Starting with polynomial:
P : t
Extension levels are: 1 66
-------------------------------------------------
Trying to find an order 66 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^67 - 2211*t^65 + 2299440*t^63 - 1496935440*t^61 + 684847963800*t^59 - 234354973212360*t^57 + 62338422874487760*t^55 - 13224651138373474800*t^53 + 2277946158584831034300*t^51 - 322709039132851063192500*t^49 + 37950583002023285031438000*t^47 - 3729507293198833738089498000*t^45 + 307684351688903783392383585000*t^43 - 21372228428852316646409413635000*t^41 + 1251801950832778546432551370050000*t^39 - 61839016371139260193768037680470000*t^37 + 2574049056448671705565594568449563750*t^35 - 90091716975703509694795809895734731250*t^33 + 2642690364620636284380677090274885450000*t^31 - 64676369449926098538790255104095880750000*t^29 + 1312930299833499800337442178613146379225000*t^27 - 21944692154359925234211533556819732338475000*t^25 + 299245802104908071375611821229359986433750000*t^23 - 3291703823153988785131730033522959850771250000*t^21 + 28802408452597401869902637793325898694248437500*t^19 - 197008473815766228790134042506349147068659312500*t^17 + 1030505863036315658286854991571672461589910250000*t^15 - 4007522800696783115559991633889837350627428750000*t^13 + 11163813516226752964774262408693118333890694375000*t^11 - 21172749772154186657330497671659362357378903125000*t^9 + 25407299726585023988796597205991234828854683750000*t^7 - 17211396588976951734346081978252126819546721250000*t^5 + 5378561434055297416983150618203789631108350390625*t^3 - 488960130368663401543922783473071784646213671875*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
Positive weights:   67 out of 67
Indefinite weights: 0 out of 67
Negative weights:   0 out of 67
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (15.264624201947383929 - 5.6275270694575687367e-1488j)  +/-  (8.77e-499, 8.77e-499j)
| (12.994645118902295298 - 7.1097139177490206619e-1483j)  +/-  (1.45e-495, 1.45e-495j)
| (11.826802865181200393 + 2.7450135012707732359e-1486j)  +/-  (1.64e-494, 1.64e-494j)
| (14.379793032887999051 + 7.1209120364417319635e-1496j)  +/-  (2.46e-497, 2.46e-497j)
| (13.64770020625596564 + 6.0088594928567037415e-1494j)  +/-  (2.7e-496, 2.7e-496j)
| (12.392506093090578518 + 2.7838889710780383988e-1495j)  +/-  (5.52e-495, 5.52e-495j)
| (-15.264624201947383929 - 6.8716926060647303392e-1504j)  +/-  (9.04e-499, 9.04e-499j)
| (-10.27503075662262582 + 1.8375773274937413507e-1512j)  +/-  (8.4e-494, 8.4e-494j)
| (-7.53863782197562159 + 5.534754955106850301e-1534j)  +/-  (2.36e-494, 2.36e-494j)
| (-12.392506093090578518 + 2.0224331498120620322e-1552j)  +/-  (5.79e-495, 5.79e-495j)
| (10.772936083352530467 + 7.2388184715664889778e-1564j)  +/-  (5.57e-494, 5.57e-494j)
| (6.2739794533815913203 - 1.6435818166242497187e-1572j)  +/-  (2.2e-495, 2.2e-495j)
| (-4.6514083391621951486 - 4.3962401854850898678e-1572j)  +/-  (9.95e-498, 9.95e-498j)
| (-1.9162379750526731343 + 6.6597804097909904791e-1589j)  +/-  (8.13e-504, 8.13e-504j)
| (-1.5317299262014045143 - 1.5186783157102717477e-1590j)  +/-  (6.92e-505, 6.92e-505j)
| (-2.6886856748747498296 - 3.8732199103306921868e-1584j)  +/-  (1.02e-501, 1.02e-501j)
| (4.2541583465331534523 + 1.7291172146032297676e-1580j)  +/-  (2.34e-498, 2.34e-498j)
| (-5.862506193009521263 + 1.3526091361059390956e-1592j)  +/-  (8.19e-496, 8.19e-496j)
| (-10.772936083352530467 - 5.0663716147663961161e-1629j)  +/-  (5.02e-494, 5.02e-494j)
| (-9.7921731848036076613 + 6.1985560227273957372e-1653j)  +/-  (9.69e-494, 9.69e-494j)
| (11.288853065963810018 + 6.3840210038336328176e-1660j)  +/-  (2.74e-494, 2.74e-494j)
| (-13.64770020625596564 - 8.3085648451727941424e-1663j)  +/-  (2.74e-496, 2.74e-496j)
| (7.53863782197562159 - 5.8430984424083879279e-1660j)  +/-  (2.31e-494, 2.31e-494j)
| (-5.0516370781638383272 - 3.9881643962641146941e-1663j)  +/-  (4.65e-497, 4.65e-497j)
| (-1.1480663616274027868 + 9.3578046072055150485e-1673j)  +/-  (5.96e-506, 5.96e-506j)
| (9.7921731848036076613 - 1.6553266316475452344e-1659j)  +/-  (9.69e-494, 9.69e-494j)
| (-14.379793032887999051 + 7.434836895522434573e-1665j)  +/-  (2.41e-497, 2.41e-497j)
| (-12.994645118902295298 + 5.7364802544400236989e-1662j)  +/-  (1.48e-495, 1.48e-495j)
| (10.27503075662262582 + 6.1705204260550522566e-1660j)  +/-  (8.31e-494, 8.31e-494j)
| (6.6901129108492879142 - 2.5591612482060598544e-1661j)  +/-  (5.5e-495, 5.5e-495j)
| (7.9723754846728459966 + 2.6711981336761846438e-1659j)  +/-  (3.83e-494, 3.83e-494j)
| (3.8595566264334967868 - 5.0668472863238706408e-1665j)  +/-  (3.13e-499, 3.13e-499j)
| (-6.6901129108492879142 + 2.5491179768851086808e-1659j)  +/-  (5.39e-495, 5.39e-495j)
| (3.467297534802916001 - 1.5500154410761366782e-1670j)  +/-  (5.98e-500, 5.98e-500j)
| (-5.4552045944209666446 - 1.2407974837354821869e-1666j)  +/-  (1.82e-496, 1.82e-496j)
| (-0.76503091768879568534 - 2.0456759439724722125e-1677j)  +/-  (3.89e-507, 3.89e-507j)
| (-11.826802865181200393 + 5.2678360639113087853e-1663j)  +/-  (1.72e-494, 1.72e-494j)
| (-7.9723754846728459966 - 1.0508913321729395732e-1680j)  +/-  (3.54e-494, 3.54e-494j)
| (4.6514083391621951486 - 7.06041175245190033e-1706j)  +/-  (9.75e-498, 9.75e-498j)
| (-8.4135075864625061758 - 1.4667061803571699672e-1711j)  +/-  (8.51e-494, 8.51e-494j)
| (2.1087270132226174541e-1753 - 2.2925552466306230927e-1753j)  +/-  (2.09e-1751, 2.09e-1751j)
| (3.0770963008397611555 - 5.0942673917338577274e-1736j)  +/-  (8.88e-501, 8.88e-501j)
| (1.1480663616274027868 - 3.6420607874881325877e-1741j)  +/-  (5.44e-506, 5.44e-506j)
| (5.862506193009521263 - 7.0481451650043801815e-1729j)  +/-  (7.93e-496, 7.93e-496j)
| (-7.111456969655272205 + 1.9947797773539308606e-1745j)  +/-  (1.24e-494, 1.24e-494j)
| (-3.467297534802916001 - 2.7975201250376599907e-1764j)  +/-  (6.36e-500, 6.36e-500j)
| (-4.2541583465331534523 + 1.0388984907850113387e-1760j)  +/-  (2.47e-498, 2.47e-498j)
| (8.8630213645642223785 - 8.2340662767418122548e-1783j)  +/-  (1.02e-493, 1.02e-493j)
| (1.9162379750526731343 - 2.4106929178713472806e-1809j)  +/-  (7.94e-504, 7.94e-504j)
| (-9.3220976832211984473 - 1.6655646898905478743e-1830j)  +/-  (1.04e-493, 1.04e-493j)
| (2.6886856748747498296 - 1.1933878426752962167e-1863j)  +/-  (9.74e-502, 9.74e-502j)
| (-3.8595566264334967868 - 1.4340298365495218932e-1855j)  +/-  (3.45e-499, 3.45e-499j)
| (5.0516370781638383272 - 4.3099862428862388551e-1867j)  +/-  (4.8e-497, 4.8e-497j)
| (1.5317299262014045143 - 6.5200083514755414226e-1886j)  +/-  (6.72e-505, 6.72e-505j)
| (-8.8630213645642223785 - 1.9892876241322053909e-1907j)  +/-  (1.02e-493, 1.02e-493j)
| (-11.288853065963810018 - 2.4625465383436728774e-1943j)  +/-  (2.5e-494, 2.5e-494j)
| (-3.0770963008397611555 - 1.3273428844392665348e-1962j)  +/-  (9.34e-501, 9.34e-501j)
| (9.3220976832211984473 - 1.5343956065487538528e-1954j)  +/-  (9.76e-494, 9.76e-494j)
| (8.4135075864625061758 - 3.6975576359359388679e-1965j)  +/-  (7.79e-494, 7.79e-494j)
| (-2.301813052534884597 - 5.3274285965623369051e-1984j)  +/-  (1.13e-502, 1.13e-502j)
| (0.76503091768879568534 - 6.2869031929180274322e-1989j)  +/-  (3.94e-507, 3.94e-507j)
| (0.38241175526073925476 - 7.0683980280530690313e-1990j)  +/-  (1.03e-508, 1.03e-508j)
| (-0.38241175526073925476 + 1.8143188024345008895e-1998j)  +/-  (1.06e-508, 1.06e-508j)
| (-6.2739794533815913203 + 1.1615393780447483039e-1975j)  +/-  (2.19e-495, 2.19e-495j)
| (7.111456969655272205 - 5.0391849392092579015e-1979j)  +/-  (1.27e-494, 1.27e-494j)
| (2.301813052534884597 - 7.2929545539602314893e-1989j)  +/-  (1.06e-502, 1.06e-502j)
| (5.4552045944209666446 + 2.8596179133844545311e-1983j)  +/-  (1.67e-496, 1.67e-496j)
-------------------------------------------------
The weights are:
| (1.0313638986011786187e-51 + 1.5454149973622359424e-1527j)  +/-  (2.72e-175, 1.81e-422j)
| (5.3549531688116472322e-38 + 2.6395921999487821418e-1519j)  +/-  (5.2e-171, 3.47e-418j)
| (9.3050506475666727304e-32 - 1.0806905715604454896e-1516j)  +/-  (5.79e-169, 3.86e-416j)
| (3.9476218841310833539e-46 - 1.7082812584656300199e-1524j)  +/-  (2.37e-174, 1.58e-421j)
| (9.804825837887367041e-42 + 6.4486828916642160613e-1522j)  +/-  (7.88e-173, 5.25e-420j)
| (1.041629288631964857e-34 - 4.2993004430473726555e-1518j)  +/-  (2.15e-170, 1.43e-417j)
| (1.0313638986011786187e-51 - 8.7710484347772017047e-1529j)  +/-  (4.23e-183, 2.82e-430j)
| (2.3199198078876532451e-24 - 4.9985370641740727939e-1515j)  +/-  (1.14e-172, 7.58e-420j)
| (7.8343709230080569737e-14 - 1.0324530761948948839e-1509j)  +/-  (4.44e-165, 2.96e-412j)
| (1.041629288631964857e-34 - 3.0855581661941085138e-1520j)  +/-  (1.02e-177, 6.78e-425j)
| (1.2708165561759089922e-26 - 6.0890396552780046503e-1516j)  +/-  (7.78e-171, 5.19e-418j)
| (4.6782805875057352032e-10 + 2.0333188804448073871e-1507j)  +/-  (3.33e-160, 2.22e-407j)
| (3.1873220251188608311e-06 + 7.573364807183260105e-1506j)  +/-  (1.99e-154, 1.33e-401j)
| (0.024491616264140157303 - 7.7325343322916246126e-1504j)  +/-  (4.36e-134, 2.91e-381j)
| (0.047405302164065690694 + 1.1011936849977890314e-1503j)  +/-  (2.77e-129, 1.85e-376j)
| (0.0041641892562583844885 - 3.0469813296982075881e-1504j)  +/-  (4.08e-142, 2.72e-389j)
| (1.8559439997800087379e-05 - 3.3455393218321755252e-1505j)  +/-  (1.23e-153, 8.21e-401j)
| (5.6212654846090911637e-09 - 2.9923703460634330349e-1507j)  +/-  (1.25e-160, 8.32e-408j)
| (1.2708165561759089922e-26 + 3.6266631113637555269e-1516j)  +/-  (4.33e-175, 2.89e-422j)
| (2.8649509099438850454e-22 + 5.6651225613542251551e-1514j)  +/-  (7.6e-173, 5.07e-420j)
| (4.4582577420761828225e-29 + 3.9530812472258057994e-1516j)  +/-  (1.21e-174, 8.1e-422j)
| (9.804825837887367041e-42 - 9.0440478949435002566e-1524j)  +/-  (1.16e-182, 7.71e-430j)
| (7.8343709230080569737e-14 - 2.9747275145535151169e-1509j)  +/-  (2.79e-169, 1.86e-416j)
| (4.6086076695475525981e-07 - 2.8212155980880610114e-1506j)  +/-  (1.48e-160, 9.88e-408j)
| (0.079113810062758233857 - 1.4568657916513967451e-1503j)  +/-  (1.31e-134, 8.74e-382j)
| (2.8649509099438850454e-22 + 1.7297761115410049507e-1513j)  +/-  (9.02e-174, 6.01e-421j)
| (3.9476218841310833539e-46 + 5.5929728897005534969e-1526j)  +/-  (1.35e-184, 9.03e-432j)
| (5.3549531688116472322e-38 + 6.8427143548204878795e-1522j)  +/-  (2.4e-181, 1.6e-428j)
| (2.3199198078876532451e-24 - 9.9535614361560186204e-1515j)  +/-  (1.63e-174, 1.09e-421j)
| (3.1897774030097699715e-11 - 5.5320057009162087552e-1508j)  +/-  (8.75e-169, 5.84e-416j)
| (2.7546216953863355014e-15 + 5.7915257875064216671e-1510j)  +/-  (1.55e-171, 1.03e-418j)
| (9.1423952322012523283e-05 + 7.1714932906993123578e-1505j)  +/-  (1.26e-161, 8.38e-409j)
| (3.1897774030097699715e-11 - 2.1664461543801295348e-1508j)  +/-  (1.46e-170, 9.73e-418j)
| (0.00038257295265715795519 - 1.4184460510032120883e-1504j)  +/-  (6.48e-161, 4.32e-408j)
| (5.5797682968392183546e-08 + 9.6191603909174165734e-1507j)  +/-  (1.08e-166, 7.17e-414j)
| (0.11396801561181019666 + 1.7916286525761382457e-1503j)  +/-  (1.94e-147, 1.29e-394j)
| (9.3050506475666727304e-32 + 9.4205580424327699384e-1519j)  +/-  (1.71e-181, 1.14e-428j)
| (2.7546216953863355014e-15 + 1.8986930106966607196e-1510j)  +/-  (2.67e-174, 1.78e-421j)
| (3.1873220251188608311e-06 + 1.437140335387121971e-1505j)  +/-  (1.45e-167, 9.64e-415j)
| (7.5541387741002222968e-17 - 3.083824642130117829e-1511j)  +/-  (1.22e-175, 8.13e-423j)
| (0.15254644653934667817 + 2.1797333115656850118e-1503j)  +/-  (3e-153, 2e-400j)
| (0.0013648643900232862688 + 2.5931934880584070164e-1504j)  +/-  (1.9e-163, 1.27e-410j)
| (0.079113810062758233857 - 1.7007625812661154782e-1503j)  +/-  (4.38e-154, 2.92e-401j)
| (5.6212654846090911637e-09 - 6.7693061090296549205e-1507j)  +/-  (7.58e-171, 5.05e-418j)
| (1.7647457073424086122e-12 + 4.9967339480892694092e-1509j)  +/-  (9.13e-173, 6.09e-420j)
| (0.00038257295265715795519 - 8.8394583388581273553e-1505j)  +/-  (2.94e-166, 1.96e-413j)
| (1.8559439997800087379e-05 - 1.8659310429953368149e-1505j)  +/-  (8.53e-168, 5.69e-415j)
| (1.5865090288992520442e-18 + 1.4570893962511088042e-1511j)  +/-  (9.17e-179, 6.12e-426j)
| (0.024491616264140157303 - 1.0018832715790229276e-1503j)  +/-  (2.52e-163, 1.68e-410j)
| (2.4963022410449452697e-20 - 5.3923651700592101695e-1513j)  +/-  (1.88e-178, 1.25e-425j)
| (0.0041641892562583844885 - 4.3885883568159790358e-1504j)  +/-  (2.33e-166, 1.55e-413j)
| (9.1423952322012523283e-05 + 4.2296435961758835271e-1505j)  +/-  (2.3e-168, 1.54e-415j)
| (4.6086076695475525981e-07 - 5.6713089934354407626e-1506j)  +/-  (7.92e-172, 5.28e-419j)
| (0.047405302164065690694 + 1.3541130130282892675e-1503j)  +/-  (9.29e-164, 6.2e-411j)
| (1.5865090288992520442e-18 + 4.3832234503222052536e-1512j)  +/-  (1.32e-177, 8.82e-425j)
| (4.4582577420761828225e-29 - 2.1050881122418206077e-1517j)  +/-  (5.7e-183, 3.8e-430j)
| (0.0013648643900232862688 + 1.7062910437746133047e-1504j)  +/-  (9.07e-169, 6.05e-416j)
| (2.4963022410449452697e-20 - 1.7960406634269505095e-1512j)  +/-  (7.02e-181, 4.68e-428j)
| (7.5541387741002222968e-17 - 9.8922458127307157612e-1511j)  +/-  (2.1e-179, 1.4e-426j)
| (0.010893927022801872381 + 5.0403537276336201813e-1504j)  +/-  (1.31e-169, 8.76e-417j)
| (0.11396801561181019666 + 1.9861289298894814107e-1503j)  +/-  (1.05e-168, 6.97e-416j)
| (0.1418287855101795881 - 2.1572438189295300407e-1503j)  +/-  (1.41e-168, 9.39e-416j)
| (0.1418287855101795881 - 2.0489741798970278158e-1503j)  +/-  (2.17e-168, 1.45e-415j)
| (4.6782805875057352032e-10 + 8.4623571136428196825e-1508j)  +/-  (4.97e-175, 3.32e-422j)
| (1.7647457073424086122e-12 + 1.3559769072114342187e-1508j)  +/-  (9.66e-178, 6.43e-425j)
| (0.010893927022801872381 + 6.88386634223363554e-1504j)  +/-  (1.76e-172, 1.09e-419j)
| (5.5797682968392183546e-08 + 2.050347923809324794e-1506j)  +/-  (1.59e-175, 1.07e-422j)
