Starting with polynomial:
P : t
Extension levels are: 1 36
-------------------------------------------------
Trying to find an order 36 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^37 - 666*t^35 + 198135*t^33 - 34871760*t^31 + 4053842100*t^29 - 329171978520*t^27 + 19256560743420*t^25 - 825281174718000*t^23 + 26099517150456750*t^21 - 608988733510657500*t^19 + 10413707343032243250*t^17 - 128751290786580462000*t^15 + 1126573794382579042500*t^13 - 6759442766295474255000*t^11 + 26554953724732220287500*t^9 - 63731888939357328690000*t^7 + 83648104232906493905625*t^5 - 49204767195827349356250*t^3 + 8200794532637891559375*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
Positive weights:   37 out of 37
Indefinite weights: 0 out of 37
Negative weights:   0 out of 37
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (5.8768878925942023475 + 1.5018510976624965515e-557j)  +/-  (1.39e-246, 1.39e-246j)
| (10.955745943561653856 - 1.4425299290996886756e-565j)  +/-  (1.61e-248, 1.61e-248j)
| (-9.9698009456910974414 + 2.5308879625221212007e-576j)  +/-  (1.48e-247, 1.48e-247j)
| (7.7312090357769069197 + 8.9717763686645880855e-594j)  +/-  (2.5e-246, 2.5e-246j)
| (-7.7312090357769069197 - 2.8911507576367652666e-622j)  +/-  (2.28e-246, 2.28e-246j)
| (-9.149282977696766065 - 1.469611731102174391e-648j)  +/-  (6.53e-247, 6.53e-247j)
| (8.4133646794888803544 - 5.7925677117085610787e-656j)  +/-  (1.68e-246, 1.68e-246j)
| (-2.0617644826257039935 - 1.3857347753070170928e-663j)  +/-  (1.12e-250, 1.12e-250j)
| (-4.1869902256279117453 - 2.507918611794153989e-659j)  +/-  (9.91e-248, 9.91e-248j)
| (2.0617644826257039935 + 5.9221054793752142191e-673j)  +/-  (1.16e-250, 1.16e-250j)
| (-10.955745943561653856 - 1.6679103753433159307e-666j)  +/-  (1.18e-248, 1.18e-248j)
| (7.0869156850173470094 - 1.2460204062939896056e-674j)  +/-  (2.73e-246, 2.73e-246j)
| (6.470920475390299407 - 4.8432977425855805571e-687j)  +/-  (2.33e-246, 2.33e-246j)
| (9.9698009456910974414 + 1.8865113863893621873e-701j)  +/-  (1.28e-247, 1.28e-247j)
| (-7.0869156850173470094 - 1.2514223900414111561e-719j)  +/-  (2.8e-246, 2.8e-246j)
| (9.149282977696766065 + 7.7061884898014171738e-735j)  +/-  (5.9e-247, 5.9e-247j)
| (-5.8768878925942023475 + 1.8998102733059796367e-738j)  +/-  (1.47e-246, 1.47e-246j)
| (-4.7378952997039537849 + 6.6894286564619472111e-747j)  +/-  (2.95e-247, 2.95e-247j)
| (-3.6455269935152947217 + 4.0084576279039457987e-754j)  +/-  (3.33e-248, 3.33e-248j)
| (-5.3003284739914221724 + 1.7271185407576166698e-759j)  +/-  (7.85e-247, 7.85e-247j)
| (3.1117802749918151946 + 1.2449552972696971454e-768j)  +/-  (5.68e-249, 5.68e-249j)
| (1.5430820266565580812 - 2.7391167093181325014e-771j)  +/-  (1.18e-251, 1.18e-251j)
| (4.7378952997039537849 - 2.2400750726249206639e-769j)  +/-  (3.57e-247, 3.57e-247j)
| (-3.1117802749918151946 - 3.4029667898161664874e-769j)  +/-  (5.03e-249, 5.03e-249j)
| (-2.5842847182107744054 - 1.2448574648146024178e-772j)  +/-  (9.87e-250, 9.87e-250j)
| (2.5842847182107744054 - 5.7580122306559836029e-772j)  +/-  (8.23e-250, 8.23e-250j)
| (3.6455269935152947217 + 1.45614627310656368e-769j)  +/-  (3.04e-248, 3.04e-248j)
| (-1.5430820266565580812 - 7.4679616430272076539e-781j)  +/-  (1.08e-251, 1.08e-251j)
| (-8.4133646794888803544 - 1.1101017936721786374e-778j)  +/-  (1.6e-246, 1.6e-246j)
| (-1.0271993366918350837 - 1.5794507611743593426e-800j)  +/-  (1.02e-252, 1.02e-252j)
| (-6.470920475390299407 - 1.2906854140034571051e-793j)  +/-  (2.33e-246, 2.33e-246j)
| (1.0271993366918350837 + 8.1154702314115044402e-808j)  +/-  (1.19e-252, 1.19e-252j)
| (0.51314725682843031574 + 2.2186078701444481879e-808j)  +/-  (6.75e-254, 6.75e-254j)
| (5.3003284739914221724 - 3.416503000291482114e-800j)  +/-  (6.87e-247, 6.87e-247j)
| (3.9440574603536807939e-821 + 7.5863522076659181999e-822j)  +/-  (1.49e-819, 1.49e-819j)
| (-0.51314725682843031574 - 3.6175971351877929889e-811j)  +/-  (6.75e-254, 6.75e-254j)
| (4.1869902256279117453 + 4.3686800424258066141e-804j)  +/-  (1.04e-247, 1.04e-247j)
-------------------------------------------------
The weights are:
| (7.3794298312026888896e-09 - 3.2566200649383206474e-565j)  +/-  (2.76e-83, 5.52e-207j)
| (3.9127019002727728942e-27 - 1.5889512968416994025e-575j)  +/-  (3.16e-93, 6.32e-217j)
| (9.1679979501948441604e-23 - 7.79537484840380287e-574j)  +/-  (1.18e-92, 2.36e-216j)
| (2.7672028592899436569e-14 - 1.1573742847669152109e-568j)  +/-  (2.59e-88, 5.19e-212j)
| (2.7672028592899436569e-14 + 1.577107819055007956e-569j)  +/-  (1.82e-89, 3.65e-213j)
| (2.0450331890969116957e-19 + 3.8827563376340681444e-572j)  +/-  (1.37e-91, 2.74e-215j)
| (1.1988380927638336458e-16 + 5.5691338372713386594e-570j)  +/-  (2.47e-90, 4.95e-214j)
| (0.024785617000462675669 + 2.5585349990782853735e-563j)  +/-  (7.49e-74, 1.5e-197j)
| (3.397941877127308644e-05 + 7.4727574209846731106e-565j)  +/-  (8.85e-83, 1.77e-206j)
| (0.024785617000462675669 + 5.3238959176116933318e-563j)  +/-  (6.71e-75, 1.34e-198j)
| (3.9127019002727728942e-27 + 4.794293136244348288e-576j)  +/-  (5.87e-95, 1.18e-218j)
| (3.114550633753990909e-12 + 1.8816577450636083854e-567j)  +/-  (1.71e-88, 3.42e-212j)
| (1.9475295367767133532e-10 - 3.0308890577712402878e-566j)  +/-  (1.13e-87, 2.26e-211j)
| (9.1679979501948441604e-23 + 3.0181652529115195343e-573j)  +/-  (2.52e-94, 5.04e-218j)
| (3.114550633753990909e-12 - 1.7563195506042360578e-568j)  +/-  (1.63e-91, 3.26e-215j)
| (2.0450331890969116957e-19 - 1.7828825267034065136e-571j)  +/-  (7.6e-93, 1.52e-216j)
| (7.3794298312026888896e-09 - 9.4291442976827896858e-567j)  +/-  (3.26e-90, 6.52e-214j)
| (2.9632046975083860874e-06 - 2.0922230321686416322e-565j)  +/-  (1.4e-88, 2.81e-212j)
| (0.00027880641347148790664 - 2.2622602281503653632e-564j)  +/-  (3.64e-87, 7.3e-211j)
| (1.801392729842890064e-07 + 4.8990156281269428521e-566j)  +/-  (1.38e-89, 2.77e-213j)
| (0.0016704526231192335596 + 1.9069676373829540132e-563j)  +/-  (2.64e-88, 5.29e-212j)
| (0.062726126861015712807 - 7.4557796281650038988e-563j)  +/-  (8.9e-84, 1.78e-207j)
| (2.9632046975083860874e-06 - 1.9498365498626868767e-564j)  +/-  (3.66e-91, 7.33e-215j)
| (0.0016704526231192335596 + 5.8662425204032574251e-564j)  +/-  (1.06e-87, 2.13e-211j)
| (0.0074248364607565074657 - 1.3138662939020659219e-563j)  +/-  (4.97e-87, 9.94e-211j)
| (0.0074248364607565074657 - 3.376310144724846929e-563j)  +/-  (4.9e-88, 9.8e-212j)
| (0.00027880641347148790664 - 9.6542789118895956623e-564j)  +/-  (3.39e-90, 6.79e-214j)
| (0.062726126861015712807 - 4.3547213586200915081e-563j)  +/-  (5.7e-87, 1.14e-210j)
| (1.1988380927638336458e-16 - 9.8850448094559445847e-571j)  +/-  (7e-97, 1.4e-220j)
| (0.12118164648126216477 + 6.5050469393157904003e-563j)  +/-  (6.61e-88, 1.3e-211j)
| (1.9475295367767133532e-10 + 1.4581104609822842741e-567j)  +/-  (1.3e-93, 2.59e-217j)
| (0.12118164648126216477 + 9.2606795223945755724e-563j)  +/-  (2.19e-88, 4.32e-212j)
| (0.17956725902444822291 - 1.0192579028823451421e-562j)  +/-  (2.03e-88, 4.02e-212j)
| (1.801392729842890064e-07 + 9.4972618419029289819e-565j)  +/-  (2.31e-93, 4.56e-217j)
| (0.20465624959079420304 + 9.9312377642245748552e-563j)  +/-  (1.92e-89, 3.41e-213j)
| (0.17956725902444822291 - 8.5555633172212014208e-563j)  +/-  (1.38e-89, 2.3e-213j)
| (3.397941877127308644e-05 + 4.4502647327064288851e-564j)  +/-  (2.9e-92, 6.04e-216j)
