Starting with polynomial:
P : t^5 - 10*t^3 + 15*t
Extension levels are: 5 60
-------------------------------------------------
Trying to find an order 60 Kronrod extension for:
P1 : t^5 - 10*t^3 + 15*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^65 - 540956032532368228424697928936684578649524899223079360/274964871045848058956059254065666169824960138389627*t^63 + 6983894833415406599898512354192362924268980461268374348435/3849508194641872825384829556919326377549441937454778*t^61 - 2008201685800646726024755953387782033889770755991495973220425/1924754097320936412692414778459663188774720968727389*t^59 + 85097094277150605756633799213601040470231807659950307615399725/202605694454835411862359450364175072502602207234462*t^57 - 1822529959603467853656731379724853392496772948807116239930604430/14471835318202529418739960740298219464471586231033*t^55 + 845741398043641797795961083682512292432262420987900635278247400475/28943670636405058837479921480596438928943172462066*t^53 - 77874029140105640864836754106527501753747665556734964975071426906575/14471835318202529418739960740298219464471586231033*t^51 + 23168120513827813516300943433791615722865423195363918490054141954129375/28943670636405058837479921480596438928943172462066*t^49 - 1409351224357057402241524830523172643836578244614785111910493992329727500/14471835318202529418739960740298219464471586231033*t^47 + 6580668998367972128146697657780441805729066900077058729427711448713016625/673108619451280438080928406525498579742864475862*t^45 - 11792355456179989254407530747869721845292527344198369644992410947670651338125/14471835318202529418739960740298219464471586231033*t^43 + 38107513131742953590085825957237766269272464468267595775492973771130839738125/673108619451280438080928406525498579742864475862*t^41 - 1106066079821714352546868085509515172325680335947048644818014667784340765793750/336554309725640219040464203262749289871432237931*t^39 + 107374694902202107225004924821102333325285311008393377531826924122189610645928125/673108619451280438080928406525498579742864475862*t^37 - 2177681343212744969340659359861483257442659483652051169864058436557483510663748125/336554309725640219040464203262749289871432237931*t^35 + 147349982747406991232557299848507337914547278161622354274673712817988396879090753125/673108619451280438080928406525498579742864475862*t^33 - 2072304364575575680601871388360069655185498743065086971217057593559901696724701475000/336554309725640219040464203262749289871432237931*t^31 + 96480234546382193524797164860196558914391561487107767222655241937935815003400038109375/673108619451280438080928406525498579742864475862*t^29 - 923759183759587325986172109917649701647197772025002281472195246428095069752712446453125/336554309725640219040464203262749289871432237931*t^27 + 28879595696569997440970318832828229330643321227342515436526212337342453089797520018621875/673108619451280438080928406525498579742864475862*t^25 - 182489688334594185923688297720799193606704857342928680124871604917369955905238022926093750/336554309725640219040464203262749289871432237931*t^23 + 3685064823556891863317955006102078504044017990013155905131816247618326147570965558591171875/673108619451280438080928406525498579742864475862*t^21 - 14644811008787761555859656947880501175951576807664531038778456660547161815235299790343359375/336554309725640219040464203262749289871432237931*t^19 + 179927400416269950615733274610954397617806149036948193059381631465711986084992255617471484375/673108619451280438080928406525498579742864475862*t^17 - 417373172812827905279953623266462298941576843022593494988676292469919037333815956232848062500/336554309725640219040464203262749289871432237931*t^15 + 2839400354072702188897134883750304613349855719160988271521185631176715864475021899002844296875/673108619451280438080928406525498579742864475862*t^13 - 3405703325742365899961810262912759079299233740012666178405844603830529464471957339123738203125/336554309725640219040464203262749289871432237931*t^11 + 10930839303456732692465603882102092170726411545825133857772552752603675920989855733986887109375/673108619451280438080928406525498579742864475862*t^9 - 5441177690350806213646115610298578356257971919227576046517209015207906830014529441553328906250/336554309725640219040464203262749289871432237931*t^7 + 5983745537651497564410911857786614639169945074441123947598954680507157560402081691897823359375/673108619451280438080928406525498579742864475862*t^5 - 741421410111578170922055996229373484526528435312860924311353328795396490924114492271327734375/336554309725640219040464203262749289871432237931*t^3 + 104541846218104535837360921701346146979176039125436929874548402077539464072660051372819140625/673108619451280438080928406525498579742864475862*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
Positive weights:   65 out of 65
Indefinite weights: 0 out of 65
Negative weights:   0 out of 65
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-13.880298228017123683 - 8.9629506727755721943e-617j)  +/-  (5.12e-243, 5.12e-243j)
| (13.140666248536168356 + 9.4250575758153196232e-613j)  +/-  (4.35e-242, 4.35e-242j)
| (14.773937541771491078 + 7.4057540578118206198e-620j)  +/-  (2.15e-244, 2.15e-244j)
| (-11.300008490763034088 - 6.446943502147404885e-617j)  +/-  (2.53e-240, 2.53e-240j)
| (5.2647846945562484022 + 3.8306445547783866788e-619j)  +/-  (3.25e-242, 3.25e-242j)
| (-12.480690200501525113 - 9.2587524444870118514e-621j)  +/-  (2.45e-241, 2.45e-241j)
| (-9.2416597773728305286 - 3.3170645555617693985e-618j)  +/-  (1.17e-239, 1.17e-239j)
| (-13.140666248536168356 + 1.72092799442906682e-622j)  +/-  (4.93e-242, 4.93e-242j)
| (-4.8533025983458407249 + 1.097937173705272681e-622j)  +/-  (8.24e-243, 8.24e-243j)
| (7.3995983549550464344 + 7.7061916487205155744e-618j)  +/-  (3.66e-240, 3.66e-240j)
| (-14.773937541771491078 + 1.1311729446665595201e-631j)  +/-  (2.11e-244, 2.11e-244j)
| (2.0902937841552013654 - 2.1694754671240915831e-646j)  +/-  (2.16e-248, 2.16e-248j)
| (12.480690200501525113 + 1.8274835881425182228e-636j)  +/-  (2.59e-241, 2.59e-241j)
| (-3.6434793412683620992 + 1.1869428576511620281e-659j)  +/-  (7.26e-245, 7.26e-245j)
| (-6.5281471483886493072 - 2.1193221352725099747e-653j)  +/-  (7.92e-241, 7.92e-241j)
| (3.6434793412683620992 + 2.1991920368238624657e-660j)  +/-  (7.24e-245, 7.24e-245j)
| (11.872005091096504769 - 5.1319053199814766532e-660j)  +/-  (8.79e-241, 8.79e-241j)
| (-8.3012096126595801628 - 8.0676684349888690531e-674j)  +/-  (9.44e-240, 9.44e-240j)
| (-1.7177403704018370073 + 1.6841811407582838976e-696j)  +/-  (2.83e-249, 2.83e-249j)
| (10.234057150015969996 + 2.0649555974019415292e-688j)  +/-  (8.42e-240, 8.42e-240j)
| (-6.9605293757806301979 - 2.7345060248292087743e-705j)  +/-  (1.83e-240, 1.83e-240j)
| (2.4706588013372696817 - 1.4397527624072350451e-710j)  +/-  (1.96e-247, 1.96e-247j)
| (-11.872005091096504769 - 6.7426335535346046901e-701j)  +/-  (8.9e-241, 8.9e-241j)
| (10.755947379786446227 - 7.1386975957528567679e-702j)  +/-  (5.23e-240, 5.23e-240j)
| (-3.2481104106821279258 + 5.9857442813169978599e-717j)  +/-  (1.15e-245, 1.15e-245j)
| (11.300008490763034088 - 1.2457787586654711548e-709j)  +/-  (2.58e-240, 2.58e-240j)
| (4.8533025983458407249 + 2.4206541468841164456e-717j)  +/-  (8.1e-243, 8.1e-243j)
| (6.9605293757806301979 - 9.4781274861595552371e-720j)  +/-  (1.9e-240, 1.9e-240j)
| (8.7658955725435891167 + 1.6126489841091629761e-726j)  +/-  (1.16e-239, 1.16e-239j)
| (-0.6678483657531292567 - 5.3924368672117854925e-748j)  +/-  (1.72e-252, 1.72e-252j)
| (7.846167900062278551 + 1.5835270185403553122e-734j)  +/-  (5.86e-240, 5.86e-240j)
| (6.5281471483886493072 - 7.8021666350998983996e-738j)  +/-  (8.4e-241, 8.4e-241j)
| (-10.755947379786446227 + 2.2697607500085486675e-739j)  +/-  (5.36e-240, 5.36e-240j)
| (-9.7302884649425283703 + 2.1445289006761762271e-740j)  +/-  (1.15e-239, 1.15e-239j)
| (-6.1017657483011959477 + 9.9750858255245206721e-745j)  +/-  (3.05e-241, 3.05e-241j)
| (-5.2647846945562484022 - 1.8597563442128314384e-745j)  +/-  (3.03e-242, 3.03e-242j)
| (-10.234057150015969996 + 1.1736435671844941641e-742j)  +/-  (7.92e-240, 7.92e-240j)
| (1.0061623901977874549 + 6.7117006836775304065e-761j)  +/-  (2.52e-251, 2.52e-251j)
| (5.6808065110657215492 + 7.5249245874797465785e-750j)  +/-  (1.16e-241, 1.16e-241j)
| (-1.3556261799742658658 + 9.5996427799069985678e-766j)  +/-  (2.53e-250, 2.53e-250j)
| (13.880298228017123683 - 9.6414952534931334612e-755j)  +/-  (5.06e-243, 5.06e-243j)
| (-8.7658955725435891167 + 1.5358411710970205468e-755j)  +/-  (1.22e-239, 1.22e-239j)
| (2.8569700138728056542 - 1.7780494783098991285e-773j)  +/-  (1.62e-246, 1.62e-246j)
| (1.7177403704018370073 - 2.0371067563986831816e-776j)  +/-  (2.84e-249, 2.84e-249j)
| (-5.6808065110657215492 + 2.6011108272623610189e-766j)  +/-  (1.08e-241, 1.08e-241j)
| (-2.4706588013372696817 + 1.5147428117204965519e-776j)  +/-  (2.17e-247, 2.17e-247j)
| (-2.8569700138728056542 - 1.0116287630209109351e-775j)  +/-  (1.59e-246, 1.59e-246j)
| (8.3012096126595801628 - 7.3481030403198338466e-768j)  +/-  (8.57e-240, 8.57e-240j)
| (0.33418233937765417189 - 2.0354065028747818824e-793j)  +/-  (1.37e-253, 1.37e-253j)
| (-7.3995983549550464344 + 7.0325160622323760678e-779j)  +/-  (3.65e-240, 3.65e-240j)
| (-0.33418233937765417189 - 1.7607738383512440344e-798j)  +/-  (1.02e-253, 1.02e-253j)
| (-7.846167900062278551 + 1.824633914702243294e-784j)  +/-  (6.48e-240, 6.48e-240j)
| (9.2416597773728305286 - 3.3605732841283749613e-805j)  +/-  (1.22e-239, 1.22e-239j)
| (1.3556261799742658658 - 1.0226098816866047289e-846j)  +/-  (2.49e-250, 2.49e-250j)
| (3.2481104106821279258 + 1.0896217203743311592e-837j)  +/-  (1.13e-245, 1.13e-245j)
| (6.1017657483011959477 + 1.4245670915683666137e-834j)  +/-  (3.22e-241, 3.22e-241j)
| (-1.0061623901977874549 - 1.6902100680691788352e-859j)  +/-  (2.36e-251, 2.36e-251j)
| (-4.0428088906096323898 + 1.1390628194250659786e-851j)  +/-  (3.94e-244, 3.94e-244j)
| (4.4460493575758234884 + 3.2173412258794722138e-848j)  +/-  (2.11e-243, 2.11e-243j)
| (0.6678483657531292567 - 8.3540332041950389483e-863j)  +/-  (1.74e-252, 1.74e-252j)
| (4.0428088906096323898 - 3.7651988812624520468e-851j)  +/-  (3.86e-244, 3.86e-244j)
| (-4.4460493575758234884 - 5.651240532661748547e-853j)  +/-  (1.98e-243, 1.98e-243j)
| (-2.0902937841552013654 + 1.7288099404904848297e-858j)  +/-  (2.31e-248, 2.31e-248j)
| (6.8141342994625040498e-880 + 1.8253068937528418564e-879j)  +/-  (1.27e-877, 1.27e-877j)
| (9.7302884649425283703 - 3.6111964105275958197e-849j)  +/-  (1.14e-239, 1.14e-239j)
-------------------------------------------------
The weights are:
| (4.6335928954583178051e-43 + 7.5816764660592752487e-646j)  +/-  (3.04e-59, 1.46e-178j)
| (8.8182792603266295947e-39 + 2.7729471209879007424e-643j)  +/-  (3.57e-58, 1.71e-177j)
| (1.653030201868352104e-48 + 2.4995961027465208249e-648j)  +/-  (1.99e-61, 9.53e-181j)
| (4.1600324754827625384e-29 + 1.2514353022043627672e-638j)  +/-  (1.18e-54, 5.64e-174j)
| (1.5801923162172825651e-07 - 1.8050695854598204687e-625j)  +/-  (8.37e-36, 4.01e-155j)
| (3.7717400075732407966e-35 + 9.123594844301172112e-642j)  +/-  (2.78e-57, 1.33e-176j)
| (5.4659137733721240543e-20 + 7.7187828479148992344e-634j)  +/-  (6.34e-51, 3.03e-170j)
| (8.8182792603266295947e-39 - 1.2136033732435993797e-643j)  +/-  (1.04e-58, 4.98e-178j)
| (1.2536371884284981704e-06 + 1.9371594994632534639e-626j)  +/-  (5.97e-37, 2.86e-156j)
| (2.2766676123526305897e-13 - 2.4368365128823495266e-629j)  +/-  (3.06e-48, 1.46e-167j)
| (1.653030201868352104e-48 - 1.2078903455614373638e-648j)  +/-  (6.74e-63, 3.23e-182j)
| (0.016915405628762023625 - 3.3691424216693229082e-623j)  +/-  (2.75e-19, 1.32e-138j)
| (3.7717400075732407966e-35 - 2.1881670976642585652e-641j)  +/-  (6.9e-61, 3.3e-180j)
| (0.00020772620605829973371 - 4.854278537057508798e-625j)  +/-  (1.23e-32, 5.87e-152j)
| (9.5399856854037978801e-11 + 7.893123771362932088e-629j)  +/-  (2.55e-45, 1.22e-164j)
| (0.00020772620605829973371 - 2.7024527430910121811e-624j)  +/-  (6.51e-34, 3.12e-153j)
| (5.8206360224199763278e-32 + 1.0341415876038880493e-639j)  +/-  (3.57e-60, 1.71e-179j)
| (1.9938960360419648706e-16 + 6.1739548001969241638e-632j)  +/-  (3.27e-51, 1.57e-170j)
| (0.033559354697555924464 + 2.9165382321003311588e-623j)  +/-  (1.23e-20, 5.91e-140j)
| (3.6921753742686330517e-24 - 1.451155932710117823e-635j)  +/-  (6.78e-58, 3.25e-177j)
| (5.2413045354221722672e-12 - 1.573422755337543675e-629j)  +/-  (7.83e-48, 3.75e-167j)
| (0.0072321013930817554206 + 1.8820179980127813897e-623j)  +/-  (1.27e-29, 6.1e-149j)
| (5.8206360224199763278e-32 - 4.1006025903483380607e-640j)  +/-  (1.14e-58, 5.47e-178j)
| (1.6036947442328976406e-26 + 7.8865043905862941386e-637j)  +/-  (5.13e-59, 2.46e-178j)
| (0.00080298438588784493178 + 1.2394110299174247074e-624j)  +/-  (2.07e-36, 9.91e-156j)
| (4.1600324754827625384e-29 - 3.3276755412031716297e-638j)  +/-  (5.7e-60, 2.73e-179j)
| (1.2536371884284981704e-06 + 4.8202264260470787e-625j)  +/-  (3.68e-45, 1.76e-164j)
| (5.2413045354221722672e-12 + 1.4031442779976420654e-628j)  +/-  (4.76e-52, 2.28e-171j)
| (3.8652393377887425567e-18 + 2.7475382912521296581e-632j)  +/-  (5.19e-57, 2.48e-176j)
| (0.10683870198238544383 - 1.3850916336662214373e-622j)  +/-  (9.24e-33, 4.43e-152j)
| (7.702545649889950912e-15 + 1.7144150684390792649e-630j)  +/-  (1.2e-54, 5.75e-174j)
| (9.5399856854037978801e-11 - 8.2414498490647369128e-628j)  +/-  (1.18e-51, 5.65e-171j)
| (1.6036947442328976406e-26 - 2.8030639592610980745e-637j)  +/-  (6.79e-63, 3.25e-182j)
| (5.4577288470855385906e-22 - 6.7463381818908926882e-635j)  +/-  (2.11e-61, 1.01e-180j)
| (1.3903376153531519541e-09 - 3.5669622072442572671e-628j)  +/-  (1.59e-54, 7.64e-174j)
| (1.5801923162172825651e-07 - 5.4215566528695653807e-627j)  +/-  (7.98e-53, 3.82e-172j)
| (3.6921753742686330517e-24 + 4.8543972411879557937e-636j)  +/-  (1.42e-62, 6.81e-182j)
| (0.082518527615233659237 + 1.3758238800007889034e-622j)  +/-  (4.62e-40, 2.21e-159j)
| (1.6399806418659690911e-08 - 4.0842211352273315837e-626j)  +/-  (7.92e-55, 3.79e-174j)
| (0.056661286127818332429 - 5.4807681818422876577e-623j)  +/-  (1.11e-39, 5.34e-159j)
| (4.6335928954583178051e-43 - 1.6509423751770793749e-645j)  +/-  (5.02e-73, 2.4e-192j)
| (3.8652393377887425567e-18 - 7.4585238763295628644e-633j)  +/-  (3.02e-60, 1.45e-179j)
| (0.0026199256565097379224 - 1.013767393152658948e-623j)  +/-  (1.39e-48, 6.63e-168j)
| (0.033559354697555924464 + 5.7742350628402166532e-623j)  +/-  (5.27e-44, 2.52e-163j)
| (1.6399806418659690911e-08 + 1.4601618046084283438e-627j)  +/-  (7.75e-55, 3.71e-174j)
| (0.0072321013930817554206 + 6.7402596037142581789e-624j)  +/-  (1.58e-48, 7.58e-168j)
| (0.0026199256565097379224 - 2.9752969232537579218e-624j)  +/-  (1.32e-49, 6.34e-169j)
| (1.9938960360419648706e-16 - 2.4254730015627197019e-631j)  +/-  (3.93e-62, 1.88e-181j)
| (0.12585261940985229888 + 2.0277950409438707852e-622j)  +/-  (5.05e-44, 2.42e-163j)
| (2.2766676123526305897e-13 + 2.8058783628777270025e-630j)  +/-  (5.01e-59, 2.4e-178j)
| (0.12585261940985229888 + 1.7838201643629959995e-622j)  +/-  (1.79e-45, 8.59e-165j)
| (7.702545649889950912e-15 - 4.4398413923120553652e-631j)  +/-  (7.75e-60, 3.71e-179j)
| (5.4659137733721240543e-20 - 2.6458759495729078313e-633j)  +/-  (2.35e-65, 1.12e-184j)
| (0.056661286127818332429 - 9.3233726603411696168e-623j)  +/-  (8.4e-50, 3.96e-169j)
| (0.00080298438588784493178 + 5.2933373526738631921e-624j)  +/-  (1.12e-54, 5.28e-174j)
| (1.3903376153531519541e-09 + 5.2323296771578928406e-627j)  +/-  (1.4e-59, 6.61e-179j)
| (0.082518527615233659237 + 9.3128332674769326182e-623j)  +/-  (5.64e-51, 2.63e-170j)
| (4.5210163232542788093e-05 + 1.7809599025680632363e-625j)  +/-  (6.02e-57, 2.8e-176j)
| (8.2446798770875195697e-06 - 7.3259234716803299645e-625j)  +/-  (9.71e-58, 4.59e-177j)
| (0.10683870198238544383 - 1.7913936666104028383e-622j)  +/-  (1.47e-52, 6.98e-172j)
| (4.5210163232542788093e-05 + 1.3753139625363842758e-624j)  +/-  (3.25e-57, 1.52e-176j)
| (8.2446798770875195697e-06 - 6.1185145373407260854e-626j)  +/-  (4.05e-58, 1.77e-177j)
| (0.016915405628762023625 - 1.4438860951927802475e-623j)  +/-  (1.76e-55, 7.14e-175j)
| (0.13347296501260846195 - 2.0179203773011054554e-622j)  +/-  (2.28e-54, 7.33e-174j)
| (5.4577288470855385906e-22 + 2.1525337983016048245e-634j)  +/-  (1.64e-67, 9.14e-187j)
