Starting with polynomial:
P : t^6 - 15*t^4 + 45*t^2 - 15
Extension levels are: 6 36
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P1 : t^6 - 15*t^4 + 45*t^2 - 15
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^42 - 3034580767631041954755812001645/3851212004369392141445256644*t^40 + 66904820630722889096541460493618475/238775144270902312769605911928*t^38 - 14238310080101542043226848882662613613/238775144270902312769605911928*t^36 + 2027739466444894952486144733975716621415/238775144270902312769605911928*t^34 - 204740627388926662504588724585108106720975/238775144270902312769605911928*t^32 + 122188790921062616387547693334929856949085/1925606002184696070722628322*t^30 - 6758083653471907364204167090343617990471275/1925606002184696070722628322*t^28 + 282380438285173669280935109108025915887491665/1925606002184696070722628322*t^26 - 4476560989251459098446341458500236367717659000/962803001092348035361314161*t^24 + 430457897470113219644110809745424734716142720875/3851212004369392141445256644*t^22 - 7802777702128209494428135437857562233774591434125/3851212004369392141445256644*t^20 + 105557770700905948695271613258382192106774018269375/3851212004369392141445256644*t^18 - 1049234031024426376596218242645910173164183191629875/3851212004369392141445256644*t^16 + 3747884391564568983101410836414769740312460754645625/1925606002184696070722628322*t^14 - 18666405766587398776758995542743006134023305948519375/1925606002184696070722628322*t^12 + 62131956997532428823017621627284467004127650489226875/1925606002184696070722628322*t^10 - 260296745481186468807134991322551447173924756305284375/3851212004369392141445256644*t^8 + 627229620803636210203093774928277027686973917499148125/7702424008738784282890513288*t^6 - 375179883534611341500122406476328619474372472126596875/7702424008738784282890513288*t^4 + 83707624737910196500364428937573890044338298607940625/7702424008738784282890513288*t^2 - 2948887721619820238294005934732940088412922491690625/7702424008738784282890513288
-------------------------------------------------
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
Positive weights:   42 out of 42
Indefinite weights: 0 out of 42
Negative weights:   0 out of 42
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-11.456287114869977347 + 9.0348842910809526109e-661j)  +/-  (7.89e-248, 7.89e-248j)
| (-10.488185017281171677 - 3.9382848467931424587e-660j)  +/-  (9.66e-247, 9.66e-247j)
| (-8.2962949572772457395 - 1.8626860494010682144e-658j)  +/-  (2.18e-245, 2.18e-245j)
| (-2.3541198295529453263 + 2.9172131726462487658e-662j)  +/-  (2.61e-249, 2.61e-249j)
| (-4.8548120855076049247 + 9.4133272020252496594e-659j)  +/-  (3.36e-246, 3.36e-246j)
| (-9.6836860779625966299 - 4.4068421996814980013e-659j)  +/-  (4.51e-246, 4.51e-246j)
| (-5.3861228449347318315 - 5.5772263413933165554e-658j)  +/-  (9.84e-246, 9.84e-246j)
| (-7.6674461067179680978 + 7.1688411923267606986e-658j)  +/-  (2.91e-245, 2.91e-245j)
| (-8.9631716146606224825 - 3.1011011584382902493e-659j)  +/-  (1.15e-245, 1.15e-245j)
| (-1.8891758777537106755 - 1.115991607345032028e-663j)  +/-  (3.52e-250, 3.52e-250j)
| (-5.930310057437978864 - 3.5083210925662135204e-657j)  +/-  (1.73e-245, 1.73e-245j)
| (-3.3242574335521189524 - 1.0061500715837848487e-661j)  +/-  (7.9e-248, 7.9e-248j)
| (-3.8247066919014174554 - 1.7904802184591042167e-661j)  +/-  (2.96e-247, 2.96e-247j)
| (-4.3347126540668819187 + 4.6247227493170611472e-661j)  +/-  (1.08e-246, 1.08e-246j)
| (-6.4896617243517169719 - 1.7010622998200934711e-658j)  +/-  (2.77e-245, 2.77e-245j)
| (-2.8335911259625465831 - 9.3731059102528966215e-666j)  +/-  (1.34e-248, 1.34e-248j)
| (-7.0672803442834625839 + 2.233043213742038284e-661j)  +/-  (3.41e-245, 3.41e-245j)
| (9.6836860779625966299 + 7.1769204507885858467e-667j)  +/-  (4.74e-246, 4.74e-246j)
| (3.8247066919014174554 - 2.9869877035173967662e-678j)  +/-  (2.92e-247, 2.92e-247j)
| (11.456287114869977347 + 4.1990674499678062287e-702j)  +/-  (9.19e-248, 9.19e-248j)
| (5.930310057437978864 + 1.4858716930284216217e-729j)  +/-  (1.76e-245, 1.76e-245j)
| (1.4443479079056581894 + 2.6533083292548203041e-747j)  +/-  (3.93e-251, 3.93e-251j)
| (7.0672803442834625839 - 1.3033658200820955179e-746j)  +/-  (3.82e-245, 3.82e-245j)
| (10.488185017281171677 - 9.0204677277571406204e-756j)  +/-  (9.7e-247, 9.7e-247j)
| (3.3242574335521189524 + 1.2316179191821652986e-759j)  +/-  (6.92e-248, 6.92e-248j)
| (4.3347126540668819187 + 3.3796664968642391724e-758j)  +/-  (1.15e-246, 1.15e-246j)
| (-1.4443479079056581894 - 6.037384561480275551e-767j)  +/-  (4.29e-251, 4.29e-251j)
| (0.20714609660711684513 + 2.9276268576074068301e-767j)  +/-  (2.32e-254, 2.32e-254j)
| (8.9631716146606224825 - 3.0925248796075637603e-758j)  +/-  (1.27e-245, 1.27e-245j)
| (2.3541198295529453263 + 1.3541014012033856686e-767j)  +/-  (2.24e-249, 2.24e-249j)
| (2.8335911259625465831 + 5.0620446239993938033e-766j)  +/-  (1.35e-248, 1.35e-248j)
| (1.8891758777537106755 + 1.1521782159906518555e-770j)  +/-  (3.51e-250, 3.51e-250j)
| (-0.61670659019259415219 + 4.9452322127924013965e-774j)  +/-  (4.64e-253, 4.64e-253j)
| (1.023328315217132181 - 7.6555796154911764041e-774j)  +/-  (5.07e-252, 5.07e-252j)
| (5.3861228449347318315 - 1.1271854023913502088e-765j)  +/-  (8.78e-246, 8.78e-246j)
| (4.8548120855076049247 + 3.6703822831116633664e-786j)  +/-  (3.33e-246, 3.33e-246j)
| (7.6674461067179680978 + 1.0313432457261424072e-819j)  +/-  (3.12e-245, 3.12e-245j)
| (-1.023328315217132181 - 2.2104555089841901396e-846j)  +/-  (5.31e-252, 5.31e-252j)
| (0.61670659019259415219 - 2.2791750106821311602e-846j)  +/-  (4.64e-253, 4.64e-253j)
| (-0.20714609660711684513 - 1.0960216593061625153e-847j)  +/-  (2.32e-254, 2.32e-254j)
| (8.2962949572772457395 - 7.2189513362660671466e-864j)  +/-  (2.09e-245, 2.09e-245j)
| (6.4896617243517169719 - 2.4978925718345541358e-895j)  +/-  (2.73e-245, 2.73e-245j)
-------------------------------------------------
The weights are:
| (1.4088669482595457004e-29 + 7.6064585692112857295e-678j)  +/-  (1.48e-71, 1.04e-193j)
| (4.478641299371403558e-25 - 2.2044664886266216466e-675j)  +/-  (4.14e-70, 2.91e-192j)
| (2.9186043748969567228e-16 + 2.5683809896132815026e-670j)  +/-  (6.61e-67, 4.64e-189j)
| (0.011812339516118651045 - 7.1052994055160682657e-663j)  +/-  (1.33e-47, 9.33e-170j)
| (1.5976235191951427411e-06 + 5.3069046019062968773e-664j)  +/-  (2.92e-59, 2.05e-181j)
| (1.3072735673127715561e-21 + 1.9076621912807449726e-673j)  +/-  (1.76e-69, 1.23e-191j)
| (1.0757619493386860499e-07 + 5.7270593483791829237e-665j)  +/-  (2.29e-61, 1.6e-183j)
| (4.1931537120358654402e-14 - 5.6485775789051634262e-669j)  +/-  (1.38e-66, 9.67e-189j)
| (9.8782973966303947065e-19 - 8.6128551301413051948e-672j)  +/-  (1.36e-68, 9.56e-191j)
| (0.030537030861057863392 + 1.0695159593366563543e-662j)  +/-  (6e-50, 4.22e-172j)
| (5.0764633338662181482e-09 - 8.3509780809053097672e-665j)  +/-  (1.37e-63, 9.65e-186j)
| (0.00078791757072726419444 - 2.6157237598569576007e-663j)  +/-  (1.19e-57, 8.37e-180j)
| (0.00013423146906094167618 + 1.3960136533810301094e-663j)  +/-  (2.52e-59, 1.77e-181j)
| (1.7080632601877824756e-05 - 1.0762182670085066408e-663j)  +/-  (1.22e-60, 8.59e-183j)
| (1.6212910960433060143e-10 - 2.8762885007634215093e-666j)  +/-  (5.32e-66, 3.74e-188j)
| (0.0034955396305646906612 + 4.9441583306112825701e-663j)  +/-  (4.74e-58, 3.33e-180j)
| (3.3465191706950877165e-12 + 1.1485373078005218818e-667j)  +/-  (2.99e-67, 2.1e-189j)
| (1.3072735673127715561e-21 + 7.3249061307136414439e-675j)  +/-  (6.25e-84, 4.39e-206j)
| (0.00013423146906094167618 + 5.0167169404885393314e-666j)  +/-  (1.76e-71, 1.24e-193j)
| (1.4088669482595457004e-29 + 5.3368480320257760519e-679j)  +/-  (6.85e-87, 4.81e-209j)
| (5.0764633338662181482e-09 + 3.1171943547174492532e-668j)  +/-  (5.47e-78, 3.84e-200j)
| (0.060847229209829029716 + 2.0887708565436081397e-663j)  +/-  (7.6e-63, 5.34e-185j)
| (3.3465191706950877165e-12 + 6.4124490443962518746e-670j)  +/-  (2.05e-80, 1.44e-202j)
| (4.478641299371403558e-25 - 1.1515154192042703021e-676j)  +/-  (1.15e-85, 8.09e-208j)
| (0.00078791757072726419444 - 6.4982401480238230557e-666j)  +/-  (1.45e-72, 1.02e-194j)
| (1.7080632601877824756e-05 - 2.0675585491568373356e-666j)  +/-  (3.42e-75, 2.4e-197j)
| (0.060847229209829029716 - 1.6644475592035526315e-662j)  +/-  (4.79e-65, 3.36e-187j)
| (0.16137606455860043512 - 1.5403503166309763972e-662j)  +/-  (4.2e-65, 2.95e-187j)
| (9.8782973966303947065e-19 - 2.3381887219046003766e-673j)  +/-  (5.96e-84, 4.18e-206j)
| (0.011812339516118651045 + 1.4510848416215459508e-664j)  +/-  (2.98e-71, 2.09e-193j)
| (0.0034955396305646906612 - 1.4899300970204257509e-665j)  +/-  (2.32e-72, 1.63e-194j)
| (0.030537030861057863392 - 6.4386950275242341386e-664j)  +/-  (2.25e-70, 1.58e-192j)
| (0.13391155717107383927 - 2.3307911164711591096e-662j)  +/-  (1.09e-68, 7.64e-191j)
| (0.097079298938670091058 - 5.185038896128277522e-663j)  +/-  (6.17e-69, 4.33e-191j)
| (1.0757619493386860499e-07 - 1.5640548621790577011e-667j)  +/-  (1.46e-78, 1.02e-200j)
| (1.5976235191951427411e-06 + 6.363783935146185288e-667j)  +/-  (1.61e-77, 1.13e-199j)
| (4.1931537120358654402e-14 - 6.3309278643026337233e-671j)  +/-  (1.74e-83, 1.22e-205j)
| (0.097079298938670091058 + 2.1827075026554011992e-662j)  +/-  (5.02e-73, 3.53e-195j)
| (0.13391155717107383927 + 9.9244090308690684621e-663j)  +/-  (3.01e-73, 2.12e-195j)
| (0.16137606455860043512 + 2.0477602012950138419e-662j)  +/-  (4.58e-73, 3.22e-195j)
| (2.9186043748969567228e-16 + 4.6245368380627963909e-672j)  +/-  (1.03e-84, 7.23e-207j)
| (1.6212910960433060143e-10 - 5.0165078638984954069e-669j)  +/-  (1.62e-81, 1.14e-203j)
