Starting with polynomial:
P : 2*t
Extension levels are: 1 66
-------------------------------------------------
Trying to find an order 66 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^67 - 2211*t^65 + 1149720*t^63 - 374233860*t^61 + 85605995475*t^59 - 29294371651545/2*t^57 + 3896151429655485/2*t^55 - 826540696148342175/4*t^53 + 569486539646207758575/32*t^51 - 80677259783212765798125/64*t^49 + 2371911437626455314464875/32*t^47 - 233094205824927108630593625/64*t^45 + 38460543961112972924047948125/256*t^43 - 2671528553606539580801176704375/512*t^41 + 78237621927048659152034460628125/512*t^39 - 3864938523196203762110502355029375/1024*t^37 + 1287024528224335852782797284224781875/16384*t^35 - 45045858487851754847397904947867365625/32768*t^33 + 165168147788789767773792318142180340625/8192*t^31 - 4042273090620381158674390944005992546875/16384*t^29 + 164116287479187475042180272326643297403125/65536*t^27 - 2743086519294990654276441694602466542309375/131072*t^25 + 18702862631556754460975738826834999152109375/131072*t^23 - 205731488947124299070733127095184990673203125/262144*t^21 + 7200602113149350467475659448331474673562109375/2097152*t^19 - 49252118453941557197533510626587286767164828125/4194304*t^17 + 64406616439769728642928436973229528849369390625/2097152*t^15 - 250470175043548944722499477118114834414214296875/4194304*t^13 + 1395476689528344120596782801086639791736336796875/16777216*t^11 - 2646593721519273332166312208957420294672362890625/33554432*t^9 + 1587956232911563999299787325374452176803417734375/33554432*t^7 - 1075712286811059483396630123640757926221670078125/67108864*t^5 + 5378561434055297416983150618203789631108350390625/2147483648*t^3 - 488960130368663401543922783473071784646213671875/4294967296*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
  current precision for roots: 848
  current precision for roots: 1696
 current precision for weights: 848
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-8.7628250943199566498 + 4.4870186404319294836e-1130j)  +/-  (4.21e-495, 4.21e-495j)
| (9.1886016826884831591 - 3.3766206905790119372e-1138j)  +/-  (1e-495, 1e-495j)
| (8.3628125057261163876 - 7.7993280041033294743e-1137j)  +/-  (1.26e-494, 1.26e-494j)
| (-7.2655439249082009264 - 1.6700675272235694486e-1134j)  +/-  (5.58e-494, 5.58e-494j)
| (9.6503813634446366132 - 6.7912390655910129864e-1146j)  +/-  (1.78e-496, 1.78e-496j)
| (-10.168049165614174934 + 2.1765885550257094146e-1145j)  +/-  (1.76e-497, 1.76e-497j)
| (-8.3628125057261163876 + 6.4855481443075864187e-1142j)  +/-  (1.35e-494, 1.35e-494j)
| (-2.1758356606878358047 - 7.7696549833258668845e-1158j)  +/-  (6.17e-501, 6.17e-501j)
| (-3.0081442150749433554 - 2.358934221291375924e-1155j)  +/-  (1.65e-498, 1.65e-498j)
| (3.0081442150749433554 + 7.6237819654102670192e-1156j)  +/-  (1.58e-498, 1.58e-498j)
| (7.6176161578278200639 + 7.5233932711655178219e-1154j)  +/-  (3.48e-494, 3.48e-494j)
| (5.6373207673775578811 - 1.4744711525743282531e-1151j)  +/-  (2.74e-494, 2.74e-494j)
| (-10.793719285461286437 - 7.8648689010479947108e-1154j)  +/-  (6.6e-499, 6.6e-499j)
| (-1.0830966177633831296 - 4.6938724554212724502e-1162j)  +/-  (4.73e-505, 4.73e-505j)
| (-4.4363734165111919384 - 1.0355023290589733481e-1150j)  +/-  (1.52e-495, 1.52e-495j)
| (-7.9824245547615579574 - 1.373520885490880394e-1160j)  +/-  (1.68e-494, 1.68e-494j)
| (10.793719285461286437 - 1.4864962114416138715e-1185j)  +/-  (6.72e-499, 6.72e-499j)
| (-7.6176161578278200639 - 9.1161167615419567521e-1190j)  +/-  (3.37e-494, 3.37e-494j)
| (-1.9011878731830645867 + 8.3792172532366645212e-1212j)  +/-  (6.64e-502, 6.64e-502j)
| (2.7291186629246001574 - 6.6368785177803628535e-1209j)  +/-  (2.57e-499, 2.57e-499j)
| (4.4363734165111919384 - 1.4941813524219835966e-1203j)  +/-  (1.61e-495, 1.61e-495j)
| (1.9011878731830645867 + 2.3729095383378139318e-1216j)  +/-  (6.97e-502, 6.97e-502j)
| (3.8574121614750751952 + 7.9194348342605126884e-1208j)  +/-  (1.07e-496, 1.07e-496j)
| (-6.9241120615277027967 - 3.5581949541464020238e-1212j)  +/-  (6.97e-494, 6.97e-494j)
| (8.7628250943199566498 + 2.3972240672015257566e-1224j)  +/-  (4.03e-495, 4.03e-495j)
| (1.6276276184711236641 + 2.5208453579837272534e-1232j)  +/-  (8.48e-503, 8.48e-503j)
| (4.7306242061652039546 + 5.4326034809393714169e-1224j)  +/-  (3.69e-495, 3.69e-495j)
| (7.2655439249082009264 + 8.175589445375212183e-1222j)  +/-  (5.99e-494, 5.99e-494j)
| (-9.6503813634446366132 - 4.4939110498363477382e-1224j)  +/-  (1.84e-496, 1.84e-496j)
| (-5.0285594473595789011 - 2.219615739535849505e-1232j)  +/-  (8.16e-495, 8.16e-495j)
| (5.0285594473595789011 - 4.15759598097510764e-1240j)  +/-  (8.25e-495, 8.25e-495j)
| (7.9824245547615579574 - 1.2585780346429747608e-1240j)  +/-  (1.77e-494, 1.77e-494j)
| (-9.1886016826884831591 + 8.9303195102367333261e-1249j)  +/-  (1.02e-495, 1.02e-495j)
| (6.9241120615277027967 + 3.8208645130752955764e-1263j)  +/-  (7.3e-494, 7.3e-494j)
| (-3.8574121614750751952 - 2.0998959000236936526e-1289j)  +/-  (1.12e-496, 1.12e-496j)
| (-5.6373207673775578811 - 1.7274912637182275104e-1320j)  +/-  (2.85e-494, 2.85e-494j)
| (-4.1454178838251632997 - 2.5963519034701309321e-1338j)  +/-  (5.82e-496, 5.82e-496j)
| (1.3549848665269234559 - 1.9518577991620168519e-1360j)  +/-  (5.89e-504, 5.89e-504j)
| (-0.27040594535031911636 - 6.2173616320393509521e-1372j)  +/-  (7.17e-509, 7.17e-509j)
| (-3.5720468340630475013 + 2.8209986012824367426e-1349j)  +/-  (3.25e-497, 3.25e-497j)
| (-0.81180550955890364357 + 5.5529742760063873023e-1373j)  +/-  (4.5e-506, 4.5e-506j)
| (1.0830966177633831296 + 1.8943817050612049007e-1372j)  +/-  (4.9e-505, 4.9e-505j)
| (3.5720468340630475013 + 5.6542164685849905719e-1361j)  +/-  (3.04e-497, 3.04e-497j)
| (0.81180550955890364357 + 6.6621756414139850474e-1389j)  +/-  (4.24e-506, 4.24e-506j)
| (5.9492482679521009309 + 1.0243037011651969054e-1400j)  +/-  (5.37e-494, 5.37e-494j)
| (-5.330621924828347066 - 3.1013689641155895193e-1451j)  +/-  (1.74e-494, 1.74e-494j)
| (-2.7291186629246001574 - 1.5275848497308735826e-1471j)  +/-  (2.42e-499, 2.42e-499j)
| (-3.2890423786892447591 - 2.7925371853176577045e-1481j)  +/-  (7.57e-498, 7.57e-498j)
| (2.4517495992505411744 + 1.2828442952959279523e-1496j)  +/-  (4.36e-500, 4.36e-500j)
| (10.168049165614174934 + 2.1070785744140207122e-1501j)  +/-  (1.82e-497, 1.82e-497j)
| (-6.2671025086846094481 - 6.9590438992779817964e-1541j)  +/-  (6.97e-494, 6.97e-494j)
| (-2.4517495992505411744 - 5.1008094646444381569e-1573j)  +/-  (4.12e-500, 4.12e-500j)
| (-6.5917184866891135901 - 4.9490213780550947827e-1579j)  +/-  (7.37e-494, 7.37e-494j)
| (-4.7306242061652039546 - 3.5103985505764434797e-1595j)  +/-  (3.92e-495, 3.92e-495j)
| (2.1758356606878358047 - 4.9432761473621364927e-1610j)  +/-  (6.4e-501, 6.4e-501j)
| (4.1454178838251632997 + 1.8393239919301829072e-1604j)  +/-  (5.57e-496, 5.57e-496j)
| (-0.54095854971511490061 + 2.2352999421274243555e-1616j)  +/-  (2.72e-507, 2.72e-507j)
| (6.5917184866891135901 - 1.3431644081442231451e-1601j)  +/-  (7.51e-494, 7.51e-494j)
| (4.7149864334788078524e-1644 - 1.3319906937431694925e-1643j)  +/-  (9.47e-1642, 9.47e-1642j)
| (0.54095854971511490061 + 3.400189955165637999e-1624j)  +/-  (3.26e-507, 3.26e-507j)
| (5.330621924828347066 - 4.0916107234123806558e-1610j)  +/-  (1.75e-494, 1.75e-494j)
| (-5.9492482679521009309 - 1.5376537169453437206e-1619j)  +/-  (5.95e-494, 5.95e-494j)
| (-1.3549848665269234559 + 9.0637806665912776863e-1638j)  +/-  (5.72e-504, 5.72e-504j)
| (6.2671025086846094481 + 3.9606833514759895937e-1628j)  +/-  (6.56e-494, 6.56e-494j)
| (0.27040594535031911636 + 1.7358976706358115662e-1665j)  +/-  (7.17e-509, 7.17e-509j)
| (-1.6276276184711236641 - 3.7807627900102515278e-1636j)  +/-  (8.49e-503, 8.49e-503j)
| (3.2890423786892447591 + 3.0589145906820729964e-1632j)  +/-  (7.3e-498, 7.3e-498j)
-------------------------------------------------
The weights are:
| (1.041629288631964857e-34 + 5.8294766470392235577e-1163j)  +/-  (4.23e-187, 1.21e-431j)
| (5.3549531688116472322e-38 + 2.9870508657608586032e-1166j)  +/-  (8.27e-189, 2.36e-433j)
| (9.3050506475666727304e-32 + 4.1498827133020323466e-1163j)  +/-  (2.04e-186, 5.83e-431j)
| (2.3199198078876532451e-24 - 2.7683937214467242708e-1157j)  +/-  (2.63e-183, 7.53e-428j)
| (9.804825837887367041e-42 - 3.9298111932582561269e-1168j)  +/-  (1.56e-190, 4.47e-435j)
| (3.9476218841310833539e-46 - 1.0937710266992112547e-1169j)  +/-  (4.07e-193, 1.16e-437j)
| (9.3050506475666727304e-32 - 1.0563796075508008602e-1161j)  +/-  (6.17e-187, 1.76e-431j)
| (0.0013648643900232862688 + 1.5895406552083825288e-1148j)  +/-  (2.94e-154, 8.4e-399j)
| (1.8559439997800087379e-05 - 2.2311732943945879411e-1149j)  +/-  (1.76e-162, 5.02e-407j)
| (1.8559439997800087379e-05 - 8.9905918624681230918e-1150j)  +/-  (4.82e-164, 1.38e-408j)
| (1.2708165561759089922e-26 + 1.6115885406218916807e-1160j)  +/-  (1.61e-186, 4.6e-431j)
| (2.7546216953863355014e-15 + 8.6779820446960570252e-1155j)  +/-  (7.9e-180, 2.26e-424j)
| (1.0313638986011786187e-51 + 1.5912434796655775257e-1172j)  +/-  (5.08e-196, 1.45e-440j)
| (0.047405302164065690694 + 7.6599422916171681359e-1148j)  +/-  (6.11e-143, 1.75e-387j)
| (4.6782805875057352032e-10 + 1.7157668123655390275e-1151j)  +/-  (9.47e-175, 2.71e-419j)
| (4.4582577420761828225e-29 + 2.7610382252609656311e-1160j)  +/-  (3.93e-187, 1.12e-431j)
| (1.0313638986011786187e-51 - 3.7714697919090735873e-1173j)  +/-  (1.13e-198, 3.23e-443j)
| (1.2708165561759089922e-26 - 8.595581942342168406e-1159j)  +/-  (3.28e-186, 9.37e-431j)
| (0.0041641892562583844885 - 2.6293011581739808589e-1148j)  +/-  (2.37e-158, 6.78e-403j)
| (9.1423952322012523283e-05 + 2.052486982166695277e-1149j)  +/-  (6.93e-167, 1.98e-411j)
| (4.6782805875057352032e-10 + 3.951301874983564332e-1152j)  +/-  (6.55e-178, 1.87e-422j)
| (0.0041641892562583844885 - 1.5135813734916245978e-1148j)  +/-  (3.5e-161, 1e-405j)
| (5.5797682968392183546e-08 + 4.544913267211340188e-1151j)  +/-  (5.43e-175, 1.55e-419j)
| (2.8649509099438850454e-22 + 1.2188730205553163375e-1156j)  +/-  (1.36e-186, 3.89e-431j)
| (1.041629288631964857e-34 - 1.352967240244627896e-1164j)  +/-  (1.09e-192, 3.12e-437j)
| (0.010893927022801872381 + 2.5254128462352525066e-1148j)  +/-  (7.7e-161, 2.2e-405j)
| (3.1897774030097699715e-11 - 1.0059159667361593723e-1152j)  +/-  (6.16e-180, 1.76e-424j)
| (2.3199198078876532451e-24 - 2.2311595089350781136e-1159j)  +/-  (2.66e-189, 7.62e-434j)
| (9.804825837887367041e-42 + 1.7242685005258528823e-1167j)  +/-  (7.04e-197, 2.01e-441j)
| (1.7647457073424086122e-12 + 1.3476862626764949754e-1152j)  +/-  (2.49e-184, 7.11e-429j)
| (1.7647457073424086122e-12 + 2.3075188458516225451e-1153j)  +/-  (3.23e-182, 9.22e-427j)
| (4.4582577420761828225e-29 - 9.3132676225277756224e-1162j)  +/-  (2.32e-191, 6.62e-436j)
| (5.3549531688116472322e-38 - 5.7203058507155102332e-1166j)  +/-  (1.17e-195, 3.35e-440j)
| (2.8649509099438850454e-22 + 2.5401962848732721939e-1158j)  +/-  (4.55e-189, 1.3e-433j)
| (5.5797682968392183546e-08 + 1.5425211982343010995e-1150j)  +/-  (1.05e-181, 2.99e-426j)
| (2.7546216953863355014e-15 + 7.4305064922497598402e-1154j)  +/-  (4.57e-188, 1.3e-432j)
| (5.6212654846090911637e-09 - 5.3688632491113947403e-1151j)  +/-  (7.54e-183, 2.16e-427j)
| (0.024491616264140157303 - 3.9095822387364189501e-1148j)  +/-  (2.65e-170, 7.58e-415j)
| (0.1418287855101795881 - 1.1664042368892477211e-1147j)  +/-  (2.03e-168, 5.79e-413j)
| (4.6086076695475525981e-07 - 4.0764716942990898148e-1150j)  +/-  (2.58e-181, 7.36e-426j)
| (0.079113810062758233857 - 9.4662633031659976991e-1148j)  +/-  (6.44e-169, 1.84e-413j)
| (0.047405302164065690694 + 5.6212179320190966173e-1148j)  +/-  (1.56e-169, 4.47e-414j)
| (4.6086076695475525981e-07 - 1.3413581716335798014e-1150j)  +/-  (1.18e-181, 3.36e-426j)
| (0.079113810062758233857 - 7.5125498687115466373e-1148j)  +/-  (1.6e-169, 4.56e-414j)
| (7.5541387741002222968e-17 - 1.4024934648788317006e-1155j)  +/-  (2.19e-189, 6.25e-434j)
| (7.8343709230080569737e-14 - 3.3062130715940891758e-1153j)  +/-  (2.08e-187, 5.94e-432j)
| (9.1423952322012523283e-05 + 4.6358022326345773535e-1149j)  +/-  (8.24e-180, 2.36e-424j)
| (3.1873220251188608311e-06 + 9.9268112236873446407e-1150j)  +/-  (3.27e-181, 9.35e-426j)
| (0.00038257295265715795519 - 4.3214442814378824065e-1149j)  +/-  (6.84e-180, 1.95e-424j)
| (3.9476218841310833539e-46 + 2.4183642150787800286e-1170j)  +/-  (6.77e-204, 1.94e-448j)
| (1.5865090288992520442e-18 + 2.9778754077014780626e-1155j)  +/-  (2.16e-191, 6.17e-436j)
| (0.00038257295265715795519 - 8.9164291546629575327e-1149j)  +/-  (5.61e-181, 1.6e-425j)
| (2.4963022410449452697e-20 - 5.6312090537311223281e-1156j)  +/-  (4.41e-192, 1.26e-436j)
| (3.1897774030097699715e-11 - 5.0260006428529648889e-1152j)  +/-  (8.64e-187, 2.47e-431j)
| (0.0013648643900232862688 + 8.4069449032486196252e-1149j)  +/-  (2.21e-182, 6.31e-427j)
| (5.6212654846090911637e-09 - 1.4053567491460789755e-1151j)  +/-  (4.7e-188, 1.34e-432j)
| (0.11396801561181019666 + 1.0889837414374383037e-1147j)  +/-  (6.51e-181, 1.86e-425j)
| (2.4963022410449452697e-20 - 2.4290901633720018914e-1157j)  +/-  (3.35e-195, 9.57e-440j)
| (0.15254644653934667817 + 1.1633125190042924036e-1147j)  +/-  (7.91e-183, 2.23e-427j)
| (0.11396801561181019666 + 9.3386590513738897406e-1148j)  +/-  (1.55e-183, 4.3e-428j)
| (7.8343709230080569737e-14 - 4.7429463231616469801e-1154j)  +/-  (5.52e-192, 1.57e-436j)
| (7.5541387741002222968e-17 - 1.5381496634154459113e-1154j)  +/-  (5.93e-193, 1.64e-437j)
| (0.024491616264140157303 - 5.7677498685537607022e-1148j)  +/-  (2.35e-185, 6.41e-430j)
| (1.5865090288992520442e-18 + 1.9838413353283788099e-1156j)  +/-  (1.6e-194, 4.57e-439j)
| (0.1418287855101795881 - 1.0802825917077910528e-1147j)  +/-  (6.44e-185, 1.8e-429j)
| (0.010893927022801872381 + 4.0392841420235637887e-1148j)  +/-  (6.68e-186, 1.72e-430j)
| (3.1873220251188608311e-06 + 3.6243402512123278756e-1150j)  +/-  (3.5e-188, 1.04e-432j)
