Starting with polynomial:
P : 64*t^6 - 480*t^4 + 720*t^2 - 120
Extension levels are: 6 63
-------------------------------------------------
Trying to find an order 63 Kronrod extension for:
P1 : 64*t^6 - 480*t^4 + 720*t^2 - 120
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 64*t^69 - 266829227512486179953432993409618144707194042608730509220275888197365079727711072/3873083718309467034356100955213777793878106552535640935627498330485698046729*t^67 + 3915613215145093893534949162350400871294709293240450117433391610287620077453261297520/112319427830974543996326927701199556022465090023533587133197451584085243355141*t^65 - 23549790872111200471830389726456896632298494812379304906276901863416802871989744805088120/2134069128788516335930211626322791564426836710447138155530751580097619623747679*t^63 + 5235267336337784358682820356965526946362800538000408759704257854399360387964107998324258780/2134069128788516335930211626322791564426836710447138155530751580097619623747679*t^61 - 869917742441580776935955009666072546259729035803289751249695641740332603697606009051857361930/2134069128788516335930211626322791564426836710447138155530751580097619623747679*t^59 + 65623398166113882308687103516679061615508591558449821721455152323562326515956965982944659335/1247264248269150400894337595746809798028542788104697928422414716597089201489*t^57 - 710548384035530972578111729872179354787751955370958247960382904373915113364242517194345778475/131290973502015831673088167973348399792478188221547150360254180694430442262*t^55 + 118600623045834113409360184843340531122879452242659636794556385532631163253759409240174341643575/262581947004031663346176335946696799584956376443094300720508361388860884524*t^53 - 16268855742259943063951420898217647663635495432138630762806695147844178667506457467833414720165725/525163894008063326692352671893393599169912752886188601441016722777721769048*t^51 + 1851107335829780741037918577271834803226690469136464701486093635238031743612015164868987022717653625/1050327788016126653384705343786787198339825505772377202882033445555443538096*t^49 - 175871995041433398851181832277187821236079229073968668682911300465502502486772431940142809974646406375/2100655576032253306769410687573574396679651011544754405764066891110887076192*t^47 + 14016900403198505933534170909605896437861722928851087328428835520063351784044953670659899444567206859375/4201311152064506613538821375147148793359302023089508811528133782221774152384*t^45 - 939891648062995415464978327275157125977104222479598436060323463676173614082086039068420767822338995868125/8402622304129013227077642750294297586718604046179017623056267564443548304768*t^43 + 53106121095297088781844619809815064205349813596636810131738705202195494403776449718628540027313118690860625/16805244608258026454155285500588595173437208092358035246112535128887096609536*t^41 - 2529202515581389526946924368881935509239268831365625229938669803730249456643114766889781110253254892770154375/33610489216516052908310571001177190346874416184716070492225070257774193219072*t^39 + 101444642069876696500860115026179356434408033451710372568617217347885983684125150988027837912895487549197320625/67220978433032105816621142002354380693748832369432140984450140515548386438144*t^37 - 3420097997518874707639787722839548756855971448957407315574794790582122497595149183822291566501845565938582846875/134441956866064211633242284004708761387497664738864281968900281031096772876288*t^35 + 96626018954097983118276613222265938937599946097415267008066724242761046330896423730345334730312106223525806534375/268883913732128423266484568009417522774995329477728563937800562062193545752576*t^33 - 2278174246088224527201219338362110230315686846576604290571385063466636563981738776879255171755104983907269999540625/537767827464256846532969136018835045549990658955457127875601124124387091505152*t^31 + 44584527614373114366877188303757184957410983478076664313793260799546712550741206518748693772911298826244155156615625/1075535654928513693065938272037670091099981317910914255751202248248774183010304*t^29 - 719409337003033774067145771957330278558107573156143978796823881284562009856916794908205998564688644899571211711446875/2151071309857027386131876544075340182199962635821828511502404496497548366020608*t^27 + 30523879176567723346739748730347552895814220743441305650054782594280407189420997902766802411628611691960296245890625/13833256011942298303098884527815692490031914056732016151140864929244684025856*t^25 - 101422575030245193720812292288608614008077339166032582712709965119737770423788280010920067648248641907015529341035390625/8604285239428109544527506176301360728799850543287314046009617985990193464082432*t^23 + 866863268804497038558526027673211427104928065267157795956503903032703868680180057401149186499082419740098963445591328125/17208570478856219089055012352602721457599701086574628092019235971980386928164864*t^21 - 5841196239114460459139180694876414571868354038319884363708967328524880782760880727359211727380087705425518781087646109375/34417140957712438178110024705205442915199402173149256184038471943960773856329728*t^19 + 30480238741602310353245213980481469252806540533120891724791707888274701674303119955023568862728191262879678058241773421875/68834281915424876356220049410410885830398804346298512368076943887921547712659456*t^17 - 120459071311990455976978370347748517123604276204462703990037751191294913371955111632843740693006844901873163174795785078125/137668563830849752712440098820821771660797608692597024736153887775843095425318912*t^15 + 350479058458077646360280268004239593907587981682382343575249399023603857552150016003050451708636982005939225717866704453125/275337127661699505424880197641643543321595217385194049472307775551686190850637824*t^13 - 723200397006924227271616222366980712955545073216460509427383824004642908187231152786406214122970674484940094943909294609375/550674255323399010849760395283287086643190434770388098944615551103372381701275648*t^11 + 1004958001255176144643546006817791363900277499432691879900111677657501314926983091276058853497493897104862383995597000546875/1101348510646798021699520790566574173286380869540776197889231102206744763402551296*t^9 - 871049670861909783381013644036381337864238468842662423328862479393224322114792580681311787233698421758056046854991415078125/2202697021293596043399041581133148346572761739081552395778462204413489526805102592*t^7 + 25996047268441670871094186631159584923432550914816678633781650024782478171336325635779169452132228359227253121479480078125/275337127661699505424880197641643543321595217385194049472307775551686190850637824*t^5 - 10873132031107224033992067893501040070534885904924542030584688318262183740878364494745350281193833573612758307800273828125/1101348510646798021699520790566574173286380869540776197889231102206744763402551296*t^3 + 1157836495791911396137300524888798179947835184975171255160835578936430546658569009717187050033322783547062553437336328125/4405394042587192086798083162266296693145523478163104791556924408826979053610205184*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
Sufficient bits for target precision reached
Positive weights:   69 out of 69
Indefinite weights: 0 out of 69
Negative weights:   0 out of 69
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (10.708657994858956036 - 1.1047096110129216884e-734j)  +/-  (4.4e-244, 4.4e-244j)
| (-9.099664136444710536 + 2.0491075006185079929e-729j)  +/-  (5.68e-241, 5.68e-241j)
| (10.081516087750509764 - 2.5508956659430981831e-735j)  +/-  (1.09e-242, 1.09e-242j)
| (-9.5625926940253842496 - 2.7496551872412998819e-732j)  +/-  (9.69e-242, 9.69e-242j)
| (8.672804586297967672 - 3.8145178589762245714e-733j)  +/-  (2.12e-240, 2.12e-240j)
| (-8.672804586297967672 + 9.0467913523366462746e-731j)  +/-  (2.27e-240, 2.27e-240j)
| (-6.17036844409493152 + 2.4608984452821438777e-746j)  +/-  (3.65e-239, 3.65e-239j)
| (-1.5512593089268884234 + 2.0343369027711746019e-774j)  +/-  (1.36e-247, 1.36e-247j)
| (-2.0774514212592482241 - 8.9412814397866780606e-773j)  +/-  (5.01e-246, 5.01e-246j)
| (5.538863537176352736 + 6.3995679617085213885e-764j)  +/-  (1.73e-239, 1.73e-239j)
| (5.2313435654107309397 + 5.1042670371352664833e-765j)  +/-  (9.79e-240, 9.79e-240j)
| (5.8516406240482113938 - 9.1869463854740842725e-764j)  +/-  (2.99e-239, 2.99e-239j)
| (9.099664136444710536 - 6.4935383025272573554e-767j)  +/-  (5.53e-241, 5.53e-241j)
| (-3.1858834042579449489 - 1.9927991890656424132e-770j)  +/-  (4.34e-243, 4.34e-243j)
| (-7.5245784116837094617 + 1.0289667318875405111e-772j)  +/-  (2.19e-239, 2.19e-239j)
| (2.0774514212592482241 + 9.1602117565860545207e-799j)  +/-  (4.83e-246, 4.83e-246j)
| (3.1858834042579449489 - 1.032098562878656827e-795j)  +/-  (4.11e-243, 4.11e-243j)
| (-4.6298174370896833479 - 8.7749590288454753787e-793j)  +/-  (1.92e-240, 1.92e-240j)
| (-10.081516087750509764 - 1.039301283949825914e-801j)  +/-  (1.07e-242, 1.07e-242j)
| (4.0433149992900180594 - 5.2828925579520595785e-810j)  +/-  (2.35e-241, 2.35e-241j)
| (-10.708657994858956036 + 5.9468389230726865767e-808j)  +/-  (4.17e-244, 4.17e-244j)
| (1.5512593089268884234 - 7.7567431981840580644e-827j)  +/-  (1.35e-247, 1.35e-247j)
| (-6.8291869632800218696 - 2.0131960568883047988e-817j)  +/-  (3.93e-239, 3.93e-239j)
| (4.928494874964410633 - 1.5049139660244323484e-842j)  +/-  (4.54e-240, 4.54e-240j)
| (-2.6266449083870267681 + 3.2786415685966847446e-849j)  +/-  (1.68e-244, 1.68e-244j)
| (-7.8903632637224606081 - 2.9047153420946799994e-842j)  +/-  (1.34e-239, 1.34e-239j)
| (8.2717546150542150383 + 7.3765540310998437547e-853j)  +/-  (6.77e-240, 6.77e-240j)
| (6.4958791157253554273 - 1.1659018532840654529e-852j)  +/-  (4.23e-239, 4.23e-239j)
| (7.1715523802769227897 + 7.8697771818869670243e-855j)  +/-  (3.36e-239, 3.36e-239j)
| (4.6298174370896833479 - 5.7598598920266984602e-864j)  +/-  (1.98e-240, 1.98e-240j)
| (-6.4958791157253554273 + 2.1510607243869617403e-869j)  +/-  (4.17e-239, 4.17e-239j)
| (2.9051015048690439525 + 5.6063990537881497207e-888j)  +/-  (8.38e-244, 8.38e-244j)
| (9.5625926940253842496 - 6.0412486643186782387e-886j)  +/-  (9.72e-242, 9.72e-242j)
| (-2.9051015048690439525 - 3.1506179767668936541e-887j)  +/-  (9.21e-244, 9.21e-244j)
| (-0.69079208510670039548 + 3.7875891570215086266e-895j)  +/-  (2.07e-251, 2.07e-251j)
| (7.5245784116837094617 - 7.1062738498641601095e-883j)  +/-  (2.27e-239, 2.27e-239j)
| (-4.3348812144519829992 + 5.7092089429953963544e-883j)  +/-  (7.61e-241, 7.61e-241j)
| (1.1686124772502373741 - 3.823343000290244721e-903j)  +/-  (6.26e-249, 6.26e-249j)
| (4.3348812144519829992 + 1.9499890726424357818e-893j)  +/-  (8.06e-241, 8.06e-241j)
| (-8.2717546150542150383 + 4.3249702882788412938e-891j)  +/-  (6.55e-240, 6.55e-240j)
| (-1.8088049566691975024 - 1.8650303891303192877e-908j)  +/-  (7.67e-247, 7.67e-247j)
| (-0.94437090455162696219 + 2.8607528525270398163e-911j)  +/-  (3.62e-250, 3.62e-250j)
| (6.17036844409493152 - 1.7096740055076986659e-898j)  +/-  (3.64e-239, 3.64e-239j)
| (0.94437090455162696219 + 2.1763410253784077986e-912j)  +/-  (3.97e-250, 3.97e-250j)
| (7.8903632637224606081 + 4.9942411267465734357e-900j)  +/-  (1.33e-239, 1.33e-239j)
| (-5.8516406240482113938 + 5.0065644563207837836e-910j)  +/-  (2.72e-239, 2.72e-239j)
| (-7.1715523802769227897 + 2.2268903368144510639e-920j)  +/-  (3.24e-239, 3.24e-239j)
| (6.8291869632800218696 - 1.2936479742168497501e-927j)  +/-  (4.3e-239, 4.3e-239j)
| (0.69079208510670039548 - 6.6254580699740272823e-940j)  +/-  (2.11e-251, 2.11e-251j)
| (-2.3506049736744922228 - 3.8190088469636419796e-933j)  +/-  (3.1e-245, 3.1e-245j)
| (-4.0433149992900180594 - 2.1330962266375130138e-929j)  +/-  (2.33e-241, 2.33e-241j)
| (-1.3358490740136969497 + 7.5218766069521663187e-937j)  +/-  (2.98e-248, 2.98e-248j)
| (0.19744572806734265644 + 3.116103791390232683e-942j)  +/-  (6.95e-254, 6.95e-254j)
| (3.4690623817711084244 + 1.2232548029452011057e-931j)  +/-  (1.94e-242, 1.94e-242j)
| (2.6266449083870267681 - 1.8465477696407561536e-933j)  +/-  (1.54e-244, 1.54e-244j)
| (-4.928494874964410633 + 7.5031364547141663153e-927j)  +/-  (4.62e-240, 4.62e-240j)
| (-1.1686124772502373741 + 4.317629050395557284e-953j)  +/-  (5.82e-249, 5.82e-249j)
| (-5.2313435654107309397 + 3.0795220785973766045e-942j)  +/-  (9.95e-240, 9.95e-240j)
| (2.3506049736744922228 + 1.5042423527046025263e-963j)  +/-  (2.99e-245, 2.99e-245j)
| (0.43607741192761650868 - 6.4147232928206123905e-971j)  +/-  (1.19e-252, 1.19e-252j)
| (1.8088049566691975024 + 1.6240790242980754684e-964j)  +/-  (8.23e-247, 8.23e-247j)
| (4.2590591642679226598e-998 + 3.1668676271289798574e-998j)  +/-  (3.66e-996, 3.66e-996j)
| (-0.43607741192761650868 - 4.1499070057808055991e-970j)  +/-  (1.19e-252, 1.19e-252j)
| (-3.7547991675660930199 - 1.8447087629752346661e-956j)  +/-  (7.41e-242, 7.41e-242j)
| (1.3358490740136969497 - 2.9108224311163745321e-968j)  +/-  (3.26e-248, 3.26e-248j)
| (3.7547991675660930199 - 2.5767171917471644747e-962j)  +/-  (7.18e-242, 7.18e-242j)
| (-3.4690623817711084244 + 1.1928212565612799842e-958j)  +/-  (1.88e-242, 1.88e-242j)
| (-5.538863537176352736 - 1.3623619847550815085e-960j)  +/-  (1.81e-239, 1.81e-239j)
| (-0.19744572806734265644 + 3.2685764987634799962e-986j)  +/-  (6.95e-254, 6.95e-254j)
-------------------------------------------------
The weights are:
| (6.4379611981199995542e-51 + 1.5995798501973431348e-774j)  +/-  (6.07e-67, 1.55e-185j)
| (2.7304441211370302879e-37 + 7.4213873060060368727e-765j)  +/-  (1.15e-62, 2.92e-181j)
| (2.2822799353149846956e-45 - 1.1308074647621971014e-771j)  +/-  (1.45e-65, 3.7e-184j)
| (5.3091227467357265005e-41 + 2.1634210470240474378e-768j)  +/-  (2.17e-64, 5.53e-183j)
| (5.0174239934687051832e-34 + 2.7821374780149697815e-765j)  +/-  (3.31e-62, 8.43e-181j)
| (5.0174239934687051832e-34 + 3.4458122867832559941e-763j)  +/-  (1.19e-61, 3.04e-180j)
| (5.2984487697441278371e-18 - 2.5279016014094670823e-756j)  +/-  (1.3e-53, 3.32e-172j)
| (0.012492723938700778558 - 6.0289343946634101444e-747j)  +/-  (1.27e-17, 3.24e-136j)
| (0.0020446811984016417691 - 6.5860769888883657945e-748j)  +/-  (2.03e-25, 5.18e-144j)
| (8.3008434028776626416e-15 - 2.1890240542577085026e-755j)  +/-  (3.73e-52, 9.51e-171j)
| (2.2415148651170277756e-13 + 1.3834291648541724047e-754j)  +/-  (5.4e-51, 1.38e-169j)
| (2.3967241324613713762e-16 + 3.0854673721917660989e-756j)  +/-  (7.28e-54, 1.86e-172j)
| (2.7304441211370302879e-37 - 1.1701837610736718381e-767j)  +/-  (1.89e-65, 4.82e-184j)
| (6.2170858352317529881e-06 - 9.3343742408072648627e-750j)  +/-  (4.69e-41, 1.2e-159j)
| (5.2129492268008090495e-26 - 3.4453095341120887107e-760j)  +/-  (4.61e-62, 1.18e-180j)
| (0.0020446811984016417691 - 3.9506677435515222532e-748j)  +/-  (1.81e-32, 4.62e-151j)
| (6.2170858352317529881e-06 - 4.1626159110269172839e-750j)  +/-  (3.71e-42, 9.46e-161j)
| (8.2150173307370349632e-11 + 1.4132519932487272887e-752j)  +/-  (3.14e-51, 8.01e-170j)
| (2.2822799353149846956e-45 + 5.3226250985498464776e-771j)  +/-  (3e-70, 7.67e-189j)
| (1.2995486829471858015e-08 + 8.1481636987428616719e-752j)  +/-  (3.56e-49, 9.08e-168j)
| (6.4379611981199995542e-51 - 9.5118307575343109171e-774j)  +/-  (8.37e-73, 2.14e-191j)
| (0.012492723938700778558 - 4.1308649845858342286e-747j)  +/-  (1.34e-30, 3.42e-149j)
| (1.0599690121140208438e-21 - 3.742391807861573717e-758j)  +/-  (4.33e-61, 1.1e-179j)
| (4.7917979399959074714e-12 - 7.8552693954147822669e-754j)  +/-  (9.09e-54, 2.32e-172j)
| (0.00015777471398865804965 - 8.2493928609552276617e-749j)  +/-  (2.09e-42, 5.34e-161j)
| (1.9272557844473238826e-28 + 2.8992729831301756409e-761j)  +/-  (5.84e-64, 1.49e-182j)
| (4.2430999217482109143e-31 - 5.2339126340784136993e-764j)  +/-  (3.09e-67, 7.88e-186j)
| (8.7746705968310562442e-20 + 4.16217428680972304e-758j)  +/-  (8.08e-62, 2.06e-180j)
| (9.0360032537534298916e-24 + 3.0835106976667126624e-760j)  +/-  (1.29e-64, 3.29e-183j)
| (8.2150173307370349632e-11 + 4.0384355398033575516e-753j)  +/-  (3.52e-55, 8.98e-174j)
| (8.7746705968310562442e-20 + 3.265432146853437219e-757j)  +/-  (8.15e-64, 2.08e-182j)
| (3.40965770164442089e-05 + 1.3660756980200963894e-749j)  +/-  (5.57e-49, 1.42e-167j)
| (5.3091227467357265005e-41 + 1.9021841582031942447e-769j)  +/-  (1.76e-72, 4.49e-191j)
| (3.40965770164442089e-05 + 2.8341094539376870593e-749j)  +/-  (2.25e-51, 5.73e-170j)
| (0.089830388317026199502 - 2.4166598110596949459e-746j)  +/-  (1.21e-40, 3.08e-159j)
| (5.2129492268008090495e-26 - 2.0422663512417280176e-761j)  +/-  (3.93e-66, 1e-184j)
| (1.1420037477738585828e-09 - 6.0025334079544526678e-752j)  +/-  (2.93e-59, 7.47e-178j)
| (0.027298736810577308052 - 1.6849702853243243152e-746j)  +/-  (1.16e-40, 2.96e-159j)
| (1.1420037477738585828e-09 - 1.8932231252175224042e-752j)  +/-  (7.75e-56, 1.98e-174j)
| (4.2430999217482109143e-31 - 2.6759543299166212952e-762j)  +/-  (2.95e-70, 7.53e-189j)
| (0.005674203591995294039 + 1.9177075708031847015e-747j)  +/-  (2.81e-47, 7.18e-166j)
| (0.057089487205621103946 + 2.1939889098941077707e-746j)  +/-  (2.37e-42, 6.04e-161j)
| (5.2984487697441278371e-18 - 3.8366860210769009073e-757j)  +/-  (7.47e-62, 1.91e-180j)
| (0.057089487205621103946 + 1.7458020492824406404e-746j)  +/-  (2.05e-44, 5.24e-163j)
| (1.9272557844473238826e-28 + 1.117171240426393395e-762j)  +/-  (1.64e-67, 4.17e-186j)
| (2.3967241324613713762e-16 + 1.7445860505254491938e-755j)  +/-  (4.17e-65, 1.06e-183j)
| (9.0360032537534298916e-24 + 3.7996222039910297952e-759j)  +/-  (9.3e-68, 2.37e-186j)
| (1.0599690121140208438e-21 - 3.8888378566582801735e-759j)  +/-  (6.49e-65, 1.66e-183j)
| (0.089830388317026199502 - 2.0453406673623405205e-746j)  +/-  (8.11e-48, 2.07e-166j)
| (0.00061759079405803648692 + 2.3363665795231685508e-748j)  +/-  (1.26e-53, 3.22e-172j)
| (1.2995486829471858015e-08 + 2.3538480538316501078e-751j)  +/-  (1.06e-60, 2.71e-179j)
| (0.016659418451415875629 + 1.5943941678344299762e-746j)  +/-  (2.33e-50, 5.95e-169j)
| (0.11994145524512434956 - 4.5417068840541111843e-746j)  +/-  (1.3e-49, 3.31e-168j)
| (9.5262675994048616296e-07 + 1.1995788746072793636e-750j)  +/-  (4.99e-58, 1.27e-176j)
| (0.00015777471398865804965 - 4.2867244279309250463e-749j)  +/-  (2.85e-56, 7.27e-175j)
| (4.7917979399959074714e-12 - 3.0548498334305407398e-753j)  +/-  (1.05e-63, 2.68e-182j)
| (0.027298736810577308052 - 2.2370362794700301194e-746j)  +/-  (1.74e-52, 4.43e-171j)
| (2.2415148651170277756e-13 + 6.0281778589558012812e-754j)  +/-  (9.9e-65, 2.52e-183j)
| (0.00061759079405803648692 + 1.3058226969133355433e-748j)  +/-  (9.76e-57, 2.47e-175j)
| (0.11683059473455854791 + 2.8940567585918990582e-746j)  +/-  (6.57e-53, 1.66e-171j)
| (0.005674203591995294039 + 1.2317321865609908783e-747j)  +/-  (5.92e-56, 1.5e-174j)
| (0.10264308487419880868 + 5.6724213541017971943e-746j)  +/-  (2.48e-53, 6.26e-172j)
| (0.11683059473455854791 + 3.214998804195031762e-746j)  +/-  (4.59e-54, 1.16e-172j)
| (1.2204715593982361306e-07 - 8.5714140665971897568e-751j)  +/-  (5.59e-62, 1.42e-180j)
| (0.016659418451415875629 + 1.1524426853974838455e-746j)  +/-  (1.13e-55, 2.89e-174j)
| (1.2204715593982361306e-07 - 3.2409764313833693936e-751j)  +/-  (3.72e-61, 9.57e-180j)
| (9.5262675994048616296e-07 + 2.9162412202591135744e-750j)  +/-  (1.72e-61, 4.29e-180j)
| (8.3008434028776626416e-15 - 1.0796592538384344871e-754j)  +/-  (1.92e-66, 5.1e-185j)
| (0.11994145524512434956 - 4.7630423991016090172e-746j)  +/-  (2.7e-56, 4.98e-175j)
