Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 58
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Trying to find an order 58 Kronrod extension for:
P2 : 4*t^5 - 14*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^63 - 492244951036495519031005917339353859656122845227156862587749829183341559/134094278364037108667269878114219623605730279713457992112198785595916*t^61 + 181056842712111241122917634668850787980397081671034324323079923626348894041/114937952883460378857659895526473963090625954040106850381884673367928*t^59 - 84574113680665078028708531242201599606496722533051707549613485769486131097849/201141417546055663000904817171329435408595419570186988168298178393874*t^57 + 6003072704453338127610171674452281267968812830169508767328666757942893417233963/76625301922306919238439930350982642060417302693404566921256448911952*t^55 - 1107472062282512187273022728265579892088829115266686192389267062426430288919197505/102167069229742558984586573801310189413889736924539422561675265215936*t^53 + 236387233084824448615367192580653971588805105496929556032139027102727600040747872935/204334138459485117969173147602620378827779473849078845123350530431872*t^51 - 19953492860197876586297548391503644254175211404052993365199123642500787110576611316825/204334138459485117969173147602620378827779473849078845123350530431872*t^49 + 1355345461137853142521937106439230258557726364642797157459547344828627048665885621342475/204334138459485117969173147602620378827779473849078845123350530431872*t^47 - 599886896616351319091567841741532803949363553666406987456354453593773794764542233208617075/1634673107675880943753385180820963030622235790792630760986804243454976*t^45 + 54525946932954008600828658894679329863802732024157541649360880083559562919205238821858454625/3269346215351761887506770361641926061244471581585261521973608486909952*t^43 - 1023613792447317668308931387008702278121538328400046308292477352972938405811991904027796928875/1634673107675880943753385180820963030622235790792630760986804243454976*t^41 + 127455082545295814650642640605518058455467514242548775059779418704052423601097770969819746146375/6538692430703523775013540723283852122488943163170523043947216973819904*t^39 - 13180278904538253952006288843253405949370916768295929632309383083984827902648834068842600065554625/26154769722814095100054162893135408489955772652682092175788867895279616*t^37 + 566057250861111891201642010372207367910807198229448594303366896632021345891570309581091459205221375/52309539445628190200108325786270816979911545305364184351577735790559232*t^35 - 10082568210430102243352370827206489700410278746404866233453436026775389332211383735958804412916254375/52309539445628190200108325786270816979911545305364184351577735790559232*t^33 + 2321057926554982262813690865677576049878014384451854369249984860353119065576183282405447898986976875/817336553837940471876692590410481515311117895396315380493402121727488*t^31 - 14420277019847743743920233351369499644261871308720124462120095165915158694463232184133710955021165525625/418476315565025521600866606290166535839292362442913474812621886324473856*t^29 + 286551004907065092338270252092648663016951699887440708268170006498059437901300678367689978613116155006875/836952631130051043201733212580333071678584724885826949625243772648947712*t^27 - 36149734832924952976677284302345992391265221132335531931458600843211453571192065655486701435645321213125/13077384861407047550027081446567704244977886326341046087894433947639808*t^25 + 30069311976321908647206070365453808031621900743887710736372524344012298103715699698568427299641915716484375/1673905262260102086403466425160666143357169449771653899250487545297895424*t^23 - 621635346825401945171066403345459477517638197365681092268388612873688550682450068902943941462088675536796875/6695621049040408345613865700642664573428677799086615597001950181191581696*t^21 + 5035412028356950171485966463051207161631888600936214502781963910195502662861900005121734436651922606219328125/13391242098080816691227731401285329146857355598173231194003900362383163392*t^19 - 15690372647399488891495215725298553804983693266420527075175325928343929392549509739202629885010819674957984375/13391242098080816691227731401285329146857355598173231194003900362383163392*t^17 + 36758402613548150911526924198037038500987081103343147705579538632535902740673704123886710982316950550794984375/13391242098080816691227731401285329146857355598173231194003900362383163392*t^15 - 503043489544054392579509144066076861724575759950174064261912931543324934670204724948556199419924676558302765625/107129936784646533529821851210282633174858844785385849552031202899065307136*t^13 + 1210106144776656129098228163424125017523606575170933911608626685218009034898048451763470641832544215328523421875/214259873569293067059643702420565266349717689570771699104062405798130614272*t^11 - 486622950079600104639844949344733815393206227280880917089286879966807134199760773359734259560089514441205484375/107129936784646533529821851210282633174858844785385849552031202899065307136*t^9 + 976202326485979699469550604609900249537112693513810531540980470307681784360197039145071835699685209092004015625/428519747138586134119287404841130532699435379141543398208124811596261228544*t^7 - 1099706733591692942422626261430363835106060116487450861231346821948720354070862110714346086257974672748645421875/1714078988554344536477149619364522130797741516566173592832499246385044914176*t^5 + 289980129814260404123084633250867520402497739057508471248351922841217660555797014054256991250265836128618828125/3428157977108689072954299238729044261595483033132347185664998492770089828352*t^3 - 11685665056427044973903075599360722831692665676964142599229064574494868489447326295943260462326120957898515625/3428157977108689072954299238729044261595483033132347185664998492770089828352*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: 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:   63 out of 63
Indefinite weights: 0 out of 63
Negative weights:   0 out of 63
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-8.6230003697761625227 + 1.7640445268047811116e-706j)  +/-  (7.83e-242, 7.83e-242j)
| (9.0930690672150988231 - 2.2746510733139070166e-713j)  +/-  (1.51e-242, 1.51e-242j)
| (-9.0930690672150988231 + 4.9913900656833872629e-723j)  +/-  (1.69e-242, 1.69e-242j)
| (7.0215216888386503098 - 1.5436471035874812646e-726j)  +/-  (2.06e-240, 2.06e-240j)
| (-10.255754843159670757 - 1.3458697813870755546e-742j)  +/-  (8.33e-245, 8.33e-245j)
| (10.255754843159670757 - 1.2228795239350018361e-739j)  +/-  (8.3e-245, 8.3e-245j)
| (7.781644790431492144 - 1.2897197703418035329e-736j)  +/-  (6.65e-241, 6.65e-241j)
| (-1.7320508075688772935 + 2.8736524793668114837e-748j)  +/-  (9.69e-248, 9.69e-248j)
| (-4.0677894278500689512 + 1.0652081191276470229e-741j)  +/-  (4.19e-242, 4.19e-242j)
| (2.8788226927271321245 - 1.2416492602293482582e-744j)  +/-  (1.75e-244, 1.75e-244j)
| (1.4530481542277834089 + 1.6041941841305657912e-748j)  +/-  (1.15e-248, 1.15e-248j)
| (-3.7659375887036572311 + 7.1466302279604179191e-742j)  +/-  (1.3e-242, 1.3e-242j)
| (-0.92523529252765127377 + 9.3327699666098781593e-751j)  +/-  (1.67e-250, 1.67e-250j)
| (-2.3004045716275282696 + 7.3608455793128601562e-746j)  +/-  (5.46e-246, 5.46e-246j)
| (-4.9970333806266458523 - 2.1577331794695238911e-740j)  +/-  (6.27e-241, 6.27e-241j)
| (-5.9735881582730382146 + 5.0252952639881504128e-739j)  +/-  (2.25e-240, 2.25e-240j)
| (-7.781644790431492144 - 3.1487938002608038344e-743j)  +/-  (6.5e-241, 6.5e-241j)
| (-2.8788226927271321245 + 5.9514079468254127568e-755j)  +/-  (1.67e-244, 1.67e-244j)
| (8.6230003697761625227 - 8.6723916657874975592e-750j)  +/-  (7.51e-242, 7.51e-242j)
| (5.9735881582730382146 + 2.6741380276640610667e-761j)  +/-  (2.24e-240, 2.24e-240j)
| (-9.6196970644533293386 - 2.2920548432824566525e-773j)  +/-  (1.71e-243, 1.71e-243j)
| (8.1893206439477634295 - 2.0291290150571989598e-769j)  +/-  (2.48e-241, 2.48e-241j)
| (-3.1717409812697827506 - 1.9946604343692383225e-775j)  +/-  (8.5e-244, 8.5e-244j)
| (4.9970333806266458523 + 1.084322920627709878e-771j)  +/-  (6.15e-241, 6.15e-241j)
| (-6.6620876391940584612 + 6.1224787190205932867e-774j)  +/-  (2.55e-240, 2.55e-240j)
| (3.1717409812697827506 - 6.4490781242639746155e-787j)  +/-  (8.17e-244, 8.17e-244j)
| (3.4673598620969835536 + 2.3471760240862899428e-785j)  +/-  (3.63e-243, 3.63e-243j)
| (5.6416195313516295456 + 1.4622204508879038388e-782j)  +/-  (1.66e-240, 1.66e-240j)
| (-3.4673598620969835536 + 3.9534680261963283441e-797j)  +/-  (3.51e-243, 3.51e-243j)
| (-2.5884120067834823667 + 4.6772972329154781685e-799j)  +/-  (2.91e-245, 2.91e-245j)
| (-8.1893206439477634295 + 3.2490043061340999146e-794j)  +/-  (2.78e-241, 2.78e-241j)
| (3.7659375887036572311 - 5.6676522352261257569e-797j)  +/-  (1.29e-242, 1.29e-242j)
| (4.6828665501716125718 - 1.4795665438307034983e-802j)  +/-  (2.88e-241, 2.88e-241j)
| (2.0148413598926000687 - 6.5061544838683032334e-825j)  +/-  (7.61e-247, 7.61e-247j)
| (6.3133180980344797138 - 1.1730160551172112166e-819j)  +/-  (2.57e-240, 2.57e-240j)
| (-4.6828665501716125718 - 2.2629490780203861718e-835j)  +/-  (2.8e-241, 2.8e-241j)
| (9.6196970644533293386 + 1.7078530724133156751e-833j)  +/-  (1.79e-243, 1.79e-243j)
| (0.92523529252765127377 + 7.094515320803729048e-854j)  +/-  (1.9e-250, 1.9e-250j)
| (7.3937460559777345241 + 1.0577451121584157513e-842j)  +/-  (1.28e-240, 1.28e-240j)
| (-5.3163828930029397968 + 4.5188310671307317575e-848j)  +/-  (1.13e-240, 1.13e-240j)
| (-1.4530481542277834089 + 2.7150950065738224336e-861j)  +/-  (1.28e-248, 1.28e-248j)
| (-7.3937460559777345241 - 4.1784988591830457493e-852j)  +/-  (1.25e-240, 1.25e-240j)
| (1.1808536158925948792 + 7.007512650324006491e-873j)  +/-  (1.41e-249, 1.41e-249j)
| (0.7071067811865475244 - 2.4138647166193990695e-874j)  +/-  (2.39e-251, 2.39e-251j)
| (-7.0215216888386503098 - 2.6247809642482250434e-863j)  +/-  (1.98e-240, 1.98e-240j)
| (-4.3732875729924717352 - 2.817146094727952551e-872j)  +/-  (1.14e-241, 1.14e-241j)
| (-5.6416195313516295456 + 6.8961871275592644753e-877j)  +/-  (1.72e-240, 1.72e-240j)
| (5.3163828930029397968 + 9.5123179303968430855e-904j)  +/-  (1.14e-240, 1.14e-240j)
| (0.50190771198730390019 + 4.3541998914318332742e-939j)  +/-  (2.54e-252, 2.54e-252j)
| (2.5884120067834823667 - 2.7410202741771853726e-927j)  +/-  (2.96e-245, 2.96e-245j)
| (-1.1808536158925948792 - 4.3984736732082569789e-940j)  +/-  (1.46e-249, 1.46e-249j)
| (-0.50190771198730390019 + 7.1821605392785722469e-945j)  +/-  (2.37e-252, 2.37e-252j)
| (6.6620876391940584612 + 1.6172084253718593573e-932j)  +/-  (2.43e-240, 2.43e-240j)
| (1.7320508075688772935 - 5.5768039399572614729e-951j)  +/-  (9.37e-248, 9.37e-248j)
| (4.3732875729924717352 + 1.6327111474028312593e-944j)  +/-  (1.08e-241, 1.08e-241j)
| (4.0677894278500689512 - 4.2218120401921899703e-945j)  +/-  (4.33e-242, 4.33e-242j)
| (-0.7071067811865475244 + 1.5653918134570620888e-953j)  +/-  (2.08e-251, 2.08e-251j)
| (-0.26048250302670058931 + 8.4355736831913440883e-956j)  +/-  (1.44e-253, 1.44e-253j)
| (2.3004045716275282696 + 5.2594904295048266208e-949j)  +/-  (5.07e-246, 5.07e-246j)
| (0.26048250302670058931 - 7.7566140244537649371e-956j)  +/-  (1.44e-253, 1.44e-253j)
| (4.4262245319795873028e-979 + 2.6169865396119043482e-980j)  +/-  (2.79e-977, 2.79e-977j)
| (-6.3133180980344797138 - 8.8917079632250033045e-942j)  +/-  (2.62e-240, 2.62e-240j)
| (-2.0148413598926000687 + 1.0002529179708127508e-956j)  +/-  (7.62e-247, 7.62e-247j)
-------------------------------------------------
The weights are:
| (1.2936409253557694441e-33 + 2.0210079371285876416e-738j)  +/-  (5.16e-64, 1.25e-183j)
| (3.4328570967791193059e-37 - 1.8860141478689715906e-742j)  +/-  (2.36e-66, 5.74e-186j)
| (3.4328570967791193059e-37 + 7.1080611560849053336e-741j)  +/-  (1.3e-65, 3.15e-185j)
| (7.9934686930050490361e-23 + 5.4830846624630194739e-735j)  +/-  (4.9e-60, 1.19e-179j)
| (8.6755760824024057025e-47 + 2.5548417375001206862e-746j)  +/-  (1.22e-69, 2.96e-189j)
| (8.6755760824024057025e-47 - 2.2095892372710095696e-747j)  +/-  (2.99e-70, 7.26e-190j)
| (1.1269750838037401753e-27 + 1.5962317297306258819e-737j)  +/-  (1.07e-62, 2.61e-182j)
| (0.0078976282934652988498 - 2.2966945941377649131e-723j)  +/-  (3.22e-28, 7.84e-148j)
| (1.1155941943136796397e-08 - 6.7324225229274686592e-727j)  +/-  (9.03e-49, 2.19e-168j)
| (4.1400191043703928456e-05 - 3.3198741569304990472e-725j)  +/-  (1.45e-41, 3.52e-161j)
| (0.018880917978643084661 + 3.6410424759094277868e-723j)  +/-  (5.25e-26, 1.27e-145j)
| (1.1735075323085161087e-07 + 2.3986474956750028672e-726j)  +/-  (3.9e-47, 9.48e-167j)
| (0.057607479045972277872 + 2.5272972852154593809e-722j)  +/-  (2.87e-27, 6.98e-147j)
| (0.00081431383488580429377 - 4.3079532793425941111e-724j)  +/-  (9.21e-37, 2.24e-156j)
| (2.5557806807221628715e-12 + 8.4163046393804846618e-729j)  +/-  (1.9e-54, 4.6e-174j)
| (6.0265115553759929834e-17 - 3.8958031110695889348e-731j)  +/-  (4.2e-59, 1.02e-178j)
| (1.1269750838037401753e-27 + 3.1123126208469004356e-736j)  +/-  (2.71e-65, 6.57e-185j)
| (4.1400191043703928456e-05 - 6.647532059760274755e-725j)  +/-  (1.98e-43, 4.81e-163j)
| (1.2936409253557694441e-33 + 1.3232285170485657732e-740j)  +/-  (3.5e-69, 8.49e-189j)
| (6.0265115553759929834e-17 - 7.0712332594828896996e-732j)  +/-  (1.46e-62, 3.55e-182j)
| (2.0702703831420576291e-41 - 2.3249676951748552393e-743j)  +/-  (1.26e-71, 3.07e-191j)
| (1.7705063633414198742e-30 - 5.5706292715126152787e-739j)  +/-  (4.85e-68, 1.18e-187j)
| (7.0979999618251103272e-06 + 2.3697285943933823735e-725j)  +/-  (5.58e-48, 1.35e-167j)
| (2.5557806807221628715e-12 + 2.2406143136997356398e-729j)  +/-  (6.18e-60, 1.5e-179j)
| (1.058538727021207303e-20 - 5.5967319758381433503e-733j)  +/-  (1.06e-63, 2.58e-183j)
| (7.0979999618251103272e-06 + 1.0952342927415806043e-725j)  +/-  (6.41e-52, 1.56e-171j)
| (1.0067302920225026301e-06 - 3.345808317904430385e-726j)  +/-  (8.35e-54, 2.03e-173j)
| (2.7875535756053836663e-15 + 5.5245792107337174305e-731j)  +/-  (2.64e-62, 6.42e-182j)
| (1.0067302920225026301e-06 - 7.8461692459697555125e-726j)  +/-  (7.53e-52, 1.83e-171j)
| (0.00020086553542852618155 + 1.7433865272028432205e-724j)  +/-  (8.13e-48, 1.98e-167j)
| (1.7705063633414198742e-30 - 2.159547842555397321e-737j)  +/-  (3.31e-69, 8.04e-189j)
| (1.1735075323085161087e-07 + 9.4038580725524924903e-727j)  +/-  (2.27e-56, 5.52e-176j)
| (5.2665731817557231498e-11 - 1.1880665769662521288e-728j)  +/-  (4.61e-60, 1.12e-179j)
| (0.0027675635447174756001 + 6.2921577471101680245e-724j)  +/-  (1.1e-49, 2.67e-169j)
| (9.5037556459997741648e-19 + 7.7603099350881850753e-733j)  +/-  (2.76e-65, 6.7e-185j)
| (5.2665731817557231498e-11 - 4.0121114129145845055e-728j)  +/-  (9.01e-61, 2.19e-180j)
| (2.0702703831420576291e-41 + 1.2702550226871971114e-744j)  +/-  (2.81e-76, 6.84e-196j)
| (0.057607479045972277872 + 2.0375011103410071398e-722j)  +/-  (3.96e-49, 9.61e-169j)
| (3.8801730919559842044e-25 - 3.3625562254555536618e-736j)  +/-  (1.38e-68, 3.36e-188j)
| (9.6524174479501763477e-14 - 1.5816989592576258221e-729j)  +/-  (7.14e-64, 1.74e-183j)
| (0.018880917978643084661 + 5.1168152335032241141e-723j)  +/-  (9.75e-51, 2.37e-170j)
| (3.8801730919559842044e-25 - 4.3812912411896376696e-735j)  +/-  (1.28e-70, 3.11e-190j)
| (0.037294757689701618658 - 8.6943004893735445392e-723j)  +/-  (4.87e-52, 1.18e-171j)
| (0.068166042243180305193 - 3.6757112311319098536e-722j)  +/-  (2.87e-52, 6.96e-172j)
| (7.9934686930050490361e-23 + 5.3563148524060604196e-734j)  +/-  (1.08e-69, 2.64e-189j)
| (8.5714181038173236791e-10 + 1.7251250067403734403e-727j)  +/-  (6.6e-62, 1.6e-181j)
| (2.7875535756053836663e-15 + 2.6432726159308009816e-730j)  +/-  (8.77e-66, 2.13e-185j)
| (9.6524174479501763477e-14 - 3.7520120372418535796e-730j)  +/-  (2.62e-67, 6.38e-187j)
| (0.097632660356836844441 + 4.4084668399197031748e-722j)  +/-  (1.33e-55, 3.23e-175j)
| (0.00020086553542852618155 + 9.3838489444705782227e-725j)  +/-  (2.23e-61, 5.42e-181j)
| (0.037294757689701618658 - 1.1453368957471317593e-722j)  +/-  (3.55e-57, 8.63e-177j)
| (0.097632660356836844441 + 4.9533796018778128734e-722j)  +/-  (3.53e-57, 8.58e-177j)
| (1.058538727021207303e-20 - 7.1800063019364274122e-734j)  +/-  (6.64e-71, 1.61e-190j)
| (0.0078976282934652988498 - 1.5283755056794917508e-723j)  +/-  (1.5e-59, 3.63e-179j)
| (8.5714181038173236791e-10 + 5.6410613612979685757e-728j)  +/-  (4.2e-66, 1.02e-185j)
| (1.1155941943136796397e-08 - 2.4165245091094920478e-727j)  +/-  (1.71e-65, 4.15e-185j)
| (0.068166042243180305193 - 4.3323952353686672421e-722j)  +/-  (2.15e-59, 5.22e-179j)
| (0.1345091531052439026 - 4.4255193273052131182e-722j)  +/-  (9.53e-60, 2.31e-179j)
| (0.00081431383488580429377 - 2.4934942338641112922e-724j)  +/-  (1.97e-62, 4.79e-182j)
| (0.1345091531052439026 - 4.1659881562754828627e-722j)  +/-  (3.16e-60, 7.67e-180j)
| (0.14835796806293888058 + 4.0788017010091040126e-722j)  +/-  (2.99e-60, 7.25e-180j)
| (9.5037556459997741648e-19 + 5.0184591808332818794e-732j)  +/-  (2.35e-72, 5.87e-192j)
| (0.0027675635447174756001 + 1.0129141610210808993e-723j)  +/-  (3.39e-63, 7.93e-183j)
