Starting with polynomial:
P : t^23 - 253*t^21 + 26565*t^19 - 1514205*t^17 + 51482970*t^15 - 1081142370*t^13 + 14054850810*t^11 - 110430970650*t^9 + 496939367925*t^7 - 1159525191825*t^5 + 1159525191825*t^3 - 316234143225*t
Extension levels are: 23 40
-------------------------------------------------
Trying to find an order 40 Kronrod extension for:
P1 : t^23 - 253*t^21 + 26565*t^19 - 1514205*t^17 + 51482970*t^15 - 1081142370*t^13 + 14054850810*t^11 - 110430970650*t^9 + 496939367925*t^7 - 1159525191825*t^5 + 1159525191825*t^3 - 316234143225*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^63 - 101576178119894402028670598122530462113/68193586028690041510290950788710897*t^61 + 1908278450767544297327510289326949028643137/1841226822774631120777855671295194219*t^59 - 10727602027881127741883004351727170784281204433/23935948696070204570112123726837524847*t^57 + 26965399612705452523011802586316673810771562193677/199466239133918371417601031056979373725*t^55 - 6036619648667560182847948983620382234879275575250981/199466239133918371417601031056979373725*t^53 + 208380889092568679341000092485319884140207298747917243/39893247826783674283520206211395874745*t^51 - 9479187643929794922145583797699495962855326693451887269/13297749275594558094506735403798624915*t^49 + 23129054287045141339555982258356949452319079108524983259/295505539457656846544594120084413887*t^47 - 31027016849414722096581023251168433850338896785081452132117/4432583091864852698168911801266208305*t^45 + 84431468027332244047808845726595999856462992326266748141933/164169744143142692524774511158007715*t^43 - 9227910751418192239078511104683158792809980839286115968235253/295505539457656846544594120084413887*t^41 + 464787530040205749313032148933846630814433278352833746730652347/295505539457656846544594120084413887*t^39 - 498901589749156105242442056211340637063793113836008697550016693/7577065114298893501143438976523433*t^37 + 17365422298110295844929544862038984414519110949941117167860218727/7577065114298893501143438976523433*t^35 - 502054692953474992100359126725820309136201943976286416538947525211/7577065114298893501143438976523433*t^33 + 4009052286121965279938548246331886105318477918062644643511762774185/2525688371432964500381146325507811*t^31 - 8808535840401325290629592355091904004220932959547370085954530925425/280632041270329388931238480611979*t^29 + 429071158380283692904851202177170348182880597474051330174884303556265/841896123810988166793715441835937*t^27 - 1893716925308936145367090963165837151293666398126306883336740443925375/280632041270329388931238480611979*t^25 + 20268431108929061603591301254911552234259884821147553474416596200995825/280632041270329388931238480611979*t^23 - 173443947202974478781259683225826377160540289832552158591097751287183625/280632041270329388931238480611979*t^21 + 1170543430789285315615223118089464006042026344799026321570971900909825875/280632041270329388931238480611979*t^19 - 6124323394678754124607400231337404265109120953816716349369186448913322375/280632041270329388931238480611979*t^17 + 24307580658897131636795402970939372502316826605495970620429045692800184125/280632041270329388931238480611979*t^15 - 71168844974628612351311108469936831385423971620235521036118637908590116125/280632041270329388931238480611979*t^13 + 148131162606660819867922704156823534123270007645899012785803446311995784375/280632041270329388931238480611979*t^11 - 208354537352068978708205876973364687655820538235457879348067394202966241875/280632041270329388931238480611979*t^9 + 184055051774275561779045286426490164682047939389850504611743521998202288125/280632041270329388931238480611979*t^7 - 91034982005097905145522440858992727834030191379812125195035188321904053125/280632041270329388931238480611979*t^5 + 20520763577746853237416445346092614787121339481541213449796871073329984375/280632041270329388931238480611979*t^3 - 1307886506810393190133249938351352539627413446813812509274544609814596875/280632041270329388931238480611979*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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: 0
  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:
| (10.358073847308782025 + 1.6655824674205294848e-631j)  +/-  (1.69e-241, 1.69e-241j)
| (-9.7668144925881207445 + 1.2369546141791572803e-637j)  +/-  (5.03e-241, 5.03e-241j)
| (-9.2003479250474877529 + 7.6332312048969931093e-637j)  +/-  (1.43e-240, 1.43e-240j)
| (-8.3522442444688698433 + 1.2923895955881995677e-635j)  +/-  (5.7e-239, 5.7e-239j)
| (-6.3103498544483998284 + 4.7637788697929424912e-637j)  +/-  (4.61e-241, 4.61e-241j)
| (-13.34805889136494851 + 9.0936999976203719992e-642j)  +/-  (3.36e-245, 3.36e-245j)
| (13.34805889136494851 - 1.0170861899516102355e-640j)  +/-  (3.24e-245, 3.24e-245j)
| (10.986023422966255701 - 1.7654929692372653791e-635j)  +/-  (3.75e-242, 3.75e-242j)
| (-8.2933860274173525895 - 6.6338007549181406108e-635j)  +/-  (4.57e-239, 4.57e-239j)
| (12.428185253215704318 + 6.5279363160692962605e-639j)  +/-  (7.58e-244, 7.58e-244j)
| (11.666297539251795901 + 4.289053117348629234e-637j)  +/-  (7.04e-243, 7.04e-243j)
| (-7.214659435051861386 + 9.4401847346687549238e-637j)  +/-  (1.4e-240, 1.4e-240j)
| (-12.428185253215704318 - 4.432096649463262087e-641j)  +/-  (7.24e-244, 7.24e-244j)
| (-5.8915418337704185406 + 3.0424355337764178885e-637j)  +/-  (2.37e-241, 2.37e-241j)
| (5.8915418337704185406 - 4.2921658691657257616e-634j)  +/-  (2.47e-241, 2.47e-241j)
| (-10.986023422966255701 + 1.3877719605953723942e-644j)  +/-  (3.69e-242, 3.69e-242j)
| (-4.3614599815168807729 - 3.1896683573985840836e-645j)  +/-  (5.5e-243, 5.5e-243j)
| (4.7307241974514732943 - 8.2484136844356367358e-641j)  +/-  (1.68e-242, 1.68e-242j)
| (-10.358073847308782025 + 3.1450438875226243592e-645j)  +/-  (1.56e-241, 1.56e-241j)
| (-11.666297539251795901 - 4.2378181920248786517e-647j)  +/-  (6.59e-243, 6.59e-243j)
| (-3.3050400217529645672 - 3.4698425128110525737e-648j)  +/-  (8.12e-245, 8.12e-245j)
| (-8.6149799617271466702 + 2.2161765836747969378e-643j)  +/-  (1.1e-239, 1.1e-239j)
| (2.2945024471295498719 + 1.5423955568548507728e-649j)  +/-  (4.09e-247, 4.09e-247j)
| (5.4934739864717941286 - 9.7010368020670989363e-642j)  +/-  (1.15e-241, 1.15e-241j)
| (-6.7517060533539318013 - 4.2084014079800135044e-653j)  +/-  (8.2e-241, 8.2e-241j)
| (-0.64847115353449581672 + 8.4505968357575438607e-664j)  +/-  (2.04e-252, 2.04e-252j)
| (4.3614599815168807729 + 4.8162735910221714569e-650j)  +/-  (5.71e-243, 5.71e-243j)
| (3.6552798046715457129 - 1.2525913506145149907e-654j)  +/-  (3.75e-244, 3.75e-244j)
| (1.29987646830397887 - 2.6035005125887606304e-668j)  +/-  (4.41e-250, 4.41e-250j)
| (-1.9573275529334241074 - 2.6378891082225006873e-667j)  +/-  (4.37e-248, 4.37e-248j)
| (-1.29987646830397887 - 9.0719934539978350015e-669j)  +/-  (4.14e-250, 4.14e-250j)
| (1.9573275529334241074 - 1.9725326293088247667e-667j)  +/-  (4.12e-248, 4.12e-248j)
| (1.6214692019303439902 + 8.89859848091799501e-667j)  +/-  (4.09e-249, 4.09e-249j)
| (-2.2945024471295498719 + 1.8952867100896418795e-666j)  +/-  (4.11e-247, 4.11e-247j)
| (-0.98061729261387009478 + 1.5211036286289551857e-669j)  +/-  (3.34e-251, 3.34e-251j)
| (-5.4934739864717941286 + 4.0107892472715267952e-660j)  +/-  (1.12e-241, 1.12e-241j)
| (-1.6214692019303439902 + 1.8488484992117502726e-668j)  +/-  (4.46e-249, 4.46e-249j)
| (2.6243236340591817707 - 1.1662890757527484923e-663j)  +/-  (2.37e-246, 2.37e-246j)
| (-2.9585969162363449978 - 3.1627980657280528199e-664j)  +/-  (1.52e-245, 1.52e-245j)
| (-3.6552798046715457129 + 2.0876941097423568597e-662j)  +/-  (4.23e-244, 4.23e-244j)
| (-2.6243236340591817707 + 5.478846297564056124e-665j)  +/-  (2.35e-246, 2.35e-246j)
| (-5.1086892454025084625 + 4.1254666111757229414e-661j)  +/-  (4.58e-242, 4.58e-242j)
| (0.64847115353449581672 + 1.5630552579785512809e-670j)  +/-  (2.02e-252, 2.02e-252j)
| (3.3050400217529645672 + 2.4166317658549071084e-657j)  +/-  (8.05e-245, 8.05e-245j)
| (6.3103498544483998284 - 1.4133408080323188093e-659j)  +/-  (4.81e-241, 4.81e-241j)
| (0.98061729261387009478 + 5.8932179836242000306e-688j)  +/-  (3.63e-251, 3.63e-251j)
| (-4.7307241974514732943 - 6.8917858590866757219e-678j)  +/-  (1.75e-242, 1.75e-242j)
| (2.9585969162363449978 - 7.4278417665321179901e-683j)  +/-  (1.33e-245, 1.33e-245j)
| (-7.7012743599252764534 - 3.4543757823434522095e-674j)  +/-  (2.86e-240, 2.86e-240j)
| (-3.8500191241577525824e-711 - 2.8658149746517751704e-711j)  +/-  (3.02e-709, 3.02e-709j)
| (-4.0047753217333040671 + 1.4808754205191596454e-680j)  +/-  (1.67e-243, 1.67e-243j)
| (0.31656966836215005809 - 4.0828160509869900448e-710j)  +/-  (1.17e-253, 1.17e-253j)
| (4.0047753217333040671 - 7.8266639050755276548e-676j)  +/-  (1.52e-243, 1.52e-243j)
| (5.1086892454025084625 + 9.4381504991562586298e-702j)  +/-  (4.8e-242, 4.8e-242j)
| (-0.31656966836215005809 - 9.5686897590474470285e-741j)  +/-  (1.17e-253, 1.17e-253j)
| (8.3522442444688698433 - 3.4052790688004588009e-734j)  +/-  (5.18e-239, 5.18e-239j)
| (8.2933860274173525895 + 8.5641839135355742007e-781j)  +/-  (4.91e-239, 4.91e-239j)
| (8.6149799617271466702 + 7.7942144023712604171e-807j)  +/-  (1.05e-239, 1.05e-239j)
| (9.2003479250474877529 + 1.8836734007866613815e-818j)  +/-  (1.47e-240, 1.47e-240j)
| (9.7668144925881207445 - 1.0465847943120778504e-827j)  +/-  (5.07e-241, 5.07e-241j)
| (7.7012743599252764534 - 3.8937698170195475823e-842j)  +/-  (2.81e-240, 2.81e-240j)
| (7.214659435051861386 - 1.9337301470383355612e-860j)  +/-  (1.5e-240, 1.5e-240j)
| (6.7517060533539318013 + 7.2871381512814319622e-870j)  +/-  (8.37e-241, 8.37e-241j)
-------------------------------------------------
The weights are:
| (1.2213538574413495589e-24 - 1.622786717309980119e-653j)  +/-  (3.23e-39, 1.53e-158j)
| (4.4472493795946292688e-22 - 2.1700220232551055274e-652j)  +/-  (6.3e-38, 2.99e-157j)
| (9.2873142625338072228e-20 + 1.0671516578546435793e-650j)  +/-  (1.87e-36, 8.86e-156j)
| (-4.8486422964257297629e-16 + 3.0139096734325627086e-647j)  +/-  (1.99e-34, 9.42e-154j)
| (3.8695537246362738975e-10 - 2.4075664460232516184e-644j)  +/-  (2.25e-28, 1.07e-147j)
| (8.6688747303511180279e-40 + 2.5923670002594626364e-663j)  +/-  (4.31e-48, 2.05e-167j)
| (8.6688747303511180279e-40 - 6.654711139649935144e-663j)  +/-  (4.15e-50, 1.97e-169j)
| (1.6079659491838775324e-27 + 1.8734270132876641291e-655j)  +/-  (6.45e-45, 3.06e-164j)
| (8.940557927720131358e-16 - 3.6013046520647642091e-647j)  +/-  (1.91e-35, 9.08e-155j)
| (9.4255515142244793895e-35 + 6.3863994750430488954e-660j)  +/-  (1.34e-48, 6.35e-168j)
| (7.9519807474868139236e-31 - 1.5705705053604751759e-657j)  +/-  (8.48e-47, 4.02e-166j)
| (9.4125914627168536672e-13 - 4.1168500300678103595e-646j)  +/-  (5.49e-35, 2.6e-154j)
| (9.4255515142244793895e-35 - 2.2951869500417297885e-660j)  +/-  (2.71e-49, 1.28e-168j)
| (4.7200659486321839891e-09 + 1.7494588169057322427e-643j)  +/-  (3.52e-32, 1.67e-151j)
| (4.7200659486321839891e-09 + 9.0548333181860232162e-642j)  +/-  (1.33e-36, 6.3e-156j)
| (1.6079659491838775324e-27 - 5.784554165887377638e-656j)  +/-  (4.82e-46, 2.29e-165j)
| (1.0721770237652910085e-05 + 8.506451548835700311e-641j)  +/-  (3.33e-29, 1.58e-148j)
| (2.0639694297471738016e-06 - 1.9615574944286587422e-640j)  +/-  (7.69e-34, 3.65e-153j)
| (1.2213538574413495589e-24 + 4.0746441340495294005e-654j)  +/-  (2.32e-44, 1.1e-163j)
| (7.9519807474868139236e-31 + 5.2232803038308984154e-658j)  +/-  (4.44e-48, 2.1e-167j)
| (0.00059319303310389729507 - 2.464294884734415286e-639j)  +/-  (2.73e-27, 1.3e-146j)
| (2.2699355236343114705e-17 - 1.4459895994927142624e-648j)  +/-  (1.8e-39, 8.53e-159j)
| (0.00955473598913334872 + 6.5864130544839516426e-638j)  +/-  (2.62e-24, 1.24e-143j)
| (4.3522276507404004191e-08 - 2.8228996798551485478e-641j)  +/-  (3.27e-39, 1.55e-158j)
| (2.2779186887424935942e-11 + 3.3647794676956621323e-645j)  +/-  (5.02e-37, 2.38e-156j)
| (0.10855925137117746403 - 2.6405066168139610605e-637j)  +/-  (1.04e-17, 4.92e-137j)
| (1.0721770237652910085e-05 + 5.7004175154321234341e-640j)  +/-  (2.06e-35, 9.77e-155j)
| (0.00017494129893633645814 + 3.8092711271013975494e-639j)  +/-  (4.63e-33, 2.2e-152j)
| (0.054196253999309859032 - 2.3645234500998657499e-637j)  +/-  (7.94e-18, 3.76e-137j)
| (0.019941539097255430691 - 5.3373532448768322962e-638j)  +/-  (7.62e-24, 3.61e-143j)
| (0.054196253999309859032 - 1.5093868116438483055e-637j)  +/-  (2.14e-18, 1.01e-137j)
| (0.019941539097255430691 - 1.0651717174420676897e-637j)  +/-  (2.93e-24, 1.39e-143j)
| (0.035298313811165060543 + 1.6669422931190572502e-637j)  +/-  (9.82e-22, 4.66e-141j)
| (0.00955473598913334872 + 2.8930425684313849423e-638j)  +/-  (1.28e-26, 6.06e-146j)
| (0.080328553743685386062 + 2.0739041601165082133e-637j)  +/-  (3.01e-19, 1.43e-138j)
| (4.3522276507404004191e-08 - 9.9628591843036985023e-643j)  +/-  (2.77e-37, 1.31e-156j)
| (0.035298313811165060543 + 9.4715262780441280093e-638j)  +/-  (7.58e-23, 3.59e-142j)
| (0.0041960628204675324384 - 3.7895880593854351558e-638j)  +/-  (2.18e-30, 1.03e-149j)
| (0.0017090337186543978816 + 6.3518610559107304209e-639j)  +/-  (1.85e-30, 8.76e-150j)
| (0.00017494129893633645814 + 8.9191759345210001665e-640j)  +/-  (2.85e-33, 1.35e-152j)
| (0.0041960628204675324384 - 1.4533134164998494012e-638j)  +/-  (2.04e-29, 9.67e-149j)
| (3.2697330560761453034e-07 + 4.8802721839437000684e-642j)  +/-  (1.59e-37, 7.56e-157j)
| (0.10855925137117746403 - 3.2940488251356395545e-637j)  +/-  (2.56e-25, 1.21e-144j)
| (0.00059319303310389729507 - 8.7660165010645517889e-639j)  +/-  (5.85e-37, 2.77e-156j)
| (3.8695537246362738975e-10 + 7.4445216984028473804e-643j)  +/-  (2.27e-48, 1.08e-167j)
| (0.080328553743685386062 + 2.9026433671918294692e-637j)  +/-  (4.65e-27, 2.21e-146j)
| (2.0639694297471738016e-06 - 2.1448583074556592238e-641j)  +/-  (4.87e-37, 2.31e-156j)
| (0.0017090337186543978816 + 1.9175239221879326348e-638j)  +/-  (4.98e-36, 2.36e-155j)
| (2.6481469224543532894e-14 + 5.3465506849080388946e-647j)  +/-  (7.18e-44, 3.41e-163j)
| (0.12434919192894131445 - 3.7573677678707839909e-637j)  +/-  (6.43e-29, 3.05e-148j)
| (4.6126224206956128095e-05 - 2.950747124091297417e-640j)  +/-  (1.44e-35, 6.81e-155j)
| (0.12321423756241547781 + 3.6744541582102874409e-637j)  +/-  (7.5e-29, 3.56e-148j)
| (4.6126224206956128095e-05 - 1.5481815286915019942e-639j)  +/-  (1.49e-40, 7.08e-160j)
| (3.2697330560761453034e-07 + 6.8417064419306708611e-641j)  +/-  (1.6e-44, 7.58e-164j)
| (0.12321423756241547781 + 3.2995264641750908552e-637j)  +/-  (1.58e-32, 7.51e-152j)
| (-4.8486422964257297629e-16 - 1.8081326920960677167e-646j)  +/-  (1.5e-56, 7.09e-176j)
| (8.940557927720131358e-16 + 2.1899774233518840078e-646j)  +/-  (1.77e-56, 8.37e-176j)
| (2.2699355236343114705e-17 + 7.7779451378188500294e-648j)  +/-  (5.14e-58, 2.44e-177j)
| (9.2873142625338072228e-20 - 4.9240282148349062681e-650j)  +/-  (2.82e-60, 1.34e-179j)
| (4.4472493795946292688e-22 + 8.9676876544828205468e-652j)  +/-  (8.16e-62, 3.87e-181j)
| (2.6481469224543532894e-14 - 4.0040377085332743515e-646j)  +/-  (1.23e-57, 5.81e-177j)
| (9.4125914627168536672e-13 + 4.1200254031401051164e-645j)  +/-  (3.47e-57, 1.65e-176j)
| (2.2779186887424935942e-11 - 4.946296997446831794e-644j)  +/-  (2.88e-56, 1.36e-175j)
