Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 65
-------------------------------------------------
Trying to find an order 65 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^67 - 36938424790696347617960961225075282318695521/17201262424585284698480207686516181275521*t^65 + 37278652695060015998285470585473819350702675440/17201262424585284698480207686516181275521*t^63 - 373460550613890248230212595467649899262940760080/273035911501353725372701709309780655167*t^61 + 165481573195813351498749962660072176845143897330600/273035911501353725372701709309780655167*t^59 - 54787912003031149118691196242222266378857898227598120/273035911501353725372701709309780655167*t^57 + 14084175889149021848299701299736643801787809573784868720/273035911501353725372701709309780655167*t^55 - 2884032752922180096582271918939659235571019436465360959600/273035911501353725372701709309780655167*t^53 + 478890861109506795436322537490961065387922475056545593300100/273035911501353725372701709309780655167*t^51 - 65309336408157143141816071067146825555237720725773807852122500/273035911501353725372701709309780655167*t^49 + 7382434177114176854986006440393522021229123480259950022439546000/273035911501353725372701709309780655167*t^47 - 696212192221093513117317527279737647553857870402325560093501306000/273035911501353725372701709309780655167*t^45 + 55021926625527240812558344785666232059271430000176172608499096295000/273035911501353725372701709309780655167*t^43 - 3654117822747021762617154476491612284646205836924686101375673412695000/273035911501353725372701709309780655167*t^41 + 204199209845212105752366931092344811637631787831339884129890748989350000/273035911501353725372701709309780655167*t^39 - 9601953021004359079755588968086365216480270206154581652424221814329990000/273035911501353725372701709309780655167*t^37 + 379472858774149370633704470361278576721811190139480502325125366164895996250/273035911501353725372701709309780655167*t^35 - 12574254806714730310040389247408677045767089653172179017883237475790715556250/273035911501353725372701709309780655167*t^33 + 348097480319137491005099579610396381250609771109567853328687889317095423150000/273035911501353725372701709309780655167*t^31 - 8011464270168891852936405247527067350463367592769977989039598836584914912750000/273035911501353725372701709309780655167*t^29 + 152325124870304464684868711905791742806963727719683961539420905859625321940575000/273035911501353725372701709309780655167*t^27 - 2373721490224729956621431783221961450391995416688296039779505824911356274974575000/273035911501353725372701709309780655167*t^25 + 30019599844131033164747543517136025448843856539804781279482147201005503602461250000/273035911501353725372701709309780655167*t^23 - 304372973037173236131231189893698342315765531372460782181681364685417638007961250000/273035911501353725372701709309780655167*t^21 + 2437140543152919690189594759615378541074675607061853490029267213898028943402426562500/273035911501353725372701709309780655167*t^19 - 15123360194057123179339469596400532654302995251964377930026745809702790310968714562500/273035911501353725372701709309780655167*t^17 + 71016475150806365083783350039859044150811864300811238707786512583948327702800656750000/273035911501353725372701709309780655167*t^15 - 244712778849383239824059067494345832991433058239854767099333943797438780080709888750000/273035911501353725372701709309780655167*t^13 + 594054620408066238231152322036691900747046127887069092600030467212004415097900360625000/273035911501353725372701709309780655167*t^11 - 960431538907623047914699202367324422127653022220684549694521207046750285659221290625000/273035911501353725372701709309780655167*t^9 + 953049315897868703848517628632555666578607100207347743004712592222811327083461311250000/273035911501353725372701709309780655167*t^7 - 510490209265754346909268403319702018022085227378946921093419175992902210932032211250000/273035911501353725372701709309780655167*t^5 + 117301989320781519431005754078002581846961038237302484926340972529041322671706749609375/273035911501353725372701709309780655167*t^3 - 6825071658728618677533193828963480278365494810789459728271677505481882220650312109375/273035911501353725372701709309780655167*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
  current precision for roots: 848
  current precision for roots: 1696
 current precision for weights: 848
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   67 out of 67
Indefinite weights: 0 out of 67
Negative weights:   0 out of 67
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (13.520854674086064079 + 1.2477803570979903766e-1038j)  +/-  (6.96e-497, 6.96e-497j)
| (12.866031636946204119 - 4.966693555385965862e-1038j)  +/-  (3.89e-496, 3.89e-496j)
| (10.63789336447703417 - 2.5883757556191308696e-1035j)  +/-  (1.81e-494, 1.81e-494j)
| (7.3930629757024977827 + 1.2438845730963290814e-1037j)  +/-  (6.05e-495, 6.05e-495j)
| (10.138455987252957184 - 2.9780093084197810381e-1036j)  +/-  (2.43e-494, 2.43e-494j)
| (9.654080356605732183 - 8.4739677358409125463e-1036j)  +/-  (2.8e-494, 2.8e-494j)
| (8.270909999478677115 - 3.8746550487211647457e-1039j)  +/-  (1.93e-494, 1.93e-494j)
| (14.254867148718380089 - 4.1261276914630987356e-1044j)  +/-  (7.31e-498, 7.31e-498j)
| (9.1824967195523932059 - 4.4119186963969156311e-1040j)  +/-  (2.99e-494, 2.99e-494j)
| (15.141934151981499104 + 3.8136633777302401249e-1047j)  +/-  (3.19e-499, 3.19e-499j)
| (12.262214523528283073 - 1.0133766151983470074e-1042j)  +/-  (1.51e-495, 1.51e-495j)
| (8.721919394924967824 - 1.3778273596118845826e-1039j)  +/-  (2.52e-494, 2.52e-494j)
| (11.155362143371785668 + 7.7942266248527912642e-1042j)  +/-  (9.54e-495, 9.54e-495j)
| (6.9644018457126038442 - 1.069841354592972348e-1040j)  +/-  (2.84e-495, 2.84e-495j)
| (7.8282868834666151793 - 2.1258934088600098639e-1039j)  +/-  (1.16e-494, 1.16e-494j)
| (11.694891664839195383 + 2.5061050603967957174e-1043j)  +/-  (4.83e-495, 4.83e-495j)
| (-11.155362143371785668 - 6.7573993224460989295e-1045j)  +/-  (9.48e-495, 9.48e-495j)
| (-8.721919394924967824 - 1.1122237693761810604e-1082j)  +/-  (2.47e-494, 2.47e-494j)
| (-9.654080356605732183 - 4.1110187204051783815e-1110j)  +/-  (3.05e-494, 3.05e-494j)
| (-11.694891664839195383 - 2.2766151971484472732e-1132j)  +/-  (4.31e-495, 4.31e-495j)
| (-15.141934151981499104 + 4.6096430909807005433e-1149j)  +/-  (2.97e-499, 2.97e-499j)
| (-10.63789336447703417 + 1.5205792543930316879e-1169j)  +/-  (1.7e-494, 1.7e-494j)
| (-10.138455987252957184 + 1.8192002227147687029e-1216j)  +/-  (2.44e-494, 2.44e-494j)
| (5.7110779175530318739 + 3.7622800251228871909e-1240j)  +/-  (1.46e-496, 1.46e-496j)
| (-1.757960239582256997 + 2.0636992688673675149e-1248j)  +/-  (1.69e-504, 1.69e-504j)
| (-4.4958667062021075966 - 1.0391859058681552917e-1238j)  +/-  (2.04e-498, 2.04e-498j)
| (-12.866031636946204119 - 8.6580313166876593367e-1264j)  +/-  (3.93e-496, 3.93e-496j)
| (-8.270909999478677115 + 6.2246286591962499043e-1305j)  +/-  (1.75e-494, 1.75e-494j)
| (-13.520854674086064079 - 5.7365484652502225278e-1330j)  +/-  (7.35e-497, 7.35e-497j)
| (-9.1824967195523932059 - 1.9896241032474399645e-1345j)  +/-  (2.95e-494, 2.95e-494j)
| (-6.5415858781955589819 + 3.6128167587523580306e-1359j)  +/-  (1.21e-495, 1.21e-495j)
| (4.0973750719876732659 + 3.1776518948174590156e-1373j)  +/-  (4.01e-499, 4.01e-499j)
| (-3.7016471873382767723 - 3.0654293696726396945e-1373j)  +/-  (6.38e-500, 6.38e-500j)
| (-12.262214523528283073 + 2.3241456908020001432e-1367j)  +/-  (1.63e-495, 1.63e-495j)
| (-6.9644018457126038442 - 3.2483726591448418953e-1382j)  +/-  (2.92e-495, 2.92e-495j)
| (-6.1239927682033949834 - 2.7308078193189540385e-1409j)  +/-  (4.68e-496, 4.68e-496j)
| (-1 + 1.0765906567270948148e-1437j)  +/-  (1.26e-506, 1.26e-506j)
| (4.4958667062021075966 - 9.945631152604516731e-1430j)  +/-  (2.04e-498, 2.04e-498j)
| (2.5287929173979097308 - 1.5606948997676836584e-1433j)  +/-  (1.6e-502, 1.6e-502j)
| (-4.0973750719876732659 - 1.3044280500993716143e-1425j)  +/-  (4.14e-499, 4.14e-499j)
| (-14.254867148718380089 + 3.3369424351333019879e-1430j)  +/-  (6.99e-498, 6.99e-498j)
| (5.3023611673631568381 - 1.0663314361732309113e-1445j)  +/-  (4.09e-497, 4.09e-497j)
| (-7.8282868834666151793 + 7.7726595928263525295e-1456j)  +/-  (1.22e-494, 1.22e-494j)
| (-5.7110779175530318739 + 3.8167084504796338998e-1485j)  +/-  (1.41e-496, 1.41e-496j)
| (-1.3766491649827591755 - 2.1801163182535187623e-1513j)  +/-  (1.27e-505, 1.27e-505j)
| (2.1422126056458269722 + 1.0501538647541528049e-1511j)  +/-  (1.73e-503, 1.73e-503j)
| (-3.3084308643248325357 - 6.3173162700558467623e-1504j)  +/-  (9.82e-501, 9.82e-501j)
| (1.757960239582256997 + 5.8307095605907227781e-1514j)  +/-  (1.69e-504, 1.69e-504j)
| (6.5415858781955589819 + 1.1828309651054715323e-1504j)  +/-  (1.2e-495, 1.2e-495j)
| (-2.5287929173979097308 + 1.1499419234825424127e-1510j)  +/-  (1.63e-502, 1.63e-502j)
| (1.3766491649827591755 - 1.3143734227405835579e-1514j)  +/-  (1.36e-505, 1.36e-505j)
| (-2.1422126056458269722 + 5.3484987109034768796e-1512j)  +/-  (1.72e-503, 1.72e-503j)
| (3.7016471873382767723 + 4.1633217173589579159e-1508j)  +/-  (6.75e-500, 6.75e-500j)
| (6.1239927682033949834 - 1.4891555390934799219e-1504j)  +/-  (4.33e-496, 4.33e-496j)
| (1 + 1.2600745124671707872e-1514j)  +/-  (1.22e-506, 1.22e-506j)
| (-7.3930629757024977827 - 2.5274323939164621809e-1501j)  +/-  (6.27e-495, 6.27e-495j)
| (6.3643213755188344869e-1565 + 3.1838010428248838339e-1565j)  +/-  (4.77e-1563, 4.77e-1563j)
| (-0.63308384166519171553 + 1.0104464847853476221e-1530j)  +/-  (7.7e-508, 7.7e-508j)
| (3.3084308643248325357 - 4.4799137910521881267e-1524j)  +/-  (1e-500, 1e-500j)
| (0.29172250435539759542 - 2.6932658682410791277e-1531j)  +/-  (5.75e-509, 5.75e-509j)
| (4.8974168682048993418 + 5.4057842051421402628e-1521j)  +/-  (9.99e-498, 9.99e-498j)
| (-2.9175240303235622876 - 1.385909209509251976e-1523j)  +/-  (1.39e-501, 1.39e-501j)
| (-0.29172250435539759542 + 3.7032300452096572458e-1531j)  +/-  (5.75e-509, 5.75e-509j)
| (-4.8974168682048993418 + 1.0001269036675017143e-1517j)  +/-  (9.41e-498, 9.41e-498j)
| (0.63308384166519171553 - 1.2243866136123209056e-1532j)  +/-  (8.56e-508, 8.56e-508j)
| (2.9175240303235622876 + 8.9741979148062336947e-1528j)  +/-  (1.48e-501, 1.48e-501j)
| (-5.3023611673631568381 + 6.1456181585995350187e-1520j)  +/-  (3.79e-497, 3.79e-497j)
-------------------------------------------------
The weights are:
| (5.5072066713249745944e-41 + 4.0420901282675510884e-1065j)  +/-  (2.11e-156, 2.3e-403j)
| (2.832606172608546832e-37 - 3.4132244181704764217e-1063j)  +/-  (4.77e-155, 5.19e-402j)
| (5.4107424460210759944e-26 - 3.0599655345612886071e-1057j)  +/-  (1.52e-150, 1.66e-397j)
| (2.330812830644435449e-13 - 1.1110399546445444598e-1049j)  +/-  (5.45e-142, 5.92e-389j)
| (9.3804001590786502318e-24 + 5.0963283590626415845e-1056j)  +/-  (1.29e-149, 1.41e-396j)
| (1.1005739959560595537e-21 - 6.3342379285047601569e-1055j)  +/-  (9.32e-149, 1.01e-395j)
| (2.4903874321349195669e-16 + 9.7459902166936932352e-1052j)  +/-  (7.14e-146, 7.77e-393j)
| (2.3672012032294788873e-45 - 2.2435807729093990226e-1067j)  +/-  (4.65e-161, 5.06e-408j)
| (9.1127500304649361478e-20 + 8.0186924305458872581e-1054j)  +/-  (2.45e-148, 2.67e-395j)
| (6.6768505922666973546e-51 + 3.1398277789010495253e-1070j)  +/-  (8.41e-164, 9.15e-411j)
| (5.2057255683263019424e-34 + 1.7272898058025456752e-1061j)  +/-  (1.37e-156, 1.49e-403j)
| (5.5039427006493804588e-18 - 8.9508963713018507262e-1053j)  +/-  (2.53e-148, 2.75e-395j)
| (2.0000873355164682707e-28 + 1.5292340180091684094e-1058j)  +/-  (2.96e-154, 3.22e-401j)
| (4.9850601103342242265e-12 + 3.3470109970446585239e-1049j)  +/-  (1.96e-146, 2.14e-393j)
| (8.6281189739448666606e-15 - 1.2050267493407108526e-1050j)  +/-  (2.05e-147, 2.23e-394j)
| (4.4028674524075836318e-31 - 5.9701976382120197684e-1060j)  +/-  (6.9e-156, 7.51e-403j)
| (2.0000873355164682707e-28 - 3.0717724630856474142e-1059j)  +/-  (2.21e-170, 2.4e-417j)
| (5.5039427006493804588e-18 + 7.4984573440824017594e-1054j)  +/-  (9.1e-165, 9.9e-412j)
| (1.1005739959560595537e-21 + 9.0574570498750358764e-1056j)  +/-  (3.19e-167, 3.47e-414j)
| (4.4028674524075836318e-31 + 1.3359630689975980843e-1060j)  +/-  (2.27e-172, 2.47e-419j)
| (6.6768505922666973546e-51 - 1.0765828376394980717e-1070j)  +/-  (9e-181, 9.79e-428j)
| (5.4107424460210759944e-26 + 5.449794543447837364e-1058j)  +/-  (5.31e-170, 5.78e-417j)
| (9.3804001590786502318e-24 - 7.7430765427455909049e-1057j)  +/-  (4.79e-169, 5.21e-416j)
| (1.3549212166031911724e-08 - 5.4274934437443617229e-1048j)  +/-  (5.3e-155, 5.76e-402j)
| (0.03258104828090394324 - 4.939564698412492209e-1045j)  +/-  (8.53e-139, 9.28e-386j)
| (6.5129565774966606903e-06 + 2.1394303521095655931e-1047j)  +/-  (1.32e-156, 1.43e-403j)
| (2.832606172608546832e-37 + 9.1782448086236112997e-1064j)  +/-  (1.27e-176, 1.39e-423j)
| (2.4903874321349195669e-16 - 5.471497324974229987e-1053j)  +/-  (3.75e-167, 4.08e-414j)
| (5.5072066713249745944e-41 - 1.1797233888581053104e-1065j)  +/-  (1.49e-178, 1.62e-425j)
| (9.1127500304649361478e-20 - 8.9107868859226253082e-1055j)  +/-  (2.91e-168, 3.16e-415j)
| (8.5512772763777480369e-11 - 4.5539202388869476998e-1050j)  +/-  (1.49e-165, 1.62e-412j)
| (3.58259717268770156e-05 - 1.9824813346143399636e-1046j)  +/-  (2.18e-158, 2.37e-405j)
| (0.0001665294702157253057 + 1.4057766548030723419e-1046j)  +/-  (3.41e-158, 3.71e-405j)
| (5.2057255683263019424e-34 - 4.2550038320285610047e-1062j)  +/-  (1.17e-175, 1.28e-422j)
| (4.9850601103342242265e-12 + 1.0025561263615765362e-1050j)  +/-  (1.46e-166, 1.58e-413j)
| (1.1895961672466542523e-09 + 1.8699510858893681991e-1049j)  +/-  (2.57e-165, 2.79e-412j)
| (0.090288280587517783817 - 1.5131217056980867811e-1044j)  +/-  (1.66e-151, 1.8e-398j)
| (6.5129565774966606903e-06 + 8.7677958630931480358e-1047j)  +/-  (3.9e-162, 4.24e-409j)
| (0.0063205323499002442921 - 2.8739034452627134316e-1045j)  +/-  (9.68e-157, 1.05e-403j)
| (3.58259717268770156e-05 - 5.692814145615355036e-1047j)  +/-  (2.22e-161, 2.42e-408j)
| (2.3672012032294788873e-45 + 7.0878526753544777296e-1068j)  +/-  (2.26e-182, 2.46e-429j)
| (1.27394368269843341e-07 + 1.4417501222402648985e-1047j)  +/-  (2.26e-164, 2.45e-411j)
| (8.6281189739448666606e-15 + 3.5011486544015360963e-1052j)  +/-  (1.95e-168, 2.12e-415j)
| (1.3549212166031911724e-08 - 6.9783988887402632121e-1049j)  +/-  (1.65e-165, 1.8e-412j)
| (0.058682015985830131824 + 8.7222332199960233434e-1045j)  +/-  (5.19e-154, 5.65e-401j)
| (0.015502306718837723022 + 4.9030009434005721214e-1045j)  +/-  (1.96e-158, 2.13e-405j)
| (0.00065675083174334594574 - 3.2343568484553914883e-1046j)  +/-  (1.19e-161, 1.3e-408j)
| (0.03258104828090394324 - 8.0179387321307395133e-1045j)  +/-  (2.96e-157, 3.22e-404j)
| (8.5512772763777480369e-11 - 7.4492179850960350898e-1049j)  +/-  (3.9e-167, 4.24e-414j)
| (0.0063205323499002442921 - 1.409885775083887093e-1045j)  +/-  (1.4e-160, 1.53e-407j)
| (0.058682015985830131824 + 1.2709404160109235643e-1044j)  +/-  (3.51e-157, 3.82e-404j)
| (0.015502306718837723022 + 2.7014543695895091562e-1045j)  +/-  (1.62e-159, 1.77e-406j)
| (0.0001665294702157253057 + 4.2207690328883968175e-1046j)  +/-  (5.06e-164, 5.51e-411j)
| (1.1895961672466542523e-09 + 1.9885080998232615137e-1048j)  +/-  (5.4e-167, 5.88e-414j)
| (0.090288280587517783817 - 1.9859904361413344104e-1044j)  +/-  (2.02e-159, 2.2e-406j)
| (2.330812830644435449e-13 - 1.983278102462029524e-1051j)  +/-  (9.42e-170, 1.02e-416j)
| (0.10964675094305348145 + 5.5679097370780554556e-1044j)  +/-  (6.89e-160, 7.5e-407j)
| (0.11699289383020766546 + 2.6270372892837726505e-1044j)  +/-  (3.22e-160, 3.5e-407j)
| (0.00065675083174334594574 - 8.4662013393044596593e-1046j)  +/-  (3.51e-164, 3.82e-411j)
| (0.12173777979812161942 - 4.7529291264959054037e-1044j)  +/-  (1.58e-160, 1.72e-407j)
| (9.9588183747367329774e-07 - 3.6551908320150917802e-1047j)  +/-  (1.15e-165, 1.25e-412j)
| (0.0022050096411368295654 + 6.9633454294129655186e-1046j)  +/-  (3.42e-164, 3.72e-411j)
| (0.12173777979812161942 - 4.3923934857131558938e-1044j)  +/-  (2.58e-161, 2.81e-408j)
| (9.9588183747367329774e-07 - 7.4329777100592726699e-1048j)  +/-  (1.2e-167, 1.31e-414j)
| (0.11699289383020766546 + 3.1186011666207915644e-1044j)  +/-  (3.58e-163, 4.1e-410j)
| (0.0022050096411368295654 + 1.6029450480188053346e-1045j)  +/-  (2.16e-165, 2.43e-412j)
| (1.27394368269843341e-07 + 2.3781324644264057186e-1048j)  +/-  (3.42e-168, 3.71e-415j)
