Starting with polynomial:
P : t^16 - 120*t^14 + 5460*t^12 - 120120*t^10 + 1351350*t^8 - 7567560*t^6 + 18918900*t^4 - 16216200*t^2 + 2027025
Extension levels are: 16 23
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Trying to find an order 23 Kronrod extension for:
P1 : t^16 - 120*t^14 + 5460*t^12 - 120120*t^10 + 1351350*t^8 - 7567560*t^6 + 18918900*t^4 - 16216200*t^2 + 2027025
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^39 - 265156989870445/517583353637*t^37 + 60440795944927665/517583353637*t^35 - 1160684062907266755/73940479091*t^33 + 102832387408357757700/73940479091*t^31 - 6357534990615583645860/73940479091*t^29 + 283317919004477132414100/73940479091*t^27 - 9271446808777613896659300/73940479091*t^25 + 224921346094866122225543250/73940479091*t^23 - 4055942418136064219829161250/73940479091*t^21 + 54196987585233036110199806250/73940479091*t^19 - 531956833819080554467616591250/73940479091*t^17 + 3778492655502392241903566962500/73940479091*t^15 - 18991889528363942573598978262500/73940479091*t^13 + 65377944725878348263616429012500/73940479091*t^11 - 146796379320773639404873768342500/73940479091*t^9 + 198930385082023356722484470821875/73940479091*t^7 - 142422541931580126074411975296875/73940479091*t^5 + 42617326845917264694121427934375/73940479091*t^3 - 3785124500229339318122368171875/73940479091*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 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:
| (-5.4722257059493430884 - 2.6103283595791624033e-587j)  +/-  (3.15e-246, 3.15e-246j)
| (9.9218097297637320362 + 1.2068649306027061951e-599j)  +/-  (9.14e-249, 9.14e-249j)
| (-9.9218097297637320362 + 3.6250032824602136862e-600j)  +/-  (9.75e-249, 9.75e-249j)
| (8.9093207615244621015 - 9.452378383445712022e-603j)  +/-  (8.61e-248, 8.61e-248j)
| (8.0680447242593927824 + 8.2828197918255106106e-613j)  +/-  (3.71e-247, 3.71e-247j)
| (1.8666236688856028509 - 3.0004276850134576267e-624j)  +/-  (5.59e-249, 5.59e-249j)
| (-4.4929553025200112427 + 1.5562856291695990159e-624j)  +/-  (1.5e-246, 1.5e-246j)
| (-8.0680447242593927824 - 3.3704139233305516917e-634j)  +/-  (3.65e-247, 3.65e-247j)
| (-8.9093207615244621015 + 2.7198444532833340262e-639j)  +/-  (9.02e-248, 9.02e-248j)
| (5.0044747704150725869 - 1.7213649854773565951e-640j)  +/-  (2.67e-246, 2.67e-246j)
| (6.6308781983931284802 - 9.1828026905946462271e-643j)  +/-  (1.92e-246, 1.92e-246j)
| (2.7602450476307016168 + 1.4101804703744015157e-645j)  +/-  (1.82e-248, 1.82e-248j)
| (-1.9519803457163334645 + 7.0443715857279556258e-646j)  +/-  (1.66e-248, 1.66e-248j)
| (5.4722257059493430884 - 1.5962449554197981254e-642j)  +/-  (3.27e-246, 3.27e-246j)
| (7.3173125900949559053 + 8.7403543828100406499e-645j)  +/-  (9.4e-247, 9.4e-247j)
| (-7.3173125900949559053 - 9.4504405827182817825e-647j)  +/-  (9.59e-247, 9.59e-247j)
| (3.6008736241715482882 - 6.5091075433813595059e-657j)  +/-  (6.94e-247, 6.94e-247j)
| (-3.9430636356795411594 - 6.930595347683918211e-673j)  +/-  (9.51e-247, 9.51e-247j)
| (-1.8666236688856028509 - 3.1480424518209475918e-689j)  +/-  (5.68e-249, 5.68e-249j)
| (6.00752277014523139 - 1.8576032971474821037e-686j)  +/-  (2.71e-246, 2.71e-246j)
| (1.9519803457163334645 - 1.3563758034584753886e-691j)  +/-  (1.64e-248, 1.64e-248j)
| (3.3269264534958401955 - 6.9067823209424666002e-689j)  +/-  (2.32e-247, 2.32e-247j)
| (0.63822626843395679167 + 6.5557244928269988552e-700j)  +/-  (5.41e-253, 5.41e-253j)
| (-0.38676060450055734772 + 1.5644997312760175868e-705j)  +/-  (9.82e-254, 9.82e-254j)
| (-3.6008736241715482882 + 2.6907766967259323366e-693j)  +/-  (6.86e-247, 6.86e-247j)
| (-6.00752277014523139 + 4.7906716830054267478e-709j)  +/-  (2.8e-246, 2.8e-246j)
| (2.0495175789359637984 + 2.3746530232834918673e-726j)  +/-  (1.34e-248, 1.34e-248j)
| (-6.6308781983931284802 + 3.225743337993725521e-726j)  +/-  (1.86e-246, 1.86e-246j)
| (-1.1638291005549647742 + 9.1835964418174141424e-738j)  +/-  (7.93e-252, 7.93e-252j)
| (-0.63822626843395679167 + 7.3620684102795666874e-739j)  +/-  (5e-253, 5e-253j)
| (-3.3269264534958401955 + 4.3908902895638301752e-735j)  +/-  (2.3e-247, 2.3e-247j)
| (3.9430636356795411594 + 9.1136027008159594363e-743j)  +/-  (9.82e-247, 9.82e-247j)
| (0.38676060450055734772 + 6.2498249955075118739e-749j)  +/-  (9.82e-254, 9.82e-254j)
| (-2.7602450476307016168 + 1.1069230382976792281e-742j)  +/-  (1.82e-248, 1.82e-248j)
| (-5.0044747704150725869 + 5.5469360646628782681e-760j)  +/-  (2.32e-246, 2.32e-246j)
| (-2.0495175789359637984 + 4.2371115764843778324e-774j)  +/-  (1.27e-248, 1.27e-248j)
| (3.9652742268129463881e-785 + 1.5499829808941043607e-784j)  +/-  (6.24e-783, 6.24e-783j)
| (1.1638291005549647742 + 5.4312496017342640596e-779j)  +/-  (8.81e-252, 8.81e-252j)
| (4.4929553025200112427 + 5.2731503259950671533e-785j)  +/-  (1.45e-246, 1.45e-246j)
-------------------------------------------------
The weights are:
| (6.0830682400886961448e-08 - 7.5646783548598875782e-594j)  +/-  (2.36e-87, 1.99e-209j)
| (1.956251481219858178e-22 - 9.8617269294368493595e-606j)  +/-  (1.64e-97, 1.39e-219j)
| (1.956251481219858178e-22 + 3.411819464394258076e-605j)  +/-  (4.42e-98, 3.73e-220j)
| (2.0946636917631573257e-18 + 2.9691130020759830933e-603j)  +/-  (5.95e-96, 5.02e-218j)
| (2.3078811048743511789e-15 - 2.7396086362456495395e-601j)  +/-  (1.11e-94, 9.4e-217j)
| (0.24564887928048390418 + 1.9416003353375922879e-589j)  +/-  (1.42e-74, 1.2e-196j)
| (8.9229825069056125418e-06 - 8.2446358279247496458e-593j)  +/-  (3.98e-87, 3.36e-209j)
| (2.3078811048743511789e-15 + 1.4290303578964972671e-600j)  +/-  (5.43e-96, 4.58e-218j)
| (2.0946636917631573257e-18 - 1.2423408697200389362e-602j)  +/-  (2.16e-97, 1.82e-219j)
| (6.9394321764125698016e-07 + 1.1032566133990831678e-594j)  +/-  (7.33e-91, 6.18e-213j)
| (7.4252360808492088198e-11 - 4.4403032316670908147e-598j)  +/-  (1.58e-94, 1.33e-216j)
| (0.0051793324840222993134 - 1.7510126759065015565e-591j)  +/-  (7.75e-85, 6.54e-207j)
| (-0.33468184900578713506 - 6.3786595431081440364e-589j)  +/-  (3.12e-82, 2.63e-204j)
| (6.0830682400886961448e-08 - 1.4508544049175062324e-595j)  +/-  (2.11e-92, 1.78e-214j)
| (6.7505966146377972348e-13 + 1.3502847062375424781e-599j)  +/-  (5.47e-96, 4.62e-218j)
| (6.7505966146377972348e-13 - 9.3597315711150422305e-599j)  +/-  (3.52e-98, 2.97e-220j)
| (5.7255789326214789798e-05 - 4.5456045532455450645e-592j)  +/-  (2.6e-89, 2.19e-211j)
| (9.1149570763336520248e-05 + 5.9419034166661909016e-592j)  +/-  (9.85e-92, 8.31e-214j)
| (0.24564887928048390418 + 3.9519370858730500048e-589j)  +/-  (1.57e-84, 1.32e-206j)
| (3.3982370564314561994e-09 + 1.04277126718869304e-596j)  +/-  (6.01e-94, 5.07e-216j)
| (-0.33468184900578713506 - 3.0244913065276022397e-589j)  +/-  (6.88e-85, 5.8e-207j)
| (0.00083791148335366884001 + 7.6700394260750369629e-592j)  +/-  (5.69e-89, 4.8e-211j)
| (0.14407609986030057247 + 1.2091651190788517497e-589j)  +/-  (2.34e-85, 1.97e-207j)
| (0.072505020419435823504 - 2.1369710954373273794e-589j)  +/-  (7.12e-86, 6e-208j)
| (5.7255789326214789798e-05 - 2.203899631108744369e-591j)  +/-  (1.26e-91, 1.06e-213j)
| (3.3982370564314561994e-09 - 2.2362819948222230365e-595j)  +/-  (6.83e-97, 5.76e-219j)
| (0.15309272836567013638 + 1.2159015391732282124e-589j)  +/-  (7.36e-87, 6.2e-209j)
| (7.4252360808492088198e-11 + 4.6382717622524636466e-597j)  +/-  (3.75e-98, 3.16e-220j)
| (0.11488171697337078897 - 5.3695338131357198712e-590j)  +/-  (1.99e-87, 1.67e-209j)
| (0.14407609986030057247 + 1.5284539199343401482e-589j)  +/-  (7.65e-87, 6.45e-209j)
| (0.00083791148335366884001 + 3.1459407773433989026e-591j)  +/-  (2.53e-92, 2.13e-214j)
| (9.1149570763336520248e-05 + 9.6504026592140218716e-593j)  +/-  (2.97e-93, 2.47e-215j)
| (0.072505020419435823504 - 1.8548416659155526891e-589j)  +/-  (1.63e-88, 1.39e-210j)
| (0.0051793324840222993134 - 5.3153626296454627181e-591j)  +/-  (4.06e-92, 3.44e-214j)
| (6.9394321764125698016e-07 + 2.4710777059052008085e-593j)  +/-  (1.68e-95, 1.42e-217j)
| (0.15309272836567013638 + 2.6720651887248076178e-589j)  +/-  (2.21e-90, 1.92e-212j)
| (0.19660414709897331091 + 1.8133442662517793463e-589j)  +/-  (5.65e-91, 9.01e-213j)
| (0.11488171697337078897 - 3.4861196791788808129e-590j)  +/-  (6.86e-91, 5.83e-213j)
| (8.9229825069056125418e-06 - 8.1019379843456679933e-594j)  +/-  (9.31e-95, 7.51e-217j)
