Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 59
-------------------------------------------------
Trying to find an order 59 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^61 - 260091737486205446841488965384642191193/146996893367385334241715463617070179*t^59 + 214883771474186898743656349975464314345088/146996893367385334241715463617070179*t^57 - 1934417907603300352001242973934094185162602/2578892866094479548100271291527547*t^55 + 691733028237392907214153655481081083277502065/2578892866094479548100271291527547*t^53 - 183360375321157889990906318158644145406369770695/2578892866094479548100271291527547*t^51 + 37416814712769187635138276384174248155560244108650/2578892866094479548100271291527547*t^49 - 6026084344525110372731105306818951389260841206694900/2578892866094479548100271291527547*t^47 + 779150183313337749725307196970682005568369234598833075/2578892866094479548100271291527547*t^45 - 81842829152999195636885616829319852512915403125731956625/2578892866094479548100271291527547*t^43 + 7041516174180270864000066011865381002521910197236982432500/2578892866094479548100271291527547*t^41 - 498904763472060525166479625065037004087690798510972975367750/2578892866094479548100271291527547*t^39 + 29201359063379655294547202558186291180948275176369289233404625/2578892866094479548100271291527547*t^37 - 1413730955557805824969447383607073887801136507750836473877581375/2578892866094479548100271291527547*t^35 + 56586787507878022575313906959719513395654993245964736298708423750/2578892866094479548100271291527547*t^33 - 1868768331040135275147805764088071206903611308920666070508211295000/2578892866094479548100271291527547*t^31 + 50733875621148645773420083217826076697517349240391790114711064025625/2578892866094479548100271291527547*t^29 - 1126212275194470835636468643249299357730928758529549962202503431756875/2578892866094479548100271291527547*t^27 + 20295214421252960908165406566985672056550641939347636623652487139055000/2578892866094479548100271291527547*t^25 - 294146675940216955601363283009631683747602732958458668174044589876593750/2578892866094479548100271291527547*t^23 + 3388208862937226521636190116895753943308576188068778989710633982156046875/2578892866094479548100271291527547*t^21 - 30554622752307085549151347037196670872099778042130558270196039023731828125/2578892866094479548100271291527547*t^19 + 211629264803016632082357981219523736145475400400501766181902783483156593750/2578892866094479548100271291527547*t^17 - 1098441134098019653853293345692854267377415726973941315614282950251584312500/2578892866094479548100271291527547*t^15 + 4136602855627459097781403782394360795789002252835092995180099459376224765625/2578892866094479548100271291527547*t^13 - 10818680338677376495058505433433350616021649384496681331788858355573516671875/2578892866094479548100271291527547*t^11 + 18469761047263055126044104177646009815576486373389730327841128918620256312500/2578892866094479548100271291527547*t^9 - 18738469529765290221850031712756832129681362834305051476889820215985123656250/2578892866094479548100271291527547*t^7 + 9637943247384880206730943391489238378945557878067846887493601405357429171875/2578892866094479548100271291527547*t^5 - 1800701499119238878301504482210638848493135734623070747351668154733108828125/2578892866094479548100271291527547*t^3 + 27797429224369147841992503632154032493607909749860808522278410072227656250/2578892866094479548100271291527547*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: 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:
| (-9.2637501665552150611 + 8.2534377043066315452e-588j)  +/-  (2.09e-240, 2.09e-240j)
| (10.85431303643515662 - 2.0992175441554631471e-592j)  +/-  (5.56e-241, 5.56e-241j)
| (13.463814015443814254 - 7.8336570634395409017e-603j)  +/-  (1.65e-243, 1.65e-243j)
| (5.5723311583741005694 - 3.5002718160474671129e-602j)  +/-  (2.04e-242, 2.04e-242j)
| (9.7745133264239097334 + 2.0048929572560564533e-608j)  +/-  (1.68e-240, 1.68e-240j)
| (14.366421808601246992 - 2.1787715457411066272e-622j)  +/-  (8.24e-245, 8.24e-245j)
| (-9.7745133264239097334 - 1.5563338510800434941e-618j)  +/-  (1.64e-240, 1.64e-240j)
| (-13.463814015443814254 + 1.0843748891148406661e-621j)  +/-  (1.69e-243, 1.69e-243j)
| (11.433268351750515426 - 8.2238749760253650966e-619j)  +/-  (2.4e-241, 2.4e-241j)
| (6.4485685432745338004 - 1.0901257121776953145e-621j)  +/-  (1.49e-241, 1.49e-241j)
| (12.049036308047634671 - 1.4810441710056456865e-626j)  +/-  (6.92e-242, 6.92e-242j)
| (-6.8958145975277241505 + 2.1057531963890430592e-631j)  +/-  (3.57e-241, 3.57e-241j)
| (-14.366421808601246992 + 7.9399704830651778826e-641j)  +/-  (7.68e-245, 7.68e-245j)
| (12.716348445117217316 + 2.3556445497275824624e-635j)  +/-  (1.4e-242, 1.4e-242j)
| (10.303335729832383829 + 9.9449770502491630975e-648j)  +/-  (1.09e-240, 1.09e-240j)
| (-10.85431303643515662 - 1.6714381929683890407e-659j)  +/-  (5.25e-241, 5.25e-241j)
| (-8.7680248146091628971 + 2.7490737969851018458e-682j)  +/-  (2.09e-240, 2.09e-240j)
| (7.8129277513497308286 - 2.8923746202267644147e-710j)  +/-  (1.29e-240, 1.29e-240j)
| (-12.716348445117217316 - 2.5955847508237963261e-730j)  +/-  (1.41e-242, 1.41e-242j)
| (-6.4485685432745338004 + 1.4823544272816567251e-726j)  +/-  (1.5e-241, 1.5e-241j)
| (-3.0453803658369785836 - 1.0749895603712454268e-734j)  +/-  (1.46e-246, 1.46e-246j)
| (-5.5723311583741005694 - 7.0445714485580778562e-730j)  +/-  (2.03e-242, 2.03e-242j)
| (6.0076570486560817367 + 1.5758592743866170699e-727j)  +/-  (5.8e-242, 5.8e-242j)
| (-11.433268351750515426 + 9.8466517170978528837e-737j)  +/-  (2.39e-241, 2.39e-241j)
| (1.8159255857884159443 - 6.5618465508082090741e-759j)  +/-  (1.9e-249, 1.9e-249j)
| (8.2850248537319664825 - 1.1241908627450625219e-748j)  +/-  (1.59e-240, 1.59e-240j)
| (-12.049036308047634671 - 2.1062134484146343187e-764j)  +/-  (6.82e-242, 6.82e-242j)
| (-7.350261916236641154 - 1.1404086314103098146e-763j)  +/-  (7.21e-241, 7.21e-241j)
| (-4.2936661898445793888 - 1.2929158453686875758e-774j)  +/-  (2.96e-244, 2.96e-244j)
| (-1.4081543092456500481 + 3.5825856541607264911e-790j)  +/-  (1.49e-250, 1.49e-250j)
| (-2.6340204023963675175 - 1.0458341830834008613e-784j)  +/-  (1.81e-247, 1.81e-247j)
| (9.2637501665552150611 + 1.3606347493562334245e-778j)  +/-  (1.91e-240, 1.91e-240j)
| (2.6340204023963675175 + 3.9936750835886331245e-801j)  +/-  (1.78e-247, 1.78e-247j)
| (-8.2850248537319664825 + 4.7347902767405558552e-793j)  +/-  (1.61e-240, 1.61e-240j)
| (-3.8747962411508963994 - 5.3735137364920089884e-798j)  +/-  (5.68e-245, 5.68e-245j)
| (-10.303335729832383829 + 5.0351463273274023727e-793j)  +/-  (1.05e-240, 1.05e-240j)
| (8.7680248146091628971 + 4.5786887678529028649e-800j)  +/-  (1.99e-240, 1.99e-240j)
| (1.4081543092456500481 - 3.7718145405848591037e-821j)  +/-  (1.39e-250, 1.39e-250j)
| (4.2936661898445793888 + 9.8749852818720093934e-815j)  +/-  (2.94e-244, 2.94e-244j)
| (-1 - 4.1691263360160805346e-823j)  +/-  (1.01e-251, 1.01e-251j)
| (-1.8159255857884159443 - 1.7802415884666919378e-820j)  +/-  (1.82e-249, 1.82e-249j)
| (7.350261916236641154 - 2.5446995482668625394e-810j)  +/-  (6.81e-241, 6.81e-241j)
| (3.8747962411508963994 + 2.5778310159835838716e-826j)  +/-  (5.68e-245, 5.68e-245j)
| (2.224352111721629842 + 7.687793477214020048e-830j)  +/-  (2.16e-248, 2.16e-248j)
| (-3.4588387726956778264 + 7.0311651984690408997e-828j)  +/-  (9.71e-246, 9.71e-246j)
| (3.4588387726956778264 + 2.1938298067777571659e-827j)  +/-  (1.01e-245, 1.01e-245j)
| (4.7158874746728267498 + 1.8256161361295336153e-825j)  +/-  (1.42e-243, 1.42e-243j)
| (5.1419351120949663873 - 1.0150069640019996685e-823j)  +/-  (5.57e-243, 5.57e-243j)
| (0.58831862292423400775 + 5.0736004603290254734e-835j)  +/-  (5.28e-253, 5.28e-253j)
| (-4.7158874746728267498 - 1.5383619975267590402e-825j)  +/-  (1.45e-243, 1.45e-243j)
| (6.8958145975277241505 + 9.9928522266827726046e-822j)  +/-  (3.53e-241, 3.53e-241j)
| (-2.224352111721629842 + 1.2068509965996668528e-838j)  +/-  (2.02e-248, 2.02e-248j)
| (-6.0076570486560817367 - 1.612332953495789364e-832j)  +/-  (5.74e-242, 5.74e-242j)
| (3.0453803658369785836 + 5.4017659685847132289e-837j)  +/-  (1.35e-246, 1.35e-246j)
| (1 + 7.172986981549512133e-842j)  +/-  (9.19e-252, 9.19e-252j)
| (0.13007561662552436611 + 2.5989898290531768034e-844j)  +/-  (1.85e-254, 1.85e-254j)
| (-0.13007561662552436611 - 2.6960611220075247362e-844j)  +/-  (1.85e-254, 1.85e-254j)
| (-7.6353913203720086317e-862 + 1.7857986804492991032e-861j)  +/-  (1.18e-859, 1.18e-859j)
| (-0.58831862292423400775 - 1.6013082765125596458e-843j)  +/-  (5.22e-253, 5.22e-253j)
| (-5.1419351120949663873 + 2.07280852195646765e-834j)  +/-  (5.28e-243, 5.28e-243j)
| (-7.8129277513497308286 - 1.2301893184748605175e-829j)  +/-  (1.17e-240, 1.17e-240j)
-------------------------------------------------
The weights are:
| (4.6491508279481578551e-20 + 1.818741828312459874e-606j)  +/-  (4.34e-51, 8.32e-170j)
| (5.8694086544224041223e-27 - 5.7838102937177147341e-612j)  +/-  (1.56e-55, 3e-174j)
| (1.391038049347346494e-40 - 6.3540694642111681809e-619j)  +/-  (1.81e-61, 3.48e-180j)
| (3.1227977579111792547e-08 + 3.5240454561689593559e-602j)  +/-  (2.24e-40, 4.3e-159j)
| (3.7133757276179693567e-22 - 1.7071411317333329126e-609j)  +/-  (1.29e-53, 2.48e-172j)
| (6.3263397141545952718e-46 + 1.2214160996709728265e-621j)  +/-  (1.42e-63, 2.74e-182j)
| (3.7133757276179693567e-22 + 6.3632249976513917496e-608j)  +/-  (2.66e-56, 5.1e-175j)
| (1.391038049347346494e-40 + 3.4383408088331496431e-618j)  +/-  (3.7e-65, 7.11e-184j)
| (9.7816715405306167021e-30 + 2.1788819720330305422e-613j)  +/-  (8.95e-58, 1.72e-176j)
| (1.653410009309195512e-10 + 2.0922111593005628496e-603j)  +/-  (6.24e-47, 1.2e-165j)
| (7.5977851638238022204e-33 - 5.5957150798942286936e-615j)  +/-  (2.14e-59, 4.1e-178j)
| (8.4907698656548293094e-12 - 2.94194416385384438e-603j)  +/-  (5.15e-52, 9.9e-171j)
| (6.3263397141545952718e-46 - 5.6563056895302184529e-621j)  +/-  (8.59e-69, 1.65e-187j)
| (2.1504327194466677188e-36 + 8.6491791851155823612e-617j)  +/-  (3.84e-61, 7.36e-180j)
| (1.907683359479909468e-24 + 1.1294204406839142934e-610j)  +/-  (2.27e-56, 4.36e-175j)
| (5.8694086544224041223e-27 + 7.3155988393093937723e-611j)  +/-  (2.26e-62, 4.34e-181j)
| (3.9476454111579254295e-18 - 7.5359121570928757185e-606j)  +/-  (8.88e-58, 1.7e-176j)
| (1.0358784968767196744e-14 - 1.2576206336822816869e-605j)  +/-  (1.32e-54, 2.54e-173j)
| (2.1504327194466677188e-36 - 5.506281754793691722e-616j)  +/-  (1.91e-66, 3.67e-185j)
| (1.653410009309195512e-10 + 1.1677218515711472791e-602j)  +/-  (1.23e-53, 2.36e-172j)
| (0.0015932014751987108589 + 3.4754096281243918899e-599j)  +/-  (1.03e-42, 1.97e-161j)
| (3.1227977579111792547e-08 + 1.4163393947444348017e-601j)  +/-  (5.55e-52, 1.07e-170j)
| (2.5416784618597787217e-09 - 9.0593697415151793917e-603j)  +/-  (1.57e-52, 3.01e-171j)
| (9.7816715405306167021e-30 - 2.078634054724735643e-612j)  +/-  (2.01e-64, 3.86e-183j)
| (0.031295970333382649443 - 1.4503437070129684952e-598j)  +/-  (1.18e-37, 2.27e-156j)
| (2.3677680834222043969e-16 + 1.7447768205996917952e-606j)  +/-  (2.31e-58, 4.44e-177j)
| (7.5977851638238022204e-33 + 4.2817955864811290209e-614j)  +/-  (8.7e-66, 1.67e-184j)
| (3.3919990388300880606e-13 + 6.8267420421999498393e-604j)  +/-  (2.86e-57, 5.49e-176j)
| (1.6649909024259568345e-05 - 3.1525209048189593961e-600j)  +/-  (1.56e-51, 3e-170j)
| (0.060351643452606899708 + 3.6646702865160971435e-598j)  +/-  (4.86e-38, 9.33e-157j)
| (0.0051001521082702330633 - 6.743659476368079387e-599j)  +/-  (1.36e-45, 2.61e-164j)
| (4.6491508279481578551e-20 + 2.071054967533923786e-608j)  +/-  (1.09e-61, 2.09e-180j)
| (0.0051001521082702330633 - 3.7577325551187566572e-599j)  +/-  (5.76e-48, 1.11e-166j)
| (2.3677680834222043969e-16 + 3.1284261376183705855e-605j)  +/-  (1.9e-59, 3.65e-178j)
| (9.1441767563411977718e-05 + 7.5504584582596120652e-600j)  +/-  (2.1e-51, 4.02e-170j)
| (1.907683359479909468e-24 - 2.125796670007939528e-609j)  +/-  (6.84e-63, 1.31e-181j)
| (3.9476454111579254295e-18 - 2.0717551793859812743e-607j)  +/-  (1.73e-61, 3.32e-180j)
| (0.060351643452606899708 + 2.6975661864146550679e-598j)  +/-  (1.58e-44, 3.03e-163j)
| (1.6649909024259568345e-05 - 1.1556990849729273655e-600j)  +/-  (5.84e-56, 1.12e-174j)
| (0.098965349218941590441 - 6.2877991939828631061e-598j)  +/-  (2.91e-45, 5.58e-164j)
| (0.031295970333382649443 - 2.1575881483557311304e-598j)  +/-  (2.39e-47, 4.6e-166j)
| (3.3919990388300880606e-13 + 7.8625739045259816896e-605j)  +/-  (3.38e-60, 6.5e-179j)
| (9.1441767563411977718e-05 + 3.0969234678680120613e-600j)  +/-  (2.14e-55, 4.1e-174j)
| (0.013747016779266244112 + 7.566931583436090669e-599j)  +/-  (4.67e-51, 8.97e-170j)
| (0.00041756741207800553543 - 1.6780539013012662457e-599j)  +/-  (1.93e-54, 3.7e-173j)
| (0.00041756741207800553543 - 7.6564245151487498085e-600j)  +/-  (6.31e-55, 1.21e-173j)
| (2.5064687997418454464e-06 + 3.9592061676419974379e-601j)  +/-  (1.78e-57, 3.42e-176j)
| (3.0990051799280638998e-07 - 1.2390276797856281019e-601j)  +/-  (3.15e-58, 6.05e-177j)
| (0.13977271435188680499 + 1.0692827834539266096e-597j)  +/-  (2.47e-52, 4.74e-171j)
| (2.5064687997418454464e-06 + 1.2170171055348620347e-600j)  +/-  (5.17e-60, 9.92e-179j)
| (8.4907698656548293094e-12 - 4.310966203299125844e-604j)  +/-  (3.54e-61, 6.81e-180j)
| (0.013747016779266244112 + 1.2349022396016281776e-598j)  +/-  (8.4e-56, 1.61e-174j)
| (2.5416784618597787217e-09 - 4.2489368082409222976e-602j)  +/-  (4.91e-62, 9.43e-181j)
| (0.0015932014751987108589 + 1.7557196382739739632e-599j)  +/-  (1.31e-56, 2.51e-175j)
| (0.098965349218941590441 - 5.0625551782824807383e-598j)  +/-  (1.64e-54, 3.15e-173j)
| (0.28760154381777067733 - 8.2291244757859710385e-597j)  +/-  (6.01e-55, 1.15e-173j)
| (0.28760154381777067733 - 8.4635117298442741846e-597j)  +/-  (1.6e-55, 3.08e-174j)
| (-0.27791220187828966582 + 1.5139098753756153438e-596j)  +/-  (3.03e-55, 5.83e-174j)
| (0.13977271435188680499 + 1.2143081868573150121e-597j)  +/-  (7.24e-57, 1.39e-175j)
| (3.0990051799280638998e-07 - 4.3303840089795309271e-601j)  +/-  (1.1e-62, 2.08e-181j)
| (1.0358784968767196744e-14 - 1.4802627727178918887e-604j)  +/-  (7.84e-67, 1.56e-185j)
