Starting with polynomial:
P : 2*t
Extension levels are: 1 68
-------------------------------------------------
Trying to find an order 68 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^69 - 34*t^67 + 2211/8*t^65 - 1430*t^63 + 42315/8*t^61 - 119133/8*t^59 + 67945521/2048*t^57 - 61474519/1024*t^55 + 2944827765/32768*t^53 - 3695785665/32768*t^51 + 62828356305/524288*t^49 - 14230767915/131072*t^47 + 176821380645/2097152*t^45 - 118119545775/2097152*t^43 + 2176774486425/67108864*t^41 - 540895478445/33554432*t^39 + 14844575908435/2147483648*t^37 - 5486397089355/2147483648*t^35 + 27900908274925/34359738368*t^33 - 950185730725/4294967296*t^31 + 3534690918297/68719476736*t^29 - 697319977079/68719476736*t^27 + 7416948847113/4398046511104*t^25 - 514589420475/2199023255552*t^23 + 1886827875075/70368744177664*t^21 - 176103935007/70368744177664*t^19 + 210585824379/1125899906842624*t^17 - 3083513363/281474976710656*t^15 + 2202509545/4503599627370496*t^13 - 72243795/4503599627370496*t^11 + 52978783/144115188075855872*t^9 - 394383/72057594037927936*t^7 + 435897/9223372036854775808*t^5 - 1785/9223372036854775808*t^3 + 35/147573952589676412928*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
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (0.75307146600361093353 - 2.9848478747833765027e-810j)  +/-  (2.36e-235, 2.36e-235j)
| (0.99597429399523902958 - 7.4098349056978051245e-805j)  +/-  (1.2e-231, 1.2e-231j)
| (-0.91952777255145063832 - 6.6201186835850876528e-807j)  +/-  (4.91e-232, 4.91e-232j)
| (-0.97492791218182360702 - 5.3012302983308956769e-807j)  +/-  (2.47e-231, 2.47e-231j)
| (0.90096886790241912624 - 2.7501028070334281644e-818j)  +/-  (2.42e-232, 2.42e-232j)
| (0.93623487063973720951 + 2.3170527410319536885e-817j)  +/-  (9.82e-232, 9.82e-232j)
| (0.99899306654131464737 + 1.4427088538157606615e-815j)  +/-  (3.68e-232, 3.68e-232j)
| (-0.93623487063973720951 - 9.3274579223839188458e-817j)  +/-  (1.01e-231, 1.01e-231j)
| (-0.95105651629515357212 - 9.9735781928495778819e-829j)  +/-  (1.51e-231, 1.51e-231j)
| (-0.99094976176793475525 + 5.0211916504063648145e-848j)  +/-  (2.2e-231, 2.2e-231j)
| (0.88059553185673799519 + 3.363694150204434664e-863j)  +/-  (1.18e-232, 1.18e-232j)
| (0.97492791218182360702 + 4.7494240352444168411e-860j)  +/-  (2.67e-231, 2.67e-231j)
| (-0.90096886790241912624 - 3.3468729127784758175e-863j)  +/-  (2.69e-232, 2.69e-232j)
| (-0.85844879360186611853 + 8.7952567183421460819e-867j)  +/-  (3.48e-233, 3.48e-233j)
| (-0.99597429399523902958 + 2.7576692999557849214e-863j)  +/-  (1.2e-231, 1.2e-231j)
| (0.83457325372130265093 - 7.3990023342879740937e-881j)  +/-  (1.36e-233, 1.36e-233j)
| (0.95105651629515357212 + 8.7702455366879745077e-878j)  +/-  (1.45e-231, 1.45e-231j)
| (0.3090169943749474241 + 2.6242394807722007618e-896j)  +/-  (7.87e-247, 7.87e-247j)
| (-0.78183148246802980871 - 6.7287931467149277764e-883j)  +/-  (1.05e-234, 1.05e-234j)
| (-0.88059553185673799519 - 1.8726924272396703769e-880j)  +/-  (1e-232, 1e-232j)
| (-0.089639308903433499765 - 7.510410095494962107e-903j)  +/-  (2.58e-253, 2.58e-253j)
| (0.78183148246802980871 + 1.7651665127588733792e-884j)  +/-  (1.12e-234, 1.12e-234j)
| (-0.17855689479863664801 + 1.8440657228131645404e-899j)  +/-  (1.13e-250, 1.13e-250j)
| (-0.83457325372130265093 + 2.6201934391226440633e-882j)  +/-  (1.42e-233, 1.42e-233j)
| (-0.8090169943749474241 - 3.0122356843318714062e-883j)  +/-  (4.17e-234, 4.17e-234j)
| (0.85844879360186611853 - 2.3137175886291648603e-882j)  +/-  (3.64e-233, 3.64e-233j)
| (0.6910626489868646759 - 4.6725327818454257154e-886j)  +/-  (8.43e-237, 8.43e-237j)
| (0.8090169943749474241 + 1.1662884506039191035e-883j)  +/-  (3.74e-234, 3.74e-234j)
| (-0.99899306654131464737 + 7.6496689466033345078e-878j)  +/-  (3.49e-232, 3.49e-232j)
| (-0.62348980185873353053 - 7.2662244270035177656e-900j)  +/-  (2.17e-238, 2.17e-238j)
| (0.96396286069585329189 + 2.6031886237729479453e-891j)  +/-  (2.05e-231, 2.05e-231j)
| (0.17855689479863664801 - 2.3882752236797840965e-913j)  +/-  (1.15e-250, 1.15e-250j)
| (0.72279486382739152855 + 2.6634588139359056328e-899j)  +/-  (4.77e-236, 4.77e-236j)
| (-0.9839295885986296554 + 5.5256928100579411396e-893j)  +/-  (2.71e-231, 2.71e-231j)
| (-0.6910626489868646759 - 1.8595745757358384112e-910j)  +/-  (8.38e-237, 8.38e-237j)
| (-0.75307146600361093353 - 4.5006010357585761528e-910j)  +/-  (2.02e-235, 2.02e-235j)
| (0.26603684556667510738 + 6.1783627265168984704e-922j)  +/-  (4.15e-248, 4.15e-248j)
| (0.58778525229247312917 + 8.9448190243010372444e-914j)  +/-  (3e-239, 3e-239j)
| (0.044864830350514925458 - 1.1623459871159163894e-928j)  +/-  (1.07e-254, 1.07e-254j)
| (-0.96396286069585329189 - 7.4818906654939270494e-904j)  +/-  (2.15e-231, 2.15e-231j)
| (-0.55089698145210252269 - 4.1076736685253676909e-919j)  +/-  (2.83e-240, 2.83e-240j)
| (-0.13423326581765547604 - 2.6765798370676041758e-931j)  +/-  (4.99e-252, 4.99e-252j)
| (0.65793872593971261237 + 1.0669302651016130716e-915j)  +/-  (1.28e-237, 1.28e-237j)
| (0.55089698145210252269 + 4.8276596563973278885e-919j)  +/-  (2.71e-240, 2.71e-240j)
| (0.91952777255145063832 - 1.3485978795354462953e-909j)  +/-  (4.51e-232, 4.51e-232j)
| (-0.58778525229247312917 + 3.3157405170628535613e-918j)  +/-  (2.27e-239, 2.27e-239j)
| (-0.65793872593971261237 - 1.3767634183537260661e-917j)  +/-  (1.31e-237, 1.31e-237j)
| (0.9839295885986296554 - 6.2385848442700182904e-909j)  +/-  (2.49e-231, 2.49e-231j)
| (0.51289927740590614391 - 1.4440029919562837296e-924j)  +/-  (2.52e-241, 2.52e-241j)
| (0.62348980185873353053 + 5.0163044921072990756e-922j)  +/-  (2.02e-238, 2.02e-238j)
| (-0.72279486382739152855 + 2.2499639637942470041e-919j)  +/-  (4.79e-236, 4.79e-236j)
| (-0.51289927740590614391 - 1.9864208427227909435e-925j)  +/-  (2.41e-241, 2.41e-241j)
| (-0.26603684556667510738 - 2.8567090952626293746e-932j)  +/-  (4.73e-248, 4.73e-248j)
| (0.47386866247299867071 + 2.1663346191179885615e-925j)  +/-  (2.36e-242, 2.36e-242j)
| (0.43388373911755812048 + 2.3908247719863602318e-927j)  +/-  (2.06e-243, 2.06e-243j)
| (-0.22252093395631440429 - 2.6893893596371731332e-934j)  +/-  (2.08e-249, 2.08e-249j)
| (-0.47386866247299867071 + 7.1233078786337027656e-926j)  +/-  (2.39e-242, 2.39e-242j)
| (0.99094976176793475525 + 4.6930604709398347319e-932j)  +/-  (2.08e-231, 2.08e-231j)
| (0.13423326581765547604 - 5.3315552078062225865e-960j)  +/-  (4.84e-252, 4.84e-252j)
| (0.39302503165392361819 - 3.0855646707222705977e-952j)  +/-  (1.66e-244, 1.66e-244j)
| (0.089639308903433499765 + 1.6183226422665282197e-961j)  +/-  (2.19e-253, 2.19e-253j)
| (-0.39302503165392361819 + 7.3789967117335541081e-952j)  +/-  (1.65e-244, 1.65e-244j)
| (-0.43388373911755812048 + 1.2312960096132415141e-951j)  +/-  (2.16e-243, 2.16e-243j)
| (-8.1597279973563698271e-999 + 9.7988721195947590293e-999j)  +/-  (8.8e-997, 8.8e-997j)
| (0.35137482408134270489 + 5.6897692677856819074e-953j)  +/-  (1.04e-245, 1.04e-245j)
| (0.22252093395631440429 - 3.5203131019774498893e-957j)  +/-  (2.48e-249, 2.48e-249j)
| (-0.044864830350514925458 - 5.1842856200058739759e-963j)  +/-  (1.07e-254, 1.07e-254j)
| (-0.3090169943749474241 + 1.3865879959932434323e-955j)  +/-  (6.59e-247, 6.59e-247j)
| (-0.35137482408134270489 + 1.6357968808766855742e-953j)  +/-  (1.09e-245, 1.09e-245j)
-------------------------------------------------
The weights are:
| (0.0061840481013024608854 + 1.8908149148220205393e-806j)  +/-  (8.43e-37, 2.3e-147j)
| (0.00011478865286693103289 + 1.5815000679643911327e-806j)  +/-  (2.51e-37, 6.84e-148j)
| (0.0022066953643795380293 - 1.1952334651810211467e-807j)  +/-  (1.67e-37, 4.56e-148j)
| (0.0007073652292684348126 - 2.9216540659611751599e-808j)  +/-  (4.13e-38, 1.13e-148j)
| (0.0026893585581519033534 + 2.099265679737021675e-806j)  +/-  (1.17e-37, 3.19e-148j)
| (0.0017637752428313504748 + 2.1888305803379634141e-806j)  +/-  (9.95e-38, 2.72e-148j)
| (2.8755042891149788702e-05 + 7.0579946391422833394e-807j)  +/-  (4.6e-38, 1.25e-148j)
| (0.0017637752428313504748 + 2.1915530374758896753e-808j)  +/-  (7.29e-38, 1.99e-148j)
| (0.001364164325893232685 - 5.3567520471560981721e-808j)  +/-  (3.8e-38, 1.04e-148j)
| (0.0002574081378867622008 + 1.3033498533630833699e-809j)  +/-  (1.02e-39, 2.79e-150j)
| (0.0032078787039135534094 - 2.06224702213555374e-806j)  +/-  (4.41e-39, 1.2e-149j)
| (0.0007073652292684348126 - 2.4908711658366459808e-806j)  +/-  (2.29e-39, 6.25e-150j)
| (0.0026893585581519033534 + 2.2026060863741370301e-807j)  +/-  (2.2e-39, 6.01e-150j)
| (0.0037580809823357237807 + 2.0800099710922463346e-807j)  +/-  (1.15e-40, 3.13e-151j)
| (0.00011478865286693103289 + 3.8465356401945928086e-810j)  +/-  (2.39e-40, 6.52e-151j)
| (0.0043355354881862598701 - 1.9933115664046267428e-806j)  +/-  (3.7e-41, 1.01e-151j)
| (0.001364164325893232685 - 2.251241908330686219e-806j)  +/-  (3.07e-40, 8.38e-151j)
| (0.012921549959821053029 + 1.4060840443235860162e-806j)  +/-  (1.78e-44, 4.87e-155j)
| (0.0055534219003120399694 - 2.7341166216461648486e-807j)  +/-  (5.51e-43, 1.51e-153j)
| (0.0032078787039135534094 - 1.9924194014363015826e-807j)  +/-  (1.14e-40, 3.1e-151j)
| (0.014170925632847354681 - 9.8702890218627349005e-807j)  +/-  (4.94e-46, 1.35e-156j)
| (0.0055534219003120399694 - 1.9253910450166251641e-806j)  +/-  (1.67e-43, 4.55e-154j)
| (0.013830249075998122925 - 8.9408450215809928088e-807j)  +/-  (4.04e-46, 1.1e-156j)
| (0.0043355354881862598701 - 2.2565832238069103512e-807j)  +/-  (1.06e-42, 2.88e-153j)
| (0.0049355928973218041136 + 2.479533603305550063e-807j)  +/-  (2.73e-43, 7.45e-154j)
| (0.0037580809823357237807 + 2.0273186535202884918e-806j)  +/-  (4.55e-44, 1.24e-154j)
| (0.0074633202167893923247 + 1.8191832496148616578e-806j)  +/-  (7.27e-47, 1.98e-157j)
| (0.0049355928973218041136 + 1.9594953996100843439e-806j)  +/-  (6.7e-45, 1.83e-155j)
| (2.8755042891149788702e-05 - 1.9505467270061775451e-810j)  +/-  (3.18e-45, 8.68e-156j)
| (0.0087322923854022457449 + 4.3224631927926441622e-807j)  +/-  (1.57e-49, 4.28e-160j)
| (0.0010110800457009562962 + 2.3410242563660019772e-806j)  +/-  (9.1e-46, 2.48e-156j)
| (0.013830249075998122925 - 1.2684042807972153747e-806j)  +/-  (9.82e-51, 2.68e-161j)
| (0.0068223940689248933896 - 1.8554828081484803779e-806j)  +/-  (2.02e-46, 5.51e-157j)
| (0.00045546520971616278922 - 1.4459011584393351091e-808j)  +/-  (8.54e-45, 2.33e-155j)
| (0.0074633202167893923247 + 3.6337083482705693359e-807j)  +/-  (4.37e-49, 1.19e-159j)
| (0.0061840481013024608854 + 3.0135973570684865612e-807j)  +/-  (1.06e-47, 2.91e-158j)
| (0.013274634240013329418 - 1.3606430927848520457e-806j)  +/-  (1.53e-51, 4.17e-162j)
| (0.0093501213883924816007 - 1.7046181013786482038e-806j)  +/-  (3.08e-51, 8.4e-162j)
| (0.014256959242823135926 + 1.127924901547292885e-806j)  +/-  (1.97e-52, 5.38e-163j)
| (0.0010110800457009562962 + 7.2044376539950199597e-808j)  +/-  (6.92e-46, 1.89e-156j)
| (0.0099501787975280258442 + 5.0694542299281887032e-807j)  +/-  (2.05e-52, 5.59e-163j)
| (0.014028306147827523513 + 9.4039651578128750331e-807j)  +/-  (1.64e-52, 4.47e-163j)
| (0.0081016661844118248288 - 1.7819637546440125247e-806j)  +/-  (3.31e-51, 9.02e-162j)
| (0.0099501787975280258442 + 1.6644992210533058845e-806j)  +/-  (8.73e-53, 2.38e-163j)
| (0.0022066953643795380293 - 2.1403212173620662166e-806j)  +/-  (5.15e-50, 1.41e-160j)
| (0.0093501213883924816007 - 4.6892230507891557519e-807j)  +/-  (5.6e-53, 1.53e-163j)
| (0.0081016661844118248288 - 3.970234063836132747e-807j)  +/-  (4.89e-52, 1.34e-162j)
| (0.00045546520971616278922 + 2.8022773927420256374e-806j)  +/-  (2.94e-52, 8.03e-163j)
| (0.010527633303378561934 - 1.6234517842671560849e-806j)  +/-  (1.27e-54, 3.47e-165j)
| (0.0087322923854022457449 + 1.7437778357186076609e-806j)  +/-  (7.8e-53, 2.13e-163j)
| (0.0068223940689248933896 - 3.3142555758653666571e-807j)  +/-  (8.84e-53, 2.41e-163j)
| (0.010527633303378561934 - 5.4621631731920808795e-807j)  +/-  (4.06e-56, 1.11e-166j)
| (0.013274634240013329418 - 8.0279212080515547046e-807j)  +/-  (2.6e-58, 7.1e-169j)
| (0.011077835581800732305 + 1.5815185833810390289e-806j)  +/-  (2.2e-56, 6.01e-167j)
| (0.011596355727562382361 - 1.5387520320869807808e-806j)  +/-  (4.03e-57, 1.1e-167j)
| (0.013578349056445850902 + 8.4818549971027114668e-807j)  +/-  (1.09e-58, 2.96e-169j)
| (0.011077835581800732305 + 5.8663942007579575083e-807j)  +/-  (2.47e-58, 6.76e-169j)
| (0.0002574081378867622008 - 3.7962366452839580363e-806j)  +/-  (5.25e-56, 1.43e-166j)
| (0.014028306147827523513 + 1.2217737754658359104e-806j)  +/-  (1.16e-59, 3.15e-170j)
| (0.012079018921334747685 + 1.4952122721296571162e-806j)  +/-  (6.97e-59, 1.9e-169j)
| (0.014170925632847354681 - 1.1749177836624547293e-806j)  +/-  (7.22e-60, 1.97e-170j)
| (0.012079018921334747685 + 6.7056941924997200131e-807j)  +/-  (4.48e-61, 1.22e-171j)
| (0.011596355727562382361 - 6.2812125846471288637e-807j)  +/-  (1.41e-60, 3.84e-171j)
| (0.014285714285714285714 - 1.0808850441382639483e-806j)  +/-  (2.85e-61, 7.77e-172j)
| (0.01252193904288293524 - 1.4509657385754091413e-806j)  +/-  (1.01e-60, 2.77e-171j)
| (0.013578349056445850902 + 1.3147223568127214772e-806j)  +/-  (3.77e-61, 1.03e-171j)
| (0.014256959242823135926 + 1.0338891474613409842e-806j)  +/-  (1.47e-61, 4.03e-172j)
| (0.012921549959821053029 + 7.579968384654606735e-807j)  +/-  (9.45e-63, 2.59e-173j)
| (0.01252193904288293524 - 7.1389191958887856299e-807j)  +/-  (8.7e-63, 2.37e-173j)
