Starting with polynomial:
P : 33554432*t^26 - 218103808*t^24 + 627048448*t^22 - 1049624576*t^20 + 1133117440*t^18 - 825556992*t^16 + 412778496*t^14 - 141213696*t^12 + 32361472*t^10 - 4759040*t^8 + 416416*t^6 - 18928*t^4 + 338*t^2 - 1
Extension levels are: 26 52
-------------------------------------------------
Trying to find an order 52 Kronrod extension for:
P1 : 33554432*t^26 - 218103808*t^24 + 627048448*t^22 - 1049624576*t^20 + 1133117440*t^18 - 825556992*t^16 + 412778496*t^14 - 141213696*t^12 + 32361472*t^10 - 4759040*t^8 + 416416*t^6 - 18928*t^4 + 338*t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 33554432*t^78 - 654311424*t^76 + 6134169600*t^74 - 36818649088*t^72 + 158967005184*t^70 - 525897695232*t^68 + 1386568228864*t^66 - 2992141701120*t^64 + 5385855062016*t^62 - 8200202835968*t^60 + 10672322808576*t^58 - 11968351155072*t^56 + 11635896956320*t^54 - 9852644109168*t^52 + 58324134324807/8*t^50 - 75605359309935/16*t^48 + 343882440732285/128*t^46 - 343219215195675/256*t^44 + 1202538435463365/2048*t^42 - 923626755516465/4096*t^40 + 1242118740177315/16384*t^38 - 729498307723185/32768*t^36 + 2984311258867575/524288*t^34 - 1323477166976055/1048576*t^32 + 506515952793305/2097152*t^30 - 166290142992519/4194304*t^28 + 185969449855539/33554432*t^26 - 43892571679775/67108864*t^24 + 17306213976597/268435456*t^22 - 2813325424767/536870912*t^20 + 5939242563397/17179869184*t^18 - 623681614413/34359738368*t^16 + 406748878965/549755813888*t^14 - 24925352179/1099511627776*t^12 + 4398591561/8796093022208*t^10 - 131519349/17592186044416*t^8 + 4871087/70368744177664*t^6 - 48165/140737488355328*t^4 + 1521/2251799813685248*t^2 - 1/4503599627370496
-------------------------------------------------
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:
| (0.99817555422331747084 - 2.1391913279281665397e-771j)  +/-  (1.6e-227, 1.6e-227j)
| (-0.48245941480719334593 - 4.8068788843966509166e-787j)  +/-  (2.1e-240, 2.1e-240j)
| (-0.95472086650854562606 + 1.2823447676156729366e-771j)  +/-  (7.13e-228, 7.13e-228j)
| (-0.99493483506264562328 + 1.3704355843207233566e-781j)  +/-  (2.56e-227, 2.56e-227j)
| (0.94196734599126486468 + 7.9594502740654992563e-794j)  +/-  (3.98e-228, 3.98e-228j)
| (0.92768595099414288028 - 5.2854574282073483194e-794j)  +/-  (2.05e-228, 2.05e-228j)
| (0.99979722898485011697 - 5.5811873224153726547e-791j)  +/-  (5.8e-228, 5.8e-228j)
| (-0.92768595099414288028 - 4.8344419808715945373e-796j)  +/-  (2.13e-228, 2.13e-228j)
| (0.98361990694714358842 - 2.0571627017001103294e-796j)  +/-  (2.34e-227, 2.34e-227j)
| (-0.99979722898485011697 - 6.4452043873374419682e-807j)  +/-  (6.43e-228, 6.43e-228j)
| (0.85578127230144752264 + 2.2097142245979054258e-828j)  +/-  (4.11e-230, 4.11e-230j)
| (0.99008032796116404265 + 1.797923688012573188e-824j)  +/-  (2.57e-227, 2.57e-227j)
| (-0.89463463610514737239 + 7.4057573326747183836e-824j)  +/-  (3.7e-229, 3.7e-229j)
| (-0.87591832556688785493 - 4.5660077463233809214e-828j)  +/-  (1.26e-229, 1.26e-229j)
| (0.97556405084709386164 - 5.9210391134713629211e-827j)  +/-  (1.76e-227, 1.76e-227j)
| (0.87591832556688785493 - 1.4822144713244255553e-832j)  +/-  (1.2e-229, 1.2e-229j)
| (0.89463463610514737239 - 1.2591534012782051245e-830j)  +/-  (3.2e-229, 3.2e-229j)
| (0.99493483506264562328 - 1.6274346496652010905e-828j)  +/-  (2.4e-227, 2.4e-227j)
| (-0.7871834806090501818 - 2.4419404947099377493e-832j)  +/-  (8.14e-232, 8.14e-232j)
| (-0.91189984599209007718 - 9.6464790142369799157e-827j)  +/-  (8.66e-229, 8.66e-229j)
| (0.96592582628906828675 - 6.1204203372743931458e-830j)  +/-  (1.26e-227, 1.26e-227j)
| (0.73500563559632856751 + 7.7823175777806212069e-836j)  +/-  (3.15e-233, 3.15e-233j)
| (0.8113778385565730064 + 1.9494426457104453612e-833j)  +/-  (3.23e-231, 3.23e-231j)
| (-0.83425613868286131895 + 1.57166024499918331e-832j)  +/-  (1.15e-230, 1.15e-230j)
| (-0.85578127230144752264 + 4.4518015590365525193e-831j)  +/-  (4.54e-230, 4.54e-230j)
| (-0.99817555422331747084 + 4.4809179368826206676e-828j)  +/-  (1.85e-227, 1.85e-227j)
| (0.7071067811865475244 - 8.9521468476175320853e-850j)  +/-  (6.7e-234, 6.7e-234j)
| (0.7871834806090501818 - 2.4065433078036138773e-847j)  +/-  (8.18e-232, 8.18e-232j)
| (-0.98361990694714358842 - 2.5673018979839565955e-840j)  +/-  (2.18e-227, 2.18e-227j)
| (-0.64791539538053876978 - 2.8549085787497293504e-859j)  +/-  (1.43e-235, 1.43e-235j)
| (-0.97556405084709386164 - 4.2379541991155918184e-850j)  +/-  (1.78e-227, 1.78e-227j)
| (0.83425613868286131895 + 7.6352471906315782169e-864j)  +/-  (1.17e-230, 1.17e-230j)
| (0.67806099699189088499 - 3.0676627532696793271e-867j)  +/-  (1.03e-234, 1.03e-234j)
| (0.10052200743551707078 - 1.5306447686496419936e-884j)  +/-  (1.22e-252, 1.22e-252j)
| (-0.7071067811865475244 + 3.2241352803546471331e-866j)  +/-  (5.84e-234, 5.84e-234j)
| (-0.73500563559632856751 - 8.2551854790375091362e-865j)  +/-  (3.42e-233, 3.42e-233j)
| (0.91189984599209007718 + 1.1229883399099298456e-860j)  +/-  (8.42e-229, 8.42e-229j)
| (0.58452202960988882686 + 4.6383352321950633561e-870j)  +/-  (2.32e-237, 2.32e-237j)
| (0.25881904510252076235 - 1.81333119792446417e-879j)  +/-  (1.94e-247, 1.94e-247j)
| (-0.8113778385565730064 + 1.9531755581975549455e-862j)  +/-  (3.6e-231, 3.6e-231j)
| (-0.58452202960988882686 + 1.639444741665882422e-869j)  +/-  (2.58e-237, 2.58e-237j)
| (-0.76171230817735912451 - 5.3955273327121627164e-864j)  +/-  (1.63e-232, 1.63e-232j)
| (0.76171230817735912451 + 5.8193460512270490249e-866j)  +/-  (1.67e-232, 1.67e-232j)
| (0.61671887262854305846 + 1.5097514780149038935e-868j)  +/-  (1.92e-236, 1.92e-236j)
| (-0.94196734599126486468 + 3.3330525523693595232e-858j)  +/-  (4.35e-228, 4.35e-228j)
| (-0.55137708972169170284 + 2.9395537509400503675e-870j)  +/-  (2.39e-238, 2.39e-238j)
| (-0.67806099699189088499 - 4.2324877632826551577e-867j)  +/-  (9.98e-235, 9.98e-235j)
| (0.55137708972169170284 + 1.9164277650365114153e-871j)  +/-  (2.76e-238, 2.76e-238j)
| (0.48245941480719334593 + 2.5448028170435425271e-872j)  +/-  (2.44e-240, 2.44e-240j)
| (-0.96592582628906828675 + 1.3563565851302539711e-857j)  +/-  (1.25e-227, 1.25e-227j)
| (-0.61671887262854305846 - 9.3837077605181039613e-879j)  +/-  (1.99e-236, 1.99e-236j)
| (-0.51733781417765677104 + 4.1523148503288806301e-882j)  +/-  (2.4e-239, 2.4e-239j)
| (-0.99008032796116404265 + 1.0968877404270553565e-877j)  +/-  (2.35e-227, 2.35e-227j)
| (0.64791539538053876978 - 5.5949160509568298716e-889j)  +/-  (1.63e-235, 1.63e-235j)
| (0.51733781417765677104 - 9.9213581043188003222e-893j)  +/-  (2.46e-239, 2.46e-239j)
| (-0.020137053265440332284 - 2.1678143217720100976e-908j)  +/-  (3.76e-255, 3.76e-255j)
| (-0.446798464501625768 - 1.5561898459339432299e-894j)  +/-  (2.04e-241, 2.04e-241j)
| (-0.33570451156660481864 + 9.1448843834320974762e-899j)  +/-  (6.25e-245, 6.25e-245j)
| (0.21971523091221705855 - 1.5524770715660063785e-901j)  +/-  (1.08e-248, 1.08e-248j)
| (0.37336145533262098419 - 6.124530063493671498e-897j)  +/-  (9.3e-244, 9.3e-244j)
| (0.95472086650854562606 - 2.9750940749683373033e-902j)  +/-  (7.15e-228, 7.15e-228j)
| (-0.29750305385520297665 + 6.9924556991640479146e-923j)  +/-  (3.28e-246, 3.28e-246j)
| (-0.41041280545275679642 - 7.389745445592917854e-920j)  +/-  (1.39e-242, 1.39e-242j)
| (-0.060378497422286053438 - 1.4101641903835889804e-931j)  +/-  (5.85e-254, 5.85e-254j)
| (0.41041280545275679642 + 1.537518534087639582e-919j)  +/-  (1.56e-242, 1.56e-242j)
| (0.446798464501625768 + 2.4338847228488188181e-918j)  +/-  (1.75e-241, 1.75e-241j)
| (-0.25881904510252076235 - 5.0363664512358529794e-925j)  +/-  (2.36e-247, 2.36e-247j)
| (-0.37336145533262098419 + 1.1346551018997688484e-920j)  +/-  (1.04e-243, 1.04e-243j)
| (-0.14050247038509269848 + 7.9015037714196810956e-929j)  +/-  (2.71e-251, 2.71e-251j)
| (0.18025503781390574017 + 3.6419798761535033248e-927j)  +/-  (4.5e-250, 4.5e-250j)
| (0.33570451156660481864 + 9.7687156376758979451e-922j)  +/-  (5.75e-245, 5.75e-245j)
| (0.060378497422286053438 - 3.3090781884093774855e-932j)  +/-  (4.55e-254, 4.55e-254j)
| (-0.18025503781390574017 - 2.3069166636866106898e-927j)  +/-  (5.7e-250, 5.7e-250j)
| (-0.21971523091221705855 - 6.0530788974484694096e-926j)  +/-  (9.91e-249, 9.91e-249j)
| (0.020137053265440332284 - 4.6761844951828042316e-933j)  +/-  (3.23e-255, 3.23e-255j)
| (0.29750305385520297665 - 4.3289047266703012426e-924j)  +/-  (3.17e-246, 3.17e-246j)
| (0.14050247038509269848 + 2.6829736114105177218e-928j)  +/-  (2.93e-251, 2.93e-251j)
| (-0.10052200743551707078 + 2.3364372564402195704e-929j)  +/-  (1.22e-252, 1.22e-252j)
-------------------------------------------------
The weights are:
| (0.012820512820512820513 + 3.7529233118634399514e-771j)  +/-  (1.04e-17, 1.84e-123j)
| (0.012820512820512820513 + 1.6621844757850716107e-772j)  +/-  (4.87e-18, 8.66e-124j)
| (0.012820512820512820513 + 1.9472768696734898229e-773j)  +/-  (2.04e-18, 3.64e-124j)
| (0.012820512820512820513 + 1.610435745300720728e-772j)  +/-  (1.57e-18, 2.79e-124j)
| (0.012820512820512820513 - 2.7030964388430506127e-771j)  +/-  (6.75e-19, 1.2e-124j)
| (0.012820512820512820513 + 2.3949369969327624008e-771j)  +/-  (5.23e-19, 9.31e-125j)
| (0.012820512820512820513 + 5.6409041843291631392e-771j)  +/-  (4.69e-19, 8.35e-125j)
| (0.012820512820512820513 + 6.7511373140730481142e-772j)  +/-  (6.93e-21, 1.23e-126j)
| (0.012820512820512820513 - 5.6199398743260603237e-771j)  +/-  (7.29e-20, 1.3e-125j)
| (0.012820512820512820513 + 2.9264893192731459421e-773j)  +/-  (6.95e-23, 1.24e-128j)
| (0.012820512820512820513 + 1.6344772705806654666e-771j)  +/-  (4.58e-22, 8.15e-128j)
| (0.012820512820512820513 + 7.8796641749899831318e-771j)  +/-  (1.06e-19, 1.89e-125j)
| (0.012820512820512820513 + 3.0369792586094915406e-772j)  +/-  (1.04e-22, 1.84e-128j)
| (0.012820512820512820513 - 2.2139472067942106765e-772j)  +/-  (5.8e-23, 1.03e-128j)
| (0.012820512820512820513 + 4.4074164080081976744e-771j)  +/-  (7.65e-21, 1.36e-126j)
| (0.012820512820512820513 - 1.7779353047616282653e-771j)  +/-  (4.55e-23, 8.09e-129j)
| (0.012820512820512820513 + 1.9467227456295913588e-771j)  +/-  (6.13e-23, 1.09e-128j)
| (0.012820512820512820513 - 1.4086550245067603712e-770j)  +/-  (1.17e-20, 2.08e-126j)
| (0.012820512820512820513 - 4.6516155208397347835e-773j)  +/-  (5.05e-28, 8.97e-134j)
| (0.012820512820512820513 - 4.3204380584000863404e-772j)  +/-  (3.84e-26, 6.83e-132j)
| (0.012820512820512820513 - 3.6379340305147183901e-771j)  +/-  (7.79e-22, 1.39e-127j)
| (0.012820512820512820513 - 1.1481462786062156668e-771j)  +/-  (6.26e-28, 1.11e-133j)
| (0.012820512820512820513 + 1.4030636999761500968e-771j)  +/-  (3.15e-26, 5.61e-132j)
| (0.012820512820512820513 - 1.1625778109369032977e-772j)  +/-  (3.42e-28, 6.09e-134j)
| (0.012820512820512820513 + 1.6220030066866835656e-772j)  +/-  (9.7e-28, 1.72e-133j)
| (0.012820512820512820513 - 9.0520716171547628936e-773j)  +/-  (6.64e-29, 1.18e-134j)
| (0.012820512820512820513 + 1.079960492018838492e-771j)  +/-  (2.27e-30, 4.03e-136j)
| (0.012820512820512820513 - 1.3081161725591143137e-771j)  +/-  (8.1e-29, 1.44e-134j)
| (0.012820512820512820513 + 3.8599968650721915955e-772j)  +/-  (7.93e-30, 1.41e-135j)
| (0.012820512820512820513 - 7.2991303943919586982e-773j)  +/-  (3.01e-34, 5.36e-140j)
| (0.012820512820512820513 - 6.3308958884720054811e-772j)  +/-  (6.18e-30, 1.1e-135j)
| (0.012820512820512820513 - 1.5108544452532375874e-771j)  +/-  (2.87e-28, 5.11e-134j)
| (0.012820512820512820513 - 1.0180607072822892585e-771j)  +/-  (6.38e-32, 1.13e-137j)
| (0.012820512820512820513 - 4.5134983666074247506e-772j)  +/-  (2.21e-37, 3.93e-143j)
| (0.012820512820512820513 - 3.054039574506714343e-773j)  +/-  (5.84e-34, 1.04e-139j)
| (0.012820512820512820513 + 7.1636928027879600302e-774j)  +/-  (1.18e-33, 2.1e-139j)
| (0.012820512820512820513 - 2.1486026502624551003e-771j)  +/-  (4.52e-29, 8.04e-135j)
| (0.012820512820512820513 + 8.6183229484436887561e-772j)  +/-  (6.01e-36, 1.07e-141j)
| (0.012820512820512820513 - 5.4943518514372020232e-772j)  +/-  (3.73e-39, 6.63e-145j)
| (0.012820512820512820513 + 7.8618132310481822413e-773j)  +/-  (6.96e-33, 1.24e-138j)
| (0.012820512820512820513 - 1.1174413639872684146e-772j)  +/-  (2.5e-37, 4.44e-143j)
| (0.012820512820512820513 + 1.828022936070473868e-773j)  +/-  (7.97e-34, 1.42e-139j)
| (0.012820512820512820513 + 1.2237332674300733726e-771j)  +/-  (4.44e-33, 7.89e-139j)
| (0.012820512820512820513 - 9.0967167028605347991e-772j)  +/-  (1.77e-36, 3.16e-142j)
| (0.012820512820512820513 - 1.3760124162383553748e-771j)  +/-  (8.79e-34, 1.56e-139j)
| (0.012820512820512820513 + 1.3024984594604175161e-772j)  +/-  (1.83e-38, 3.25e-144j)
| (0.012820512820512820513 + 5.235932881466949726e-773j)  +/-  (3.46e-36, 6.16e-142j)
| (0.012820512820512820513 - 8.1751605594688737736e-772j)  +/-  (2.94e-39, 5.22e-145j)
| (0.012820512820512820513 - 7.3780174942552146829e-772j)  +/-  (4.06e-41, 7.21e-147j)
| (0.012820512820512820513 + 1.3363082650685641693e-771j)  +/-  (9.47e-35, 1.68e-140j)
| (0.012820512820512820513 + 9.271464486991033481e-773j)  +/-  (1.13e-37, 2e-143j)
| (0.012820512820512820513 - 1.4836975030048153713e-772j)  +/-  (6.64e-40, 1.18e-145j)
| (0.012820512820512820513 - 2.5168065595059490334e-772j)  +/-  (2.8e-35, 4.98e-141j)
| (0.012820512820512820513 + 9.615441128857732815e-772j)  +/-  (1.62e-38, 2.88e-144j)
| (0.012820512820512820513 + 7.7629384433761842125e-772j)  +/-  (4.88e-41, 8.68e-147j)
| (0.012820512820512820513 + 3.8685082366377283252e-772j)  +/-  (2.3e-46, 4.09e-152j)
| (0.012820512820512820513 - 1.8389332476058297703e-772j)  +/-  (1.44e-42, 2.56e-148j)
| (0.012820512820512820513 + 2.3667698055202415183e-772j)  +/-  (3e-45, 5.34e-151j)
| (0.012820512820512820513 + 5.2333213868177140066e-772j)  +/-  (2.71e-46, 4.82e-152j)
| (0.012820512820512820513 + 6.3580760337747272375e-772j)  +/-  (1.45e-45, 2.58e-151j)
| (0.012820512820512820513 + 3.1011546236313281837e-771j)  +/-  (1.42e-39, 2.52e-145j)
| (0.012820512820512820513 - 2.5442099928836935501e-772j)  +/-  (2e-46, 3.55e-152j)
| (0.012820512820512820513 + 2.0147903119026206464e-772j)  +/-  (1.54e-44, 2.74e-150j)
| (0.012820512820512820513 - 3.6664147745418023496e-772j)  +/-  (3.03e-48, 5.38e-154j)
| (0.012820512820512820513 - 6.6780800012516170036e-772j)  +/-  (6.22e-46, 1.11e-151j)
| (0.012820512820512820513 + 7.0172891543231297565e-772j)  +/-  (2.18e-45, 3.87e-151j)
| (0.012820512820512820513 + 2.7234294939929089387e-772j)  +/-  (3.08e-48, 5.48e-154j)
| (0.012820512820512820513 - 2.1905080102956999204e-772j)  +/-  (1.72e-46, 3.06e-152j)
| (0.012820512820512820513 - 3.2775333678667787556e-772j)  +/-  (8.07e-50, 1.44e-155j)
| (0.012820512820512820513 - 4.9835522407012802416e-772j)  +/-  (7.12e-50, 1.27e-155j)
| (0.012820512820512820513 - 6.0552620249737352174e-772j)  +/-  (5.69e-49, 1.01e-154j)
| (0.012820512820512820513 + 4.2913171293587708794e-772j)  +/-  (1.44e-50, 2.57e-156j)
| (0.012820512820512820513 + 3.089519536430661548e-772j)  +/-  (1.54e-50, 2.73e-156j)
| (0.012820512820512820513 - 2.9050088907097100044e-772j)  +/-  (2.6e-50, 4.63e-156j)
| (0.012820512820512820513 - 4.0765737527999774091e-772j)  +/-  (3.04e-51, 5.45e-157j)
| (0.012820512820512820513 + 5.767872512181377514e-772j)  +/-  (3.27e-51, 5.86e-157j)
| (0.012820512820512820513 + 4.74394256780827505e-772j)  +/-  (1.63e-51, 2.96e-157j)
| (0.012820512820512820513 + 3.469631897716048635e-772j)  +/-  (1.45e-51, 2.49e-157j)
