Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 5 34
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Trying to find an order 34 Kronrod extension for:
P2 : 16*t^9 - 168*t^7 + 432*t^5 - 270*t^3 + 45*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^43 - 122695471448047212375445027146342412790803612788321936/20059506747419960058056579667371585555506498480433*t^41 + 21153288736822286920143107262431779549202694140894318676/20059506747419960058056579667371585555506498480433*t^39 - 2181079380165469439056721936055972495011117155412129854086/20059506747419960058056579667371585555506498480433*t^37 + 150401439024545424137986941881490107856187814350504649784348/20059506747419960058056579667371585555506498480433*t^35 - 14698447451988240151112010271496672452663613958671157767775465/40119013494839920116113159334743171111012996960866*t^33 + 8486928595370068021033693648493508430455596648323888692720495/647080862819998711550212247334567275984080596143*t^31 - 454040833980762622623080628151384721233442936714882080548388245/1294161725639997423100424494669134551968161192286*t^29 + 36702544264378477454387379962532957026844069397845411086870686305/5176646902559989692401697978676538207872644769144*t^27 - 140755463001991737402183745616052639160905629097219834943308115785/1294161725639997423100424494669134551968161192286*t^25 + 26216274323046414990175458407205279907171778676808906038416286958125/20706587610239958769606791914706152831490579076576*t^23 - 460942491476060615073093380512460500747642575825093942370998598639875/41413175220479917539213583829412305662981158153152*t^21 + 3031829784578989550438825137552049469305318591128375385773960255506375/41413175220479917539213583829412305662981158153152*t^19 - 58838771972872479536383427565042301250465151707645965176163423140751125/165652700881919670156854335317649222651924632612608*t^17 + 206408566984943518666886136474731799327700455437827334205111026604040875/165652700881919670156854335317649222651924632612608*t^15 - 1018949641977010177509218893200936070045780258465927257077101609283180625/331305401763839340313708670635298445303849265225216*t^13 + 13642969518169130880219279309759024292472915833167002849463155758984434375/2650443214110714722509669365082387562430794121801728*t^11 - 14717364834653151069140199657438269547776372547869242867117208383216108125/2650443214110714722509669365082387562430794121801728*t^9 + 38123286340579468912421916378365224863238683289983072327241009523025541875/10601772856442858890038677460329550249723176487206912*t^7 - 26716644994983363570748602427077799763813671295959198742986804091838373125/21203545712885717780077354920659100499446352974413824*t^5 + 1070725224047482042589955799865463950501852486614964451982510312951715625/5300886428221429445019338730164775124861588243603456*t^3 - 863817637993491677133618565073031744825507495853918668437442550713534375/84814182851542871120309419682636401997785411897655296*t
-------------------------------------------------
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: 1
Sufficient bits for target precision reached
Positive weights:   43 out of 43
Indefinite weights: 0 out of 43
Negative weights:   0 out of 43
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-6.759807247900089296 - 4.6003470505539505208e-425j)  +/-  (1.18e-118, 1.18e-118j)
| (-2.9890043371415964516 - 2.4411833205486515402e-426j)  +/-  (3.56e-119, 3.56e-119j)
| (-3.3501300031545809306 + 2.6681759143510274096e-426j)  +/-  (9.84e-119, 9.84e-119j)
| (8.0174625295495712035 - 1.8404227371496862374e-424j)  +/-  (2.45e-120, 2.45e-120j)
| (-0.73395630342256598469 + 2.442027094887495035e-432j)  +/-  (3.49e-124, 3.49e-124j)
| (5.7761836728603130393 - 4.5966821744391497404e-425j)  +/-  (6.47e-118, 6.47e-118j)
| (-4.1039451377709207211 - 5.3525948611901814392e-437j)  +/-  (4.17e-118, 4.17e-118j)
| (6.2488516763922684585 + 1.1377614749307248746e-434j)  +/-  (3.38e-118, 3.38e-118j)
| (-7.3305256602314312943 - 5.1722629950020931919e-441j)  +/-  (2.46e-119, 2.46e-119j)
| (2.6384291054842239697 - 3.0536714428544095324e-440j)  +/-  (1.07e-119, 1.07e-119j)
| (3.7216301147250190808 + 4.8291639022318711582e-438j)  +/-  (2.65e-118, 2.65e-118j)
| (6.759807247900089296 - 1.36559496173026081e-440j)  +/-  (1.17e-118, 1.17e-118j)
| (4.4981853250819714251 + 1.0247094579795864038e-444j)  +/-  (6.94e-118, 6.94e-118j)
| (-4.9062054001022849491 + 1.7588506500360386197e-451j)  +/-  (9.49e-118, 9.49e-118j)
| (4.1039451377709207211 - 3.3764061216229318521e-451j)  +/-  (4.35e-118, 4.35e-118j)
| (-2.6384291054842239697 + 9.2097084342947159501e-457j)  +/-  (1.15e-119, 1.15e-119j)
| (3.3501300031545809306 - 3.8292561482538406403e-454j)  +/-  (9.96e-119, 9.96e-119j)
| (-5.7761836728603130393 - 3.7042856043377640708e-456j)  +/-  (6.2e-118, 6.2e-118j)
| (-6.2488516763922684585 - 3.6962616834410422334e-457j)  +/-  (3.85e-118, 3.85e-118j)
| (-2.2989231109427180284 + 1.2596022380577601323e-460j)  +/-  (2.88e-120, 2.88e-120j)
| (2.9890043371415964516 + 5.5267047572196040328e-458j)  +/-  (3.68e-119, 3.68e-119j)
| (1.9704058235392024759 - 1.3911540293595384316e-461j)  +/-  (7.07e-121, 7.07e-121j)
| (-5.3308074334583320483 - 3.3759644158535432763e-457j)  +/-  (8.59e-118, 8.59e-118j)
| (-0.29745556841942901462 - 4.0019568280072659689e-466j)  +/-  (4.59e-126, 4.59e-126j)
| (1.6506801238857845559 + 5.5526147520645164716e-463j)  +/-  (1.07e-121, 1.07e-121j)
| (2.2989231109427180284 + 2.5646907278795333066e-460j)  +/-  (2.63e-120, 2.63e-120j)
| (-8.0174625295495712035 + 9.4495988108106969205e-462j)  +/-  (2.24e-120, 2.24e-120j)
| (-3.9463387837157852204e-469 + 1.2159350229111400947e-469j)  +/-  (1.78e-467, 1.78e-467j)
| (5.3308074334583320483 - 1.0938200124196497515e-457j)  +/-  (8.55e-118, 8.55e-118j)
| (-1.0245034852438086692 + 1.2114964422311703065e-476j)  +/-  (2.13e-123, 2.13e-123j)
| (-3.7216301147250190808 - 3.8074556403656874792e-472j)  +/-  (2.25e-118, 2.25e-118j)
| (4.9062054001022849491 + 1.1587094378134248884e-473j)  +/-  (8.94e-118, 8.94e-118j)
| (0.73395630342256598469 - 1.1056420809067908435e-485j)  +/-  (3.37e-124, 3.37e-124j)
| (1.0245034852438086692 + 2.0195682874037624736e-484j)  +/-  (2.5e-123, 2.5e-123j)
| (-0.52464762327529031788 + 9.0245772114906110568e-486j)  +/-  (6.84e-125, 6.84e-125j)
| (-1.6506801238857845559 + 5.3162450760345241754e-482j)  +/-  (1.13e-121, 1.13e-121j)
| (0.52464762327529031788 - 1.2604072634689211258e-485j)  +/-  (6.24e-125, 6.24e-125j)
| (1.3356979472959219452 + 9.036308598934062532e-484j)  +/-  (1.68e-122, 1.68e-122j)
| (-1.3356979472959219452 - 4.8082760123008480154e-483j)  +/-  (1.53e-122, 1.53e-122j)
| (-4.4981853250819714251 + 4.5630080351512738263e-482j)  +/-  (6.94e-118, 6.94e-118j)
| (-1.9704058235392024759 + 2.1415933961996990201e-488j)  +/-  (6.25e-121, 6.25e-121j)
| (7.3305256602314312943 - 6.7419345887958626615e-491j)  +/-  (2.4e-119, 2.4e-119j)
| (0.29745556841942901462 + 1.4381357425429044343e-498j)  +/-  (4.59e-126, 4.59e-126j)
-------------------------------------------------
The weights are:
| (4.318591274079584513e-21 - 1.2621312010933875649e-440j)  +/-  (2.43e-31, 1.6e-89j)
| (2.6468708687641042177e-05 - 3.7977935795144369484e-430j)  +/-  (8.45e-17, 5.55e-75j)
| (2.7606189420115163309e-06 - 2.8079849626741579058e-432j)  +/-  (8.05e-19, 5.29e-77j)
| (5.4188787241313338874e-29 + 2.2975976301538911523e-445j)  +/-  (2.18e-36, 1.43e-94j)
| (0.085821381406640468478 + 1.4014756083965844366e-427j)  +/-  (3.57e-18, 2.35e-76j)
| (8.3568853425773988253e-16 + 4.554463113691779079e-438j)  +/-  (6.25e-31, 4.1e-89j)
| (1.0610820764235525593e-08 - 5.8214379859811311009e-433j)  +/-  (1.35e-24, 8.87e-83j)
| (3.0388706017234895021e-18 - 1.7531295302523198262e-439j)  +/-  (2.62e-32, 1.72e-90j)
| (1.5912516672036339924e-24 + 1.5058241805967362754e-442j)  +/-  (2.88e-35, 1.89e-93j)
| (0.00018456221971718079784 + 7.5695256717804217135e-431j)  +/-  (2.79e-20, 1.83e-78j)
| (2.0525949802941106134e-07 - 5.3431563765923199818e-433j)  +/-  (1.84e-25, 1.21e-83j)
| (4.318591274079584513e-21 + 4.5968585896701570294e-441j)  +/-  (2.38e-34, 1.57e-92j)
| (3.6891708736702472478e-10 - 9.3615720611921610577e-435j)  +/-  (1.44e-28, 9.49e-87j)
| (8.2493134455166614401e-12 - 4.1906768247684750794e-435j)  +/-  (2.21e-31, 1.45e-89j)
| (1.0610820764235525593e-08 + 7.7065720494269595343e-434j)  +/-  (2.39e-27, 1.57e-85j)
| (0.00018456221971718079784 + 1.0139859973733861975e-429j)  +/-  (2.51e-23, 1.65e-81j)
| (2.7606189420115163309e-06 + 3.1838772673367909302e-432j)  +/-  (1.99e-25, 1.31e-83j)
| (8.3568853425773988253e-16 - 1.4465366629173792613e-437j)  +/-  (1.87e-34, 1.23e-92j)
| (3.0388706017234895021e-18 + 5.3666750682228071651e-439j)  +/-  (1.13e-35, 7.44e-94j)
| (0.00095441113540359080956 - 2.09419233809624565e-429j)  +/-  (6.27e-24, 4.12e-82j)
| (2.6468708687641042177e-05 - 1.6550016135801563273e-431j)  +/-  (3.83e-26, 2.51e-84j)
| (0.0037599745777965557711 + 1.0799310254436138755e-429j)  +/-  (8.21e-24, 5.39e-82j)
| (1.1155474801868701746e-13 + 2.7928019985623620051e-436j)  +/-  (9.15e-34, 6.01e-92j)
| (0.1433918443648865347 + 1.9035455899192765691e-427j)  +/-  (3.39e-22, 2.23e-80j)
| (0.011714207340238712143 - 3.3872604862481787656e-429j)  +/-  (4.11e-23, 2.7e-81j)
| (0.00095441113540359080956 - 3.0501778880036881251e-430j)  +/-  (5.64e-25, 3.71e-83j)
| (5.4188787241313338874e-29 - 5.252544073931838166e-445j)  +/-  (2.97e-42, 1.95e-100j)
| (0.17257519981350182192 - 1.4822232725754241187e-427j)  +/-  (1.03e-22, 6.74e-81j)
| (1.1155474801868701746e-13 - 7.4078166900483495869e-437j)  +/-  (1.53e-34, 1e-92j)
| (0.060600263992876204664 - 5.6534436799912504147e-428j)  +/-  (8.18e-24, 5.36e-82j)
| (2.0525949802941106134e-07 + 6.7018804992107310094e-432j)  +/-  (6.41e-31, 4.21e-89j)
| (8.2493134455166614401e-12 + 9.333527891833176231e-436j)  +/-  (2.2e-33, 1.45e-91j)
| (0.085821381406640468478 + 8.6513466293752220279e-428j)  +/-  (2.57e-24, 1.68e-82j)
| (0.060600263992876204664 - 2.8453138305576215247e-428j)  +/-  (8.42e-25, 5.5e-83j)
| (0.077540388955545309964 - 2.1339873135279673967e-427j)  +/-  (9.22e-24, 6.01e-82j)
| (0.011714207340238712143 - 1.1125323076766890894e-428j)  +/-  (2.8e-27, 1.82e-85j)
| (0.077540388955545309964 - 1.5166092656034685589e-427j)  +/-  (1e-24, 6.58e-83j)
| (0.029715920524917291214 + 9.8031873714232911595e-429j)  +/-  (3.46e-26, 2.28e-84j)
| (0.029715920524917291214 + 2.4657186703241101722e-428j)  +/-  (1.21e-26, 7.92e-85j)
| (3.6891708736702472478e-10 + 5.2234898815198280611e-434j)  +/-  (2.02e-33, 1.33e-91j)
| (0.0037599745777965557711 + 4.8772812862995849271e-429j)  +/-  (3.48e-28, 2.24e-86j)
| (1.5912516672036339924e-24 - 6.0221895391541543646e-443j)  +/-  (6.19e-42, 4.4e-100j)
| (0.1433918443648865347 + 1.5704875138360117495e-427j)  +/-  (4.75e-26, 3e-84j)
