Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 69
-------------------------------------------------
Trying to find an order 69 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^71 - 170533302021161046858015404403489641244020743786/35236959593376964507038384782516353459077539*t^69 + 97323173567289427238063346370812517899603918642183/35236959593376964507038384782516353459077539*t^67 - 1040914220490846905432907238648761973305486381592647/1051849540100804910657862232313920998778434*t^65 + 131465559126396314462125296738416212462992855555766530/525924770050402455328931116156960499389217*t^63 - 24922676250728288346870059023971954847792015637826691935/525924770050402455328931116156960499389217*t^61 + 7371889285241769826182549516454023137476265608611715071105/1051849540100804910657862232313920998778434*t^59 - 1745797417039075061420115684764397525621325513141605807654555/2103699080201609821315724464627841997556868*t^57 + 674188092475407813175146809750777710917170003475926698768677555/8414796320806439285262897858511367990227472*t^55 - 107547497566117071679205131111292533503386135989378192246725964725/16829592641612878570525795717022735980454944*t^53 + 14311075670608517506625621120968789420409524709640484433294254310175/33659185283225757141051591434045471960909888*t^51 - 1599789579561161884837944395261079213469714622448130347101075465326125/67318370566451514282103182868090943921819776*t^49 + 75498974022333216420806216232628933916387936978572295382263710326670875/67318370566451514282103182868090943921819776*t^47 - 6037655968962248463369381755566126943765646608555252789296713492569455125/134636741132903028564206365736181887843639552*t^45 + 409950646330370827284314735375137081014002952907219351655783544748559731875/269273482265806057128412731472363775687279104*t^43 - 23655756358304355896468036005721502154475597917409498815320229449858421250625/538546964531612114256825462944727551374558208*t^41 + 4639659180541679538036166613081249166541184704309900495497269348699977061686875/4308375716252896914054603703557820410996465664*t^39 - 193091013879679170171565994772781557649318825302540153928572571776036619137868125/8616751432505793828109207407115640821992931328*t^37 + 6806056453395598128323084787841799477869613011325351279829156562408635045598179375/17233502865011587656218414814231281643985862656*t^35 - 202542553104190781125128711716260809842899239181144554434693217979833133365350878125/34467005730023175312436829628462563287971725312*t^33 + 1266857296107712318750396154557024450473955731113494725070103223619128422313997359375/17233502865011587656218414814231281643985862656*t^31 - 26503532852543378531659447975277538739662907851838926512148691046937216497797890440625/34467005730023175312436829628462563287971725312*t^29 + 460537344738949528279155014838986893038428143317404124976568597717138876345865944409375/68934011460046350624873659256925126575943450624*t^27 - 6592146836884960106147448134403977550298580828181484673118308412665331683894006858353125/137868022920092701249747318513850253151886901248*t^25 + 153902333144931391800868699971846269410050478034716790322463705634662512893179748909296875/551472091680370804998989274055401012607547604992*t^23 - 1447170073121516463194278109425962172633880725892752213827733373641240344932774382760828125/1102944183360741609997978548110802025215095209984*t^21 + 10797622781208796949476563260720631567538101113675992577474928835174468171968447629904234375/2205888366721483219995957096221604050430190419968*t^19 - 62741573283069752537662498012594806665621279538458965812468891388766994584910980399098453125/4411776733442966439991914192443208100860380839936*t^17 + 138667062692508254483840231622471727789455421581212805254639281328232391815005305535665453125/4411776733442966439991914192443208100860380839936*t^15 - 452447654422205053258707298189909901243179732749919062803264888785973057310303936576539296875/8823553466885932879983828384886416201720761679872*t^13 + 1047344764545302364045678528762194186929316331276437890903993842286803244030944318086395078125/17647106933771865759967656769772832403441523359744*t^11 - 1629287403793804433194499823312394989820970795392572323179756243714651924130013292227688359375/35294213867543731519935313539545664806883046719488*t^9 + 12603442350548974307094194505517105864196455478942535494736355872929295737717096116460791640625/564707421880699704318965016632730636910128747511808*t^7 - 6709371497152360091642294018959872521820837872314858233271303533362460827986228020009701484375/1129414843761399408637930033265461273820257495023616*t^5 + 1587756055708799515146286280173728728093134888725377878845299107579386846301533252005023828125/2258829687522798817275860066530922547640514990047232*t^3 - 103042933151280922975271916459365113341491076580278437215379757937244614962962977150196484375/4517659375045597634551720133061845095281029980094464*t
-------------------------------------------------
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
  current precision for roots: 848
  current precision for roots: 1696
 current precision for weights: 848
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-3.3626721365868921886 + 2.9630979284655558545e-1854j)  +/-  (1.4e-497, 1.4e-497j)
| (-8.648761747209017543 + 5.2545748075018470949e-1849j)  +/-  (1.98e-494, 1.98e-494j)
| (-10.437866050677712847 + 1.3895204439902864175e-1862j)  +/-  (2.33e-497, 2.33e-497j)
| (-8.272091822844416926 + 2.5317183164688825325e-1872j)  +/-  (4.61e-494, 4.61e-494j)
| (-7.5625670916282138641 + 2.1252597281704868763e-1896j)  +/-  (1.37e-493, 1.37e-493j)
| (8.272091822844416926 - 1.9120000289354248341e-1912j)  +/-  (4.36e-494, 4.36e-494j)
| (9.4668791640426499973 - 5.3973520488161080475e-1917j)  +/-  (1.48e-495, 1.48e-495j)
| (-6.5752270046748982944 - 1.2177378689021340746e-1920j)  +/-  (1.94e-493, 1.94e-493j)
| (8.648761747209017543 - 2.1105274633950066379e-1935j)  +/-  (1.99e-494, 1.99e-494j)
| (-9.4668791640426499973 - 1.0850075630588842384e-1934j)  +/-  (1.44e-495, 1.44e-495j)
| (11.058456051922748693 - 1.7402639159646505021e-1940j)  +/-  (8.31e-499, 8.31e-499j)
| (7.2248122168958316997 + 3.3339937500308192933e-1934j)  +/-  (1.68e-493, 1.68e-493j)
| (9.0449924223161157914 - 4.9278871889320372166e-1938j)  +/-  (6.17e-495, 6.17e-495j)
| (-5.6502308904062497914 + 1.5689062014330271718e-1935j)  +/-  (6.47e-494, 6.47e-494j)
| (-9.9245887044709588313 - 1.2316045151185698348e-1947j)  +/-  (2.38e-496, 2.38e-496j)
| (2.0110894200975410629 + 2.5141063465074711198e-1952j)  +/-  (1.2e-501, 1.2e-501j)
| (-0.7071067811865475244 + 7.6539617123959448173e-1958j)  +/-  (1.11e-506, 1.11e-506j)
| (4.4814467393342831457 + 6.1024933898502498915e-1946j)  +/-  (2.67e-495, 2.67e-495j)
| (-1.4821741264101416991 - 2.6517721244961720069e-1954j)  +/-  (1.69e-503, 1.69e-503j)
| (5.05824636402646528 - 2.0414626479524558606e-1944j)  +/-  (1.62e-494, 1.62e-494j)
| (4.1978267227624248164 + 7.1779857361490769052e-1947j)  +/-  (8.42e-496, 8.42e-496j)
| (3.6386828022446280604 + 1.9805706073119852382e-1947j)  +/-  (6.35e-497, 6.35e-497j)
| (5.9530409313457505926 - 9.5737555605089954944e-1944j)  +/-  (1.14e-493, 1.14e-493j)
| (5.3521320175500809263 - 4.2460602175041486259e-1948j)  +/-  (3.43e-494, 3.43e-494j)
| (-6.2611437714728942288 - 4.1364002194787657027e-1950j)  +/-  (1.54e-493, 1.54e-493j)
| (3.0887587526129700626 + 6.8771237334590904779e-1966j)  +/-  (2.8e-498, 2.8e-498j)
| (1.2206141435396294632 + 9.1515856157970159467e-1972j)  +/-  (1.53e-504, 1.53e-504j)
| (-4.7681432104867915462 - 3.1237217085160353565e-1960j)  +/-  (7.19e-495, 7.19e-495j)
| (9.9245887044709588313 - 5.6704711842494942697e-1964j)  +/-  (2.27e-496, 2.27e-496j)
| (6.2611437714728942288 - 1.3614910058276804835e-1959j)  +/-  (1.63e-493, 1.63e-493j)
| (3.3626721365868921886 + 5.905405437464461608e-1974j)  +/-  (1.46e-497, 1.46e-497j)
| (-11.058456051922748693 + 8.2993856217315908043e-1971j)  +/-  (7.82e-499, 7.82e-499j)
| (1.7457691386215530418 - 1.4046599852338598683e-1978j)  +/-  (1.68e-502, 1.68e-502j)
| (10.437866050677712847 + 3.8375550552075007824e-1971j)  +/-  (2.21e-497, 2.21e-497j)
| (-7.9109674242305422766 + 3.3756804910769563296e-1968j)  +/-  (8.66e-494, 8.66e-494j)
| (5.6502308904062497914 - 4.0003520154731273177e-1978j)  +/-  (6.92e-494, 6.92e-494j)
| (-4.4814467393342831457 + 3.4594840835921590514e-1980j)  +/-  (2.83e-495, 2.83e-495j)
| (6.8961149559177564285 + 1.4383132536853412716e-1977j)  +/-  (2.05e-493, 2.05e-493j)
| (-5.3521320175500809263 - 4.1442510360973266816e-1983j)  +/-  (3.56e-494, 3.56e-494j)
| (7.5625670916282138641 + 1.9106891209255700217e-1992j)  +/-  (1.36e-493, 1.36e-493j)
| (-7.2248122168958316997 + 6.1475698132187020006e-2006j)  +/-  (1.73e-493, 1.73e-493j)
| (-2.54655981332620413 + 1.2859432724113682396e-2026j)  +/-  (7.75e-500, 7.75e-500j)
| (1.4821741264101416991 + 7.3775500635865583515e-2031j)  +/-  (1.81e-503, 1.81e-503j)
| (-9.0449924223161157914 + 1.2883290475420950175e-2019j)  +/-  (6.03e-495, 6.03e-495j)
| (-5.05824636402646528 + 6.2643241165939639771e-2024j)  +/-  (1.75e-494, 1.75e-494j)
| (-2.8167693077844070291 - 8.1512463010810769532e-2034j)  +/-  (5.47e-499, 5.47e-499j)
| (-4.1978267227624248164 - 5.2863060293018918148e-2031j)  +/-  (8.48e-496, 8.48e-496j)
| (2.54655981332620413 - 3.4208901571152871696e-2034j)  +/-  (7.72e-500, 7.72e-500j)
| (2.2780209971676431108 + 7.0724576587889261091e-2035j)  +/-  (1.1e-500, 1.1e-500j)
| (-2.2780209971676431108 - 1.1631634710477845111e-2035j)  +/-  (1.15e-500, 1.15e-500j)
| (-3.0887587526129700626 + 2.8122752071870805937e-2033j)  +/-  (2.93e-498, 2.93e-498j)
| (-0.9617756374868082612 - 1.5959838512333773936e-2040j)  +/-  (1.34e-505, 1.34e-505j)
| (-1.7457691386215530418 - 1.0684509414442538979e-2037j)  +/-  (1.73e-502, 1.73e-502j)
| (7.9109674242305422766 - 2.8570114454346886338e-2027j)  +/-  (8.74e-494, 8.74e-494j)
| (0.9617756374868082612 - 6.3204041978023638291e-2050j)  +/-  (1.34e-505, 1.34e-505j)
| (6.5752270046748982944 - 3.828186679477537926e-2038j)  +/-  (1.79e-493, 1.79e-493j)
| (-0.45952151713027287136 + 2.0167825408996158617e-2075j)  +/-  (8.83e-508, 8.83e-508j)
| (-5.9530409313457505926 + 1.0540308164433984499e-2060j)  +/-  (1.06e-493, 1.06e-493j)
| (1.8380717455354081334e-2128 + 4.3351994483222531865e-2130j)  +/-  (1.31e-2126, 1.31e-2126j)
| (0.7071067811865475244 - 1.0834967419210518565e-2091j)  +/-  (1.13e-506, 1.13e-506j)
| (0.45952151713027287136 - 2.9066423480842650801e-2091j)  +/-  (7.88e-508, 7.88e-508j)
| (3.916991502047773858 + 6.2898023983491897248e-2080j)  +/-  (2.56e-496, 2.56e-496j)
| (-0.22356943356747651631 + 3.7513675479973916626e-2093j)  +/-  (5.84e-509, 5.84e-509j)
| (4.7681432104867915462 - 2.4285516695725035649e-2080j)  +/-  (7.21e-495, 7.21e-495j)
| (2.8167693077844070291 + 1.3189330283859499956e-2087j)  +/-  (5.25e-499, 5.25e-499j)
| (-3.6386828022446280604 - 1.7827853997454456221e-2084j)  +/-  (6.7e-497, 6.7e-497j)
| (-3.916991502047773858 - 1.5324792996397096091e-2089j)  +/-  (2.58e-496, 2.58e-496j)
| (-1.2206141435396294632 + 8.566970340914185667e-2098j)  +/-  (1.67e-504, 1.67e-504j)
| (-2.0110894200975410629 + 3.1258985168292971425e-2101j)  +/-  (1.24e-501, 1.24e-501j)
| (-6.8961149559177564285 + 4.9080602648733268519e-2104j)  +/-  (1.94e-493, 1.94e-493j)
| (0.22356943356747651631 - 2.1377438379424534149e-2124j)  +/-  (5.84e-509, 5.84e-509j)
-------------------------------------------------
The weights are:
| (1.9047408677629432244e-06 + 2.0625915468080218106e-1859j)  +/-  (5.44e-142, 1.92e-387j)
| (7.1108302499220327328e-34 + 8.0848689380525463247e-1875j)  +/-  (5.19e-171, 1.83e-416j)
| (1.5069865151741890644e-48 + 2.3051546000816245881e-1882j)  +/-  (2.41e-177, 8.48e-423j)
| (3.9810301994665695113e-31 - 2.1532559913650270216e-1873j)  +/-  (7.31e-170, 2.58e-415j)
| (2.8059865747664269326e-26 - 7.3071076683341862285e-1871j)  +/-  (8.65e-168, 3.05e-413j)
| (3.9810301994665695113e-31 + 9.0859050705823161458e-1874j)  +/-  (1.73e-174, 6.1e-420j)
| (2.9528572468549260524e-40 - 1.9615823628452872242e-1878j)  +/-  (6.42e-179, 2.26e-424j)
| (2.997951315286949436e-20 + 1.1350108647019793444e-1867j)  +/-  (7.58e-167, 2.67e-412j)
| (7.1108302499220327328e-34 - 3.5580534797647417139e-1875j)  +/-  (3.21e-176, 1.13e-421j)
| (2.9528572468549260524e-40 + 4.1227664716326025168e-1878j)  +/-  (2.85e-177, 1.01e-422j)
| (3.1443286200839398177e-54 + 1.5420986295732099921e-1885j)  +/-  (5.04e-185, 1.78e-430j)
| (4.0234259961152633488e-24 - 3.6325495428321078075e-1870j)  +/-  (3.23e-173, 1.14e-418j)
| (6.7829810550940176274e-37 + 1.0173403606432650266e-1876j)  +/-  (1.08e-177, 3.8e-423j)
| (2.3130011216165801898e-15 - 5.1477776282854281884e-1865j)  +/-  (1.38e-166, 4.85e-412j)
| (4.5346745059333287366e-44 - 4.5339850666494849752e-1880j)  +/-  (6.44e-180, 2.27e-425j)
| (0.0026304470162099877663 - 6.4198533888219218741e-1859j)  +/-  (1.35e-144, 4.75e-390j)
| (0.08615781283651643238 + 1.8156364530753579903e-1857j)  +/-  (6.14e-139, 2.16e-384j)
| (3.0502667612791860293e-10 + 6.8600218399322804739e-1863j)  +/-  (9.47e-164, 3.34e-409j)
| (0.016471397250010959814 - 6.101263952953784036e-1858j)  +/-  (6.14e-139, 2.16e-384j)
| (1.2732214426029378169e-12 + 3.6618850210769738876e-1864j)  +/-  (8.46e-167, 2.98e-412j)
| (3.5393689451121150051e-09 - 2.5863494603541015578e-1862j)  +/-  (1.05e-162, 3.7e-408j)
| (2.7799356776987904069e-07 - 2.8498981369702009938e-1861j)  +/-  (2.28e-160, 8.05e-406j)
| (7.0047865430741006217e-17 - 2.0886047413043670788e-1866j)  +/-  (1.42e-171, 5.02e-417j)
| (6.0546547776178553386e-14 - 7.2956665325899543623e-1865j)  +/-  (1.01e-168, 3.57e-414j)
| (1.6556288748527794925e-18 - 9.8151687952047530231e-1867j)  +/-  (1.34e-174, 4.72e-420j)
| (1.1069086485711632904e-05 - 2.2920187434271879334e-1860j)  +/-  (3.51e-159, 1.24e-404j)
| (0.033108801409974194843 + 4.2216314768440787786e-1858j)  +/-  (2.57e-143, 9.06e-389j)
| (2.1755266579386946739e-11 + 9.6160639060061656149e-1863j)  +/-  (2.84e-170, 1e-415j)
| (4.5346745059333287366e-44 + 2.2391095678048468485e-1880j)  +/-  (1.52e-185, 5.37e-431j)
| (1.6556288748527794925e-18 + 2.9561026679875036109e-1867j)  +/-  (1.59e-173, 5.6e-419j)
| (1.9047408677629432244e-06 + 8.3920368425101306938e-1861j)  +/-  (8.8e-162, 3.1e-407j)
| (3.1443286200839398177e-54 - 2.8897383011776697049e-1885j)  +/-  (3e-192, 1.06e-437j)
| (0.0070831941629188521408 + 1.2662452146998269958e-1858j)  +/-  (3.73e-153, 1.31e-398j)
| (1.5069865151741890644e-48 - 1.1817956689090391419e-1882j)  +/-  (7.87e-188, 2.77e-433j)
| (1.322050009444030383e-28 + 4.4281860552449770467e-1872j)  +/-  (1.43e-181, 5.05e-427j)
| (2.3130011216165801898e-15 + 1.3065539036196660672e-1865j)  +/-  (2.53e-171, 8.92e-417j)
| (3.0502667612791860293e-10 - 4.8098005692171725548e-1862j)  +/-  (8.87e-173, 3.12e-418j)
| (4.0672488125935718671e-22 + 3.9481730678931961186e-1869j)  +/-  (1.42e-176, 5e-422j)
| (6.0546547776178553386e-14 + 3.1958576443415417295e-1864j)  +/-  (1.65e-175, 5.82e-421j)
| (2.8059865747664269326e-26 + 2.8090079102944036405e-1871j)  +/-  (5.57e-179, 1.96e-424j)
| (4.0234259961152633488e-24 + 9.9580962327929163243e-1870j)  +/-  (8.91e-181, 3.14e-426j)
| (0.0002319378604696116469 - 1.0008065072518742142e-1858j)  +/-  (6.58e-168, 2.32e-413j)
| (0.016471397250010959814 - 2.3681689941479970505e-1858j)  +/-  (4.17e-159, 1.47e-404j)
| (6.7829810550940176274e-37 - 2.2214193845314240437e-1876j)  +/-  (3.32e-186, 1.17e-431j)
| (1.2732214426029378169e-12 - 1.8186426235442238735e-1863j)  +/-  (3.66e-175, 1.29e-420j)
| (5.4795497065206225671e-05 + 6.5939451480189468544e-1859j)  +/-  (4.54e-170, 1.6e-415j)
| (3.5393689451121150051e-09 + 2.3413739924629985249e-1861j)  +/-  (4.98e-174, 1.75e-419j)
| (0.0002319378604696116469 - 1.3821940446348740698e-1859j)  +/-  (4.27e-168, 1.5e-413j)
| (0.00084217429877639366942 + 3.0722252257398060784e-1859j)  +/-  (6.64e-167, 2.34e-412j)
| (0.00084217429877639366942 + 1.597700786805436561e-1858j)  +/-  (3.78e-169, 1.33e-414j)
| (1.1069086485711632904e-05 - 5.39834905842597165e-1859j)  +/-  (1.78e-171, 6.28e-417j)
| (0.057514834602646305786 - 1.2991301771935128007e-1857j)  +/-  (8.47e-165, 2.99e-410j)
| (0.0070831941629188521408 + 4.0005735297629669907e-1858j)  +/-  (1.27e-167, 4.47e-413j)
| (1.322050009444030383e-28 - 1.7865301133524304144e-1872j)  +/-  (2.19e-184, 7.72e-430j)
| (0.057514834602646305786 - 7.2126598666439045502e-1858j)  +/-  (3.81e-166, 1.34e-411j)
| (2.997951315286949436e-20 - 3.6690698473603546651e-1868j)  +/-  (2.74e-180, 9.65e-426j)
| (0.11080352098205949731 - 2.4405936764622478312e-1857j)  +/-  (3.77e-166, 1.33e-411j)
| (7.0047865430741006217e-17 + 7.5112249628962272808e-1866j)  +/-  (6.9e-180, 2.43e-425j)
| (0.12444814290588640902 - 3.147101506305394343e-1857j)  +/-  (1.03e-166, 3.63e-412j)
| (0.08615781283651643238 + 1.1847182257225683346e-1857j)  +/-  (3.77e-167, 1.33e-412j)
| (0.11080352098205949731 - 1.8537551159235271144e-1857j)  +/-  (3.07e-167, 1.08e-412j)
| (3.4241492661774809613e-08 + 8.9459157043093580709e-1862j)  +/-  (2.05e-174, 7.21e-420j)
| (0.12286372270050840713 + 3.0161128828808134716e-1857j)  +/-  (1.04e-167, 3.67e-413j)
| (2.1755266579386946739e-11 - 1.662207167836809626e-1863j)  +/-  (2.82e-176, 9.93e-422j)
| (5.4795497065206225671e-05 + 5.8252081966648689339e-1860j)  +/-  (1.64e-172, 5.78e-418j)
| (2.7799356776987904069e-07 + 7.2291222724687434436e-1860j)  +/-  (1.94e-176, 6.82e-422j)
| (3.4241492661774809613e-08 - 1.1748328079671186304e-1860j)  +/-  (5.25e-177, 1.85e-422j)
| (0.033108801409974194843 + 9.0328766635403543631e-1858j)  +/-  (7.32e-173, 2.58e-418j)
| (0.0026304470162099877663 - 2.5524713367630309536e-1858j)  +/-  (3.13e-174, 1.1e-419j)
| (4.0672488125935718671e-22 - 1.1462890423442147917e-1868j)  +/-  (1e-184, 3.57e-430j)
| (0.12286372270050840713 + 2.6400586562376900519e-1857j)  +/-  (1.17e-172, 3.96e-418j)
