Starting with polynomial:
P : t^6 - 15*t^4 + 45*t^2 - 15
Extension levels are: 6 39
-------------------------------------------------
Trying to find an order 39 Kronrod extension for:
P1 : t^6 - 15*t^4 + 45*t^2 - 15
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^45 - 9659591676117606105841859958087650835/10905070395460721410598644805409721*t^43 + 66026150776609822680135103251503248599315/185386196722832263980176961691965257*t^41 - 175880274472361865700135118522932866764501055/2039248163951154903781946578611617827*t^39 + 4100530828361821789987832545741615955720196390/291321166278736414825992368373088261*t^37 - 3347335912119531540956256674494767729080719599930/2039248163951154903781946578611617827*t^35 + 2425351217010781982476109949914452470707555392200/17136539192866847930940727551358133*t^33 - 14349209198313966133576365057884405634810856323900/1557867199351531630085520686487103*t^31 + 713418404937074956521331087900746910595995762990650/1557867199351531630085520686487103*t^29 - 27260463800328845882379494790813627214888040140851150/1557867199351531630085520686487103*t^27 + 801499649820815206771988984558960218787571948661202550/1557867199351531630085520686487103*t^25 - 18076921915240586359987348867381039322594830699962596250/1557867199351531630085520686487103*t^23 + 310515178370373468207105876581764491292941657659624580000/1557867199351531630085520686487103*t^21 - 4015764983051732752872278534569806322322785643305089165000/1557867199351531630085520686487103*t^19 + 38457955222727674306905682385349469678439171055253798927500/1557867199351531630085520686487103*t^17 - 266591658856582137426066766239621397432605728171534069347500/1557867199351531630085520686487103*t^15 + 1296981356592082893691869923813386274864644667644460818359375/1557867199351531630085520686487103*t^13 - 4246021766847439435279913592239737053710175103456785363703125/1557867199351531630085520686487103*t^11 + 8826108208950043300659734483356338566893539535189633120378125/1557867199351531630085520686487103*t^9 - 10735517765412670192671527674991336573659965427425836507221875/1557867199351531630085520686487103*t^7 + 6803747694776334268646772073314693767481453618295309847343750/1557867199351531630085520686487103*t^5 - 1908155273320102121285580171810588974242370090200118716218750/1557867199351531630085520686487103*t^3 + 177654722484639906157541093836411386007129188614788946812500/1557867199351531630085520686487103*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:
| (-6.9362244414270950769 - 8.810384717625451411e-533j)  +/-  (1.26e-244, 1.26e-244j)
| (11.841779962517686511 + 6.4727239567104415596e-537j)  +/-  (2.11e-247, 2.11e-247j)
| (-10.883796111088663696 - 1.2618803427520475284e-541j)  +/-  (2.76e-246, 2.76e-246j)
| (10.088316539168294295 - 6.6660857777917756786e-548j)  +/-  (1.35e-245, 1.35e-245j)
| (-8.0973948964825173287 - 4.8921894187108754102e-553j)  +/-  (1.23e-244, 1.23e-244j)
| (5.8490911189105055119 - 7.770882566746957442e-558j)  +/-  (4.41e-245, 4.41e-245j)
| (-8.7179141361956481804 - 6.6150430195150163994e-563j)  +/-  (8.59e-245, 8.59e-245j)
| (-11.841779962517686511 - 7.1045405287635125145e-572j)  +/-  (2.04e-247, 2.04e-247j)
| (-4.8128785045289757827 - 1.9168699509040427742e-568j)  +/-  (7.35e-246, 7.35e-246j)
| (3.8133728980120139761 + 1.0783265486064242894e-569j)  +/-  (5.86e-247, 5.86e-247j)
| (1.4206298131907716616 + 1.2854969154315412991e-583j)  +/-  (4.68e-251, 4.68e-251j)
| (6.9362244414270950769 - 9.4115529148400448814e-576j)  +/-  (1.23e-244, 1.23e-244j)
| (-5.3256483734436532509 + 1.2118369244378072792e-582j)  +/-  (1.81e-245, 1.81e-245j)
| (-0.96251947261888847212 - 2.1112536429791660989e-598j)  +/-  (4.78e-252, 4.78e-252j)
| (-5.8490911189105055119 + 4.8113521540929318191e-590j)  +/-  (4.45e-245, 4.45e-245j)
| (2.362747193404601996 - 1.9826724859686181287e-601j)  +/-  (3.34e-249, 3.34e-249j)
| (4.3092179121204436984 - 2.9710803941340321539e-599j)  +/-  (2.31e-246, 2.31e-246j)
| (3.3242574335521189524 - 1.3311847511941654958e-617j)  +/-  (1.26e-247, 1.26e-247j)
| (10.883796111088663696 - 2.8804777761037883722e-660j)  +/-  (2.56e-246, 2.56e-246j)
| (9.3763897751872501149 + 4.7796511320058069752e-707j)  +/-  (4.33e-245, 4.33e-245j)
| (8.7179141361956481804 + 3.0806783638335154054e-735j)  +/-  (9.28e-245, 9.28e-245j)
| (0.61670659019259415219 - 1.8128388133188156066e-750j)  +/-  (1.08e-252, 1.08e-252j)
| (-10.088316539168294295 - 2.5768404960799047193e-743j)  +/-  (1.35e-245, 1.35e-245j)
| (-3.8133728980120139761 + 3.8411961373434342685e-744j)  +/-  (6.19e-247, 6.19e-247j)
| (-7.5055402973253820537 - 6.7476597144837074584e-742j)  +/-  (1.41e-244, 1.41e-244j)
| (0.96251947261888847212 + 3.2832808282719787658e-754j)  +/-  (4.78e-252, 4.78e-252j)
| (7.5055402973253820537 + 6.4109220697582333448e-745j)  +/-  (1.33e-244, 1.33e-244j)
| (2.8409595001218048997 + 1.7385021369208180321e-758j)  +/-  (2.07e-248, 2.07e-248j)
| (-6.3851360579556496311 - 1.3276943806469743443e-752j)  +/-  (8.27e-245, 8.27e-245j)
| (-3.3242574335521189524 + 1.1363070594409330193e-757j)  +/-  (1.28e-247, 1.28e-247j)
| (-1.8891758777537106755 + 7.960531772397333106e-760j)  +/-  (3.94e-250, 3.94e-250j)
| (6.3851360579556496311 + 3.0894598674564226702e-753j)  +/-  (8.62e-245, 8.62e-245j)
| (-2.362747193404601996 + 2.5156638380313193091e-763j)  +/-  (3.04e-249, 3.04e-249j)
| (4.8128785045289757827 - 2.6441038576987189604e-758j)  +/-  (7.69e-246, 7.69e-246j)
| (-9.3763897751872501149 - 2.2192314080352600255e-758j)  +/-  (4.23e-245, 4.23e-245j)
| (-2.8409595001218048997 - 6.2480327993921315328e-768j)  +/-  (1.98e-248, 1.98e-248j)
| (-1.4206298131907716616 + 6.1775698286812181731e-769j)  +/-  (4.43e-251, 4.43e-251j)
| (5.3256483734436532509 - 3.1902590749330870331e-762j)  +/-  (2e-245, 2e-245j)
| (-1.5666442810880964572e-790 - 5.2106777608267770228e-790j)  +/-  (2.45e-788, 2.45e-788j)
| (-0.42623232131330470219 - 2.9926124333830518752e-781j)  +/-  (2.44e-253, 2.44e-253j)
| (-0.61670659019259415219 + 4.4129605686854357588e-781j)  +/-  (1.14e-252, 1.14e-252j)
| (8.0973948964825173287 + 6.2471642213930491262e-772j)  +/-  (1.26e-244, 1.26e-244j)
| (-4.3092179121204436984 + 1.9735046794707896164e-778j)  +/-  (2.17e-246, 2.17e-246j)
| (0.42623232131330470219 - 1.1671431615997995795e-788j)  +/-  (2.66e-253, 2.66e-253j)
| (1.8891758777537106755 - 5.7225535800347645069e-786j)  +/-  (3.88e-250, 3.88e-250j)
-------------------------------------------------
The weights are:
| (7.9719876156563112566e-12 - 2.700342903161341885e-543j)  +/-  (6.24e-80, 2.13e-201j)
| (1.5639636194459927554e-31 + 1.2217153103362112119e-555j)  +/-  (7.89e-91, 2.69e-212j)
| (6.4629075640307463379e-27 + 1.4967067292163164958e-552j)  +/-  (4.5e-89, 1.53e-210j)
| (2.3662166233139632393e-23 + 2.5929100819339037608e-551j)  +/-  (3.59e-88, 1.22e-209j)
| (1.3956348273525253752e-15 + 5.3135461518263133693e-546j)  +/-  (1.32e-83, 4.5e-205j)
| (7.8644737622407902602e-09 - 2.6752915985522119983e-543j)  +/-  (6.24e-80, 2.13e-201j)
| (7.9765199906329463565e-18 - 2.1455704803738845968e-547j)  +/-  (4.24e-85, 1.44e-206j)
| (1.5639636194459927554e-31 - 4.6766111155698763231e-555j)  +/-  (2.33e-91, 7.93e-213j)
| (1.8914778311137072864e-06 - 4.0589732578917723175e-541j)  +/-  (4.36e-77, 1.49e-198j)
| (0.00013659601406473292725 - 1.1909640588453000836e-540j)  +/-  (4.25e-75, 1.45e-196j)
| (0.067669598987800672556 + 3.3358405603803332079e-538j)  +/-  (1.1e-60, 3.75e-182j)
| (7.9719876156563112566e-12 - 5.0630049857223326616e-545j)  +/-  (2.97e-84, 1.01e-205j)
| (1.4329890241734728532e-07 + 1.1472614792805413969e-541j)  +/-  (6.19e-79, 2.11e-200j)
| (0.1116097609263269262 - 1.685357372503602311e-537j)  +/-  (7.3e-63, 2.49e-184j)
| (7.8644737622407902602e-09 - 3.146297385516045319e-542j)  +/-  (2.88e-80, 9.82e-202j)
| (0.011645104356298250776 + 3.821124173076753189e-539j)  +/-  (3.57e-70, 1.22e-191j)
| (1.8501598516883854386e-05 + 3.1331111118860137e-541j)  +/-  (3.53e-78, 1.2e-199j)
| (0.0007726473368696213951 + 4.0885591102348090166e-540j)  +/-  (8.53e-75, 2.91e-196j)
| (6.4629075640307463379e-27 - 3.3155725407999968741e-553j)  +/-  (2.09e-93, 7.12e-215j)
| (2.2066213689794447216e-20 - 1.0107614394807097881e-549j)  +/-  (4.27e-91, 1.46e-212j)
| (7.9765199906329463565e-18 + 2.4420001109134370361e-548j)  +/-  (3.13e-90, 1.07e-211j)
| (0.053715748344850351565 + 4.3397609293651913866e-537j)  +/-  (3.26e-70, 1.11e-191j)
| (2.3662166233139632393e-23 - 1.4004382670333448267e-550j)  +/-  (1.72e-93, 5.85e-215j)
| (0.00013659601406473292725 - 4.0995813923102090698e-540j)  +/-  (3.15e-82, 1.07e-203j)
| (1.3538255200944435016e-13 - 1.306538458524060376e-544j)  +/-  (2.29e-88, 7.79e-210j)
| (0.1116097609263269262 - 1.2746112318490322362e-537j)  +/-  (7.2e-73, 2.45e-194j)
| (1.3538255200944435016e-13 + 5.1505690214061629798e-546j)  +/-  (1.68e-89, 5.71e-211j)
| (0.0033894803638465204951 - 1.2893543490624962887e-539j)  +/-  (3.29e-79, 1.12e-200j)
| (3.0388619872363127258e-10 + 9.7529188069850294974e-543j)  +/-  (1.59e-86, 5.42e-208j)
| (0.0007726473368696213951 + 1.1614332731690127541e-539j)  +/-  (1.66e-82, 5.65e-204j)
| (0.031562634737493842694 - 1.9295857302629222243e-538j)  +/-  (2.11e-79, 7.18e-201j)
| (3.0388619872363127258e-10 + 4.034663171016285119e-544j)  +/-  (4.78e-88, 1.63e-209j)
| (0.011645104356298250776 + 7.7692581315399013736e-539j)  +/-  (2.09e-81, 7.13e-203j)
| (1.8914778311137072864e-06 - 7.335542479086432331e-542j)  +/-  (1.01e-85, 3.45e-207j)
| (2.2066213689794447216e-20 + 6.7569853563472218425e-549j)  +/-  (1.99e-93, 6.81e-215j)
| (0.0033894803638465204951 - 3.0782513017588823552e-539j)  +/-  (6.19e-83, 2.11e-204j)
| (0.067669598987800672556 + 5.0542389821450228275e-538j)  +/-  (1.16e-80, 3.96e-202j)
| (1.4329890241734728532e-07 + 1.5069083737416441793e-542j)  +/-  (8.03e-87, 2.73e-208j)
| (0.17836848652338451998 + 3.3011462014493819931e-537j)  +/-  (3.73e-80, 1.27e-201j)
| (0.13029364111903767172 - 5.5658903773675725973e-537j)  +/-  (2.29e-80, 7.8e-202j)
| (0.053715748344850351565 + 5.1867746503493486472e-537j)  +/-  (2.05e-80, 6.98e-202j)
| (1.3956348273525253752e-15 - 4.1040900826287344644e-547j)  +/-  (4.15e-92, 1.4e-213j)
| (1.8501598516883854386e-05 + 1.3411927227023150088e-540j)  +/-  (5.26e-86, 1.87e-207j)
| (0.13029364111903767172 - 4.9214418047859839734e-537j)  +/-  (5.39e-82, 2.63e-203j)
| (0.031562634737493842694 - 1.1034868148974671413e-538j)  +/-  (1.38e-83, 3.99e-205j)
