Starting with polynomial:
P : t
Extension levels are: 1 2 66
-------------------------------------------------
Trying to find an order 2 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Trying to find an order 66 Kronrod extension for:
P2 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^69 - 29416145360067734608038557393760395427/12899315859236120166926605504352704*t^67 + 31584683012233305857088598242248983406985/12899315859236120166926605504352704*t^65 - 1328158750919508347882924755713486819008265/806207241202257510432912844022044*t^63 + 628694089441573733036324006643837012328285635/806207241202257510432912844022044*t^61 - 445725537522582581140168920959332910421875266905/1612414482404515020865825688044088*t^59 + 122977269948833281262141328792291710949845193870315/1612414482404515020865825688044088*t^57 - 13548726049012350997482471513175556511659961150617175/806207241202257510432912844022044*t^55 + 2427611791991087034706879355360542386616348968378422925/806207241202257510432912844022044*t^53 - 1433267789663557929141053894190705665756229652970279162925/3224828964809030041731651376088176*t^51 + 175919173566929922347490890423043058271589925063311401742375/3224828964809030041731651376088176*t^49 - 4519493723801484124224748940455519671165691581421471800206625/806207241202257510432912844022044*t^47 + 390704723571565371980056889795486078016177248070410549387596875/806207241202257510432912844022044*t^45 - 57005477484426704401821379909675084830507178726044996763925304375/1612414482404515020865825688044088*t^43 + 3515483499542997663560106824057199249024195567115794485447133733125/1612414482404515020865825688044088*t^41 - 91679107836639592414208080267703051057138534908312769242976332464375/806207241202257510432912844022044*t^39 + 4041614688384750080006873208892588004808953232359763906865292380093125/806207241202257510432912844022044*t^37 - 32504532946603445954801517462103158699113037742122008652693826133053125/174315079178866488742251425734496*t^35 + 1017258676499942237943286933726895294872632812335110011450254416814659375/174315079178866488742251425734496*t^33 - 3334952065937852148269573578357637948839785292324824875481046614346884375/21789384897358311092781428216812*t^31 + 72918247956154263624852339825002752516731329223197708679846804272283028125/21789384897358311092781428216812*t^29 - 2640889267997800639027567632856696345286922482127271908184025290758705121875/43578769794716622185562856433624*t^27 + 39284445676069562849129841916384703510651908283459344424650223933144806265625/43578769794716622185562856433624*t^25 - 237617631426827887666908143830501937926770999973973927345459577866225092265625/21789384897358311092781428216812*t^23 + 2308966089019172185766303400674967491598769888296787039005403204609206931171875/21789384897358311092781428216812*t^21 - 70998356130705933071876723980594029021775048302762523955401312869521778094265625/87157539589433244371125712867248*t^19 + 423655470601264361540114107017117873296814394205644753132223244191299567865296875/87157539589433244371125712867248*t^17 - 478972121765115521827678729320642044524455438922106280998671599297461564310234375/21789384897358311092781428216812*t^15 + 1591695635399062484212607186768425376698458930389141328810093897160935995185078125/21789384897358311092781428216812*t^13 - 7462425759031548786384185711005969706314232914206204144983669321558517771595078125/43578769794716622185562856433624*t^11 + 11664815654697338521863658339811440955252442958136734047479654595552690635287734375/43578769794716622185562856433624*t^9 - 5602364952292357317303663605484350776797363236261860933058273478337605690571640625/21789384897358311092781428216812*t^7 + 2908244808880096034138011251907157288613652717174654702514680072254683013090234375/21789384897358311092781428216812*t^5 - 10375455116694945836584209758619196993716537263284669904047845693819695959965234375/348630158357732977484502851468992*t^3 + 586793765457355774739240758726528971676756750344501233328366321474199602308203125/348630158357732977484502851468992*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:   69 out of 69
Indefinite weights: 0 out of 69
Negative weights:   0 out of 69
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (10.91363173269995607 - 6.9832737801027567004e-1035j)  +/-  (4.42e-494, 4.42e-494j)
| (6.8481107906895666789 - 4.9703652801040227645e-1036j)  +/-  (5.08e-495, 5.08e-495j)
| (11.427719306517122758 + 2.3484498977253547499e-1035j)  +/-  (2.49e-494, 2.49e-494j)
| (-13.127880991700014761 + 1.1452056907743842892e-1035j)  +/-  (9.67e-496, 9.67e-496j)
| (-15.391208562386270265 + 1.9505265150740747618e-1039j)  +/-  (5.96e-499, 5.96e-499j)
| (11.963827109648268101 - 1.3920660375345606231e-1035j)  +/-  (1.11e-494, 1.11e-494j)
| (15.391208562386270265 - 7.0548504751513937296e-1041j)  +/-  (6.15e-499, 6.15e-499j)
| (-10.91363173269995607 + 2.9333988640995744963e-1033j)  +/-  (4.41e-494, 4.41e-494j)
| (6.434120830072299399 + 2.8795527951493089107e-1047j)  +/-  (1.92e-495, 1.92e-495j)
| (2.1104738756583152929 - 3.4972329040130156107e-1055j)  +/-  (1.6e-503, 1.6e-503j)
| (-14.508868113935086524 - 2.430529115559645437e-1047j)  +/-  (1.5e-497, 1.5e-497j)
| (-10.417554374259398987 + 6.5413592406515043149e-1045j)  +/-  (6.41e-494, 6.41e-494j)
| (-11.427719306517122758 + 8.9765084318495138229e-1066j)  +/-  (2.57e-494, 2.57e-494j)
| (14.508868113935086524 + 2.7789541708680115128e-1082j)  +/-  (1.4e-497, 1.4e-497j)
| (8.124293298381007739 + 1.3296559421635120882e-1076j)  +/-  (3.92e-494, 3.92e-494j)
| (2.4911245736236391703 - 5.7385699813724631001e-1100j)  +/-  (1.71e-502, 1.71e-502j)
| (-9.9365322486269591728 + 7.1959439603434174111e-1089j)  +/-  (8.3e-494, 8.3e-494j)
| (13.778932361915564287 - 2.1272141894608407463e-1106j)  +/-  (1.61e-496, 1.61e-496j)
| (13.127880991700014761 + 1.2469074839460302757e-1105j)  +/-  (8.94e-496, 8.94e-496j)
| (-4.0346331124744559534 + 5.9316165008095906124e-1109j)  +/-  (5.16e-499, 5.16e-499j)
| (-13.778932361915564287 + 1.0186310354987921525e-1102j)  +/-  (1.64e-496, 1.64e-496j)
| (4.4264026323521635468 - 1.587773734229355754e-1109j)  +/-  (2.73e-498, 2.73e-498j)
| (-3.2585382806070719081 + 5.2927500462698414146e-1112j)  +/-  (1.23e-500, 1.23e-500j)
| (9.9365322486269591728 - 2.2621573063003673165e-1103j)  +/-  (7.85e-494, 7.85e-494j)
| (8.5634901702830108438 + 1.3817026753726876872e-1105j)  +/-  (5.7e-494, 5.7e-494j)
| (7.6925319142208657824 - 6.5940964396852966116e-1107j)  +/-  (2.04e-494, 2.04e-494j)
| (12.527660813571660197 + 1.9776756438142010398e-1109j)  +/-  (3.65e-495, 3.65e-495j)
| (-11.963827109648268101 + 2.0042694598004018696e-1111j)  +/-  (1.11e-494, 1.11e-494j)
| (-12.527660813571660197 + 5.8099656567314293868e-1142j)  +/-  (3.85e-495, 3.85e-495j)
| (-0.9854713537856208646 - 8.6827775470756824161e-1166j)  +/-  (1.01e-506, 1.01e-506j)
| (9.4683072530207968436 + 3.0628447728878639845e-1197j)  +/-  (8.53e-494, 8.53e-494j)
| (-9.4683072530207968436 + 3.1235174836096284206e-1278j)  +/-  (8.33e-494, 8.33e-494j)
| (2.8738106103856353128 - 3.8760488176162108555e-1326j)  +/-  (1.61e-501, 1.61e-501j)
| (-9.0111033041248919585 - 5.7760933267131043923e-1356j)  +/-  (7.2e-494, 7.2e-494j)
| (-2.4911245736236391703 + 3.1656440174438431845e-1396j)  +/-  (1.75e-502, 1.75e-502j)
| (-8.5634901702830108438 + 2.406439425670581729e-1395j)  +/-  (5.22e-494, 5.22e-494j)
| (6.0248647872872294237 - 5.2181395749913058253e-1416j)  +/-  (7.09e-496, 7.09e-496j)
| (1.7320508075688772935 + 7.2455994014270958214e-1424j)  +/-  (1.52e-504, 1.52e-504j)
| (-4.8209918935254833995 - 5.3202161391912753041e-1413j)  +/-  (1.3e-497, 1.3e-497j)
| (-5.619865824627826405 + 2.7414488753945362907e-1413j)  +/-  (2.29e-496, 2.29e-496j)
| (-6.0248647872872294237 - 4.7290926317713046013e-1447j)  +/-  (7.06e-496, 7.06e-496j)
| (-7.2673752464324534096 - 4.3838935760914822581e-1481j)  +/-  (1.06e-494, 1.06e-494j)
| (-4.4264026323521635468 + 1.714251303922148236e-1499j)  +/-  (2.92e-498, 2.92e-498j)
| (7.2673752464324534096 + 7.9754940910513378744e-1496j)  +/-  (1.08e-494, 1.08e-494j)
| (1.3564780368491437434 + 7.9048756405586015093e-1509j)  +/-  (1.22e-505, 1.22e-505j)
| (-5.2187006531567361091 - 2.5257954754697109372e-1496j)  +/-  (6.08e-497, 6.08e-497j)
| (5.619865824627826405 - 4.925786821257479321e-1501j)  +/-  (2.09e-496, 2.09e-496j)
| (5.2187006531567361091 + 7.795580585056193236e-1502j)  +/-  (5.83e-497, 5.83e-497j)
| (0.62404741456342304117 - 1.0205386723532437392e-1512j)  +/-  (7.16e-508, 7.16e-508j)
| (4.0346331124744559534 - 1.7069713908268502869e-1504j)  +/-  (5.71e-499, 5.71e-499j)
| (-2.1104738756583152929 - 9.5061472236802702989e-1510j)  +/-  (1.73e-503, 1.73e-503j)
| (10.417554374259398987 - 2.6972028488514446416e-1498j)  +/-  (6.72e-494, 6.72e-494j)
| (-7.6925319142208657824 - 2.9822318563571211594e-1508j)  +/-  (2.02e-494, 2.02e-494j)
| (3.2585382806070719081 + 2.8233734195645148439e-1529j)  +/-  (1.23e-500, 1.23e-500j)
| (4.8209918935254833995 + 6.6471394758439382481e-1525j)  +/-  (1.4e-497, 1.4e-497j)
| (-6.434120830072299399 + 1.0357427426615075933e-1520j)  +/-  (1.9e-495, 1.9e-495j)
| (-1.7320508075688772935 + 4.8772686418812551883e-1538j)  +/-  (1.47e-504, 1.47e-504j)
| (-3.6454198733018653125 - 3.8391206438405373967e-1532j)  +/-  (9.34e-500, 9.34e-500j)
| (-1.3564780368491437434 - 7.4250570379026060032e-1538j)  +/-  (1.22e-505, 1.22e-505j)
| (0.9854713537856208646 + 5.2471540694679681724e-1540j)  +/-  (9.89e-507, 9.89e-507j)
| (1.7748724481829221099e-1575 - 1.4853618263195854201e-1575j)  +/-  (1.6e-1573, 1.6e-1573j)
| (-2.8738106103856353128 - 7.1237684168566848661e-1534j)  +/-  (1.7e-501, 1.7e-501j)
| (-0.62404741456342304117 + 3.025158421232030143e-1540j)  +/-  (6.68e-508, 6.68e-508j)
| (9.0111033041248919585 - 2.5860960527844825458e-1527j)  +/-  (6.9e-494, 6.9e-494j)
| (0.28774956922463914685 - 4.1624186090817600268e-1576j)  +/-  (5.11e-509, 5.11e-509j)
| (3.6454198733018653125 - 2.4990867897631629829e-1533j)  +/-  (8.68e-500, 8.68e-500j)
| (-8.124293298381007739 - 2.9714859986810811092e-1525j)  +/-  (3.56e-494, 3.56e-494j)
| (-0.28774956922463914685 - 6.6756621380075522687e-1545j)  +/-  (5.11e-509, 5.11e-509j)
| (-6.8481107906895666789 - 1.1007044982918943784e-1533j)  +/-  (5.14e-495, 5.14e-495j)
-------------------------------------------------
The weights are:
| (2.7539246101301393949e-27 + 1.3297085574293354946e-1055j)  +/-  (4.78e-162, 5.21e-407j)
| (1.0891448638613615995e-11 + 1.9324286800116859973e-1046j)  +/-  (2.47e-149, 2.69e-394j)
| (9.1758003354073781521e-30 - 6.5075251646628411883e-1057j)  +/-  (1.68e-163, 1.83e-408j)
| (9.367486935054320508e-39 - 4.1504993462082577185e-1062j)  +/-  (3.01e-170, 3.28e-415j)
| (1.4776340983466071655e-52 + 3.9939139695945813128e-1069j)  +/-  (5.29e-175, 5.76e-420j)
| (1.8170975912512028351e-32 + 2.4763591979583774754e-1058j)  +/-  (9.04e-166, 9.85e-411j)
| (1.4776340983466071655e-52 - 1.039619762466729886e-1068j)  +/-  (1.54e-174, 1.67e-419j)
| (2.7539246101301393949e-27 - 3.0390805169914609062e-1056j)  +/-  (3.11e-166, 3.39e-411j)
| (1.6822034634053751429e-10 - 5.468690401319768488e-1046j)  +/-  (4.08e-151, 4.45e-396j)
| (0.016331761683645408925 + 1.4174363975283525225e-1042j)  +/-  (3.7e-124, 4.03e-369j)
| (6.1007151359138547065e-47 - 2.8347716736208028512e-1066j)  +/-  (5.63e-174, 6.14e-419j)
| (5.2898183522664510176e-25 + 4.5434282378880032979e-1055j)  +/-  (1.36e-165, 1.48e-410j)
| (9.1758003354073781521e-30 + 1.6315394794496053154e-1057j)  +/-  (1.13e-167, 1.23e-412j)
| (6.1007151359138547065e-47 + 7.9022251272828020509e-1066j)  +/-  (4.69e-175, 5.12e-420j)
| (8.0744103292629312004e-16 + 3.0798597300321528689e-1049j)  +/-  (1.07e-160, 1.17e-405j)
| (0.0068400271837329892186 - 8.4839564705895303286e-1043j)  +/-  (1.63e-134, 1.77e-379j)
| (6.8706029476238687447e-23 - 5.5853691197487665842e-1054j)  +/-  (3.16e-166, 3.45e-411j)
| (1.6164506195177449561e-42 - 1.4970304691390557595e-1063j)  +/-  (8.99e-174, 9.79e-419j)
| (9.367486935054320508e-39 + 1.3201028827875525357e-1061j)  +/-  (1.82e-172, 1.98e-417j)
| (4.5466959521724048549e-05 - 1.7206242437025594289e-1044j)  +/-  (9.18e-151, 1e-395j)
| (1.6164506195177449561e-42 + 5.03064334864344407e-1064j)  +/-  (1.02e-175, 1.11e-420j)
| (8.7271875641584818138e-06 + 3.0898800034721625282e-1044j)  +/-  (3.46e-151, 3.77e-396j)
| (0.0007613149241829602201 - 9.367668132098545877e-1044j)  +/-  (5.23e-147, 5.69e-392j)
| (6.8706029476238687447e-23 + 3.0362708456280933221e-1053j)  +/-  (7.45e-167, 8.12e-412j)
| (2.1057108341790109107e-17 - 3.510787594296439392e-1050j)  +/-  (7.55e-164, 8.23e-409j)
| (2.4154144071967535845e-14 - 2.6883919192223305781e-1048j)  +/-  (9.59e-162, 1.04e-406j)
| (1.9272238797015505067e-35 - 6.9374634506702588066e-1060j)  +/-  (6.79e-172, 7.4e-417j)
| (1.8170975912512028351e-32 - 6.7359986743245530779e-1059j)  +/-  (1.02e-174, 1.11e-419j)
| (1.9272238797015505067e-35 + 2.0339130859758742365e-1060j)  +/-  (5.91e-176, 6.44e-421j)
| (0.090228993034118249162 - 4.1136362039746602716e-1042j)  +/-  (4.9e-134, 5.34e-379j)
| (6.2947275421271641311e-21 - 3.5947432639349207111e-1052j)  +/-  (1.05e-167, 1.14e-412j)
| (6.2947275421271641311e-21 + 5.7716819895289165983e-1053j)  +/-  (1.15e-171, 1.25e-416j)
| (0.0024633344748206660021 + 4.8505385524841994348e-1043j)  +/-  (4.13e-152, 4.5e-397j)
| (4.2061287463607234172e-19 - 5.1001111490444685529e-1052j)  +/-  (1.03e-171, 1.13e-416j)
| (0.0068400271837329892186 - 3.9579306647702233738e-1043j)  +/-  (6.59e-154, 7.18e-399j)
| (2.1057108341790109107e-17 + 3.9072717040162828389e-1051j)  +/-  (1.11e-171, 1.21e-416j)
| (2.1297764987398587979e-09 + 1.0447655135610476386e-1045j)  +/-  (1.4e-164, 1.53e-409j)
| (0.033573136685853614709 - 2.2777315923680705164e-1042j)  +/-  (1.01e-148, 1.1e-393j)
| (1.4183468505819886119e-06 - 2.3746787863345555397e-1045j)  +/-  (5.79e-165, 6.31e-410j)
| (2.2289177705651460702e-08 - 2.3917989080311105808e-1046j)  +/-  (1.03e-167, 1.13e-412j)
| (2.1297764987398587979e-09 + 6.6811719177244180739e-1047j)  +/-  (5.34e-169, 5.82e-414j)
| (5.7246652016430005338e-13 - 8.2859947025984538272e-1049j)  +/-  (4.67e-172, 5.09e-417j)
| (8.7271875641584818138e-06 + 6.636747559244105175e-1045j)  +/-  (6.57e-165, 7.16e-410j)
| (5.7246652016430005338e-13 + 2.7898307536502323093e-1047j)  +/-  (1.32e-170, 1.44e-415j)
| (0.059416960850843420763 + 3.5587961071303722745e-1042j)  +/-  (3.13e-154, 3.41e-399j)
| (1.9423350624349255015e-07 + 7.8535879756458120599e-1046j)  +/-  (3.35e-167, 3.66e-412j)
| (2.2289177705651460702e-08 - 2.4280103580903931477e-1045j)  +/-  (9.42e-169, 1.03e-413j)
| (1.9423350624349255015e-07 + 5.8162544046159078382e-1045j)  +/-  (1.52e-168, 1.65e-413j)
| (0.11589833818688259755 + 8.5512116078206939686e-1042j)  +/-  (9.89e-157, 1.08e-401j)
| (4.5466959521724048549e-05 - 6.6556437746685349395e-1044j)  +/-  (5.31e-167, 5.79e-412j)
| (0.016331761683645408925 + 7.4958637632337188137e-1043j)  +/-  (1.79e-163, 1.95e-408j)
| (5.2898183522664510176e-25 - 2.1988456169039302827e-1054j)  +/-  (1.58e-178, 1.72e-423j)
| (2.4154144071967535845e-14 + 1.5611272712477040921e-1049j)  +/-  (1.43e-175, 1.56e-420j)
| (0.0007613149241829602201 - 2.6375634462187428337e-1043j)  +/-  (3.37e-166, 3.67e-411j)
| (1.4183468505819886119e-06 - 1.3670196913638564133e-1044j)  +/-  (1.56e-168, 1.7e-413j)
| (1.6822034634053751429e-10 - 1.7044446496764207776e-1047j)  +/-  (1.81e-173, 1.97e-418j)
| (0.033573136685853614709 - 1.3581234483614559428e-1042j)  +/-  (1.57e-165, 1.71e-410j)
| (0.00020140419951069480344 + 4.1530299152973467643e-1044j)  +/-  (6.15e-169, 6.7e-414j)
| (0.059416960850843420763 + 2.3820182826847088724e-1042j)  +/-  (2e-165, 2.18e-410j)
| (0.090228993034118249162 - 5.4966113739694361598e-1042j)  +/-  (9.37e-165, 1.02e-409j)
| (0.1082310126179047499 + 1.5089880288709100145e-1041j)  +/-  (8.48e-165, 9.23e-410j)
| (0.0024633344748206660021 + 1.9828620972385613676e-1043j)  +/-  (6.47e-168, 7.05e-413j)
| (0.11589833818688259755 + 7.1228595786775704178e-1042j)  +/-  (1.92e-165, 2.09e-410j)
| (4.2061287463607234172e-19 + 3.7399121236115151247e-1051j)  +/-  (1.61e-177, 1.76e-422j)
| (0.12011339114135086672 - 1.2935339029358358771e-1041j)  +/-  (9.14e-166, 9.93e-411j)
| (0.00020140419951069480344 + 1.360754106959786749e-1043j)  +/-  (3.16e-169, 3.44e-414j)
| (8.0744103292629312004e-16 - 2.6249238970521097144e-1050j)  +/-  (3.75e-177, 4.07e-422j)
| (0.12011339114135086672 - 1.1892103090690305857e-1041j)  +/-  (9.32e-168, 7.8e-413j)
| (1.0891448638613615995e-11 + 3.9523117667973946147e-1048j)  +/-  (5.93e-175, 6.48e-420j)
