Starting with polynomial:
P : t^5 - 10*t^3 + 15*t
Extension levels are: 5 34
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P1 : t^5 - 10*t^3 + 15*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^39 - 850021374965916870649/1197449949929852181*t^37 + 4058305368660464448012727/17961749248947782715*t^35 - 153488632143528736870280003/3592349849789556543*t^33 + 207149931558386023883485964/38627417739672651*t^31 - 18262619486258512712656341340/38627417739672651*t^29 + 1167488660125707013498246764460/38627417739672651*t^27 - 18364800434819606621505825745572/12875805913224217*t^25 + 645307756606056548891989182430350/12875805913224217*t^23 - 16913005996506294746141772413862150/12875805913224217*t^21 + 329230110456389462502804037431765750/12875805913224217*t^19 - 4712101379079733764068435362432311750/12875805913224217*t^17 + 48773415602562297849888182329160027700/12875805913224217*t^15 - 356298594987328033983151668984703678500/12875805913224217*t^13 + 1774037113201522577944103887719636736500/12875805913224217*t^11 - 5726007926844709419934969135736283232500/12875805913224217*t^9 + 11120145374060218342455763230277246670625/12875805913224217*t^7 - 11544674399865881289867482768486791567125/12875805913224217*t^5 + 5188336940221526480407053246696052693125/12875805913224217*t^3 - 624530389960994686840541252268800038125/12875805913224217*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:
| (-10.172180255048597491 + 8.1029949496255777394e-635j)  +/-  (3.67e-247, 3.67e-247j)
| (8.623514106693984079 + 5.2162444205744561994e-641j)  +/-  (3.99e-246, 3.99e-246j)
| (11.154107796673860745 - 6.4993764096451692113e-649j)  +/-  (4.02e-248, 4.02e-248j)
| (2.8569700138728056542 + 2.0876858609236962086e-656j)  +/-  (5.99e-249, 5.99e-249j)
| (-11.154107796673860745 - 3.8767445541642658033e-672j)  +/-  (3.59e-248, 3.59e-248j)
| (-7.9454183144939166793 + 1.5416163240500977991e-718j)  +/-  (7.06e-246, 7.06e-246j)
| (-7.3054014463183911178 - 1.111033224615879035e-743j)  +/-  (8.1e-246, 8.1e-246j)
| (9.3555209134822511243 + 6.3287762155918780518e-753j)  +/-  (1.6e-246, 1.6e-246j)
| (7.3054014463183911178 + 1.3689618494964951153e-755j)  +/-  (8.7e-246, 8.7e-246j)
| (-8.623514106693984079 - 1.5510792582435322962e-766j)  +/-  (4.24e-246, 4.24e-246j)
| (1.8465817053288804839 + 1.1817085920094123723e-781j)  +/-  (1.13e-250, 1.13e-250j)
| (3.3738897530669338409 + 6.6857103071288776457e-778j)  +/-  (3.53e-248, 3.53e-248j)
| (4.4327866157728596195 - 5.596453708534524694e-777j)  +/-  (5.12e-247, 5.12e-247j)
| (-4.9770904704058474999 + 1.512462999571400373e-795j)  +/-  (1.46e-246, 1.46e-246j)
| (-6.6939634412307984303 - 1.3591287412766707163e-823j)  +/-  (9.57e-246, 9.57e-246j)
| (3.8988502723134710172 + 4.8147727387310238854e-837j)  +/-  (1.63e-247, 1.63e-247j)
| (7.9454183144939166793 - 2.473493483584752685e-835j)  +/-  (6.65e-246, 6.65e-246j)
| (-2.8569700138728056542 - 7.0697957191199880754e-847j)  +/-  (6.06e-249, 6.06e-249j)
| (-0.87982516197097236476 + 1.2017104752291804437e-852j)  +/-  (1.19e-252, 1.19e-252j)
| (-0.42754849537695331972 + 2.0794349864824115469e-856j)  +/-  (8.23e-254, 8.23e-254j)
| (-6.1048395929307439587 + 2.9884606294913176737e-844j)  +/-  (6.22e-246, 6.22e-246j)
| (5.5336267720474913607 - 3.2197820137939212313e-856j)  +/-  (3.26e-246, 3.26e-246j)
| (-3.8988502723134710172 - 3.4467161282146036213e-856j)  +/-  (1.57e-247, 1.57e-247j)
| (-5.5336267720474913607 - 7.7349801063502293711e-857j)  +/-  (3.25e-246, 3.25e-246j)
| (-4.4327866157728596195 + 1.5359988779771127259e-859j)  +/-  (5.6e-247, 5.6e-247j)
| (6.1048395929307439587 - 1.6649239533604050582e-857j)  +/-  (6.2e-246, 6.2e-246j)
| (1.3556261799742658658 + 2.8273662264476741383e-868j)  +/-  (1.21e-251, 1.21e-251j)
| (6.6939634412307984303 - 3.1370261927563851565e-862j)  +/-  (7.73e-246, 7.73e-246j)
| (-1.8465817053288804839 - 5.1214043947811903105e-873j)  +/-  (1.17e-250, 1.17e-250j)
| (-9.3555209134822511243 + 9.0481388466104781895e-871j)  +/-  (1.55e-246, 1.55e-246j)
| (-1.732570551620634279e-896 - 2.6370565919806500408e-896j)  +/-  (1.23e-894, 1.23e-894j)
| (4.9770904704058474999 + 1.8978085627741577619e-878j)  +/-  (1.56e-246, 1.56e-246j)
| (0.42754849537695331972 + 3.0231113808741867688e-898j)  +/-  (1.09e-253, 1.09e-253j)
| (-1.3556261799742658658 + 6.2037088438980401815e-888j)  +/-  (1.29e-251, 1.29e-251j)
| (-2.3477097618347438978 + 1.2291197917950282102e-885j)  +/-  (9.65e-250, 9.65e-250j)
| (10.172180255048597491 - 1.8851832556688867734e-881j)  +/-  (3.83e-247, 3.83e-247j)
| (-3.3738897530669338409 + 4.1002357675842081252e-884j)  +/-  (3.4e-248, 3.4e-248j)
| (0.87982516197097236476 + 4.3460978547898296066e-890j)  +/-  (1.21e-252, 1.21e-252j)
| (2.3477097618347438978 - 2.4300377837651297529e-887j)  +/-  (9.63e-250, 9.63e-250j)
-------------------------------------------------
The weights are:
| (1.1890374331346980121e-23 + 4.9777720998089674556e-657j)  +/-  (1.72e-92, 4.99e-216j)
| (1.9900223465732893273e-17 + 7.1681282133577260723e-656j)  +/-  (2.94e-90, 8.54e-214j)
| (4.3499893387873990463e-28 - 2.5543210331312499032e-661j)  +/-  (1.66e-94, 4.82e-218j)
| (0.0034568571640740576121 + 3.992381823187301573e-648j)  +/-  (9.97e-74, 2.9e-197j)
| (4.3499893387873990463e-28 + 5.5142249731146858434e-660j)  +/-  (1.48e-94, 4.3e-218j)
| (5.1298442427271611874e-15 - 1.1105995721932918404e-653j)  +/-  (6.46e-90, 1.88e-213j)
| (6.4197631553082042852e-13 + 1.0404102094878472191e-652j)  +/-  (6e-89, 1.74e-212j)
| (3.0185529438506378865e-20 - 2.7170059397991909499e-657j)  +/-  (3.3e-93, 9.61e-217j)
| (6.4197631553082042852e-13 + 1.690377263606629965e-653j)  +/-  (3.53e-90, 1.03e-213j)
| (1.9900223465732893273e-17 + 9.2550660601462124126e-655j)  +/-  (1.26e-91, 3.67e-215j)
| (0.036012043599063422527 + 2.0364868697855655058e-647j)  +/-  (1.17e-73, 3.41e-197j)
| (0.00070110970191212535038 - 1.4856167097472446786e-648j)  +/-  (8.15e-81, 2.37e-204j)
| (1.1628474935098572038e-05 - 1.3763264984848713339e-649j)  +/-  (1.39e-84, 4.05e-208j)
| (9.1680571493548539831e-07 + 9.7729019849064822488e-650j)  +/-  (1.61e-87, 4.67e-211j)
| (4.4510306909838208953e-11 - 7.7303738269978156194e-652j)  +/-  (5.05e-90, 1.47e-213j)
| (0.0001056115368677351552 + 4.8540025006198233393e-649j)  +/-  (7.71e-84, 2.24e-207j)
| (5.1298442427271611874e-15 - 1.3387126817998440206e-654j)  +/-  (2.56e-92, 7.45e-216j)
| (0.0034568571640740576121 + 7.1192148645420171481e-648j)  +/-  (5.6e-84, 1.63e-207j)
| (0.12611791649368110969 + 8.10847018862461719e-647j)  +/-  (5.51e-78, 1.6e-201j)
| (0.15956538897466822011 - 1.1078549172931549047e-646j)  +/-  (5.07e-78, 1.48e-201j)
| (1.8669155742433244597e-09 + 4.6594711059340648924e-651j)  +/-  (8.36e-90, 2.43e-213j)
| (5.0403869069842600853e-08 - 6.8435279291056456962e-651j)  +/-  (1.29e-89, 3.75e-213j)
| (0.0001056115368677351552 + 1.0907064160058125124e-648j)  +/-  (3.13e-87, 9.09e-211j)
| (5.0403869069842600853e-08 - 2.325178332470687662e-650j)  +/-  (1.79e-89, 5.2e-213j)
| (1.1628474935098572038e-05 - 3.5100655995181386896e-649j)  +/-  (4.36e-88, 1.27e-211j)
| (1.8669155742433244597e-09 + 1.1591024874021205322e-651j)  +/-  (4.15e-92, 1.21e-215j)
| (0.077122863369598148969 - 3.9314421467242894158e-647j)  +/-  (1.24e-83, 3.6e-207j)
| (4.4510306909838208953e-11 - 1.5843638039107427975e-652j)  +/-  (4.49e-93, 1.31e-216j)
| (0.036012043599063422527 + 2.9419402944389345484e-647j)  +/-  (8.97e-87, 2.62e-210j)
| (3.0185529438506378865e-20 - 6.3734757346717299163e-656j)  +/-  (9.67e-98, 2.81e-221j)
| (0.16818467693660332258 + 1.2126154155110017392e-646j)  +/-  (6.54e-85, 1.91e-208j)
| (9.1680571493548539831e-07 + 3.3422305625170420107e-650j)  +/-  (1.04e-90, 3.01e-214j)
| (0.15956538897466822011 - 1.0183225725296784545e-646j)  +/-  (2.89e-85, 8.45e-209j)
| (0.077122863369598148969 - 5.1430514790844546628e-647j)  +/-  (1.25e-86, 3.66e-210j)
| (0.012813273095241408152 - 1.5252172995561293487e-647j)  +/-  (3.53e-88, 1.03e-211j)
| (1.1890374331346980121e-23 + 4.7808943641994392206e-659j)  +/-  (2.05e-100, 5.9e-224j)
| (0.00070110970191212535038 - 2.9645203597806197403e-648j)  +/-  (2.04e-89, 5.97e-213j)
| (0.12611791649368110969 + 6.8152557765369686336e-647j)  +/-  (6.25e-88, 1.99e-211j)
| (0.012813273095241408152 - 9.5231942334007245248e-648j)  +/-  (4.82e-89, 1.32e-212j)
