Starting with polynomial:
P : 8*t^4 - 8*t^2 + 1
Extension levels are: 4 72
-------------------------------------------------
Trying to find an order 72 Kronrod extension for:
P1 : 8*t^4 - 8*t^2 + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 8*t^76 - 152*t^74 + 1387*t^72 - 8094*t^70 + 1085945/32*t^68 - 3484201/32*t^66 + 71177249/256*t^64 - 9283989/16*t^62 + 1032707247/1024*t^60 - 1515664865/1024*t^58 + 15184206193/8192*t^56 - 8176111027/4096*t^54 + 3900004959879/2097152*t^52 - 3157146872283/2097152*t^50 + 17822603311275/16777216*t^48 - 2746433952885/4194304*t^46 + 189503942749065/536870912*t^44 - 89367263130915/536870912*t^42 + 294809247339915/4294967296*t^40 - 53081997443475/2147483648*t^38 + 1066189834364655/137438953472*t^36 - 290779045735815/137438953472*t^34 + 549249308612095/1099511627776*t^32 - 13967783894155/137438953472*t^30 + 155794512665575/8796093022208*t^28 - 23094245406897/8796093022208*t^26 + 23094245406897/70368744177664*t^24 - 1204461778591/35184372088832*t^22 + 13249079564501/4503599627370496*t^20 - 923450153065/4503599627370496*t^18 + 409530067881/36028797018963968*t^16 - 4403549117/9007199254740992*t^14 + 36429360877/2305843009213693952*t^12 - 847194439/2305843009213693952*t^10 + 106789215/18446744073709551616*t^8 - 520923/9223372036854775808*t^6 + 173641/590295810358705651712*t^4 - 361/590295810358705651712*t^2 + 1/4722366482869645213696
-------------------------------------------------
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
-------------------------------------------------
The nodes are:
| (0.99807829846586812328 - 4.163448089503295395e-788j)  +/-  (3.13e-228, 3.13e-228j)
| (-0.95232576287481453578 - 1.2063337154666845393e-795j)  +/-  (1.23e-228, 1.23e-228j)
| (-0.90727593318155995601 - 4.5464355045886396846e-797j)  +/-  (1.25e-229, 1.25e-229j)
| (-0.99807829846586812328 - 1.3063301945578538575e-793j)  +/-  (2.58e-228, 2.58e-228j)
| (0.90727593318155995601 - 4.40098409835784148e-797j)  +/-  (1.45e-229, 1.45e-229j)
| (0.95232576287481453578 - 4.8289786801650791544e-796j)  +/-  (1.15e-228, 1.15e-228j)
| (0.97426664263228751672 - 2.9589228217370142509e-802j)  +/-  (2.71e-228, 2.71e-228j)
| (-0.92387953251128675613 + 2.6926911327343183204e-819j)  +/-  (3.09e-229, 3.09e-229j)
| (-0.98274897304735937662 + 8.3100467018218126885e-818j)  +/-  (3.53e-228, 3.53e-228j)
| (0.98274897304735937662 - 9.8767472956713372767e-826j)  +/-  (3.46e-228, 3.46e-228j)
| (0.88912226813918519696 + 7.0029948297285552831e-840j)  +/-  (5.52e-230, 5.52e-230j)
| (-0.97426664263228751672 + 8.1225256979391134886e-840j)  +/-  (2.53e-228, 2.53e-228j)
| (-0.88912226813918519696 + 5.6727665887382009643e-843j)  +/-  (4.72e-230, 4.72e-230j)
| (-0.86944955261636686927 - 3.6846452520512673852e-843j)  +/-  (1.67e-230, 1.67e-230j)
| (0.99466498011324257229 - 9.5597248631528390658e-838j)  +/-  (3.55e-228, 3.55e-228j)
| (0.8256839499965558397 - 2.0836084213678308811e-855j)  +/-  (1.66e-231, 1.66e-231j)
| (0.92387953251128675613 + 5.0473282950210550065e-853j)  +/-  (2.74e-229, 2.74e-229j)
| (-0.98955229332720276916 - 2.848780479623237485e-849j)  +/-  (3.81e-228, 3.81e-228j)
| (-0.74956408374112603823 - 1.0724370283488268771e-858j)  +/-  (2.17e-233, 2.17e-233j)
| (-0.93890469915742953058 - 1.9966537446986257112e-852j)  +/-  (7.62e-229, 7.62e-229j)
| (0.93890469915742953058 - 1.4661374798742251305e-852j)  +/-  (6.57e-229, 6.57e-229j)
| (0.80166583569748851717 - 1.4863115794876136521e-861j)  +/-  (4.04e-232, 4.04e-232j)
| (-0.99978641678793101844 - 3.8142117008785100594e-857j)  +/-  (8.89e-229, 8.89e-229j)
| (-0.84829139711757373375 - 1.1208175246746604304e-860j)  +/-  (6.15e-231, 6.15e-231j)
| (-0.77627808876575741313 - 4.4123369391298406663e-863j)  +/-  (9.6e-233, 9.6e-233j)
| (-0.9641197940012136225 - 2.2914226839599301511e-857j)  +/-  (1.72e-228, 1.72e-228j)
| (0.72156946105306217149 + 1.9635221598587457694e-863j)  +/-  (4.15e-234, 4.15e-234j)
| (0.84829139711757373375 + 4.326918369386715522e-860j)  +/-  (6.19e-231, 6.19e-231j)
| (0.99978641678793101844 - 5.0323322069168631757e-855j)  +/-  (9.66e-229, 9.66e-229j)
| (-0.6619317822595665273 + 1.7276884302204826467e-879j)  +/-  (9.53e-236, 9.53e-236j)
| (-0.14417440400734677525 + 2.5783879853106783987e-895j)  +/-  (2.93e-251, 2.93e-251j)
| (0.77627808876575741313 + 2.6372035936729632193e-875j)  +/-  (9.65e-233, 9.65e-233j)
| (0.74956408374112603823 - 1.2342861309568746845e-876j)  +/-  (2.52e-233, 2.52e-233j)
| (-0.99466498011324257229 + 6.5870101850984015828e-871j)  +/-  (3.5e-228, 3.5e-228j)
| (-0.80166583569748851717 + 2.5065723853278957539e-876j)  +/-  (3.96e-232, 3.96e-232j)
| (-0.72156946105306217149 - 3.3134452294683246546e-878j)  +/-  (3.71e-234, 3.71e-234j)
| (0.86944955261636686927 - 1.4832953366378303107e-872j)  +/-  (1.67e-230, 1.67e-230j)
| (0.59777243820324080367 - 3.8288371316397520887e-881j)  +/-  (1.82e-237, 1.82e-237j)
| (0.69234204904482971468 + 1.3380186511669583013e-878j)  +/-  (6.21e-235, 6.21e-235j)
| (0.020666901227554299394 - 4.726948571111147592e-899j)  +/-  (3.34e-255, 3.34e-255j)
| (-0.56413297609525103506 - 6.1559498118257002188e-883j)  +/-  (1.87e-238, 1.87e-238j)
| (-0.10315802119235691397 - 2.7925620568135344458e-897j)  +/-  (1.31e-252, 1.31e-252j)
| (0.6619317822595665273 + 4.4535770109624762841e-880j)  +/-  (1.02e-235, 1.02e-235j)
| (0.6303906161279551077 + 2.8510847602810923933e-880j)  +/-  (1.5e-236, 1.5e-236j)
| (-0.69234204904482971468 + 4.196209656447953678e-880j)  +/-  (6.33e-235, 6.33e-235j)
| (-0.6303906161279551077 - 7.0376046258367714189e-881j)  +/-  (1.44e-236, 1.44e-236j)
| (-0.8256839499965558397 - 8.4427315093732059469e-877j)  +/-  (1.53e-231, 1.53e-231j)
| (0.9641197940012136225 + 8.728141795445635364e-882j)  +/-  (1.77e-228, 1.77e-228j)
| (0.49402173581250400172 + 1.6380061558471084568e-907j)  +/-  (1.9e-240, 1.9e-240j)
| (0.26546755510807231045 + 1.6644422673674879624e-914j)  +/-  (1.92e-247, 1.92e-247j)
| (-0.52952970226070871205 + 2.4914969015460051898e-905j)  +/-  (1.85e-239, 1.85e-239j)
| (-0.49402173581250400172 - 4.59149995872046592e-907j)  +/-  (2.27e-240, 2.27e-240j)
| (-0.34417723036263852609 - 6.1563755026837214191e-912j)  +/-  (5.07e-245, 5.07e-245j)
| (0.56413297609525103506 - 1.0818715146978437e-905j)  +/-  (2.15e-238, 2.15e-238j)
| (0.52952970226070871205 + 5.2262427791732990064e-906j)  +/-  (2.25e-239, 2.25e-239j)
| (-0.020666901227554299394 + 4.6726268508230935144e-922j)  +/-  (3.34e-255, 3.34e-255j)
| (-0.45766974151568165475 - 4.0561281929218651522e-907j)  +/-  (1.45e-241, 1.45e-241j)
| (-0.59777243820324080367 + 2.3004587268480472327e-904j)  +/-  (1.81e-237, 1.81e-237j)
| (0.2253985560158062863 + 9.7507153217576367832e-916j)  +/-  (9.33e-249, 9.33e-249j)
| (0.38268343236508977173 - 1.8128779582597003877e-910j)  +/-  (9.55e-244, 9.55e-244j)
| (0.1849444672715583388 - 1.4347357746140033635e-916j)  +/-  (6.09e-250, 6.09e-250j)
| (-0.30508300733554878941 + 1.4649680232894134328e-912j)  +/-  (3.66e-246, 3.66e-246j)
| (-0.42053582614270755375 + 5.3751236414845377934e-909j)  +/-  (1.17e-242, 1.17e-242j)
| (-0.061965394628594665534 - 4.441493475646076051e-920j)  +/-  (6.32e-254, 6.32e-254j)
| (0.45766974151568165475 - 1.4632336203114789624e-907j)  +/-  (1.75e-241, 1.75e-241j)
| (0.42053582614270755375 - 5.5187070791305935925e-909j)  +/-  (1.27e-242, 1.27e-242j)
| (0.98955229332720276916 - 9.5051529142628470025e-915j)  +/-  (4.55e-228, 4.55e-228j)
| (-0.38268343236508977173 - 7.2866668978757502851e-936j)  +/-  (8.79e-244, 8.79e-244j)
| (-0.1849444672715583388 + 1.1392136848768641093e-942j)  +/-  (5.6e-250, 5.6e-250j)
| (0.14417440400734677525 + 6.1340708631463935394e-944j)  +/-  (2.63e-251, 2.63e-251j)
| (0.34417723036263852609 + 2.9585190351249042119e-938j)  +/-  (5.28e-245, 5.28e-245j)
| (0.10315802119235691397 - 3.2561904164434288211e-945j)  +/-  (1.21e-252, 1.21e-252j)
| (-0.2253985560158062863 - 8.1122980412381498742e-942j)  +/-  (9.64e-249, 9.64e-249j)
| (-0.26546755510807231045 + 4.8976088772865668415e-940j)  +/-  (1.94e-247, 1.94e-247j)
| (0.061965394628594665534 + 1.9876094246081309705e-946j)  +/-  (5.19e-254, 5.19e-254j)
| (0.30508300733554878941 + 1.0432294130800005406e-939j)  +/-  (3.19e-246, 3.19e-246j)
-------------------------------------------------
The weights are:
| (0.013157894736842105263 + 7.1199303349798158535e-788j)  +/-  (3.42e-20, 2.81e-127j)
| (0.013157894736842105263 - 1.3830627440399433092e-789j)  +/-  (1.56e-20, 1.29e-127j)
| (0.013157894736842105263 + 1.9514000605862485454e-789j)  +/-  (1.19e-20, 9.76e-128j)
| (0.013157894736842105263 - 2.7466177450948761402e-790j)  +/-  (2.84e-21, 2.33e-128j)
| (0.013157894736842105263 - 4.0944563695692646453e-788j)  +/-  (1.38e-21, 1.14e-128j)
| (0.013157894736842105263 + 5.8951278140938323033e-788j)  +/-  (8.36e-22, 6.87e-129j)
| (0.013157894736842105263 + 8.368582273570257381e-788j)  +/-  (5.01e-22, 4.12e-129j)
| (0.013157894736842105263 - 1.7604416084492382102e-789j)  +/-  (8.79e-22, 7.23e-129j)
| (0.013157894736842105263 + 8.2577353257505203727e-790j)  +/-  (7.61e-23, 6.26e-130j)
| (0.013157894736842105263 - 1.0666173701942288643e-787j)  +/-  (8.33e-23, 6.85e-130j)
| (0.013157894736842105263 + 3.7135677422765695671e-788j)  +/-  (1.83e-23, 1.5e-130j)
| (0.013157894736842105263 - 1.0105812341227691645e-789j)  +/-  (7.77e-23, 6.39e-130j)
| (0.013157894736842105263 - 2.1441153973674085457e-789j)  +/-  (1.78e-23, 1.47e-130j)
| (0.013157894736842105263 + 2.33877881156045459e-789j)  +/-  (3.62e-24, 2.98e-131j)
| (0.013157894736842105263 - 2.6718775520657062433e-787j)  +/-  (2.02e-24, 1.66e-131j)
| (0.013157894736842105263 - 2.8930033385516934538e-788j)  +/-  (7.96e-27, 6.55e-134j)
| (0.013157894736842105263 + 4.5596696184280514434e-788j)  +/-  (8.39e-25, 6.9e-132j)
| (0.013157894736842105263 - 6.4174168927476888873e-790j)  +/-  (5.57e-25, 4.58e-132j)
| (0.013157894736842105263 - 3.3485794873609764593e-789j)  +/-  (8.89e-29, 7.3e-136j)
| (0.013157894736842105263 + 1.5710559270949495723e-789j)  +/-  (7e-25, 5.76e-132j)
| (0.013157894736842105263 - 5.1421475855572483911e-788j)  +/-  (5.8e-27, 4.77e-134j)
| (0.013157894736842105263 + 2.6906508029567117158e-788j)  +/-  (6.59e-30, 5.42e-137j)
| (0.013157894736842105263 + 9.111771028905576043e-791j)  +/-  (8.26e-26, 6.79e-133j)
| (0.013157894736842105263 - 2.5355889166916051901e-789j)  +/-  (1.18e-27, 9.68e-135j)
| (0.013157894736842105263 + 3.1410160395037085702e-789j)  +/-  (1.32e-29, 1.08e-136j)
| (0.013157894736842105263 + 1.1962921446341058037e-789j)  +/-  (5.03e-25, 4.14e-132j)
| (0.013157894736842105263 - 2.2136158486898044418e-788j)  +/-  (7.91e-33, 6.51e-140j)
| (0.013157894736842105263 + 3.1254096085076535214e-788j)  +/-  (2.63e-30, 2.16e-137j)
| (0.013157894736842105263 + 1.0696649210170881563e-787j)  +/-  (1.19e-29, 9.82e-137j)
| (0.013157894736842105263 + 3.9920422553693508766e-789j)  +/-  (7.83e-34, 6.44e-141j)
| (0.013157894736842105263 + 7.6589410130721028967e-789j)  +/-  (2.48e-37, 2.04e-144j)
| (0.013157894736842105263 - 2.5126864695922926301e-788j)  +/-  (5.27e-32, 4.33e-139j)
| (0.013157894736842105263 + 2.3547919169028496036e-788j)  +/-  (1.07e-32, 8.79e-140j)
| (0.013157894736842105263 + 4.5849719227974819099e-790j)  +/-  (2.34e-27, 1.92e-134j)
| (0.013157894736842105263 - 2.936486296016882484e-789j)  +/-  (2.42e-31, 1.99e-138j)
| (0.013157894736842105263 + 3.5594266414457039941e-789j)  +/-  (4.42e-33, 3.63e-140j)
| (0.013157894736842105263 - 3.395458755703276532e-788j)  +/-  (3.41e-31, 2.8e-138j)
| (0.013157894736842105263 - 1.7704844363269534893e-788j)  +/-  (1.19e-37, 9.78e-145j)
| (0.013157894736842105263 + 2.0865163909979901636e-788j)  +/-  (1.8e-35, 1.48e-142j)
| (0.013157894736842105263 + 9.0431864708611934523e-789j)  +/-  (2.21e-41, 1.81e-148j)
| (0.013157894736842105263 - 4.6727154326432537255e-789j)  +/-  (2.46e-39, 2.02e-146j)
| (0.013157894736842105263 - 7.9852464502505061497e-789j)  +/-  (6.77e-41, 5.56e-148j)
| (0.013157894736842105263 - 1.97138193985563943e-788j)  +/-  (9.48e-37, 7.8e-144j)
| (0.013157894736842105263 + 1.8665038849202836144e-788j)  +/-  (1.39e-37, 1.14e-144j)
| (0.013157894736842105263 - 3.7738212513473995232e-789j)  +/-  (2.07e-37, 1.7e-144j)
| (0.013157894736842105263 - 4.2143853702566218973e-789j)  +/-  (4.22e-39, 3.47e-146j)
| (0.013157894736842105263 + 2.734752693694741454e-789j)  +/-  (2.25e-35, 1.85e-142j)
| (0.013157894736842105263 - 6.9111967572598725336e-788j)  +/-  (4.6e-36, 3.78e-143j)
| (0.013157894736842105263 + 1.5249511055156462943e-788j)  +/-  (5.01e-43, 4.12e-150j)
| (0.013157894736842105263 + 1.1634530188865428398e-788j)  +/-  (3.86e-45, 3.17e-152j)
| (0.013157894736842105263 + 4.9093945139271321098e-789j)  +/-  (3.63e-42, 2.99e-149j)
| (0.013157894736842105263 - 5.151584558486877707e-789j)  +/-  (3.4e-43, 2.79e-150j)
| (0.013157894736842105263 - 6.18414204938851531e-789j)  +/-  (1.02e-45, 8.42e-153j)
| (0.013157894736842105263 + 1.6821687225828766237e-788j)  +/-  (2.66e-43, 2.19e-150j)
| (0.013157894736842105263 - 1.6005939958568413198e-788j)  +/-  (4.12e-44, 3.39e-151j)
| (0.013157894736842105263 - 8.6762772763069295311e-789j)  +/-  (3.29e-47, 2.71e-154j)
| (0.013157894736842105263 + 5.3996958048996959755e-789j)  +/-  (6.81e-45, 5.6e-152j)
| (0.013157894736842105263 + 4.4411648494210949844e-789j)  +/-  (2.14e-42, 1.76e-149j)
| (0.013157894736842105263 - 1.114729545533607798e-788j)  +/-  (1.58e-48, 1.3e-155j)
| (0.013157894736842105263 - 1.3272490666401257348e-788j)  +/-  (1.83e-48, 1.5e-155j)
| (0.013157894736842105263 + 1.0684934135515999727e-788j)  +/-  (6.15e-49, 5.05e-156j)
| (0.013157894736842105263 + 6.4607102992762030392e-789j)  +/-  (9.91e-49, 8.15e-156j)
| (0.013157894736842105263 - 5.654169294442573069e-789j)  +/-  (2.26e-47, 1.86e-154j)
| (0.013157894736842105263 + 8.3240127212073800672e-789j)  +/-  (5.69e-49, 4.67e-156j)
| (0.013157894736842105263 - 1.4545549079995463923e-788j)  +/-  (9.87e-49, 8.12e-156j)
| (0.013157894736842105263 + 1.3888212789515679869e-788j)  +/-  (3.32e-49, 2.73e-156j)
| (0.013157894736842105263 + 1.4949715309897474676e-787j)  +/-  (2.41e-47, 1.98e-154j)
| (0.013157894736842105263 + 5.9154802767450156532e-789j)  +/-  (4.26e-49, 3.5e-156j)
| (0.013157894736842105263 - 7.3441548598422561209e-789j)  +/-  (8.28e-51, 6.81e-158j)
| (0.013157894736842105263 - 1.024521599825275639e-788j)  +/-  (1.06e-51, 8.74e-159j)
| (0.013157894736842105263 + 1.2694057876439633125e-788j)  +/-  (1.93e-51, 1.59e-158j)
| (0.013157894736842105263 + 9.8261622664926305826e-789j)  +/-  (4.44e-52, 3.65e-159j)
| (0.013157894736842105263 + 7.0400311412347819872e-789j)  +/-  (3.26e-52, 2.67e-159j)
| (0.013157894736842105263 - 6.7457880258702065223e-789j)  +/-  (3.49e-52, 2.86e-159j)
| (0.013157894736842105263 - 9.4260107245395795572e-789j)  +/-  (1.06e-52, 8.82e-160j)
| (0.013157894736842105263 - 1.2149161877700300459e-788j)  +/-  (8.83e-53, 6.9e-160j)
