Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 17 20
-------------------------------------------------
Trying to find an order 17 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 20 Kronrod extension for:
P2 : 3/2*t^19 - 746491/110950*t^17 + 2101438/166425*t^15 - 6950314/540485*t^13 + 120809429/15674065*t^11 - 684437/248211*t^9 + 60910694/106868625*t^7 - 153288694/2457978375*t^5 + 61922653/20647018350*t^3 - 276029/6882339450*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^39 - 65822967321607937893021911009189595903753315170710917011696513958504519/4633173321540989010239063358278102538075518218024572741092259737356050*t^37 + 35320036367130670499997349372840131824851360521327049525178887705546161679/569880318549541648259404793068206612183288740817022447154347947694794150*t^35 - 118279847937202673476396291497827179523680570627325691368807075007948239077181/716241866647879644722370212636495447523733954851428583653503196318465710410*t^33 + 3876902667696297838022273069575368325963856015841361189945754083372134266703446/12903205749156498448104517921587774047056358671490130090363868188222056510265*t^31 - 113187805319753967608795194349123423669676508621626331466346368359281754229266/286286705056029312538589618716581611429574598376098873759450104569521631463*t^29 + 5305520267551881860034818138685690958969736132363774461792471739861927113092816926618/13647113236807930690209963929666690942678805716578413355469882681101750040160019125*t^27 - 23687190258203757537522616619865677547157191656089757097985165090373379259162508668358/81377230782447290411992747876901379324862508161819427786320411542865990980213447375*t^25 + 8296264155339676416150737192363523295566698799898352225044289588663095043213112873837353/49513162297272229378272867518221875236419344465977412642308791199141383552001069920845*t^23 - 20650823889996757908948712225294825083412621639725086697268992062905416457922136324875131/277704258102092069121617387384809648065134584178742879602514524551706020791658174773435*t^21 + 1089626305666082919814739143287552343887502274484071170815850277497396331634383066354226611/42956503695783882468903463433933555533971899699365733619930182095043690641994548114987953*t^19 - 49554242068496087416435635824713602941091517754009677951430351629200446778277673629323114593/7517388146762179432058106100938372218445082447389003383487781866632645862349045920122891775*t^17 + 1705427102580346665675759775291827825178082861167860906763902336819590684037490700619965654/1326597908252149311539665782518536273843249843656882950027255623523408093355713985904039725*t^15 - 16265400660935600281872787906422773928368304108841628115257138430853696798440337698263794/88439860550143287435977718834569084922883322910458863335150374901560539557047599060269315*t^13 + 229989400348362417397899773458112951382675757433239362204145567651646671390637843253574/12314410962678179263237403888357720685464766481203132869451318024267923229462323919784335*t^11 - 44340998383219707640297175195744717873659523907544280846008074698355703463569074420747566/34544609530885968072492896976782684570878225928825232018709736436549546750982792192941194439*t^9 + 9982598703727009371899144158477012783832666818846401729869051977834003001935141854652423/179532916916790873495034769234175242393453145508231492570355261050167895300806626092346709450*t^7 - 153988806270284725465170747428524493683498611123277281854003137751593689070812463852429/113582049477969736292777098903253724779531581852146454483285981480718464373979702221688734550*t^5 + 7253066459715012358328570183150708984825301732473909136966890761572874499750280072479/477044607807472892429663815393665644074032643779015108829801122219017550370714749331092685110*t^3 - 181002163623370687013291906464961455131166248185749094250946784198009571022787358911/3657341993190625508627422584684769937900916935639115834361808603679134552842146411538377252510*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 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: 1
  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
-------------------------------------------------
The nodes are:
| (0.92981760888247565982 + 1.9348598647502087492e-935j)  +/-  (1.4e-242, 1.4e-242j)
| (0.99863808581647805167 + 8.762940288228002885e-933j)  +/-  (1.03e-242, 1.03e-242j)
| (-0.92981760888247565982 - 7.422043541469728872e-940j)  +/-  (1.35e-242, 1.35e-242j)
| (-0.99182888880131013627 - 3.523058145160782642e-958j)  +/-  (2.58e-242, 2.58e-242j)
| (0.95722644075867400963 + 2.071883994160878889e-970j)  +/-  (2.31e-242, 2.31e-242j)
| (0.81041322502523245672 + 8.8590639221651455703e-980j)  +/-  (8.19e-244, 8.19e-244j)
| (-0.97803621428030244756 - 1.1846256285041320934e-979j)  +/-  (2.72e-242, 2.72e-242j)
| (-0.89611184706327993449 - 7.9020006132119345607e-999j)  +/-  (7.02e-243, 7.02e-243j)
| (-0.14443509436305699224 - 3.9442969182595782662e-1012j)  +/-  (3.63e-253, 3.63e-253j)
| (-0.99863808581647805167 + 1.5703642188524318847e-1009j)  +/-  (9.94e-243, 9.94e-243j)
| (0.89611184706327993449 - 9.4783194544252160237e-1019j)  +/-  (6.91e-243, 6.91e-243j)
| (0.97803621428030244756 + 1.4858378254807038505e-1023j)  +/-  (2.85e-242, 2.85e-242j)
| (-0.70292907683295212742 - 7.9348764278130393253e-1035j)  +/-  (4.69e-245, 4.69e-245j)
| (-0.75913297880534811813 - 4.3607157326184421352e-1035j)  +/-  (2.29e-244, 2.29e-244j)
| (0.99182888880131013627 + 1.1030187098084885199e-1029j)  +/-  (2.55e-242, 2.55e-242j)
| (0.85623362151771762389 + 3.4273143142865696551e-1036j)  +/-  (2.78e-243, 2.78e-243j)
| (0.64219653306555369485 + 1.0158789264886971232e-1039j)  +/-  (6.74e-246, 6.74e-246j)
| (-0.95722644075867400963 - 7.9631482692411401791e-1036j)  +/-  (2.46e-242, 2.46e-242j)
| (-0.81041322502523245672 + 1.6990104767749311276e-1044j)  +/-  (8.38e-244, 8.38e-244j)
| (-0.85623362151771762389 - 7.1203073644439938016e-1055j)  +/-  (2.66e-243, 2.66e-243j)
| (0.43837095597551267509 - 9.0134769661654050939e-1062j)  +/-  (1.07e-248, 1.07e-248j)
| (0.75913297880534811813 - 1.3078188504904299436e-1058j)  +/-  (2.06e-244, 2.06e-244j)
| (0.072308224433399522721 + 2.8028321220231742017e-1069j)  +/-  (1.69e-254, 1.69e-254j)
| (-0.43837095597551267509 - 5.8678897494913044701e-1064j)  +/-  (1.05e-248, 1.05e-248j)
| (-0.57735026918962576451 - 1.9793886284340385322e-1062j)  +/-  (9.45e-247, 9.45e-247j)
| (-1.3372020886750194937e-1067 + 6.0774487523732157664e-1068j)  +/-  (5.73e-1066, 5.73e-1066j)
| (0.70292907683295212742 + 6.8479482379121414876e-1063j)  +/-  (4.08e-245, 4.08e-245j)
| (0.29186238049804889916 + 3.5900843492702513566e-1070j)  +/-  (7.25e-251, 7.25e-251j)
| (-0.29186238049804889916 - 2.3581261347836859747e-1069j)  +/-  (7.52e-251, 7.52e-251j)
| (-0.64219653306555369485 + 5.3458107042212810568e-1065j)  +/-  (7.46e-246, 7.46e-246j)
| (-0.21760818717427072216 + 1.0717154001009656262e-1072j)  +/-  (5.15e-252, 5.15e-252j)
| (0.36579533891893381721 + 1.0603168798571075267e-1068j)  +/-  (1.19e-249, 1.19e-249j)
| (0.50910782190642149248 + 9.3478150695173283613e-1066j)  +/-  (1.16e-247, 1.16e-247j)
| (-0.072308224433399522721 + 6.7486878743666823995e-1073j)  +/-  (1.69e-254, 1.69e-254j)
| (-0.50910782190642149248 + 2.9410315228244178999e-1067j)  +/-  (1.1e-247, 1.1e-247j)
| (-0.36579533891893381721 + 3.7291599012813266707e-1069j)  +/-  (1.06e-249, 1.06e-249j)
| (0.21760818717427072216 + 1.4567694541048412825e-1071j)  +/-  (5.41e-252, 5.41e-252j)
| (0.57735026918962576451 - 5.1588941936939076009e-1069j)  +/-  (1e-246, 1e-246j)
| (0.14443509436305699224 + 1.1276084377187730842e-1075j)  +/-  (3.26e-253, 3.26e-253j)
-------------------------------------------------
The weights are:
| (0.030586589601169037618 - 4.4363428088496463154e-933j)  +/-  (1.7e-80, 5.89e-198j)
| (0.0036624227062888572958 - 9.3805022631168902204e-933j)  +/-  (3.6e-81, 1.25e-198j)
| (0.030586589601169037618 - 1.5851831491590851519e-934j)  +/-  (4.87e-81, 1.69e-198j)
| (0.010208318702963117008 + 4.7925226054176813982e-935j)  +/-  (1.99e-81, 6.92e-199j)
| (0.024179654588414780601 + 5.4521690882144092244e-933j)  +/-  (3.38e-81, 1.17e-198j)
| (0.048645469757152079492 + 3.2890336850864438089e-933j)  +/-  (1.86e-82, 6.45e-200j)
| (0.017361401803001529932 - 8.0105857915210119663e-935j)  +/-  (1.36e-81, 4.74e-199j)
| (0.036810554417176413693 + 2.0848340823661405321e-934j)  +/-  (2.99e-82, 1.04e-199j)
| (0.072452283075643099361 + 5.3100084267628263274e-933j)  +/-  (1.13e-83, 3.92e-201j)
| (0.0036624227062888572958 - 1.6100928155779656236e-935j)  +/-  (9.13e-82, 3.17e-199j)
| (0.036810554417176413693 + 3.8678381404827484351e-933j)  +/-  (1.38e-82, 4.81e-200j)
| (0.017361401803001529932 - 7.6641142225599278266e-933j)  +/-  (1.44e-82, 5.01e-200j)
| (0.058524117823972256459 + 5.6143536560393187843e-934j)  +/-  (5.72e-85, 1.99e-202j)
| (0.053821228593152671197 - 4.373497606794818035e-934j)  +/-  (8.5e-85, 2.95e-202j)
| (0.010208318702963117008 + 1.397848194618178156e-932j)  +/-  (4.94e-83, 1.72e-200j)
| (0.042910539324775002125 - 3.495344755335396619e-933j)  +/-  (3.82e-84, 1.33e-201j)
| (0.062878281902872703905 - 3.3339594097831252266e-933j)  +/-  (5.65e-87, 1.96e-204j)
| (0.024179654588414780601 + 1.1601062421283915447e-934j)  +/-  (3.35e-84, 1.17e-201j)
| (0.048645469757152079492 + 3.4185646960015318662e-934j)  +/-  (1.12e-85, 3.88e-203j)
| (0.042910539324775002125 - 2.6788430405893074525e-934j)  +/-  (2.18e-85, 7.58e-203j)
| (0.071732023254246382832 + 4.2932200484132837109e-933j)  +/-  (3.53e-89, 1.23e-206j)
| (0.053821228593152671197 - 3.2120384090902564318e-933j)  +/-  (5.23e-87, 1.82e-204j)
| (0.072081926317540799871 - 7.4153694986549777148e-933j)  +/-  (5.57e-90, 1.93e-207j)
| (0.071732023254246382832 + 1.6735682731323264179e-933j)  +/-  (4.91e-90, 1.71e-207j)
| (0.066692554266833152633 + 9.4365456032736104133e-934j)  +/-  (1.8e-89, 6.26e-207j)
| (0.072461743528380496911 + 7.149088748041627161e-933j)  +/-  (2.45e-90, 8.51e-208j)
| (0.058524117823972256459 + 3.2322399809153964392e-933j)  +/-  (2.54e-89, 8.82e-207j)
| (0.074337989091868654079 + 5.5393177594448838305e-933j)  +/-  (2.87e-91, 9.97e-209j)
| (0.074337989091868654079 + 3.0334471967116900266e-933j)  +/-  (2.71e-91, 9.43e-209j)
| (0.062878281902872703905 - 7.2396849532827803966e-934j)  +/-  (2.17e-90, 7.52e-208j)
| (0.073895285461154258874 - 4.0819610543258040194e-933j)  +/-  (2.89e-91, 1.01e-208j)
| (0.073356147497652123841 - 4.851788952187187312e-933j)  +/-  (2.96e-92, 1.03e-209j)
| (0.069632340049932830727 - 3.849202121594393668e-933j)  +/-  (2.03e-92, 7.05e-210j)
| (0.072081926317540799871 - 6.4138830275314837511e-933j)  +/-  (5.56e-92, 1.93e-209j)
| (0.069632340049932830727 - 1.2494673136235313649e-933j)  +/-  (2.63e-92, 9.13e-210j)
| (0.073356147497652123841 - 2.2500258002274159401e-933j)  +/-  (2.52e-92, 8.74e-210j)
| (0.073895285461154258874 - 6.3570188551833599736e-933j)  +/-  (8.96e-94, 3.12e-211j)
| (0.066692554266833152633 + 3.5311223321068834258e-933j)  +/-  (2.77e-94, 1.01e-211j)
| (0.072452283075643099361 + 7.1060448735876087675e-933j)  +/-  (1.05e-93, 3.61e-211j)
