Starting with polynomial:
P : 4*t^2 - 1
Extension levels are: 2 66
-------------------------------------------------
Trying to find an order 66 Kronrod extension for:
P1 : 4*t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^68 - 67*t^66 + 2145/4*t^64 - 2730*t^62 + 39711/4*t^60 - 7028847/256*t^58 + 61474519/1024*t^56 - 109067695/1024*t^54 + 2558620845/16384*t^52 - 12565671261/65536*t^50 + 52179482355/262144*t^48 - 23063658345/131072*t^46 + 139595826825/1048576*t^44 - 725591495475/8388608*t^42 + 1622686435335/33554432*t^40 - 781293468865/33554432*t^38 + 10363194502115/1073741824*t^36 - 14771069086725/4294967296*t^34 + 18053528883775/17179869184*t^32 - 1178230306099/4294967296*t^30 + 2091959931237/34359738368*t^28 - 6275879793711/549755813888*t^26 + 3945185556975/2199023255552*t^24 - 514589420475/2199023255552*t^22 + 880519675035/35184372088832*t^20 - 304179524103/140737488355328*t^18 + 83254860801/562949953421312*t^16 - 2202509545/281474976710656*t^14 + 698356685/2251799813685248*t^12 - 158936349/18014398509481984*t^10 + 12225873/72057594037927936*t^8 - 145299/72057594037927936*t^6 + 58905/4611686018427387904*t^4 - 595/18446744073709551616*t^2 + 1/73786976294838206464
-------------------------------------------------
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
Positive weights:   68 out of 68
Indefinite weights: 0 out of 68
Negative weights:   0 out of 68
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (0.99068594603633075234 - 3.0230234177348409987e-827j)  +/-  (8.93e-232, 8.93e-232j)
| (0.20345601305263378988 + 1.9004471976348703002e-855j)  +/-  (4.72e-250, 4.72e-250j)
| (-0.94963969890031929609 - 9.3693184183850777632e-837j)  +/-  (7.55e-232, 7.55e-232j)
| (-0.9958568425315312589 - 1.388065193683076706e-835j)  +/-  (5.24e-232, 5.24e-232j)
| (0.93439383716067110687 + 2.3357414806487699903e-835j)  +/-  (3.99e-232, 3.99e-232j)
| (0.91721130150545301784 - 4.1221567259667673751e-840j)  +/-  (2.24e-232, 2.24e-232j)
| (0.98346170163374209223 - 4.0961516066274240109e-850j)  +/-  (1.13e-231, 1.13e-231j)
| (-0.89812770536369612031 - 2.0234397731312869868e-865j)  +/-  (9.87e-233, 9.87e-233j)
| (0.9958568425315312589 + 2.2219217735860483155e-861j)  +/-  (6.44e-232, 6.44e-232j)
| (-0.99896367364672757126 + 2.4227764809418006709e-870j)  +/-  (1.51e-232, 1.51e-232j)
| (0.8771826024025942357 + 4.1455931843123235081e-874j)  +/-  (3.76e-233, 3.76e-233j)
| (0.94963969890031929609 + 3.6455117991625364203e-878j)  +/-  (6.33e-232, 6.33e-232j)
| (-0.93439383716067110687 + 8.460131350243373334e-899j)  +/-  (3.86e-232, 3.86e-232j)
| (-0.82988529199902514439 + 1.9065303630390712509e-900j)  +/-  (4.92e-234, 4.92e-234j)
| (0.97419908267347904548 + 1.137353575299864457e-896j)  +/-  (1.06e-231, 1.06e-231j)
| (0.85441940454648855255 - 3.9732561996479825085e-913j)  +/-  (1.56e-233, 1.56e-233j)
| (0.82988529199902514439 - 2.1155764696771884447e-914j)  +/-  (4.38e-234, 4.38e-234j)
| (-0.99068594603633075234 - 2.2503024181608323424e-909j)  +/-  (8.77e-232, 8.77e-232j)
| (-0.80363111545497818741 + 2.7336631508233140924e-914j)  +/-  (1.47e-234, 1.47e-234j)
| (-0.96291728734779929502 - 1.450632837850385694e-909j)  +/-  (9.83e-232, 9.83e-232j)
| (0.80363111545497818741 + 4.2086205113894640845e-914j)  +/-  (1.23e-234, 1.23e-234j)
| (0.77571129070441980704 - 7.2258142165418684872e-915j)  +/-  (3.49e-235, 3.49e-235j)
| (-0.24780778599289991265 - 8.1296303874865368593e-929j)  +/-  (9.5e-249, 9.5e-249j)
| (-0.85441940454648855255 + 3.5627915425091686161e-913j)  +/-  (1.4e-233, 1.4e-233j)
| (-0.77571129070441980704 + 3.1108421612429333469e-915j)  +/-  (3.03e-235, 3.03e-235j)
| (0.99896367364672757126 - 5.0840627781738008301e-910j)  +/-  (1.7e-232, 1.7e-232j)
| (0.74618368584768550622 - 8.2303375094561787144e-929j)  +/-  (7.72e-236, 7.72e-236j)
| (0.96291728734779929502 - 6.5489379491980549057e-925j)  +/-  (9.93e-232, 9.93e-232j)
| (-0.91721130150545301784 + 1.5982687570307634529e-936j)  +/-  (2.17e-232, 2.17e-232j)
| (-0.64858208946275594027 + 2.8089094845582313886e-941j)  +/-  (3.71e-238, 3.71e-238j)
| (0.89812770536369612031 + 6.9893004616233074224e-937j)  +/-  (9.32e-233, 9.32e-233j)
| (-0.98346170163374209223 - 4.2388898134584523184e-933j)  +/-  (1.04e-231, 1.04e-231j)
| (0.64858208946275594027 - 8.1201503365597602303e-946j)  +/-  (3.94e-238, 3.94e-238j)
| (0.022763197856105683154 - 3.538735958054958221e-962j)  +/-  (2.91e-255, 2.91e-255j)
| (-0.61326675028371629767 - 1.5604015926420341093e-945j)  +/-  (5.77e-239, 5.77e-239j)
| (-0.71510950135489938236 - 2.9547623026774624129e-942j)  +/-  (1.55e-236, 1.55e-236j)
| (0.24780778599289991265 + 3.4647478741920837235e-956j)  +/-  (9.68e-249, 9.68e-249j)
| (0.61326675028371629767 + 1.2549834535982665841e-947j)  +/-  (5.59e-239, 5.59e-239j)
| (-0.74618368584768550622 + 1.5194290907706678523e-941j)  +/-  (7.42e-236, 7.42e-236j)
| (-0.68255314321865408287 - 3.0708635974156315304e-943j)  +/-  (2.73e-237, 2.73e-237j)
| (-0.57668032211486714125 + 1.3482727247884334667e-946j)  +/-  (6.79e-240, 6.79e-240j)
| (-0.20345601305263378988 + 3.7685078321299486749e-957j)  +/-  (4.81e-250, 4.81e-250j)
| (0.68255314321865408287 - 3.611458065779626628e-945j)  +/-  (2.55e-237, 2.55e-237j)
| (0.57668032211486714125 + 8.6300636910739993441e-949j)  +/-  (6.64e-240, 6.64e-240j)
| (-0.97419908267347904548 + 1.0568022382258820982e-938j)  +/-  (1.21e-231, 1.21e-231j)
| (-0.53889863591557544522 + 4.688208349123967591e-950j)  +/-  (7.96e-241, 7.96e-241j)
| (-0.8771826024025942357 - 2.5393662787118396655e-949j)  +/-  (4.12e-233, 4.12e-233j)
| (0.11358018605047483044 + 1.5036382501059226699e-971j)  +/-  (1.14e-252, 1.14e-252j)
| (0.46006503773115212604 - 2.1030583585813788527e-960j)  +/-  (7.52e-243, 7.52e-243j)
| (0.5 + 4.478903552300034202e-958j)  +/-  (8.84e-242, 8.84e-242j)
| (-0.33487961217098615196 + 4.6718252156355416227e-963j)  +/-  (2.85e-246, 2.85e-246j)
| (-0.5 - 2.510359074489511681e-959j)  +/-  (8.7e-242, 8.7e-242j)
| (-0.41917652041666411765 + 3.5328326683962087622e-960j)  +/-  (6.05e-244, 6.05e-244j)
| (0.53889863591557544522 - 7.8116085525260393514e-957j)  +/-  (7.97e-241, 7.97e-241j)
| (0.37741919575261445467 - 2.8296114794930230162e-964j)  +/-  (4.34e-245, 4.34e-245j)
| (0.71510950135489938236 + 1.2954492701641266011e-963j)  +/-  (1.53e-236, 1.53e-236j)
| (-0.46006503773115212604 + 7.4353407853765250154e-971j)  +/-  (6.79e-243, 6.79e-243j)
| (-0.11358018605047483044 + 1.5188355779586056451e-980j)  +/-  (1.12e-252, 1.12e-252j)
| (0.15868254645625129983 + 2.7210702081145892956e-979j)  +/-  (2.26e-251, 2.26e-251j)
| (0.41917652041666411765 - 1.6098676174639327639e-972j)  +/-  (5.96e-244, 5.96e-244j)
| (0.068242413364670975921 - 3.5763228912588819708e-982j)  +/-  (4.61e-254, 4.61e-254j)
| (-0.15868254645625129983 + 2.0868681385214184285e-979j)  +/-  (2.06e-251, 2.06e-251j)
| (-0.2916459394548249626 - 1.7259100860024969141e-975j)  +/-  (1.83e-247, 1.83e-247j)
| (-0.022763197856105683154 + 8.8087711262939957378e-983j)  +/-  (2.91e-255, 2.91e-255j)
| (0.33487961217098615196 + 6.6537224823252537673e-975j)  +/-  (2.53e-246, 2.53e-246j)
| (0.2916459394548249626 - 1.0459527529031060444e-975j)  +/-  (1.75e-247, 1.75e-247j)
| (-0.068242413364670975921 - 7.7911930504092367389e-982j)  +/-  (4.65e-254, 4.65e-254j)
| (-0.37741919575261445467 + 3.0438710862269344235e-973j)  +/-  (4.06e-245, 4.06e-245j)
-------------------------------------------------
The weights are:
| (0.00026871530907391815206 + 6.5105800201722040215e-829j)  +/-  (1.06e-38, 2.37e-148j)
| (0.013892835518155456651 - 5.3349555933101497164e-829j)  +/-  (5.7e-39, 1.27e-148j)
| (0.0014229629314856653086 - 2.2169729695662191979e-830j)  +/-  (1.48e-39, 3.3e-149j)
| (0.00011984274178447759256 + 1.8237050721346651082e-831j)  +/-  (1.26e-39, 2.82e-149j)
| (0.0018392486532776412593 - 9.8772134975252038387e-829j)  +/-  (9.44e-40, 2.11e-149j)
| (0.0023003395418938109937 + 9.4644629816196819999e-829j)  +/-  (6.87e-40, 1.53e-149j)
| (0.00047540697709658618212 - 1.9893657287469552702e-828j)  +/-  (2.87e-40, 6.41e-150j)
| (0.0028024148530165485676 + 4.4852307862846304601e-830j)  +/-  (4.9e-43, 1.09e-152j)
| (0.00011984274178447759256 + 7.0062786102141801108e-829j)  +/-  (1.1e-40, 2.46e-150j)
| (3.0022880206295225342e-05 - 4.5616140401691198225e-832j)  +/-  (5.06e-43, 1.13e-152j)
| (0.0033413142324958301071 + 8.8991839356407464596e-829j)  +/-  (9.61e-42, 2.15e-151j)
| (0.0014229629314856653086 + 1.048000846538847794e-828j)  +/-  (7.23e-41, 1.62e-150j)
| (0.0018392486532776412593 + 2.88823936579241274e-830j)  +/-  (1.29e-43, 2.88e-153j)
| (0.0045114551032419242415 - 7.4911838802672580437e-830j)  +/-  (1.36e-44, 3.03e-154j)
| (0.00073820503359640492528 + 1.3535692310390386768e-828j)  +/-  (6.53e-41, 1.46e-150j)
| (0.0039125721903539701011 - 8.6798985119128978352e-829j)  +/-  (1.27e-42, 2.84e-152j)
| (0.0045114551032419242415 + 8.4814546705766992349e-829j)  +/-  (1.72e-43, 3.85e-153j)
| (0.00026871530907391815206 - 4.0998423383327249396e-831j)  +/-  (1.17e-44, 2.62e-154j)
| (0.0051330004387331524449 + 8.6479588141714539292e-830j)  +/-  (1.83e-46, 4.09e-156j)
| (0.0010549318511124017931 + 1.6324106384591641666e-830j)  +/-  (9.65e-45, 2.16e-154j)
| (0.0051330004387331524449 - 8.2955252456855845522e-829j)  +/-  (1.36e-44, 3.04e-154j)
| (0.0057720578764301899284 + 8.1168016181401910965e-829j)  +/-  (1.55e-45, 3.46e-155j)
| (0.013602772481178219099 - 3.3202832389055996842e-829j)  +/-  (5.03e-50, 1.12e-159j)
| (0.0039125721903539701011 + 6.4103639437705698944e-830j)  +/-  (9.35e-47, 2.09e-156j)
| (0.0057720578764301899284 - 9.8783361507547776588e-830j)  +/-  (4.76e-48, 1.06e-157j)
| (3.0022880206295225342e-05 - 1.0964346049390995095e-829j)  +/-  (3.62e-44, 8.07e-154j)
| (0.006423331985141486736 - 7.9418011020632399815e-829j)  +/-  (6.24e-47, 1.39e-156j)
| (0.0010549318511124017931 - 1.1484471402150630533e-828j)  +/-  (1.63e-43, 3.64e-153j)
| (0.0023003395418938109937 - 3.6448397419747843601e-830j)  +/-  (1.77e-46, 3.94e-156j)
| (0.0083962503366395021727 - 1.5483777231638575973e-829j)  +/-  (5.06e-51, 1.13e-160j)
| (0.0028024148530165485676 - 9.1529028972536210723e-829j)  +/-  (1.87e-44, 4.18e-154j)
| (0.00047540697709658618212 + 7.2799284331299701858e-831j)  +/-  (1.92e-47, 4.29e-157j)
| (0.0083962503366395021727 + 7.4194023578771074914e-829j)  +/-  (1.76e-50, 3.92e-160j)
| (0.014485244011932808487 - 4.5240420398933224206e-829j)  +/-  (2.2e-53, 4.92e-163j)
| (0.009042085405745651541 + 1.7041921325074564525e-829j)  +/-  (1.02e-51, 2.28e-161j)
| (0.0070814261024919878032 - 1.2549755947355384324e-829j)  +/-  (7.36e-51, 1.64e-160j)
| (0.013602772481178219099 + 5.5354299274621343114e-829j)  +/-  (2.03e-54, 4.52e-164j)
| (0.009042085405745651541 - 7.2424604935776931275e-829j)  +/-  (3.57e-52, 7.98e-162j)
| (0.006423331985141486736 + 1.1179815825378818878e-829j)  +/-  (1.58e-50, 3.52e-160j)
| (0.0077408870533671809849 + 1.3985378805301096114e-829j)  +/-  (1.74e-51, 3.89e-161j)
| (0.0096730406679056967533 - 1.865666553145171318e-829j)  +/-  (1.08e-53, 2.42e-163j)
| (0.013892835518155456651 + 3.5170330345769339311e-829j)  +/-  (1.67e-56, 3.74e-166j)
| (0.0077408870533671809849 - 7.5944147540451082766e-829j)  +/-  (2.35e-53, 5.24e-163j)
| (0.0096730406679056967533 + 7.0631476962578015738e-829j)  +/-  (4.39e-55, 9.79e-165j)
| (0.00073820503359640492528 - 1.135745910742715695e-830j)  +/-  (2.43e-51, 5.42e-161j)
| (0.010283887829106261722 + 2.0324756085422548172e-829j)  +/-  (1.84e-55, 4.11e-165j)
| (0.0033413142324958301071 - 5.4076988503668695559e-830j)  +/-  (1.21e-51, 2.69e-161j)
| (0.014305790454155645257 - 4.9306186022485872893e-829j)  +/-  (1.97e-58, 4.39e-168j)
| (0.011425219725470051748 - 6.5091115873948114262e-829j)  +/-  (4.9e-58, 1.1e-167j)
| (0.010869565217391304348 + 6.6965338418481630037e-829j)  +/-  (1.5e-57, 3.35e-167j)
| (0.012867473121046520341 - 2.9344963221804877564e-829j)  +/-  (2.7e-59, 6.04e-169j)
| (0.010869565217391304348 - 2.2042838818048119267e-829j)  +/-  (8.48e-58, 1.89e-167j)
| (0.01194624702509243435 - 2.5615111604998274261e-829j)  +/-  (3.71e-59, 8.29e-169j)
| (0.010283887829106261722 - 6.8812100897079672438e-829j)  +/-  (2.11e-58, 4.72e-168j)
| (0.012428329719963039003 - 6.1263931262174139588e-829j)  +/-  (8.53e-61, 1.91e-170j)
| (0.0070814261024919878032 + 7.7681955570164437177e-829j)  +/-  (2.5e-57, 5.59e-167j)
| (0.011425219725470051748 + 2.3807467338826872122e-829j)  +/-  (3.27e-59, 7.31e-169j)
| (0.014305790454155645257 + 3.9163330665282406198e-829j)  +/-  (1.63e-62, 3.65e-172j)
| (0.014127823905074777508 + 5.1332413726663505782e-829j)  +/-  (7.26e-62, 1.62e-171j)
| (0.01194624702509243435 + 6.3190182242347548822e-829j)  +/-  (4.73e-61, 1.06e-170j)
| (0.014425260478524135887 + 4.7274330499900864295e-829j)  +/-  (2.07e-62, 4.62e-172j)
| (0.014127823905074777508 - 3.7158442120721552025e-829j)  +/-  (5.36e-63, 1.2e-172j)
| (0.013260038347819022785 + 3.1259775189294195353e-829j)  +/-  (7.33e-63, 1.64e-172j)
| (0.014485244011932808487 + 4.3208119802805503602e-829j)  +/-  (1.57e-63, 3.5e-173j)
| (0.012867473121046520341 + 5.9314268268253332299e-829j)  +/-  (1.07e-63, 2.39e-173j)
| (0.013260038347819022785 - 5.734350868623777787e-829j)  +/-  (8.89e-64, 1.98e-173j)
| (0.014425260478524135887 - 4.1181162058679524448e-829j)  +/-  (3.13e-64, 7.05e-174j)
| (0.012428329719963039003 + 2.7462166896480751296e-829j)  +/-  (2.26e-64, 4.92e-174j)
