Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 71
-------------------------------------------------
Trying to find an order 71 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 4*t^73 - 5885950926476709673862933153630584138051734298522/1148596789480616685491341991404158861898656261*t^71 + 3562792415424148912806670352273914901360216563432895/1148596789480616685491341991404158861898656261*t^69 - 39314628601445941994894592805688066612165656197635305/33292660564655556101198318591424894547787138*t^67 + 10571604416236954005539292962434108870089028132430229475/33292660564655556101198318591424894547787138*t^65 - 1068873348685925722392917655172402546345040395456856159185/16646330282327778050599159295712447273893569*t^63 + 337966597296084278282273248152914604200367517103385231441735/33292660564655556101198318591424894547787138*t^61 - 85752471836952359011991827595914041229246660776940246145116725/66585321129311112202396637182849789095574276*t^59 + 35567762806809587196974214383696051391267063157960859158427368575/266341284517244448809586548731399156382297104*t^57 - 6110003292604337034578222613681203905352365777895833637015174290875/532682569034488897619173097462798312764594208*t^55 + 878029512148964430024613154683065742552025794833321325115480440335825/1065365138068977795238346194925596625529188416*t^53 - 106321911973367515340998947836463944337219311302952313397721630263719075/2130730276137955590476692389851193251058376832*t^51 + 170416155241812943890065862297869469967118840177013315417193225526668125/66585321129311112202396637182849789095574276*t^49 - 475672312121821068308692907223366374241342762571598799387459390408715426875/4261460552275911180953384779702386502116753664*t^47 + 35366396095368933848082509228005736732014019668237034054153588523643930453125/8522921104551822361906769559404773004233507328*t^45 - 2244270228828453129407462349614021724581361972033482213641296708828126616539375/17045842209103644723813539118809546008467014656*t^43 + 486346389693097158057963904608059334209842044326219530569184071827866425581191875/136366737672829157790508312950476368067736117248*t^41 - 22479999746300014009694024159318686856368360661295410009132543384881310548968721875/272733475345658315581016625900952736135472234496*t^39 + 885121961774388424121082408339627398714902795840454407207966249394286079931614940625/545466950691316631162033251801905472270944468992*t^37 - 29613068423114626148710563554333855660378904200460474430559163274205166691991350171875/1090933901382633262324066503603810944541888937984*t^35 + 419479206913532626836690152645716219990016438243045340698213021029348781593978124821875/1090933901382633262324066503603810944541888937984*t^33 - 5009261978703528099227905596146148236972415361767602704754792425032974622960496084809375/1090933901382633262324066503603810944541888937984*t^31 + 100293547626352031401404573926290372082460723066244664068719622509374757484722367820765625/2181867802765266524648133007207621889083777875968*t^29 - 1671828786240540749212361682060908856172047550804918901764723467560267566478988780432796875/4363735605530533049296266014415243778167555751936*t^27 + 46017809002169740398167505458751806622357724471079559746798067325750438182072127174644609375/17454942422122132197185064057660975112670223007744*t^25 - 517615512081643966582481180606664350420196696973382899403735678704356600535605990259558921875/34909884844244264394370128115321950225340446015488*t^23 + 4700130037797096740073035800546218323351595275935930911808127731670234982701755883427530015625/69819769688488528788740256230643900450680892030976*t^21 - 33938045378698792673889353014718842098538988465846911839920624245408119408328244992219746796875/139639539376977057577480512461287800901361784061952*t^19 + 47818201511114718126544831395601550246809931592186211933464675078644324202276111271254807890625/69819769688488528788740256230643900450680892030976*t^17 - 411004007085948060703873737638734134775366404102601587802877970532394992326390263687465539453125/279279078753954115154961024922575601802723568123904*t^15 + 1307271917236767057462609974208632880152976729554029260804339908386440924196219503390376806796875/558558157507908230309922049845151203605447136247808*t^13 - 2959042746918446464258375019392655177748043273884462297267462572675514557080829049749054502890625/1117116315015816460619844099690302407210894272495616*t^11 + 36146284210049772311342435699789670163423849952897023426059912627787686087450366049189994787890625/17873861040253063369917505595044838515374308359929856*t^9 - 34478978890877351715416961690469452690340478061690207561482416234131324016406544724724171084765625/35747722080506126739835011190089677030748616719859712*t^7 + 18236429483028860615145300814571899095600242450189374304913845769963034228722811279215744263671875/71495444161012253479670022380179354061497233439719424*t^5 - 4336291160819648200051464368832190184904760061490614234815216566728811119400115359390445522265625/142990888322024506959340044760358708122994466879438848*t^3 + 144257245746531866490654163895874192842060452145772920699912740442126709608071383768063980859375/142990888322024506959340044760358708122994466879438848*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
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (10.102458227829109268 - 6.6286464016754412064e-622j)  +/-  (9.85e-241, 9.85e-241j)
| (9.647266477217705962 + 3.9194657476194548682e-621j)  +/-  (6.5e-240, 6.5e-240j)
| (-8.1006077389812125825 + 7.8845114404380662543e-623j)  +/-  (4.62e-238, 4.62e-238j)
| (-8.4594820094512085855 - 3.1273868534385580248e-622j)  +/-  (2.27e-238, 2.27e-238j)
| (-10.613011441639733753 + 5.5226891407866895572e-625j)  +/-  (8.98e-242, 8.98e-242j)
| (8.4594820094512085855 - 8.1169384700845367964e-620j)  +/-  (2.27e-238, 2.27e-238j)
| (9.2277787478995842701 + 2.736237256724552832e-623j)  +/-  (2.79e-239, 2.79e-239j)
| (10.613011441639733753 - 1.2005771100624522305e-627j)  +/-  (9.21e-242, 9.21e-242j)
| (-11.23043942079517354 + 2.0304484202654783653e-638j)  +/-  (3.35e-243, 3.35e-243j)
| (6.1561477221438225071 - 1.1610461070234629811e-630j)  +/-  (6.85e-238, 6.85e-238j)
| (5.268340354452103043 - 4.783483879563818954e-641j)  +/-  (1.21e-238, 1.21e-238j)
| (-7.7544420926871772364 - 4.5691253179989349552e-646j)  +/-  (7.22e-238, 7.22e-238j)
| (8.1006077389812125825 + 2.8743594180678467961e-657j)  +/-  (4.9e-238, 4.9e-238j)
| (11.23043942079517354 + 2.1669983964017776039e-668j)  +/-  (3.12e-243, 3.12e-243j)
| (-9.647266477217705962 + 3.5594822334323056106e-671j)  +/-  (6.17e-240, 6.17e-240j)
| (0.95701501289418667713 - 1.0082256134639064552e-681j)  +/-  (2.8e-250, 2.8e-250j)
| (4.1369249208312639552 + 6.3286735853121751179e-671j)  +/-  (2.64e-240, 2.64e-240j)
| (-5.268340354452103043 + 9.0959907603798689737e-670j)  +/-  (1.3e-238, 1.3e-238j)
| (-0.95701501289418667713 - 9.471481695499632565e-682j)  +/-  (2.65e-250, 2.65e-250j)
| (-10.102458227829109268 + 2.3439837677168159869e-672j)  +/-  (9.44e-241, 9.44e-241j)
| (-7.418916402185043394 - 3.641159544247622983e-668j)  +/-  (1.03e-237, 1.03e-237j)
| (4.4152334272975432514 - 2.7776143414250551505e-671j)  +/-  (7.68e-240, 7.68e-240j)
| (-9.2277787478995842701 + 1.8715470675787308499e-673j)  +/-  (2.97e-239, 2.97e-239j)
| (-2.5142124060770188122 - 6.5711726565278432493e-681j)  +/-  (1.84e-244, 1.84e-244j)
| (-8.8338733163329692086 + 1.7173413439289600082e-673j)  +/-  (8.66e-239, 8.66e-239j)
| (-3.3165820123420140277 + 3.1321860795724513282e-682j)  +/-  (3.81e-242, 3.81e-242j)
| (2.250148059991007948 - 1.0940656140202205537e-684j)  +/-  (2.75e-245, 2.75e-245j)
| (-1.7268805171296574906 - 1.5865794813375084749e-686j)  +/-  (3.96e-247, 3.96e-247j)
| (7.7544420926871772364 + 5.8366375347861173403e-676j)  +/-  (7.15e-238, 7.15e-238j)
| (-1.4678757067711433912 + 2.690082380014587895e-697j)  +/-  (4.14e-248, 4.14e-248j)
| (3.8611928985770070072 - 1.0846849529044775867e-689j)  +/-  (6.81e-241, 6.81e-241j)
| (1.7268805171296574906 + 6.8180564450070675454e-696j)  +/-  (3.58e-247, 3.58e-247j)
| (2.5142124060770188122 - 4.1832290162556813463e-693j)  +/-  (1.84e-244, 1.84e-244j)
| (-7.0924507583366683232 + 6.5559780647732654881e-685j)  +/-  (1.13e-237, 1.13e-237j)
| (4.6963735770373660823 - 2.6054961894759933602e-694j)  +/-  (2.22e-239, 2.22e-239j)
| (5.5598658166231233309 - 6.35123267041759758e-713j)  +/-  (2.56e-238, 2.56e-238j)
| (2.7799136302565575554 + 2.3225575591449557142e-739j)  +/-  (1.29e-243, 1.29e-243j)
| (6.7738034471284256907 + 3.8499177190238028932e-733j)  +/-  (1.12e-237, 1.12e-237j)
| (1.9876901380545742288 + 1.5922406049104054693e-752j)  +/-  (3.45e-246, 3.45e-246j)
| (-4.6963735770373660823 - 2.8383118252510105631e-747j)  +/-  (2.29e-239, 2.29e-239j)
| (-0.7071067811865475244 + 3.0544764581025679053e-758j)  +/-  (2.01e-251, 2.01e-251j)
| (-3.0473314135931361969 - 1.4700106257225419676e-749j)  +/-  (7.56e-243, 7.56e-243j)
| (4.9806336563978831061 - 1.3137892875871135724e-743j)  +/-  (5.47e-239, 5.47e-239j)
| (7.418916402185043394 - 1.6220314363095217385e-745j)  +/-  (9.56e-238, 9.56e-238j)
| (-6.4619755394980525083 + 8.9143637758311344405e-755j)  +/-  (1.01e-237, 1.01e-237j)
| (-1.9876901380545742288 + 3.7495623869246297907e-766j)  +/-  (3.17e-246, 3.17e-246j)
| (-2.7799136302565575554 - 7.1915554779059537314e-764j)  +/-  (1.2e-243, 1.2e-243j)
| (-6.7738034471284256907 + 3.2566780438948702429e-756j)  +/-  (1.08e-237, 1.08e-237j)
| (5.8556369512223884381 - 1.9067140722721929123e-758j)  +/-  (4.23e-238, 4.23e-238j)
| (3.0473314135931361969 + 5.1545900116206513129e-774j)  +/-  (7.1e-243, 7.1e-243j)
| (-4.4152334272975432514 + 3.3980080346216618679e-770j)  +/-  (7.84e-240, 7.84e-240j)
| (-0.46336251695749085391 + 1.7297828030297747282e-783j)  +/-  (1.41e-252, 1.41e-252j)
| (-5.5598658166231233309 - 3.0520031752280180447e-768j)  +/-  (2.55e-238, 2.55e-238j)
| (8.8338733163329692086 + 2.3344826129297187494e-773j)  +/-  (9.06e-239, 9.06e-239j)
| (-3.5878115496283329865 - 3.5576465506615054512e-785j)  +/-  (1.72e-241, 1.72e-241j)
| (-6.1561477221438225071 + 3.7789376944432279495e-781j)  +/-  (6.91e-238, 6.91e-238j)
| (0.22800223187125722987 - 1.3039448618204897854e-828j)  +/-  (7.99e-254, 7.99e-254j)
| (-4.9806336563978831061 - 2.8431529539816583098e-785j)  +/-  (5.57e-239, 5.57e-239j)
| (1.211025164280226075 + 6.3815965780510138295e-801j)  +/-  (3.4e-249, 3.4e-249j)
| (0.46336251695749085391 - 8.9713285943732323685e-804j)  +/-  (1.54e-252, 1.54e-252j)
| (-4.1369249208312639552 - 3.1666265889500483704e-789j)  +/-  (2.41e-240, 2.41e-240j)
| (-5.8556369512223884381 - 2.3941981876965708468e-796j)  +/-  (4.47e-238, 4.47e-238j)
| (-2.250148059991007948 + 7.5574885525563039032e-815j)  +/-  (2.58e-245, 2.58e-245j)
| (7.0924507583366683232 + 2.3274164960355801409e-824j)  +/-  (1.13e-237, 1.13e-237j)
| (1.4678757067711433912 - 1.2455220997009502212e-863j)  +/-  (3.6e-248, 3.6e-248j)
| (1.7471620215435693353e-878 - 1.6800714129431221589e-878j)  +/-  (1.77e-876, 1.77e-876j)
| (6.4619755394980525083 - 5.8143956712731758275e-851j)  +/-  (9.36e-238, 9.36e-238j)
| (-1.211025164280226075 - 1.2205516450688808008e-872j)  +/-  (3.26e-249, 3.26e-249j)
| (-3.8611928985770070072 + 5.2999734007947989709e-864j)  +/-  (7.24e-241, 7.24e-241j)
| (3.3165820123420140277 - 6.1030707380057110523e-865j)  +/-  (3.66e-242, 3.66e-242j)
| (0.7071067811865475244 + 8.7833613802286304199e-875j)  +/-  (2.02e-251, 2.02e-251j)
| (3.5878115496283329865 + 3.3305431269121531813e-864j)  +/-  (1.7e-241, 1.7e-241j)
| (-0.22800223187125722987 - 2.7642308001730072569e-876j)  +/-  (9.72e-254, 9.72e-254j)
-------------------------------------------------
The weights are:
| (1.2798139256632624201e-45 - 1.9462756730278396358e-658j)  +/-  (3.79e-50, 4.55e-169j)
| (9.3407135138267793214e-42 + 2.4068357052051797085e-656j)  +/-  (1.02e-48, 1.22e-167j)
| (6.3064368782677504309e-30 + 2.7033065295010840104e-651j)  +/-  (2.97e-45, 3.57e-164j)
| (1.7205318898680980318e-32 + 1.0568757956967575323e-652j)  +/-  (1.18e-46, 1.42e-165j)
| (3.7550267898145805099e-50 - 1.008938631075289755e-661j)  +/-  (1.95e-54, 2.34e-173j)
| (1.7205318898680980318e-32 + 1.1976645523155628017e-650j)  +/-  (1.95e-47, 2.33e-166j)
| (2.3897616669951665293e-38 - 1.9664307049753008159e-654j)  +/-  (1.79e-49, 2.14e-168j)
| (3.7550267898145805099e-50 + 7.661268739993526639e-661j)  +/-  (2.6e-54, 3.11e-173j)
| (6.7696857300004541395e-56 + 1.2085515741417923092e-664j)  +/-  (1.53e-58, 1.83e-177j)
| (5.9429423339821421544e-18 - 1.5354543417831163138e-644j)  +/-  (4.86e-41, 5.84e-160j)
| (1.4425369845637500279e-13 + 2.0152867357448392181e-642j)  +/-  (2.44e-37, 2.93e-156j)
| (1.4752992219145569414e-27 + 2.1144626126172280347e-651j)  +/-  (2.87e-48, 3.45e-167j)
| (6.3064368782677504309e-30 - 7.7752371832287030777e-650j)  +/-  (2.46e-47, 2.95e-166j)
| (6.7696857300004541395e-56 - 7.5608521132918360609e-664j)  +/-  (2.66e-57, 3.19e-176j)
| (9.3407135138267793214e-42 - 1.9977521301291615944e-657j)  +/-  (3.66e-55, 4.4e-174j)
| (0.056946229860232888847 + 2.5130742477555074761e-636j)  +/-  (1.76e-20, 2.11e-139j)
| (5.7715700505173863963e-09 + 3.7672504303820209004e-640j)  +/-  (2.24e-34, 2.69e-153j)
| (1.4425369845637500279e-13 + 4.2262106931265197209e-643j)  +/-  (2.97e-42, 3.56e-161j)
| (0.056946229860232888847 + 1.9809109428848062326e-636j)  +/-  (9.84e-21, 1.18e-139j)
| (1.2798139256632624201e-45 + 2.0779506382741503939e-659j)  +/-  (1.31e-56, 1.57e-175j)
| (2.3293584927920562219e-25 - 1.9399519248425215341e-649j)  +/-  (2.78e-49, 3.33e-168j)
| (5.3929238093116934865e-10 - 1.1553302722642538813e-640j)  +/-  (2.36e-38, 2.83e-157j)
| (2.3897616669951665293e-38 + 1.1674308532757035841e-655j)  +/-  (2.25e-54, 2.7e-173j)
| (0.0002686412868620378782 + 5.0023203127711649894e-638j)  +/-  (7.55e-30, 9.06e-149j)
| (2.7787150063127329126e-35 - 4.9667628766341112032e-654j)  +/-  (3.61e-53, 4.33e-172j)
| (2.5469236183653494191e-06 - 3.4407027515013712496e-639j)  +/-  (6.84e-36, 8.21e-155j)
| (0.00093952110357792266789 - 1.8914113031197794116e-637j)  +/-  (1.07e-28, 1.28e-147j)
| (0.0074334673738808570752 - 4.045846070959569217e-637j)  +/-  (2.96e-23, 3.55e-142j)
| (1.4752992219145569414e-27 + 6.3192667462151722259e-649j)  +/-  (9.12e-53, 1.1e-171j)
| (0.01687723249194028091 + 7.2336661564627288807e-637j)  +/-  (7.74e-21, 9.29e-140j)
| (5.1902349701935824907e-08 - 1.1354263729367205599e-639j)  +/-  (7.99e-39, 9.59e-158j)
| (0.0074334673738808570752 - 6.2449813404899533907e-637j)  +/-  (2.5e-25, 3e-144j)
| (0.0002686412868620378782 + 9.5221267439497645e-638j)  +/-  (8.9e-32, 1.07e-150j)
| (2.5913687250442631027e-23 + 2.8285957126305834169e-648j)  +/-  (1.65e-51, 1.98e-170j)
| (4.206357691505427168e-11 + 3.2652615700543088202e-641j)  +/-  (1.06e-42, 1.28e-161j)
| (6.225609144374617422e-15 - 4.3701024580830977712e-643j)  +/-  (1.14e-46, 1.37e-165j)
| (6.6221531396994199552e-05 - 4.5006356611188332655e-638j)  +/-  (2.32e-35, 2.78e-154j)
| (2.1014023778206436642e-21 - 3.6041517703633670267e-646j)  +/-  (9.4e-52, 1.13e-170j)
| (0.0028397749047388989496 + 3.5368975233602523497e-637j)  +/-  (5.56e-31, 6.67e-150j)
| (4.206357691505427168e-11 + 8.6280662828949734673e-642j)  +/-  (7.62e-49, 9.14e-168j)
| (0.084603759293540555045 - 3.0362172778706959462e-636j)  +/-  (1.19e-28, 1.42e-147j)
| (1.4031611141378222706e-05 + 9.0072464819316717267e-639j)  +/-  (4.46e-41, 5.36e-160j)
| (2.7180651515333456377e-12 - 8.4778471429075558047e-642j)  +/-  (1.01e-44, 1.22e-163j)
| (2.3293584927920562219e-25 - 5.6196041625856027143e-648j)  +/-  (1.04e-53, 1.25e-172j)
| (1.276664874702488689e-19 + 2.6948154228089571306e-646j)  +/-  (2.7e-54, 3.24e-173j)
| (0.0028397749047388989496 + 2.1403701731542162426e-637j)  +/-  (6.19e-37, 7.42e-156j)
| (6.6221531396994199552e-05 - 2.1962374182506571125e-638j)  +/-  (2.98e-41, 3.58e-160j)
| (2.1014023778206436642e-21 - 3.0387062299166580479e-647j)  +/-  (1.06e-54, 1.27e-173j)
| (2.1598227003866561063e-16 + 8.6095406248381329703e-644j)  +/-  (3.05e-50, 3.66e-169j)
| (1.4031611141378222706e-05 + 1.9919532528837272867e-638j)  +/-  (4.66e-42, 5.59e-161j)
| (5.3929238093116934865e-10 - 3.3830558131122647392e-641j)  +/-  (7.03e-50, 8.43e-169j)
| (0.10916287719823802849 + 4.3628483874022380008e-636j)  +/-  (2.56e-36, 3.07e-155j)
| (6.225609144374617422e-15 - 8.0241455330656550744e-644j)  +/-  (3.65e-53, 4.38e-172j)
| (2.7787150063127329126e-35 + 1.4364608081797283222e-652j)  +/-  (1.31e-61, 1.58e-180j)
| (3.9447846214700179774e-07 + 1.220542988977112217e-639j)  +/-  (5.43e-48, 6.51e-167j)
| (5.9429423339821421544e-18 - 2.0490167986377433811e-645j)  +/-  (7.52e-55, 9.02e-174j)
| (0.12371042061538569957 - 6.0059391752914814417e-636j)  +/-  (2.11e-41, 2.54e-160j)
| (2.7180651515333456377e-12 - 2.0055085616702043902e-642j)  +/-  (3.23e-52, 3.87e-171j)
| (0.033268149212337308677 - 1.6600472347430140383e-636j)  +/-  (4.07e-43, 4.88e-162j)
| (0.10916287719823802849 + 4.8935402638118984852e-636j)  +/-  (8e-42, 9.6e-161j)
| (5.7715700505173863963e-09 + 1.2145140859631200613e-640j)  +/-  (8.12e-51, 9.74e-170j)
| (2.1598227003866561063e-16 + 1.3624011062481011494e-644j)  +/-  (2.14e-54, 2.57e-173j)
| (0.00093952110357792266789 - 1.0674256295606987913e-637j)  +/-  (1.36e-46, 1.64e-165j)
| (2.5913687250442631027e-23 + 4.7162764739678336187e-647j)  +/-  (4.85e-60, 5.82e-179j)
| (0.01687723249194028091 + 1.0444768577498192127e-636j)  +/-  (4.88e-47, 5.86e-166j)
| (0.12773334771300432062 + 6.3646495401389959567e-636j)  +/-  (1.3e-45, 1.55e-164j)
| (1.276664874702488689e-19 + 2.4847268066851978248e-645j)  +/-  (2.98e-58, 3.57e-177j)
| (0.033268149212337308677 - 1.2273657781719233963e-636j)  +/-  (2.14e-47, 2.56e-166j)
| (5.1902349701935824907e-08 - 4.0082554760045905701e-640j)  +/-  (1.87e-51, 2.24e-170j)
| (2.5469236183653494191e-06 - 8.2348770961098552239e-639j)  +/-  (2.98e-52, 3.57e-171j)
| (0.084603759293540555045 - 3.6184508702617633273e-636j)  +/-  (1.26e-48, 1.38e-167j)
| (3.9447846214700179774e-07 + 3.1719025245467340456e-639j)  +/-  (9.68e-53, 1.17e-171j)
| (0.12371042061538569957 - 5.6763716023914375776e-636j)  +/-  (2.74e-48, 2.88e-167j)
