Starting with polynomial:
P : 16*t^4 - 12*t^2 + 1
Extension levels are: 4 60
-------------------------------------------------
Trying to find an order 60 Kronrod extension for:
P1 : 16*t^4 - 12*t^2 + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^64 - 252*t^62 + 1891*t^60 - 17995/2*t^58 + 487635/16*t^56 - 2503193/32*t^54 + 20237679/128*t^52 - 66096459/256*t^50 + 1420494075/4096*t^48 - 3179201025/8192*t^46 + 11965356585/32768*t^44 - 19055938265/65536*t^42 + 103189703435/524288*t^40 - 119065042425/1048576*t^38 + 234461414075/4194304*t^36 - 196947587823/8388608*t^34 + 2254848913647/268435456*t^32 - 1370594437707/536870912*t^30 + 1409476549415/2147483648*t^28 - 609590544255/4294967296*t^26 + 880519675035/34359738368*t^24 - 263012370465/68719476736*t^22 + 128447901855/274877906944*t^20 - 25264080075/549755813888*t^18 + 31426050825/8796093022208*t^16 - 3771126099/17592186044416*t^14 + 676868787/70368744177664*t^12 - 43541267/140737488355328*t^10 + 7565085/1125899906842624*t^8 - 202895/2251799813685248*t^6 + 5797/9007199254740992*t^4 - 33/18014398509481984*t^2 + 1/1152921504606846976
-------------------------------------------------
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:
| (0.98950639945105110237 - 2.0241101668340108557e-882j)  +/-  (2.89e-233, 2.89e-233j)
| (-0.26270737819858692381 + 1.2251695355621622745e-906j)  +/-  (9.25e-249, 9.25e-249j)
| (-0.92617464895777650552 - 1.1623417952552983827e-890j)  +/-  (1.1e-233, 1.1e-233j)
| (-0.97094181742605202716 + 1.0922904013508674428e-889j)  +/-  (3.58e-233, 3.58e-233j)
| (0.94331181325774310261 - 2.9097762528523799814e-892j)  +/-  (1.88e-233, 1.88e-233j)
| (0.92617464895777650552 + 5.905773576958263804e-896j)  +/-  (1.14e-233, 1.14e-233j)
| (-0.99533163471764862901 - 3.9939779830433902482e-897j)  +/-  (1.85e-233, 1.85e-233j)
| (-0.95824582910916621069 - 1.5135154070127693033e-898j)  +/-  (2.91e-233, 2.91e-233j)
| (-0.98137012613941344325 + 2.6567910750286563261e-896j)  +/-  (3.42e-233, 3.42e-233j)
| (0.99883222683232658826 - 1.1820846138186926607e-894j)  +/-  (5.03e-234, 5.03e-234j)
| (0.8854560256532098959 + 8.6659402389028222451e-912j)  +/-  (2.31e-234, 2.31e-234j)
| (0.95824582910916621069 - 3.5728399228010595162e-910j)  +/-  (2.72e-233, 2.72e-233j)
| (-0.86196966688004923168 + 4.9826987603383519741e-928j)  +/-  (8.31e-235, 8.31e-235j)
| (-0.77967435406322239177 + 2.3512805617879576506e-929j)  +/-  (2.26e-236, 2.26e-236j)
| (0.97094181742605202716 + 1.0798113950849719585e-924j)  +/-  (3.43e-233, 3.43e-233j)
| (0.8090169943749474241 - 2.5255788129059612331e-942j)  +/-  (8.44e-236, 8.44e-236j)
| (0.77967435406322239177 + 3.9640003307067824987e-943j)  +/-  (2.08e-236, 2.08e-236j)
| (-0.99883222683232658826 + 3.7575423756322698196e-938j)  +/-  (4.94e-234, 4.94e-234j)
| (-0.8090169943749474241 + 5.2580261925380022134e-949j)  +/-  (8.72e-236, 8.72e-236j)
| (0.072434800161762362766 + 4.8192818788217709673e-967j)  +/-  (5.46e-254, 5.46e-254j)
| (0.99533163471764862901 - 2.4650547386888746353e-946j)  +/-  (1.73e-233, 1.73e-233j)
| (0.71559896074412108127 - 8.3583294544584981896e-966j)  +/-  (1.12e-237, 1.12e-237j)
| (0.90687436085054544282 - 6.0214328933743833544e-962j)  +/-  (5.66e-234, 5.66e-234j)
| (-0.74851074817110109863 + 2.2382674734802202526e-970j)  +/-  (4.79e-237, 4.79e-237j)
| (-0.71559896074412108127 - 2.3097157327002579787e-972j)  +/-  (1.05e-237, 1.05e-237j)
| (0.86196966688004923168 - 4.3400254903281844345e-968j)  +/-  (8.76e-235, 8.76e-235j)
| (0.74851074817110109863 - 1.7907058225399232281e-973j)  +/-  (5.71e-237, 5.71e-237j)
| (0.12053668025532305335 - 6.6594937534614128533e-989j)  +/-  (1.24e-252, 1.24e-252j)
| (-0.94331181325774310261 + 1.7828408904428192583e-968j)  +/-  (1.77e-233, 1.77e-233j)
| (-0.60716250781871119919 - 3.8263453772714292555e-976j)  +/-  (4.12e-240, 4.12e-240j)
| (-0.83647013801022674627 + 3.4750203555207993638e-970j)  +/-  (3.06e-235, 3.06e-235j)
| (0.68101585878679713652 + 4.9022363842172703343e-976j)  +/-  (1.8e-238, 1.8e-238j)
| (0.64484221273617061787 - 2.661362733311007449e-976j)  +/-  (2.71e-239, 2.71e-239j)
| (-0.98950639945105110237 - 4.5925345491893839131e-968j)  +/-  (3.06e-233, 3.06e-233j)
| (-0.68101585878679713652 + 6.6870788494984060354e-978j)  +/-  (1.72e-238, 1.72e-238j)
| (-0.21578419676780614184 - 1.021743555753060053e-988j)  +/-  (4.29e-250, 4.29e-250j)
| (-0.8854560256532098959 + 1.3836361202650587313e-971j)  +/-  (2.56e-234, 2.56e-234j)
| (0.60716250781871119919 - 1.495771507500236192e-979j)  +/-  (4.16e-240, 4.16e-240j)
| (0.83647013801022674627 + 1.6992462348819657366e-973j)  +/-  (2.91e-235, 2.91e-235j)
| (-0.024163745236132288599 - 6.3579392519341032577e-1001j)  +/-  (3.12e-255, 3.12e-255j)
| (-0.52764024410613273347 - 2.0164449262329113002e-987j)  +/-  (5.41e-242, 5.41e-242j)
| (-0.39936458356569555946 + 1.3256114167028126001e-991j)  +/-  (3.21e-245, 3.21e-245j)
| (0.52764024410613273347 + 8.089602579159399331e-987j)  +/-  (5.4e-242, 5.4e-242j)
| (0.48598341324260608274 + 3.184429055179567521e-988j)  +/-  (4.84e-243, 4.84e-243j)
| (0.98137012613941344325 - 8.9137004877698926635e-984j)  +/-  (3.58e-233, 3.58e-233j)
| (-0.56806474673115580251 - 8.4210744146487507034e-1005j)  +/-  (5.01e-241, 5.01e-241j)
| (-0.64484221273617061787 + 5.8888302631105094883e-1002j)  +/-  (2.98e-239, 2.98e-239j)
| (-0.90687436085054544282 - 9.5101825275194545184e-1012j)  +/-  (5.78e-234, 5.78e-234j)
| (0.44319154559924132244 - 4.313969158276618416e-1021j)  +/-  (4.2e-244, 4.2e-244j)
| (0.56806474673115580251 + 2.8030026974531775864e-1022j)  +/-  (6.03e-241, 6.03e-241j)
| (0.16835704134703855236 + 3.5539792175018375849e-1032j)  +/-  (2.27e-251, 2.27e-251j)
| (-0.48598341324260608274 - 8.8465942762991588047e-1024j)  +/-  (5.27e-243, 5.27e-243j)
| (-0.072434800161762362766 - 2.2115678633067420437e-1035j)  +/-  (4.24e-254, 4.24e-254j)
| (0.35460488704253562597 + 4.4847914856919650337e-1028j)  +/-  (2.23e-246, 2.23e-246j)
| (0.3090169943749474241 + 9.6966909442435909082e-1029j)  +/-  (2.04e-247, 2.04e-247j)
| (-0.12053668025532305335 - 6.6922926174071651105e-1035j)  +/-  (9.22e-253, 9.22e-253j)
| (-0.44319154559924132244 + 1.3418119533495850975e-1025j)  +/-  (4.97e-244, 4.97e-244j)
| (-0.16835704134703855236 + 1.3061130985385720884e-1033j)  +/-  (2.5e-251, 2.5e-251j)
| (0.26270737819858692381 - 4.3772420632265888536e-1030j)  +/-  (8.57e-249, 8.57e-249j)
| (0.39936458356569555946 - 4.789264351331639239e-1027j)  +/-  (3.79e-245, 3.79e-245j)
| (0.21578419676780614184 - 4.966735243877324972e-1032j)  +/-  (4.25e-250, 4.25e-250j)
| (-0.35460488704253562597 + 3.0890129983349642928e-1029j)  +/-  (2.18e-246, 2.18e-246j)
| (-0.3090169943749474241 - 1.07424620704918088e-1029j)  +/-  (1.45e-247, 1.45e-247j)
| (0.024163745236132288599 - 4.6558575667800015692e-1037j)  +/-  (3.12e-255, 3.12e-255j)
-------------------------------------------------
The weights are:
| (0.00032118592992949068699 + 4.622007605377751777e-884j)  +/-  (7.3e-43, 1.06e-153j)
| (0.01432284359138499409 - 2.3151805843998110655e-884j)  +/-  (4.08e-43, 5.94e-154j)
| (0.0021877003019682993748 + 2.3115203472960112109e-885j)  +/-  (1.38e-43, 2.01e-154j)
| (0.00088110749497530849307 - 9.0971762172310961781e-886j)  +/-  (1.08e-43, 1.57e-154j)
| (0.001694812661052135448 + 7.4261679043927879121e-884j)  +/-  (3.17e-44, 4.61e-155j)
| (0.0021877003019682993748 - 6.9919848768088152991e-884j)  +/-  (2.72e-44, 3.95e-155j)
| (0.00014330672200451197499 + 1.4614286390070425048e-886j)  +/-  (1.91e-45, 2.78e-156j)
| (0.0012579220153059481056 + 1.3072260998384510941e-885j)  +/-  (7.16e-45, 1.04e-155j)
| (0.00056788731570941149603 + 5.8323209672218476175e-886j)  +/-  (6.78e-45, 9.86e-156j)
| (3.5910502171933622962e-05 - 7.7941408941753986759e-885j)  +/-  (4.29e-47, 6.24e-158j)
| (0.0033225788712988015191 - 6.4634709201077332385e-884j)  +/-  (2.59e-47, 3.76e-158j)
| (0.0012579220153059481056 - 8.144997705366408464e-884j)  +/-  (1.16e-46, 1.69e-157j)
| (0.0039539737442876455174 - 4.3226428570577885468e-885j)  +/-  (6.94e-49, 1.01e-159j)
| (0.0060324292556322604474 + 6.9016658829245051743e-885j)  +/-  (1.79e-49, 2.6e-160j)
| (0.00088110749497530849307 + 9.6067804546294891144e-884j)  +/-  (4.89e-47, 7.12e-158j)
| (0.0053152538894234813531 + 5.9608259937125516307e-884j)  +/-  (7.55e-50, 1.1e-160j)
| (0.0060324292556322604474 - 5.8190832001462834938e-884j)  +/-  (2.97e-50, 4.33e-161j)
| (3.5910502171933622962e-05 - 3.6556702491252358343e-887j)  +/-  (1.11e-49, 1.62e-160j)
| (0.0053152538894234813531 - 5.9819361140354164837e-885j)  +/-  (1.27e-50, 1.85e-161j)
| (0.015303895380392700787 + 3.377791726153165225e-884j)  +/-  (1.73e-53, 2.52e-164j)
| (0.00014330672200451197499 + 4.9795172171685822502e-884j)  +/-  (1.94e-48, 2.82e-159j)
| (0.0075064327289528285492 - 5.5470733945653224419e-884j)  +/-  (5.22e-52, 7.59e-163j)
| (0.0027319829789525337087 + 6.692119187925868667e-884j)  +/-  (4.84e-49, 7.03e-160j)
| (0.0067651024595744380512 - 7.8786944914195808637e-885j)  +/-  (1.98e-52, 2.87e-163j)
| (0.0075064327289528285492 + 8.9107928334456252773e-885j)  +/-  (4.18e-53, 6.08e-164j)
| (0.0039539737442876455174 + 6.2752732192124555452e-884j)  +/-  (1.03e-50, 1.5e-161j)
| (0.0067651024595744380512 + 5.6819749580253131204e-884j)  +/-  (3.22e-52, 4.69e-163j)
| (0.015161090903277323286 - 3.531505885609829576e-884j)  +/-  (4.51e-56, 6.56e-167j)
| (0.001694812661052135448 - 1.7748574531624167343e-885j)  +/-  (1.7e-52, 2.47e-163j)
| (0.0097131336784506686447 - 1.231341533742614373e-884j)  +/-  (4.19e-56, 6.09e-167j)
| (0.004620272434110034158 + 5.121606039815546566e-885j)  +/-  (4.32e-53, 6.28e-164j)
| (0.0082494984627827874059 + 5.4127732701311253898e-884j)  +/-  (1.18e-54, 1.71e-165j)
| (0.008987361856515681172 - 5.2780100105230060727e-884j)  +/-  (1.1e-55, 1.6e-166j)
| (0.00032118592992949068699 - 3.2850700268876984454e-886j)  +/-  (4.86e-53, 7.06e-164j)
| (0.0082494984627827874059 - 9.9956093279232588838e-885j)  +/-  (1.6e-55, 2.32e-166j)
| (0.014668264314234964945 + 2.4633213085160027796e-884j)  +/-  (5.41e-59, 7.86e-170j)
| (0.0033225788712988015191 + 3.586875046752238955e-885j)  +/-  (5.72e-54, 8.32e-165j)
| (0.0097131336784506686447 + 5.1420861634428429461e-884j)  +/-  (3.93e-57, 5.71e-168j)
| (0.004620272434110034158 - 6.1109310132872646999e-884j)  +/-  (6.01e-54, 8.74e-165j)
| (0.01537563251409481991 + 3.0702267657917056781e-884j)  +/-  (7.06e-60, 1.03e-170j)
| (0.011101473427686471711 - 1.4811093370162498575e-884j)  +/-  (5.21e-59, 7.57e-170j)
| (0.01293089122143690105 + 1.8845195042013352188e-884j)  +/-  (6.38e-60, 9.28e-171j)
| (0.011101473427686471711 + 4.8651767531913819862e-884j)  +/-  (7.23e-60, 1.05e-170j)
| (0.011751078800816405642 - 4.7238116699649892651e-884j)  +/-  (1.51e-60, 2.2e-171j)
| (0.00056788731570941149603 - 1.4127677930603463481e-883j)  +/-  (1.06e-56, 1.54e-167j)
| (0.010420037592634889431 + 1.3541146520201901085e-884j)  +/-  (2.05e-59, 2.98e-170j)
| (0.008987361856515681172 + 1.1130676066893663986e-884j)  +/-  (1.14e-58, 1.65e-169j)
| (0.0027319829789525337087 - 2.9159874888215143963e-885j)  +/-  (2.93e-57, 4.26e-168j)
| (0.01236278852168239384 + 4.5804438934175955814e-884j)  +/-  (2.68e-62, 3.9e-173j)
| (0.010420037592634889431 - 5.0045607859373199725e-884j)  +/-  (2.21e-60, 3.22e-171j)
| (0.014948552409674946943 + 3.6847761385526968132e-884j)  +/-  (4.41e-64, 6.42e-175j)
| (0.011751078800816405642 + 1.6120391688134711469e-884j)  +/-  (1.97e-62, 2.87e-173j)
| (0.015303895380392700787 - 2.9169946556956888797e-884j)  +/-  (1.72e-64, 2.5e-175j)
| (0.01345008267823923922 + 4.2879797550908540232e-884j)  +/-  (1.55e-64, 2.26e-175j)
| (0.013915515341345749416 - 4.1391585197655543665e-884j)  +/-  (6.48e-65, 9.43e-176j)
| (0.015161090903277323286 + 2.7645517907209028544e-884j)  +/-  (1.61e-65, 2.35e-176j)
| (0.01236278852168239384 - 1.7466097396999813394e-884j)  +/-  (3.71e-65, 5.39e-176j)
| (0.014948552409674946943 - 2.6132195930186599745e-884j)  +/-  (1.12e-65, 1.64e-176j)
| (0.01432284359138499409 + 3.9888623215713238575e-884j)  +/-  (2.38e-66, 3.46e-177j)
| (0.01293089122143690105 - 4.4351284745292549773e-884j)  +/-  (4.91e-66, 7.14e-177j)
| (0.014668264314234964945 - 3.8373180541702868032e-884j)  +/-  (1.61e-66, 2.35e-177j)
| (0.01345008267823923922 - 2.0254606742662714668e-884j)  +/-  (8.09e-68, 1.18e-178j)
| (0.013915515341345749416 + 2.1691201633463670704e-884j)  +/-  (6.81e-68, 9.95e-179j)
| (0.01537563251409481991 - 3.2239300885899940759e-884j)  +/-  (7.3e-68, 1.03e-178j)
