Starting with polynomial:
P : t
Extension levels are: 1 50
-------------------------------------------------
Trying to find an order 50 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^51 - 1275/101*t^49 + 83300/1111*t^47 - 90047300/323301*t^45 + 135070950/186143*t^43 - 8131271190/5770433*t^41 + 158753389900/75015629*t^39 - 68037167100/27029923*t^37 + 1888031387025/783867767*t^35 - 1468468856575/783867767*t^33 + 77535155627160/65061024661*t^31 - 11747750852600/18888684579*t^29 + 41117127984100/154366146387*t^27 - 5873875426300/62889911491*t^25 + 1678250121800/62889911491*t^23 - 7719950560280/1252080965139*t^21 + 33774783701225/29632582841623*t^19 - 4923689695575/29632582841623*t^17 + 111603633099700/5956149151166223*t^15 - 41117127984100/25809979655053633*t^13 + 587387542630/5956149151166223*t^11 - 4615187834950/1089975294663418809*t^9 + 839125060900/7145393598349078859*t^7 - 255385888100/135762478368632498321*t^5 + 63846472025/4480161786164872444593*t^3 - 2553858881/79149524888912746521143*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: 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:
| (0.99890999084890349517 - 1.585562150986149792e-857j)  +/-  (3.56e-238, 3.56e-238j)
| (-0.99890999084890349517 - 3.5164543689841095803e-854j)  +/-  (3.57e-238, 3.57e-238j)
| (-0.91637386230978023082 - 3.9459354378744449977e-866j)  +/-  (4.3e-238, 4.3e-238j)
| (0.97390336801932386723 - 5.996252371420697103e-870j)  +/-  (1.66e-237, 1.66e-237j)
| (0.91637386230978023082 + 4.1053117586320131878e-872j)  +/-  (4.19e-238, 4.19e-238j)
| (0.93906754400296238344 + 1.2600899046627829734e-872j)  +/-  (8.34e-238, 8.34e-238j)
| (0.82823976382306483285 - 1.7329557672694859207e-874j)  +/-  (2.4e-239, 2.4e-239j)
| (-0.82823976382306483285 - 1.1040032003385015698e-872j)  +/-  (2.32e-239, 2.32e-239j)
| (-0.86085671118229237147 + 5.6066615876220034884e-876j)  +/-  (7.99e-239, 7.99e-239j)
| (-0.95826784861390819456 + 3.7517407573525677629e-887j)  +/-  (1.41e-237, 1.41e-237j)
| (0.89027121802952730328 - 4.3812916185387321271e-905j)  +/-  (1.91e-238, 1.91e-238j)
| (0.62175570460072327376 + 5.7817780720643744937e-910j)  +/-  (7.65e-243, 7.65e-243j)
| (-0.93906754400296238344 + 1.7047826145302537576e-902j)  +/-  (8.44e-238, 8.44e-238j)
| (-0.89027121802952730328 + 8.7028613899399767749e-913j)  +/-  (1.97e-238, 1.97e-238j)
| (-0.97390336801932386723 + 7.9788522092556194863e-922j)  +/-  (1.66e-237, 1.66e-237j)
| (0.86085671118229237147 + 1.4778648375542926083e-936j)  +/-  (7.4e-239, 7.4e-239j)
| (0.71244445757703664458 - 1.6435278086735913987e-939j)  +/-  (3.14e-241, 3.14e-241j)
| (0.99426126043675257462 + 9.0564690386777580708e-934j)  +/-  (1.13e-237, 1.13e-237j)
| (-0.75389535448537552576 - 8.4967996494009736388e-942j)  +/-  (1.49e-240, 1.49e-240j)
| (-0.99426126043675257462 + 1.0127325989380519632e-944j)  +/-  (1.05e-237, 1.05e-237j)
| (0.95826784861390819456 + 4.6843885496410660029e-960j)  +/-  (1.21e-237, 1.21e-237j)
| (0.75389535448537552576 - 5.0720632197468420569e-966j)  +/-  (1.53e-240, 1.53e-240j)
| (-0.98591599173590299658 - 1.1224959543547201058e-964j)  +/-  (1.52e-237, 1.52e-237j)
| (-0.79254171209938120523 - 6.7241935424829755679e-975j)  +/-  (6.6e-240, 6.6e-240j)
| (-0.71244445757703664458 - 3.7038248853344660432e-976j)  +/-  (3e-241, 3e-241j)
| (0.30028760633533193953 + 6.7802558697357870661e-984j)  +/-  (3.1e-249, 3.1e-249j)
| (0.79254171209938120523 + 1.8015148950952448497e-972j)  +/-  (6.41e-240, 6.41e-240j)
| (0.35787645668840950978 - 4.5092974001029549951e-982j)  +/-  (5.09e-248, 5.09e-248j)
| (0.98591599173590299658 + 5.4156472803631284344e-979j)  +/-  (1.65e-237, 1.65e-237j)
| (-0.62175570460072327376 - 1.6844569752450779937e-983j)  +/-  (7.67e-243, 7.67e-243j)
| (-0.24158166644779870385 + 3.2061820523858576007e-993j)  +/-  (1.7e-250, 1.7e-250j)
| (0.41413398322630387794 + 1.7355341306322786381e-989j)  +/-  (7.64e-247, 7.64e-247j)
| (0.66834322117537008686 - 1.0085906372550311893e-985j)  +/-  (5.53e-242, 5.53e-242j)
| (-0.41413398322630387794 - 6.5649768934370589131e-989j)  +/-  (6.93e-247, 6.93e-247j)
| (-0.66834322117537008686 + 8.6032275733179680872e-987j)  +/-  (5.03e-242, 5.03e-242j)
| (-0.46885090428604106361 + 1.238384874076614617e-990j)  +/-  (8.14e-246, 8.14e-246j)
| (-1.2407689033912810068e-1008 + 1.0721464336673199313e-1007j)  +/-  (5.5e-1006, 5.5e-1006j)
| (0.57285521635130383652 - 3.9487428764434931586e-990j)  +/-  (8.63e-244, 8.63e-244j)
| (0.12169542101888876696 + 1.0838714109942903413e-999j)  +/-  (4.72e-253, 4.72e-253j)
| (-0.18197702695707754532 + 2.7244421036448115894e-998j)  +/-  (1.02e-251, 1.02e-251j)
| (-0.57285521635130383652 + 7.3180978650868563932e-990j)  +/-  (8.55e-244, 8.55e-244j)
| (-0.12169542101888876696 - 4.7633899643280919253e-1002j)  +/-  (4.72e-253, 4.72e-253j)
| (0.24158166644779870385 - 7.4880469458102570293e-999j)  +/-  (1.69e-250, 1.69e-250j)
| (0.52182366936618584251 + 3.4761946410515702554e-993j)  +/-  (8.94e-245, 8.94e-245j)
| (-0.060961100150578724734 + 8.6701599339541801374e-1003j)  +/-  (2.55e-254, 2.55e-254j)
| (-0.52182366936618584251 - 6.5037288273624739215e-995j)  +/-  (9.45e-245, 9.45e-245j)
| (-0.35787645668840950978 + 8.6721030226844742906e-999j)  +/-  (5.35e-248, 5.35e-248j)
| (0.18197702695707754532 + 8.0545900379269382788e-1004j)  +/-  (9.49e-252, 9.49e-252j)
| (0.46885090428604106361 + 3.698434082033564259e-997j)  +/-  (8.75e-246, 8.75e-246j)
| (0.060961100150578724734 - 5.0093184736357866252e-1006j)  +/-  (2.21e-254, 2.21e-254j)
| (-0.30028760633533193953 - 4.245695932473590712e-1000j)  +/-  (3.31e-249, 3.31e-249j)
-------------------------------------------------
The weights are:
| (0.0027968071710898955755 - 2.8897349622058678207e-857j)  +/-  (7.9e-62, 3.27e-175j)
| (0.0027968071710898955755 - 4.5088965486729603796e-854j)  +/-  (2.5e-62, 1.04e-175j)
| (0.024413300573781434273 - 3.0192314905022152795e-854j)  +/-  (2.47e-62, 1.02e-175j)
| (0.013832634006477822297 + 5.1989537035737770349e-856j)  +/-  (1.63e-62, 6.75e-176j)
| (0.024413300573781434273 - 1.2875014237214296594e-855j)  +/-  (5.42e-63, 2.25e-176j)
| (0.02095998840170321058 + 1.0081003035283590587e-855j)  +/-  (6.21e-63, 2.57e-176j)
| (0.034178693204188336236 + 2.2480425652782022618e-855j)  +/-  (4.72e-64, 1.96e-177j)
| (0.034178693204188336236 + 2.418266254597031292e-854j)  +/-  (2.96e-64, 1.23e-177j)
| (0.031034971290160008454 - 2.5868816778659983057e-854j)  +/-  (3.35e-64, 1.39e-177j)
| (0.01742871472340105226 - 3.6995424403617692684e-854j)  +/-  (2.86e-65, 1.19e-178j)
| (0.027775798594162477196 + 1.5881366501015304493e-855j)  +/-  (1.51e-64, 6.25e-178j)
| (0.047773626240623102 - 4.2001214522647350814e-855j)  +/-  (9.83e-67, 4.07e-180j)
| (0.02095998840170321058 + 3.3130309798353632042e-854j)  +/-  (4.21e-65, 1.75e-178j)
| (0.027775798594162477196 + 2.7834540872214863019e-854j)  +/-  (3.39e-65, 1.4e-178j)
| (0.013832634006477822297 + 4.252796960249994027e-854j)  +/-  (4.78e-66, 1.98e-179j)
| (0.031034971290160008454 - 1.9086808682177951558e-855j)  +/-  (1.58e-66, 6.56e-180j)
| (0.042802607997880086654 - 3.3706789968784229962e-855j)  +/-  (1.68e-68, 6.96e-182j)
| (0.0065003377832526002921 + 1.3907390944697886284e-856j)  +/-  (3.03e-67, 1.26e-180j)
| (0.040073476285496453187 + 2.1384318225051653765e-854j)  +/-  (6.14e-69, 2.54e-182j)
| (0.0065003377832526002921 + 7.3919153668978861544e-854j)  +/-  (4e-67, 1.66e-180j)
| (0.01742871472340105226 - 7.5156127525485569117e-856j)  +/-  (2.48e-67, 1.03e-180j)
| (0.040073476285496453187 + 2.9797372276985927218e-855j)  +/-  (2.93e-69, 1.22e-182j)
| (0.010185191297821729939 - 5.1749792124272107663e-854j)  +/-  (5.81e-67, 2.41e-180j)
| (0.037195268923260292843 - 2.2704029273854742616e-854j)  +/-  (4.36e-69, 1.8e-182j)
| (0.042802607997880086654 - 2.0189410337575070843e-854j)  +/-  (7.37e-71, 3.05e-184j)
| (0.058183473982592140598 - 7.0495979952466063341e-855j)  +/-  (9.37e-75, 3.88e-188j)
| (0.037195268923260292843 - 2.6053141207292503272e-855j)  +/-  (1.86e-70, 7.72e-184j)
| (0.0569585077202586621 + 6.5375815494569752434e-855j)  +/-  (9.19e-75, 3.81e-188j)
| (0.010185191297821729939 - 3.1545582458607221035e-856j)  +/-  (7.96e-70, 3.3e-183j)
| (0.047773626240623102 - 1.8081437323958401537e-854j)  +/-  (1.04e-74, 4.3e-188j)
| (0.059191993922961543784 + 1.2416361016323050661e-854j)  +/-  (3.21e-77, 1.33e-190j)
| (0.055521652095738693017 - 6.0404746025673789892e-855j)  +/-  (4.29e-75, 1.78e-188j)
| (0.045372511407650068748 + 3.7776156090120101782e-855j)  +/-  (7.09e-73, 2.94e-186j)
| (0.055521652095738693017 - 1.4609306062663630129e-854j)  +/-  (3.98e-77, 1.65e-190j)
| (0.045372511407650068748 + 1.9094578880260864755e-854j)  +/-  (6.88e-75, 2.85e-188j)
| (0.053878252313045561434 + 1.5407542693984456811e-854j)  +/-  (6.28e-77, 2.6e-190j)
| (0.06099892484120588016 + 9.8460814415187119856e-855j)  +/-  (3.68e-79, 1.52e-192j)
| (0.04999702015005740978 + 4.6378624092522170216e-855j)  +/-  (1.73e-76, 7.16e-190j)
| (0.060545506934737795138 + 8.6780594541272116092e-855j)  +/-  (3.53e-79, 1.46e-192j)
| (0.05998031577750325209 - 1.174070803149617496e-854j)  +/-  (2.21e-79, 9.15e-193j)
| (0.04999702015005740978 + 1.7136022498442575686e-854j)  +/-  (3.79e-78, 1.57e-191j)
| (0.060545506934737795138 + 1.1088336826514312252e-854j)  +/-  (9.34e-80, 3.87e-193j)
| (0.059191993922961543784 + 7.57675734083668429e-855j)  +/-  (5.82e-80, 2.41e-193j)
| (0.052034421936697087564 - 5.0905924418037468624e-855j)  +/-  (2.91e-79, 1.2e-192j)
| (0.060885464844856343881 - 1.0457319750516278413e-854j)  +/-  (3.34e-80, 1.38e-193j)
| (0.052034421936697087564 - 1.6247544154933055379e-854j)  +/-  (6.77e-80, 2.79e-193j)
| (0.0569585077202586621 + 1.3847456389321785947e-854j)  +/-  (9.38e-81, 3.9e-194j)
| (0.05998031577750325209 - 8.1194141585655476063e-855j)  +/-  (3.77e-81, 1.6e-194j)
| (0.053878252313045561434 + 5.558152948624974615e-855j)  +/-  (5.23e-81, 2.19e-194j)
| (0.060885464844856343881 - 9.2533398363516900382e-855j)  +/-  (2.41e-81, 1.04e-194j)
| (0.058183473982592140598 - 1.3117650818047652171e-854j)  +/-  (1.81e-81, 6.98e-195j)
