Starting with polynomial:
P : t
Extension levels are: 1 78
-------------------------------------------------
Trying to find an order 78 Kronrod extension for:
P1 : t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^79 - 3081*t^77 + 4507503*t^75 - 4169440275*t^73 + 2739322260675*t^71 - 1361443163555475*t^69 + 532324276950190725*t^67 - 168138425190981670425*t^65 + 43715990549655234310500*t^63 - 9486369949275185845378500*t^61 + 1736005700717359009704265500*t^59 - 270027795811581933236727115500*t^57 + 35913696842940397120484706361500*t^55 - 4102449216289729978763060688217500*t^53 + 403798215717660565052535544883122500*t^51 - 34322848336001148029465521315065412500*t^49 + 2522729352696084380165715816657307818750*t^47 - 160415907662615718527008164576855867768750*t^45 + 8822874921443864518985449051727072727281250*t^43 - 419318739687568929507571604932081403828156250*t^41 + 17192068327190326109810435802215337556954406250*t^39 - 606634410973715792731882520449598339509676906250*t^37 + 18364478077658850816337898119065113368792946343750*t^35 - 475081063313348531987871712210597498018774046718750*t^33 + 10451783392893667703733177668633144956413029027812500*t^31 - 194403171107822219289437104636576496189282339917312500*t^29 + 3035680287299070039673517864709617594340331923324187500*t^27 - 39463843734887910515755732241225028726424315003214437500*t^25 + 422826897159513326954525702584553879211689089320154687500*t^23 - 3688800171770926611017069060479039015191632399931004687500*t^21 + 25821601202396486277119483423353273106341426799517032812500*t^19 - 142435284051929004947981666625593861328528515571529439062500*t^17 + 605349957220698271028922083158773910646246191179000116015625*t^15 - 1926113500247676316910206628232462442965328790115000369140625*t^13 + 4418730971156433903499885794180355016214577812616765552734375*t^11 - 6943720097531538991214106247997700739765765134112060154296875*t^9 + 6943720097531538991214106247997700739765765134112060154296875*t^7 - 3941030325626008616635033275890586906353542373414953060546875*t^5 + 1037113243585791741219745598918575501671984835109198173828125*t^3 - 79777941814291672401518892224505807820921910393015244140625*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: 0
  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
-------------------------------------------------
The nodes are:
| (12.348751314660212011 - 1.0143169232027050207e-1062j)  +/-  (2.12e-491, 2.12e-491j)
| (4.269216526674332956 + 6.5171811768946151632e-1068j)  +/-  (4.93e-497, 4.93e-497j)
| (15.128554467325382801 - 1.1578829043967099386e-1065j)  +/-  (1.71e-494, 1.71e-494j)
| (15.83857762108172073 + 4.1957321536372365055e-1067j)  +/-  (1.18e-495, 1.18e-495j)
| (13.366162853451256694 - 1.6099397354115957768e-1063j)  +/-  (2.97e-492, 2.97e-492j)
| (16.697751110468240406 + 7.1470735645485134866e-1068j)  +/-  (5.99e-497, 5.99e-497j)
| (14.495867635352908662 - 5.0685320089644957556e-1064j)  +/-  (1.65e-493, 1.65e-493j)
| (4.999023959358752958 - 2.3814638716779224092e-1066j)  +/-  (1.31e-495, 1.31e-495j)
| (11.403815571663619728 + 6.1050045242874758629e-1062j)  +/-  (7.2e-491, 7.2e-491j)
| (10.951609695601093978 - 1.6362764829355527803e-1062j)  +/-  (6.65e-491, 6.65e-491j)
| (3.907229555330404938 - 1.2483348698641148045e-1068j)  +/-  (6.18e-498, 6.18e-498j)
| (13.913108517007461482 + 5.7579859386001868972e-1064j)  +/-  (7.62e-493, 7.62e-493j)
| (3.5469263252454943132 + 3.7067345129399816172e-1069j)  +/-  (1.14e-498, 1.14e-498j)
| (10.510446413502762425 - 1.8075021608621763466e-1061j)  +/-  (8.83e-491, 8.83e-491j)
| (6.4882464779266470979 + 5.7153227818983211092e-1065j)  +/-  (3.36e-493, 3.36e-493j)
| (2.8306519057036480638 - 4.5941598128423103617e-1071j)  +/-  (2.23e-500, 2.23e-500j)
| (11.868795180683996098 - 3.6488207630888777886e-1062j)  +/-  (4.18e-491, 4.18e-491j)
| (7.2519439599502686803 - 2.1052777999725181306e-1063j)  +/-  (2.21e-492, 2.21e-492j)
| (9.6559273984088882761 - 4.1493480692347065639e-1062j)  +/-  (7.67e-491, 7.67e-491j)
| (12.846568460402761684 + 1.9546192164714942488e-1062j)  +/-  (9.12e-492, 9.12e-492j)
| (6.8682457220219452902 - 3.5617571456246635057e-1064j)  +/-  (9.45e-493, 9.45e-493j)
| (1.0576404912799522627 - 1.2084724387383912893e-1076j)  +/-  (8.34e-506, 8.34e-506j)
| (2.4743423741629485739 + 5.1159719934004755501e-1072j)  +/-  (1.9e-501, 1.9e-501j)
| (5.36726785834576977 + 1.57469417993819846e-1065j)  +/-  (5.82e-495, 5.82e-495j)
| (9.2404767091970180019 - 5.2971086345809955542e-1062j)  +/-  (5.42e-491, 5.42e-491j)
| (5.7380465444535226364 - 3.815661790821458683e-1065j)  +/-  (3.18e-494, 3.18e-494j)
| (1.4108332608326109725 + 5.3392073317923872851e-1075j)  +/-  (7.06e-505, 7.06e-505j)
| (8.4291327432016416564 - 1.0613964772879212773e-1062j)  +/-  (2.4e-491, 2.4e-491j)
| (8.8317752133681527789 + 5.8378170947672793886e-1062j)  +/-  (3.73e-491, 3.73e-491j)
| (3.1881247865325013726 - 1.6736999988527031491e-1070j)  +/-  (1.81e-499, 1.81e-499j)
| (8.0319516208515425742 - 2.5165921000709116648e-1063j)  +/-  (1.54e-491, 1.54e-491j)
| (6.1116140502839499261 - 6.3498384241553260449e-1065j)  +/-  (1.04e-493, 1.04e-493j)
| (-0.70486367337050123587 - 1.2753257625207862564e-1077j)  +/-  (3.45e-507, 3.45e-507j)
| (1.7645839545509862343 + 3.0706484435635260199e-1074j)  +/-  (1.26e-503, 1.26e-503j)
| (2.1190374567336003392 - 4.065550944297754398e-1073j)  +/-  (2.1e-502, 2.1e-502j)
| (7.5946579507254638902e-1118 + 1.4892240349937708043e-1117j)  +/-  (1.32e-1115, 1.32e-1115j)
| (4.6330797681601383843 + 6.8240793405640755634e-1067j)  +/-  (2.54e-496, 2.54e-496j)
| (0.70486367337050123587 - 2.5246215976528714065e-1077j)  +/-  (3.55e-507, 3.55e-507j)
| (0.35236298070591520244 - 1.2913447764986014638e-1078j)  +/-  (9.81e-509, 9.81e-509j)
| (10.078933092272832786 - 1.2731968541395706573e-1062j)  +/-  (7.92e-491, 7.92e-491j)
| (7.6397091212600469431 - 1.2953798452241391883e-1063j)  +/-  (4.75e-492, 4.75e-492j)
| (-0.35236298070591520244 + 1.3612739591095172162e-1078j)  +/-  (9.81e-509, 9.81e-509j)
| (-13.366162853451256694 - 1.1444529056412749422e-1060j)  +/-  (2.78e-492, 2.78e-492j)
| (-14.495867635352908662 + 1.4910872830432428734e-1066j)  +/-  (1.49e-493, 1.49e-493j)
| (-7.2519439599502686803 + 2.4517924402860909223e-1076j)  +/-  (2.16e-492, 2.16e-492j)
| (-4.6330797681601383843 - 4.5154040615180358932e-1083j)  +/-  (2.65e-496, 2.65e-496j)
| (-13.913108517007461482 + 1.3427258099697021121e-1076j)  +/-  (8.06e-493, 8.06e-493j)
| (-16.697751110468240406 - 1.641306567175694841e-1090j)  +/-  (5.67e-497, 5.67e-497j)
| (-4.269216526674332956 - 2.4571779299697301745e-1098j)  +/-  (5.2e-497, 5.2e-497j)
| (-11.868795180683996098 + 8.6936596225645413634e-1092j)  +/-  (4.19e-491, 4.19e-491j)
| (-15.128554467325382801 - 4.2490970844914762647e-1102j)  +/-  (1.8e-494, 1.8e-494j)
| (-3.1881247865325013726 + 5.0428471870646463075e-1129j)  +/-  (1.64e-499, 1.64e-499j)
| (-3.907229555330404938 - 2.4669712685670366962e-1126j)  +/-  (6.15e-498, 6.15e-498j)
| (-8.8317752133681527789 - 9.7777408645757162388e-1118j)  +/-  (3.72e-491, 3.72e-491j)
| (-10.510446413502762425 - 3.4409737184358057953e-1164j)  +/-  (8.43e-491, 8.43e-491j)
| (-9.6559273984088882761 + 2.9413493502778372559e-1230j)  +/-  (7.69e-491, 7.69e-491j)
| (-10.078933092272832786 - 3.7800886099198120306e-1292j)  +/-  (8.08e-491, 8.08e-491j)
| (-10.951609695601093978 + 2.396459606419903102e-1329j)  +/-  (6.68e-491, 6.68e-491j)
| (-4.999023959358752958 - 1.5672535498860894149e-1348j)  +/-  (1.34e-495, 1.34e-495j)
| (-7.6397091212600469431 - 1.5509162485218484344e-1344j)  +/-  (4.44e-492, 4.44e-492j)
| (-5.36726785834576977 + 1.63605497473037248e-1356j)  +/-  (6.09e-495, 6.09e-495j)
| (-15.83857762108172073 - 8.4878173551020981129e-1352j)  +/-  (1.29e-495, 1.29e-495j)
| (-1.7645839545509862343 - 2.0953664854407389439e-1373j)  +/-  (1.23e-503, 1.23e-503j)
| (-1.4108332608326109725 + 2.5193196329842265337e-1374j)  +/-  (6.53e-505, 6.53e-505j)
| (-6.1116140502839499261 + 3.4581308882844743836e-1362j)  +/-  (1.05e-493, 1.05e-493j)
| (-9.2404767091970180019 + 4.7543476053111715353e-1368j)  +/-  (5.41e-491, 5.41e-491j)
| (-8.4291327432016416564 - 1.0130822725632768979e-1406j)  +/-  (2.46e-491, 2.46e-491j)
| (-2.8306519057036480638 - 1.7054519547101554263e-1447j)  +/-  (2.15e-500, 2.15e-500j)
| (-8.0319516208515425742 - 3.2733274841276946267e-1456j)  +/-  (1.48e-491, 1.48e-491j)
| (-3.5469263252454943132 - 1.9823863929436221502e-1489j)  +/-  (1.05e-498, 1.05e-498j)
| (-12.348751314660212011 - 7.7791764961983577761e-1488j)  +/-  (2.06e-491, 2.06e-491j)
| (-2.4743423741629485739 + 4.8599003276594091206e-1534j)  +/-  (1.97e-501, 1.97e-501j)
| (-2.1190374567336003392 + 3.2812651340972990049e-1535j)  +/-  (2.08e-502, 2.08e-502j)
| (-1.0576404912799522627 + 7.3456047695196990049e-1539j)  +/-  (8.06e-506, 8.06e-506j)
| (-12.846568460402761684 + 4.5582583291801762845e-1522j)  +/-  (9.49e-492, 9.49e-492j)
| (-5.7380465444535226364 + 1.1174271563347110176e-1545j)  +/-  (3.33e-494, 3.33e-494j)
| (-11.403815571663619728 - 3.2802889818596290084e-1544j)  +/-  (7.1e-491, 7.1e-491j)
| (-6.8682457220219452902 + 1.4986498686902079011e-1557j)  +/-  (9.26e-493, 9.26e-493j)
| (-6.4882464779266470979 + 4.4414656331556095703e-1558j)  +/-  (3.15e-493, 3.15e-493j)
-------------------------------------------------
The weights are:
| (1.5013596040616161412e-34 - 1.4522280658142346021e-1086j)  +/-  (5.5e-106, 2.25e-349j)
| (1.5955718941990400444e-05 + 4.376064053323295345e-1071j)  +/-  (4.59e-71, 1.88e-314j)
| (5.3028909816444483723e-51 + 6.2186597086986245024e-1095j)  +/-  (3.29e-113, 1.35e-356j)
| (1.025592995973795585e-55 - 2.552257980166002634e-1097j)  +/-  (4.65e-115, 1.9e-358j)
| (3.409252519522319812e-40 - 1.916724922830018197e-1089j)  +/-  (8.28e-110, 3.39e-353j)
| (1.1329876713480747513e-61 + 2.4820072383446901332e-1100j)  +/-  (9.54e-118, 3.9e-361j)
| (5.6654542201425358984e-47 - 6.8651042275725536215e-1093j)  +/-  (2.54e-112, 1.04e-355j)
| (5.4837919545336387227e-07 + 1.2451829862985870981e-1071j)  +/-  (4.96e-83, 2.03e-326j)
| (1.0536163024308886128e-29 - 4.4266897175206902434e-1084j)  +/-  (1.39e-106, 5.68e-350j)
| (1.6088246924441335068e-27 + 5.8909938001898040707e-1083j)  +/-  (6.61e-106, 2.7e-349j)
| (6.9741034328077704447e-05 - 5.5140889553345731729e-1071j)  +/-  (1.83e-78, 7.5e-322j)
| (2.0764015051268940555e-43 + 4.4338258515051414354e-1091j)  +/-  (3.24e-112, 1.32e-355j)
| (0.00026593482889812568371 + 7.9120853973489604874e-1071j)  +/-  (7.53e-77, 3.08e-320j)
| (1.7880590415809924636e-25 - 6.7037996336204616148e-1082j)  +/-  (1.49e-105, 6.08e-349j)
| (1.0898892488872911351e-10 - 8.3176901451283284491e-1074j)  +/-  (9.01e-95, 3.68e-338j)
| (0.0025912018096928620156 + 1.7605747892060869961e-1070j)  +/-  (1.08e-73, 4.4e-317j)
| (4.8499586338459609891e-32 + 2.7964703677114876179e-1085j)  +/-  (3.34e-108, 1.37e-351j)
| (5.8505830578215785681e-13 + 3.4887278327002268898e-1075j)  +/-  (2.62e-98, 1.07e-341j)
| (9.4856480261573583326e-22 - 5.6516300621593461057e-1080j)  +/-  (4.86e-105, 1.99e-348j)
| (2.9510531479492569294e-37 + 6.0212391262379289168e-1088j)  +/-  (4.99e-111, 2.04e-354j)
| (8.6954503879020341791e-12 + 9.1334289042384167886e-1075j)  +/-  (3e-97, 1.23e-340j)
| (0.080488819117948347654 - 5.7418128572418558495e-1070j)  +/-  (4.97e-59, 2.03e-302j)
| (0.0066471785494577698364 - 2.4813482368152282402e-1070j)  +/-  (3.33e-76, 1.36e-319j)
| (8.1847776661144290219e-08 - 3.7595830405505762587e-1072j)  +/-  (4.14e-92, 1.69e-335j)
| (4.72425906296962681e-20 + 4.4024607404880632696e-1079j)  +/-  (8.09e-105, 3.31e-348j)
| (1.0519425583191010138e-08 - 1.100966957735913607e-1072j)  +/-  (2.59e-94, 1.06e-337j)
| (0.052121221082627972365 + 5.0440911193121631584e-1070j)  +/-  (3.53e-70, 1.44e-313j)
| (5.9484171334629495776e-17 + 2.7948098169200123875e-1077j)  +/-  (1.18e-103, 4.82e-347j)
| (1.8682330947014850157e-18 - 3.7751810880887309568e-1078j)  +/-  (1.44e-104, 5.9e-348j)
| (0.00088676896610576800903 - 1.1836764018613813025e-1070j)  +/-  (3.91e-86, 1.6e-329j)
| (1.5432773430140979249e-15 - 1.2551829254988575276e-1076j)  +/-  (5.04e-103, 2.06e-346j)
| (1.1591922045293333208e-09 + 9.213092748764664999e-1073j)  +/-  (1.52e-97, 6.22e-341j)
| (0.10973008292045317944 + 4.72063429118911032e-1070j)  +/-  (4.35e-72, 1.78e-315j)
| (0.029775904463893488257 - 4.1971352781639597452e-1070j)  +/-  (8.37e-80, 3.42e-323j)
| (0.014993372717141088275 + 3.3120254542439960656e-1070j)  +/-  (2.72e-82, 1.11e-325j)
| (0.14056334382809643396 + 6.0605632589932446158e-1070j)  +/-  (1.19e-73, 4.88e-317j)
| (3.176054453114683817e-06 - 2.9405675906494868717e-1071j)  +/-  (2.3e-93, 9.42e-337j)
| (0.10973008292045317944 + 6.1847287831375323793e-1070j)  +/-  (3.72e-75, 1.52e-318j)
| (0.13212832879811609223 - 6.2985880848795188318e-1070j)  +/-  (4.96e-75, 2.03e-318j)
| (1.4878081391909368048e-23 + 6.6186051706095576517e-1081j)  +/-  (6.72e-109, 2.75e-352j)
| (3.2965973959660529458e-14 + 1.211804756044008293e-1075j)  +/-  (2.39e-102, 9.77e-346j)
| (0.13212832879811609223 - 5.5062213765922081028e-1070j)  +/-  (1.16e-78, 4.73e-322j)
| (3.409252519522319812e-40 + 8.404823047389747616e-1090j)  +/-  (2.22e-142, 9.09e-386j)
| (5.6654542201425358984e-47 + 3.2300180803695559188e-1093j)  +/-  (4.48e-145, 1.83e-388j)
| (5.8505830578215785681e-13 + 5.1869451707757739461e-1076j)  +/-  (4.85e-128, 1.98e-371j)
| (3.176054453114683817e-06 - 1.5292575197761440703e-1072j)  +/-  (1.64e-117, 6.73e-361j)
| (2.0764015051268940555e-43 - 2.0149592573187972292e-1091j)  +/-  (7.63e-144, 3.12e-387j)
| (1.1329876713480747513e-61 - 1.2994022363697947529e-1100j)  +/-  (7.64e-151, 3.13e-394j)
| (1.5955718941990400444e-05 + 3.5588447350955150278e-1072j)  +/-  (1.02e-117, 4.18e-361j)
| (4.8499586338459609891e-32 - 1.0902421876531506991e-1085j)  +/-  (1.95e-141, 7.96e-385j)
| (5.3028909816444483723e-51 - 3.0278451584523869049e-1095j)  +/-  (4.51e-147, 1.84e-390j)
| (0.00088676896610576800903 - 2.993545025878590741e-1071j)  +/-  (3.78e-114, 1.55e-357j)
| (6.9741034328077704447e-05 - 7.7349251735773839089e-1072j)  +/-  (2.62e-117, 1.07e-360j)
| (1.8682330947014850157e-18 + 8.2277787624063916986e-1079j)  +/-  (8.46e-136, 3.46e-379j)
| (1.7880590415809924636e-25 + 2.2739937836996656116e-1082j)  +/-  (7.64e-140, 3.13e-383j)
| (9.4856480261573583326e-22 + 1.751335604741810142e-1080j)  +/-  (2.22e-138, 9.1e-382j)
| (1.4878081391909368048e-23 - 2.1327611632375503846e-1081j)  +/-  (3.12e-139, 1.28e-382j)
| (1.6088246924441335068e-27 - 2.0982129022026283029e-1083j)  +/-  (2.09e-141, 8.53e-385j)
| (5.4837919545336387227e-07 + 6.1272371089314099513e-1073j)  +/-  (5.07e-128, 2.08e-371j)
| (3.2965973959660529458e-14 - 1.1941595276582207901e-1076j)  +/-  (1.11e-135, 4.54e-379j)
| (8.1847776661144290219e-08 - 2.2849461508335723357e-1073j)  +/-  (5.55e-130, 2.27e-373j)
| (1.025592995973795585e-55 + 1.2866991839204321573e-1097j)  +/-  (4.62e-154, 1.89e-397j)
| (0.029775904463893488257 - 2.0872052749119795447e-1070j)  +/-  (8.56e-119, 3.5e-362j)
| (0.052121221082627972365 + 2.9083062493961214953e-1070j)  +/-  (1.47e-116, 6.01e-360j)
| (1.1591922045293333208e-09 - 2.540870665690833094e-1074j)  +/-  (5.92e-133, 2.42e-376j)
| (4.72425906296962681e-20 - 1.2714334742010216873e-1079j)  +/-  (5.7e-139, 2.33e-382j)
| (5.9484171334629495776e-17 - 4.7794961534260240762e-1078j)  +/-  (5.64e-138, 2.31e-381j)
| (0.0025912018096928620156 + 5.3438849767827785679e-1071j)  +/-  (3.38e-127, 1.38e-370j)
| (1.5432773430140979249e-15 + 2.5073563744969765843e-1077j)  +/-  (2.14e-137, 8.74e-381j)
| (0.00026593482889812568371 + 1.5723799814062626475e-1071j)  +/-  (6.64e-129, 2.72e-372j)
| (1.5013596040616161412e-34 + 5.9003107905608609599e-1087j)  +/-  (5.08e-148, 2.08e-391j)
| (0.0066471785494577698364 - 8.9544110515930510976e-1071j)  +/-  (3.2e-128, 1.31e-371j)
| (0.014993372717141088275 + 1.4097630888288406635e-1070j)  +/-  (1.22e-127, 4.97e-371j)
| (0.080488819117948347654 - 3.8166964391420124161e-1070j)  +/-  (5.68e-126, 2.32e-369j)
| (2.9510531479492569294e-37 - 2.5438647657549524e-1088j)  +/-  (2.45e-149, 1e-392j)
| (1.0519425583191010138e-08 + 7.9148049986194968513e-1074j)  +/-  (2.35e-135, 9.6e-379j)
| (1.0536163024308886128e-29 + 1.6518386692813789903e-1084j)  +/-  (5.68e-146, 2.33e-389j)
| (8.6954503879020341791e-12 - 2.0630685446760996796e-1075j)  +/-  (5.87e-138, 2.4e-381j)
| (1.0898892488872911351e-10 + 7.5407358826823617754e-1075j)  +/-  (2.19e-137, 8.93e-381j)
