Starting with polynomial:
P : 8*t^3 - 12*t
Extension levels are: 3 66
-------------------------------------------------
Trying to find an order 66 Kronrod extension for:
P1 : 8*t^3 - 12*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 8*t^69 - 29416145360067734608038557393760395427/3224828964809030041731651376088176*t^67 + 31584683012233305857088598242248983406985/6449657929618060083463302752176352*t^65 - 1328158750919508347882924755713486819008265/806207241202257510432912844022044*t^63 + 628694089441573733036324006643837012328285635/1612414482404515020865825688044088*t^61 - 445725537522582581140168920959332910421875266905/6449657929618060083463302752176352*t^59 + 122977269948833281262141328792291710949845193870315/12899315859236120166926605504352704*t^57 - 13548726049012350997482471513175556511659961150617175/12899315859236120166926605504352704*t^55 + 2427611791991087034706879355360542386616348968378422925/25798631718472240333853211008705408*t^53 - 1433267789663557929141053894190705665756229652970279162925/206389053747777922670825688069643264*t^51 + 175919173566929922347490890423043058271589925063311401742375/412778107495555845341651376139286528*t^49 - 4519493723801484124224748940455519671165691581421471800206625/206389053747777922670825688069643264*t^47 + 390704723571565371980056889795486078016177248070410549387596875/412778107495555845341651376139286528*t^45 - 57005477484426704401821379909675084830507178726044996763925304375/1651112429982223381366605504557146112*t^43 + 3515483499542997663560106824057199249024195567115794485447133733125/3302224859964446762733211009114292224*t^41 - 91679107836639592414208080267703051057138534908312769242976332464375/3302224859964446762733211009114292224*t^39 + 4041614688384750080006873208892588004808953232359763906865292380093125/6604449719928893525466422018228584448*t^37 - 32504532946603445954801517462103158699113037742122008652693826133053125/2855978257266548551553047359233982464*t^35 + 1017258676499942237943286933726895294872632812335110011450254416814659375/5711956514533097103106094718467964928*t^33 - 3334952065937852148269573578357637948839785292324824875481046614346884375/1427989128633274275776523679616991232*t^31 + 72918247956154263624852339825002752516731329223197708679846804272283028125/2855978257266548551553047359233982464*t^29 - 2640889267997800639027567632856696345286922482127271908184025290758705121875/11423913029066194206212189436935929856*t^27 + 39284445676069562849129841916384703510651908283459344424650223933144806265625/22847826058132388412424378873871859712*t^25 - 237617631426827887666908143830501937926770999973973927345459577866225092265625/22847826058132388412424378873871859712*t^23 + 2308966089019172185766303400674967491598769888296787039005403204609206931171875/45695652116264776824848757747743719424*t^21 - 70998356130705933071876723980594029021775048302762523955401312869521778094265625/365565216930118214598790061981949755392*t^19 + 423655470601264361540114107017117873296814394205644753132223244191299567865296875/731130433860236429197580123963899510784*t^17 - 478972121765115521827678729320642044524455438922106280998671599297461564310234375/365565216930118214598790061981949755392*t^15 + 1591695635399062484212607186768425376698458930389141328810093897160935995185078125/731130433860236429197580123963899510784*t^13 - 7462425759031548786384185711005969706314232914206204144983669321558517771595078125/2924521735440945716790320495855598043136*t^11 + 11664815654697338521863658339811440955252442958136734047479654595552690635287734375/5849043470881891433580640991711196086272*t^9 - 5602364952292357317303663605484350776797363236261860933058273478337605690571640625/5849043470881891433580640991711196086272*t^7 + 2908244808880096034138011251907157288613652717174654702514680072254683013090234375/11698086941763782867161281983422392172544*t^5 - 10375455116694945836584209758619196993716537263284669904047845693819695959965234375/374338782136441051749161023469516549521408*t^3 + 586793765457355774739240758726528971676756750344501233328366321474199602308203125/748677564272882103498322046939033099042816*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:
| (8.8583939136815018661 + 1.8665512290305899793e-611j)  +/-  (5.2e-240, 5.2e-240j)
| (10.883227945119785101 - 7.0550922540440614915e-623j)  +/-  (7.75e-244, 7.75e-244j)
| (9.7431765106212673779 - 3.8679879575877321127e-633j)  +/-  (1.92e-241, 1.92e-241j)
| (-8.8583939136815018661 + 1.4277314333623355206e-649j)  +/-  (5.47e-240, 5.47e-240j)
| (7.7171030055648293572 - 8.6520938191873232862e-653j)  +/-  (5.53e-239, 5.53e-239j)
| (8.4597032781757432285 + 2.7642602306202538765e-666j)  +/-  (1.44e-239, 1.44e-239j)
| (-9.2828136718410588547 + 5.9988148120152100684e-680j)  +/-  (1.22e-240, 1.22e-240j)
| (10.259319030704773703 - 2.0406707113524832745e-676j)  +/-  (1.79e-242, 1.79e-242j)
| (-2.3041345149732135922 + 1.9176133974423870226e-689j)  +/-  (1.63e-245, 1.63e-245j)
| (6.0553019700314595482 + 2.0555701276568835849e-681j)  +/-  (7.65e-239, 7.65e-239j)
| (-7.7171030055648293572 - 4.7276683976974880301e-699j)  +/-  (5.69e-239, 5.69e-239j)
| (5.7447428836336336962 - 1.614478381395236084e-707j)  +/-  (5.02e-239, 5.02e-239j)
| (-3.408956059957243411 + 6.3659923125354422301e-725j)  +/-  (1.81e-242, 1.81e-242j)
| (-2.0320909704495340096 - 6.6830622231505407535e-729j)  +/-  (2.39e-246, 2.39e-246j)
| (-7.0261893344829362626 + 1.3962338523678614682e-720j)  +/-  (1.1e-238, 1.1e-238j)
| (6.6951042649687774604 + 7.8519228380238502437e-722j)  +/-  (1.25e-238, 1.25e-238j)
| (3.408956059957243411 - 5.0040024384351543359e-737j)  +/-  (1.78e-242, 1.78e-242j)
| (-5.1388103181796447255 - 6.1295355427897335296e-736j)  +/-  (1.53e-239, 1.53e-239j)
| (-9.7431765106212673779 - 2.6943208871304724859e-737j)  +/-  (2.19e-241, 2.19e-241j)
| (4.8423455784133623795 - 1.4611362735133982774e-733j)  +/-  (6.76e-240, 6.76e-240j)
| (-10.883227945119785101 - 1.9873393459070747693e-744j)  +/-  (8.17e-244, 8.17e-244j)
| (8.0806178151346877413 - 2.2405459500022993363e-738j)  +/-  (3.27e-239, 3.27e-239j)
| (9.2828136718410588547 + 8.1450044822569260936e-755j)  +/-  (1.22e-240, 1.22e-240j)
| (-8.0806178151346877413 - 1.569083277483657973e-762j)  +/-  (3.51e-239, 3.51e-239j)
| (-3.9738452339528649093 - 1.8541173820708317937e-764j)  +/-  (2.83e-241, 2.83e-241j)
| (-6.6951042649687774604 - 1.1623996299576096374e-762j)  +/-  (1.25e-238, 1.25e-238j)
| (-7.3663233414184018556 + 1.0915799938224543151e-761j)  +/-  (9.2e-239, 9.2e-239j)
| (3.9738452339528649093 + 3.8637491256872896341e-764j)  +/-  (2.92e-241, 2.92e-241j)
| (4.5496104699177409378 - 4.2213266578841733506e-762j)  +/-  (2.71e-240, 2.71e-240j)
| (4.2602227468228461311 - 7.9614944795192127743e-765j)  +/-  (9.28e-241, 9.28e-241j)
| (-3.129939317598199277 + 2.5430485151126760535e-772j)  +/-  (3.73e-243, 3.73e-243j)
| (3.129939317598199277 + 2.9163079521548041349e-772j)  +/-  (3.5e-243, 3.5e-243j)
| (0.69683347692689977507 - 3.0258829894790922399e-780j)  +/-  (1.23e-251, 1.23e-251j)
| (-1.4923303889950492595 + 8.917306903366388234e-778j)  +/-  (2.45e-248, 2.45e-248j)
| (-10.259319030704773703 + 1.5500788460023586681e-772j)  +/-  (2e-242, 2e-242j)
| (7.0261893344829362626 - 5.0589624432959949131e-766j)  +/-  (1.12e-238, 1.12e-238j)
| (3.690178620829792846 - 7.7983690661019994604e-780j)  +/-  (7.52e-242, 7.52e-242j)
| (2.8529164334304743129 + 4.6948199527741155284e-782j)  +/-  (6.32e-244, 6.32e-244j)
| (-4.2602227468228461311 + 6.2618352966476148639e-780j)  +/-  (9.5e-241, 9.5e-241j)
| (-8.4597032781757432285 + 1.8384380193166510071e-779j)  +/-  (1.46e-239, 1.46e-239j)
| (-2.5777011126839538752 - 1.3006550958676719125e-783j)  +/-  (1.09e-244, 1.09e-244j)
| (2.5777011126839538752 - 3.9771126530514603374e-783j)  +/-  (1.15e-244, 1.15e-244j)
| (5.4394414810395073114 - 3.4226572194945012911e-776j)  +/-  (3.09e-239, 3.09e-239j)
| (6.3718122523192153882 + 6.6328960561035053811e-787j)  +/-  (9.81e-239, 9.81e-239j)
| (-6.3718122523192153882 - 7.0590480625034795254e-802j)  +/-  (9.35e-239, 9.35e-239j)
| (-0.95917481838664503469 + 2.5163114199152585376e-816j)  +/-  (1.62e-250, 1.62e-250j)
| (-5.4394414810395073114 - 1.877992045138430143e-804j)  +/-  (2.92e-239, 2.92e-239j)
| (-0.20346967168225022281 + 2.8987423707667505191e-819j)  +/-  (6.93e-254, 6.93e-254j)
| (0.95917481838664503469 - 2.4689275599623100224e-816j)  +/-  (1.59e-250, 1.59e-250j)
| (-4.8423455784133623795 - 1.0313272249448737928e-804j)  +/-  (6.99e-240, 6.99e-240j)
| (-2.8529164334304743129 + 1.4199525419156096771e-809j)  +/-  (6.92e-244, 6.92e-244j)
| (-0.44126815861972908728 + 4.8484621488788027358e-818j)  +/-  (9.22e-253, 9.22e-253j)
| (-6.0553019700314595482 + 1.533808837912070081e-802j)  +/-  (7.79e-239, 7.79e-239j)
| (2.3041345149732135922 - 2.9368721887846073144e-812j)  +/-  (1.61e-245, 1.61e-245j)
| (2.0320909704495340096 - 3.9087826153826381518e-813j)  +/-  (2.22e-246, 2.22e-246j)
| (-5.7447428836336336962 - 1.7059662966088002482e-805j)  +/-  (5.21e-239, 5.21e-239j)
| (-1.7614910787897221214 - 3.0780517549914736006e-814j)  +/-  (2.36e-247, 2.36e-247j)
| (-4.5496104699177409378 - 4.2608179609928696829e-808j)  +/-  (2.78e-240, 2.78e-240j)
| (1.7614910787897221214 + 1.7328260680475736816e-813j)  +/-  (2.45e-247, 2.45e-247j)
| (0.20346967168225022281 + 7.3427411259259950151e-820j)  +/-  (7.03e-254, 7.03e-254j)
| (5.1388103181796447255 + 5.2092837439228105775e-804j)  +/-  (1.48e-239, 1.48e-239j)
| (-3.690178620829792846 - 2.8475532029371911312e-824j)  +/-  (7.73e-242, 7.73e-242j)
| (-1.2247448713915890491 - 4.2015733862878085608e-840j)  +/-  (2.05e-249, 2.05e-249j)
| (7.3663233414184018556 + 2.3643404536331259136e-827j)  +/-  (8.77e-239, 8.77e-239j)
| (0.44126815861972908728 - 2.7034453816405943339e-867j)  +/-  (9.51e-253, 9.51e-253j)
| (1.4923303889950492595 + 1.9533209367743281756e-862j)  +/-  (2.27e-248, 2.27e-248j)
| (-5.6968709924319459785e-880 + 2.2645597514306646324e-880j)  +/-  (4.23e-878, 4.23e-878j)
| (-0.69683347692689977507 - 4.2450567147131426125e-866j)  +/-  (1.32e-251, 1.32e-251j)
| (1.2247448713915890491 + 6.9743563353243930049e-865j)  +/-  (1.93e-249, 1.93e-249j)
-------------------------------------------------
The weights are:
| (1.9272238797015505067e-35 - 3.2271718295360072014e-645j)  +/-  (4.75e-50, 6.47e-169j)
| (1.4776340983466071655e-52 + 4.0045813707819977908e-655j)  +/-  (1.34e-56, 1.82e-175j)
| (1.6164506195177449561e-42 + 1.0706211161191706262e-649j)  +/-  (2.87e-53, 3.9e-172j)
| (1.9272238797015505067e-35 - 2.0304256823114269268e-647j)  +/-  (3.36e-54, 4.58e-173j)
| (2.7539246101301393949e-27 + 4.324441699887922608e-642j)  +/-  (1.01e-47, 1.37e-166j)
| (1.8170975912512028351e-32 + 2.9009606894627611029e-644j)  +/-  (1.23e-49, 1.67e-168j)
| (9.367486935054320508e-39 + 4.1719831924001551123e-649j)  +/-  (1.59e-56, 2.17e-175j)
| (6.1007151359138547065e-47 - 3.9451454541243865587e-652j)  +/-  (3.08e-55, 4.19e-174j)
| (0.0007613149241829602201 + 7.7436059074537856991e-631j)  +/-  (1.38e-20, 1.88e-139j)
| (2.1057108341790109107e-17 - 1.9614857962717501186e-637j)  +/-  (2.29e-43, 3.12e-162j)
| (2.7539246101301393949e-27 + 2.9775553751465468619e-643j)  +/-  (1.51e-52, 2.05e-171j)
| (8.0744103292629312004e-16 + 1.1524755975064254292e-636j)  +/-  (1.98e-42, 2.7e-161j)
| (1.4183468505819886119e-06 + 2.0623510050045193771e-632j)  +/-  (1.27e-32, 1.73e-151j)
| (0.0024633344748206660021 - 1.6160835740350350124e-630j)  +/-  (1.19e-19, 1.62e-138j)
| (6.8706029476238687447e-23 + 5.3896212442907980282e-641j)  +/-  (1.4e-50, 1.91e-169j)
| (6.2947275421271641311e-21 - 3.9750665183057492146e-639j)  +/-  (1.39e-46, 1.9e-165j)
| (1.4183468505819886119e-06 + 4.6426039209871480051e-632j)  +/-  (1.34e-33, 1.82e-152j)
| (5.7246652016430005338e-13 + 7.6292683794926591169e-636j)  +/-  (6.25e-44, 8.51e-163j)
| (1.6164506195177449561e-42 - 5.0924030060433772926e-651j)  +/-  (1.46e-59, 1.99e-178j)
| (1.0891448638613615995e-11 - 1.230646952087094124e-634j)  +/-  (9.58e-42, 1.3e-160j)
| (1.4776340983466071655e-52 - 4.1073690394936552409e-656j)  +/-  (6.66e-64, 9.06e-183j)
| (9.1758003354073781521e-30 - 3.498227393063851076e-643j)  +/-  (2.34e-51, 3.19e-170j)
| (9.367486935054320508e-39 - 1.783253764264887564e-647j)  +/-  (5.09e-55, 6.93e-174j)
| (9.1758003354073781521e-30 - 1.6062552509944714886e-644j)  +/-  (3.25e-55, 4.43e-174j)
| (2.2289177705651460702e-08 + 2.121739486066829789e-633j)  +/-  (5.05e-42, 6.88e-161j)
| (6.2947275421271641311e-21 - 5.5288014009601989433e-640j)  +/-  (5.19e-52, 7.06e-171j)
| (5.2898183522664510176e-25 - 4.4164607088141994936e-642j)  +/-  (2.61e-53, 3.55e-172j)
| (2.2289177705651460702e-08 + 5.5740397484790721139e-633j)  +/-  (1.77e-43, 2.41e-162j)
| (1.6822034634053751429e-10 + 4.797081597596946601e-634j)  +/-  (1.15e-45, 1.57e-164j)
| (2.1297764987398587979e-09 - 1.7077414693938360488e-633j)  +/-  (9.85e-45, 1.34e-163j)
| (8.7271875641584818138e-06 - 5.6985472367050332737e-632j)  +/-  (2.96e-42, 4.03e-161j)
| (8.7271875641584818138e-06 - 1.1925744031299051281e-631j)  +/-  (9.83e-42, 1.34e-160j)
| (0.090228993034118249162 + 3.6047633909497034118e-629j)  +/-  (2.82e-32, 3.84e-151j)
| (0.016331761683645408925 - 5.9231879825482015598e-630j)  +/-  (2.82e-32, 3.84e-151j)
| (6.1007151359138547065e-47 + 2.8909594850967464407e-653j)  +/-  (2.14e-66, 2.91e-185j)
| (6.8706029476238687447e-23 + 4.6726161643183283816e-640j)  +/-  (2.61e-54, 3.55e-173j)
| (1.9423350624349255015e-07 - 1.6741422972881198358e-632j)  +/-  (1.38e-43, 1.87e-162j)
| (4.5466959521724048549e-05 + 2.8467264943887901795e-631j)  +/-  (8.3e-42, 1.13e-160j)
| (2.1297764987398587979e-09 - 5.9857588557006283279e-634j)  +/-  (1.4e-49, 1.9e-168j)
| (1.8170975912512028351e-32 + 6.6784811751890635684e-646j)  +/-  (1.32e-60, 1.8e-179j)
| (0.00020140419951069480344 - 3.479179858166112381e-631j)  +/-  (2.11e-42, 2.88e-161j)
| (0.00020140419951069480344 - 6.3350067791064190006e-631j)  +/-  (2.67e-42, 3.64e-161j)
| (2.4154144071967535845e-14 - 6.062011175578994502e-636j)  +/-  (1.22e-50, 1.66e-169j)
| (4.2061287463607234172e-19 + 2.9701012968717472246e-638j)  +/-  (4.14e-53, 5.64e-172j)
| (4.2061287463607234172e-19 + 4.8491788861509250341e-639j)  +/-  (4.44e-57, 6.05e-176j)
| (0.059416960850843420763 - 1.8174484235704653541e-629j)  +/-  (2.51e-41, 3.41e-160j)
| (2.4154144071967535845e-14 - 1.4495710212960650354e-636j)  +/-  (1.66e-55, 2.26e-174j)
| (0.12011339114135086672 + 8.549690700333653327e-629j)  +/-  (4.76e-42, 6.49e-161j)
| (0.059416960850843420763 - 2.2588213594455208649e-629j)  +/-  (5.41e-42, 7.36e-161j)
| (1.0891448638613615995e-11 - 3.6073510091070953635e-635j)  +/-  (3.9e-54, 5.3e-173j)
| (4.5466959521724048549e-05 + 1.4597813009627667961e-631j)  +/-  (1.94e-48, 2.64e-167j)
| (0.11589833818688259755 - 5.2251233263811255869e-629j)  +/-  (2.72e-43, 3.7e-162j)
| (2.1057108341790109107e-17 - 3.686695153223464608e-638j)  +/-  (2.36e-57, 3.22e-176j)
| (0.0007613149241829602201 + 1.3188098887158280679e-630j)  +/-  (4.7e-49, 6.4e-168j)
| (0.0024633344748206660021 - 2.5782526619289150513e-630j)  +/-  (6.36e-49, 8.66e-168j)
| (8.0744103292629312004e-16 + 2.4572849526004998908e-637j)  +/-  (8.46e-57, 1.15e-175j)
| (0.0068400271837329892186 + 3.1777918863952371422e-630j)  +/-  (2.73e-48, 3.72e-167j)
| (1.6822034634053751429e-10 + 1.5415855465704281721e-634j)  +/-  (2.78e-54, 3.78e-173j)
| (0.0068400271837329892186 + 4.7552834170992588567e-630j)  +/-  (2.64e-50, 3.55e-169j)
| (0.12011339114135086672 + 8.9516821473159403463e-629j)  +/-  (3.73e-48, 5.09e-167j)
| (5.7246652016430005338e-13 + 2.8709780249751551037e-635j)  +/-  (1.87e-56, 2.51e-175j)
| (1.9423350624349255015e-07 - 6.8950693789740434788e-633j)  +/-  (6.98e-53, 9.64e-172j)
| (0.033573136685853614709 + 1.0551242355936017545e-629j)  +/-  (1.35e-49, 1.85e-168j)
| (5.2898183522664510176e-25 - 4.8024421633143280127e-641j)  +/-  (7.49e-63, 1e-181j)
| (0.11589833818688259755 - 5.7729779304083103401e-629j)  +/-  (1.45e-49, 2.03e-168j)
| (0.016331761683645408925 - 8.323208942580098335e-630j)  +/-  (2.59e-51, 3.5e-170j)
| (0.1082310126179047499 - 1.0650358134909393917e-628j)  +/-  (1.1e-49, 1.77e-168j)
| (0.090228993034118249162 + 3.0789946772332328984e-629j)  +/-  (2.2e-50, 3.84e-169j)
| (0.033573136685853614709 + 1.3936931137448529622e-629j)  +/-  (4.68e-51, 6.06e-170j)
