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 29
-------------------------------------------------
Trying to find an order 29 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^45 - 40673026117210/54781808743*t^43 + 780890100414867695/3122563098351*t^41 - 475301711137281015260/9367689295053*t^39 + 368598525047330277275485/53083572671967*t^37 - 36109560277349411480277650/53083572671967*t^35 + 154281011254783803186521725/3122563098351*t^33 - 48117582578412088809961093200/17694524223989*t^31 + 2033700966701239790827109887650/17694524223989*t^29 - 66497469656383924808915742176700/17694524223989*t^27 + 1686773053182286842506113508978850/17694524223989*t^25 - 33151407096148806289521051019665000/17694524223989*t^23 + 502290276868032859682746921889988750/17694524223989*t^21 - 5814688355653503084785698450936657500/17694524223989*t^19 + 2670961648898939981914095253593356250/931290748631*t^17 - 1014709706077812781558631018339430000/54781808743*t^15 + 4727477031459026498823808831038721875/54781808743*t^13 - 15343153668396050083574240565293231250/54781808743*t^11 + 33031731022332477284369275096387921875/54781808743*t^9 - 43907269985768209862439333904681012500/54781808743*t^7 + 32188792549970940351820893609333890625/54781808743*t^5 - 10645534828058559223751383147376906250/54781808743*t^3 + 1003682319559068824048192135332640625/54781808743*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:
| (-7.8598883309684942197 - 5.0524788362998874275e-530j)  +/-  (5.21e-245, 5.21e-245j)
| (-7.2297585191550022081 + 2.4906130914234436129e-529j)  +/-  (8.08e-245, 8.08e-245j)
| (-11.042667953224214855 + 1.0940154822625769014e-532j)  +/-  (8.78e-248, 8.78e-248j)
| (-9.2552988499183704381 - 4.1921051237125876319e-532j)  +/-  (6.29e-246, 6.29e-246j)
| (-10.066155102423954403 + 3.1776721476883450929e-531j)  +/-  (1.15e-246, 1.15e-246j)
| (6.6308781983931284802 + 9.3269697870130009355e-528j)  +/-  (1.22e-244, 1.22e-244j)
| (7.8598883309684942197 + 7.1815858053171855302e-531j)  +/-  (4.66e-245, 4.66e-245j)
| (-5.4722257059493430884 + 2.2709852778247059997e-535j)  +/-  (3.07e-243, 3.07e-243j)
| (3.6008736241715482882 - 1.4204337527752278583e-536j)  +/-  (1.85e-246, 1.85e-246j)
| (11.042667953224214855 + 5.4094018205618713197e-539j)  +/-  (9.26e-248, 9.26e-248j)
| (-3.6008736241715482882 + 3.8166583276219594056e-538j)  +/-  (1.86e-246, 1.86e-246j)
| (-2.7602450476307016168 + 1.1530252969558003114e-539j)  +/-  (8.54e-248, 8.54e-248j)
| (10.066155102423954403 + 2.789423285001348756e-538j)  +/-  (1.1e-246, 1.1e-246j)
| (-4.4929553025200112427 + 2.428540096873738269e-538j)  +/-  (2.25e-245, 2.25e-245j)
| (-6.0580931458019962757 - 7.0006194778942462646e-537j)  +/-  (1.89e-244, 1.89e-244j)
| (1.9519803457163334645 - 1.6786075442263482068e-541j)  +/-  (2.03e-249, 2.03e-249j)
| (2.3490719676970335688 + 6.1715416591091046434e-540j)  +/-  (1.45e-248, 1.45e-248j)
| (8.5299767637446989804 - 5.5393377052650204182e-537j)  +/-  (1.94e-245, 1.94e-245j)
| (-1.5588257106763188875 - 3.4859989664924545656e-542j)  +/-  (2.28e-250, 2.28e-250j)
| (7.2297585191550022081 - 2.8792911466536051619e-535j)  +/-  (8.32e-245, 8.32e-245j)
| (4.9884332514673021193 - 1.442871033207803793e-546j)  +/-  (9.06e-245, 9.06e-245j)
| (9.2552988499183704381 - 1.110812621182169657e-557j)  +/-  (6.8e-246, 6.8e-246j)
| (4.4929553025200112427 + 1.2907202530900495477e-567j)  +/-  (2.44e-245, 2.44e-245j)
| (4.031806921455782101 + 1.273836102126548133e-590j)  +/-  (6.68e-246, 6.68e-246j)
| (-3.1804741575688080752 + 1.0547082108778175514e-605j)  +/-  (4.56e-247, 4.56e-247j)
| (0.38676060450055734772 + 4.9933520566132291476e-613j)  +/-  (9.23e-254, 9.23e-254j)
| (1.5588257106763188875 + 6.5884683634657843391e-611j)  +/-  (2.06e-250, 2.06e-250j)
| (-6.6308781983931284802 - 4.8098574348384445437e-602j)  +/-  (1.28e-244, 1.28e-244j)
| (-2.3490719676970335688 - 1.9916294361705526285e-613j)  +/-  (1.42e-248, 1.42e-248j)
| (-4.9884332514673021193 + 6.1406274285466194675e-607j)  +/-  (1.05e-244, 1.05e-244j)
| (-8.5299767637446989804 - 3.5382191633343462502e-639j)  +/-  (2.05e-245, 2.05e-245j)
| (5.4722257059493430884 + 1.2002371305311497316e-688j)  +/-  (3.05e-243, 3.05e-243j)
| (-4.031806921455782101 - 6.6574213154687919339e-722j)  +/-  (6.79e-246, 6.79e-246j)
| (-5.4970334808911648795 + 1.5377258988076063282e-719j)  +/-  (3.14e-243, 3.14e-243j)
| (-0.77289470754446145115 + 1.5618581182133535468e-733j)  +/-  (1.87e-252, 1.87e-252j)
| (-1.9519803457163334645 + 6.54202287518373766e-731j)  +/-  (2.13e-249, 2.13e-249j)
| (5.4970334808911648795 + 1.6941672997044689226e-726j)  +/-  (3.2e-243, 3.2e-243j)
| (0.77289470754446145115 - 4.4032046805141970197e-749j)  +/-  (1.8e-252, 1.8e-252j)
| (3.1804741575688080752 + 1.3996353301825078837e-743j)  +/-  (4.69e-247, 4.69e-247j)
| (-1.1638291005549647742 + 1.0665441777382216531e-749j)  +/-  (1.92e-251, 1.92e-251j)
| (-0.38676060450055734772 - 2.908132730478207381e-752j)  +/-  (9.23e-254, 9.23e-254j)
| (-1.8715520306649135575e-773 + 3.6098936992650572897e-773j)  +/-  (1.83e-771, 1.83e-771j)
| (2.7602450476307016168 + 9.5101948889997654385e-748j)  +/-  (8.7e-248, 8.7e-248j)
| (1.1638291005549647742 - 1.5840703421114714555e-751j)  +/-  (2.13e-251, 2.13e-251j)
| (6.0580931458019962757 - 1.2973832511626598989e-750j)  +/-  (1.93e-244, 1.93e-244j)
-------------------------------------------------
The weights are:
| (9.9487423322792935216e-15 - 6.0932212998503538458e-542j)  +/-  (4.89e-75, 1.55e-196j)
| (1.0927090650433648755e-12 + 3.4537722402751875791e-540j)  +/-  (1.38e-73, 4.39e-195j)
| (1.4911138079121161812e-27 - 9.0285472482051452275e-550j)  +/-  (1.44e-82, 4.56e-204j)
| (7.6087888755726549598e-20 - 3.4755750154644228891e-545j)  +/-  (3.51e-79, 1.11e-200j)
| (3.4546971867991819822e-23 + 3.3052140142785603466e-547j)  +/-  (8.94e-81, 2.84e-202j)
| (6.6153534575554185084e-11 - 3.2510171181555594008e-537j)  +/-  (6.51e-78, 2.06e-199j)
| (9.9487423322792935216e-15 + 8.8337006050925241384e-541j)  +/-  (4.37e-81, 1.39e-202j)
| (-3.791053442218921833e-08 + 3.4644529574961588269e-535j)  +/-  (2.26e-73, 7.17e-195j)
| (0.0002574113800683421032 + 1.9439724583753371092e-533j)  +/-  (5.82e-69, 1.85e-190j)
| (1.4911138079121161812e-27 + 3.7880388688011984417e-549j)  +/-  (5.13e-88, 1.63e-209j)
| (0.0002574113800683421032 + 5.9039350638683507625e-534j)  +/-  (1.24e-68, 3.94e-190j)
| (0.0036930222634369101539 + 4.4787734277464983478e-533j)  +/-  (2.67e-65, 8.47e-187j)
| (3.4546971867991819822e-23 - 1.7066995300611122258e-546j)  +/-  (1.67e-86, 5.32e-208j)
| (7.9008917724609767006e-06 + 4.4946347815147895201e-535j)  +/-  (7e-72, 2.22e-193j)
| (2.4011511878015804114e-09 + 1.2341262603745725091e-537j)  +/-  (1.1e-75, 3.48e-197j)
| (0.02332407980373135126 + 3.961918091442582021e-532j)  +/-  (4.26e-64, 1.35e-185j)
| (0.010197491547766158596 - 2.19671161663380506e-532j)  +/-  (1.68e-66, 5.33e-188j)
| (4.3928615496876208458e-17 - 1.6650444601730129527e-542j)  +/-  (3.57e-84, 1.13e-205j)
| (0.046701548958422386802 - 3.8802541492627248586e-532j)  +/-  (2.44e-63, 7.75e-185j)
| (1.0927090650433648755e-12 - 4.6843813141070053343e-539j)  +/-  (1.12e-81, 3.55e-203j)
| (8.0540158238963900832e-07 - 8.6995931656187373798e-535j)  +/-  (4.27e-78, 1.35e-199j)
| (7.6087888755726549598e-20 + 2.2864696774532376998e-544j)  +/-  (5.16e-86, 1.64e-207j)
| (7.9008917724609767006e-06 + 2.2507478547126563782e-534j)  +/-  (4.53e-77, 1.44e-198j)
| (5.2270400062856920035e-05 - 6.9397389586282231894e-534j)  +/-  (5.71e-76, 1.81e-197j)
| (0.0010674953496461608717 - 1.7109616672122186235e-533j)  +/-  (1.16e-74, 3.67e-196j)
| (0.14283552473962536231 + 1.250571019596627916e-531j)  +/-  (2.36e-69, 7.49e-191j)
| (0.046701548958422386802 - 6.2112279402578566253e-532j)  +/-  (2.01e-69, 6.37e-191j)
| (6.6153534575554185084e-11 - 5.6750566949780531934e-539j)  +/-  (1.66e-82, 5.27e-204j)
| (0.010197491547766158596 - 1.0621052054436108258e-532j)  +/-  (1.26e-73, 4.01e-195j)
| (8.0540158238963900832e-07 - 1.2921091417069956713e-535j)  +/-  (1.95e-79, 6.19e-201j)
| (4.3928615496876208458e-17 + 1.8300816462228662961e-543j)  +/-  (6.59e-87, 2.09e-208j)
| (-3.791053442218921833e-08 + 3.3880000022242621746e-534j)  +/-  (3.6e-82, 1.14e-203j)
| (5.2270400062856920035e-05 - 1.7443989276201664619e-534j)  +/-  (1.09e-78, 3.48e-200j)
| (9.1419232374405518143e-08 - 3.1013906911767635913e-535j)  +/-  (9.73e-80, 3.09e-201j)
| (0.11472678679144468656 - 8.8099651736105236073e-532j)  +/-  (1.38e-75, 4.36e-197j)
| (0.02332407980373135126 + 2.1840627562031992787e-532j)  +/-  (3.62e-76, 1.15e-197j)
| (9.1419232374405518143e-08 - 3.1023306976880831762e-534j)  +/-  (2.75e-82, 8.71e-204j)
| (0.11472678679144468656 - 1.108857805409085617e-531j)  +/-  (4.55e-77, 1.37e-198j)
| (0.0010674953496461608717 - 4.7649136150938002851e-533j)  +/-  (1.85e-80, 5.67e-202j)
| (0.079862359440432036219 + 6.1610404121984510095e-532j)  +/-  (1.46e-77, 4.38e-199j)
| (0.14283552473962536231 + 1.1150214883776445842e-531j)  +/-  (1.4e-77, 4.17e-199j)
| (0.15454649410980704235 - 1.2498323391137978179e-531j)  +/-  (1.66e-77, 4.89e-199j)
| (0.0036930222634369101539 + 1.068246555722949542e-532j)  +/-  (3.82e-80, 1.17e-201j)
| (0.079862359440432036219 + 8.7286318101963151374e-532j)  +/-  (1.21e-78, 3.33e-200j)
| (2.4011511878015804114e-09 + 2.4678867691155525365e-536j)  +/-  (4.63e-85, 1.55e-206j)
