Starting with polynomial:
P : 4*t^2 - 1
Extension levels are: 2 12 60
-------------------------------------------------
Trying to find an order 12 Kronrod extension for:
P1 : 4*t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 60 Kronrod extension for:
P2 : 4*t^14 - 13*t^12 + 33/2*t^10 - 165/16*t^8 + 105/32*t^6 - 63/128*t^4 + 7/256*t^2 - 1/4096
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^74 - 73*t^72 + 639*t^70 - 57155/16*t^68 + 916895/64*t^66 - 11238513/256*t^64 + 3420417/32*t^62 - 54353013/256*t^60 + 717946515/2048*t^58 - 3995843735/8192*t^56 + 4733537963/8192*t^54 - 615790256823/1048576*t^52 + 2160153123141/4194304*t^50 - 6566222272575/16777216*t^48 + 2168237331225/8388608*t^46 - 9973891723635/67108864*t^44 + 79960182801345/1073741824*t^42 - 139646485582065/4294967296*t^40 + 53081997443475/4294967296*t^38 - 280576272201225/68719476736*t^36 + 321387366339585/274877906944*t^34 - 317986441828055/1099511627776*t^32 + 16908369977135/274877906944*t^30 - 24599133578775/2199023255552*t^28 + 30387165009075/17592186044416*t^26 - 15801325804719/70368744177664*t^24 + 1711603580103/70368744177664*t^22 - 4881239839553/2251799813685248*t^20 + 1409476549415/9007199254740992*t^18 - 323313211485/36028797018963968*t^16 + 7184738033/18014398509481984*t^14 - 1917334783/144115188075855872*t^12 + 1471442973/4611686018427387904*t^10 - 95548245/18446744073709551616*t^8 + 959595/18446744073709551616*t^6 - 82251/295147905179352825856*t^4 + 703/1180591620717411303424*t^2 - 1/4722366482869645213696
-------------------------------------------------
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:   74 out of 74
Indefinite weights: 0 out of 74
Negative weights:   0 out of 74
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-0.96858316112863111949 - 2.9142999482011833081e-781j)  +/-  (2.01e-229, 2.01e-229j)
| (-0.99211470131447783105 - 1.4811342881204713737e-796j)  +/-  (1.93e-229, 1.93e-229j)
| (-0.9135454576426008955 + 8.3535045927780696532e-811j)  +/-  (2.91e-230, 2.91e-230j)
| (-0.98599603707050492781 + 4.8629444417467578461e-819j)  +/-  (2.35e-229, 2.35e-229j)
| (0.9135454576426008955 - 7.0505063383075699437e-836j)  +/-  (2.77e-230, 2.77e-230j)
| (0.92977648588825140366 + 3.581081214233287692e-835j)  +/-  (4.83e-230, 4.83e-230j)
| (0.99912283009885835015 - 2.2877548681722093825e-833j)  +/-  (3.05e-230, 3.05e-230j)
| (-0.92977648588825140366 - 1.2624636623012496429e-834j)  +/-  (5.2e-230, 5.2e-230j)
| (-0.97814760073380563793 + 2.6216438808455829765e-846j)  +/-  (2.41e-229, 2.41e-229j)
| (0.97814760073380563793 + 4.6768239651013823268e-849j)  +/-  (2.53e-229, 2.53e-229j)
| (0.89571176023941286035 + 1.6857420514268932178e-850j)  +/-  (1.16e-230, 1.16e-230j)
| (-0.99649285924950433832 + 1.0364146301174547794e-846j)  +/-  (1.09e-229, 1.09e-229j)
| (-0.94437637023748105566 + 1.4501822999123897094e-856j)  +/-  (9.14e-230, 9.14e-230j)
| (-0.83292124071009948428 - 1.4681102967737629008e-864j)  +/-  (5.53e-232, 5.53e-232j)
| (0.94437637023748105566 - 1.5697435526815680318e-860j)  +/-  (9.58e-230, 9.58e-230j)
| (0.83292124071009948428 + 8.2011612369639946732e-863j)  +/-  (4.98e-232, 4.98e-232j)
| (0.85536426016050662785 - 1.9605809383164181872e-863j)  +/-  (1.7e-231, 1.7e-231j)
| (0.99649285924950433832 + 1.3068393777954454278e-859j)  +/-  (1.05e-229, 1.05e-229j)
| (-0.8090169943749474241 - 1.5096334802543464258e-866j)  +/-  (1.51e-232, 1.51e-232j)
| (-0.89571176023941286035 - 2.0380299517534412946e-863j)  +/-  (1.14e-230, 1.14e-230j)
| (0.87630668004386358731 - 2.0674013360028790212e-868j)  +/-  (5.3e-231, 5.3e-231j)
| (0.8090169943749474241 + 5.9390593765388800002e-871j)  +/-  (1.64e-232, 1.64e-232j)
| (0.53582679497899661827 - 1.3199122936077318483e-877j)  +/-  (1.55e-239, 1.55e-239j)
| (-0.85536426016050662785 - 3.1643186030348690235e-870j)  +/-  (2.08e-231, 2.08e-231j)
| (-0.78369345732583978928 - 1.1041775221782964564e-872j)  +/-  (3.59e-233, 3.59e-233j)
| (0.99211470131447783105 - 2.6743393331419135136e-866j)  +/-  (1.65e-229, 1.65e-229j)
| (0.69966334051336541372 - 7.1676183447241050746e-878j)  +/-  (3.41e-235, 3.41e-235j)
| (0.72896862742141152315 + 1.8412673699422504099e-877j)  +/-  (1.59e-234, 1.59e-234j)
| (-0.69966334051336541372 - 2.8905997848177417266e-877j)  +/-  (3.01e-235, 3.01e-235j)
| (-0.63742398974868971018 + 2.8474980912954585385e-879j)  +/-  (7.79e-237, 7.79e-237j)
| (-0.95731949753206726492 - 8.6375143566849363132e-872j)  +/-  (1.5e-229, 1.5e-229j)
| (0.98599603707050492781 + 2.5382073122039253426e-874j)  +/-  (2.65e-229, 2.65e-229j)
| (0.66913060635885821383 + 1.4134650615231870505e-885j)  +/-  (6.19e-236, 6.19e-236j)
| (-0.1045284632676534714 - 3.8787147747598094913e-903j)  +/-  (1.29e-252, 1.29e-252j)
| (-0.60459911486237485817 + 2.707600407127199814e-887j)  +/-  (1.29e-237, 1.29e-237j)
| (-0.72896862742141152315 - 5.4581220589763964102e-884j)  +/-  (1.69e-234, 1.69e-234j)
| (-0.87630668004386358731 - 7.5579327543575590448e-879j)  +/-  (5.3e-231, 5.3e-231j)
| (0.57071356768443168945 + 9.013072167213719151e-889j)  +/-  (1.24e-238, 1.24e-238j)
| (0.95731949753206726492 + 2.6016364315056851547e-881j)  +/-  (1.44e-229, 1.44e-229j)
| (-0.75699505565175642512 - 1.9653841410425093343e-886j)  +/-  (8.39e-234, 8.39e-234j)
| (-0.57071356768443168945 - 9.0655560062977663514e-892j)  +/-  (1.27e-238, 1.27e-238j)
| (-0.99912283009885835015 + 1.1221080074510206932e-885j)  +/-  (3.19e-230, 3.19e-230j)
| (0.63742398974868971018 + 2.047174383536730189e-901j)  +/-  (8.86e-237, 8.86e-237j)
| (0.60459911486237485817 + 1.5328880254722737273e-901j)  +/-  (1.16e-237, 1.16e-237j)
| (0.5 - 2.3917467167790938484e-904j)  +/-  (1.66e-240, 1.66e-240j)
| (-0.53582679497899661827 - 2.0618629819601374497e-904j)  +/-  (1.5e-239, 1.5e-239j)
| (-0.66913060635885821383 + 8.6579228081039373058e-901j)  +/-  (5.1e-236, 5.1e-236j)
| (0.75699505565175642512 + 5.6856326049370667594e-898j)  +/-  (8.78e-234, 8.78e-234j)
| (0.46329603511986173188 + 8.9004893728217662513e-906j)  +/-  (1.29e-241, 1.29e-241j)
| (0.96858316112863111949 + 1.6042648254925743069e-898j)  +/-  (2.03e-229, 2.03e-229j)
| (-0.38751558645210297288 + 4.7538661121820746035e-917j)  +/-  (7.56e-244, 7.56e-244j)
| (-0.5 + 2.1196628349327232799e-911j)  +/-  (1.62e-240, 1.62e-240j)
| (0.020942419883356959456 + 8.8459385484621679741e-926j)  +/-  (3.35e-255, 3.35e-255j)
| (0.38751558645210297288 + 2.1388391986713881477e-914j)  +/-  (7e-244, 7e-244j)
| (0.34857204732181521764 - 3.1600762755856787907e-915j)  +/-  (4.57e-245, 4.57e-245j)
| (0.78369345732583978928 + 1.8804738467027368848e-918j)  +/-  (3.74e-233, 3.74e-233j)
| (-0.46329603511986173188 - 1.0304371030131017165e-926j)  +/-  (1.26e-241, 1.26e-241j)
| (-0.3090169943749474241 + 2.407979632478206163e-931j)  +/-  (3.3e-246, 3.3e-246j)
| (0.1045284632676534714 + 3.6302086062136326335e-939j)  +/-  (1.07e-252, 1.07e-252j)
| (0.42577929156507264886 - 3.0036755250340464039e-928j)  +/-  (1.08e-242, 1.08e-242j)
| (0.062790519529313376076 - 4.5332558127249730003e-939j)  +/-  (6.31e-254, 6.31e-254j)
| (-0.18738131458572463054 + 4.9341548321800396228e-936j)  +/-  (5.23e-250, 5.23e-250j)
| (-0.42577929156507264886 - 1.1165527864619268889e-928j)  +/-  (1.07e-242, 1.07e-242j)
| (-0.062790519529313376076 + 5.0350073675312078461e-939j)  +/-  (6.49e-254, 6.49e-254j)
| (0.26891982061526570577 + 1.0013204100415286878e-933j)  +/-  (1.98e-247, 1.98e-247j)
| (0.22835087011065574178 - 8.5575577306512301175e-935j)  +/-  (1.03e-248, 1.03e-248j)
| (-0.020942419883356959456 + 4.3041573595497488867e-940j)  +/-  (3.35e-255, 3.35e-255j)
| (-0.34857204732181521764 - 1.2060639280151542214e-931j)  +/-  (4.37e-245, 4.37e-245j)
| (-0.14608302856241161438 + 5.1795965527506438322e-939j)  +/-  (2.02e-251, 2.02e-251j)
| (0.18738131458572463054 + 6.5377858940818706593e-936j)  +/-  (4.52e-250, 4.52e-250j)
| (0.3090169943749474241 - 4.6096001240406043171e-932j)  +/-  (3.32e-246, 3.32e-246j)
| (0.14608302856241161438 + 1.0051106590764614644e-936j)  +/-  (2.4e-251, 2.4e-251j)
| (-0.26891982061526570577 + 2.3092070780788415269e-932j)  +/-  (1.76e-247, 1.76e-247j)
| (-0.22835087011065574178 - 1.0513616775927749402e-933j)  +/-  (1.11e-248, 1.11e-248j)
-------------------------------------------------
The weights are:
| (0.00082462213304090941795 - 5.6454837126114109244e-783j)  +/-  (3.06e-24, 3.88e-131j)
| (0.00020944559247579253673 - 2.5939112972736598754e-783j)  +/-  (9.71e-25, 1.23e-131j)
| (0.0022057959576076119078 - 1.1679904207176625897e-782j)  +/-  (3.59e-25, 4.55e-132j)
| (0.00037082419841679296223 + 6.2062863472138922504e-783j)  +/-  (9.58e-25, 1.22e-131j)
| (0.0022057959576076119078 + 3.4154685184028804884e-784j)  +/-  (1.14e-26, 1.45e-133j)
| (0.0018068758171905898457 - 2.7738569499827102045e-784j)  +/-  (1.03e-26, 1.3e-133j)
| (2.3380938336637744553e-05 - 3.4628683191055418692e-786j)  +/-  (3.86e-28, 4.9e-135j)
| (0.0018068758171905898457 + 1.356925855623229747e-782j)  +/-  (1.4e-25, 1.77e-132j)
| (0.00057636361571599402999 - 1.7561890970772876452e-782j)  +/-  (4.99e-25, 6.33e-132j)
| (0.00057636361571599402999 - 8.6282935901172187065e-785j)  +/-  (6.81e-29, 8.64e-136j)
| (0.0026360059009175009455 - 4.1206526780991542906e-784j)  +/-  (4.11e-28, 5.21e-135j)
| (9.3359752863300481239e-05 + 9.7485226015435810292e-784j)  +/-  (6.87e-26, 8.71e-133j)
| (0.0014420436178277347381 - 1.7361027571298817234e-782j)  +/-  (4.43e-26, 5.62e-133j)
| (0.0040832294236526468475 - 8.7716252734241299515e-783j)  +/-  (5.75e-29, 7.29e-136j)
| (0.0014420436178277347381 + 2.1968826688863742217e-784j)  +/-  (2.94e-29, 3.73e-136j)
| (0.0040832294236526468475 + 6.6054544666661924508e-784j)  +/-  (9.68e-31, 1.23e-137j)
| (0.0035780264325342551208 - 5.7169642750047502585e-784j)  +/-  (1.91e-30, 2.43e-137j)
| (9.3359752863300481239e-05 + 1.3845689434510338676e-785j)  +/-  (2.11e-31, 2.67e-138j)
| (0.0046065533708336838393 + 8.4133613805049701268e-783j)  +/-  (8.38e-32, 1.06e-138j)
| (0.0026360059009175009455 + 1.0542012046921546165e-782j)  +/-  (3.14e-30, 3.98e-137j)
| (0.0030944880334733558782 + 4.8882410832340760863e-784j)  +/-  (2.93e-30, 3.71e-137j)
| (0.0046065533708336838393 - 7.5522485798857471979e-784j)  +/-  (3.66e-32, 4.64e-139j)
| (0.0095051952771004843257 + 1.8413192488679787478e-783j)  +/-  (3.59e-36, 4.55e-143j)
| (0.0035780264325342551208 + 9.2099836315605723075e-783j)  +/-  (1.01e-31, 1.28e-138j)
| (0.0051443275325956283881 - 8.1086794739875688896e-783j)  +/-  (1.65e-33, 2.1e-140j)
| (0.00020944559247579253673 - 3.1131123820505458155e-785j)  +/-  (2.84e-32, 3.6e-139j)
| (0.0068062827992223797297 - 1.189005916673161928e-783j)  +/-  (3.36e-35, 4.26e-142j)
| (0.0062480632031379108262 + 1.0726465249590671435e-783j)  +/-  (8.37e-35, 1.06e-141j)
| (0.0068062827992223797297 + 7.3760087909601919119e-783j)  +/-  (2.4e-36, 3.04e-143j)
| (0.007915875430571497537 + 6.9662075977397638246e-783j)  +/-  (1.54e-37, 1.95e-144j)
| (0.0011138583952660034382 + 2.8819375115370474052e-782j)  +/-  (3.67e-32, 4.66e-139j)
| (0.00037082419841679296223 + 5.5290312269439264033e-785j)  +/-  (9.35e-34, 1.19e-140j)
| (0.0073635230884510231427 + 1.3103336725423818485e-783j)  +/-  (7.04e-37, 8.92e-144j)
| (0.013187650671558704253 + 4.4479556403271203092e-783j)  +/-  (1.24e-41, 1.58e-148j)
| (0.0084594654707684380385 - 6.7732143856755849625e-783j)  +/-  (1.68e-38, 2.12e-145j)
| (0.0062480632031379108262 - 7.5991760547844826821e-783j)  +/-  (1.48e-36, 1.88e-143j)
| (0.0030944880334733558782 - 9.7730930022961855543e-783j)  +/-  (2.12e-34, 2.69e-141j)
| (0.0089904803154787681176 - 1.7021381145860570561e-783j)  +/-  (2.23e-40, 2.83e-147j)
| (0.0011138583952660034382 - 1.685504430366467306e-784j)  +/-  (8.86e-36, 1.12e-142j)
| (0.0056927798095839225708 + 7.840926533559041844e-783j)  +/-  (3.18e-36, 4.04e-143j)
| (0.0089904803154787681176 + 6.5853125620614085611e-783j)  +/-  (2.37e-40, 3e-147j)
| (2.3380938336637744553e-05 - 2.2311658796886854322e-784j)  +/-  (1.29e-35, 1.63e-142j)
| (0.007915875430571497537 - 1.4364341618702872665e-783j)  +/-  (1.6e-40, 2.03e-147j)
| (0.0084594654707684380385 + 1.5671051066056563672e-783j)  +/-  (4.82e-41, 6.12e-148j)
| (0.01 - 1.9844296362226384296e-783j)  +/-  (1.89e-43, 2.4e-150j)
| (0.0095051952771004843257 - 6.4010589492097425801e-783j)  +/-  (3.16e-43, 4.01e-150j)
| (0.0073635230884510231427 - 7.1662487474016276908e-783j)  +/-  (4.85e-40, 6.15e-147j)
| (0.0056927798095839225708 - 9.6144398108744844801e-784j)  +/-  (3.36e-41, 4.26e-148j)
| (0.01047142378456287793 + 2.131246118590036734e-783j)  +/-  (4.05e-45, 5.13e-152j)
| (0.00082462213304090941795 + 1.2405730019125935499e-784j)  +/-  (7.03e-40, 8.92e-147j)
| (0.011331088936755769425 - 5.6830209326055230478e-783j)  +/-  (1.43e-47, 1.81e-154j)
| (0.01 + 6.2193868451904852069e-783j)  +/-  (4.47e-45, 5.67e-152j)
| (0.013327485533992389001 - 3.9251426286164370164e-783j)  +/-  (2.32e-50, 2.94e-157j)
| (0.011331088936755769425 + 2.4350875598374798841e-783j)  +/-  (7.63e-48, 9.67e-155j)
| (0.011713300371011709501 - 2.5916513441618879153e-783j)  +/-  (1.28e-48, 1.62e-155j)
| (0.0051443275325956283881 + 8.5557915364964340774e-784j)  +/-  (6.73e-43, 8.54e-150j)
| (0.01047142378456287793 - 6.0395106509035797427e-783j)  +/-  (1.44e-47, 1.83e-154j)
| (0.012060113295832982827 - 5.3287735673791898493e-783j)  +/-  (2.37e-50, 3e-157j)
| (0.013187650671558704253 - 3.581432611042721068e-783j)  +/-  (7.03e-52, 8.92e-159j)
| (0.010916159931657931401 - 2.2815419521608993961e-783j)  +/-  (3.09e-48, 3.91e-155j)
| (0.013280764675429852207 + 3.7526778636610900003e-783j)  +/-  (8.22e-52, 1.04e-158j)
| (0.012865176572588342691 + 4.7993976953604157377e-783j)  +/-  (9.82e-53, 1.25e-159j)
| (0.010916159931657931401 + 5.8608580570668638094e-783j)  +/-  (3.32e-50, 4.2e-157j)
| (0.013280764675429852207 - 4.2729571899965031351e-783j)  +/-  (1.2e-52, 1.52e-159j)
| (0.012369095067736710852 - 2.9129023240333998427e-783j)  +/-  (5.7e-53, 7.23e-160j)
| (0.012638078401596085736 + 3.0771245757796315029e-783j)  +/-  (2.14e-53, 2.72e-160j)
| (0.013327485533992389001 + 4.0986302837008501795e-783j)  +/-  (2.39e-53, 3.02e-160j)
| (0.011713300371011709501 + 5.5057191563731361447e-783j)  +/-  (2.04e-53, 2.58e-160j)
| (0.013048796650213781766 - 4.6234773583752748942e-783j)  +/-  (5.35e-54, 6.78e-161j)
| (0.012865176572588342691 - 3.2434373379790572124e-783j)  +/-  (1.79e-54, 2.27e-161j)
| (0.012060113295832982827 + 2.751000569461655851e-783j)  +/-  (3.05e-54, 3.87e-161j)
| (0.013048796650213781766 + 3.4116139660023427085e-783j)  +/-  (1.36e-54, 1.72e-161j)
| (0.012369095067736710852 + 5.1520854428004711389e-783j)  +/-  (6.27e-56, 7.99e-163j)
| (0.012638078401596085736 - 4.9756207177186710216e-783j)  +/-  (6.43e-56, 8.11e-163j)
