Starting with polynomial:
P : t
Extension levels are: 1 2 50
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 50 Kronrod extension for:
P2 : t^3 - 3/5*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^53 - 128008855888268914275007/9701955052549987287720*t^51 + 5364296462613634358954995/65326497353836581070648*t^49 - 172748407299210768799924955/538943603169151793832846*t^47 + 138040832771579462429334749455/156832588522223172005358186*t^45 - 5727406076855738697016014385/3168335121661074181926428*t^43 + 5378306362613267443914227477811/1866149386658372693154666092*t^41 - 132976559276599064129406314500265/36389913039838267516515988794*t^39 + 16368331589521401348641119957445/4370718300331451833967507426*t^37 - 1589973202587501408535836459432545/507003322838448412740230861416*t^35 + 3286369145518671556412073074434085/1521009968515345238220692584248*t^33 - 587962648291561846345252651647241/478196315858991116561808653381*t^31 + 2651016654740423961154755078071305/4581429219681301987705070001747*t^29 - 16846552184933839587005890940907035/74882670694101280764558730373382*t^27 + 2197193447041675678828099366383605/30507754727226447718894297559526*t^25 - 95984007807722684090354146748025/5084625787871074619815716259921*t^23 + 1220199969975860935511756411434574/303690831148299638656265962069827*t^21 - 39483519400353729502267728683369515/57498797364078064918919688818553912*t^19 + 5338203688015920249198578223270605/57498797364078064918919688818553912*t^17 - 28131979262829389427934216610657495/2889314567544922762175714363132334078*t^15 + 9662181712287501394480833597420215/12520363126027998636094762240240114338*t^13 - 257909406328835822834957588601641/5778629135089845524351428726264668156*t^11 + 172433388736213944042459168178115/96135375611040157359664677900584933868*t^9 - 161670783020038095449732155252715/3466214376198059007023465330971090115574*t^7 + 810553339279027439368009219805/1155404792066019669007821776990363371858*t^5 - 43439138205086096238509925544699/8693265655504731989614851050075494009859592*t^3 + 2302969785587148311136753817/216250389440416218647135598260584428105960*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:
| (0.99901876186063649471 - 1.4666528570038824052e-864j)  +/-  (2.38e-237, 2.38e-237j)
| (-0.96228832795772968133 - 3.0638155871711944565e-881j)  +/-  (8.29e-237, 8.29e-237j)
| (-0.90031566237018694564 - 2.6368130834780764262e-883j)  +/-  (1.45e-237, 1.45e-237j)
| (-0.99483149820568338586 + 9.7461021885876259755e-881j)  +/-  (6.95e-237, 6.95e-237j)
| (0.90031566237018694564 + 1.3417025498811195766e-883j)  +/-  (1.55e-237, 1.55e-237j)
| (0.94484874076139116482 - 7.6024946827379642928e-894j)  +/-  (5.91e-237, 5.91e-237j)
| (-0.98730505810320053379 - 1.0653229880889946121e-898j)  +/-  (1.08e-236, 1.08e-236j)
| (-0.9241732447559803354 + 1.9200370975275712826e-899j)  +/-  (3.27e-237, 3.27e-237j)
| (-0.99901876186063649471 + 1.3981669233469673536e-899j)  +/-  (2.52e-237, 2.52e-237j)
| (0.99483149820568338586 + 1.5455397644646446527e-896j)  +/-  (7.41e-237, 7.41e-237j)
| (0.87334278657458524358 - 2.5848485027166626865e-908j)  +/-  (6.25e-238, 6.25e-238j)
| (0.98730505810320053379 - 1.3678090241815879376e-906j)  +/-  (9.99e-237, 9.99e-237j)
| (-0.87334278657458524358 - 7.1294334029643691692e-921j)  +/-  (6.68e-238, 6.68e-238j)
| (-0.77459666924148337704 - 4.3023068427847895592e-924j)  +/-  (1.46e-239, 1.46e-239j)
| (6.5140506795380199376e-949 + 2.0771649898824529003e-948j)  +/-  (1.15e-946, 1.15e-946j)
| (0.84333457701676405722 + 1.7065406855938266535e-920j)  +/-  (1.94e-238, 1.94e-238j)
| (0.81038400785226866495 + 1.0046266405606623133e-924j)  +/-  (6.09e-239, 6.09e-239j)
| (-0.94484874076139116482 - 1.4894860358983234549e-921j)  +/-  (5.64e-237, 5.64e-237j)
| (-0.81038400785226866495 - 1.6535734496840747047e-924j)  +/-  (5.95e-239, 5.95e-239j)
| (-0.97645051901325477526 + 4.3309022704915951205e-922j)  +/-  (1.08e-236, 1.08e-236j)
| (0.96228832795772968133 - 1.1037158547730201879e-920j)  +/-  (8.53e-237, 8.53e-237j)
| (0.73609020999773502478 + 7.7290490776400217145e-943j)  +/-  (3.24e-240, 3.24e-240j)
| (0.97645051901325477526 + 2.824808792341669079e-947j)  +/-  (1.08e-236, 1.08e-236j)
| (-0.73609020999773502478 - 1.6433183011791074858e-963j)  +/-  (3.02e-240, 3.02e-240j)
| (-0.84333457701676405722 - 3.0399264185618189153e-961j)  +/-  (2.12e-238, 2.12e-238j)
| (0.77459666924148337704 - 8.3098570150729048581e-962j)  +/-  (1.51e-239, 1.51e-239j)
| (0.694993685949841542 - 2.407205558100509886e-969j)  +/-  (6e-241, 6e-241j)
| (0.9241732447559803354 + 8.3093087382318154657e-977j)  +/-  (3.36e-237, 3.36e-237j)
| (-0.059169510590580290731 + 5.5548209002090507703e-1007j)  +/-  (1.81e-254, 1.81e-254j)
| (-0.65144685669215758066 + 9.8337308122815618547e-993j)  +/-  (8.69e-242, 8.69e-242j)
| (-0.694993685949841542 - 2.0711764711870107879e-993j)  +/-  (5.86e-241, 5.86e-241j)
| (0.50764729669073048309 + 1.6777611078635853899e-995j)  +/-  (1.53e-244, 1.53e-244j)
| (0.65144685669215758066 - 9.6701625894478428091e-993j)  +/-  (8.71e-242, 8.71e-242j)
| (0.059169510590580290731 - 1.3484580250785022879e-1007j)  +/-  (1.81e-254, 1.81e-254j)
| (-0.55761045196734733484 + 8.09611815793066116e-996j)  +/-  (1.33e-243, 1.33e-243j)
| (-0.60559945631738100404 - 3.3377798334946621665e-996j)  +/-  (1.19e-242, 1.19e-242j)
| (0.23457927269494499743 - 1.6175533629859531636e-1003j)  +/-  (1.71e-250, 1.71e-250j)
| (0.60559945631738100404 + 1.5289386528730155291e-996j)  +/-  (1.18e-242, 1.18e-242j)
| (0.40250626881689739876 - 2.9937557686230338096e-1003j)  +/-  (8.99e-247, 8.99e-247j)
| (-0.29165711145732195843 + 1.608183538376037107e-1007j)  +/-  (3.25e-249, 3.25e-249j)
| (-0.50764729669073048309 - 9.1202892604684005181e-1002j)  +/-  (1.39e-244, 1.39e-244j)
| (-0.23457927269494499743 + 6.7426805452329866375e-1007j)  +/-  (1.96e-250, 1.96e-250j)
| (0.34769896077377761463 - 1.1685132457513620315e-1003j)  +/-  (6.24e-248, 6.24e-248j)
| (0.55761045196734733484 - 1.7229610035734460228e-1002j)  +/-  (1.46e-243, 1.46e-243j)
| (0.17666791910386119928 + 4.0367323925392754626e-1011j)  +/-  (8.94e-252, 8.94e-252j)
| (-0.45588517892427737581 + 6.2094620480096860457e-1005j)  +/-  (1.15e-245, 1.15e-245j)
| (-0.34769896077377761463 + 3.5929124346487302744e-1007j)  +/-  (6.19e-248, 6.19e-248j)
| (0.11812867063396060338 + 6.1693901823359694405e-1012j)  +/-  (4.24e-253, 4.24e-253j)
| (0.45588517892427737581 + 2.7604649074801324016e-1005j)  +/-  (1.24e-245, 1.24e-245j)
| (0.29165711145732195843 + 1.7289163589586190419e-1008j)  +/-  (3.45e-249, 3.45e-249j)
| (-0.17666791910386119928 + 8.2624535331583726856e-1011j)  +/-  (8.75e-252, 8.75e-252j)
| (-0.40250626881689739876 + 7.8516753131565236638e-1006j)  +/-  (1.02e-246, 1.02e-246j)
| (-0.11812867063396060338 - 4.4567521816644932363e-1012j)  +/-  (4.23e-253, 4.23e-253j)
-------------------------------------------------
The weights are:
| (0.0025179962158078495486 + 1.8731591948322851218e-864j)  +/-  (1.37e-54, 3.65e-168j)
| (0.01580682352927404846 + 2.7008769507168420872e-866j)  +/-  (6.77e-55, 1.81e-168j)
| (0.025427458489351718276 - 5.144466458902499341e-866j)  +/-  (3.45e-55, 9.21e-169j)
| (0.0058577825760126687635 - 6.4209598544056317207e-867j)  +/-  (1.58e-55, 4.21e-169j)
| (0.025427458489351718276 - 9.8994482342875312765e-865j)  +/-  (3.41e-57, 9.11e-171j)
| (0.019065454940340952587 - 1.255508840125887189e-864j)  +/-  (2.72e-57, 7.27e-171j)
| (0.0091931509219526216537 + 1.2440688456945457977e-866j)  +/-  (9.8e-56, 2.62e-169j)
| (0.022276577153298408922 + 4.3173174131827008101e-866j)  +/-  (1.66e-56, 4.44e-170j)
| (0.0025179962158078495486 + 1.8483268206902834967e-867j)  +/-  (6.54e-56, 1.75e-169j)
| (0.0058577825760126687635 - 3.0574698730609398075e-864j)  +/-  (2.52e-58, 6.74e-172j)
| (0.028504963705454113394 + 8.8980666249744099251e-865j)  +/-  (3.98e-59, 1.06e-172j)
| (0.0091931509219526216537 + 2.109600543986207699e-864j)  +/-  (1.14e-58, 3.04e-172j)
| (0.028504963705454113394 + 5.9725281273186188411e-866j)  +/-  (3.57e-58, 9.55e-172j)
| (0.037167480463902345534 - 8.4339304659792583815e-866j)  +/-  (8.86e-60, 2.37e-173j)
| (0.059204595342033490206 + 2.3013398804133087796e-865j)  +/-  (5.28e-62, 1.41e-175j)
| (0.031495952864809232103 - 8.043975149304765711e-865j)  +/-  (6.45e-60, 1.72e-173j)
| (0.034387577662022581503 + 7.3069319118480808363e-865j)  +/-  (1.41e-60, 3.76e-174j)
| (0.019065454940340952587 - 3.4987436267219925077e-866j)  +/-  (1.9e-58, 5.08e-172j)
| (0.034387577662022581503 + 7.6176588585970490591e-866j)  +/-  (5.35e-61, 1.43e-174j)
| (0.012512540970833807148 - 1.9412783614583886708e-866j)  +/-  (3.13e-58, 8.37e-172j)
| (0.01580682352927404846 + 1.4421961706661864828e-864j)  +/-  (5.53e-61, 1.48e-174j)
| (0.039823916939217552853 + 6.1030650256552173993e-865j)  +/-  (5.86e-64, 1.57e-177j)
| (0.012512540970833807148 - 1.6992620092845097107e-864j)  +/-  (6.46e-61, 1.73e-174j)
| (0.039823916939217552853 + 9.2482378637117019505e-866j)  +/-  (1.71e-63, 4.56e-177j)
| (0.031495952864809232103 - 6.7973916164580758056e-866j)  +/-  (2.62e-61, 7e-175j)
| (0.037167480463902345534 - 6.6653639330811973006e-865j)  +/-  (1.63e-63, 4.36e-177j)
| (0.042345825705216776963 - 5.607397415742477179e-865j)  +/-  (3.19e-65, 8.53e-179j)
| (0.022276577153298408922 + 1.1093557316799111308e-864j)  +/-  (6.21e-62, 1.66e-175j)
| (0.059099354252736530765 - 2.1694997835761439376e-865j)  +/-  (7.42e-69, 1.98e-182j)
| (0.044722864756343231936 + 1.0883812917131245726e-865j)  +/-  (4.72e-67, 1.26e-180j)
| (0.042345825705216776963 - 1.006361805184225673e-865j)  +/-  (3.8e-66, 1.02e-179j)
| (0.050892441583476921931 - 4.1141728252997246323e-865j)  +/-  (8e-70, 2.14e-183j)
| (0.044722864756343231936 + 5.1682425280543078373e-865j)  +/-  (9.94e-68, 2.66e-181j)
| (0.059099354252736530765 - 2.4426675075427292831e-865j)  +/-  (5.06e-71, 1.35e-184j)
| (0.049004658337447097696 + 1.2556020347432285821e-865j)  +/-  (1.16e-69, 3.11e-183j)
| (0.046945429012484642374 - 1.1713069764562597641e-865j)  +/-  (9.88e-69, 2.64e-182j)
| (0.057528630053091771463 + 2.9372557130339809533e-865j)  +/-  (3.37e-72, 9e-186j)
| (0.046945429012484642374 - 4.7773469349843040363e-865j)  +/-  (7.22e-70, 1.93e-183j)
| (0.054124988812978718683 - 3.5755456300146255409e-865j)  +/-  (5.01e-72, 1.34e-185j)
| (0.05659328874314518202 - 1.7160770169938609322e-865j)  +/-  (1.49e-73, 3.99e-187j)
| (0.050892441583476921931 - 1.3417619104484624549e-865j)  +/-  (3.02e-72, 8.08e-186j)
| (0.057528630053091771463 + 1.8201668565641165709e-865j)  +/-  (1.08e-73, 2.88e-187j)
| (0.055457305045117246322 + 3.3431299071320907965e-865j)  +/-  (1.63e-73, 4.36e-187j)
| (0.049004658337447097696 + 4.4278885657944971706e-865j)  +/-  (2.79e-72, 7.45e-186j)
| (0.058259794102390158422 - 2.759071949936310629e-865j)  +/-  (3.98e-74, 1.06e-187j)
| (0.052601419635627123228 + 1.4303125592355770175e-865j)  +/-  (2.26e-74, 6.05e-188j)
| (0.055457305045117246322 + 1.6168545713212548314e-865j)  +/-  (6.79e-75, 1.81e-188j)
| (0.05878402585664995235 + 2.594761180019252284e-865j)  +/-  (9.32e-75, 2.49e-188j)
| (0.052601419635627123228 + 3.8314098858251435387e-865j)  +/-  (1.84e-74, 4.9e-188j)
| (0.05659328874314518202 - 3.1312118791378715193e-865j)  +/-  (7.86e-75, 2.1e-188j)
| (0.058259794102390158422 - 1.9298722865477619614e-865j)  +/-  (1.79e-76, 4.8e-190j)
| (0.054124988812978718683 - 1.521812019811441822e-865j)  +/-  (1.58e-76, 4.42e-190j)
| (0.05878402585664995235 + 2.0460141124565943835e-865j)  +/-  (1.81e-76, 4.78e-190j)
