Starting with polynomial:
P : t
Extension levels are: 1 12 26
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 26 Kronrod extension for:
P2 : t^13 - 78*t^11 + 2145*t^9 - 25740*t^7 + 135135*t^5 - 270270*t^3 + 135135*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^39 - 998308440773553/1727893965901*t^37 + 257797121629388445/1727893965901*t^35 - 670600399023694791405/29374197420317*t^33 + 957335975157389397570/413721090427*t^31 - 4833290940455632562068590/29374197420317*t^29 + 1743983194628973421245455190/205619381942219*t^27 - 66407769738530164501070406750/205619381942219*t^25 + 1886275941158732992361667603000/205619381942219*t^23 - 40081393642039013752801121952000/205619381942219*t^21 + 4775691777988514452177397503500/1546010390543*t^19 - 3290540115190505881160881066500/90941787679*t^17 + 28057244555319864163368451683750/90941787679*t^15 - 170198127402598137979760926623750/90941787679*t^13 + 710631850751208144414730604351250/90941787679*t^11 - 1947383105495281531721738296166250/90941787679*t^9 + 3263757841954301373168344757095625/90941787679*t^7 - 2992249040222128651171112083303125/90941787679*t^5 + 1230875600141909941353488131903125/90941787679*t^3 - 144526707157778177345428818628125/90941787679*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
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (7.7536421690600401603 - 6.7460164721226385765e-331j)  +/-  (8.17e-119, 8.17e-119j)
| (10.328022074184259532 + 7.6923097301495117559e-333j)  +/-  (8.22e-121, 8.22e-121j)
| (9.3290002218463357595 - 1.1296963900317417184e-332j)  +/-  (7.61e-120, 7.61e-120j)
| (4.5913984489365206271 - 2.1484479649475620661e-330j)  +/-  (4.47e-118, 4.47e-118j)
| (8.498072749082787188 - 6.8257575205867419275e-332j)  +/-  (2.9e-119, 2.9e-119j)
| (-10.328022074184259532 - 6.8905993539926574557e-330j)  +/-  (7.42e-121, 7.42e-121j)
| (-5.2147152656207254655 - 1.1609347708455933079e-339j)  +/-  (3.6e-118, 3.6e-118j)
| (-9.3290002218463357595 + 3.1606449418399084949e-357j)  +/-  (7.44e-120, 7.44e-120j)
| (-3.5634443802816340916 + 6.8547489456709613006e-364j)  +/-  (9.52e-120, 9.52e-120j)
| (-7.7536421690600401603 - 1.7499811347112335099e-369j)  +/-  (8e-119, 8e-119j)
| (4.0777858944846385058 + 4.397280160362894376e-380j)  +/-  (4.83e-119, 4.83e-119j)
| (0.43207313713522883454 + 3.1879140318815790149e-386j)  +/-  (3.75e-126, 3.75e-126j)
| (6.4164816385733154353 - 7.4522896142388824658e-379j)  +/-  (2.1e-118, 2.1e-118j)
| (7.0649044249778185303 - 9.6664652611376927419e-379j)  +/-  (1.54e-118, 1.54e-118j)
| (-4.0777858944846385058 - 2.2557598916752968999e-378j)  +/-  (4.72e-119, 4.72e-119j)
| (2.6206899734322147806 - 3.1873897793617738081e-395j)  +/-  (4.01e-121, 4.01e-121j)
| (-4.7733296440484549897 - 1.234374001817658466e-390j)  +/-  (5.65e-118, 5.65e-118j)
| (-2.1734680739885215303 - 2.0268026549622294404e-405j)  +/-  (5.87e-122, 5.87e-122j)
| (-1.7254183795882391615 - 1.1231257473222591629e-408j)  +/-  (7.05e-123, 7.05e-123j)
| (-7.0649044249778185303 - 2.8436441062002578248e-408j)  +/-  (1.53e-118, 1.53e-118j)
| (5.8001672523865003059 - 9.3314047123349467886e-420j)  +/-  (2.56e-118, 2.56e-118j)
| (3.5634443802816340916 + 2.0704988949823732359e-421j)  +/-  (9.28e-120, 9.28e-120j)
| (-8.498072749082787188 + 4.2056281215550855529e-419j)  +/-  (2.97e-119, 2.97e-119j)
| (-6.4164816385733154353 + 7.5323712198989243477e-427j)  +/-  (2.28e-118, 2.28e-118j)
| (-7.8194857429834279935e-449 + 6.5878789145736864031e-449j)  +/-  (3.99e-447, 3.99e-447j)
| (5.2147152656207254655 + 1.719967851563555077e-432j)  +/-  (3.51e-118, 3.51e-118j)
| (1.7254183795882391615 + 1.9671909823686613097e-436j)  +/-  (7.29e-123, 7.29e-123j)
| (-4.5913984489365206271 - 5.3714658099435752051e-431j)  +/-  (4.05e-118, 4.05e-118j)
| (-1.2842171079722259307 + 2.4678881717366554243e-445j)  +/-  (8.24e-124, 8.24e-124j)
| (3.0782313099432724455 - 8.2613970132530589212e-443j)  +/-  (1.97e-120, 1.97e-120j)
| (-3.0782313099432724455 - 6.9691842479327337987e-440j)  +/-  (2.19e-120, 2.19e-120j)
| (0.8566794935194500339 - 7.7234430629377908053e-450j)  +/-  (5.89e-125, 5.89e-125j)
| (1.2842171079722259307 - 1.2539982370932301527e-448j)  +/-  (7.01e-124, 7.01e-124j)
| (-0.8566794935194500339 - 1.9098645404134644404e-449j)  +/-  (6.58e-125, 6.58e-125j)
| (-5.8001672523865003059 + 1.8233795249299005331e-441j)  +/-  (2.79e-118, 2.79e-118j)
| (-2.6206899734322147806 + 1.3313244126194480441e-453j)  +/-  (3.84e-121, 3.84e-121j)
| (2.1734680739885215303 + 2.5135450211071280942e-454j)  +/-  (6.1e-122, 6.1e-122j)
| (4.7733296440484549897 + 2.9551845077550036922e-449j)  +/-  (6.15e-118, 6.15e-118j)
| (-0.43207313713522883454 + 2.4538889632890637954e-458j)  +/-  (3.75e-126, 3.75e-126j)
-------------------------------------------------
The weights are:
| (2.5086742999285877097e-14 - 9.5907367001142383874e-343j)  +/-  (6.19e-24, 3.57e-83j)
| (3.1580233298266404617e-24 + 8.8974125672219761882e-349j)  +/-  (3.99e-29, 2.3e-88j)
| (4.5008488891243231881e-20 - 2.5580457439880198331e-346j)  +/-  (1.94e-27, 1.12e-86j)
| (4.6339888313855082895e-06 - 1.6971642394272472926e-335j)  +/-  (2.23e-18, 1.28e-77j)
| (6.4783247520340071955e-17 + 2.2743612047669568777e-344j)  +/-  (5.66e-26, 3.27e-85j)
| (3.1580233298266404617e-24 - 3.3983698616278853304e-349j)  +/-  (1.59e-33, 9.19e-93j)
| (2.8071882207863676135e-07 + 4.767717364007238683e-338j)  +/-  (7.94e-24, 4.58e-83j)
| (4.5008488891243231881e-20 + 8.6120057712321891725e-347j)  +/-  (3.74e-32, 2.16e-91j)
| (0.00034940706979373584276 + 5.1526925945456928357e-336j)  +/-  (1.37e-19, 7.88e-79j)
| (2.5086742999285877097e-14 + 2.6762511638973816831e-343j)  +/-  (9.81e-30, 5.66e-89j)
| (5.1350292296219335767e-05 - 2.936986609894719927e-335j)  +/-  (5.68e-21, 3.28e-80j)
| (0.15560799119154123475 - 7.7635345592284730398e-334j)  +/-  (9.74e-17, 5.62e-76j)
| (2.89086932638706746e-10 - 8.5734694897519676902e-340j)  +/-  (1.68e-26, 9.7e-86j)
| (3.8585552962993312986e-12 + 3.279896088238892937e-341j)  +/-  (2.37e-27, 1.37e-86j)
| (5.1350292296219335767e-05 - 1.7453033171472920927e-336j)  +/-  (2.26e-23, 1.31e-82j)
| (0.005777209741387757663 + 1.491101562643143827e-334j)  +/-  (3.23e-19, 1.86e-78j)
| (6.995033314055429034e-07 - 6.3321803619366951792e-337j)  +/-  (3.54e-25, 2.04e-84j)
| (0.01682864675876060769 - 9.0859208443275534973e-335j)  +/-  (1.29e-18, 7.45e-78j)
| (0.040225303341331917178 + 1.7955293983751285999e-334j)  +/-  (9.57e-17, 5.52e-76j)
| (3.8585552962993312986e-12 - 7.1189239247407785686e-342j)  +/-  (4.96e-31, 2.86e-90j)
| (1.1884272443741244748e-08 + 2.1412749572131893576e-338j)  +/-  (5.35e-28, 3.09e-87j)
| (0.00034940706979373584276 + 4.0777944187999441481e-335j)  +/-  (3.95e-24, 2.28e-83j)
| (6.4783247520340071955e-17 - 6.6304316512888896002e-345j)  +/-  (7.13e-34, 4.11e-93j)
| (2.89086932638706746e-10 + 1.4371317994469183812e-340j)  +/-  (2.41e-30, 1.39e-89j)
| (0.17324574083039866619 + 7.41941825080071577e-334j)  +/-  (1.69e-20, 9.74e-80j)
| (2.8071882207863676135e-07 - 7.4624317312766531402e-337j)  +/-  (7.33e-28, 4.24e-87j)
| (0.040225303341331917178 + 3.9536266819957243412e-334j)  +/-  (1.74e-22, 1e-81j)
| (4.6339888313855082895e-06 + 1.0883053657955633496e-336j)  +/-  (1.33e-26, 7.63e-86j)
| (0.075929577910496021752 - 3.1930704750498305359e-334j)  +/-  (1.14e-21, 6.58e-81j)
| (0.0016406785980255262493 - 7.8738262277691167385e-335j)  +/-  (2.27e-25, 1.31e-84j)
| (0.0016406785980255262493 - 1.5564962680687096838e-335j)  +/-  (1.57e-25, 9.04e-85j)
| (0.11696133829293969351 + 7.163787080834068742e-334j)  +/-  (1.06e-22, 6.09e-82j)
| (0.075929577910496021752 - 5.6688758280812210059e-334j)  +/-  (1.67e-23, 9.56e-83j)
| (0.11696133829293969351 + 4.9131368554427245399e-334j)  +/-  (3.33e-23, 1.9e-82j)
| (1.1884272443741244748e-08 - 2.5084577305526031843e-339j)  +/-  (1.08e-29, 6.21e-89j)
| (0.005777209741387757663 + 4.0809049512593079682e-335j)  +/-  (3.4e-25, 1.96e-84j)
| (0.01682864675876060769 - 2.5388440167337106194e-334j)  +/-  (1.55e-25, 8.52e-85j)
| (6.995033314055429034e-07 + 3.2460236801776287585e-335j)  +/-  (5.33e-28, 3.25e-87j)
| (0.15560799119154123475 - 6.4295290997744009949e-334j)  +/-  (2.7e-24, 1.14e-83j)
