Starting with polynomial:
P : t^7 - 21*t^5 + 105*t^3 - 105*t
Extension levels are: 7 40
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P1 : t^7 - 21*t^5 + 105*t^3 - 105*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^47 - 29489850349848120765366333948308786701/30229520413264054439634042230102181*t^45 + 4374565959746955679221300719564444926465/10076506804421351479878014076700727*t^43 - 20043160977742038095258341406173758391941805/171300615675162975157926239303912359*t^41 + 3662968541530098150486838626595366910225478025/171300615675162975157926239303912359*t^39 - 481653659978986061803553836561684777603426424505/171300615675162975157926239303912359*t^37 + 47192752650206445411960224360827302413260671351255/171300615675162975157926239303912359*t^35 - 207122810427720357384657829975682284471027497934275/10076506804421351479878014076700727*t^33 + 11925999482010571412929395396337813370174087557374150/10076506804421351479878014076700727*t^31 - 17224708219845454378860666730030991020100062169270250/325048606594237144512194002474217*t^29 + 601564544008296335748093410752195380275894979819948150/325048606594237144512194002474217*t^27 - 16378276125387518102897999018929246872912472676793225150/325048606594237144512194002474217*t^25 + 346237531748327637497973711232414883446047728410245828750/325048606594237144512194002474217*t^23 - 5641458772927257730296603734605613873404243181123347428750/325048606594237144512194002474217*t^21 + 70069505626252901878222757426001048007411440129655914431250/325048606594237144512194002474217*t^19 - 653399166594965081451676413635169510681757693883388210416250/325048606594237144512194002474217*t^17 + 4482461486906210681369193956276739006145013661027011303938125/325048606594237144512194002474217*t^15 - 22022629004975606999276595757477413491850117269849694717103125/325048606594237144512194002474217*t^13 + 74762968223193501667439366939426243898821887981854138786946875/325048606594237144512194002474217*t^11 - 167032862720640462540482307669067523742848279352080548936359375/325048606594237144512194002474217*t^9 + 229185226256258907389982777205890464948959796456746133861446875/325048606594237144512194002474217*t^7 - 173755859918439226628844803263684297895697102090236708301196875/325048606594237144512194002474217*t^5 + 60451945614242210330039493030950543969613413108851433618953125/325048606594237144512194002474217*t^3 - 6256346681180566489229743524278615609711128802947346644265625/325048606594237144512194002474217*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:
| (7.2998110497404020483 - 2.3838044943793955636e-739j)  +/-  (4.44e-244, 4.44e-244j)
| (8.4470245016025736501 + 6.4522117712545515e-740j)  +/-  (3.92e-244, 3.92e-244j)
| (12.155109115613161104 + 2.2168904818248625926e-744j)  +/-  (3.91e-247, 3.91e-247j)
| (-9.0607223212719491979 - 8.2139536323620125607e-741j)  +/-  (2.24e-244, 2.24e-244j)
| (-10.417308665924522767 - 1.6407317004506426806e-744j)  +/-  (3.05e-245, 3.05e-245j)
| (-11.205433539040077801 + 1.991324281436946813e-748j)  +/-  (5.79e-246, 5.79e-246j)
| (-5.7121631108316661502 + 2.8754225546332667756e-750j)  +/-  (1.03e-244, 1.03e-244j)
| (-7.8620698045831619739 + 6.86884659047723547e-761j)  +/-  (5.06e-244, 5.06e-244j)
| (-9.7123622518962980773 - 5.3535592576309724048e-767j)  +/-  (1.06e-244, 1.06e-244j)
| (6.7560139153022934193 + 1.1443750336187621627e-769j)  +/-  (3.12e-244, 3.12e-244j)
| (11.205433539040077801 + 3.0521870169560200921e-772j)  +/-  (5.4e-246, 5.4e-246j)
| (-4.2279909502247981035 - 1.5723048324455102204e-769j)  +/-  (4.33e-246, 4.33e-246j)
| (-12.155109115613161104 - 1.1679564050023478122e-776j)  +/-  (3.99e-247, 3.99e-247j)
| (9.7123622518962980773 - 7.9158852803416194716e-776j)  +/-  (1.06e-244, 1.06e-244j)
| (4.7135921826806440208 + 1.202881002640211045e-775j)  +/-  (1.39e-245, 1.39e-245j)
| (1.9293169100434639487 + 1.651100061324113189e-780j)  +/-  (1.07e-249, 1.07e-249j)
| (3.2806170630707789176 - 6.2717155830716307594e-778j)  +/-  (2.26e-247, 2.26e-247j)
| (6.2275784011924734435 + 3.9892912706361806308e-775j)  +/-  (1.94e-244, 1.94e-244j)
| (-0.41260830154776375845 - 3.1231233156070494845e-790j)  +/-  (1.09e-253, 1.09e-253j)
| (-1.9293169100434639487 + 2.7710785218744377174e-782j)  +/-  (9.93e-250, 9.93e-250j)
| (-7.2998110497404020483 + 2.4840485246152276434e-783j)  +/-  (4.77e-244, 4.77e-244j)
| (10.417308665924522767 + 3.4490873124198346573e-799j)  +/-  (3.05e-245, 3.05e-245j)
| (9.0607223212719491979 + 8.2692397796512751329e-798j)  +/-  (2.21e-244, 2.21e-244j)
| (-2.8188422131142829985 - 6.0635476190921345892e-802j)  +/-  (4.4e-248, 4.4e-248j)
| (-5.2079654922625032193 + 9.4364454227105967202e-828j)  +/-  (4.57e-245, 4.57e-245j)
| (2.8188422131142829985 - 1.7988246274249746082e-853j)  +/-  (4.26e-248, 4.26e-248j)
| (0.80159303425324313313 - 4.3575379672925044717e-862j)  +/-  (2.25e-252, 2.25e-252j)
| (-6.7560139153022934193 - 2.5232098381654497209e-871j)  +/-  (3.57e-244, 3.57e-244j)
| (5.2079654922625032193 - 5.5187823585392912332e-888j)  +/-  (4.2e-245, 4.2e-245j)
| (-3.2806170630707789176 + 1.429116937653219242e-902j)  +/-  (2.33e-247, 2.33e-247j)
| (-6.2275784011924734435 - 5.0468570816570186455e-924j)  +/-  (2.06e-244, 2.06e-244j)
| (2.3667594107345412886 + 6.9934942319065781168e-943j)  +/-  (6.46e-249, 6.46e-249j)
| (5.7121631108316661502 + 2.5664903163422083015e-938j)  +/-  (1.03e-244, 1.03e-244j)
| (-1.5195756121268246055 + 4.8921097328784388735e-945j)  +/-  (1.45e-250, 1.45e-250j)
| (7.8620698045831619739 + 4.2058787806764816675e-937j)  +/-  (4.71e-244, 4.71e-244j)
| (-3.7504397177257422563 - 1.9933095892309808557e-938j)  +/-  (1.07e-246, 1.07e-246j)
| (-8.4470245016025736501 + 1.5202909501675561066e-950j)  +/-  (3.57e-244, 3.57e-244j)
| (1.1544053947399681272 - 2.1541713447728683982e-968j)  +/-  (2.32e-251, 2.32e-251j)
| (1.5195756121268246055 - 5.1491552921691015295e-968j)  +/-  (1.48e-250, 1.48e-250j)
| (-2.3667594107345412886 - 4.5065226418164569009e-961j)  +/-  (6.56e-249, 6.56e-249j)
| (-1.1544053947399681272 + 2.980808509207895177e-969j)  +/-  (2.32e-251, 2.32e-251j)
| (3.7504397177257422563 - 2.4558058763734974587e-961j)  +/-  (9.95e-247, 9.95e-247j)
| (-3.2849709512523690141e-972 + 4.8941069253128385258e-973j)  +/-  (1.56e-970, 1.56e-970j)
| (0.41260830154776375845 - 1.1306939984686731765e-973j)  +/-  (1.09e-253, 1.09e-253j)
| (4.2279909502247981035 + 1.015037478838953669e-963j)  +/-  (4.23e-246, 4.23e-246j)
| (-0.80159303425324313313 - 1.4708678061729157635e-972j)  +/-  (2.05e-252, 2.05e-252j)
| (-4.7135921826806440208 - 3.677771411308992072e-978j)  +/-  (1.4e-245, 1.4e-245j)
-------------------------------------------------
The weights are:
| (5.9157813333696771303e-13 + 5.667232019556546861e-751j)  +/-  (2.47e-74, 5.48e-196j)
| (7.6516995713374044417e-17 - 9.5864839691913177567e-754j)  +/-  (2.3e-77, 5.1e-199j)
| (3.6129001663297951564e-33 + 5.4035190088187364654e-763j)  +/-  (3.61e-85, 8e-207j)
| (3.7472269444432170123e-19 - 3.7778990218176259584e-756j)  +/-  (4.5e-81, 9.97e-203j)
| (8.0348872417117790948e-25 - 3.4333796136118281765e-759j)  +/-  (4.39e-84, 9.73e-206j)
| (1.8354485894362492387e-28 + 4.0385299190161230536e-761j)  +/-  (7.44e-86, 1.65e-207j)
| (1.6704584124661042161e-08 - 3.496140519781218997e-750j)  +/-  (4.24e-75, 9.41e-197j)
| (8.6409552401172028829e-15 - 9.1430172503402992692e-754j)  +/-  (4.16e-80, 9.22e-202j)
| (8.8449058863044020409e-22 + 1.4450854056076019957e-757j)  +/-  (5.63e-83, 1.25e-204j)
| (2.6205979103981148928e-11 - 2.1253071385680920035e-750j)  +/-  (1.73e-79, 3.84e-201j)
| (1.8354485894362492387e-28 - 1.9101130531543729616e-760j)  +/-  (6.75e-89, 1.5e-210j)
| (2.5222545551333817779e-05 + 3.3265448589364187042e-748j)  +/-  (2.55e-73, 5.66e-195j)
| (3.6129001663297951564e-33 - 1.3504054406772829471e-763j)  +/-  (2.68e-89, 5.93e-211j)
| (8.8449058863044020409e-22 - 1.0157627987211845145e-756j)  +/-  (1.94e-86, 4.29e-208j)
| (2.9268223997300351842e-06 - 3.8354519330469448014e-748j)  +/-  (7.69e-77, 1.71e-198j)
| (0.026474197852329798139 - 1.5881493768408326996e-745j)  +/-  (1.1e-65, 2.43e-187j)
| (0.00085544556145507123385 + 1.0456568603735971981e-746j)  +/-  (1.36e-72, 3.02e-194j)
| (7.8826500035564676314e-10 + 7.3467105521599572966e-750j)  +/-  (4.8e-80, 1.06e-201j)
| (0.14846788519676983462 - 6.0957161553737869091e-745j)  +/-  (5.98e-67, 1.32e-188j)
| (0.026474197852329798139 - 9.2391331421390214196e-746j)  +/-  (4.5e-68, 9.97e-190j)
| (5.9157813333696771303e-13 + 9.6220188233595485872e-753j)  +/-  (3.66e-83, 8.11e-205j)
| (8.0348872417117790948e-25 + 1.9466939606161696035e-758j)  +/-  (1.95e-88, 4.31e-210j)
| (3.7472269444432170123e-19 + 3.4649409405264060514e-755j)  +/-  (8.89e-86, 1.97e-207j)
| (0.0034336786376143764177 - 1.2069157317794946137e-746j)  +/-  (1.28e-74, 2.83e-196j)
| (2.5669592555479535792e-07 + 1.8148661248806880567e-749j)  +/-  (1.2e-80, 2.65e-202j)
| (0.0034336786376143764177 - 2.7264979057408549512e-746j)  +/-  (3e-75, 6.66e-197j)
| (0.10673301796354118969 + 7.010611889209168143e-745j)  +/-  (7.7e-72, 1.71e-193j)
| (2.6205979103981148928e-11 - 8.2021314505170858616e-752j)  +/-  (1.39e-83, 3.07e-205j)
| (2.5669592555479535792e-07 + 1.0863483471941722118e-748j)  +/-  (2.16e-81, 4.78e-203j)
| (0.00085544556145507123385 + 3.9701655016658557806e-747j)  +/-  (5.08e-78, 1.13e-199j)
| (7.8826500035564676314e-10 + 5.8128808465878171248e-751j)  +/-  (7.95e-83, 1.76e-204j)
| (0.010812556122187590302 + 6.7352486787903802067e-746j)  +/-  (5.19e-76, 1.15e-197j)
| (1.6704584124661042161e-08 - 2.8692863227560500403e-749j)  +/-  (1.82e-82, 4.03e-204j)
| (0.048882967308989196546 + 2.2501387495610184969e-745j)  +/-  (4.11e-75, 9.11e-197j)
| (8.6409552401172028829e-15 + 2.4854542826561829789e-752j)  +/-  (5.13e-86, 1.14e-207j)
| (0.00016674036930501058982 - 1.2048593547859194691e-747j)  +/-  (3.05e-80, 6.75e-202j)
| (7.6516995713374044417e-17 + 6.7998926534638139882e-755j)  +/-  (1.35e-87, 3e-209j)
| (0.071133610836144728144 - 5.7903947266365287424e-745j)  +/-  (4.51e-76, 1e-197j)
| (0.048882967308989196546 + 3.4339173581980515717e-745j)  +/-  (6.07e-77, 1.35e-198j)
| (0.010812556122187590302 + 3.4360013326357098134e-746j)  +/-  (9.06e-79, 2.01e-200j)
| (0.071133610836144728144 - 4.208426023146708233e-745j)  +/-  (2.15e-77, 4.76e-199j)
| (0.00016674036930501058982 - 3.7533487732976843968e-747j)  +/-  (1.48e-81, 3.28e-203j)
| (0.16602295313626237113 + 6.3850570199922477915e-745j)  +/-  (6.44e-78, 1.43e-199j)
| (0.14846788519676983462 - 6.8264605256860010437e-745j)  +/-  (4.09e-78, 9.11e-200j)
| (2.5222545551333817779e-05 + 1.2492831209552622167e-747j)  +/-  (3.36e-82, 7.45e-204j)
| (0.10673301796354118969 + 5.6226980934597729381e-745j)  +/-  (6.97e-79, 1.52e-200j)
| (2.9268223997300351842e-06 - 8.2495569402932669566e-749j)  +/-  (3.16e-83, 6.96e-205j)
