Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 45
-------------------------------------------------
Trying to find an order 45 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^49 - 192242686175104680264709912002749643/177036531294596661352651300338773*t^47 + 3920982342577665816618725850213749451714/7258497783078463115458703313889693*t^45 - 1186702874162973090656914567924403496259695/7258497783078463115458703313889693*t^43 + 34965454477640133000074576736527867030969970/1036928254725494730779814759127099*t^41 - 127247659754142243730128142495189565478602655/25290933042085237336093042905539*t^39 + 14232411242774429989702588509821069370586119030/25290933042085237336093042905539*t^37 - 1220198608672994909977428334590228588078095557515/25290933042085237336093042905539*t^35 + 81324391553517566590936800966531494909763308536725/25290933042085237336093042905539*t^33 - 4249136329214965214325472664290569624681192908706450/25290933042085237336093042905539*t^31 + 174767894158207184678046979505125137679628691841998300/25290933042085237336093042905539*t^29 - 5661932228281337298918192411156070964994159272959105050/25290933042085237336093042905539*t^27 + 144111860120839583188629501234677313799067335938753999900/25290933042085237336093042905539*t^25 - 2865665932269094068017066897179861738999385407814174808750/25290933042085237336093042905539*t^23 + 44127304372998175719611360772170250957520393261334407717500/25290933042085237336093042905539*t^21 - 519697893625352087523106388526405335496031515349042489863750/25290933042085237336093042905539*t^19 + 4603751540668158721607946838813222071680194616838732863998125/25290933042085237336093042905539*t^17 - 30007910595611815205288734318782151561744497850917476123750625/25290933042085237336093042905539*t^15 + 139812544175308898719589604422381223373947184313968173025443750/25290933042085237336093042905539*t^13 - 448052262212855383779882714893668301507279472013641326525653125/25290933042085237336093042905539*t^11 + 937379897779636255634643891060860850619149845687381610045581250/25290933042085237336093042905539*t^9 - 1189917545610040054649328395141714403404856090350855364239971875/25290933042085237336093042905539*t^7 + 822043198741113219480660792446736245311746276691689335828868750/25290933042085237336093042905539*t^5 - 3261050198515998960740257038511926601880901339443975128640625/320138392937787814380924593741*t^3 + 24309741925743407605982199737485515009888509581513105291546875/25290933042085237336093042905539*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
  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:   49 out of 49
Indefinite weights: 0 out of 49
Negative weights:   0 out of 49
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (10.126424109573828185 - 1.4293947439710252776e-542j)  +/-  (2.6e-244, 2.6e-244j)
| (11.608814072770111605 + 3.8822181366132757813e-551j)  +/-  (1.3e-245, 1.3e-245j)
| (12.551658736872013674 - 3.2250785719590936174e-563j)  +/-  (9.83e-247, 9.83e-247j)
| (-7.1890365460803540374 + 7.0999934798212761977e-580j)  +/-  (1.09e-243, 1.09e-243j)
| (10.826353897773325801 + 5.5076670776923156697e-595j)  +/-  (7.51e-245, 7.51e-245j)
| (-12.551658736872013674 - 9.2240117084146705593e-593j)  +/-  (1.07e-246, 1.07e-246j)
| (5.6473147907100613111 - 3.8771987856632129251e-597j)  +/-  (1.76e-244, 1.76e-244j)
| (-9.4793323176909771779 - 3.8143978882590503694e-600j)  +/-  (6.74e-244, 6.74e-244j)
| (-1.4565351129602412324 + 4.5569708279483419454e-617j)  +/-  (1.09e-250, 1.09e-250j)
| (2.7894730757095061075 + 3.7465254835373558082e-614j)  +/-  (4.48e-248, 4.48e-248j)
| (6.1499391010217420602 + 1.5005435079364942084e-609j)  +/-  (4.15e-244, 4.15e-244j)
| (-7.729792726209170461 + 3.7010971429582255383e-614j)  +/-  (1.37e-243, 1.37e-243j)
| (-11.608814072770111605 - 5.1269382334646339852e-623j)  +/-  (1.24e-245, 1.24e-245j)
| (-10.126424109573828185 - 8.1054009347140872396e-622j)  +/-  (2.74e-244, 2.74e-244j)
| (-8.869789748503537914 - 2.7319808637339161481e-624j)  +/-  (1.07e-243, 1.07e-243j)
| (8.2886255632396028485 + 4.4473198584669546005e-632j)  +/-  (1.32e-243, 1.32e-243j)
| (7.729792726209170461 - 4.7850105837474792663e-632j)  +/-  (1.35e-243, 1.35e-243j)
| (-4.6682925382236538474 + 7.1335055240094908482e-632j)  +/-  (2.15e-245, 2.15e-245j)
| (-2.7894730757095061075 + 1.4872576003955275341e-641j)  +/-  (4.54e-248, 4.54e-248j)
| (-0.74196378430272585765 + 2.4993634411923489559e-646j)  +/-  (2.02e-252, 2.02e-252j)
| (3.250615334245814074 - 9.654327740468270573e-641j)  +/-  (2.75e-247, 2.75e-247j)
| (1.8876318144362226133 + 1.0267790196483386395e-643j)  +/-  (9.01e-250, 9.01e-250j)
| (8.869789748503537914 + 2.3146474035522362058e-637j)  +/-  (1.05e-243, 1.05e-243j)
| (-3.250615334245814074 - 6.5004455406119010386e-640j)  +/-  (2.71e-247, 2.71e-247j)
| (-2.3344142183389772393 + 9.9856238797333175154e-642j)  +/-  (6.16e-249, 6.16e-249j)
| (2.3344142183389772393 + 2.0548305408793976916e-642j)  +/-  (6.73e-249, 6.73e-249j)
| (3.3575280190579838341e-661 + 6.1939488434153223339e-661j)  +/-  (3.45e-659, 3.45e-659j)
| (-4.1897007102747378643 - 3.8832343813842854273e-637j)  +/-  (6.51e-246, 6.51e-246j)
| (0.39707429248417521974 + 5.4212634035140669439e-649j)  +/-  (1.24e-253, 1.24e-253j)
| (5.1538382985192034747 + 1.3701897000960093495e-639j)  +/-  (7.12e-245, 7.12e-245j)
| (7.1890365460803540374 + 4.4725162836392707868e-639j)  +/-  (1.13e-243, 1.13e-243j)
| (-10.826353897773325801 + 9.8500387115362609558e-639j)  +/-  (8.72e-245, 8.72e-245j)
| (9.4793323176909771779 + 4.5034734665891154449e-645j)  +/-  (5.99e-244, 5.99e-244j)
| (-0.39707429248417521974 - 2.8719937127579164089e-665j)  +/-  (1.24e-253, 1.24e-253j)
| (-5.6473147907100613111 - 6.3498032262022959186e-665j)  +/-  (2.06e-244, 2.06e-244j)
| (-6.6632184128275994975 - 2.1205459261372877725e-702j)  +/-  (7.93e-244, 7.93e-244j)
| (4.6682925382236538474 - 4.2249280838431800408e-726j)  +/-  (2.27e-245, 2.27e-245j)
| (1.0658902021432014906 - 2.3957775928975830176e-741j)  +/-  (1.41e-251, 1.41e-251j)
| (-1.0658902021432014906 + 1.5626785323750377244e-739j)  +/-  (1.56e-251, 1.56e-251j)
| (-6.1499391010217420602 + 3.1353124179277062264e-734j)  +/-  (4.04e-244, 4.04e-244j)
| (-8.2886255632396028485 - 3.1869766852035792095e-759j)  +/-  (1.4e-243, 1.4e-243j)
| (-5.1538382985192034747 + 1.0092247731521743881e-778j)  +/-  (7.59e-245, 7.59e-245j)
| (1.4565351129602412324 - 1.0649472585109509431e-791j)  +/-  (1.1e-250, 1.1e-250j)
| (6.6632184128275994975 - 1.4276443484984961679e-783j)  +/-  (8.04e-244, 8.04e-244j)
| (3.7173094956842427541 - 1.9733217916384954903e-790j)  +/-  (1.38e-246, 1.38e-246j)
| (4.1897007102747378643 + 1.419327763116485449e-789j)  +/-  (5.9e-246, 5.9e-246j)
| (-1.8876318144362226133 + 1.3529839578561415369e-792j)  +/-  (8.79e-250, 8.79e-250j)
| (-3.7173094956842427541 - 5.386656237394635633e-787j)  +/-  (1.52e-246, 1.52e-246j)
| (0.74196378430272585765 + 3.2066114492867836026e-799j)  +/-  (2.02e-252, 2.02e-252j)
-------------------------------------------------
The weights are:
| (1.4449880318050814315e-23 + 1.0867770567261927801e-564j)  +/-  (3.01e-75, 1.47e-196j)
| (1.8290919884439727426e-30 - 3.7676561581256596101e-569j)  +/-  (1.98e-78, 9.65e-200j)
| (2.674475228359958319e-35 + 7.5287435890152515264e-572j)  +/-  (1.87e-80, 9.12e-202j)
| (1.2730504144515024616e-12 - 7.0585976742563885374e-561j)  +/-  (3.39e-72, 1.65e-193j)
| (1.0349787829284476959e-26 + 6.9052461711861996967e-567j)  +/-  (4.28e-77, 2.09e-198j)
| (2.674475228359958319e-35 - 8.0513726736951732168e-573j)  +/-  (7e-84, 3.41e-205j)
| (2.3588036089823954853e-08 + 6.0551935103263015018e-558j)  +/-  (9.91e-68, 4.83e-189j)
| (7.6809979059024349017e-21 - 2.7737303185320720168e-565j)  +/-  (1.93e-78, 9.42e-200j)
| (0.057659473371696423402 - 6.6204894049650686657e-554j)  +/-  (5.89e-46, 2.87e-167j)
| (0.0037357596275115011919 + 6.3208286652912731869e-555j)  +/-  (4.38e-57, 2.13e-178j)
| (1.2405238448355309884e-09 - 1.3157139914271831614e-558j)  +/-  (1.5e-69, 7.32e-191j)
| (2.3235642036955718315e-14 + 7.9883873506557371047e-562j)  +/-  (7.41e-75, 3.62e-196j)
| (1.8290919884439727426e-30 + 2.5696224843063928534e-570j)  +/-  (5.21e-83, 2.54e-204j)
| (1.4449880318050814315e-23 + 1.0198359635204426825e-566j)  +/-  (3.12e-80, 1.52e-201j)
| (1.9549764073749221806e-18 + 5.2205207856521366347e-564j)  +/-  (8.19e-78, 3.99e-199j)
| (2.7406347688648023884e-16 - 7.3231566402032637822e-562j)  +/-  (2.81e-78, 1.37e-199j)
| (2.3235642036955718315e-14 + 5.9517862317789182393e-561j)  +/-  (2.34e-77, 1.14e-198j)
| (3.5613040904494425307e-06 + 3.320138779559919841e-557j)  +/-  (3.84e-72, 1.87e-193j)
| (0.0037357596275115011919 + 3.5905837392020765181e-555j)  +/-  (1.86e-65, 9.09e-187j)
| (0.095015362750756517083 - 2.5273658952503652566e-553j)  +/-  (3.37e-57, 1.65e-178j)
| (0.00093946368096637148523 - 2.4506926379327532247e-555j)  +/-  (3.47e-67, 1.69e-188j)
| (0.029621532966743131568 + 3.7059772469214895382e-554j)  +/-  (4.15e-61, 2.03e-182j)
| (1.9549764073749221806e-18 + 7.8917251005599434957e-563j)  +/-  (9.33e-80, 4.55e-201j)
| (0.00093946368096637148523 - 1.2596579397329398278e-555j)  +/-  (2.33e-68, 1.14e-189j)
| (0.011809937169940381734 - 9.6938927932638111037e-555j)  +/-  (1.1e-64, 5.38e-186j)
| (0.011809937169940381734 - 1.5502294343962212229e-554j)  +/-  (1.08e-64, 5.27e-186j)
| (0.16180064120540309745 - 2.7652955166804568572e-553j)  +/-  (1.55e-60, 7.55e-182j)
| (2.9257784483368892124e-05 - 1.2276364356652661969e-556j)  +/-  (8.39e-72, 4.09e-193j)
| (0.13978598210621204096 + 3.0083988808868474541e-553j)  +/-  (5.19e-61, 2.53e-182j)
| (3.3314684070619536168e-07 - 2.4687850609984333885e-557j)  +/-  (5.55e-74, 2.71e-195j)
| (1.2730504144515024616e-12 - 4.16093782896517709e-560j)  +/-  (1.24e-77, 6.05e-199j)
| (1.0349787829284476959e-26 - 2.3067048619317884101e-568j)  +/-  (8e-86, 3.9e-207j)
| (7.6809979059024349017e-21 - 8.4039206959911191843e-564j)  +/-  (9.85e-82, 4.81e-203j)
| (0.13978598210621204096 + 2.7813721239093614719e-553j)  +/-  (3.04e-64, 1.48e-185j)
| (2.3588036089823954853e-08 + 1.7194321429481884522e-558j)  +/-  (1.4e-77, 6.83e-199j)
| (4.7340771495054329053e-11 + 5.1756393953623082431e-560j)  +/-  (1.82e-79, 8.89e-201j)
| (3.5613040904494425307e-06 + 8.9995105161618343712e-557j)  +/-  (1.67e-76, 8.17e-198j)
| (0.080311963460921780325 + 1.9518268996556923352e-553j)  +/-  (2.02e-68, 9.88e-190j)
| (0.080311963460921780325 + 1.5800658660248118151e-553j)  +/-  (3.63e-68, 1.77e-189j)
| (1.2405238448355309884e-09 - 3.2144262786205844597e-559j)  +/-  (8.4e-79, 4.1e-200j)
| (2.7406347688648023884e-16 - 7.3084172277884766163e-563j)  +/-  (1.84e-82, 8.99e-204j)
| (3.3314684070619536168e-07 - 8.0340541523424666188e-558j)  +/-  (1.8e-77, 8.78e-199j)
| (0.057659473371696423402 - 8.8449643174076521941e-554j)  +/-  (3.1e-72, 1.51e-193j)
| (4.7340771495054329053e-11 + 2.5091531627664300471e-559j)  +/-  (1.29e-80, 6.27e-202j)
| (0.00018702714993851075371 + 8.8737695445981731819e-556j)  +/-  (3.24e-77, 1.58e-198j)
| (2.9257784483368892124e-05 - 2.9603866079486331498e-556j)  +/-  (7.34e-78, 3.59e-199j)
| (0.029621532966743131568 + 2.5414212303499216207e-554j)  +/-  (1.36e-75, 6.64e-197j)
| (0.00018702714993851075371 + 4.1082129785395912865e-556j)  +/-  (1.04e-77, 4.88e-199j)
| (0.095015362750756517083 - 2.9270082612387838498e-553j)  +/-  (1.24e-74, 6.82e-196j)
