-  (7.64e-37, 8.03e-142j)
| (0.012820512820512820513 - 4.269365516262321092e-808j)  +/-  (4.98e-35, 5.23e-140j)
| (0.012820512820512820513 - 1.3338421308454467755e-808j)  +/-  (2.17e-40, 2.28e-145j)
| (0.012820512820512820513 + 4.6814047399846305565e-809j)  +/-  (1.49e-36, 1.56e-141j)
| (0.012820512820512820513 - 3.7958784387833594907e-809j)  +/-  (4.14e-32, 4.35e-137j)
| (0.012820512820512820513 - 3.3132162610244776484e-807j)  +/-  (4.35e-33, 4.57e-138j)
| (0.012820512820512820513 + 1.9514430107223439675e-808j)  +/-  (3.97e-40, 4.18e-145j)
| (0.012820512820512820513 + 6.1947695493008080878e-807j)  +/-  (2.37e-33, 2.49e-138j)
| (0.012820512820512820513 + 4.5055268727947926731e-809j)  +/-  (9.61e-36, 1.01e-140j)
| (0.012820512820512820513 - 4.7788521694904115997e-809j)  +/-  (1.82e-38, 1.91e-143j)
| (0.012820512820512820513 - 7.2106242706545337255e-809j)  +/-  (5.37e-44, 5.64e-149j)
| (0.012820512820512820513 - 2.6015398138666413206e-808j)  +/-  (7.24e-39, 7.61e-144j)
| (0.012820512820512820513 - 3.2663185473218382276e-808j)  +/-  (3.04e-38, 3.19e-143j)
| (0.012820512820512820513 + 3.6793385799982000745e-809j)  +/-  (8.65e-35, 9.09e-140j)
| (0.012820512820512820513 + 5.1152444852660710004e-809j)  +/-  (7.24e-42, 7.61e-147j)
| (0.012820512820512820513 + 7.5042779136961139842e-809j)  +/-  (6.93e-45, 7.28e-150j)
| (0.012820512820512820513 - 1.7930569241715107853e-808j)  +/-  (4.89e-42, 5.14e-147j)
| (0.012820512820512820513 + 1.6552383791649798227e-808j)  +/-  (7.13e-43, 7.49e-148j)
| (0.012820512820512820513 - 1.6476028691176223228e-807j)  +/-  (1.02e-36, 1.07e-141j)
| (0.012820512820512820513 + 4.8832808506736043621e-809j)  +/-  (1.09e-41, 1.14e-146j)
| (0.012820512820512820513 - 4.9952195918959013668e-809j)  +/-  (1.75e-42, 1.84e-147j)
| (0.012820512820512820513 + 8.9636081301030177521e-809j)  +/-  (4.94e-48, 5.19e-153j)
| (0.012820512820512820513 - 1.5345101015218289833e-808j)  +/-  (1.17e-44, 1.23e-149j)
| (0.012820512820512820513 - 2.1348396537628837848e-808j)  +/-  (2.7e-42, 2.84e-147j)
| (0.012820512820512820513 - 6.2442775307636654678e-809j)  +/-  (5.18e-48, 5.45e-153j)
| (0.012820512820512820513 - 5.5304816064677317792e-809j)  +/-  (2.88e-47, 3.03e-152j)
| (0.012820512820512820513 - 4.4459433382922885681e-809j)  +/-  (1.38e-40, 1.45e-145j)
| (0.012820512820512820513 + 9.9163646583185559942e-809j)  +/-  (1.84e-49, 1.94e-154j)
| (0.012820512820512820513 + 1.4281151301153111066e-808j)  +/-  (1.28e-46, 1.35e-151j)
| (0.012820512820512820513 - 8.5494356134427197799e-809j)  +/-  (1.43e-49, 1.5e-154j)
| (0.012820512820512820513 + 5.3821429698648785106e-809j)  +/-  (1.34e-47, 1.41e-152j)
| (0.012820512820512820513 - 5.2439870562255886593e-809j)  +/-  (4.26e-47, 4.47e-152j)
| (0.012820512820512820513 + 3.7123265181217520855e-808j)  +/-  (8.94e-45, 9.4e-150j)
| (0.012820512820512820513 + 1.2498988340996484868e-808j)  +/-  (4.36e-49, 4.58e-154j)
| (0.012820512820512820513 - 1.0466123739785472989e-808j)  +/-  (2.51e-50, 2.63e-155j)
| (0.012820512820512820513 + 6.939858350494263727e-809j)  +/-  (3.18e-51, 3.35e-156j)
| (0.012820512820512820513 + 5.6898568092573868902e-809j)  +/-  (2.33e-50, 2.45e-155j)
| (0.012820512820512820513 - 6.6897908740932459166e-809j)  +/-  (1.71e-51, 1.8e-156j)
| (0.012820512820512820513 + 1.1073921724744787111e-808j)  +/-  (1.9e-51, 2e-156j)
| (0.012820512820512820513 - 1.1748188663679657887e-808j)  +/-  (3.18e-51, 3.35e-156j)
| (0.012820512820512820513 - 7.8233178527114985403e-809j)  +/-  (6.01e-53, 6.31e-158j)
| (0.012820512820512820513 - 5.8612191228643497398e-809j)  +/-  (2.19e-52, 2.3e-157j)
| (0.012820512820512820513 + 6.4584967562609527276e-809j)  +/-  (9.63e-53, 1.01e-157j)
| (0.012820512820512820513 + 8.1706063863905215411e-809j)  +/-  (2.01e-53, 2.12e-158j)
| (0.012820512820512820513 - 9.417536225654850907e-809j)  +/-  (1.91e-53, 1.99e-158j)
