Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 54
-------------------------------------------------
Trying to find an order 54 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^56 - 8534356927971986410813862099312321/5690528076652076761835015119628*t^54 + 5942442592107288732311488554251426991/5690528076652076761835015119628*t^52 - 196470795276521120381312398399126202421/437732928973236673987308855356*t^50 + 58462678616552042308360469448321815439075/437732928973236673987308855356*t^48 - 6402096673066718641193685104843586900421875/218866464486618336993654427678*t^46 + 1071156551687148291975743346645591595832025525/218866464486618336993654427678*t^44 - 140271721456813155279273558288508367281264088775/218866464486618336993654427678*t^42 + 14613783788427381554149440380477957693814241854075/218866464486618336993654427678*t^40 - 2449342749544642860370291102026901742223622266648375/437732928973236673987308855356*t^38 + 166303763862726332803567281428731644471616815618239625/437732928973236673987308855356*t^36 - 9187618312041135608141359271139310979354107373762913375/437732928973236673987308855356*t^34 + 413763984433396423279665695826096598496855015628995804625/437732928973236673987308855356*t^32 - 3796372675736911527150894836159797744608021802329796208625/109433232243309168496827213839*t^30 + 113288712320038825826216774528064076750529489238032755044375/109433232243309168496827213839*t^28 - 2737191295827955095882174779501307834198605186372620422883125/109433232243309168496827213839*t^26 + 53208736774190801800418638955687831477641053392669688191287500/109433232243309168496827213839*t^24 - 3300198587557141020598034434343641395336924975682862267247571875/437732928973236673987308855356*t^22 + 40360309867884152083094769497711196026870185485624201587148778125/437732928973236673987308855356*t^20 - 383680711954516610685147637546789941469165004499850040779537171875/437732928973236673987308855356*t^18 + 2782751188010966509126008987890979608422655379197454202510037203125/437732928973236673987308855356*t^16 - 7515271227342516990030395852997189041731995639917301694447471546875/218866464486618336993654427678*t^14 + 29284729749703945446034986745174259427515127630618673442583188578125/218866464486618336993654427678*t^12 - 78865881821583202634709573151946505914746175545401805732035702609375/218866464486618336993654427678*t^10 + 138182478286334259925950916288698762217037417239210648081235207109375/218866464486618336993654427678*t^8 - 287820799072128033402479897735195129890393691940976119329383776890625/437732928973236673987308855356*t^6 + 153526642374731148790863313259829826393052059191992530936615782609375/437732928973236673987308855356*t^4 - 31333960832513668684510203619514735248570954691187776228745846515625/437732928973236673987308855356*t^2 + 1019674643792792614045464439014307863841956611338868691445212984375/437732928973236673987308855356
-------------------------------------------------
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:   56 out of 56
Indefinite weights: 0 out of 56
Negative weights:   0 out of 56
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (12.799947649970989902 - 4.5059819139693849099e-535j)  +/-  (2.76e-244, 2.76e-244j)
| (-3.4823476856850558401 - 1.4301537816116621867e-551j)  +/-  (4.84e-246, 4.84e-246j)
| (11.364262234356831214 + 3.2112873003475254052e-546j)  +/-  (1.03e-242, 1.03e-242j)
| (-12.799947649970989902 + 1.7810119873927303705e-555j)  +/-  (2.8e-244, 2.8e-244j)
| (13.715229435206691003 + 8.5556267865623633343e-555j)  +/-  (1.47e-245, 1.47e-245j)
| (2.6394179720361093464 + 4.1194970671729001288e-560j)  +/-  (9.83e-248, 9.83e-248j)
| (-13.715229435206691003 + 2.7686857491194968363e-558j)  +/-  (1.56e-245, 1.56e-245j)
| (-10.150878313328408644 - 1.9361328588860836626e-553j)  +/-  (6.04e-242, 6.04e-242j)
| (-12.041596534521041307 - 9.9285787676990818339e-561j)  +/-  (2.18e-243, 2.18e-243j)
| (9.590991856087503082 - 8.3117295428767290565e-568j)  +/-  (1.12e-241, 1.12e-241j)
| (1.4043760087119985866 + 2.5931037246698078756e-585j)  +/-  (1.06e-250, 1.06e-250j)
| (-8.5341146214883823403 - 2.8110368075130760056e-575j)  +/-  (1.51e-241, 1.51e-241j)
| (6.1252599812198465999 - 7.9802868976052096621e-575j)  +/-  (1.27e-242, 1.27e-242j)
| (-1.8122680634236867229 + 1.7284218372201210142e-592j)  +/-  (1.26e-249, 1.26e-249j)
| (-4.7794641841682858425 + 3.2726937783207666309e-586j)  +/-  (4.93e-244, 4.93e-244j)
| (7.538629468950535776 - 1.4088864538150879172e-583j)  +/-  (1.04e-241, 1.04e-241j)
| (-8.0299487891357577544 - 8.1870177226771847168e-591j)  +/-  (1.43e-241, 1.43e-241j)
| (10.738990724447664933 + 4.083452083044513318e-592j)  +/-  (2.91e-242, 2.91e-242j)
| (12.041596534521041307 - 3.5156474818711002112e-602j)  +/-  (2.02e-243, 2.02e-243j)
| (-6.1252599812198465999 + 4.0224267560260728897e-608j)  +/-  (1.36e-242, 1.36e-242j)
| (-5.2219346260761680418 + 3.5570218393695819655e-609j)  +/-  (1.69e-243, 1.69e-243j)
| (-11.364262234356831214 + 9.218498345039128848e-607j)  +/-  (9.6e-243, 9.6e-243j)
| (4.7794641841682858425 - 2.2351964824208850697e-609j)  +/-  (5.48e-244, 5.48e-244j)
| (7.0583360637076923089 + 1.1160272321861517505e-618j)  +/-  (5.85e-242, 5.85e-242j)
| (-1.4043760087119985866 + 6.2822524417407011971e-637j)  +/-  (1.06e-250, 1.06e-250j)
| (-10.738990724447664933 + 9.0901000230510101882e-628j)  +/-  (3.03e-242, 3.03e-242j)
| (-7.0583360637076923089 - 2.9352636001329047482e-638j)  +/-  (6.05e-242, 6.05e-242j)
| (9.0534481504967627775 - 1.8982419830024814977e-651j)  +/-  (1.35e-241, 1.35e-241j)
| (6.587609333061074403 + 9.039824263414338467e-664j)  +/-  (3.28e-242, 3.28e-242j)
| (3.4823476856850558401 - 3.6939660521676523682e-674j)  +/-  (4.53e-246, 4.53e-246j)
| (-4.3423330284433757608 + 1.5188579265329004742e-678j)  +/-  (1.16e-244, 1.16e-244j)
| (5.2219346260761680418 + 3.1314870497375537814e-676j)  +/-  (1.66e-243, 1.66e-243j)
| (4.3423330284433757608 + 1.2703777432661368069e-689j)  +/-  (1.25e-244, 1.25e-244j)
| (2.2239146358061525468 - 8.5714076341195170115e-700j)  +/-  (1.25e-248, 1.25e-248j)
| (-2.6394179720361093464 + 2.4847008256953238119e-703j)  +/-  (1.04e-247, 1.04e-247j)
| (8.0299487891357577544 - 1.875820599520730611e-702j)  +/-  (1.3e-241, 1.3e-241j)
| (8.5341146214883823403 - 3.5145682210232704145e-718j)  +/-  (1.42e-241, 1.42e-241j)
| (-3.058856172431529435 - 2.9028737842273451456e-730j)  +/-  (7.36e-247, 7.36e-247j)
| (-7.538629468950535776 + 2.1709353622383344811e-724j)  +/-  (1.01e-241, 1.01e-241j)
| (-3.9100820921065514238 - 2.3712091821602969382e-734j)  +/-  (2.5e-245, 2.5e-245j)
| (3.058856172431529435 + 3.2544165028781746198e-736j)  +/-  (7.29e-247, 7.29e-247j)
| (10.150878313328408644 - 8.0807439354746454822e-733j)  +/-  (6.73e-242, 6.73e-242j)
| (-0.19929158914553546235 + 8.3485098984441650515e-750j)  +/-  (4e-254, 4e-254j)
| (-6.587609333061074403 - 2.1211948490631280824e-737j)  +/-  (3.12e-242, 3.12e-242j)
| (-9.590991856087503082 - 2.8515132722355967891e-737j)  +/-  (9.63e-242, 9.63e-242j)
| (-1 + 2.2991623017040725776e-749j)  +/-  (9.93e-252, 9.93e-252j)
| (-9.0534481504967627775 + 7.0148670550456265995e-741j)  +/-  (1.31e-241, 1.31e-241j)
| (-0.5986157703312524562 + 3.8732989492409475514e-754j)  +/-  (6.16e-253, 6.16e-253j)
| (3.9100820921065514238 + 5.5861665341702506209e-745j)  +/-  (2.65e-245, 2.65e-245j)
| (1.8122680634236867229 + 1.7475471850271865591e-751j)  +/-  (1.18e-249, 1.18e-249j)
| (5.6703068855673204434 - 2.7625438558174099464e-744j)  +/-  (5.28e-243, 5.28e-243j)
| (-2.2239146358061525468 - 1.0810682075999493135e-748j)  +/-  (1.23e-248, 1.23e-248j)
| (-5.6703068855673204434 + 1.4189216559256021211e-750j)  +/-  (4.87e-243, 4.87e-243j)
| (1 + 4.1245142805032579437e-759j)  +/-  (9.97e-252, 9.97e-252j)
| (0.5986157703312524562 + 3.6782416158735599945e-761j)  +/-  (5.82e-253, 5.82e-253j)
| (0.19929158914553546235 - 7.7755886472736361149e-762j)  +/-  (3.15e-254, 3.15e-254j)
-------------------------------------------------
The weights are:
| (8.6221302606313086284e-37 + 2.5210497503571978793e-570j)  +/-  (2.2e-66, 1.35e-187j)
| (0.00039499943532179117596 - 1.2507521360315548364e-554j)  +/-  (1.18e-36, 7.29e-158j)
| (2.3374161055904308565e-29 + 1.6134924728650201721e-567j)  +/-  (9.39e-64, 5.78e-185j)
| (8.6221302606313086284e-37 - 5.9750959346146793344e-573j)  +/-  (6.01e-68, 3.7e-189j)
| (5.9974082151052294676e-42 + 1.034792393883441506e-573j)  +/-  (1.41e-68, 8.67e-190j)
| (0.0051139732356104537937 + 1.4682295070535478313e-554j)  +/-  (1.74e-33, 1.07e-154j)
| (5.9974082151052294676e-42 + 1.5477289375585248619e-575j)  +/-  (7.88e-70, 4.85e-191j)
| (9.6384664334530491249e-24 - 1.699628639687569265e-566j)  +/-  (7.04e-64, 4.33e-185j)
| (9.2566639748152735365e-33 + 6.1796961555985090611e-571j)  +/-  (5.59e-67, 3.44e-188j)
| (2.3166931490999194433e-21 - 8.7141697482760309889e-564j)  +/-  (1.8e-63, 1.11e-184j)
| (0.060428756312179493667 - 6.3984459114051578039e-554j)  +/-  (9.38e-26, 5.77e-147j)
| (3.122632297082646589e-17 + 1.0961379660805593883e-563j)  +/-  (4.47e-61, 2.75e-182j)
| (1.3036046452169927472e-09 + 5.1667867382829988781e-558j)  +/-  (1.74e-55, 1.07e-176j)
| (0.031640563304104243491 - 6.4607312383219145485e-554j)  +/-  (5.8e-33, 3.57e-154j)
| (1.9218857684121982142e-06 - 1.5991874460756232435e-556j)  +/-  (7.02e-51, 4.32e-172j)
| (8.8399857985441396167e-14 - 4.3019010752065209729e-560j)  +/-  (1.14e-59, 7.01e-181j)
| (1.9767312268636436592e-15 + 1.4935396232028970911e-563j)  +/-  (2e-60, 1.23e-181j)
| (2.1870046696082441411e-26 - 3.6667653640457846905e-566j)  +/-  (5.51e-66, 3.39e-187j)
| (9.2566639748152735365e-33 - 5.690845066716137744e-569j)  +/-  (3.21e-68, 1.97e-189j)
| (1.3036046452169927472e-09 + 9.1668002372548422385e-559j)  +/-  (2.61e-57, 1.6e-178j)
| (2.1295076470131796096e-07 + 3.1219891489993858439e-557j)  +/-  (1.88e-54, 1.15e-175j)
| (2.3374161055904308565e-29 - 3.0361353796059375501e-569j)  +/-  (2.25e-68, 1.39e-189j)
| (1.9218857684121982142e-06 - 2.1379662461476840563e-556j)  +/-  (4.95e-56, 3.05e-177j)
| (2.8811867454052577318e-12 + 2.4203079980580346308e-559j)  +/-  (3.22e-61, 1.98e-182j)
| (0.060428756312179493667 + 8.5015212245035950752e-554j)  +/-  (2.64e-39, 1.63e-160j)
| (2.1870046696082441411e-26 + 8.8411364705534549194e-568j)  +/-  (1.71e-67, 1.05e-188j)
| (2.8811867454052577318e-12 + 1.4082749881699399804e-560j)  +/-  (6.92e-61, 4.26e-182j)
| (3.3494144496598032844e-19 + 9.5792297325040188516e-563j)  +/-  (6.5e-66, 4e-187j)
| (7.0174454940992388789e-11 - 1.1905594046747047535e-558j)  +/-  (6.58e-61, 4.05e-182j)
| (0.00039499943532179117596 + 3.5585600008698066515e-555j)  +/-  (6.7e-55, 4.12e-176j)
| (1.3948429939901309086e-05 + 8.1307566392871765542e-556j)  +/-  (8.73e-57, 5.37e-178j)
| (2.1295076470131796096e-07 + 6.8819980228849067904e-557j)  +/-  (4.58e-59, 2.82e-180j)
| (1.3948429939901309086e-05 + 6.0054414042995495354e-556j)  +/-  (2.21e-57, 1.36e-178j)
| (0.013915073855712078771 - 2.6160253079315599769e-554j)  +/-  (8.17e-52, 5.03e-173j)
| (0.0051139732356104537937 - 3.5656672775576907057e-554j)  +/-  (1.51e-54, 9.3e-176j)
| (1.9767312268636436592e-15 + 6.6137871631519101334e-561j)  +/-  (5.66e-65, 3.48e-186j)
| (3.122632297082646589e-17 - 8.6819679649198270868e-562j)  +/-  (4.57e-66, 2.81e-187j)
| (0.0015627356574277506822 + 3.2352387075585442108e-554j)  +/-  (3.33e-57, 2.05e-178j)
| (8.8399857985441396167e-14 - 1.071855250354714701e-561j)  +/-  (5.55e-67, 3.42e-188j)
| (8.2112542034731397073e-05 - 4.9072129457762329338e-555j)  +/-  (1.28e-59, 7.87e-181j)
| (0.0015627356574277506822 - 7.5542155777225365667e-555j)  +/-  (1.92e-58, 1.18e-179j)
| (9.6384664334530491249e-24 + 6.3845482478880130722e-565j)  +/-  (1.32e-70, 8.15e-192j)
| (0.15593456464366216921 - 1.2868138672970174363e-553j)  +/-  (4.41e-56, 2.72e-177j)
| (7.0174454940992388789e-11 - 1.2683930744590937648e-559j)  +/-  (1.38e-65, 8.52e-187j)
| (2.3166931490999194433e-21 + 2.2644657214092288322e-565j)  +/-  (6.64e-72, 4.09e-193j)
| (0.097456454765972437836 - 1.0549581288906080635e-553j)  +/-  (1.66e-58, 1.02e-179j)
| (3.3494144496598032844e-19 - 2.0704541256395790472e-564j)  +/-  (8.1e-71, 4.99e-192j)
| (0.13345466282003530186 + 1.2154979779459352216e-553j)  +/-  (8.53e-60, 5.25e-181j)
| (8.2112542034731397073e-05 - 1.5315599914508009287e-555j)  +/-  (3.31e-63, 2.04e-184j)
| (0.031640563304104243491 + 4.2742182471154557521e-554j)  +/-  (1.93e-61, 1.19e-182j)
| (1.8784715838239271645e-08 - 1.9934148532367297645e-557j)  +/-  (1.97e-65, 1.21e-186j)
| (0.013915073855712078771 + 4.7502613904716061708e-554j)  +/-  (4.73e-62, 2.92e-183j)
| (1.8784715838239271645e-08 - 5.6655168947134680712e-558j)  +/-  (7.35e-66, 4.52e-187j)
| (0.097456454765972437836 + 8.7593160468305143518e-554j)  +/-  (8.31e-62, 5.12e-183j)
| (0.13345466282003530186 - 1.0938655470026248236e-553j)  +/-  (4.61e-62, 2.86e-183j)
| (0.15593456464366216921 + 1.2435742392618727484e-553j)  +/-  (5.78e-62, 3.51e-183j)
