Starting with polynomial:
P : 64*t^6 - 480*t^4 + 720*t^2 - 120
Extension levels are: 6 39
-------------------------------------------------
Trying to find an order 39 Kronrod extension for:
P1 : 64*t^6 - 480*t^4 + 720*t^2 - 120
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 64*t^45 - 309106933635763395386939518658804826720/10905070395460721410598644805409721*t^43 + 1056418412425757162882161652024051977589040/185386196722832263980176961691965257*t^41 - 1407042195778894925601080948183462934116008440/2039248163951154903781946578611617827*t^39 + 16402123313447287159951330182966463822880785560/291321166278736414825992368373088261*t^37 - 6694671824239063081912513348989535458161439199860/2039248163951154903781946578611617827*t^35 + 2425351217010781982476109949914452470707555392200/17136539192866847930940727551358133*t^33 - 7174604599156983066788182528942202817405428161950/1557867199351531630085520686487103*t^31 + 356709202468537478260665543950373455297997881495325/3115734398703063260171041372974206*t^29 - 13630231900164422941189747395406813607444020070425575/6231468797406126520342082745948412*t^27 + 400749824910407603385994492279480109393785974330601275/12462937594812253040684165491896824*t^25 - 9038460957620293179993674433690519661297415349981298125/24925875189624506081368330983793648*t^23 + 9703599324074170881472058643180140352904426801863268125/3115734398703063260171041372974206*t^21 - 501970622881466594109034816821225790290348205413136145625/24925875189624506081368330983793648*t^19 + 9614488805681918576726420596337367419609792763813449731875/99703500758498024325473323935174592*t^17 - 66647914714145534356516691559905349358151432042883517336875/199407001516996048650946647870349184*t^15 + 1296981356592082893691869923813386274864644667644460818359375/1595256012135968389207573182962793472*t^13 - 4246021766847439435279913592239737053710175103456785363703125/3190512024271936778415146365925586944*t^11 + 8826108208950043300659734483356338566893539535189633120378125/6381024048543873556830292731851173888*t^9 - 10735517765412670192671527674991336573659965427425836507221875/12762048097087747113660585463702347776*t^7 + 3401873847388167134323386036657346883740726809147654923671875/12762048097087747113660585463702347776*t^5 - 954077636660051060642790085905294487121185045100059358109375/25524096194175494227321170927404695552*t^3 + 44413680621159976539385273459102846501782297153697236703125/25524096194175494227321170927404695552*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:
| (4.9046513383649717442 + 2.7054191478290852437e-904j)  +/-  (7.94e-245, 7.94e-245j)
| (-7.6960060352025686125 + 5.7235572486198437968e-905j)  +/-  (1.76e-246, 1.76e-246j)
| (7.6960060352025686125 + 1.4449262241390472631e-907j)  +/-  (1.8e-246, 1.8e-246j)
| (-8.3734029128152367012 + 1.8117516604665540912e-907j)  +/-  (1.49e-247, 1.49e-247j)
| (7.1335170356023034723 + 3.6844098214339287013e-907j)  +/-  (9.22e-246, 9.22e-246j)
| (8.3734029128152367012 + 5.5793974429769420069e-909j)  +/-  (1.36e-247, 1.36e-247j)
| (-4.514973005379180176 - 3.3147548611173829808e-905j)  +/-  (5.54e-245, 5.54e-245j)
| (-3.0470772072709017615 - 3.1430160275978734009e-907j)  +/-  (1.58e-246, 1.58e-246j)
| (-4.1359319939596292478 + 4.0339073417202045549e-905j)  +/-  (2.95e-245, 2.95e-245j)
| (-7.1335170356023034723 - 1.5260438924258723658e-904j)  +/-  (9.43e-246, 9.43e-246j)
| (-6.6301087930831124014 + 2.7006075390489348437e-918j)  +/-  (3.05e-245, 3.05e-245j)
| (5.3072184407076737754 - 3.4736313547611259052e-930j)  +/-  (8.87e-245, 8.87e-245j)
| (5.7257228412481300231 + 1.3021373217922818471e-932j)  +/-  (8.78e-245, 8.78e-245j)
| (-2.6964618353772917757 + 1.3360394917271509513e-933j)  +/-  (4.06e-247, 4.06e-247j)
| (-4.9046513383649717442 + 1.1390879854656246835e-937j)  +/-  (7.83e-245, 7.83e-245j)
| (1.0045369744629728633 - 3.6674757090374954407e-962j)  +/-  (2.98e-251, 2.98e-251j)
| (1.3358490740136969497 - 2.3232831772595905042e-961j)  +/-  (2.56e-250, 2.56e-250j)
| (-3.7658020790771140551 + 8.3478444809859683147e-955j)  +/-  (1.5e-245, 1.5e-245j)
| (-1.6707145626858771877 - 1.5034291897446658883e-965j)  +/-  (2.15e-249, 2.15e-249j)
| (6.6301087930831124014 - 1.3578065507500859496e-959j)  +/-  (2.93e-245, 2.93e-245j)
| (6.1644962035060056711 + 5.2593492099188039265e-959j)  +/-  (5.95e-245, 5.95e-245j)
| (2.0088617276124725322 + 4.9061910082444124751e-965j)  +/-  (1.41e-248, 1.41e-248j)
| (4.514973005379180176 + 1.2384580150135259695e-960j)  +/-  (5.71e-245, 5.71e-245j)
| (-5.3072184407076737754 + 6.2661146098257961131e-973j)  +/-  (9.72e-245, 9.72e-245j)
| (-2.0088617276124725322 + 9.2721863550580865424e-996j)  +/-  (1.49e-248, 1.49e-248j)
| (1.6707145626858771877 + 4.6906350796657506649e-997j)  +/-  (2.18e-249, 2.18e-249j)
| (2.3506049736744922228 + 2.1989101414054005453e-994j)  +/-  (8.97e-248, 8.97e-248j)
| (3.0470772072709017615 + 8.9006971762542683563e-993j)  +/-  (1.48e-246, 1.48e-246j)
| (2.6964618353772917757 - 5.8629704126119533557e-997j)  +/-  (3.92e-247, 3.92e-247j)
| (-0.68060404611291549212 - 1.3276140718513424131e-1010j)  +/-  (3.42e-252, 3.42e-252j)
| (-5.7257228412481300231 - 3.6625846424346031334e-1002j)  +/-  (9.25e-245, 9.25e-245j)
| (-4.7970038459505450355e-1040 + 2.6396147586578229944e-1042j)  +/-  (2.16e-1038, 2.16e-1038j)
| (0.68060404611291549212 - 3.5252660777524085136e-1028j)  +/-  (3.82e-252, 3.82e-252j)
| (-6.1644962035060056711 + 2.3745395112606995957e-1020j)  +/-  (6.28e-245, 6.28e-245j)
| (-1.0045369744629728633 - 4.7319884996652616632e-1035j)  +/-  (3.13e-251, 3.13e-251j)
| (-3.4032190275794085572 + 4.5996775637620035391e-1029j)  +/-  (4.54e-246, 4.54e-246j)
| (4.1359319939596292478 - 1.6399721972576243663e-1028j)  +/-  (3.11e-245, 3.11e-245j)
| (3.4032190275794085572 - 4.2337712557562337382e-1029j)  +/-  (5.08e-246, 5.08e-246j)
| (0.3013917647615211648 + 5.6311548491285906569e-1039j)  +/-  (1.78e-253, 1.78e-253j)
| (-1.3358490740136969497 - 9.8720489877444948944e-1036j)  +/-  (2.59e-250, 2.59e-250j)
| (-0.43607741192761650868 + 2.0838677820848001224e-1038j)  +/-  (6.92e-253, 6.92e-253j)
| (-0.3013917647615211648 - 7.8738482630795612594e-1040j)  +/-  (1.92e-253, 1.92e-253j)
| (0.43607741192761650868 - 2.4855895192811823861e-1038j)  +/-  (6.92e-253, 6.92e-253j)
| (3.7658020790771140551 - 4.5230600286901543712e-1035j)  +/-  (1.31e-245, 1.31e-245j)
| (-2.3506049736744922228 - 1.3524822128751174933e-1037j)  +/-  (8.68e-248, 8.68e-248j)
-------------------------------------------------
The weights are:
| (7.9719876156563112566e-12 - 1.0720540382279463619e-914j)  +/-  (5.3e-76, 7.76e-198j)
| (6.4629075640307463379e-27 - 2.2411411732944317854e-923j)  +/-  (3.04e-85, 4.45e-207j)
| (6.4629075640307463379e-27 + 1.2945719096329546578e-923j)  +/-  (4.52e-85, 6.62e-207j)
| (1.5639636194459927554e-31 + 7.3771861548740820354e-926j)  +/-  (2.67e-87, 3.91e-209j)
| (2.3662166233139632393e-23 - 1.1140548620443289603e-921j)  +/-  (6.79e-84, 9.94e-206j)
| (1.5639636194459927554e-31 - 4.397008630063083871e-926j)  +/-  (4.82e-87, 7.06e-209j)
| (3.0388619872363127258e-10 + 8.8090345958957788505e-914j)  +/-  (3.43e-78, 5.02e-200j)
| (1.8501598516883854386e-05 - 5.5449933564371842119e-911j)  +/-  (1.81e-72, 2.66e-194j)
| (7.8644737622407902602e-09 + 1.6120893541331396223e-912j)  +/-  (6.34e-77, 9.28e-199j)
| (2.3662166233139632393e-23 + 1.9726592481630864677e-921j)  +/-  (2.89e-86, 4.23e-208j)
| (2.2066213689794447216e-20 - 8.7907507073276167312e-920j)  +/-  (2.66e-85, 3.9e-207j)
| (1.3538255200944435016e-13 - 6.6933039025101005168e-916j)  +/-  (1.6e-83, 2.34e-205j)
| (1.3956348273525253752e-15 + 3.11676823093258561e-917j)  +/-  (8.07e-85, 1.18e-206j)
| (0.00013659601406473292725 + 1.5077697113101641195e-910j)  +/-  (1.78e-74, 2.61e-196j)
| (7.9719876156563112566e-12 - 1.269628722608041487e-914j)  +/-  (4.52e-82, 6.61e-204j)
| (0.067669598987800672556 - 4.9171814095916325392e-909j)  +/-  (5.85e-65, 8.56e-187j)
| (0.031562634737493842694 + 1.4914967731551726089e-909j)  +/-  (6.85e-69, 1e-190j)
| (1.4329890241734728532e-07 - 4.6027204242658549828e-912j)  +/-  (1.79e-78, 2.62e-200j)
| (0.011645104356298250776 - 1.8311350962253339092e-909j)  +/-  (4.41e-71, 6.46e-193j)
| (2.2066213689794447216e-20 + 4.9132556364655166049e-920j)  +/-  (3.6e-88, 5.27e-210j)
| (7.9765199906329463565e-18 - 1.4115420248146818972e-918j)  +/-  (4.82e-87, 7.05e-209j)
| (0.0033894803638465204951 + 1.3396867465821083947e-910j)  +/-  (7.65e-77, 1.12e-198j)
| (3.0388619872363127258e-10 + 3.4302464251614477708e-914j)  +/-  (1.67e-84, 2.45e-206j)
| (1.3538255200944435016e-13 + 8.4166175774037358663e-916j)  +/-  (5.64e-86, 8.26e-208j)
| (0.0033894803638465204951 + 7.8837341308815059678e-910j)  +/-  (6.03e-77, 8.83e-199j)
| (0.011645104356298250776 - 4.6213447077137028737e-910j)  +/-  (1.53e-75, 2.23e-197j)
| (0.0007726473368696213951 - 3.3826352007988055906e-911j)  +/-  (3.22e-79, 4.71e-201j)
| (1.8501598516883854386e-05 - 5.5254231947702555429e-913j)  +/-  (1.9e-82, 2.78e-204j)
| (0.00013659601406473292725 + 6.582265388214248109e-912j)  +/-  (5.15e-81, 7.54e-203j)
| (0.1116097609263269262 + 3.3432008820014120501e-908j)  +/-  (2.12e-77, 3.1e-199j)
| (1.3956348273525253752e-15 - 5.113042162477763429e-917j)  +/-  (4.13e-89, 6.05e-211j)
| (0.17836848652338451998 - 5.8919961514755616308e-908j)  +/-  (3.49e-78, 5.11e-200j)
| (0.1116097609263269262 + 2.0157527713235339485e-908j)  +/-  (4.69e-78, 6.87e-200j)
| (7.9765199906329463565e-18 + 2.4905942855735829918e-918j)  +/-  (2.37e-90, 3.47e-212j)
| (0.067669598987800672556 - 1.0549278719697631424e-908j)  +/-  (7.77e-80, 1.14e-201j)
| (1.8914778311137072864e-06 + 8.050037422346764358e-912j)  +/-  (5.84e-84, 8.54e-206j)
| (7.8644737622407902602e-09 - 8.3010859816400524031e-914j)  +/-  (3.99e-87, 5.83e-209j)
| (1.8914778311137072864e-06 - 2.7785128350093595225e-913j)  +/-  (1.01e-85, 1.47e-207j)
| (0.13029364111903767172 + 8.3525221724956373234e-908j)  +/-  (5.28e-80, 7.73e-202j)
| (0.031562634737493842694 + 4.2600440051602745116e-909j)  +/-  (5.2e-82, 7.6e-204j)
| (0.053715748344850351565 - 9.9103443890874641242e-908j)  +/-  (1.72e-80, 2.52e-202j)
| (0.13029364111903767172 + 1.0416744700769063852e-907j)  +/-  (1.61e-80, 2.36e-202j)
| (0.053715748344850351565 - 7.1909555396346713154e-908j)  +/-  (1.13e-80, 1.65e-202j)
| (1.4329890241734728532e-07 + 1.947455811484992233e-913j)  +/-  (4.25e-87, 6.22e-209j)
| (0.0007726473368696213951 - 3.3592046150513724643e-910j)  +/-  (1.35e-84, 1.95e-206j)
