Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 54
-------------------------------------------------
Trying to find an order 54 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^58 - 240905980609553820990869050871162091004100960073/156076154376443784020471091257586920927888413*t^56 + 4319816504751694665659618738495126129086684077976896/3901903859411094600511777281439673023197210325*t^54 - 1914444930812134195092409917939403975608567681279095676/3901903859411094600511777281439673023197210325*t^52 + 34587858134481660284478592287171583651388751293211735489/229523756435946741206575134202333707246894725*t^50 - 313103327864853580056994855510085933893495397465880034137/9180950257437869648263005368093348289875789*t^48 + 54196147575171769228021015857859068308869387394694249390984/9180950257437869648263005368093348289875789*t^46 - 7351876411998805845777536179732248881077890309256800035439888/9180950257437869648263005368093348289875789*t^44 + 794538845014129648470699268513392214962153278336572792544979633/9180950257437869648263005368093348289875789*t^42 - 69177487823800388923668858675473939865661041605149032198053267109/9180950257437869648263005368093348289875789*t^40 + 4888145302517108997879390145696515170480750914679834100904051972440/9180950257437869648263005368093348289875789*t^38 - 281567644604460219085343169128993648410944110025603715206895053907980/9180950257437869648263005368093348289875789*t^36 + 779333637989924765643210269685418935211618979283419582967216903376845/540055897496345273427235609887844017051517*t^34 - 29953719089485537915319425979961383177602128725119829198718300016537845/540055897496345273427235609887844017051517*t^32 + 30276261629021532104201474272871681040640786704618603710956776541302960/17421157983753073336362439028640129582307*t^30 - 770414776340252864935692401887155484213974516783262599472426766331475200/17421157983753073336362439028640129582307*t^28 + 15827838074432466441339204342458276552820853695777100397796891393111866025/17421157983753073336362439028640129582307*t^26 - 260447175123455310528954174062809760942587897966400013532752871124826895125/17421157983753073336362439028640129582307*t^24 + 57745406370785074640581295287043172693298460786896644549687362626254724554000/296159685723802246718161463486882202899219*t^22 - 588951779246619803436795936930930678633926104882460660593352088497066773759500/296159685723802246718161463486882202899219*t^20 + 16670128167846588697048695682599561283528776789042767862362650047380160020625/1069168540519141684903109976486939360647*t^18 - 1601719386333225827265394935155227513552067890041845876657879164516684547563125/17421157983753073336362439028640129582307*t^16 + 6905924648637554141906165847327737022719282450606705420147462656284186716535000/17421157983753073336362439028640129582307*t^14 - 20978544851996592486917274977193483162058560076712419723608664623513802145610000/17421157983753073336362439028640129582307*t^12 + 42713170349850561155381000153393496356203614985665963913784416637898486396283125/17421157983753073336362439028640129582307*t^10 - 54370761792643034557102493761731183274925589864972879043430856425611512784715625/17421157983753073336362439028640129582307*t^8 + 39097651929666837491912944793513058165272284209898825752928810035389573391525000/17421157983753073336362439028640129582307*t^6 - 13573005247103989397517150120504943550216897756238272443055338494852636004177500/17421157983753073336362439028640129582307*t^4 + 1732666741636409132971923115171010390371477989116234686321365942463579342580625/17421157983753073336362439028640129582307*t^2 - 38861352563804617800545142221247228372176854072008492018589507033117973735625/17421157983753073336362439028640129582307
-------------------------------------------------
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:   58 out of 58
Indefinite weights: 0 out of 58
Negative weights:   0 out of 58
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-10.863554677851013829 - 4.15444599054181394e-709j)  +/-  (3.81e-242, 3.81e-242j)
| (-6.2543171365325301285 - 2.2604668983402607629e-726j)  +/-  (2.27e-242, 2.27e-242j)
| (-12.920792619855984553 - 1.5954067849794112599e-728j)  +/-  (3.77e-244, 3.77e-244j)
| (12.163843329149963518 - 5.4690478234569003081e-734j)  +/-  (2.99e-243, 2.99e-243j)
| (9.7174155762297104729 + 5.0815190538112645077e-733j)  +/-  (1.36e-241, 1.36e-241j)
| (8.6619775124036161294 - 3.1118508832831907966e-734j)  +/-  (1.97e-241, 1.97e-241j)
| (10.863554677851013829 + 4.1601269229564875634e-735j)  +/-  (3.71e-242, 3.71e-242j)
| (11.487733090075930989 + 1.103580469428769217e-738j)  +/-  (1.26e-242, 1.26e-242j)
| (-10.276424108343029479 - 5.152225375395376844e-745j)  +/-  (8.12e-242, 8.12e-242j)
| (13.83436002073302728 + 1.2808679223306084663e-767j)  +/-  (2.06e-245, 2.06e-245j)
| (12.920792619855984553 - 9.6403992016061604106e-766j)  +/-  (4.01e-244, 4.01e-244j)
| (-9.1806459543947368251 - 4.9159333247191782518e-764j)  +/-  (1.87e-241, 1.87e-241j)
| (-12.163843329149963518 + 5.5770493209616590241e-772j)  +/-  (3.07e-243, 3.07e-243j)
| (-7.6674527381914569628 - 3.9852021007956450216e-776j)  +/-  (1.38e-241, 1.38e-241j)
| (-8.6619775124036161294 + 2.7723054394759327524e-787j)  +/-  (1.88e-241, 1.88e-241j)
| (-13.83436002073302728 + 2.76422072724684038e-801j)  +/-  (2e-245, 2e-245j)
| (4.0338889141860354755 + 5.0634108049697963547e-812j)  +/-  (4.34e-245, 4.34e-245j)
| (-3.6037293013712464322 + 3.3782567670513932675e-813j)  +/-  (8.28e-246, 8.28e-246j)
| (-1.9186756814014734485 + 6.5872363914175694646e-817j)  +/-  (2.94e-249, 2.94e-249j)
| (-3.1771932811702132695 + 1.2521342251790662364e-814j)  +/-  (1.37e-246, 1.37e-246j)
| (-4.0338889141860354755 + 1.5296125372570767141e-810j)  +/-  (4.52e-245, 4.52e-245j)
| (1.5084935123079939796 - 1.6054863431843123471e-817j)  +/-  (2.75e-250, 2.75e-250j)
| (6.2543171365325301285 + 1.8183092616528435617e-809j)  +/-  (2.14e-242, 2.14e-242j)
| (-9.7174155762297104729 + 1.3256255569296121416e-827j)  +/-  (1.32e-241, 1.32e-241j)
| (2.3344142183389772393 + 1.0991957432696799201e-856j)  +/-  (2.41e-248, 2.41e-248j)
| (2.7540801406784132346 - 2.8629987913811536025e-855j)  +/-  (2.02e-247, 2.02e-247j)
| (1.10924357578676461 - 1.7515489179940343076e-858j)  +/-  (2.69e-251, 2.69e-251j)
| (5.7990057750108384591 - 1.0935091502422439543e-849j)  +/-  (8.6e-243, 8.6e-243j)
| (-11.487733090075930989 + 7.6450896513136186382e-865j)  +/-  (1.31e-242, 1.31e-242j)
| (-1.5084935123079939796 - 1.0946257707828423318e-881j)  +/-  (2.57e-250, 2.57e-250j)
| (-5.3499886674347819656 + 1.8544494499798424027e-874j)  +/-  (2.91e-243, 2.91e-243j)
| (7.1874221049372287223 - 3.4159106399114781829e-873j)  +/-  (8.22e-242, 8.22e-242j)
| (6.7167832600193301528 - 3.3711367703506120718e-873j)  +/-  (5.15e-242, 5.15e-242j)
| (9.1806459543947368251 - 1.1770564708796671788e-872j)  +/-  (1.86e-241, 1.86e-241j)
| (7.6674527381914569628 + 9.722978264533983586e-873j)  +/-  (1.29e-241, 1.29e-241j)
| (-2.3344142183389772393 + 1.289757873958359637e-879j)  +/-  (2.49e-248, 2.49e-248j)
| (5.3499886674347819656 - 3.6840164758653296582e-875j)  +/-  (2.94e-243, 2.94e-243j)
| (-4.4680098419583405202 - 5.5742609493178379281e-876j)  +/-  (2.25e-244, 2.25e-244j)
| (4.4680098419583405202 + 3.3020740385077522264e-876j)  +/-  (2.07e-244, 2.07e-244j)
| (-7.1874221049372287223 + 4.3588570025905204286e-872j)  +/-  (8.22e-242, 8.22e-242j)
| (-0.74196378430272585765 - 9.9934187418930335515e-891j)  +/-  (3.14e-252, 3.14e-252j)
| (8.158358153092743243 - 1.0671613477726600343e-879j)  +/-  (1.72e-241, 1.72e-241j)
| (-6.7167832600193301528 + 5.3090372241693169138e-880j)  +/-  (4.46e-242, 4.46e-242j)
| (-8.158358153092743243 - 3.0848851160916283059e-895j)  +/-  (1.66e-241, 1.66e-241j)
| (1.9186756814014734485 + 1.1158361559338445264e-921j)  +/-  (2.79e-249, 2.79e-249j)
| (-0.16778975780224022255 + 1.5702691621886465295e-926j)  +/-  (3.43e-254, 3.43e-254j)
| (-1.10924357578676461 + 7.8218024716294607364e-923j)  +/-  (2.92e-251, 2.92e-251j)
| (10.276424108343029479 - 3.3863374813863254328e-912j)  +/-  (8.07e-242, 8.07e-242j)
| (0.45462598338641402505 + 2.58349462893272181e-930j)  +/-  (4.67e-253, 4.67e-253j)
| (0.74196378430272585765 + 7.1030482997120055016e-929j)  +/-  (3.14e-252, 3.14e-252j)
| (4.906532334142703723 + 2.1131156088959176211e-918j)  +/-  (8.59e-244, 8.59e-244j)
| (-0.45462598338641402505 - 1.7873664364629110354e-929j)  +/-  (4.21e-253, 4.21e-253j)
| (0.16778975780224022255 - 1.5913883865982144717e-931j)  +/-  (3.43e-254, 3.43e-254j)
| (3.6037293013712464322 - 4.7665201846386779074e-924j)  +/-  (8.12e-246, 8.12e-246j)
| (-4.906532334142703723 + 5.0266233588683835795e-918j)  +/-  (8.8e-244, 8.8e-244j)
| (3.1771932811702132695 - 5.443817250462751769e-927j)  +/-  (1.37e-246, 1.37e-246j)
| (-5.7990057750108384591 - 7.5639696877933460219e-928j)  +/-  (8.55e-243, 8.55e-243j)
| (-2.7540801406784132346 - 2.2982887961392129927e-941j)  +/-  (1.92e-247, 1.92e-247j)
-------------------------------------------------
The weights are:
| (5.6857060927813665791e-27 - 1.3265734013593125219e-734j)  +/-  (1.31e-57, 4.03e-178j)
| (5.8672434521941723369e-10 + 4.9780489665747393671e-727j)  +/-  (1.33e-44, 4.11e-165j)
| (1.8191259745339734668e-37 - 4.5895973309029252291e-741j)  +/-  (5.07e-62, 1.56e-182j)
| (2.1043214177409166335e-33 + 4.9764529972969262218e-740j)  +/-  (2.37e-62, 7.29e-183j)
| (6.8257075442501844749e-22 + 4.9713874437484098424e-734j)  +/-  (2.32e-57, 7.13e-178j)
| (1.0388517396585548693e-17 + 8.1389533132286939773e-732j)  +/-  (4.31e-55, 1.33e-175j)
| (5.6857060927813665791e-27 + 1.0871652770977497048e-736j)  +/-  (3.29e-60, 1.01e-180j)
| (5.6920559324973648515e-30 - 2.9899295205727702543e-738j)  +/-  (1.32e-61, 4.05e-182j)
| (2.6694095571968344075e-24 + 9.7430624977540111091e-734j)  +/-  (4.34e-62, 1.34e-182j)
| (1.1600314393262236166e-42 + 8.4201212341147448058e-745j)  +/-  (6.65e-68, 2.05e-188j)
| (1.8191259745339734668e-37 - 3.9697930930747918129e-742j)  +/-  (1.64e-65, 5.04e-186j)
| (1.0489090935776302325e-19 + 8.4451318340737506073e-732j)  +/-  (4.17e-61, 1.28e-181j)
| (2.1043214177409166335e-33 + 8.81302499915327536e-739j)  +/-  (2.19e-67, 6.74e-188j)
| (3.3172375135687517428e-14 - 3.5876150966555714822e-729j)  +/-  (1.18e-58, 3.62e-179j)
| (1.0388517396585548693e-17 - 7.2183431773725358419e-731j)  +/-  (1.98e-60, 6.09e-181j)
| (1.1600314393262236166e-42 + 7.0001030727523987695e-744j)  +/-  (1.08e-71, 3.33e-192j)
| (5.0465280883787814142e-05 + 1.0909575581666233982e-724j)  +/-  (1.32e-50, 4.08e-171j)
| (0.00025858153215758021879 + 6.3622962574514075873e-724j)  +/-  (7.08e-48, 2.18e-168j)
| (0.026175131725653390045 + 1.8773780605444675093e-722j)  +/-  (2.29e-38, 7.04e-159j)
| (0.0010891684032654553499 - 1.5911689699317336942e-723j)  +/-  (3.34e-46, 1.03e-166j)
| (5.0465280883787814142e-05 - 2.3796887331247720033e-724j)  +/-  (5.24e-50, 1.61e-170j)
| (0.051943757078499865379 + 3.1519568231459668963e-722j)  +/-  (1.23e-37, 3.78e-158j)
| (5.8672434521941723369e-10 - 1.3404125594987123969e-727j)  +/-  (1.31e-60, 4.04e-181j)
| (6.8257075442501844749e-22 - 8.9270121796162196998e-733j)  +/-  (5.58e-64, 1.72e-184j)
| (0.010928980462165859227 + 5.4954815516307914463e-723j)  +/-  (1.22e-45, 3.77e-166j)
| (0.0037894185733042754764 - 2.2388023754641150132e-723j)  +/-  (3.13e-48, 9.64e-169j)
| (0.083978805659205157232 - 7.9245242604392476857e-722j)  +/-  (1.67e-36, 5.15e-157j)
| (8.9898083325942298404e-09 + 6.2733000447831341372e-727j)  +/-  (8.46e-60, 2.6e-180j)
| (5.6920559324973648515e-30 - 1.0706678387992272878e-736j)  +/-  (9.1e-69, 2.8e-189j)
| (0.051943757078499865379 - 4.1684560913814868495e-722j)  +/-  (2.99e-42, 9.19e-163j)
| (1.08416397442637372e-07 + 7.7406212846517829111e-726j)  +/-  (8.63e-58, 2.66e-178j)
| (1.1483885907798848089e-12 - 4.2547361552163321351e-729j)  +/-  (7.66e-64, 2.36e-184j)
| (2.9716819107824230735e-11 + 2.545584599367133782e-728j)  +/-  (9.65e-63, 2.97e-183j)
| (1.0489090935776302325e-19 - 7.0905227300730603008e-733j)  +/-  (3.76e-68, 1.16e-188j)
| (3.3172375135687517428e-14 + 6.1876741441665314547e-730j)  +/-  (2.47e-65, 7.6e-186j)
| (0.010928980462165859227 - 8.5036932977606725982e-723j)  +/-  (2.04e-53, 6.27e-174j)
| (1.08416397442637372e-07 - 2.6322701720167625183e-726j)  +/-  (1.79e-61, 5.5e-182j)
| (8.0482497718407936037e-06 + 8.2598733549580083455e-725j)  +/-  (4.31e-60, 1.33e-180j)
| (8.0482497718407936037e-06 - 3.4455968520262537528e-725j)  +/-  (2.61e-60, 8.02e-181j)
| (1.1483885907798848089e-12 + 2.0892103934199477252e-728j)  +/-  (3.23e-66, 9.95e-187j)
| (0.10117569291924188556 - 2.3573576771322266089e-721j)  +/-  (1.68e-51, 5.18e-172j)
| (6.984499218113769747e-16 - 7.7238568730289992323e-731j)  +/-  (4.1e-67, 1.26e-187j)
| (2.9716819107824230735e-11 - 1.0792067674837014741e-727j)  +/-  (1.21e-65, 3.74e-186j)
| (6.984499218113769747e-16 + 5.4311223249598590201e-730j)  +/-  (7.93e-68, 2.44e-188j)
| (0.026175131725653390045 - 1.3137706890760862807e-722j)  +/-  (2.59e-57, 7.97e-178j)
| (0.12796196866842482283 - 4.3894420370071032019e-721j)  +/-  (4.42e-55, 1.36e-175j)
| (0.083978805659205157232 + 9.7268509501831063736e-722j)  +/-  (1.31e-55, 4.04e-176j)
| (2.6694095571968344075e-24 - 2.7059865509812593458e-735j)  +/-  (2.76e-72, 8.51e-193j)
| (0.092638821999250012982 - 3.6615305921210475365e-721j)  +/-  (1.56e-55, 4.8e-176j)
| (0.10117569291924188556 + 2.0559365855091435523e-721j)  +/-  (6.88e-56, 2.12e-176j)
| (1.0414243468576165756e-06 + 9.9809780237978365027e-726j)  +/-  (3.7e-63, 1.14e-183j)
| (0.092638821999250012982 + 3.9813765616179189049e-721j)  +/-  (2.92e-56, 8.99e-177j)
| (0.12796196866842482283 + 4.2559128157892261755e-721j)  +/-  (1.89e-56, 5.83e-177j)
| (0.00025858153215758021879 - 3.1926628331073225431e-724j)  +/-  (5.54e-62, 1.71e-182j)
| (1.0414243468576165756e-06 - 2.6422746557726705669e-725j)  +/-  (1.15e-64, 3.56e-185j)
| (0.0010891684032654553499 + 8.7105756679835746165e-724j)  +/-  (6.74e-62, 2.07e-182j)
| (8.9898083325942298404e-09 - 2.0639398029699375715e-726j)  +/-  (6.03e-66, 1.87e-186j)
| (0.0037894185733042754764 + 3.759453590487132844e-723j)  +/-  (3.22e-62, 9.72e-183j)
