Starting with polynomial:
P : t
Extension levels are: 1 80
-------------------------------------------------
Trying to find an order 80 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^81 - 3240*t^79 + 4991220*t^77 - 4868103240*t^75 + 3377246622750*t^73 - 1775080824917400*t^71 + 735179308319956500*t^69 - 246390093902659707000*t^67 + 68096062202347576522125*t^65 - 15737756597875884351780000*t^63 + 3073583863565160213902634000*t^61 - 511332588211294835585620020000*t^59 + 72907504869127121973916321185000*t^57 - 8950798290086683590028496047020000*t^55 + 949423961484194652228022616416050000*t^53 - 87220414595014682051347677694754460000*t^51 + 6950376788040232475966768066300746031250*t^49 - 480802535455018434808054073292333960750000*t^47 + 28874863379270829334861469623834056198375000*t^45 - 1504532355025164265342781838294511349283750000*t^43 + 67929635829386166580226599998997187420161312500*t^41 - 2652490541909364599799324380913223508787251250000*t^39 + 89340704161583598565968153011668119091425144375000*t^37 - 2586996042244116375866729995903085535429962876250000*t^35 + 64135943547302051818362681148430662232534496307031250*t^33 - 1354551127719019334403819825854855586351128562004500000*t^31 + 24225625938051691942222162270096455678972106974311250000*t^29 - 364281634475888404760822143765154111320839830798902500000*t^27 + 4566530489322743931108877587913181895486242164657670625000*t^25 - 47239970579200799287333216426688088573995608599906937500000*t^23 + 398390418551260073989843458531736213640696299192548506250000*t^21 - 2698773803089181146382810525537567898856329768723715687500000*t^19 + 14421572510257811750983143745841378459513512201617355705078125*t^17 - 59434359436214012064657804528315983954358716952120011390625000*t^15 + 183547286494190331376149102219799362211990155293311799882812500*t^13 - 409048238472767024209703713518410007215292346082237725453125000*t^11 + 624934808777838509209269562319793066578918862070085413886718750*t^9 - 608044678810869900852262276851690551265975109041164186484375000*t^7 + 336024690921796524155197574049618462541723086575380208320312500*t^5 - 86160177159435006193640403602466272446595663224456463671875000*t^3 + 6462013286957625464523030270184970433494674741834234775390625*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:   81 out of 81
Indefinite weights: 0 out of 81
Negative weights:   0 out of 81
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-14.153774548779938746 + 1.5097060148699928767e-1105j)  +/-  (2.08e-492, 2.08e-492j)
| (-15.363360220077676916 - 4.4146476422332735239e-1107j)  +/-  (4.51e-494, 4.51e-494j)
| (16.070115288084143889 - 7.2925595092841976663e-1102j)  +/-  (5.34e-495, 5.34e-495j)
| (15.363360220077676916 - 9.9017609937941849497e-1105j)  +/-  (4.46e-494, 4.46e-494j)
| (-13.092675857688906682 - 1.9594752177183177539e-1110j)  +/-  (2.5e-491, 2.5e-491j)
| (12.597501586482979433 + 1.4199247104478708232e-1122j)  +/-  (5.6e-491, 5.6e-491j)
| (-7.9173605988965080851 - 7.0128691041550208738e-1140j)  +/-  (2.22e-491, 2.22e-491j)
| (14.73368054299171006 - 1.4254855492908646306e-1139j)  +/-  (4e-493, 4e-493j)
| (-10.769581337343360089 + 2.9212471523436675249e-1146j)  +/-  (2.74e-490, 2.74e-490j)
| (6.0298628868802302844 + 1.6087636966270674872e-1152j)  +/-  (1.75e-493, 1.75e-493j)
| (16.925476835034504414 + 2.214894875309867806e-1150j)  +/-  (1.35e-496, 1.35e-496j)
| (10.340660046957301223 + 1.6164374749665281644e-1156j)  +/-  (2.82e-490, 2.82e-490j)
| (14.153774548779938746 - 6.2733730321402695827e-1174j)  +/-  (2.08e-492, 2.08e-492j)
| (-5.6620545463576693179 - 1.2954622337827355591e-1192j)  +/-  (5.26e-494, 5.26e-494j)
| (-14.73368054299171006 - 8.8997104457514699057e-1188j)  +/-  (3.93e-493, 3.93e-493j)
| (5.6620545463576693179 + 1.4294969855547715935e-1193j)  +/-  (5.26e-494, 5.26e-494j)
| (-16.925476835034504414 + 6.5559831619967642137e-1194j)  +/-  (1.35e-496, 1.35e-496j)
| (-8.3068847821466435324 + 3.3695080338425089855e-1188j)  +/-  (6.91e-491, 6.91e-491j)
| (-16.070115288084143889 + 6.0393738840883227175e-1191j)  +/-  (5.47e-495, 5.47e-495j)
| (13.092675857688906682 - 1.7559375245326437964e-1191j)  +/-  (2.51e-491, 2.51e-491j)
| (-3.1479317248132903157 + 2.1668437067608837696e-1211j)  +/-  (1.96e-499, 1.96e-499j)
| (2.795125299180344154 + 3.8920718967126137741e-1212j)  +/-  (1.9e-500, 1.9e-500j)
| (-5.2968344922231090002 + 2.4365509343988186863e-1206j)  +/-  (9.59e-495, 9.59e-495j)
| (7.9173605988965080851 - 1.4797717046592229012e-1200j)  +/-  (2.14e-491, 2.14e-491j)
| (-9.5074240510437802775 - 9.9239070535470450674e-1204j)  +/-  (2.24e-490, 2.24e-490j)
| (-10.340660046957301223 - 6.0818286461306041854e-1203j)  +/-  (2.87e-490, 2.87e-490j)
| (0.69615285599343171018 + 1.0568603805591201487e-1223j)  +/-  (4.15e-507, 4.15e-507j)
| (-11.208157786358136877 + 3.6405972963046775326e-1205j)  +/-  (2.14e-490, 2.14e-490j)
| (9.9202569218315533332 + 6.3987356455031943119e-1220j)  +/-  (2.67e-490, 2.67e-490j)
| (-0.69615285599343171018 - 2.2660552547527693797e-1261j)  +/-  (3.83e-507, 3.83e-507j)
| (-3.501982407265644993 + 6.009175335595476398e-1259j)  +/-  (1.56e-498, 1.56e-498j)
| (8.7013781230942575471 - 1.1258896013384104825e-1248j)  +/-  (1.09e-490, 1.09e-490j)
| (2.0926351547129304256 - 3.4969368409057929481e-1284j)  +/-  (2.38e-502, 2.38e-502j)
| (1.7426600709209536935 - 2.0233415078443999289e-1285j)  +/-  (1.61e-503, 1.61e-503j)
| (4.9339710978387389979 - 3.5568905480528582905e-1274j)  +/-  (2.11e-495, 2.11e-495j)
| (-3.8574381575682383409 + 1.4284912978268768294e-1280j)  +/-  (9.79e-498, 9.79e-498j)
| (-13.609582762216585361 - 1.3376002711973518322e-1289j)  +/-  (8.3e-492, 8.3e-492j)
| (9.1013598719065183208 - 6.2892364077369819873e-1344j)  +/-  (1.6e-490, 1.6e-490j)
| (-4.9339710978387389979 - 3.4036867050858254053e-1377j)  +/-  (2.09e-495, 2.09e-495j)
| (10.769581337343360089 + 2.2497654886893291237e-1392j)  +/-  (2.79e-490, 2.79e-490j)
| (-4.2144677472925451332 + 1.7046337532850130055e-1421j)  +/-  (8.06e-497, 8.06e-497j)
| (-7.1514387595211672661 - 1.250709140121689162e-1413j)  +/-  (4.76e-492, 4.76e-492j)
| (7.5323476392102699553 + 8.6060502327099967022e-1415j)  +/-  (1.09e-491, 1.09e-491j)
| (3.8574381575682383409 - 8.4670751496573741367e-1455j)  +/-  (9.69e-498, 9.69e-498j)
| (8.3068847821466435324 + 7.4994386036359026878e-1447j)  +/-  (6.61e-491, 6.61e-491j)
| (5.2968344922231090002 + 2.5053719063404610007e-1472j)  +/-  (9.85e-495, 9.85e-495j)
| (-1.0445534384991042423 + 4.8042767289017085925e-1492j)  +/-  (1.14e-505, 1.14e-505j)
| (-11.657775826461797193 - 9.6197460407357704471e-1476j)  +/-  (2.11e-490, 2.11e-490j)
| (4.5732491737465043066 + 1.1959698529188299716e-1503j)  +/-  (3.96e-496, 3.96e-496j)
| (11.657775826461797193 - 1.3888599972479094497e-1507j)  +/-  (2.03e-490, 2.03e-490j)
| (-6.7742692606393826825 + 2.1100541261009914278e-1529j)  +/-  (1.81e-492, 1.81e-492j)
| (-2.4434091567047237702 - 1.1277106334675536154e-1538j)  +/-  (2.34e-501, 2.34e-501j)
| (-9.1013598719065183208 + 5.6391109162844205763e-1527j)  +/-  (1.59e-490, 1.59e-490j)
| (4.2144677472925451332 - 9.9116273953968419534e-1535j)  +/-  (8.1e-497, 8.1e-497j)
| (3.1479317248132903157 + 8.979118993069652326e-1537j)  +/-  (1.87e-499, 1.87e-499j)
| (-8.7013781230942575471 - 1.9235944496095003928e-1527j)  +/-  (1.05e-490, 1.05e-490j)
| (-7.5323476392102699553 - 5.4151427132086523663e-1528j)  +/-  (1.13e-491, 1.13e-491j)
| (-1.3933447709042779693 + 1.1965394953502462447e-1541j)  +/-  (1.08e-504, 1.08e-504j)
| (-12.597501586482979433 - 1.4528561955750880453e-1526j)  +/-  (5.77e-491, 5.77e-491j)
| (-9.0221425211302292815e-1606 + 8.2650552919558815221e-1605j)  +/-  (6.73e-1603, 6.73e-1603j)
| (2.4434091567047237702 - 4.4826742736125664209e-1544j)  +/-  (2.44e-501, 2.44e-501j)
| (12.120159198016570132 + 9.4431919454254640318e-1532j)  +/-  (1.21e-490, 1.21e-490j)
| (-0.34801172249465353403 + 2.5516098130159284039e-1560j)  +/-  (9.46e-509, 9.46e-509j)
| (-6.4005101871838915573 + 2.2375365521894915326e-1545j)  +/-  (6.27e-493, 6.27e-493j)
| (3.501982407265644993 - 2.0426869338621010853e-1551j)  +/-  (1.55e-498, 1.55e-498j)
| (6.4005101871838915573 + 1.0506827361098507381e-1546j)  +/-  (6.02e-493, 6.02e-493j)
| (13.609582762216585361 - 2.3066565707020894404e-1542j)  +/-  (8.58e-492, 8.58e-492j)
| (-6.0298628868802302844 + 6.539435527036845806e-1558j)  +/-  (1.85e-493, 1.85e-493j)
| (6.7742692606393826825 + 3.4089783563335416935e-1554j)  +/-  (1.83e-492, 1.83e-492j)
| (9.5074240510437802775 + 7.4103776437220959471e-1556j)  +/-  (2.16e-490, 2.16e-490j)
| (1.0445534384991042423 + 6.4220995694944800701e-1586j)  +/-  (1.14e-505, 1.14e-505j)
| (7.1514387595211672661 + 2.1067708218030051589e-1570j)  +/-  (4.71e-492, 4.71e-492j)
| (-2.795125299180344154 - 6.2727752819208303295e-1594j)  +/-  (2.07e-500, 2.07e-500j)
| (-2.0926351547129304256 - 4.0410094226036863318e-1596j)  +/-  (2.39e-502, 2.39e-502j)
| (11.208157786358136877 + 1.8127410598691613355e-1582j)  +/-  (2.18e-490, 2.18e-490j)
| (0.34801172249465353403 + 8.4800572469508798435e-1614j)  +/-  (9.44e-509, 9.44e-509j)
| (1.3933447709042779693 + 1.1636912468125955651e-1610j)  +/-  (1.08e-504, 1.08e-504j)
| (-12.120159198016570132 - 1.0771045792348733367e-1596j)  +/-  (1.16e-490, 1.16e-490j)
| (-1.7426600709209536935 - 1.5230222091326030745e-1609j)  +/-  (1.61e-503, 1.61e-503j)
| (-4.5732491737465043066 + 4.8206531081237498905e-1602j)  +/-  (3.98e-496, 3.98e-496j)
| (-9.9202569218315533332 + 2.8345872537504411193e-1595j)  +/-  (2.65e-490, 2.65e-490j)
-------------------------------------------------
The weights are:
| (7.0530127309630636298e-45 + 7.5524141812650618025e-1149j)  +/-  (2.26e-165, 3.34e-409j)
| (1.4715361059410482665e-52 - 1.260182575252183516e-1153j)  +/-  (3.06e-168, 4.52e-412j)
| (2.5392599790109834562e-57 - 5.0314741511370825584e-1158j)  +/-  (1.77e-171, 2.62e-415j)
| (1.4715361059410482665e-52 + 5.6074155343032745398e-1155j)  +/-  (4.44e-170, 6.55e-414j)
| (1.2063175236617372231e-38 + 1.1575317149875618812e-1146j)  +/-  (4.06e-165, 6e-409j)
| (6.7090375039002003568e-36 - 1.1897589204797054893e-1146j)  +/-  (9.33e-165, 1.38e-408j)
| (3.7761924960082472796e-15 + 1.2231318038576599812e-1135j)  +/-  (1e-150, 1.48e-394j)
| (1.7446471278412973025e-48 - 5.5838644291636418242e-1153j)  +/-  (3.13e-169, 4.62e-413j)
| (1.1281327190756853204e-26 - 3.8799056633384775238e-1141j)  +/-  (7.69e-161, 1.14e-404j)
| (1.8743179035614485155e-09 - 2.6605710586686759703e-1133j)  +/-  (2.81e-144, 4.16e-388j)
| (2.4528055138980426567e-63 + 2.1595908868016542097e-1160j)  +/-  (7.47e-175, 1.1e-418j)
| (1.0218473057257060514e-24 + 5.0989314706183529787e-1141j)  +/-  (7.5e-161, 1.11e-404j)
| (7.0530127309630636298e-45 + 3.6175324665636932707e-1151j)  +/-  (2.02e-168, 2.98e-412j)
| (1.597570342232816154e-08 + 1.849153011450348053e-1132j)  +/-  (3.6e-145, 5.33e-389j)
| (1.7446471278412973025e-48 + 2.8706520096720405282e-1151j)  +/-  (4.85e-172, 7.17e-416j)
| (1.597570342232816154e-08 + 7.9131365941015539705e-1133j)  +/-  (9.35e-146, 1.38e-389j)
| (2.4528055138980426567e-63 - 2.2380446166840127988e-1159j)  +/-  (1.65e-178, 2.44e-422j)
| (1.6218666315382541104e-16 - 2.7030573582463914874e-1136j)  +/-  (1.65e-157, 2.44e-401j)
| (2.5392599790109834562e-57 + 3.2978833770398799561e-1156j)  +/-  (4.73e-176, 6.99e-420j)
| (1.2063175236617372231e-38 + 4.9431899402165834878e-1148j)  +/-  (1.13e-169, 1.67e-413j)
| (0.0009939500003995182953 - 3.5597160954158712868e-1130j)  +/-  (1.36e-134, 2.01e-378j)
| (0.0028263907639617890113 + 3.8953216054590710377e-1130j)  +/-  (2.99e-132, 4.42e-376j)
| (1.1739104500747905124e-07 - 4.806207353846158358e-1132j)  +/-  (4.37e-147, 6.46e-391j)
| (3.7761924960082472796e-15 + 3.4493140982074640941e-1136j)  +/-  (1.27e-158, 1.88e-402j)
| (3.8441310665003217664e-21 + 1.6540546748624148279e-1138j)  +/-  (4.41e-162, 6.51e-406j)
| (1.0218473057257060514e-24 + 3.2811916606201152047e-1140j)  +/-  (3.15e-164, 4.66e-408j)
| (0.10903458212018820244 + 2.7625381551685599763e-1129j)  +/-  (1.8e-129, 2.66e-373j)
| (9.3216634799385188745e-29 + 4.0446209930789185947e-1142j)  +/-  (1.35e-166, 2e-410j)
| (7.0910770254680814046e-23 - 4.3244282337924589025e-1140j)  +/-  (3.06e-166, 4.52e-410j)
| (0.10903458212018820244 + 3.048847771964113609e-1129j)  +/-  (7.73e-130, 1.14e-373j)
| (0.00030742200906347616497 + 2.0454814652170528707e-1130j)  +/-  (2.14e-142, 3.16e-386j)
| (5.7382219378320478147e-18 + 1.2975879824652286657e-1137j)  +/-  (1.39e-163, 2.05e-407j)
| (0.015649455812784977808 + 9.5638449359289232023e-1130j)  +/-  (2.18e-133, 3.22e-377j)
| (0.030553610014116194553 - 1.3658509430810653125e-1129j)  +/-  (1.03e-129, 1.52e-373j)
| (7.4658706303601758086e-07 + 5.617643785574660078e-1132j)  +/-  (6.23e-152, 9.21e-396j)
| (8.3465497037017889812e-05 - 1.1025866469114597351e-1130j)  +/-  (2.32e-146, 3.43e-390j)
| (1.2721951837934453471e-41 - 8.4582669467810186142e-1148j)  +/-  (3.67e-174, 5.42e-418j)
| (1.6549612938551722632e-19 - 2.1648593819742479045e-1138j)  +/-  (5.01e-165, 7.4e-409j)
| (7.4658706303601758086e-07 + 1.1644267073101793645e-1131j)  +/-  (4.48e-152, 6.61e-396j)
| (1.1281327190756853204e-26 - 5.2615474897361878831e-1142j)  +/-  (1.59e-169, 2.35e-413j)
| (1.9848557310766859849e-05 + 5.5697809747588852751e-1131j)  +/-  (2.42e-149, 3.57e-393j)
| (1.185632933426076537e-12 + 1.9309764697283029904e-1134j)  +/-  (1.71e-160, 2.52e-404j)
| (7.3091912739459153751e-14 - 1.5449316810891567314e-1135j)  +/-  (3.14e-162, 4.64e-406j)
| (8.3465497037017889812e-05 - 6.2971975405100829537e-1131j)  +/-  (1.11e-151, 1.63e-395j)
| (1.6218666315382541104e-16 - 7.0222267664323114334e-1137j)  +/-  (1.2e-163, 1.77e-407j)
| (1.1739104500747905124e-07 - 2.1856818732955567414e-1132j)  +/-  (2.94e-156, 4.34e-400j)
| (0.080589300110354234646 - 2.69088948210739254e-1129j)  +/-  (2.01e-134, 2.96e-378j)
| (5.6033548723346792668e-31 - 3.6894716766953774588e-1143j)  +/-  (2.29e-173, 3.38e-417j)
| (4.1240539582657880268e-06 - 1.3459307011715816598e-1131j)  +/-  (9.38e-155, 1.39e-398j)
| (5.6033548723346792668e-31 - 3.5737832492407183445e-1144j)  +/-  (2.39e-173, 3.53e-417j)
| (1.6232084074369367692e-11 - 6.7805773534906870043e-1134j)  +/-  (1.5e-162, 2.21e-406j)
| (0.0070805561570686025211 - 8.9294013484738121962e-1130j)  +/-  (2.89e-149, 4.27e-393j)
| (1.6549612938551722632e-19 - 9.9854670011521675015e-1138j)  +/-  (3.76e-168, 5.55e-412j)
| (1.9848557310766859849e-05 + 3.0108012203886865253e-1131j)  +/-  (6.21e-156, 9.18e-400j)
| (0.0009939500003995182953 - 2.2626719256341234503e-1130j)  +/-  (3.36e-153, 4.97e-397j)
| (5.7382219378320478147e-18 + 5.4505537744422895278e-1137j)  +/-  (2.55e-167, 3.77e-411j)
| (7.3091912739459153751e-14 - 5.0693655906662182217e-1135j)  +/-  (5.87e-165, 8.67e-409j)
| (0.052747541031847794544 + 2.2365556039404732757e-1129j)  +/-  (9.57e-149, 1.41e-392j)
| (6.7090375039002003568e-36 - 1.9974011813877376259e-1145j)  +/-  (3.09e-177, 4.57e-421j)
| (0.13882799390429277429 + 3.2708231792682754247e-1129j)  +/-  (2.51e-146, 3.71e-390j)
| (0.0070805561570686025211 - 6.2965883445553903356e-1130j)  +/-  (1.87e-153, 2.76e-397j)
| (2.3656319313870267492e-33 + 2.2783194103294404697e-1145j)  +/-  (9.03e-178, 1.33e-421j)
| (0.13069487488539791691 - 3.2536915669673403359e-1129j)  +/-  (1.16e-148, 1.72e-392j)
| (1.8874073283497851291e-10 + 2.2009334912521646293e-1133j)  +/-  (5.68e-164, 8.39e-408j)
| (0.00030742200906347616497 + 1.2330068672273042987e-1130j)  +/-  (1.7e-157, 2.51e-401j)
| (1.8874073283497851291e-10 + 8.2889133377607568501e-1134j)  +/-  (2.5e-165, 3.69e-409j)
| (1.2721951837934453471e-41 - 1.5712680070698480715e-1149j)  +/-  (6.38e-182, 9.43e-426j)
| (1.8743179035614485155e-09 - 6.6200095010715953353e-1133j)  +/-  (8.41e-165, 1.24e-408j)
| (1.6232084074369367692e-11 - 2.3868872888210315815e-1134j)  +/-  (9.55e-167, 1.41e-410j)
| (3.8441310665003217664e-21 + 3.2412693491493654464e-1139j)  +/-  (1.76e-172, 2.6e-416j)
| (0.080589300110354234646 - 2.3204361910907064588e-1129j)  +/-  (7.5e-159, 1.11e-402j)
| (1.185632933426076537e-12 + 6.3351887012505274818e-1135j)  +/-  (1.03e-167, 1.52e-411j)
| (0.0028263907639617890113 + 5.8163232665359128437e-1130j)  +/-  (2.66e-163, 3.93e-407j)
| (0.015649455812784977808 + 1.2888956920859910337e-1129j)  +/-  (1.1e-162, 1.62e-406j)
| (9.3216634799385188745e-29 + 4.6960409045805294826e-1143j)  +/-  (1.25e-176, 1.85e-420j)
| (0.13069487488539791691 - 3.0972737979000747558e-1129j)  +/-  (1.38e-160, 2.03e-404j)
| (0.052747541031847794544 + 1.8350661430279140135e-1129j)  +/-  (1.99e-161, 2.94e-405j)
| (2.3656319313870267492e-33 + 2.9243231739592017303e-1144j)  +/-  (1.03e-180, 1.52e-424j)
| (0.030553610014116194553 - 1.7501363041680894965e-1129j)  +/-  (1.18e-163, 1.67e-407j)
| (4.1240539582657880268e-06 - 2.6338230940462019067e-1131j)  +/-  (9.12e-167, 1.25e-410j)
| (7.0910770254680814046e-23 - 2.4640130740432046879e-1139j)  +/-  (1.46e-175, 2.19e-419j)
