Starting with polynomial:
P : 3/2*t^2 - 1/2
Extension levels are: 2 6 8 14
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : 3/2*t^2 - 1/2
Solvable: 1
-------------------------------------------------
Trying to find an order 8 Kronrod extension for:
P2 : 3/2*t^8 - 161/52*t^6 + 105/52*t^4 - 245/572*t^2 + 25/1716
Solvable: 1
-------------------------------------------------
Trying to find an order 14 Kronrod extension for:
P3 : 3/2*t^16 - 52675/9724*t^14 + 62424565/7972932*t^12 - 25786918405/4472814852*t^10 + 2493674299078805/1096541870671764*t^8 - 66130895817287/143027200522404*t^6 + 613871878555495/14255044318732932*t^4 - 244523487906245/156805487506062252*t^2 + 24672636591575/1411249387554560268
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 3/2*t^30 - 811032515836313108831874283311849972300045086125271882715402738549530952555354985356034209644539283875362192511/78225999154237587345921416116386677399838830466368848925702381485407983260059413884080673359780164779547539548*t^28 + 1095280343285274634868434914015376636175251798192118149788987335340537507350108224289709804974334207772941626337243541/34186247924385756184327231349767189370600165851582047988661529054371511436327904996207051791017767831793086185727412*t^26 - 560159882158493931085368032305402621536533228536388004444212021866115387505092310267244924822367305214057258509960795625/9589242542790204609703788393609696618453346521368764460819558899751208957889977351436078027380483876817960675096539066*t^24 + 5090091508133969127001971878047485286831021815653929594651172102298341540616762828071225933691251782528694138790592003523317225/72876967955947363936535701187577344210595179267315267856555358636775521169172428503926452009714035859460884341963909061904222*t^22 - 2288684500234547006106951861308426010261516202827619792313421272555476887989123654173267380418515220225217743787812304684563075/39751073430516743965383109738678551387597370509444691558121104710968466092275870093050792005298565014251391459253041306493212*t^20 + 85558999509788442767639431515996384923105259768990889268402866100327745864583018451379941727815595755513782898136686116992123925/2554529508350576020091198788996132170750336283791156231182414150110131426245728283348158791498397256968470998513050707117274308*t^18 - 906281004113461723572317666132889498148302734432117738265879195558387131561920322822742455469085872991529514556271454516518723875/65474427888867868384232915366328969330702246646320386670469523461809675738709957275488919613470358452299732161234825803662687574*t^16 + 264454770394716336639617157382103647808571420235878204722412516033011783348814486999427979566596099997334358893228099958940397875/65474427888867868384232915366328969330702246646320386670469523461809675738709957275488919613470358452299732161234825803662687574*t^14 - 11697918985342588686029415496926589631377928503506043384154041097216211685978873048868791967495271350201420787351547313609655125/14314247392707955031370758825027386007521948659519436761964997032136528299151164748487456109827527758802370593954172442906012668*t^12 + 915645956338294472576493172999283400955426912425147424883041128376011308194629268884094884896272508357747416325477627384104991/8241536377619731684728618717440010125542940137299069650828331624563455687390064552159444426870394770219546705609978073188310324*t^10 - 101802133032660987202692118436331352985640272207161547570302444778351383510347123640801590156757253609799351005467183269621733/10530852038069657152708790583395568493749312397659922331613979298053304489442860261092623434334393317502754123834971982407285414*t^8 + 686006538213074035014469343736371097568101649395544056962144005974031260339469894353457272376242653820833969957821753786387/1373589396269955280788103119573335020923823356216511608471388604093909281231677425359907404478399128369924450934996345531385054*t^6 - 1480186639197233297911305518100503128085810872599478664019759672996031674129328905196206024467089183907892938421803919088775/109137921121812810491709284227917709844311055757566467800363058179825155617862369978596279228556439835937633647016982363130048836*t^4 + 126138972210145923846385835208292897217252988823667341241777812138533913802587414016250293981367502294532374050159795732817355/795942858741380826916035809874203857894560529639932249668047783305464859921070264253902664413862115723493162187694852374307446160948*t^2 - 586370730140249328090727542962220909289733297406352874295724661938432327994619008928997210474089691576649149246584889429925/1193914288112071240374053714811305786841840794459898374502071674958197289881605396380853996620793173585239743281542278561461169241422
-------------------------------------------------
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: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (-0.99660830656555115136 - 6.126027342309227816e-432j)  +/-  (6.99e-119, 6.99e-119j)
| (-0.98219129046748981137 - 1.9008208493568579127e-435j)  +/-  (1.49e-118, 1.49e-118j)
| (-0.95472657837086943368 + 1.2848844875582783011e-437j)  +/-  (1.55e-118, 1.55e-118j)
| (0.99660830656555115136 + 2.1942840029013273286e-436j)  +/-  (6.39e-119, 6.39e-119j)
| (0.77566244475183899387 + 4.5405358916978382686e-440j)  +/-  (7.02e-119, 7.02e-119j)
| (0.85110112875893547946 - 5.8031932583518532794e-439j)  +/-  (5.87e-119, 5.87e-119j)
| (0.95472657837086943368 - 3.3800769612763894885e-438j)  +/-  (1.72e-118, 1.72e-118j)
| (-0.91135468502932062759 + 1.7720190309959018755e-439j)  +/-  (9.64e-119, 9.64e-119j)
| (-0.75725454904569163266 + 5.1947723404639026904e-439j)  +/-  (5.08e-119, 5.08e-119j)
| (0.98219129046748981137 - 1.8019374514504165333e-439j)  +/-  (1.55e-118, 1.55e-118j)
| (0.91135468502932062759 - 1.7932113878094797924e-441j)  +/-  (1.02e-118, 1.02e-118j)
| (0.75725454904569163266 + 1.3992810150379138697e-442j)  +/-  (4.99e-119, 4.99e-119j)
| (-0.77566244475183899387 + 1.2275087189618891999e-440j)  +/-  (6.87e-119, 6.87e-119j)
| (-0.85110112875893547946 + 1.2445406776139523906e-447j)  +/-  (5.97e-119, 5.97e-119j)
| (-0.14329844755128664784 + 3.1644387811347775701e-452j)  +/-  (6.83e-126, 6.83e-126j)
| (0.46136629195112002483 + 2.5085729270888812915e-456j)  +/-  (1.66e-122, 1.66e-122j)
| (0.35028676481269814376 - 3.3379991065376752707e-461j)  +/-  (6.3e-123, 6.3e-123j)
| (-0.068376101477183388292 + 4.4267602292348777824e-466j)  +/-  (5.49e-127, 5.49e-127j)
| (-0.68207094457313309068 - 5.4317237361801696392e-468j)  +/-  (3.18e-120, 3.18e-120j)
| (-0.33376257911793724078 + 2.6384323002101294369e-469j)  +/-  (4.41e-123, 4.41e-123j)
| (0.33376257911793724078 + 2.9006256766642812211e-471j)  +/-  (4.71e-123, 4.71e-123j)
| (0.57735026918962576451 - 2.0517019845737847854e-476j)  +/-  (1.78e-121, 1.78e-121j)
| (0.068376101477183388292 - 4.0579013302494695983e-481j)  +/-  (5.49e-127, 5.49e-127j)
| (-0.46136629195112002483 - 1.1433858515786940361e-487j)  +/-  (1.79e-122, 1.79e-122j)
| (-0.35028676481269814376 + 8.5649567443409510607e-487j)  +/-  (6.2e-123, 6.2e-123j)
| (0.14329844755128664784 + 4.3531289712540270149e-489j)  +/-  (6.65e-126, 6.65e-126j)
| (0.68207094457313309068 + 3.1718951634077101851e-494j)  +/-  (3.05e-120, 3.05e-120j)
| (0.2041968861768067152 + 1.5344043760552420396e-497j)  +/-  (3.88e-125, 3.88e-125j)
| (-0.2041968861768067152 + 3.111195174869551985e-503j)  +/-  (3.88e-125, 3.88e-125j)
| (-0.57735026918962576451 + 7.6621768744649129941e-503j)  +/-  (1.59e-121, 1.59e-121j)
-------------------------------------------------
The weights are:
| (0.0086609451941910271761 - 7.6582759843776515932e-432j)  +/-  (5.36e-24, 3.69e-81j)
| (0.020435976559864096342 + 1.2067793193218562506e-431j)  +/-  (3.72e-24, 2.56e-81j)
| (0.035050942180022838184 - 7.6728728619401407018e-432j)  +/-  (1.45e-24, 9.98e-82j)
| (0.0086609451941910271761 + 2.6338169790001272037e-434j)  +/-  (5.42e-26, 3.73e-83j)
| (0.077420156876623263484 - 5.4286454416420043037e-432j)  +/-  (4.97e-26, 3.42e-83j)
| (0.068506039236021882163 + 6.8402291724738911487e-433j)  +/-  (4.49e-26, 3.08e-83j)
| (0.035050942180022838184 + 1.6442850018619966794e-433j)  +/-  (1.11e-26, 7.65e-84j)
| (0.051837611056651381198 + 6.5443285928437944731e-432j)  +/-  (1.47e-26, 1.01e-83j)
| (0.00810516467983145825 - 4.7055850121225755431e-431j)  +/-  (1.05e-27, 7.22e-85j)
| (0.020435976559864096342 - 8.7474429046909414244e-434j)  +/-  (5.78e-27, 3.97e-84j)
| (0.051837611056651381198 - 2.9220406659330324748e-433j)  +/-  (4.34e-27, 2.98e-84j)
| (0.00810516467983145825 + 6.4202724271132955798e-432j)  +/-  (2.61e-27, 1.79e-84j)
| (0.077420156876623263484 + 4.3556266359555465443e-431j)  +/-  (2.14e-28, 1.47e-85j)
| (0.068506039236021882163 - 8.6896667004015542147e-432j)  +/-  (1.51e-28, 1.04e-85j)
| (0.0007458197908344766565 + 1.1076970905417819451e-430j)  +/-  (2.62e-31, 1.8e-88j)
| (0.12071895925812080547 - 7.2685583919566106719e-432j)  +/-  (4.71e-31, 3.24e-88j)
| (0.017961576689629488283 + 9.3939377773103254964e-431j)  +/-  (1.86e-31, 1.28e-88j)
| (0.1364220785548255801 - 6.5867922426932129522e-431j)  +/-  (3.13e-32, 2.15e-89j)
| (0.09818351868141187677 + 1.370256494453572331e-431j)  +/-  (1.25e-31, 8.6e-89j)
| (0.11165419967349861063 + 2.0900991874773841926e-430j)  +/-  (8.88e-33, 6.1e-90j)
| (0.11165419967349861063 - 1.0413207841444717062e-430j)  +/-  (6.49e-32, 4.46e-89j)
| (0.1107769025265025201 + 2.7708038640902765904e-432j)  +/-  (7.92e-33, 5.45e-90j)
| (0.1364220785548255801 + 5.7409439913588264287e-431j)  +/-  (2.56e-33, 1.76e-90j)
| (0.12071895925812080547 + 1.9800790684738955332e-431j)  +/-  (3.08e-34, 2.12e-91j)
| (0.017961576689629488283 - 1.9577457700832295644e-430j)  +/-  (2.52e-33, 1.73e-90j)
| (0.0007458197908344766565 - 8.2918197177865420649e-431j)  +/-  (4.82e-34, 3.31e-91j)
| (0.09818351868141187677 - 2.5670314440865175859e-432j)  +/-  (6.54e-35, 4.5e-92j)
| (0.13352010904197069519 + 6.0240535055717388354e-431j)  +/-  (3.12e-34, 2.14e-91j)
| (0.13352010904197069519 - 9.1289994113637435808e-431j)  +/-  (9.86e-35, 6.85e-92j)
| (0.1107769025265025201 - 1.0403241615169624464e-431j)  +/-  (4.62e-36, 3.09e-93j)
