Starting with polynomial:
P : t^3 - 3*t
Extension levels are: 3 70
-------------------------------------------------
Trying to find an order 70 Kronrod extension for:
P1 : t^3 - 3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^73 - 23293494351119190465563086097390638142347/9080793633948628910411934536486610364*t^71 + 28232908817535069812045283229371371828266735/9080793633948628910411934536486610364*t^69 - 1266087941575009091648907871205804285174696835/534164331408742877083054972734506492*t^67 + 681796163362117098241898257586405451469203213615/534164331408742877083054972734506492*t^65 - 69031270569939383791785719693835468768041646175110/133541082852185719270763743183626623*t^63 + 21859193418896150838767763704871892824859644472701630/133541082852185719270763743183626623*t^61 - 5555019447016709860507996348343231890752967371598723950/133541082852185719270763743183626623*t^59 + 1153945706145177914693172081410325838042746461097599620650/133541082852185719270763743183626623*t^57 - 198579928709245842746714836037190417433257825872095262418225/133541082852185719270763743183626623*t^55 + 28590232601018900090244312711186033358659888977468104528015725/133541082852185719270763743183626623*t^53 - 65452271864234964167967116276552866630955069194198329750913725/2519643072682749420203089494030691*t^51 + 6728560720212228840302110948344628054232684631016632457647035625/2519643072682749420203089494030691*t^49 - 588254880346384881507928751673175730616726027410464479846858296250/2519643072682749420203089494030691*t^47 + 43844881758688880731070028235041091225286131830279310763721205241250/2519643072682749420203089494030691*t^45 - 2789693485490276845353766247248681493410559747909226250871631091541250/2519643072682749420203089494030691*t^43 + 151569948233818754306161893736196238890929251243942265386119335084717500/2519643072682749420203089494030691*t^41 - 14055433848450542059434105413235519190347062365471907161848260254267303125/5039286145365498840406178988061382*t^39 + 555289988516983835497917228879348212848990280895460230221494797639406340625/5039286145365498840406178988061382*t^37 - 18646759730613366170511625302769136309111033962032091999928279950760136628125/5039286145365498840406178988061382*t^35 + 530417036209323749006600494230502251692976577029214670232912279542418785690625/5039286145365498840406178988061382*t^33 - 6362311628299312455823178848845542491530170092077395015025760612625095512731250/2519643072682749420203089494030691*t^31 + 128012880380149326480901312221248892731070167320703748323941111099438929074156250/2519643072682749420203089494030691*t^29 - 2145615183407826817628385586258577574647938057971858409431167317436532108956906250/2519643072682749420203089494030691*t^27 + 29711049311321036010761940717988584805673410543133002753666803494553629356116843750/2519643072682749420203089494030691*t^25 - 336509718783631257764504906843345670985448723861130915232833419659175719424867203125/2519643072682749420203089494030691*t^23 + 3079660461359490426929470417035367924946637687106940259526203651464542127069694890625/2519643072682749420203089494030691*t^21 - 22437508374745451192367053067577296639544719151660829213255989013533894664612355703125/2519643072682749420203089494030691*t^19 + 127774266091243644284762017659085575376616636643420465920132049506455390939097551640625/2519643072682749420203089494030691*t^17 - 555815413531812046727905591566524792388005315375943379635768976037463057970371932343750/2519643072682749420203089494030691*t^15 + 1793447527156064510559245333871717206051571033760288423726836088639042575206036816718750/2519643072682749420203089494030691*t^13 - 4130329236843915319049162760849245671681278392547498434220048366756878287297748576718750/2519643072682749420203089494030691*t^11 + 6442069361026446056107341262284537224266047967495294680344998095140587008116355547265625/2519643072682749420203089494030691*t^9 - 25244226965355982505886257582659345965075921590398151680905984261459444916100534087109375/10078572290730997680812357976122764*t^7 + 13821462411978091692949869012849744154558554608365478713344402804525539698013797744921875/10078572290730997680812357976122764*t^5 - 3443114939008694138630081375108708716330986218239423253852048077454524001906109502734375/10078572290730997680812357976122764*t^3 + 244770051454351601844302395545505163327579736174059144371903184229907817031642113671875/10078572290730997680812357976122764*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:   73 out of 73
Indefinite weights: 0 out of 73
Negative weights:   0 out of 73
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (12.49657256025439392 - 1.1762666400408963908e-1084j)  +/-  (6.87e-494, 6.87e-494j)
| (15.012058457415242647 + 4.9290475393145625965e-1087j)  +/-  (6.89e-497, 6.89e-497j)
| (-15.885070329336817068 - 1.9771316631743272175e-1084j)  +/-  (2.5e-498, 2.5e-498j)
| (-9.584262993688650049 - 2.2003129815604082406e-1081j)  +/-  (7.89e-493, 7.89e-493j)
| (15.885070329336817068 - 9.8556165773385692526e-1107j)  +/-  (2.56e-498, 2.56e-498j)
| (14.290176924632150248 - 4.0657195947932006593e-1103j)  +/-  (7.81e-496, 7.81e-496j)
| (-12.49657256025439392 + 6.5005862686771857253e-1103j)  +/-  (7.01e-494, 7.01e-494j)
| (-4.6995332706679908961 + 6.9431087205105394165e-1125j)  +/-  (3.11e-497, 3.11e-497j)
| (11.459898255412780038 - 1.1367423786849846813e-1121j)  +/-  (3.33e-493, 3.33e-493j)
| (11.967259818591307909 + 1.909854239482374769e-1122j)  +/-  (1.87e-493, 1.87e-493j)
| (-11.967259818591307909 + 3.5424507362058635382e-1127j)  +/-  (1.71e-493, 1.71e-493j)
| (13.646585230545750112 + 1.1283377972379887929e-1146j)  +/-  (4.78e-495, 4.78e-495j)
| (-7.8684813723896801563 + 1.7357696067191505294e-1155j)  +/-  (2.04e-493, 2.04e-493j)
| (-10.970517572934780527 - 4.2460818829201111916e-1184j)  +/-  (5.4e-493, 5.4e-493j)
| (-14.290176924632150248 + 1.1194028353818227498e-1205j)  +/-  (7.99e-496, 7.99e-496j)
| (3.1950236116560110493 - 6.4054477052161390312e-1235j)  +/-  (2.4e-500, 2.4e-500j)
| (-11.459898255412780038 + 3.3441373849913535285e-1226j)  +/-  (3.39e-493, 3.39e-493j)
| (-15.012058457415242647 + 2.4872208004986000587e-1245j)  +/-  (7.14e-497, 7.14e-497j)
| (-1.0222541340789418384 + 6.2481336587173411917e-1273j)  +/-  (1.63e-506, 1.63e-506j)
| (-3.1950236116560110493 + 1.6107386154072203679e-1266j)  +/-  (2.28e-500, 2.28e-500j)
| (6.6483111262726735908 + 5.7095772625270440717e-1259j)  +/-  (1.67e-494, 1.67e-494j)
| (-13.053487723445517 + 4.8134895392505658928e-1298j)  +/-  (2.18e-494, 2.18e-494j)
| (-9.1434909433888710043 + 1.8678978862566986232e-1356j)  +/-  (7.19e-493, 7.19e-493j)
| (-10.496193634565612627 - 7.1962085140637093393e-1393j)  +/-  (7.27e-493, 7.27e-493j)
| (-1.7320508075688772935 + 3.025872149727645714e-1418j)  +/-  (2.9e-504, 2.9e-504j)
| (2.0933498594220660058 - 3.6897836678159311145e-1417j)  +/-  (3.63e-503, 3.63e-503j)
| (8.7112207853239877419 - 1.2146711651862947623e-1406j)  +/-  (5.68e-493, 5.68e-493j)
| (13.053487723445517 - 9.9903542345543457299e-1409j)  +/-  (1.99e-494, 1.99e-494j)
| (-6.6483111262726735908 - 1.1847169827459971184e-1405j)  +/-  (1.67e-494, 1.67e-494j)
| (-13.646585230545750112 - 9.7436097431068366158e-1416j)  +/-  (4.66e-495, 4.66e-495j)
| (-4.3194817537724747291 - 1.9884900898496603392e-1427j)  +/-  (6.18e-498, 6.18e-498j)
| (4.3194817537724747291 - 2.0961020539295122572e-1427j)  +/-  (6.21e-498, 6.21e-498j)
| (9.584262993688650049 + 3.4714505889688012829e-1421j)  +/-  (8.04e-493, 8.04e-493j)
| (6.251119503323699159 + 6.3690567031524119022e-1426j)  +/-  (6.29e-495, 6.29e-495j)
| (-2.4578683091183765011 + 7.1175918024135290857e-1435j)  +/-  (3.22e-502, 3.22e-502j)
| (3.9421311014044369114 + 1.2329925699966609521e-1430j)  +/-  (1.16e-498, 1.16e-498j)
| (10.970517572934780527 - 1.6379854571117775142e-1423j)  +/-  (5.55e-493, 5.55e-493j)
| (1.7320508075688772935 + 1.9313329503460853281e-1446j)  +/-  (3.06e-504, 3.06e-504j)
| (-8.2864888844368738464 - 5.7124220936067183725e-1434j)  +/-  (3.27e-493, 3.27e-493j)
| (9.1434909433888710043 + 3.8799563014039840216e-1451j)  +/-  (7.04e-493, 7.04e-493j)
| (-2.0933498594220660058 - 2.2075099090507180366e-1460j)  +/-  (3.56e-503, 3.56e-503j)
| (-5.0824735256064445825 + 1.0962352932947239288e-1449j)  +/-  (1.37e-496, 1.37e-496j)
| (5.0824735256064445825 - 4.644487318059118266e-1456j)  +/-  (1.38e-496, 1.38e-496j)
| (3.5673400227948033637 + 5.5031199833543103132e-1459j)  +/-  (1.76e-499, 1.76e-499j)
| (-7.049953378702825435 + 3.4921914633299089667e-1451j)  +/-  (4.4e-494, 4.4e-494j)
| (-2.8251701312619993768 - 8.5320859187246107333e-1475j)  +/-  (2.75e-501, 2.75e-501j)
| (-6.251119503323699159 + 4.2675336347219185268e-1466j)  +/-  (6.36e-495, 6.36e-495j)
| (7.4565028614066660018 - 8.8997189099915449379e-1480j)  +/-  (1.07e-493, 1.07e-493j)
| (2.4578683091183765011 + 4.0671376738258083166e-1498j)  +/-  (3.34e-502, 3.34e-502j)
| (4.6995332706679908961 - 2.0861110821841404456e-1493j)  +/-  (3.02e-497, 3.02e-497j)
| (-8.7112207853239877419 + 8.7105848110037518534e-1488j)  +/-  (5.31e-493, 5.31e-493j)
| (5.4685318735422523178 + 2.0986939051326986815e-1510j)  +/-  (5.43e-496, 5.43e-496j)
| (-7.4565028614066660018 + 1.2905618502214227488e-1514j)  +/-  (9.98e-494, 9.98e-494j)
| (-7.8034596818477623376e-1583 - 2.4820234741526330571e-1583j)  +/-  (5.98e-1581, 5.98e-1581j)
| (10.034693588408951245 + 5.1425868066556104791e-1525j)  +/-  (8.79e-493, 8.79e-493j)
| (1.3746827583149426314 + 1.2247035044634858512e-1541j)  +/-  (2.72e-505, 2.72e-505j)
| (-0.33572981780734714473 + 1.4781540025745516724e-1544j)  +/-  (9.61e-509, 9.61e-509j)
| (-5.8579773667171497213 + 8.4799561737934967417e-1530j)  +/-  (1.85e-495, 1.85e-495j)
| (8.2864888844368738464 + 8.9410141345743364056e-1539j)  +/-  (3.45e-493, 3.45e-493j)
| (0.33572981780734714473 + 1.9751272918966468667e-1566j)  +/-  (7.66e-509, 7.66e-509j)
| (0.67584059839372927548 + 9.4772895257899248561e-1565j)  +/-  (1.23e-507, 1.23e-507j)
| (-3.9421311014044369114 + 8.3173248847627020974e-1551j)  +/-  (1.18e-498, 1.18e-498j)
| (-3.5673400227948033637 + 1.9770341090009989999e-1552j)  +/-  (1.78e-499, 1.78e-499j)
| (-10.034693588408951245 + 2.5481060755260294749e-1556j)  +/-  (9.11e-493, 9.11e-493j)
| (1.0222541340789418384 - 1.2129984621054583223e-1589j)  +/-  (1.61e-506, 1.61e-506j)
| (7.8684813723896801563 + 2.4070392657625933647e-1576j)  +/-  (1.91e-493, 1.91e-493j)
| (10.496193634565612627 - 1.0882638243023166511e-1575j)  +/-  (7.42e-493, 7.42e-493j)
| (-5.4685318735422523178 + 2.2611186303000244703e-1576j)  +/-  (5.3e-496, 5.3e-496j)
| (-0.67584059839372927548 + 6.7818704342970486779e-1593j)  +/-  (1.23e-507, 1.23e-507j)
| (5.8579773667171497213 - 1.8494543860945152249e-1580j)  +/-  (2.06e-495, 2.06e-495j)
| (2.8251701312619993768 + 2.4316297638160220577e-1586j)  +/-  (2.78e-501, 2.78e-501j)
| (7.049953378702825435 + 3.2610388609672564735e-1579j)  +/-  (4.28e-494, 4.28e-494j)
| (-1.3746827583149426314 + 7.1159603602947233297e-1591j)  +/-  (2.54e-505, 2.54e-505j)
-------------------------------------------------
The weights are:
| (2.6561032113841818165e-35 - 1.771066779456025683e-1110j)  +/-  (1.08e-171, 1.57e-416j)
| (3.5893105323973020181e-50 - 4.8723481042114151616e-1118j)  +/-  (1.05e-177, 1.52e-422j)
| (6.4709170753621604878e-56 - 2.4143023264032194658e-1120j)  +/-  (1.81e-181, 2.62e-426j)
| (2.0087133165927818612e-21 - 2.1634122100254215935e-1101j)  +/-  (4.86e-166, 7.05e-411j)
| (6.4709170753621604878e-56 + 5.9726941512781643776e-1121j)  +/-  (6.42e-180, 9.3e-425j)
| (1.2233352434968005637e-45 + 9.7319314527885147588e-1116j)  +/-  (1.69e-176, 2.45e-421j)
| (2.6561032113841818165e-35 + 1.3428048720527254312e-1109j)  +/-  (1.85e-175, 2.69e-420j)
| (2.43517569270909455e-06 - 6.2704690101395984252e-1095j)  +/-  (6.54e-148, 9.49e-393j)
| (6.0281902933146164495e-30 - 9.6453140447562322195e-1108j)  +/-  (1.96e-171, 2.85e-416j)
| (1.6446163003313835628e-32 + 4.7129735269061946164e-1109j)  +/-  (3.17e-172, 4.6e-417j)
| (1.6446163003313835628e-32 - 4.2623538457349392144e-1108j)  +/-  (4.82e-175, 6.99e-420j)
| (8.9285185811482255038e-42 - 8.9443247117225177621e-1114j)  +/-  (3.23e-176, 4.68e-421j)
| (5.9511599194871046766e-15 - 5.3801915907307523438e-1099j)  +/-  (4.97e-165, 7.21e-410j)
| (1.4102112884406040038e-27 - 2.3382317926813723525e-1105j)  +/-  (3.04e-173, 4.41e-418j)
| (1.2233352434968005637e-45 - 4.9372856351499987267e-1115j)  +/-  (7.16e-182, 1.04e-426j)
| (0.00089890203680102242869 - 6.5395508847333305865e-1094j)  +/-  (7.38e-147, 1.07e-391j)
| (6.0281902933146164495e-30 + 1.0821802539580306266e-1106j)  +/-  (1.46e-174, 2.11e-419j)
| (3.5893105323973020181e-50 + 2.2079284472309823651e-1117j)  +/-  (8.69e-184, 1.26e-428j)
| (0.082705365882555106827 - 2.0162402628859871807e-1092j)  +/-  (2.33e-123, 3.38e-368j)
| (0.00089890203680102242869 - 1.30799286168097913e-1093j)  +/-  (6.39e-149, 9.27e-394j)
| (4.0210752639563596474e-11 + 5.5069119228972205601e-1098j)  +/-  (1.38e-167, 2e-412j)
| (2.284308209873141354e-38 - 3.1659704265594712762e-1111j)  +/-  (5.67e-179, 8.22e-424j)
| (1.2203593659150186798e-19 + 8.1861862077221721575e-1101j)  +/-  (1.78e-171, 2.58e-416j)
| (2.2265976423712087128e-25 + 4.6655208623220587912e-1104j)  +/-  (1.16e-173, 1.68e-418j)
| (0.0319993294252561524 - 1.0261077814245084412e-1092j)  +/-  (3.31e-140, 4.8e-385j)
| (0.016190315812292202548 + 4.2897353964789852404e-1093j)  +/-  (6.61e-145, 9.59e-390j)
| (5.6808694767142169618e-18 - 1.4111268073591898653e-1101j)  +/-  (7.59e-176, 1.1e-420j)
| (2.284308209873141354e-38 + 4.8518349151777996463e-1112j)  +/-  (1.11e-182, 1.62e-427j)
| (4.0210752639563596474e-11 + 3.0447146280341177905e-1097j)  +/-  (5.57e-168, 8.08e-413j)
| (8.9285185811482255038e-42 + 5.1149130324604358904e-1113j)  +/-  (2.18e-181, 3.16e-426j)
| (1.3417094139101805775e-05 + 1.4772904481528452566e-1094j)  +/-  (5.1e-160, 7.39e-405j)
| (1.3417094139101805775e-05 + 5.5938965924275130932e-1095j)  +/-  (2.18e-163, 3.16e-408j)
| (2.0087133165927818612e-21 - 2.3057578800366569957e-1103j)  +/-  (1.69e-178, 2.45e-423j)
| (5.155474931552641791e-10 - 2.1451955642725799969e-1097j)  +/-  (6.28e-171, 9.1e-416j)
| (0.0071209172123543763559 - 4.115202973616670373e-1093j)  +/-  (5.62e-154, 8.15e-399j)
| (6.332905853959561934e-05 - 1.3588482437113570743e-1094j)  +/-  (8.98e-163, 1.3e-407j)
| (1.4102112884406040038e-27 + 1.5769492240182234602e-1106j)  +/-  (6.32e-181, 9.17e-426j)
| (0.0319993294252561524 - 7.1200005291095981897e-1093j)  +/-  (5.52e-151, 8e-396j)
| (2.0645924473981528501e-16 + 1.2594893773951979551e-1099j)  +/-  (2.8e-174, 4.05e-419j)
| (1.2203593659150186798e-19 + 1.9266816989546434491e-1102j)  +/-  (1.15e-177, 1.66e-422j)
| (0.016190315812292202548 + 6.6872847551327386165e-1093j)  +/-  (2.22e-154, 3.22e-399j)
| (3.7714788043259990714e-07 + 2.4871654974224674244e-1095j)  +/-  (1.83e-167, 2.66e-412j)
| (3.7714788043259990714e-07 + 7.6340741687173568778e-1096j)  +/-  (4.71e-169, 6.84e-414j)
| (0.00025695417733267177112 + 3.0815288967956712156e-1094j)  +/-  (3.69e-163, 5.35e-408j)
| (2.5982996853591189938e-12 - 8.4705488244572361497e-1098j)  +/-  (1.06e-172, 1.54e-417j)
| (0.0027182479199695552794 + 2.3898599518924299324e-1093j)  +/-  (8.73e-161, 1.27e-405j)
| (5.155474931552641791e-10 - 1.0191578129098112065e-1096j)  +/-  (3.04e-171, 4.41e-416j)
| (1.3789579749445821233e-13 + 2.7480742869939936149e-1099j)  +/-  (1.06e-176, 1.54e-421j)
| (0.0071209172123543763559 - 2.4353297483626981756e-1093j)  +/-  (6.15e-162, 8.92e-407j)
| (2.43517569270909455e-06 - 2.1443561487748977561e-1095j)  +/-  (4.62e-169, 6.69e-414j)
| (5.6808694767142169618e-18 - 2.9571591587093474227e-1100j)  +/-  (9.61e-177, 1.39e-421j)
| (4.9619959815997787888e-08 - 2.5168186505159892998e-1096j)  +/-  (6.95e-172, 1.01e-416j)
| (1.3789579749445821233e-13 + 2.2008726349759896809e-1098j)  +/-  (1.76e-174, 2.55e-419j)
| (0.13359903787531605297 + 2.9927088659331165839e-1092j)  +/-  (3.5e-159, 5.08e-404j)
| (2.4770579440135297832e-23 + 2.3910649970278083606e-1104j)  +/-  (2.65e-182, 3.85e-427j)
| (0.055066863508469161176 + 1.1123159729899502113e-1092j)  +/-  (4.73e-162, 6.86e-407j)
| (0.12721084399686433915 - 2.9168175458465280415e-1092j)  +/-  (6.2e-160, 8.99e-405j)
| (5.5175868450063220996e-09 + 3.1745155340480219292e-1096j)  +/-  (1.16e-172, 1.69e-417j)
| (2.0645924473981528501e-16 + 9.1464126157764513416e-1101j)  +/-  (3.45e-179, 5.01e-424j)
| (0.12721084399686433915 - 2.7193854222643678278e-1092j)  +/-  (1.83e-161, 2.66e-406j)
| (0.10895312691814828076 + 2.2058270001115480227e-1092j)  +/-  (4.52e-162, 6.55e-407j)
| (6.332905853959561934e-05 - 3.2576900385505799461e-1094j)  +/-  (1.02e-169, 1.48e-414j)
| (0.00025695417733267177112 + 6.7355099831059379898e-1094j)  +/-  (4.44e-169, 6.44e-414j)
| (2.4770579440135297832e-23 - 1.0414523556227814136e-1102j)  +/-  (1.08e-180, 1.56e-425j)
| (0.082705365882555106827 - 1.6275905450938252354e-1092j)  +/-  (2.92e-165, 4.23e-410j)
| (5.9511599194871046766e-15 - 5.2892735114290646978e-1100j)  +/-  (4.99e-179, 7.24e-424j)
| (2.2265976423712087128e-25 - 2.1187921695914562637e-1105j)  +/-  (4.11e-184, 5.95e-429j)
| (4.9619959815997787888e-08 - 9.2049635323795750334e-1096j)  +/-  (5.31e-174, 7.7e-419j)
| (0.10895312691814828076 + 2.5405186825960020168e-1092j)  +/-  (4.08e-169, 5.91e-414j)
| (5.5175868450063220996e-09 + 7.660256108592006865e-1097j)  +/-  (3.93e-176, 5.7e-421j)
| (0.0027182479199695552794 + 1.3016940563925317462e-1093j)  +/-  (1.47e-172, 2.13e-417j)
| (2.5982996853591189938e-12 - 1.2905322886531118643e-1098j)  +/-  (5.59e-178, 8.1e-423j)
| (0.055066863508469161176 + 1.484827489101492305e-1092j)  +/-  (1.22e-171, 1.76e-416j)
