Starting with polynomial:
P : -t+1
Extension levels are: 1 3 17
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 17 Kronrod extension for:
P2 : -t^4 + 49/4*t^3 - 153/4*t^2 + 57/2*t - 3/2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^21 + 118598016084408082273745249997188934753383442440971385141/325498276712413426474784314644834355978935029562200524*t^20 - 38865830351651008033689632994111865288354079350603658780095/650996553424826852949568629289668711957870059124401048*t^19 + 26579465113459963700591128086939260336170280007986307985307147/4556975873973787970646980405027680983705090413870807336*t^18 - 123641499061281825103632383495534755431161740251260672428471683/325498276712413426474784314644834355978935029562200524*t^17 + 39801748491000007311595005038345473493495357940690699157599441741/2278487936986893985323490202513840491852545206935403668*t^16 - 334012620748743931743007934385204068984439596908670087974586886960/569621984246723496330872550628460122963136301733850917*t^15 + 8345634722174601136589935511694750744554102818118945589420807061200/569621984246723496330872550628460122963136301733850917*t^14 - 22417131927469040629058557644148407484587517613989858382655919476960/81374569178103356618696078661208588994733757390550131*t^13 + 318707192502775162079599622312073442991520239830695611752819081947360/81374569178103356618696078661208588994733757390550131*t^12 - 3425631873459681319798823034223915450160949765045805719503087011210560/81374569178103356618696078661208588994733757390550131*t^11 + 27713056762838116403633195456783068089898319125063642307446443699633600/81374569178103356618696078661208588994733757390550131*t^10 - 167264836203569908428152005239840763922297094871581072546713403651600000/81374569178103356618696078661208588994733757390550131*t^9 + 742980855315723522150737872711592308296655387225512916017577348613750400/81374569178103356618696078661208588994733757390550131*t^8 - 2381348972305491048628885551582319931943276108388463762858013758327654400/81374569178103356618696078661208588994733757390550131*t^7 + 5353671128242924000000616227374594217676291350697750058433970601589094400/81374569178103356618696078661208588994733757390550131*t^6 - 8102159369976957610286260952073060063647925432259800778240250720146944000/81374569178103356618696078661208588994733757390550131*t^5 + 7763380913737484393006090879323508168510029670242887145391211757079040000/81374569178103356618696078661208588994733757390550131*t^4 - 4288998429784542667353219722035217116370752907749510483464764187234816000/81374569178103356618696078661208588994733757390550131*t^3 + 1182747513308372842391723358688122050559742500553419995429858901136896000/81374569178103356618696078661208588994733757390550131*t^2 - 131987812283596794807744269778893725750327069115501869167317002515456000/81374569178103356618696078661208588994733757390550131*t + 4394149091206022497738614096725379870733883705253691427709152302080000/81374569178103356618696078661208588994733757390550131
-------------------------------------------------
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: 1
  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:
| (62.783798871669692149 - 5.1442711970616775939e-324j)  +/-  (1e-119, 1e-119j)
| (37.692745770529379899 - 5.2480505452114205792e-327j)  +/-  (9.93e-118, 9.93e-118j)
| (44.297790438325685749 + 4.4891938413183786684e-337j)  +/-  (4.21e-118, 4.21e-118j)
| (52.293828437867888182 - 4.4461935015660234214e-347j)  +/-  (9.75e-119, 9.75e-119j)
| (32.048244182415509478 + 3.0016107189321216454e-355j)  +/-  (1.75e-117, 1.75e-117j)
| (10.097022048589877109 - 4.0665505644476024911e-362j)  +/-  (1.04e-118, 1.04e-118j)
| (3.2359787675119891949 - 8.2636629263765796238e-366j)  +/-  (7.1e-120, 7.1e-120j)
| (4.0299395572208648085 - 1.0217692479399075172e-366j)  +/-  (5.56e-120, 5.56e-120j)
| (5.8485784277512402644 - 3.4260194194546258593e-366j)  +/-  (9.63e-120, 9.63e-120j)
| (12.700832932838786733 - 4.4274250680822337081e-368j)  +/-  (2.8e-118, 2.8e-118j)
| (3.369839231310923141 - 2.1801739572854383283e-376j)  +/-  (1.1e-119, 1.1e-119j)
| (1 - 9.3694211468817496787e-380j)  +/-  (8.12e-124, 8.12e-124j)
| (7.8232631436879996743 - 2.153973140936942409e-377j)  +/-  (3.42e-119, 3.42e-119j)
| (22.827894794445323161 - 7.7659861350681197141e-392j)  +/-  (1.88e-117, 1.88e-117j)
| (0.14464422358515943007 - 1.6449557242764250051e-407j)  +/-  (4.25e-126, 4.25e-126j)
| (0.056897625001077184683 - 3.0222088771484597745e-408j)  +/-  (6.08e-127, 6.08e-127j)
| (19.024461146410393147 - 3.1101827900897349569e-414j)  +/-  (1.13e-117, 1.13e-117j)
| (1.8566488164637272941 + 2.9186134603408343345e-431j)  +/-  (1.86e-122, 1.86e-122j)
| (27.138887417517294945 + 5.1090275469525226265e-428j)  +/-  (1.81e-117, 1.81e-117j)
| (15.66453067927340033 + 7.7652744633650747376e-438j)  +/-  (5.44e-118, 5.44e-118j)
| (0.42252672455853443557 - 1.4488289092633924625e-450j)  +/-  (4.53e-125, 4.53e-125j)
-------------------------------------------------
The weights are:
| (6.8415411492112760992e-27 + 1.4282086083150198501e-349j)  +/-  (2.45e-49, 2.09e-107j)
| (2.5934614906112780785e-16 + 7.378961240794682257e-343j)  +/-  (2.29e-45, 1.95e-103j)
| (4.159790732033521774e-19 + 6.4028123919424826538e-345j)  +/-  (8.97e-47, 7.63e-105j)
| (1.7407271793754109798e-22 - 4.6106898700460788718e-347j)  +/-  (2.66e-48, 2.26e-106j)
| (6.3340934634375393275e-14 - 4.8874646008723703968e-342j)  +/-  (5.52e-45, 4.7e-103j)
| (0.00010029074996823863524 - 3.0823050014534333412e-337j)  +/-  (8.24e-39, 7.01e-97j)
| (0.24408673154186373554 + 8.102526926283288603e-334j)  +/-  (2.74e-32, 2.33e-90j)
| (0.041152964427410914741 + 1.1246954769633818363e-334j)  +/-  (9.87e-34, 8.4e-92j)
| (0.0053097172325868406208 - 7.2660612894900872935e-336j)  +/-  (2.74e-36, 2.34e-94j)
| (8.4701440699965201077e-06 + 6.3071805151463077526e-338j)  +/-  (2.94e-41, 2.51e-99j)
| (-0.2050870976328833633 - 8.7112014562387224934e-334j)  +/-  (2.36e-33, 2.01e-91j)
| (0.26260968812834674402 + 1.1039871161593065316e-334j)  +/-  (3.94e-34, 3.35e-92j)
| (0.00084792393107273727358 + 1.4414519847632352548e-336j)  +/-  (1.98e-38, 1.68e-96j)
| (4.930171583207926541e-10 - 2.8638693625103011679e-340j)  +/-  (1.33e-45, 1.13e-103j)
| (0.090417047753104840577 + 2.445160655248503116e-334j)  +/-  (1.23e-35, 1.05e-93j)
| (0.11445267006653635533 - 1.3807735072069243678e-334j)  +/-  (1.06e-35, 9.05e-94j)
| (1.9533114572871673962e-08 + 1.9584777667424284466e-339j)  +/-  (9.39e-45, 7.99e-103j)
| (0.15751880391408597342 - 9.2770404402580399777e-335j)  +/-  (7.76e-38, 6.58e-96j)
| (7.5117445278716793725e-12 + 3.7336556995094060687e-341j)  +/-  (7.23e-47, 6.14e-105j)
| (4.9656974001944777199e-07 - 1.1781279024073484503e-338j)  +/-  (7.71e-44, 6.57e-102j)
| (0.28858227314038989075 - 1.6958927272373397503e-334j)  +/-  (2.8e-38, 1.94e-96j)
