Starting with polynomial:
P : 2*t
Extension levels are: 1 72
-------------------------------------------------
Trying to find an order 72 Kronrod extension for:
P1 : 2*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 2*t^73 - 2628*t^71 + 1632645*t^69 - 638364195*t^67 + 1411423235145/8*t^65 - 36697004113770*t^63 + 11944874839032135/2*t^61 - 1561365782530629075/2*t^59 + 2671496853909906347325/32*t^57 - 118436360523339181398075/16*t^55 + 35175599075431736875228275/64*t^53 - 2203271614815678791548389225/64*t^51 + 936390436296663486408065420625/512*t^49 - 10588414933508425577075816679375/128*t^47 + 1635153791874658292688422547200625/512*t^45 - 53960075131863723658717944057620625/512*t^43 + 48725947844072942463822303484031424375/16384*t^41 - 587577606354997247357857189072143646875/8192*t^39 + 48377222923228106699130241900273160259375/32768*t^37 - 847874485970261027937387923831103282440625/32768*t^35 + 100897063830461062324549162935901290610434375/262144*t^33 - 158552528876438812224291541756416313816396875/32768*t^31 + 6702447811594913425845051537884871447693140625/131072*t^29 - 59156387206685540236806324443070821907900328125/131072*t^27 + 6921297303182208207706339959839286163224338390625/2097152*t^25 - 20763891909546624623119019879517858489673015171875/1048576*t^23 + 404097281008868925357624002270616784452867141421875/4194304*t^21 - 1571489426145601376390760008830176383983372216640625/4194304*t^19 + 38389241695842547908974280215708594523022378435078125/33554432*t^17 - 22504038235493907394915957367829176099702773565390625/8388608*t^15 + 157528267648457351764411701574804232697919414957734375/33554432*t^13 - 198180723815801184477808269723140808878027651075859375/33554432*t^11 + 10899939809869065146279454834772744488291520809172265625/2147483648*t^9 - 2972710857237017767167124045847112133170414766137890625/1073741824*t^7 + 3672172235410433712382917938987609105681100593464453125/4294967296*t^5 - 524596033630061958911845419855372729383014370494921875/4294967296*t^3 + 174865344543353986303948473285124243127671456831640625/34359738368*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:
| (8.9197179302027118654 - 9.7407573687135833754e-1029j)  +/-  (1.66e-493, 1.66e-493j)
| (-11.31108085913372469 - 2.7614213678099052342e-1038j)  +/-  (4.28e-498, 4.28e-498j)
| (10.185477993538821102 + 1.6871866426359162306e-1035j)  +/-  (1.59e-495, 1.59e-495j)
| (-8.5461882990986894354 - 9.2739147076371742419e-1034j)  +/-  (4.38e-493, 4.38e-493j)
| (11.31108085913372469 + 1.6009335491585632353e-1037j)  +/-  (4e-498, 4e-498j)
| (2.3467355617654574607 - 8.825034875113812941e-1040j)  +/-  (7.03e-500, 7.03e-500j)
| (9.3127299623383141034 - 2.003226682115382789e-1031j)  +/-  (4.86e-494, 4.86e-494j)
| (-8.1881504491623043008 + 5.3853420215590374298e-1040j)  +/-  (1.03e-492, 1.03e-492j)
| (8.1881504491623043008 - 4.672079415395168325e-1048j)  +/-  (1.02e-492, 1.02e-492j)
| (7.5080711279939011476 + 4.1508259775058768423e-1076j)  +/-  (1.65e-492, 1.65e-492j)
| (-9.7312821228925473181 - 7.4785246279504196336e-1094j)  +/-  (1.15e-494, 1.15e-494j)
| (-7.5080711279939011476 - 8.7266521224071533358e-1090j)  +/-  (1.59e-492, 1.59e-492j)
| (-9.3127299623383141034 + 3.8251671042626354153e-1092j)  +/-  (4.81e-494, 4.81e-494j)
| (-10.694938789404631188 - 1.141006872332056668e-1095j)  +/-  (1.46e-496, 1.46e-496j)
| (-8.9197179302027118654 + 3.2127931025946468741e-1092j)  +/-  (1.69e-493, 1.69e-493j)
| (10.694938789404631188 - 1.3808707404014167911e-1102j)  +/-  (1.46e-496, 1.46e-496j)
| (6.2483203822637564656 - 8.5551799972846533727e-1133j)  +/-  (1.39e-492, 1.39e-492j)
| (-6.5534194322069043264 + 8.7977375552254665435e-1163j)  +/-  (1.73e-492, 1.73e-492j)
| (7.1823851209949320532 + 5.1878777969147823746e-1201j)  +/-  (1.93e-492, 1.93e-492j)
| (7.8428000887281046128 + 1.0086707369314790819e-1244j)  +/-  (1.16e-492, 1.16e-492j)
| (-4.7918343564389148116 - 1.3379864641615977654e-1266j)  +/-  (5.22e-494, 5.22e-494j)
| (3.1449629665080241104 + 4.5574405926998221093e-1268j)  +/-  (1.65e-497, 1.65e-497j)
| (-5.3625723452058254651 + 4.6546694992608172251e-1265j)  +/-  (2.6e-493, 2.6e-493j)
| (3.6851023893880593862 - 1.6804531511428536499e-1264j)  +/-  (3.77e-496, 3.77e-496j)
| (-2.0831841274592904941 + 1.8702276873336547027e-1284j)  +/-  (1.05e-500, 1.05e-500j)
| (-3.1449629665080241104 + 4.6703810095862202456e-1276j)  +/-  (1.64e-497, 1.64e-497j)
| (4.7918343564389148116 + 6.2963841605188694826e-1275j)  +/-  (5.29e-494, 5.29e-494j)
| (3.958136635717006725 - 4.2106619546285954356e-1303j)  +/-  (1.35e-495, 1.35e-495j)
| (8.5461882990986894354 - 5.1644854894143954914e-1341j)  +/-  (4.46e-493, 4.46e-493j)
| (-4.2334370704564911292 - 2.1423244378399313722e-1367j)  +/-  (6.41e-495, 6.41e-495j)
| (6.5534194322069043264 - 5.0604854659597463999e-1384j)  +/-  (1.81e-492, 1.81e-492j)
| (5.3625723452058254651 + 7.3080409927278959578e-1412j)  +/-  (2.62e-493, 2.62e-493j)
| (3.4141124491940379828 - 2.2244901397967277966e-1428j)  +/-  (8.88e-497, 8.88e-497j)
| (-5.9485190514660777329 - 2.1569810048536550229e-1425j)  +/-  (9.95e-493, 9.95e-493j)
| (9.7312821228925473181 - 1.1748822581900402959e-1423j)  +/-  (1.07e-494, 1.07e-494j)
| (-5.6534355164057580943 + 2.0324686218118901831e-1428j)  +/-  (4.04e-493, 4.04e-493j)
| (-5.0754980166052255135 + 2.3700308070745777331e-1428j)  +/-  (1.2e-493, 1.2e-493j)
| (1.8206433462185645519 - 1.1465605473130009616e-1436j)  +/-  (1.02e-501, 1.02e-501j)
| (-2.6114443936789565896 - 4.4299519584289352502e-1434j)  +/-  (4.45e-499, 4.45e-499j)
| (-10.185477993538821102 - 2.5369424693131821529e-1430j)  +/-  (1.64e-495, 1.64e-495j)
| (-2.8774654290158658451 - 2.9779244625778762836e-1433j)  +/-  (3.33e-498, 3.33e-498j)
| (-3.958136635717006725 - 5.5260072845737095472e-1432j)  +/-  (1.29e-495, 1.29e-495j)
| (-6.2483203822637564656 + 2.0467501441615072486e-1427j)  +/-  (1.48e-492, 1.48e-492j)
| (0.77786750657853079283 - 2.4182235702818814472e-1441j)  +/-  (4.48e-506, 4.48e-506j)
| (-3.4141124491940379828 + 1.2299687600904064084e-1431j)  +/-  (8.65e-497, 8.65e-497j)
| (-2.3467355617654574607 - 6.8360358924493403634e-1435j)  +/-  (6.83e-500, 6.83e-500j)
| (-7.8428000887281046128 - 7.2751798716756348449e-1427j)  +/-  (1.08e-492, 1.08e-492j)
| (1.5589732800480509544 + 3.6764481633443254578e-1440j)  +/-  (1.04e-502, 1.04e-502j)
| (0.25913092507112633394 - 5.2462458823879442704e-1449j)  +/-  (9.86e-509, 9.86e-509j)
| (4.511246852263892294 - 2.2869639740860453847e-1428j)  +/-  (1.86e-494, 1.86e-494j)
| (5.0754980166052255135 + 5.0424040447451660179e-1444j)  +/-  (1.23e-493, 1.23e-493j)
| (-1.2980396851534750269 - 2.5106276670043451494e-1465j)  +/-  (7.45e-504, 7.45e-504j)
| (-3.6851023893880593862 + 1.8869573190602056818e-1457j)  +/-  (3.57e-496, 3.57e-496j)
| (-6.8645009305993020426 + 1.5990664943736144891e-1452j)  +/-  (2.17e-492, 2.17e-492j)
| (-7.1823851209949320532 + 9.2052193495420348596e-1457j)  +/-  (1.98e-492, 1.98e-492j)
| (5.6534355164057580943 - 1.2446762845878998373e-1456j)  +/-  (4.26e-493, 4.26e-493j)
| (-1.5589732800480509544 + 1.6539717351961889979e-1481j)  +/-  (1.05e-502, 1.05e-502j)
| (-1.8206433462185645519 - 1.5967197674822814144e-1480j)  +/-  (1.01e-501, 1.01e-501j)
| (2.6114443936789565896 - 3.8556907508806470859e-1477j)  +/-  (4.54e-499, 4.54e-499j)
| (2.0831841274592904941 + 2.6513644482422195706e-1479j)  +/-  (1.04e-500, 1.04e-500j)
| (6.8645009305993020426 + 9.4714579602285072812e-1473j)  +/-  (2.06e-492, 2.06e-492j)
| (-4.511246852263892294 + 5.0715841537854156124e-1485j)  +/-  (1.89e-494, 1.89e-494j)
| (-0.77786750657853079283 - 1.2547799005395583777e-1495j)  +/-  (4.69e-506, 4.69e-506j)
| (1.0377130137484732309 - 1.8218729795662152802e-1494j)  +/-  (5.95e-505, 5.95e-505j)
| (0.51838035636125176554 - 6.1671730476901735776e-1497j)  +/-  (3.39e-507, 3.39e-507j)
| (2.8774654290158658451 + 6.4592699304141878143e-1489j)  +/-  (3.37e-498, 3.37e-498j)
| (-0.51838035636125176554 - 9.3561092458424116677e-1497j)  +/-  (3.39e-507, 3.39e-507j)
| (-0.25913092507112633394 + 5.2139977370668900748e-1498j)  +/-  (8.62e-509, 8.62e-509j)
| (4.2334370704564911292 - 2.865741784149410403e-1486j)  +/-  (6.44e-495, 6.44e-495j)
| (5.9485190514660777329 - 8.9436017666578440377e-1498j)  +/-  (1.03e-492, 1.03e-492j)
| (-7.93715862888615325e-1555 + 2.2422226609304931246e-1554j)  +/-  (1.74e-1552, 1.74e-1552j)
| (1.2980396851534750269 - 1.5787390908939525332e-1509j)  +/-  (7.93e-504, 7.93e-504j)
| (-1.0377130137484732309 + 3.7798069046190417432e-1511j)  +/-  (6.09e-505, 6.09e-505j)
-------------------------------------------------
The weights are:
| (6.0389806802044886257e-36 - 8.1075457282746911988e-1060j)  +/-  (3.08e-165, 8.7e-412j)
| (1.097045334512777968e-56 - 1.6641223976141923243e-1070j)  +/-  (7.28e-174, 2.06e-420j)
| (2.3698636911068663879e-46 + 4.261828557012369018e-1065j)  +/-  (8.61e-170, 2.44e-416j)
| (3.9290605843798225558e-33 - 1.2486882117399467284e-1058j)  +/-  (5.29e-166, 1.5e-412j)
| (1.097045334512777968e-56 + 2.5354945915337200697e-1070j)  +/-  (1.57e-173, 4.42e-420j)
| (0.00060460144591195243957 + 1.2521318912051478772e-1042j)  +/-  (4.86e-129, 1.38e-375j)
| (4.9356648255966463786e-39 + 2.1888986555886334953e-1061j)  +/-  (5.17e-167, 1.46e-413j)
| (1.5117414074434629439e-30 + 2.5325785183417303987e-1057j)  +/-  (5.97e-166, 1.69e-412j)
| (1.5117414074434629439e-30 - 4.5670258327074170119e-1057j)  +/-  (2.93e-164, 8.3e-411j)
| (6.1409610836416112298e-26 - 1.0418125422808413383e-1054j)  +/-  (1.82e-162, 5.13e-409j)
| (1.8295476803842760544e-42 + 2.4301345299262436312e-1063j)  +/-  (3.44e-172, 9.71e-419j)
| (6.1409610836416112298e-26 + 5.4566232455526290241e-1055j)  +/-  (1.58e-165, 4.46e-412j)
| (4.9356648255966463786e-39 - 1.3075197394591265677e-1061j)  +/-  (5.66e-171, 1.6e-417j)
| (6.5394985116746441101e-51 + 1.3455290235096296871e-1067j)  +/-  (2.82e-176, 7.97e-423j)
| (6.0389806802044886257e-36 + 4.7331318559104253892e-1060j)  +/-  (1.12e-169, 3.16e-416j)
| (6.5394985116746441101e-51 - 2.1020970236982426231e-1067j)  +/-  (5.18e-177, 1.46e-423j)
| (1.8898071651522673076e-18 - 7.6456025313869175259e-1051j)  +/-  (1.03e-164, 2.92e-411j)
| (3.8739124051695607342e-20 - 4.7987829831732995535e-1052j)  +/-  (4.38e-166, 1.24e-412j)
| (7.1604829638577492307e-24 + 1.2007539516163176438e-1053j)  +/-  (3.97e-167, 1.12e-413j)
| (3.7096451329002690245e-28 + 7.6039793980948620214e-1056j)  +/-  (1.45e-168, 4.09e-415j)
| (1.6969040056110007269e-11 - 1.2521920356522578344e-1047j)  +/-  (1.39e-161, 3.92e-408j)
| (7.6651100775855474195e-06 + 7.526324219138475688e-1044j)  +/-  (2.86e-152, 8.09e-399j)
| (5.2855421926486843273e-14 - 6.4711726980229554929e-1049j)  +/-  (7.32e-164, 2.07e-410j)
| (1.941988135065754176e-07 + 7.1449290146192829909e-1045j)  +/-  (5.95e-156, 1.68e-402j)
| (0.0019352133975236287801 - 2.1548722512366556516e-1043j)  +/-  (3.77e-146, 1.07e-392j)
| (7.6651100775855474195e-06 - 1.0939707560680014083e-1044j)  +/-  (2.05e-154, 5.81e-401j)
| (1.6969040056110007269e-11 + 3.6557830008698326355e-1047j)  +/-  (3.74e-162, 1.06e-408j)
| (2.4285943169750093268e-08 - 2.0985692431493356804e-1045j)  +/-  (4.75e-158, 1.34e-404j)
| (3.9290605843798225558e-33 + 2.1936256330980080575e-1058j)  +/-  (1.32e-172, 3.74e-419j)
| (2.5687327038815620165e-09 - 1.6713814943409875368e-1046j)  +/-  (2.26e-162, 6.39e-409j)
| (3.8739124051695607342e-20 + 1.0152605851991120802e-1051j)  +/-  (1.04e-167, 2.94e-414j)
| (5.2855421926486843273e-14 + 1.6541843105343552577e-1048j)  +/-  (6.63e-165, 1.87e-411j)
| (1.3202034653564462983e-06 - 2.3358918525289853296e-1044j)  +/-  (9.82e-157, 2.78e-403j)
| (7.1984692749157402393e-17 - 2.2194432989623828038e-1050j)  +/-  (9.37e-170, 2.65e-416j)
| (1.8295476803842760544e-42 - 3.9750503918989111429e-1063j)  +/-  (5.69e-178, 1.61e-424j)
| (2.1752466349821180222e-15 + 1.2650527430838515024e-1049j)  +/-  (9.59e-169, 2.71e-415j)
| (1.0447699212823432865e-12 + 2.9883349701862581927e-1048j)  +/-  (5.03e-167, 1.42e-413j)
| (0.0053738931282384631566 + 3.0236673687612249106e-1042j)  +/-  (1.62e-153, 4.59e-400j)
| (0.00016349043374974860492 - 5.5959905135097996181e-1044j)  +/-  (2.49e-159, 7.05e-406j)
| (2.3698636911068663879e-46 - 2.6655574748525608765e-1065j)  +/-  (9.55e-184, 2.7e-430j)
| (3.8161373053170931952e-05 + 2.5659327064330662944e-1044j)  +/-  (1.04e-160, 2.95e-407j)
| (2.4285943169750093268e-08 + 5.3635775905335926338e-1046j)  +/-  (3.72e-165, 1.05e-411j)
| (1.8898071651522673076e-18 + 3.4706736440669781874e-1051j)  +/-  (9.42e-172, 2.66e-418j)
| (0.079987999875462535935 + 3.9118117139375690081e-1042j)  +/-  (2.39e-158, 6.75e-405j)
| (1.3202034653564462983e-06 + 4.3280002456621560318e-1045j)  +/-  (1.03e-163, 2.9e-410j)
| (0.00060460144591195243957 + 1.1368245877014923621e-1043j)  +/-  (2.88e-160, 8.13e-407j)
| (3.7096451329002690245e-28 - 4.1017174482871912517e-1056j)  +/-  (5.56e-177, 1.57e-423j)
| (0.01297247152510639489 - 3.1373842647249200882e-1042j)  +/-  (4.16e-159, 1.18e-405j)
| (0.1367250465995920329 + 3.8435095395952504066e-1042j)  +/-  (1.6e-158, 4.53e-405j)
| (2.2844778933329723269e-10 - 1.5152430236011522403e-1046j)  +/-  (3.63e-170, 1.03e-416j)
| (1.0447699212823432865e-12 - 8.128159547476359719e-1048j)  +/-  (1.06e-171, 3e-418j)
| (0.027268952858838580359 + 9.831419059513840435e-1043j)  +/-  (1.77e-159, 4.99e-406j)
| (1.941988135065754176e-07 - 1.585356492668225429e-1045j)  +/-  (4.76e-166, 1.35e-412j)
| (6.085029311574782796e-22 + 5.8112188020058380443e-1053j)  +/-  (1.87e-175, 5.3e-422j)
| (7.1604829638577492307e-24 - 6.0935754785142407684e-1054j)  +/-  (1.9e-176, 5.38e-423j)
| (2.1752466349821180222e-15 - 3.060593377958299704e-1049j)  +/-  (6.3e-176, 1.78e-422j)
| (0.01297247152510639489 - 6.3279684534596415324e-1043j)  +/-  (3e-164, 8.48e-411j)
| (0.0053738931282384631566 + 3.8171076127692282611e-1043j)  +/-  (1.3e-164, 3.67e-411j)
| (0.00016349043374974860492 + 1.0481623635712003775e-1042j)  +/-  (2.24e-169, 6.35e-416j)
| (0.0019352133975236287801 - 3.6220150678111656847e-1042j)  +/-  (4.48e-168, 1.27e-414j)
| (6.085029311574782796e-22 - 1.1848084838520346573e-1052j)  +/-  (3.44e-179, 9.74e-426j)
| (2.2844778933329723269e-10 + 4.7824515821218666592e-1047j)  +/-  (2.31e-171, 6.53e-418j)
| (0.079987999875462535935 + 1.9641295463670612713e-1042j)  +/-  (4.28e-167, 1.21e-413j)
| (0.049984847265092552608 - 3.7061575223929493074e-1042j)  +/-  (1.92e-167, 5.43e-414j)
| (0.11184219617973975744 - 3.9691209615356244808e-1042j)  +/-  (1.03e-166, 2.93e-413j)
| (3.8161373053170931952e-05 - 2.5257424751426502912e-1043j)  +/-  (1.71e-170, 4.83e-417j)
| (0.11184219617973975744 - 2.5328712906750937455e-1042j)  +/-  (3.03e-168, 8.56e-415j)
| (0.1367250465995920329 + 3.0791033120633502758e-1042j)  +/-  (1.95e-168, 5.52e-415j)
| (2.5687327038815620165e-09 + 5.8291516363845118884e-1046j)  +/-  (2.25e-173, 6.36e-420j)
| (7.1984692749157402393e-17 + 5.1114920321678694241e-1050j)  +/-  (2.58e-177, 7.27e-424j)
| (0.14618783860828431171 - 3.5354422671766179813e-1042j)  +/-  (5.4e-169, 1.56e-415j)
| (0.027268952858838580359 + 3.4169321138061256293e-1042j)  +/-  (1.28e-169, 3.75e-416j)
| (0.049984847265092552608 - 1.4334545083750251706e-1042j)  +/-  (1.54e-169, 4.01e-416j)
