Starting with polynomial:
P : t^5 - 10*t^3 + 15*t
Extension levels are: 5 66
-------------------------------------------------
Trying to find an order 66 Kronrod extension for:
P1 : t^5 - 10*t^3 + 15*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^71 - 35003326546863776213822690402642956169134214640016055072321/14086253957141200492463318535504016865612632846361736941*t^69 + 67358154343367023570870051065698733261498461346619718749445199939/23143715251582992409117232353833099710201555766572333794063*t^67 - 49494610376843732165384002904859605204576724697827214524285514958475/23143715251582992409117232353833099710201555766572333794063*t^65 + 3660265649992642950791014099731595580857369364005384349286864604877640/3306245035940427487016747479119014244314507966653190542009*t^63 - 45842985958538264223442481879761630105203125595566083843217037225297240/106653065675497660871507983197387556268209934408167436839*t^61 + 13876850843678679843354094513455646188358811889060603756008355841858106040/106653065675497660871507983197387556268209934408167436839*t^59 - 3361044713744682952033485821067608039783187638661977018929746918600469588920/106653065675497660871507983197387556268209934408167436839*t^57 + 663350468794716930643099527357125859230830178651285944555170918893451285959700/106653065675497660871507983197387556268209934408167436839*t^55 - 108099743618407752696978026484935913850067463531533770950208493188749392860683300/106653065675497660871507983197387556268209934408167436839*t^53 + 277102639232975344090021415612860915089311781270463036922733129158253949285708500/2012321993877314356066188362214859552230376120908819563*t^51 - 31609251586368716701035891391151750348225452318745899422972306148177651014195136500/2012321993877314356066188362214859552230376120908819563*t^49 + 3042796274831613517970254234605906994309455315189140501090923436405822340800856717000/2012321993877314356066188362214859552230376120908819563*t^47 - 248039851191617758416193907593062587343382613046201792735086898817039929097775426265000/2012321993877314356066188362214859552230376120908819563*t^45 + 17158477494688956367225738976611733328100547398312760775023905896389330675662027390245000/2012321993877314356066188362214859552230376120908819563*t^43 - 1008211144053966759835857713853649898156631411243606498896348005891706350661270335913685000/2012321993877314356066188362214859552230376120908819563*t^41 + 50313049711119317304672535034187577098955401813327316535140816478881426644084541096986791250/2012321993877314356066188362214859552230376120908819563*t^39 - 2129933818431311878172772373317068152470735165179066154453371991496678925882979891184626836250/2012321993877314356066188362214859552230376120908819563*t^37 + 76326198034567669854377116180266356570959713323576067021117987189606982488981645052005131306250/2012321993877314356066188362214859552230376120908819563*t^35 - 2307943967944675736058928539062153073447657531652193777492689776005396141232691300973869470056250/2012321993877314356066188362214859552230376120908819563*t^33 + 58637228543115047986858476578118047358816364106917639303764080767357077659140379426933123662425000/2012321993877314356066188362214859552230376120908819563*t^31 - 1244964501667795414164000392867682901875906736762230460377800959361059158631959194785894062257925000/2012321993877314356066188362214859552230376120908819563*t^29 + 21939949945439978669975510406720418138970468788410592322393151403825744060105104032398495781810025000/2012321993877314356066188362214859552230376120908819563*t^27 - 318271412860798594403437961228389061311220222215300556180627577267773680828098389043400984107851625000/2012321993877314356066188362214859552230376120908819563*t^25 + 3762105621573630773878981992307594073067450167972946554551181333650206449127087242230675885139219062500/2012321993877314356066188362214859552230376120908819563*t^23 - 35788598859974242541248909840458674508002202764978744804005678501585754829267933366697942510681252312500/2012321993877314356066188362214859552230376120908819563*t^21 + 269846798597155657668127117283262445443273755929144248010209128280660659099329780938144375048487012312500/2012321993877314356066188362214859552230376120908819563*t^19 - 1582470995378081073560507373006339613381042256830028392103758939527597021113876965224866761536700778812500/2012321993877314356066188362214859552230376120908819563*t^17 + 7047948851389449607713616452245482869632734448130040364378203136631421445830520098798652135241477121875000/2012321993877314356066188362214859552230376120908819563*t^15 - 23121669818207770970698741054571213594589342409039834342529596376145111793904043681301227891604350054375000/2012321993877314356066188362214859552230376120908819563*t^13 + 53662349774550829944684004440047047317591785257342245440828644317120130125617226747669481935027567316875000/2012321993877314356066188362214859552230376120908819563*t^11 - 83362181831496583424549360195962823550529689971291013848824332189454148867923784017788272158295850466875000/2012321993877314356066188362214859552230376120908819563*t^9 + 80012684813661528620086079144291007828250133384079076252705724869953581631714232743686626691421322158046875/2012321993877314356066188362214859552230376120908819563*t^7 - 41872097187547428345785804318212758263353657272426927945858103146454415618059371059227719992059156402734375/2012321993877314356066188362214859552230376120908819563*t^5 + 9571925348267610397258023850644842079086609557442373127432855549623580841306421296181236429537011187109375/2012321993877314356066188362214859552230376120908819563*t^3 - 578180925704029300615785991332392620429177622712373972009753390965114881025105088654300277683842052734375/2012321993877314356066188362214859552230376120908819563*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:   71 out of 71
Indefinite weights: 0 out of 71
Negative weights:   0 out of 71
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-16.136954121507783922 - 1.6576535706331207545e-1122j)  +/-  (3.6e-499, 3.6e-499j)
| (-15.047770942090173359 - 3.9414383492466159442e-1120j)  +/-  (1.53e-497, 1.53e-497j)
| (-5.9787267767184250228 - 1.3120308866618027866e-1118j)  +/-  (9.43e-496, 9.43e-496j)
| (-7.6283703985560881239 + 4.5407077056914543812e-1118j)  +/-  (4.12e-494, 4.12e-494j)
| (2.4779085881214347006 - 1.2265251985044870149e-1128j)  +/-  (2.17e-502, 2.17e-502j)
| (-9.841070700568139838 - 7.126933921031928183e-1116j)  +/-  (2.22e-493, 2.22e-493j)
| (-1.3556261799742658658 + 2.7384479435259079521e-1131j)  +/-  (1.7e-505, 1.7e-505j)
| (-2.4779085881214347006 + 5.3845139819180582584e-1128j)  +/-  (2.15e-502, 2.15e-502j)
| (-12.951636133301425455 + 3.3293876650096623883e-1119j)  +/-  (6.03e-495, 6.03e-495j)
| (-11.825597818939673261 + 1.6326947247651369314e-1123j)  +/-  (4.28e-494, 4.28e-494j)
| (-14.256912228147531413 + 3.0950221626702364259e-1130j)  +/-  (1.91e-496, 1.91e-496j)
| (-7.2081113612759225097 + 3.8579423126292237882e-1126j)  +/-  (1.85e-494, 1.85e-494j)
| (-9.3803463499883953547 + 1.534643526181654172e-1128j)  +/-  (2.09e-493, 2.09e-493j)
| (-13.573036090615992743 - 9.4484943692881625249e-1133j)  +/-  (1.31e-495, 1.31e-495j)
| (-6.79345448675068964 + 1.0982025882714111714e-1132j)  +/-  (7.87e-495, 7.87e-495j)
| (-12.372845950369796462 - 2.9091929573582378698e-1133j)  +/-  (1.95e-494, 1.95e-494j)
| (-8.4884328177840462905 - 1.1676773877163408267e-1131j)  +/-  (1.15e-493, 1.15e-493j)
| (-3.6215253748866971107 + 3.5927322648545466557e-1144j)  +/-  (1.02e-499, 1.02e-499j)
| (-8.9298963086910743485 + 1.537573471057326642e-1136j)  +/-  (1.64e-493, 1.64e-493j)
| (1.7266754584428776078 - 1.005760390136228733e-1155j)  +/-  (1.97e-504, 1.97e-504j)
| (-4.3954285631473222652 - 1.6850132297834428174e-1148j)  +/-  (3.48e-498, 3.48e-498j)
| (-5.1803812610850470023 - 4.9533886079675051644e-1147j)  +/-  (7.8e-497, 7.8e-497j)
| (-4.7863914018668054827 - 4.5370112794231827802e-1148j)  +/-  (1.64e-497, 1.64e-497j)
| (3.6215253748866971107 + 1.5435895491891472533e-1151j)  +/-  (9.18e-500, 9.18e-500j)
| (-1.7266754584428776078 - 2.1144291685218756298e-1155j)  +/-  (1.93e-504, 1.93e-504j)
| (-6.3838271249101140553 - 6.5885534835369756016e-1144j)  +/-  (2.87e-495, 2.87e-495j)
| (3.2381555123153495558 - 3.5973978112376392928e-1160j)  +/-  (1.47e-500, 1.47e-500j)
| (-5.577709515847846405 + 2.0132452016052910423e-1151j)  +/-  (2.68e-496, 2.68e-496j)
| (-0.98988757294720384989 - 8.0306278169479496188e-1171j)  +/-  (1.05e-506, 1.05e-506j)
| (1.3556261799742658658 + 2.1896424332230104688e-1170j)  +/-  (1.53e-505, 1.53e-505j)
| (-3.2381555123153495558 - 3.5913256866172877494e-1164j)  +/-  (1.4e-500, 1.4e-500j)
| (2.1010404685522115731 + 9.7287669986086919433e-1168j)  +/-  (2.1e-503, 2.1e-503j)
| (-2.8569700138728056542 - 9.6136023800279940286e-1166j)  +/-  (1.92e-501, 1.92e-501j)
| (0.98988757294720384989 + 7.7818785275215661943e-1172j)  +/-  (9.69e-507, 9.69e-507j)
| (-2.1010404685522115731 - 3.1656833480725195621e-1167j)  +/-  (2.12e-503, 2.12e-503j)
| (-0.63449304049384434457 + 8.9200329598442059108e-1173j)  +/-  (7.22e-508, 7.22e-508j)
| (2.8569700138728056542 + 4.4449699577018461575e-1162j)  +/-  (1.91e-501, 1.91e-501j)
| (0.63449304049384434457 + 1.2963237520566155119e-1172j)  +/-  (8.34e-508, 8.34e-508j)
| (-4.0072186037410834612 + 1.4224016766545795895e-1157j)  +/-  (5.79e-499, 5.79e-499j)
| (-0.30120524894125041913 + 2.0123295603775749155e-1184j)  +/-  (5.87e-509, 5.87e-509j)
| (-8.0548896569390139852 - 5.238711183662837787e-1178j)  +/-  (6.97e-494, 6.97e-494j)
| (-4.6354901859394067083e-1212 - 4.1568817451481897973e-1212j)  +/-  (4.42e-1210, 4.42e-1210j)
| (0.30120524894125041913 - 9.9275844968531895054e-1213j)  +/-  (5.87e-509, 5.87e-509j)
| (11.302925100604503776 + 2.6985315965984625477e-1217j)  +/-  (8.58e-494, 8.58e-494j)
| (15.047770942090173359 + 4.0560260410366860194e-1241j)  +/-  (1.56e-497, 1.56e-497j)
| (9.841070700568139838 + 1.9639619549222351332e-1254j)  +/-  (2.28e-493, 2.28e-493j)
| (14.256912228147531413 + 1.0705299308846929374e-1265j)  +/-  (2e-496, 2e-496j)
| (5.9787267767184250228 + 4.2849366700607718727e-1267j)  +/-  (9.4e-496, 9.4e-496j)
| (8.0548896569390139852 + 2.1868740949873419992e-1269j)  +/-  (6.91e-494, 6.91e-494j)
| (13.573036090615992743 + 6.6041422070329543881e-1283j)  +/-  (1.24e-495, 1.24e-495j)
| (4.7863914018668054827 - 3.6759359731206081634e-1297j)  +/-  (1.72e-497, 1.72e-497j)
| (-10.800082555899580936 + 8.3234632688140910883e-1298j)  +/-  (1.45e-493, 1.45e-493j)
| (12.951636133301425455 + 2.7435336768148150549e-1324j)  +/-  (6.03e-495, 6.03e-495j)
| (16.136954121507783922 + 1.0198521350424581777e-1338j)  +/-  (3.95e-499, 3.95e-499j)
| (7.2081113612759225097 - 3.2570514823592586168e-1358j)  +/-  (1.86e-494, 1.86e-494j)
| (-10.313652927090661488 + 2.4028760614171030552e-1388j)  +/-  (1.9e-493, 1.9e-493j)
| (4.3954285631473222652 - 1.854838906762324143e-1410j)  +/-  (3.26e-498, 3.26e-498j)
| (10.800082555899580936 + 5.4744499106311504363e-1438j)  +/-  (1.51e-493, 1.51e-493j)
| (4.0072186037410834612 - 2.6066372728148344867e-1472j)  +/-  (6.11e-499, 6.11e-499j)
| (12.372845950369796462 - 1.7088112573558428022e-1473j)  +/-  (1.71e-494, 1.71e-494j)
| (10.313652927090661488 - 5.3989690874311263075e-1497j)  +/-  (1.97e-493, 1.97e-493j)
| (9.3803463499883953547 + 3.3040395145868839645e-1520j)  +/-  (2.13e-493, 2.13e-493j)
| (-11.302925100604503776 + 5.7329697965940338777e-1532j)  +/-  (8.48e-494, 8.48e-494j)
| (11.825597818939673261 + 2.4854499475406730624e-1543j)  +/-  (4.68e-494, 4.68e-494j)
| (8.4884328177840462905 - 2.5458466341527851444e-1564j)  +/-  (1.17e-493, 1.17e-493j)
| (8.9298963086910743485 + 3.0189022874390987203e-1581j)  +/-  (1.64e-493, 1.64e-493j)
| (6.3838271249101140553 + 2.0595725419240090013e-1589j)  +/-  (2.97e-495, 2.97e-495j)
| (5.1803812610850470023 + 4.1519815352033489627e-1598j)  +/-  (6.86e-497, 6.86e-497j)
| (6.79345448675068964 - 4.6069726495631025084e-1599j)  +/-  (8.12e-495, 8.12e-495j)
| (7.6283703985560881239 - 1.139574392800719596e-1609j)  +/-  (3.85e-494, 3.85e-494j)
| (5.577709515847846405 - 5.6200307650244333033e-1616j)  +/-  (2.63e-496, 2.63e-496j)
-------------------------------------------------
The weights are:
| (1.8000423401646286702e-57 - 3.8839145731109773142e-1152j)  +/-  (2.48e-148, 2.58e-393j)
| (2.3628822581394312969e-50 + 9.9107871413189161182e-1149j)  +/-  (2.94e-146, 3.05e-391j)
| (2.7812345198693520178e-09 - 1.1390024185738350465e-1126j)  +/-  (4.1e-120, 4.26e-365j)
| (3.9020173943024086706e-14 + 7.5187487993144458331e-1130j)  +/-  (2.58e-127, 2.69e-372j)
| (0.0070000457415972392568 + 1.516341072941853967e-1124j)  +/-  (3.4e-97, 3.53e-342j)
| (1.736375307315185762e-22 - 1.6219485919311113551e-1134j)  +/-  (5.06e-135, 5.25e-380j)
| (0.058714575300523863019 - 1.4034985428331773693e-1123j)  +/-  (4.85e-81, 5.04e-326j)
| (0.0070000457415972392568 + 3.6722266663345196338e-1124j)  +/-  (7.94e-98, 8.26e-343j)
| (8.9556084384445394368e-38 - 1.9928973653662095062e-1142j)  +/-  (3.13e-143, 3.26e-388j)
| (9.1530669787249930516e-32 - 2.3475802337325159133e-1139j)  +/-  (5.62e-141, 5.84e-386j)
| (2.111966371546776709e-45 - 2.84626875184625451e-1146j)  +/-  (2.62e-146, 2.72e-391j)
| (8.6921230408280974367e-13 - 4.7179139892935288637e-1129j)  +/-  (1.35e-128, 1.41e-373j)
| (1.4199582785518555272e-20 + 1.6964810695776237617e-1133j)  +/-  (2.03e-135, 2.11e-380j)
| (2.5594230282843422452e-41 + 3.202093269088231776e-1144j)  +/-  (3.6e-145, 3.74e-390j)
| (1.5642119793531810207e-11 + 3.0703021814725501205e-1128j)  +/-  (2.63e-128, 2.74e-373j)
| (1.2818947967116811626e-34 + 8.0813648050549820968e-1141j)  +/-  (1.02e-142, 1.06e-387j)
| (3.9401571478796883984e-17 + 1.263626794088284078e-1131j)  +/-  (6.34e-134, 6.59e-379j)
| (0.00021768435955135942294 - 6.7386067176950717475e-1125j)  +/-  (1.63e-118, 1.7e-363j)
| (8.5907453840765746261e-19 - 1.5543854981011502813e-1132j)  +/-  (5.27e-135, 5.48e-380j)
| (0.033504724164203737587 + 5.103231628939185434e-1124j)  +/-  (5.42e-107, 5.64e-352j)
| (9.9134945736105559169e-06 - 1.7925742994731179598e-1125j)  +/-  (8.35e-123, 8.68e-368j)
| (2.3481799482671772494e-07 - 4.7310766489314863501e-1126j)  +/-  (4.91e-126, 5.1e-371j)
| (1.6593026712846493502e-06 + 9.0237515294196355495e-1126j)  +/-  (9.52e-125, 9.9e-370j)
| (0.00021768435955135942294 - 1.6474925574629721391e-1125j)  +/-  (5.28e-129, 5.49e-374j)
| (0.033504724164203737587 + 9.2633553878809970897e-1124j)  +/-  (5.97e-109, 6.21e-354j)
| (2.2980173037296650262e-10 - 2.4639298793282052963e-1127j)  +/-  (7.17e-130, 7.45e-375j)
| (0.00080600672410154282209 + 3.667480900094847096e-1125j)  +/-  (6.94e-127, 7.21e-372j)
| (2.7949227688979776568e-08 + 3.0519837713658008626e-1126j)  +/-  (1.51e-127, 1.57e-372j)
| (0.08843608114371952357 + 2.0865746130791902657e-1123j)  +/-  (1.12e-107, 1.17e-352j)
| (0.058714575300523863019 - 8.8353718388131653157e-1124j)  +/-  (3.94e-109, 4.09e-354j)
| (0.00080600672410154282209 + 1.2378947169256098773e-1124j)  +/-  (1.6e-120, 1.66e-365j)
| (0.016488444730237162296 - 2.8447272455087318838e-1124j)  +/-  (1.95e-118, 2.03e-363j)
| (0.0025610428329401276126 - 2.178729497907169693e-1124j)  +/-  (6.21e-119, 6.45e-364j)
| (0.08843608114371952357 + 1.4923995761162776983e-1123j)  +/-  (3.76e-109, 3.9e-354j)
| (0.016488444730237162296 - 5.9398297870578818055e-1124j)  +/-  (4.36e-115, 4.53e-360j)
| (0.11320155830699864296 - 3.0554898964692440549e-1123j)  +/-  (7.34e-109, 7.63e-354j)
| (0.0025610428329401276126 - 7.6742842752564236885e-1125j)  +/-  (5.38e-126, 5.59e-371j)
| (0.11320155830699864296 - 2.4677337194500709137e-1123j)  +/-  (1.86e-109, 1.93e-354j)
| (5.0305918977133438477e-05 + 3.5277653168416444465e-1125j)  +/-  (1.1e-123, 1.14e-368j)
| (0.12076751004531813688 + 4.2017471206195591557e-1123j)  +/-  (1.17e-109, 1.22e-354j)
| (1.3979366779213187905e-15 - 9.1197610090640977178e-1131j)  +/-  (3.35e-136, 3.48e-381j)
| (0.11648036427955215901 - 4.6554309997629724767e-1123j)  +/-  (1.93e-110, 2.01e-355j)
| (0.12076751004531813688 + 3.7976359397253457445e-1123j)  +/-  (8.24e-111, 8.57e-356j)
| (3.7014773692765949979e-29 - 1.6154818964936885079e-1138j)  +/-  (4.01e-163, 4.17e-408j)
| (2.3628822581394312969e-50 - 4.2956728563651179952e-1149j)  +/-  (3.25e-171, 3.37e-416j)
| (1.736375307315185762e-22 + 3.9979078994091355819e-1135j)  +/-  (1.91e-160, 1.98e-405j)
| (2.111966371546776709e-45 + 1.1706783705651187185e-1146j)  +/-  (7e-170, 7.28e-415j)
| (2.7812345198693520178e-09 - 3.0090612263309919998e-1128j)  +/-  (4.26e-150, 4.43e-395j)
| (1.3979366779213187905e-15 + 1.4399772913787301994e-1131j)  +/-  (7.75e-157, 8.05e-402j)
| (2.5594230282843422452e-41 - 1.2511531747676674002e-1144j)  +/-  (5.28e-169, 5.49e-414j)
| (1.6593026712846493502e-06 + 9.9227944796854992063e-1127j)  +/-  (7e-147, 7.27e-392j)
| (9.2539401448533548086e-27 - 9.1485883707178916368e-1137j)  +/-  (2.15e-153, 2.24e-398j)
| (8.9556084384445394368e-38 + 7.3888118399727036007e-1143j)  +/-  (3.92e-168, 4.08e-413j)
| (1.8000423401646286702e-57 + 1.7917720379973027655e-1152j)  +/-  (2.19e-175, 2.28e-420j)
| (8.6921230408280974367e-13 + 4.1450544662898171099e-1130j)  +/-  (1.09e-156, 1.14e-401j)
| (1.5244123336969071042e-24 + 1.3228357047176408344e-1135j)  +/-  (2.37e-153, 2.46e-398j)
| (9.9134945736105559169e-06 - 2.7193982541193617526e-1126j)  +/-  (1.3e-147, 1.35e-392j)
| (9.2539401448533548086e-27 + 2.6568830851237068516e-1137j)  +/-  (1.31e-164, 1.36e-409j)
| (5.0305918977133438477e-05 + 6.9295988073901612846e-1126j)  +/-  (5.84e-147, 6.07e-392j)
| (1.2818947967116811626e-34 - 2.8361651693253706828e-1141j)  +/-  (7.42e-168, 7.71e-413j)
| (1.5244123336969071042e-24 - 3.5657280628035650834e-1136j)  +/-  (5.18e-164, 5.38e-409j)
| (1.4199582785518555272e-20 - 3.8143922890620620452e-1134j)  +/-  (4.97e-163, 5.17e-408j)
| (3.7014773692765949979e-29 + 5.1958557166500102118e-1138j)  +/-  (1.84e-161, 1.91e-406j)
| (9.1530669787249930516e-32 + 7.7718991287218863063e-1140j)  +/-  (2.26e-167, 2.35e-412j)
| (3.9401571478796883984e-17 - 2.2639440304442536685e-1132j)  +/-  (2.51e-162, 2.6e-407j)
| (8.5907453840765746261e-19 + 3.1430359502286395014e-1133j)  +/-  (6.7e-163, 6.96e-408j)
| (2.2980173037296650262e-10 + 7.9198559460270453405e-1129j)  +/-  (5.49e-160, 5.7e-405j)
| (2.3481799482671772494e-07 - 3.3551503349331886304e-1127j)  +/-  (5.31e-158, 5.51e-403j)
| (1.5642119793531810207e-11 - 1.9016364900639639973e-1129j)  +/-  (6.23e-161, 6.48e-406j)
| (3.9020173943024086706e-14 - 8.156823143028285502e-1131j)  +/-  (2.55e-162, 2.66e-407j)
| (2.7949227688979776568e-08 + 1.0475673628240876066e-1127j)  +/-  (3.74e-159, 3.85e-404j)
