Starting with polynomial:
P : t
Extension levels are: 1 2 40
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P2 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^43 - 35411093473535666447/40988561757168329*t^41 + 13861901428942816040870/40988561757168329*t^39 - 171668308938568114900110/2157292724061491*t^37 + 27161461233596456941273515/2157292724061491*t^35 - 3063077734441637407449767085/2157292724061491*t^33 + 254666859223506086622142757880/2157292724061491*t^31 - 15928434026358408263678327958600/2157292724061491*t^29 + 758190404518133544238451515294950/2157292724061491*t^27 - 27612498505744536894713887580947050/2157292724061491*t^25 + 769667137058455966923844981961731500/2157292724061491*t^23 - 16352064335725244021144286739386184500/2157292724061491*t^21 + 262531229084355014053202430638919528750/2157292724061491*t^19 - 3142471370937817082532381016222870901250/2157292724061491*t^17 + 27507431340936049434138590914425049155000/2157292724061491*t^15 - 171415985549333130465738363698795466885000/2157292724061491*t^13 + 732614764596555335100969631108500999714375/2157292724061491*t^11 - 2036865469423890662057680038540916200590625/2157292724061491*t^9 + 3407013400894322244636210776402775980681250/2157292724061491*t^7 - 3028748059039901393068331104747268987568750/2157292724061491*t^5 + 1145924863808828573664109359893103314034375/2157292724061491*t^3 - 111067956871100921542007595344653162040625/2157292724061491*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:   43 out of 43
Indefinite weights: 0 out of 43
Negative weights:   0 out of 43
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-11.780599552966025399 - 1.9235678516079300909e-521j)  +/-  (1.68e-247, 1.68e-247j)
| (-10.818027726089115059 + 5.6529763307433084522e-520j)  +/-  (2.12e-246, 2.12e-246j)
| (-8.6390877371147026186 + 1.1549182833471861144e-518j)  +/-  (5.03e-245, 5.03e-245j)
| (-3.1860443658809951844 + 3.3380479455180281711e-522j)  +/-  (5.04e-248, 5.04e-248j)
| (-4.1852745445527675853 - 7.8460243142273119996e-521j)  +/-  (1.04e-246, 1.04e-246j)
| (3.1860443658809951844 - 4.9935972026394911773e-521j)  +/-  (4.95e-248, 4.95e-248j)
| (11.780599552966025399 - 1.1766459167915090152e-517j)  +/-  (1.67e-247, 1.67e-247j)
| (-7.4172551347491634152 - 9.0753194335582322651e-520j)  +/-  (7.59e-245, 7.59e-245j)
| (-6.8428202236116553919 - 3.8749428557763231198e-519j)  +/-  (6.32e-245, 6.32e-245j)
| (6.2863064514188068607 + 1.5707870972876219996e-518j)  +/-  (4.56e-245, 4.56e-245j)
| (1.2612290934209379016 + 6.058120419719906923e-532j)  +/-  (1.23e-251, 1.23e-251j)
| (-9.3019929192064639931 + 3.1084909436637411179e-526j)  +/-  (2.64e-245, 2.64e-245j)
| (-0.80441523940952121809 + 1.3330184951328636414e-533j)  +/-  (9.63e-253, 9.63e-253j)
| (-5.2149535803861753428 + 4.0404099966477251618e-527j)  +/-  (1e-245, 1e-245j)
| (1.7320508075688772935 + 9.9728137151813200835e-531j)  +/-  (1.4e-250, 1.4e-250j)
| (4.6957247870559034837 + 2.0990668841364830234e-526j)  +/-  (3.63e-246, 3.63e-246j)
| (-2.6956273013672491322 + 3.3270918022416385266e-530j)  +/-  (8.97e-249, 8.97e-249j)
| (-10.018234317663901936 - 3.8528594007516422216e-527j)  +/-  (8.64e-246, 8.64e-246j)
| (-5.7445035841160152714 - 3.2507350446775679174e-526j)  +/-  (2.5e-245, 2.5e-245j)
| (5.7445035841160152714 - 5.8523931440844804222e-525j)  +/-  (2.61e-245, 2.61e-245j)
| (0.37810272286503571117 + 4.6644457946081080697e-563j)  +/-  (8.94e-254, 8.94e-254j)
| (5.2149535803861753428 - 1.2318409605770046095e-530j)  +/-  (1.04e-245, 1.04e-245j)
| (-0.37810272286503571117 - 2.1491212620787315163e-567j)  +/-  (6.42e-254, 6.42e-254j)
| (-1.7320508075688772935 + 1.4324069549973820724e-542j)  +/-  (1.33e-250, 1.33e-250j)
| (-4.6957247870559034837 - 6.8823411391817611187e-537j)  +/-  (3.7e-246, 3.7e-246j)
| (0.80441523940952121809 - 5.3555036840676904953e-544j)  +/-  (1.01e-252, 1.01e-252j)
| (2.6956273013672491322 + 1.0167216629102103879e-538j)  +/-  (9.38e-249, 9.38e-249j)
| (4.1852745445527675853 - 4.6478079145996317927e-536j)  +/-  (1e-246, 1e-246j)
| (-3.6823684327950259835 + 8.2661753167038832426e-541j)  +/-  (2.32e-247, 2.32e-247j)
| (3.6823684327950259835 + 2.0957213234384783042e-539j)  +/-  (2.34e-247, 2.34e-247j)
| (2.2686613813189231817e-561 - 1.2067895467336932832e-560j)  +/-  (5.28e-559, 5.28e-559j)
| (-2.2108298349052367186 - 2.7917230556607969367e-543j)  +/-  (1.2e-249, 1.2e-249j)
| (-6.2863064514188068607 + 2.6403480220079133082e-538j)  +/-  (4.5e-245, 4.5e-245j)
| (-1.2612290934209379016 - 1.2090624366585421114e-545j)  +/-  (1.2e-251, 1.2e-251j)
| (-8.013955653504555409 - 7.3590995213533138612e-538j)  +/-  (7.94e-245, 7.94e-245j)
| (2.2108298349052367186 + 3.4782700061535451815e-546j)  +/-  (1.16e-249, 1.16e-249j)
| (9.3019929192064639931 + 3.7703223915441815136e-546j)  +/-  (2.74e-245, 2.74e-245j)
| (10.018234317663901936 + 2.6368665951922360445e-574j)  +/-  (8.51e-246, 8.51e-246j)
| (10.818027726089115059 + 1.7080466930575693415e-618j)  +/-  (2.21e-246, 2.21e-246j)
| (8.6390877371147026186 + 4.4421325332231149898e-674j)  +/-  (5.14e-245, 5.14e-245j)
| (7.4172551347491634152 + 5.9694029458432964145e-722j)  +/-  (7.45e-245, 7.45e-245j)
| (6.8428202236116553919 + 5.0093562568689529165e-743j)  +/-  (6.88e-245, 6.88e-245j)
| (8.013955653504555409 + 6.6936303134030370678e-757j)  +/-  (6.88e-245, 6.88e-245j)
-------------------------------------------------
The weights are:
| (3.2358980539046204018e-31 + 2.0640254668796141854e-539j)  +/-  (1.14e-81, 3.56e-204j)
| (1.3261049227294303999e-26 - 5.0144678983639091334e-537j)  +/-  (3.32e-80, 1.04e-202j)
| (1.5921155212764320595e-17 + 2.8380677299747342312e-532j)  +/-  (7.58e-77, 2.37e-199j)
| (0.0012296248512786100783 - 5.2542005373023381399e-525j)  +/-  (4.49e-61, 1.4e-183j)
| (3.1755656824418669464e-05 - 5.5316633925780887822e-525j)  +/-  (1.34e-65, 4.19e-188j)
| (0.0012296248512786100783 + 1.0624040510811769902e-523j)  +/-  (1.53e-63, 4.77e-186j)
| (3.2358980539046204018e-31 - 1.5066643323161675827e-539j)  +/-  (4.38e-86, 1.37e-208j)
| (2.6385042338165460378e-13 + 4.517973073637803818e-530j)  +/-  (3.19e-75, 9.97e-198j)
| (1.5314695576012162741e-11 - 7.6823197909762713952e-529j)  +/-  (3.27e-74, 1.02e-196j)
| (5.7423941729063554554e-10 - 3.7204150529956861053e-527j)  +/-  (3.36e-77, 1.05e-199j)
| (0.083817038992493321902 + 4.686710540527888664e-523j)  +/-  (2.65e-53, 8.29e-176j)
| (4.4488279249433285811e-20 - 1.273393957653336557e-533j)  +/-  (4.13e-79, 1.29e-201j)
| (0.12862632677767112403 - 2.6134193537707598706e-523j)  +/-  (1.09e-54, 3.4e-177j)
| (2.5992432447107276173e-07 + 2.0958027637929578647e-526j)  +/-  (1.4e-71, 4.36e-194j)
| (0.042312150259821031852 - 3.5633299678906729374e-523j)  +/-  (1.48e-59, 4.63e-182j)
| (3.3444774539518696631e-06 + 2.0873021444104507222e-525j)  +/-  (9.19e-74, 2.87e-196j)
| (0.0051415594269414952537 - 6.2833433737176273137e-525j)  +/-  (8.52e-65, 2.66e-187j)
| (4.8142279762745858616e-23 + 3.5664962507424004739e-535j)  +/-  (7.98e-81, 2.49e-203j)
| (1.4581727714690399084e-08 - 3.3023440420830669653e-527j)  +/-  (4.53e-73, 1.41e-195j)
| (1.4581727714690399084e-08 + 1.4090851345505635977e-526j)  +/-  (1.71e-77, 5.35e-200j)
| (0.14942095101960515291 + 7.7460268259293298838e-523j)  +/-  (3.01e-60, 9.39e-183j)
| (2.5992432447107276173e-07 - 5.008954505290355951e-526j)  +/-  (4.09e-76, 1.28e-198j)
| (0.14942095101960515291 + 5.2141484469580036658e-523j)  +/-  (1.45e-60, 4.51e-183j)
| (0.042312150259821031852 - 4.2372428623425902316e-524j)  +/-  (2.8e-64, 8.76e-187j)
| (3.3444774539518696631e-06 - 1.529738203768734231e-525j)  +/-  (5.44e-72, 1.7e-194j)
| (0.12862632677767112403 - 6.199755923696829018e-523j)  +/-  (4.21e-62, 1.32e-184j)
| (0.0051415594269414952537 - 2.7855954020078150706e-523j)  +/-  (1.09e-69, 3.41e-192j)
| (3.1755656824418669464e-05 - 9.2886773459899825785e-525j)  +/-  (3.21e-74, 1e-196j)
| (0.00022643545820968799392 + 1.5584106616507231035e-524j)  +/-  (6.46e-71, 2.02e-193j)
| (0.00022643545820968799392 + 5.0481842910417960673e-524j)  +/-  (4.35e-73, 1.36e-195j)
| (0.1449948945956935831 - 7.6269874490087970295e-523j)  +/-  (1.51e-64, 4.73e-187j)
| (0.016693090685981494239 + 1.3271232344619564454e-524j)  +/-  (2.59e-68, 8.08e-191j)
| (5.7423941729063554554e-10 + 5.1604400835913653144e-528j)  +/-  (3.33e-76, 1.04e-198j)
| (0.083817038992493321902 + 1.1268798521802609282e-523j)  +/-  (3.13e-67, 9.78e-190j)
| (2.7546325063580257355e-15 - 4.3502850160211208816e-531j)  +/-  (1.58e-79, 4.93e-202j)
| (0.016693090685981494239 + 2.8434504252759430134e-523j)  +/-  (8.59e-72, 2.68e-194j)
| (4.4488279249433285811e-20 + 5.4225130465905934966e-534j)  +/-  (9.78e-90, 3.06e-212j)
| (4.8142279762745858616e-23 - 1.9960582185743239694e-535j)  +/-  (3.67e-91, 1.15e-213j)
| (1.3261049227294303999e-26 + 3.2856454566798227934e-537j)  +/-  (1.01e-92, 3.15e-215j)
| (1.5921155212764320595e-17 - 6.2377653781746504747e-533j)  +/-  (2.4e-89, 7.49e-212j)
| (2.6385042338165460378e-13 + 4.4514447791503577642e-530j)  +/-  (7.09e-88, 2.21e-210j)
| (1.5314695576012162741e-11 - 1.4800223903548806992e-528j)  +/-  (6.42e-87, 2e-209j)
| (2.7546325063580257355e-15 - 5.8918064844288670322e-532j)  +/-  (6.15e-89, 1.92e-211j)
