Starting with polynomial:
P : t
Extension levels are: 1 34 36
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P2 : t^35 - 35/4*t^33 + 35*t^31 - 5425/64*t^29 + 35525/256*t^27 - 166257/1024*t^25 + 143325/1024*t^23 - 740025/8192*t^21 + 2877875/65536*t^19 - 4206125/262144*t^17 + 572033/131072*t^15 - 1820105/2097152*t^13 + 1028755/8388608*t^11 - 395675/33554432*t^9 + 24225/33554432*t^7 - 6783/268435456*t^5 + 1785/4294967296*t^3 - 35/17179869184*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^71 - 18*t^69 + 2483/16*t^67 - 13651/16*t^65 + 53755/16*t^63 - 20181/2*t^61 + 98443569/4096*t^59 - 190894559/4096*t^57 + 4912012373/65536*t^55 - 3320306715/32768*t^53 + 121960926945/1048576*t^51 - 119751427965/1048576*t^49 + 404513667285/4194304*t^47 - 73735231605/1048576*t^45 + 5956599951225/134217728*t^43 - 3258565443315/134217728*t^41 + 49461886528915/4294967296*t^39 - 10165486498895/2147483648*t^37 + 115683261704605/68719476736*t^35 - 35502394120725/68719476736*t^33 + 18737662609897/137438953472*t^31 - 264500680961/8589934592*t^29 + 52045427380169/8796093022208*t^27 - 8446127688063/8796093022208*t^25 + 18353689330275/140737488355328*t^23 - 1031465905041/70368744177664*t^21 + 3028248784491/2251799813685248*t^19 - 222919877831/2251799813685248*t^17 + 51538723353/9007199254740992*t^15 - 568688335/2251799813685248*t^13 + 2364780223/288230376151711744*t^11 - 53767549/288230376151711744*t^9 + 50916921/18446744073709551616*t^7 - 218841/9223372036854775808*t^5 + 28595/295147905179352825856*t^3 - 35/295147905179352825856*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:   71 out of 71
Indefinite weights: 0 out of 71
Negative weights:   0 out of 71
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.99597429399523902958 - 1.2231017193482628392e-840j)  +/-  (2.88e-229, 2.88e-229j)
| (-0.96396286069585329189 + 1.1747483349654637196e-841j)  +/-  (6.55e-230, 6.55e-230j)
| (-0.93623487063973720951 + 1.598066525079080871e-842j)  +/-  (1.35e-230, 1.35e-230j)
| (-0.99899306654131464737 + 2.0897563392525321999e-839j)  +/-  (3.02e-229, 3.02e-229j)
| (0.91952777255145063832 + 3.9611567558365645249e-849j)  +/-  (5.71e-231, 5.71e-231j)
| (0.93623487063973720951 + 3.8974049697126043138e-849j)  +/-  (1.44e-230, 1.44e-230j)
| (0.95105651629515357212 - 1.6402495837480578624e-848j)  +/-  (2.75e-230, 2.75e-230j)
| (-0.90096886790241912624 - 3.8765948066977522755e-848j)  +/-  (2.88e-231, 2.88e-231j)
| (0.83457325372130265093 - 1.3958556217889729498e-851j)  +/-  (6.22e-233, 6.22e-233j)
| (-0.99094976176793475525 - 1.3655124025954768686e-845j)  +/-  (2.12e-229, 2.12e-229j)
| (0.90096886790241912624 + 5.5033278935389521673e-854j)  +/-  (2.42e-231, 2.42e-231j)
| (-1 - 3.0904734724083075402e-849j)  +/-  (1.73e-229, 1.73e-229j)
| (-0.88059553185673799519 - 3.9810750740116595871e-861j)  +/-  (8.41e-232, 8.41e-232j)
| (-0.85844879360186611853 - 5.0651371990382542637e-861j)  +/-  (2.47e-232, 2.47e-232j)
| (0.99094976176793475525 - 5.0154880988876885089e-856j)  +/-  (2.39e-229, 2.39e-229j)
| (0.88059553185673799519 - 1.5907727392854275017e-860j)  +/-  (7.37e-232, 7.37e-232j)
| (0.85844879360186611853 + 3.3055641853297729217e-861j)  +/-  (2.43e-232, 2.43e-232j)
| (-0.26603684556667510738 - 1.9437264358022162455e-877j)  +/-  (4.49e-248, 4.49e-248j)
| (-0.75307146600361093353 - 4.5565033569568263003e-864j)  +/-  (7.95e-235, 7.95e-235j)
| (-0.91952777255145063832 + 7.7758999657447163368e-861j)  +/-  (6.12e-231, 6.12e-231j)
| (-0.97492791218182360702 - 6.9735663965160131736e-860j)  +/-  (1.12e-229, 1.12e-229j)
| (0.75307146600361093353 - 2.3520059385688510354e-884j)  +/-  (7.74e-235, 7.74e-235j)
| (-0.9839295885986296554 + 8.4157056904076055282e-878j)  +/-  (1.7e-229, 1.7e-229j)
| (-0.8090169943749474241 - 3.1863767927439977845e-892j)  +/-  (1.67e-233, 1.67e-233j)
| (-0.83457325372130265093 - 1.4167099842339404434e-890j)  +/-  (7.05e-233, 7.05e-233j)
| (0.99899306654131464737 - 3.3497818070948627343e-886j)  +/-  (3.26e-229, 3.26e-229j)
| (0.72279486382739152855 - 1.5951356969763548309e-896j)  +/-  (1.53e-235, 1.53e-235j)
| (0.8090169943749474241 + 1.4504754582562045283e-893j)  +/-  (1.66e-233, 1.66e-233j)
| (1 + 1.6863909585087129972e-887j)  +/-  (2e-229, 2e-229j)
| (-0.65793872593971261237 + 1.047029721651364603e-910j)  +/-  (3.04e-237, 3.04e-237j)
| (-0.6910626489868646759 - 8.2929195816633781114e-907j)  +/-  (2.18e-236, 2.18e-236j)
| (0.47386866247299867071 - 1.0591299923536899508e-916j)  +/-  (4.03e-242, 4.03e-242j)
| (0.6910626489868646759 + 5.6413786421881467283e-910j)  +/-  (2.23e-236, 2.23e-236j)
| (-0.99597429399523902958 - 1.4014200633941921096e-901j)  +/-  (3.16e-229, 3.16e-229j)
| (-0.72279486382739152855 + 5.0071849202138028612e-924j)  +/-  (1.31e-235, 1.31e-235j)
| (-0.78183148246802980871 + 3.8786555091965706297e-921j)  +/-  (4.08e-234, 4.08e-234j)
| (0.78183148246802980871 - 4.5007054073922719032e-921j)  +/-  (4.42e-234, 4.42e-234j)
| (0.58778525229247312917 - 2.7621925438828195275e-926j)  +/-  (5.11e-239, 5.11e-239j)
| (0.9839295885986296554 - 5.6833050277899500392e-915j)  +/-  (1.6e-229, 1.6e-229j)
| (-0.95105651629515357212 - 2.8787021195451658968e-938j)  +/-  (3.07e-230, 3.07e-230j)
| (-0.58778525229247312917 + 1.4019104590471524196e-960j)  +/-  (4.97e-239, 4.97e-239j)
| (0.97492791218182360702 - 1.1484507618362592786e-948j)  +/-  (1.06e-229, 1.06e-229j)
| (0.65793872593971261237 - 2.2945251994591331444e-960j)  +/-  (3.06e-237, 3.06e-237j)
| (0.62348980185873353053 + 3.4315207477305849248e-961j)  +/-  (4.48e-238, 4.48e-238j)
| (-0.17855689479863664801 + 1.5802462835119400356e-974j)  +/-  (1.19e-250, 1.19e-250j)
| (-0.51289927740590614391 - 9.6301956097459841893e-965j)  +/-  (4.79e-241, 4.79e-241j)
| (-0.55089698145210252269 - 7.2817362443953471602e-964j)  +/-  (5.55e-240, 5.55e-240j)
| (0.96396286069585329189 - 3.0855566200406622088e-970j)  +/-  (5.7e-230, 5.7e-230j)
| (0.55089698145210252269 - 4.103518570244978779e-980j)  +/-  (5.4e-240, 5.4e-240j)
| (0.17855689479863664801 + 1.0030161579329720385e-990j)  +/-  (1.12e-250, 1.12e-250j)
| (-0.62348980185873353053 + 1.2187433220984675448e-982j)  +/-  (4.37e-238, 4.37e-238j)
| (-0.43388373911755812048 - 1.7191462656714984349e-988j)  +/-  (3.47e-243, 3.47e-243j)
| (-0.044864830350514925458 - 8.1528057101169703534e-1000j)  +/-  (1.52e-254, 1.52e-254j)
| (0.43388373911755812048 - 2.1858974004337868189e-988j)  +/-  (3.81e-243, 3.81e-243j)
| (0.51289927740590614391 - 4.9153451403270479066e-988j)  +/-  (5.28e-241, 5.28e-241j)
| (-0.089639308903433499765 - 7.8917274128681556891e-999j)  +/-  (2.55e-253, 2.55e-253j)
| (-0.47386866247299867071 - 9.049546600605865302e-988j)  +/-  (4.25e-242, 4.25e-242j)
| (-0.22252093395631440429 - 6.7012630627590670152e-995j)  +/-  (2.39e-249, 2.39e-249j)
| (0.22252093395631440429 - 7.6928814817632387717e-997j)  +/-  (2.39e-249, 2.39e-249j)
| (0.39302503165392361819 + 7.4625412322489054524e-991j)  +/-  (2.21e-244, 2.21e-244j)
| (0.089639308903433499765 + 4.0476150330042103462e-999j)  +/-  (2.48e-253, 2.48e-253j)
| (-0.3090169943749474241 + 4.9143086756060555519e-992j)  +/-  (9.02e-247, 9.02e-247j)
| (-0.35137482408134270489 - 8.5776714370596167734e-991j)  +/-  (1.7e-245, 1.7e-245j)
| (0.044864830350514925458 + 4.7129283931877903275e-1000j)  +/-  (1.26e-254, 1.26e-254j)
| (0.3090169943749474241 + 1.3320114674179761867e-993j)  +/-  (7.23e-247, 7.23e-247j)
| (0.26603684556667510738 - 1.8388175717007255266e-996j)  +/-  (4.33e-248, 4.33e-248j)
| (2.4704775031479275267e-1030 - 1.4234191674766405416e-1029j)  +/-  (1.03e-1027, 1.03e-1027j)
| (-0.39302503165392361819 + 3.8914887593370215072e-990j)  +/-  (2.58e-244, 2.58e-244j)
| (-0.13423326581765547604 - 2.014539263747666391e-997j)  +/-  (6.32e-252, 6.32e-252j)
| (0.13423326581765547604 + 1.2134862133800094386e-998j)  +/-  (5.39e-252, 5.39e-252j)
| (0.35137482408134270489 + 6.7253372214130756252e-992j)  +/-  (1.69e-245, 1.69e-245j)
-------------------------------------------------
The weights are:
| (0.014285714285714285714 - 1.2315636620782432886e-840j)  +/-  (3.45e-19, 6.43e-127j)
| (0.014285714285714285714 - 8.533002533250271045e-840j)  +/-  (1.62e-19, 3.01e-127j)
| (0.014285714285714285714 - 4.6882293238630201681e-840j)  +/-  (1.33e-19, 2.48e-127j)
| (0.014285714285714285714 - 7.4040098366695465918e-839j)  +/-  (2.8e-20, 5.21e-128j)
| (0.014285714285714285714 - 7.3969882945366090566e-842j)  +/-  (1.08e-20, 2e-128j)
| (0.014285714285714285714 + 1.3922580320293355982e-841j)  +/-  (7.12e-21, 1.33e-128j)
| (0.014285714285714285714 - 2.3690262067565951337e-841j)  +/-  (3.19e-21, 5.94e-129j)
| (0.014285714285714285714 - 3.0032124327818521005e-840j)  +/-  (3.06e-22, 5.69e-130j)
| (0.014285714285714285714 + 5.3497786720613599891e-842j)  +/-  (1.14e-22, 2.12e-130j)
| (0.014285714285714285714 + 3.717373414705015144e-839j)  +/-  (1.84e-22, 3.43e-130j)
| (0.014285714285714285714 + 2.7811121584011919982e-842j)  +/-  (3.37e-22, 6.28e-130j)
| (0.0071428571428571428571 + 1.4821978224628584907e-838j)  +/-  (5.59e-22, 1.04e-129j)
| (0.014285714285714285714 + 2.4879303850348733243e-840j)  +/-  (1.64e-23, 3.05e-131j)
| (0.014285714285714285714 - 2.0958827158348223632e-840j)  +/-  (3.97e-24, 7.38e-132j)
| (0.014285714285714285714 - 3.3284684191280590365e-840j)  +/-  (4.68e-25, 8.72e-133j)
| (0.014285714285714285714 + 6.3559332731957803928e-843j)  +/-  (3.64e-24, 6.78e-132j)
| (0.014285714285714285714 - 3.26244866965563115e-842j)  +/-  (1.43e-24, 2.67e-132j)
| (0.014285714285714285714 + 3.9071410112056516804e-841j)  +/-  (3.07e-29, 5.72e-137j)
| (0.014285714285714285714 - 1.1947555018847644091e-840j)  +/-  (9.23e-28, 1.72e-135j)
| (0.014285714285714285714 + 3.6962607887580374293e-840j)  +/-  (4.12e-25, 7.67e-133j)
| (0.014285714285714285714 + 1.2555421764925526996e-839j)  +/-  (1.47e-25, 2.74e-133j)
| (0.014285714285714285714 - 9.7345068231822260475e-842j)  +/-  (1.29e-30, 2.41e-138j)
| (0.014285714285714285714 - 1.9898555956245073322e-839j)  +/-  (1.67e-25, 3.11e-133j)
| (0.014285714285714285714 - 1.5491364118218646775e-840j)  +/-  (5.38e-29, 1e-136j)
| (0.014285714285714285714 + 1.790935093276491147e-840j)  +/-  (3.53e-28, 6.57e-136j)
| (0.014285714285714285714 + 5.9365206864489754194e-840j)  +/-  (2.09e-31, 3.9e-139j)
| (0.014285714285714285714 + 1.0829372216318331083e-841j)  +/-  (2.59e-34, 4.81e-142j)
| (0.014285714285714285714 - 7.058221755761863719e-842j)  +/-  (1.17e-32, 2.17e-140j)
| (0.0071428571428571428571 - 2.2443491473935864369e-840j)  +/-  (1.2e-31, 2.23e-139j)
| (0.014285714285714285714 + 8.5846506190591165108e-841j)  +/-  (7.28e-36, 1.36e-143j)
| (0.014285714285714285714 - 9.5205526835433314962e-841j)  +/-  (2.25e-35, 4.19e-143j)
| (0.014285714285714285714 - 1.6789614960207026866e-841j)  +/-  (6.93e-40, 1.29e-147j)
| (0.014285714285714285714 - 1.1818391129720905111e-841j)  +/-  (6.25e-37, 1.16e-144j)
| (0.014285714285714285714 - 9.8940893772175976923e-839j)  +/-  (4.27e-31, 7.95e-139j)
| (0.014285714285714285714 + 1.0626832792809299811e-840j)  +/-  (4.73e-35, 8.81e-143j)
| (0.014285714285714285714 + 1.3541990118917931885e-840j)  +/-  (6.26e-34, 1.17e-141j)
| (0.014285714285714285714 + 8.4950742271585089636e-842j)  +/-  (3.44e-36, 6.41e-144j)
| (0.014285714285714285714 + 1.4410281754623833223e-841j)  +/-  (2.3e-40, 4.29e-148j)
| (0.014285714285714285714 + 1.3010957929369851043e-840j)  +/-  (3.39e-36, 6.31e-144j)
| (0.014285714285714285714 + 6.104138996089783203e-840j)  +/-  (7.58e-34, 1.41e-141j)
| (0.014285714285714285714 + 7.0984997140481987072e-841j)  +/-  (1.1e-40, 2.04e-148j)
| (0.014285714285714285714 - 6.7995304424290398962e-841j)  +/-  (1.14e-36, 2.13e-144j)
| (0.014285714285714285714 + 1.2730683795818616652e-841j)  +/-  (2.85e-40, 5.3e-148j)
| (0.014285714285714285714 - 1.3588718011157349506e-841j)  +/-  (4.9e-41, 9.11e-149j)
| (0.014285714285714285714 + 3.465607313505262545e-841j)  +/-  (8.85e-47, 1.65e-154j)
| (0.014285714285714285714 + 5.9831402679706277058e-841j)  +/-  (2.66e-44, 4.95e-152j)
| (0.014285714285714285714 - 6.5028215023583198461e-841j)  +/-  (1.58e-43, 2.95e-151j)
| (0.014285714285714285714 + 3.9473803081110717153e-841j)  +/-  (8.79e-39, 1.64e-146j)
| (0.014285714285714285714 - 1.520983800072621261e-841j)  +/-  (5.61e-44, 1.04e-151j)
| (0.014285714285714285714 + 2.3047398966584778615e-841j)  +/-  (3.96e-49, 7.37e-157j)
| (0.014285714285714285714 - 7.7858183195564762683e-841j)  +/-  (1.28e-42, 2.38e-150j)
| (0.014285714285714285714 + 5.1244039698692602837e-841j)  +/-  (1.67e-46, 3.1e-154j)
| (0.014285714285714285714 - 2.9401984999678221084e-841j)  +/-  (7.85e-50, 1.46e-157j)
| (0.014285714285714285714 + 1.7589486515196776883e-841j)  +/-  (1.22e-47, 2.27e-155j)
| (0.014285714285714285714 + 1.5999478890233754263e-841j)  +/-  (6.16e-46, 1.15e-153j)
| (0.014285714285714285714 + 3.1001110600250591774e-841j)  +/-  (6.94e-50, 1.29e-157j)
| (0.014285714285714285714 - 5.5270048951533033836e-841j)  +/-  (5.46e-47, 1.02e-154j)
| (0.014285714285714285714 - 3.6755492874251261701e-841j)  +/-  (2.66e-49, 4.95e-157j)
| (0.014285714285714285714 - 2.201964961008328894e-841j)  +/-  (3.22e-51, 6e-159j)
| (0.014285714285714285714 - 1.840755446817895545e-841j)  +/-  (6.3e-50, 1.17e-157j)
| (0.014285714285714285714 + 2.5313672228919449882e-841j)  +/-  (8.2e-52, 1.53e-159j)
| (0.014285714285714285714 - 4.1636086861477860291e-841j)  +/-  (1.9e-50, 3.54e-158j)
| (0.014285714285714285714 + 4.4487770658991988755e-841j)  +/-  (1.64e-50, 3.05e-158j)
| (0.014285714285714285714 - 2.6572608476187026212e-841j)  +/-  (2.12e-52, 3.95e-160j)
| (0.014285714285714285714 - 2.0130025652007398934e-841j)  +/-  (8.16e-53, 1.52e-160j)
| (0.014285714285714285714 + 2.1049980107342130342e-841j)  +/-  (8.04e-53, 1.5e-160j)
| (0.014285714285714285714 + 2.7930903199076176807e-841j)  +/-  (4.15e-53, 7.73e-161j)
| (0.014285714285714285714 - 4.7672120756490400608e-841j)  +/-  (1.49e-52, 2.78e-160j)
| (0.014285714285714285714 - 3.2745753281580660513e-841j)  +/-  (3.87e-53, 7.2e-161j)
| (0.014285714285714285714 - 2.4142168821009187308e-841j)  +/-  (1.15e-53, 2.16e-161j)
| (0.014285714285714285714 + 1.9251809384940769069e-841j)  +/-  (9.85e-54, 1.8e-161j)
