Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 40
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^42 - 11813770368659/769016982238*t^40 + 6649105429506085/91128512395203*t^38 - 641452871560385495/3007240909041699*t^36 + 287067938993507945/668275757564822*t^34 - 14014351434200635609/22174604682832730*t^32 + 1660141509486813386852/2361595398721685745*t^30 - 2185361894897604323212/3621112944706584809*t^28 + 98192465573809035051441/242614567295341182203*t^26 - 51736989785392369906175/242614567295341182203*t^24 + 931859234429666630802/10548459447623529661*t^22 - 18443291931889050531214/643456026305035309321*t^20 + 822583147185867336240335/113891716655991249749817*t^18 - 52934691373761462057555/37963905551997083249939*t^16 + 1189239798611433870300/5881731846084055151399*t^14 - 473969654890010692735868/22132956936814299534714437*t^12 + 6407265988109653476537/4024173988511690824493534*t^10 - 2210063442558155969265/28169217919581835771454738*t^8 + 221912352814105242055/94568088730024734375598049*t^6 - 3478282471921517325/94568088730024734375598049*t^4 + 1838019462999449821/8132855630782127156301432214*t^2 - 38757791288926567/170789968246424670282330076494
-------------------------------------------------
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:
| (0.97866045836413075624 - 2.5491014345107090642e-859j)  +/-  (4.18e-241, 4.18e-241j)
| (-0.99834630861965744153 - 2.7580811957683130895e-880j)  +/-  (1.09e-241, 1.09e-241j)
| (-0.93694626337399374781 + 4.2560555073698547568e-881j)  +/-  (2.53e-241, 2.53e-241j)
| (0.99129759995849076786 + 5.9916600664660358985e-879j)  +/-  (2.96e-241, 2.96e-241j)
| (0.90811820583256431509 + 8.5569110750930136347e-907j)  +/-  (1.36e-241, 1.36e-241j)
| (0.93694626337399374781 + 1.4678717458021143172e-925j)  +/-  (2.56e-241, 2.56e-241j)
| (-0.31534817041554394372 - 2.7821484395810434075e-947j)  +/-  (4.22e-250, 4.22e-250j)
| (-0.90811820583256431509 - 5.6239323878404025807e-938j)  +/-  (1.4e-241, 1.4e-241j)
| (-0.97866045836413075624 - 1.2967636303325268746e-936j)  +/-  (4.24e-241, 4.24e-241j)
| (0.99834630861965744153 - 2.3455454287648951208e-938j)  +/-  (1.03e-241, 1.03e-241j)
| (0.8353859830515983726 + 2.8831999291375034703e-951j)  +/-  (2.18e-242, 2.18e-242j)
| (-0.99129759995849076786 - 4.5647174854101786314e-963j)  +/-  (2.98e-241, 2.98e-241j)
| (-0.96050734061037693088 + 7.5481382248528448362e-965j)  +/-  (3.76e-241, 3.76e-241j)
| (-0.79192310657424410098 - 1.8791762389832022013e-967j)  +/-  (6.25e-243, 6.25e-243j)
| (0.96050734061037693088 - 1.3771376351988945968e-964j)  +/-  (3.65e-241, 3.65e-241j)
| (0.87419643895694575533 + 2.5506164151712751974e-974j)  +/-  (6.9e-242, 6.9e-242j)
| (0.74407492042868702323 + 1.4206051352484448349e-979j)  +/-  (1.48e-243, 1.48e-243j)
| (-0.45056824768285576066 - 2.5058471071784004393e-986j)  +/-  (6.78e-248, 6.78e-248j)
| (-0.74407492042868702323 - 2.330180878177159633e-980j)  +/-  (1.51e-243, 1.51e-243j)
| (-0.87419643895694575533 + 4.0082126955221623169e-979j)  +/-  (5.93e-242, 5.93e-242j)
| (0.45056824768285576066 - 4.9831156824914013011e-987j)  +/-  (6.43e-248, 6.43e-248j)
| (0.69213916679901767953 - 1.5603817992556111193e-982j)  +/-  (3.04e-244, 3.04e-244j)
| (0.24582280961046555355 - 3.6470202559098738352e-991j)  +/-  (2.64e-251, 2.64e-251j)
| (-0.8353859830515983726 + 2.8741823290939669514e-983j)  +/-  (2.18e-242, 2.18e-242j)
| (-0.69213916679901767953 + 1.1602025297304016404e-985j)  +/-  (3.16e-244, 3.16e-244j)
| (0.17569618181294266073 + 9.3001883788397373693e-993j)  +/-  (1.65e-252, 1.65e-252j)
| (0.79192310657424410098 + 8.7627230833037982638e-986j)  +/-  (6.35e-243, 6.35e-243j)
| (0.51524935790704568498 + 6.4284957198867054593e-990j)  +/-  (7.3e-247, 7.3e-247j)
| (-0.10538269695809222176 - 3.1466061009776703277e-999j)  +/-  (8.75e-254, 8.75e-254j)
| (-0.63644433637359227139 - 4.371665138597139115e-990j)  +/-  (4.84e-245, 4.84e-245j)
| (-0.24582280961046555355 - 8.3738680827256318483e-998j)  +/-  (2.57e-251, 2.57e-251j)
| (0.31534817041554394372 - 4.0580356974723229071e-994j)  +/-  (4.22e-250, 4.22e-250j)
| (0.57735026918962576451 + 2.3846390604516364467e-989j)  +/-  (6.1e-246, 6.1e-246j)
| (0.035111246300125718722 + 1.165193887852415787e-999j)  +/-  (3.6e-255, 3.6e-255j)
| (-0.57735026918962576451 - 9.3797151155834363573e-992j)  +/-  (7.14e-246, 7.14e-246j)
| (-0.38376918304185822055 + 9.0028407251425767159e-995j)  +/-  (5.82e-249, 5.82e-249j)
| (0.10538269695809222176 - 4.8940032526107061752e-998j)  +/-  (8.87e-254, 8.87e-254j)
| (0.63644433637359227139 - 4.0593179327021346592e-993j)  +/-  (4.76e-245, 4.76e-245j)
| (0.38376918304185822055 - 1.2514943432302312567e-999j)  +/-  (5.56e-249, 5.56e-249j)
| (-0.17569618181294266073 - 2.8467835474070610468e-1002j)  +/-  (1.64e-252, 1.64e-252j)
| (-0.51524935790704568498 - 1.5985043466588202538e-996j)  +/-  (7.02e-247, 7.02e-247j)
| (-0.035111246300125718722 - 4.4598646893808146889e-1004j)  +/-  (5.1e-255, 5.1e-255j)
-------------------------------------------------
The weights are:
| (0.015410337402216587755 + 9.4637067979348482662e-860j)  +/-  (1.46e-77, 1.15e-193j)
| (0.0042426733251110174854 - 2.865110727890573014e-862j)  +/-  (3.39e-78, 2.66e-194j)
| (0.02622077353519862245 - 4.7290760204597506469e-861j)  +/-  (3.2e-78, 2.51e-194j)
| (0.009851648700012016664 + 1.5740573362430358911e-859j)  +/-  (4.39e-78, 3.45e-194j)
| (0.031406454058351612052 - 1.7309957369122667621e-859j)  +/-  (1.32e-78, 1.04e-194j)
| (0.02622077353519862245 + 2.1716947467271559332e-859j)  +/-  (2.1e-78, 1.65e-194j)
| (0.069060012280627980934 - 6.654826005765343751e-860j)  +/-  (4.21e-80, 3.3e-196j)
| (0.031406454058351612052 + 6.4717892311082640528e-861j)  +/-  (6.41e-80, 5.03e-196j)
| (0.015410337402216587755 - 2.0069531185487250211e-861j)  +/-  (3.1e-80, 2.43e-196j)
| (0.0042426733251110174854 - 2.8773678676171374425e-860j)  +/-  (3.3e-80, 2.59e-196j)
| (0.041178625591124997918 - 1.3775597508803009085e-859j)  +/-  (4.81e-82, 3.78e-198j)
| (0.009851648700012016664 + 1.0097466467220964292e-861j)  +/-  (2.81e-80, 2.21e-196j)
| (0.020877874497633270716 + 3.2466793561674682596e-861j)  +/-  (1.79e-80, 1.4e-196j)
| (0.045702605038455089017 - 1.3654414766070747587e-860j)  +/-  (6.34e-83, 4.98e-199j)
| (0.020877874497633270716 - 3.4681954617814017795e-859j)  +/-  (5.54e-81, 4.35e-197j)
| (0.036402901144513692902 + 1.50881581597886014e-859j)  +/-  (4.43e-82, 3.48e-198j)
| (0.049944145121810990506 - 1.2419832755797379804e-859j)  +/-  (2.24e-84, 1.76e-200j)
| (0.065820102717115522099 - 4.5394061851814591319e-860j)  +/-  (1.83e-85, 1.43e-201j)
| (0.049944145121810990506 + 1.691213394670384991e-860j)  +/-  (1.73e-84, 1.36e-200j)
| (0.036402901144513692902 - 8.5066992982658986919e-861j)  +/-  (2.29e-83, 1.8e-199j)
| (0.065820102717115522099 + 1.2285448444503309869e-859j)  +/-  (3.69e-87, 2.9e-203j)
| (0.053872623359019893227 + 1.210591816352272218e-859j)  +/-  (9.79e-86, 7.69e-202j)
| (0.069905614419026582858 - 1.3360728512545835204e-859j)  +/-  (6.68e-88, 5.24e-204j)
| (0.041178625591124997918 + 1.0880049485668399055e-860j)  +/-  (5.81e-85, 4.57e-201j)
| (0.053872623359019893227 - 2.0760139370125808474e-860j)  +/-  (1.22e-86, 9.59e-203j)
| (0.07027674777795314548 + 1.3627829226098748612e-859j)  +/-  (1.86e-88, 1.46e-204j)
| (0.045702605038455089017 + 1.2946677320806941075e-859j)  +/-  (7.08e-86, 5.56e-202j)
| (0.063465062064050358813 - 1.2061491269756538176e-859j)  +/-  (6.18e-88, 4.85e-204j)
| (0.070311144294718692192 + 1.0977357096443779583e-859j)  +/-  (9.59e-90, 7.53e-206j)
| (0.057457084280976718131 + 2.5336065100582330558e-860j)  +/-  (2.41e-88, 1.9e-204j)
| (0.069905614419026582858 + 7.9962259386081526859e-860j)  +/-  (1.39e-89, 1.09e-205j)
| (0.069060012280627980934 + 1.2982425368780745241e-859j)  +/-  (1.82e-89, 1.43e-205j)
| (0.060665681215174512844 + 1.1947982131190152671e-859j)  +/-  (3.61e-89, 2.83e-205j)
| (0.070232699875394930783 + 1.3200672544747619468e-859j)  +/-  (1.45e-90, 1.14e-206j)
| (0.060665681215174512844 - 3.0814999436794530523e-860j)  +/-  (2.8e-90, 2.2e-206j)
| (0.067695189301513765176 + 5.5030041368324188188e-860j)  +/-  (1.65e-90, 1.29e-206j)
| (0.070311144294718692192 - 1.3626739795558276375e-859j)  +/-  (8.13e-91, 6.39e-207j)
| (0.057457084280976718131 - 1.1957472951805868177e-859j)  +/-  (1e-90, 7.87e-207j)
| (0.067695189301513765176 - 1.2603069273017398306e-859j)  +/-  (4.85e-91, 3.81e-207j)
| (0.07027674777795314548 - 9.479444787374343462e-860j)  +/-  (1.58e-91, 1.23e-207j)
| (0.063465062064050358813 + 3.7414768157978294704e-860j)  +/-  (8.34e-92, 6.35e-208j)
| (0.070232699875394930783 - 1.2286281142988302253e-859j)  +/-  (1.65e-91, 1.31e-207j)
