Starting with polynomial:
P : 262144*t^18 - 1114112*t^16 + 1966080*t^14 - 1863680*t^12 + 1025024*t^10 - 329472*t^8 + 59136*t^6 - 5280*t^4 + 180*t^2 - 1
Extension levels are: 18 57
-------------------------------------------------
Trying to find an order 57 Kronrod extension for:
P1 : 262144*t^18 - 1114112*t^16 + 1966080*t^14 - 1863680*t^12 + 1025024*t^10 - 329472*t^8 + 59136*t^6 - 5280*t^4 + 180*t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 262144*t^75 - 4849664*t^73 + 43057152*t^71 - 244285440*t^69 + 994954240*t^67 - 3098371584*t^65 + 7672158208*t^63 - 15511102464*t^61 + 26089446240*t^59 - 37014131440*t^57 + 44753449832*t^55 - 46474736364*t^53 + 2668424446233/64*t^51 - 4154140621425/128*t^49 + 2814095259675/128*t^47 - 3324630574545/256*t^45 + 109712808959985/16384*t^43 - 98774343460485/32768*t^41 + 77581380878925/65536*t^39 - 53081997443475/131072*t^37 + 505037289962205/4194304*t^35 - 260170725132045/8388608*t^33 + 28907858348005/4194304*t^31 - 11027197811175/8388608*t^29 + 57397978350475/268435456*t^27 - 15801325804719/536870912*t^25 + 3646459801089/1073741824*t^23 - 697319977079/2147483648*t^21 + 3486599885395/137438953472*t^19 - 437423756715/274877906944*t^17 + 21554214099/274877906944*t^15 - 1622360201/549755813888*t^13 + 5752004349/70368744177664*t^11 - 222945905/140737488355328*t^9 + 5620485/281474976710656*t^7 - 82251/562949953421312*t^5 + 9139/18014398509481984*t^3 - 19/36028797018963968*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:
| (-0.96940026593933041674 - 3.435440794394945216e-818j)  +/-  (5.27e-229, 5.27e-229j)
| (-0.95842748245825270023 - 1.0691132996436640339e-818j)  +/-  (3.42e-229, 3.42e-229j)
| (-0.91577332665505743992 - 5.9335719192926450693e-820j)  +/-  (6.65e-230, 6.65e-230j)
| (-0.99232057973704506275 + 2.7820090740279511472e-820j)  +/-  (3.87e-229, 3.87e-229j)
| (0.91577332665505743992 - 8.3745512138904025493e-821j)  +/-  (6.78e-230, 6.78e-230j)
| (0.89839098189197887157 - 5.9536757631866568931e-837j)  +/-  (2.92e-230, 2.92e-230j)
| (0.99232057973704506275 - 8.222759487337846801e-845j)  +/-  (4.15e-229, 4.15e-229j)
| (-0.89839098189197887157 + 5.9381681883128315484e-860j)  +/-  (3.01e-230, 3.01e-230j)
| (-0.94581724170063467902 + 5.3122983135580347411e-858j)  +/-  (2.35e-229, 2.35e-229j)
| (0.97871684532735448364 + 1.0590901118627121048e-856j)  +/-  (5.4e-229, 5.4e-229j)
| (0.87947375120648907139 + 5.6010917569824444442e-869j)  +/-  (1.12e-230, 1.12e-230j)
| (0.99914575838730102919 + 1.1912953837592270128e-866j)  +/-  (6.23e-230, 6.23e-230j)
| (-0.8590539543698851819 - 6.9468768264107132051e-882j)  +/-  (4.16e-231, 4.16e-231j)
| (-0.83716647826252857481 + 3.6253835308813208326e-882j)  +/-  (1.3e-231, 1.3e-231j)
| (0.9863613034027223736 - 2.7623981240433827002e-876j)  +/-  (5.52e-229, 5.52e-229j)
| (0.8590539543698851819 - 8.9512565713239611036e-888j)  +/-  (4.48e-231, 4.48e-231j)
| (0.73572391067313162477 + 1.9881338696272700107e-900j)  +/-  (5.71e-234, 5.71e-234j)
| (0.95842748245825270023 + 3.3927243954088885318e-893j)  +/-  (3.26e-229, 3.26e-229j)
| (-0.76308406819980650614 - 2.7738851176313975195e-906j)  +/-  (2.84e-233, 2.84e-233j)
| (-0.93159108805127897294 + 1.9621366794286762343e-901j)  +/-  (1.16e-229, 1.16e-229j)
| (0.94581724170063467902 - 3.9734174653515241867e-901j)  +/-  (2.13e-229, 2.13e-229j)
| (0.76308406819980650614 - 8.6305180688081023402e-912j)  +/-  (2.57e-233, 2.57e-233j)
| (-0.9863613034027223736 - 3.8599125701067148903e-904j)  +/-  (5.05e-229, 5.05e-229j)
| (-0.8138487172701949671 + 1.1495244692344431205e-910j)  +/-  (3.82e-232, 3.82e-232j)
| (-0.78914050939639359922 - 7.9732655151950647497e-911j)  +/-  (1.15e-232, 1.15e-232j)
| (0.99658449300666984982 + 5.8205380341073699416e-906j)  +/-  (2.31e-229, 2.31e-229j)
| (0.7071067811865475244 + 5.1966373735419170608e-918j)  +/-  (1.07e-234, 1.07e-234j)
| (0.8138487172701949671 + 1.1557877478116900685e-915j)  +/-  (4.24e-232, 4.24e-232j)
| (-0.97871684532735448364 + 3.7677771276196866489e-910j)  +/-  (5.57e-229, 5.57e-229j)
| (-0.64629923786094089199 - 7.8896497157462868845e-921j)  +/-  (2.4e-236, 2.4e-236j)
| (-0.87947375120648907139 - 4.9333338462830666913e-914j)  +/-  (1.36e-230, 1.36e-230j)
| (0.83716647826252857481 - 2.1935605214618337492e-915j)  +/-  (1.55e-231, 1.55e-231j)
| (0.67728157162574107476 - 2.150839576284788955e-920j)  +/-  (1.62e-235, 1.62e-235j)
| (-0.99914575838730102919 - 9.0492027116742950304e-913j)  +/-  (6.83e-230, 6.83e-230j)
| (-0.67728157162574107476 - 5.8064963326928305009e-923j)  +/-  (1.6e-235, 1.6e-235j)
| (-0.73572391067313162477 - 4.6296442514732556994e-920j)  +/-  (5.2e-234, 5.2e-234j)
| (0.96940026593933041674 - 4.18467174291813584e-914j)  +/-  (4.37e-229, 4.37e-229j)
| (0.58107681540193828 - 6.5474383875254585281e-929j)  +/-  (4.15e-238, 4.15e-238j)
| (0.93159108805127897294 - 1.0539528099604165557e-922j)  +/-  (1.17e-229, 1.17e-229j)
| (-0.99658449300666984982 - 1.9513188914205401735e-933j)  +/-  (2.52e-229, 2.52e-229j)
| (-0.54694815812242687471 - 1.4375827521013214556e-946j)  +/-  (5.02e-239, 5.02e-239j)
| (4.6852403701328244875e-989 - 6.2235841245865378329e-989j)  +/-  (5.84e-987, 5.84e-987j)
| (0.78914050939639359922 - 6.4863478718629457359e-943j)  +/-  (1.23e-232, 1.23e-232j)
| (0.61421271268966781744 + 1.5063277707592668993e-947j)  +/-  (3.21e-237, 3.21e-237j)
| (0.20521534219563429132 - 1.226769251728658006e-959j)  +/-  (2.28e-249, 2.28e-249j)
| (-0.51188504908960100217 + 8.6065335133272148382e-951j)  +/-  (4.41e-240, 4.41e-240j)
| (-0.61421271268966781744 + 1.9784029099024852496e-946j)  +/-  (3.22e-237, 3.22e-237j)
| (0.64629923786094089199 + 4.6921975157516819553e-948j)  +/-  (2.44e-236, 2.44e-236j)
| (0.47594739303707354443 + 2.0793694700766299417e-952j)  +/-  (3.95e-241, 3.95e-241j)
| (0.43919658884737036545 + 1.1739148606319734367e-952j)  +/-  (4e-242, 4e-242j)
| (-0.58107681540193828 + 1.9118396345882855137e-947j)  +/-  (4.15e-238, 4.15e-238j)
| (-0.47594739303707354443 + 9.1219541305800008362e-951j)  +/-  (4.05e-241, 4.05e-241j)
| (-0.7071067811865475244 + 9.6008936563575524064e-956j)  +/-  (9.95e-235, 9.95e-235j)
| (0.54694815812242687471 - 7.371553018083579865e-959j)  +/-  (5.38e-239, 5.38e-239j)
| (0.51188504908960100217 + 1.4884167241641961559e-963j)  +/-  (4.25e-240, 4.25e-240j)
| (-0.041324974248813211938 - 8.0867263860290259766e-977j)  +/-  (1.24e-254, 1.24e-254j)
| (-0.43919658884737036545 + 1.660177426354939753e-964j)  +/-  (3.66e-242, 3.66e-242j)
| (-0.24548548714079914892 + 3.9682986342352755669e-970j)  +/-  (4.41e-248, 4.41e-248j)
| (0.16459459028073389414 - 2.6625037511127048802e-974j)  +/-  (1.08e-250, 1.08e-250j)
| (0.40169542465296945752 - 1.4969484006919933564e-965j)  +/-  (2.9e-243, 2.9e-243j)
| (0.12369263126934761602 + 9.8323174960445480892e-976j)  +/-  (5.15e-252, 5.15e-252j)
| (-0.28533622424910530907 - 2.6469353637836351776e-969j)  +/-  (6.96e-247, 6.96e-247j)
| (-0.40169542465296945752 - 5.645283269509962599e-965j)  +/-  (3.08e-243, 3.08e-243j)
| (-0.0825793454723323246 - 8.0110091649552831737e-976j)  +/-  (3.02e-253, 3.02e-253j)
| (0.36350797056382984848 - 1.0736819652492930384e-966j)  +/-  (2.38e-244, 2.38e-244j)
| (0.24548548714079914892 + 3.292655265769641705e-971j)  +/-  (4.63e-248, 4.63e-248j)
| (-0.12369263126934761602 - 9.6509672653200815089e-976j)  +/-  (5.1e-252, 5.1e-252j)
| (-0.36350797056382984848 - 3.879043357736026734e-967j)  +/-  (1.92e-244, 1.92e-244j)
| (-0.16459459028073389414 - 6.3465071503728215984e-973j)  +/-  (1.21e-250, 1.21e-250j)
| (0.28533622424910530907 + 4.4847935068996199492e-969j)  +/-  (7.92e-247, 7.92e-247j)
| (0.32469946920468348741 + 3.805366175905737674e-968j)  +/-  (1.38e-245, 1.38e-245j)
| (0.041324974248813211938 + 3.6146734648704909249e-977j)  +/-  (1.24e-254, 1.24e-254j)
| (-0.20521534219563429132 - 3.8509000948790803623e-973j)  +/-  (2.2e-249, 2.2e-249j)
| (-0.32469946920468348741 + 7.1295194991171821084e-968j)  +/-  (1.21e-245, 1.21e-245j)
| (0.0825793454723323246 - 2.198518656832739847e-976j)  +/-  (2.58e-253, 2.58e-253j)
-------------------------------------------------
The weights are:
| (0.00079293584732572979348 - 1.4306979039894423292e-819j)  +/-  (1.19e-21, 2.36e-129j)
| (0.0010712731693254699026 + 3.1456278053913035341e-819j)  +/-  (8.65e-22, 1.72e-129j)
| (0.0021231475550938087187 - 8.4631097824167571608e-820j)  +/-  (1.55e-22, 3.07e-130j)
| (0.00020131403987282620568 - 2.3436095486172876209e-820j)  +/-  (2.41e-23, 4.78e-131j)
| (0.0021231475550938087187 - 2.6063628143347413943e-821j)  +/-  (3.52e-24, 6.99e-132j)
| (0.0025380742586206064642 + 2.1044842472195004261e-821j)  +/-  (2.88e-24, 5.73e-132j)
| (0.00020131403987282620568 + 2.7332479700235071921e-822j)  +/-  (1.52e-25, 3.03e-133j)
| (0.0025380742586206064642 + 8.6999014237964613419e-820j)  +/-  (2.92e-23, 5.8e-131j)
| (0.0013872334908132000051 - 8.2556663624020903796e-820j)  +/-  (1.08e-22, 2.14e-130j)
| (0.00055412285095356947421 + 7.7025781361564560372e-822j)  +/-  (1.15e-25, 2.29e-133j)
| (0.0029806042228787705611 - 3.2596793016623711115e-821j)  +/-  (2.05e-25, 4.07e-133j)
| (2.2470440745593093294e-05 + 3.0209880662675596723e-823j)  +/-  (1.85e-26, 3.67e-134j)
| (0.0034477145194929372077 + 7.455646741376430598e-820j)  +/-  (3.95e-26, 7.84e-134j)
| (0.00393621431149362199 - 7.1217115114682235136e-820j)  +/-  (1.13e-26, 2.25e-134j)
| (0.0003564655151274034275 - 4.8862018598444405207e-822j)  +/-  (8.55e-26, 1.7e-133j)
| (0.0034477145194929372077 + 4.1077721782760891804e-821j)  +/-  (3.74e-27, 7.42e-135j)
| (0.0060356622008399189171 - 8.3849133220603399877e-821j)  +/-  (1.51e-29, 2.99e-137j)
| (0.0010712731693254699026 + 1.5710649116578069788e-821j)  +/-  (6.47e-27, 1.28e-134j)
| (0.0054960882218372770122 + 6.4212559428490445413e-820j)  +/-  (7.02e-30, 1.39e-137j)
| (0.0017386584824136077317 + 8.298058029061273834e-820j)  +/-  (5.29e-27, 1.05e-134j)
| (0.0013872334908132000051 - 2.1603311853088965499e-821j)  +/-  (3.33e-27, 6.62e-135j)
| (0.0054960882218372770122 + 7.4651648955096385208e-821j)  +/-  (6.71e-30, 1.33e-137j)
| (0.0003564655151274034275 + 5.7195792896204985946e-820j)  +/-  (7e-29, 1.39e-136j)
| (0.0044427666499691875828 + 6.8525494145057290322e-820j)  +/-  (2.77e-29, 5.5e-137j)
| (0.004963911268810531915 - 6.6235778808209627079e-820j)  +/-  (7.38e-30, 1.47e-137j)
| (8.9728267087352805247e-05 - 1.2106396202210942281e-822j)  +/-  (2.55e-28, 5.06e-136j)
| (0.0065789473684210526316 + 9.3425014600220720401e-821j)  +/-  (1.46e-32, 2.91e-140j)
| (0.0044427666499691875828 + 5.734757451258594769e-821j)  +/-  (2.87e-31, 5.71e-139j)
| (0.00055412285095356947421 - 1.7452300982501169496e-819j)  +/-  (1.68e-29, 3.34e-137j)
| (0.0076618065150048282509 + 5.7484283157334582817e-820j)  +/-  (5.19e-35, 1.03e-142j)
| (0.0029806042228787705611 - 7.9099940589836036105e-820j)  +/-  (1.38e-29, 2.73e-137j)
| (0.00393621431149362199 - 4.9153475584804143397e-821j)  +/-  (4.26e-31, 8.47e-139j)
| (0.0071222325360021863461 - 1.0337685152183544952e-820j)  +/-  (2.87e-34, 5.7e-142j)
| (2.2470440745593093294e-05 - 2.112902639250224985e-821j)  +/-  (5.96e-32, 1.18e-139j)
| (0.0071222325360021863461 - 5.9040275265600833672e-820j)  +/-  (4.25e-35, 8.44e-143j)
| (0.0060356622008399189171 - 6.237249991325579584e-820j)  +/-  (1.15e-33, 2.29e-141j)
| (0.00079293584732572979348 - 1.1253282008039320275e-821j)  +/-  (1.88e-31, 3.73e-139j)
| (0.0087151280868729176803 + 1.3539640651036643006e-820j)  +/-  (5.87e-39, 1.17e-146j)
| (0.0017386584824136077317 + 3.160081281121953991e-821j)  +/-  (9.79e-32, 1.95e-139j)
| (8.9728267087352805247e-05 + 9.4771568491321269796e-821j)  +/-  (2.29e-32, 4.55e-140j)
| (0.0092216804253484832731 - 5.3038872671843688417e-820j)  +/-  (8.48e-40, 1.69e-147j)
| (0.013157894736842105263 - 3.3053676090901873416e-820j)  +/-  (1.08e-43, 2.15e-151j)
| (0.004963911268810531915 - 6.5825896234703089776e-821j)  +/-  (1.75e-34, 3.48e-142j)
| (0.0081939834680315733482 - 1.2437453131497070955e-820j)  +/-  (1.02e-38, 2.03e-146j)
| (0.012603771885888535789 + 2.6094205140208981292e-820j)  +/-  (3.93e-44, 7.82e-152j)
| (0.0097101802173491680555 + 5.1596582333702355736e-820j)  +/-  (9.03e-42, 1.79e-149j)
| (0.0081939834680315733482 - 5.5973964150123824607e-820j)  +/-  (9.25e-40, 1.84e-147j)
| (0.0076618065150048282509 + 1.1369699029360194411e-820j)  +/-  (1.49e-38, 2.97e-146j)
| (0.010177290513963334702 - 1.7037661270586375752e-820j)  +/-  (3.37e-43, 6.7e-151j)
| (0.010619820478221498799 + 1.8261972803668485274e-820j)  +/-  (6.3e-44, 1.25e-151j)
| (0.0087151280868729176803 + 5.4495529070293723031e-820j)  +/-  (1.28e-41, 2.54e-149j)
| (0.010177290513963334702 - 5.0163253069178441313e-820j)  +/-  (3.29e-44, 6.53e-152j)
| (0.0065789473684210526316 + 6.0660888562258894173e-820j)  +/-  (4.99e-40, 9.91e-148j)
| (0.0092216804253484832731 - 1.4674801377411263566e-820j)  +/-  (1.07e-42, 2.13e-150j)
| (0.0097101802173491680555 + 1.5841361654804991149e-820j)  +/-  (2.26e-43, 4.49e-151j)
| (0.01313542429609651217 + 3.4471174170242470807e-820j)  +/-  (2.32e-49, 4.61e-157j)
| (0.010619820478221498799 + 4.8735002904729701168e-820j)  +/-  (2.05e-46, 4.07e-154j)
| (0.01236495888951637547 - 4.1603446254106290903e-820j)  +/-  (1.34e-49, 2.67e-157j)
| (0.012801429221714701836 - 2.746324271907508177e-820j)  +/-  (1.79e-49, 3.55e-157j)
| (0.011034747181748296544 - 1.9512516521941915751e-820j)  +/-  (9.07e-48, 1.8e-155j)
| (0.012956580696969279057 + 2.8845501193663435886e-820j)  +/-  (6.9e-50, 1.37e-157j)
| (0.012086621567516635361 + 4.3031241831605463626e-820j)  +/-  (1.71e-50, 3.4e-158j)
| (0.011034747181748296544 - 4.730912291365870689e-820j)  +/-  (3.31e-49, 6.58e-157j)
| (0.013068166469754752458 - 3.589341005219796337e-820j)  +/-  (2.61e-51, 5.19e-159j)
| (0.011419236254428497531 + 2.0787472638251859829e-820j)  +/-  (3.45e-50, 6.85e-158j)
| (0.01236495888951637547 - 2.4740236726267698835e-820j)  +/-  (4.68e-51, 9.29e-159j)
| (0.012956580696969279057 + 3.7318954552836948697e-820j)  +/-  (3.91e-52, 7.77e-160j)
| (0.011419236254428497531 + 4.5883819848285685627e-820j)  +/-  (1.04e-51, 2.06e-159j)
| (0.012801429221714701836 - 3.8746519129664874713e-820j)  +/-  (1.69e-52, 3.36e-160j)
| (0.012086621567516635361 + 2.3403206182734430851e-820j)  +/-  (2.29e-52, 4.55e-160j)
| (0.011770661246028905258 - 2.208499203598712976e-820j)  +/-  (2.95e-52, 5.86e-160j)
| (0.01313542429609651217 + 3.164246015407658458e-820j)  +/-  (9.54e-54, 1.91e-161j)
| (0.012603771885888535789 + 4.0174986283619471118e-820j)  +/-  (6.15e-54, 1.26e-161j)
| (0.011770661246028905258 - 4.4458023732441236349e-820j)  +/-  (5.58e-54, 1.17e-161j)
| (0.013068166469754752458 - 3.0239164237071519215e-820j)  +/-  (6.18e-54, 1.19e-161j)
