(* This Mathematica file is a supplement to the paper Hurwitz Number Fields. It has information associated to each of the main examples. To navigate the file, search for the section number, the possibilities being two, five, six, seven, eight, nine, and ten. One can also search for equal signs, most of which have a nearby comment. *) (* Section two. The introductory degree 25 family. *) (* Specialization Polynomial *) tau4[{u_,v_}] := t^4-2 t^2 v-8 t v^2-4 u v^2+v^2 (* Main polynomial with 129 terms. *) f25[{u_,v_}] := ( 6599240005016326904296875000*u^5*v^10*x^5 - 24747150018811225891113281250*u^4*v^12*x^3 + 41859712600708007812500000000*u^4*v^10*x^6 - 3378810882568359375000000000*u^4*v^10*x^5 + 1604700529575347900390625000*u^4*v^9*x^7 - 5353888874530792236328125000*u^4*v^8*x^9 + 24747150018811225891113281250*u^3*v^14*x - 4124525003135204315185546875*u^3*v^13*x^2 - 158000470697879791259765625000*u^3*v^12*x^4 + 12670540809631347656250000000*u^3*v^12*x^3 - 30196069166064262390136718750*u^3*v^11*x^5 + 127109912504553794860839843750*u^3*v^10*x^7 - 17161355895996093750000000000*u^3*v^10*x^6 + 432487792968750000000000000*u^3*v^10*x^5 + 2398317228698730468750000000*u^3*v^9*x^8 + 579653778076171875000000000*u^3*v^9*x^7 - 23005590864257812500000000000*u^3*v^8*x^10 + 1425433491210937500000000000*u^3*v^8*x^9 - 1401806784375000000000000000*u^3*v^7*x^11 + 1574270552000000000000000000*u^3*v^6*x^13 + 7424145005643367767333984375*u^2*v^15 + 166597813926637172698974609375*u^2*v^14*x^2 - 12670540809631347656250000000*u^2*v^14*x + 45300702989101409912109375000*u^2*v^13*x^3 + 2111756801605224609375000000*u^2*v^13*x^2 - 398609300951957702636718750000*u^2*v^12*x^5 + 63877739582955837249755859375*u^2*v^12*x^4 - 1621829223632812500000000000*u^2*v^12*x^3 - 125656742127120494842529296875*u^2*v^11*x^6 + 9492055870056152343750000000*u^2*v^11*x^5 + 220498897977046966552734375000*u^2*v^10*x^8 - 43730292718048095703125000000*u^2*v^10*x^7 + 1691507812500000000000000000*u^2*v^10*x^6 - 11180109003387451171875000000*u^2*v^9*x^9 + 6813045698730468750000000000*u^2*v^9*x^8 - 240270996093750000000000000*u^2*v^9*x^7 - 22068971057812500000000000000*u^2*v^8*x^11 - 10903663196718750000000000000*u^2*v^8*x^10 + 104338125000000000000000000*u^2*v^8*x^9 + 18808565089200000000000000000*u^2*v^7*x^12 - 1577132955000000000000000000*u^2*v^7*x^11 - 4685959065600000000000000000*u^2*v^6*x^14 + 4243145848320000000000000000*u^2*v^6*x^13 - 4047437699481600000000000000*u^2*v^5*x^15 + 1206502903775232000000000000*u^2*v^4*x^17 - 13363461010158061981201171875*u*v^16 + 7127179205417633056640625000*u*v^15*x - 3801162242889404296875000000*u*v^15 + 378176047727465629577636718750*u*v^14*x^3 - 61531313806772232055664062500*u*v^14*x^2 + 1621829223632812500000000000*u*v^14*x + 228996531839668750762939453125*u*v^13*x^4 - 17932475624084472656250000000*u*v^13*x^3 - 270304870605468750000000000*u*v^13*x^2 - 467742787901937961578369140625*u*v^12*x^6 + 138516700404453277587890625000*u*v^12*x^5 - 6772713787078857421875000000*u*v^12*x^4 - 137991734557628631591796875000*u*v^11*x^7 + 16652559636474609375000000000*u*v^11*x^6 - 492555541992187500000000000*u*v^11*x^5 + 164014092408691406250000000000*u*v^10*x^9 - 10028201135888671875000000000*u*v^10*x^8 + 204157731445312500000000000*u*v^10*x^7 - 75839143099781250000000000000*u*v^9*x^10 + 26212777246406250000000000000*u*v^9*x^9 - 1617468750000000000000000000*u*v^9*x^8 + 24735689172000000000000000000*u*v^8*x^12 - 49827383864820000000000000000*u*v^8*x^11 + 5065920900000000000000000000*u*v^8*x^10 + 60149948168448000000000000000*u*v^7*x^13 - 13447559677440000000000000000*u*v^7*x^12 + 651600000000000000000000000*u*v^7*x^11 - 20735467530485760000000000000*u*v^6*x^15 + 18991332694425600000000000000*u*v^6*x^14 - 2433607680000000000000000000*u*v^6*x^13 - 14258515587209625600000000000*u*v^5*x^16 + 3786500210688000000000000000*u*v^5*x^15 + 4040846192903454720000000000*u*v^4*x^18 - 3167507671783833600000000000*u*v^4*x^17 + 1459611581477289984000000000*u*v^3*x^19 - 296404550212877549568000000*u*v^2*x^21 - 26726922020316123962402343750*v^16*x + 3563589602708816528320312500*v^16 - 22806973457336425781250000000*v^15*x^2 - 1520464897155761718750000000*v^15*x + 486548767089843750000000000*v^15 + 291802554845809936523437500000*v^14*x^4 - 87409837532043457031250000000*v^14*x^3 + 5027670593261718750000000000*v^14*x^2 + 255500251724839210510253906250*v^13*x^5 - 47227033465147018432617187500*v^13*x^4 + 1614621093750000000000000000*v^13*x^3 - 211798210579419136047363281250*v^12*x^7 + 113792874786443710327148437500*v^12*x^6 - 9389522625183105468750000000*v^12*x^5 + 150169372558593750000000000*v^12*x^4 + 2738377852981567382812500000*v^11*x^8 - 17523201052770996093750000000*v^11*x^7 + 2337996972656250000000000000*v^11*x^6 - 3629697037031250000000000000*v^10*x^10 + 100663674667800292968750000000*v^10*x^9 - 20239234233046875000000000000*v^10*x^8 + 533935546875000000000000000*v^10*x^7 - 134258438818350000000000000000*v^9*x^11 + 59022287116515000000000000000*v^9*x^10 - 3563392500000000000000000000*v^9*x^9 + 44148704244480000000000000000*v^8*x^13 - 63305730389952000000000000000*v^8*x^12 + 4684843764000000000000000000*v^8*x^11 + 405000000000000000000000000*v^8*x^10 + 35311559963443200000000000000*v^7*x^14 + 2129927760691200000000000000*v^7*x^13 - 2187840000000000000000000000*v^7*x^12 - 8262243795861504000000000000*v^6*x^16 - 12143609805746995200000000000*v^6*x^15 + 6385906483200000000000000000*v^6*x^14 - 128000000000000000000000000*v^6*x^13 + 9201541556144701440000000000*v^5*x^17 - 10627785173237760000000000000*v^5*x^16 + 707788800000000000000000000*v^5*x^15 - 2050850457252790272000000000*v^4*x^19 + 9583660556800229376000000000*v^4*x^18 - 1630745395200000000000000000*v^4*x^17 - 4303175405388045484032000000*v^3*x^20 + 2003859941621760000000000000*v^3*x^19 + 744612552310481171251200000*v^2*x^22 - 1385067991648960512000000000*v^2*x^21 + 510591464441472803143680000*v*x^23 - 78426848938210222562869248*x^25 ) (* fields25 is a 11031-element list. Each entry is a triple {{u,v},poly,discf}. {u,v} is the specialization point. poly is the polredabs'd form of the main factor of f25[{u,v}] and defines the associated degree 24 or 25 field. discf is the field discriminant of that field *) fields25 = {{{1465/4938267, -1225/57022169049}, 807988318774 + 3160768901920*x + 4610281483470*x^2 + 2669298781170*x^3 - 176181265530*x^4 - 921286754520*x^5 - 376117776805*x^6 - 40544204005*x^7 + 1355947770*x^8 + 3719006970*x^9 + 5441592015*x^10 - 397418205*x^11 - 941362005*x^12 + 82877295*x^13 + 97887645*x^14 + 6451035*x^15 + 1040145*x^16 - 2666355*x^17 - 142705*x^18 + 31295*x^19 + 16095*x^20 + 2445*x^21 - 480*x^22 - 30*x^23 - 5*x^24 + x^25, 64413629420899967622756958007812500000000000000000000000000}, {{-1437/2301289, -81/3491055413}, 3801538518075598932 + 1382347382464959300*x - 217960706601228840*x^2 + 434547365558111940*x^3 + 272444694116050020*x^4 - 44954664571150620*x^5 - 38065223067408675*x^6 + 1543387301712795*x^7 + 2431548125935655*x^8 - 90851120088235*x^9 - 112660631557480*x^10 + 3597988438400*x^11 + 3891713367440*x^12 + 9889354160*x^13 - 91385937670*x^14 - 4733364250*x^15 + 1715145650*x^16 + 197968030*x^17 - 27784880*x^18 - 3879140*x^19 + 368140*x^20 + 40300*x^21 - 2015*x^22 - 185*x^23 - 5*x^24 + x^25, 717088287172279397312102400000000000000000000000000000000000000000000000}, {{3/3481, -1/27726165}, 51205463241630336 - 225861079515759360*x + 69643110293294400*x^2 + 17889708613167840*x^3 + 18416062321319040*x^4 - 3676826354610960*x^5 + 79892351070960*x^6 + 546309313526400*x^7 + 73669848896160*x^8 - 61161073221540*x^9 - 3813672448200*x^10 + 1476180027540*x^11 - 153600791800*x^12 - 193437773810*x^13 - 25876015560*x^14 - 3865234630*x^15 - 160248740*x^16 + 3071925*x^17 + 7568910*x^18 + 294960*x^19 + 33570*x^20 + 740*x^21 - 1850*x^22 + 90*x^23 - 10*x^24 + x^25, 2019088090383335405916325312500000000000000000000000000000000000000000}, {{1/27075, -1/23149125}, -108924017697792 + 210810525350400*x - 153072866192640*x^2 + 47413462924160*x^3 + 844516936960*x^4 - 6544641373056*x^5 + 2554670958400*x^6 - 352832140000*x^7 - 107467185600*x^8 + 83155283040*x^9 - 20235858816*x^10 - 1298904480*x^11 + 2364361920*x^12 - 681780960*x^13 + 21041640*x^14 + 45671604*x^15 - 13517160*x^16 + 575460*x^17 + 393630*x^18 - 90105*x^19 + 10554*x^20 - 185*x^21 - 190*x^22 + 45*x^23 - 10*x^24 + x^25, 25496472432792156348874752000000000000000000000000000000000}, {{-641/322752, -49/476381952}, 3409069301431324224 + 14603349419855007360*x - 12392588797922282880*x^2 + 6541149817472973280*x^3 - 2516438987069531360*x^4 + 914549770599926080*x^5 - 251958760045351840*x^6 + 55353902565691120*x^7 - 10398614117502720*x^8 + 1622500403345040*x^9 - 190449007943520*x^10 + 9439133286960*x^11 + 1525809278320*x^12 - 694368779120*x^13 + 144858264640*x^14 - 23774869960*x^15 + 3016607260*x^16 - 339886680*x^17 + 29368080*x^18 - 2519310*x^19 + 70590*x^20 + 760*x^21 - 1130*x^22 + 205*x^23 - 10*x^24 + x^25, 6639706362706290715852800000000000000000000000000000000000000000000000}, {{-552/344569, -36/202262003}, 28771599049632 - 70896602041200*x + 77044801852080*x^2 - 45679321331280*x^3 + 13723301797020*x^4 + 1377657571626*x^5 - 3888609500520*x^6 + 2076072473205*x^7 - 505981884645*x^8 - 50397696675*x^9 + 97438032864*x^10 - 39608184510*x^11 + 7041602550*x^12 + 430309680*x^13 - 507707810*x^14 + 85624702*x^15 + 5187880*x^16 - 3433220*x^17 + 175180*x^18 + 135100*x^19 - 22668*x^20 - 1860*x^21 + 570*x^22 - 65*x^23 - 5*x^24 + x^25, 20749082383457158487040000000000000000000000000000000000000000}, {{59/15552, -1/5038848}, 422318866088770560 + 737171709753600000*x + 424689953451091200*x^2 + 55434902571360000*x^3 - 25191447028070400*x^4 - 5722813301414400*x^5 - 313493221360800*x^6 - 447567573986400*x^7 - 29807792949600*x^8 + 22265777001600*x^9 - 1891019147400*x^10 + 544084597800*x^11 + 316046124000*x^12 - 34902159000*x^13 - 6444991500*x^14 + 40283100*x^15 + 245560000*x^16 - 45829500*x^17 - 24450*x^18 + 204650*x^19 + 25140*x^20 + 2550*x^21 - 315*x^22 + 135*x^23 + x^25, 210084459132503729681280000000000000000000000000000000000000000000000}, {{-3/503, -27/127263527}, 200777054699848176 - 1238770277754824160*x - 8824029481207800*x^2 - 433219409533180440*x^3 + 224652261201088140*x^4 - 40902545093548140*x^5 - 414072487495530*x^6 + 1714472579821950*x^7 - 469838741425290*x^8 + 66040617138705*x^9 - 7661454480*x^10 - 1620113794320*x^11 + 349574019960*x^12 - 57740710440*x^13 + 4878391380*x^14 + 138166620*x^15 - 165299340*x^16 + 49318870*x^17 - 6431320*x^18 + 60280*x^19 + 102620*x^20 - 18140*x^21 + 710*x^22 + 70*x^23 - 10*x^24 + x^25, 48122980339837442644219845515673600000000000000000000000000000000000}, {{16/146523, -64/291434247}, -10485760000000000 - 3276800000000000*x^2 + 819200000000000*x^3 + 204800000000000*x^4 - 69632000000000*x^5 + 172800000000000*x^6 - 39808000000000*x^7 - 6048000000000*x^8 + 1416000000000*x^9 - 1848960000000*x^10 + 456000000000*x^11 + 172320000000*x^12 - 43080000000*x^13 - 3885000000*x^14 + 1061850000*x^15 - 97500000*x^16 + 18825000*x^17 + 3887500*x^18 - 909375*x^19 + 17000*x^20 - 3125*x^21 - 500*x^22 + 125*x^23 + x^25, 108190162593414320018664550781250000000000000000000000000000000000000}, {{-47/27075, -169/578728125}, 178688336094 - 26356544019*x - 527331449529*x^2 + 1125798194844*x^3 - 681494878899*x^4 - 233807932431*x^5 + 578562560550*x^6 - 90266638185*x^7 - 134874007605*x^8 + 53468969325*x^9 + 12418320606*x^10 - 9981462996*x^11 + 609314534*x^12 + 777958706*x^13 - 190710696*x^14 - 1744054*x^15 + 5459480*x^16 - 114495*x^17 - 180575*x^18 + 4780*x^19 + 9291*x^20 - 2881*x^21 + 314*x^22 + 21*x^23 - 11*x^24 + x^25, 3118369126021466283345445989415649280000000000000000000000}, {{-53/30625, -1/2953125}, -311939213124276 - 644337036058140*x + 2065834310509440*x^2 - 1688722193687390*x^3 - 12368315524300*x^4 + 665196064750734*x^5 + 15067042621390*x^6 - 69445501809880*x^7 - 8185664779890*x^8 - 290438266455*x^9 + 90835749528*x^10 + 227953804620*x^11 + 13446228720*x^12 - 7609853400*x^13 - 1114659420*x^14 - 128457384*x^15 + 154722720*x^16 + 13514250*x^17 - 2650440*x^18 - 12510*x^19 - 87828*x^20 + 14450*x^21 - 1730*x^22 + 240*x^23 - 10*x^24 + x^25, 382447086491882345233121280000000000000000000000000000000000000000000}, {{-477/310249, -81/172808693}, 675867754315363262976 - 178880349910573382400*x - 211960728356373612000*x^2 + 66557647610353735200*x^3 + 17750547909088866000*x^4 - 6709225937509715895*x^5 - 434025156363057150*x^6 + 244440842629950225*x^7 + 1817421281238000*x^8 - 3392564536036875*x^9 - 122032259610840*x^10 + 53264539472700*x^11 - 2910904041200*x^12 - 47132362950*x^13 - 10985256500*x^14 + 5875350110*x^15 + 925690000*x^16 - 107738950*x^17 - 7924600*x^18 - 740500*x^19 + 133280*x^20 - 5075*x^21 - 1150*x^22 + 25*x^23 + x^25, 1639433669804022398976000000000000000000000000000000000000000000000000000}, {{146320/458643, -800/1613964717}, 1219800107168184397824 + 1959594266680494796800*x + 1465993077335651865600*x^2 + 646393031979017011200*x^3 + 178552596779545888000*x^4 + 28049497869457486080*x^5 + 478842527594788800*x^6 - 940161819345494400*x^7 - 231151403191900800*x^8 - 21538122282324000*x^9 + 734488008345440*x^10 + 255930955012800*x^11 - 14832121670400*x^12 - 5666275494800*x^13 - 18806016000*x^14 + 85627368960*x^15 + 5797670800*x^16 - 393038400*x^17 - 45802800*x^18 + 3827000*x^19 + 517320*x^20 - 19200*x^21 - 6150*x^22 - 300*x^23 + x^25, -10455147226971833612810452992000000000000000000000000000000000000000000000\ 000}, {{-2605/917286, -800/1613964717}, 2276327465496350299776 - 2446868879448900846720*x + 67098453545318238720*x^2 + 483595004713414750080*x^3 + 15855649751652787320*x^4 - 46456251994433612520*x^5 - 5234449700942348280*x^6 + 3275617444496237280*x^7 + 337412906098261470*x^8 - 162209511126750470*x^9 - 8683716509741840*x^10 + 5555946618778080*x^11 - 96437701124380*x^12 - 96117757047220*x^13 + 6689397324720*x^14 + 492260432560*x^15 - 33610390880*x^16 - 5068755720*x^17 + 318997720*x^18 + 27786880*x^19 - 2732820*x^20 + 3980*x^21 + 8720*x^22 - 420*x^23 - 5*x^24 + x^25, 20073882675785920536596069744640000000000000000000000000000000000000\ 0000000000}, {{-19/13068, -1/1940598}, -1517659391067467175936 + 336490488338962775040*x + 1939928241370075079040*x^2 - 56508416016520522560*x^3 - 322223002933413426960*x^4 - 157080273610355371080*x^5 - 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4777293593988995638221000*x + 2307837067276958183961000*x^2 - 942790004686241358322950*x^3 + 119841992504690349122100*x^4 + 4306573801226322219330*x^5 + 1003339876756703316300*x^6 - 324810475788220366950*x^7 + 39198206231300943000*x^8 - 8119453867840222650*x^9 + 1081025107267594680*x^10 - 61893019489392900*x^11 + 1399543536290400*x^12 + 26409613478700*x^13 - 33462524064600*x^14 + 2828701121940*x^15 + 132534183300*x^16 - 19360404900*x^17 + 175769100*x^18 + 24821325*x^19 - 539190*x^20 + 178125*x^21 - 250*x^22 - 825*x^23 + x^25, 22865406985387400111216460693504\ 000000000000000000000000000000000000000000000000000}, {{-263/962361, 49/2832228423}, -110542606976 + 590457203840*x + 669840432000*x^2 - 557056691520*x^3 - 18990291840*x^4 - 16286841984*x^5 - 117099977440*x^6 - 30343249760*x^7 + 13613490720*x^8 + 39306483280*x^9 + 16129508480*x^10 - 6910828320*x^11 - 4551364800*x^12 + 29124960*x^13 + 299191920*x^14 + 3446384*x^15 - 6602360*x^16 + 4337280*x^17 + 1775080*x^18 + 368540*x^19 + 67272*x^20 + 1680*x^21 - 2430*x^22 - 390*x^23 - 10*x^24 + x^25, 1354987080615549636220234707763200000000000000000000000000000000000000000}, {{2755/6405961, 225/16213487291}, -6461649666909657 + 43446725838062505*x - 74555166209547960*x^2 + 49757797403821980*x^3 - 5655888184622130*x^4 - 14091226915138290*x^5 + 11568863343316140*x^6 - 4911621345969480*x^7 + 1462688938505565*x^8 - 384536712698865*x^9 + 100907418022560*x^10 - 24568226489880*x^11 + 5357757663060*x^12 - 1063714521180*x^13 + 183349075080*x^14 - 27549888480*x^15 + 3828446785*x^16 - 462506745*x^17 + 50343160*x^18 - 5593060*x^19 + 449310*x^20 - 25970*x^21 + 2540*x^22 - 120*x^23 - 5*x^24 + x^25, 1119186718586212624367616000000000000000000000000000000000000000000000}, {{-136/257415, 4/303492285}, -69869475526442962572 + 28150516644899427360*x + 60180542641077523920*x^2 - 6999605168522837220*x^3 - 1404524391253134750*x^4 - 273471732780622020*x^5 - 2560545042617070*x^6 + 5173453916494110*x^7 + 4812649168072590*x^8 + 157196492592450*x^9 - 409327727360940*x^10 + 35891862031590*x^11 + 13933549070030*x^12 - 3022718701380*x^13 + 75036576350*x^14 + 26843008530*x^15 - 410198605*x^16 - 442929660*x^17 + 22926135*x^18 + 2192025*x^19 - 136455*x^20 + 2035*x^21 - 705*x^22 + 55*x^23 + x^25, 430738792615111553262149400000000000000000000000000000000000000000000000}, {{-925/4678134, 625/74354261796}, 4612571337 - 21650735010*x + 43991185815*x^2 - 45313466775*x^3 + 16420514325*x^4 + 13266780741*x^5 - 14908001415*x^6 - 4600024005*x^7 + 20646055800*x^8 - 22204215695*x^9 + 15007531718*x^10 - 7485121590*x^11 + 2947638730*x^12 - 931180510*x^13 + 219170610*x^14 - 25561050*x^15 - 5907015*x^16 + 3761280*x^17 - 788365*x^18 + 17245*x^19 + 29745*x^20 - 7095*x^21 + 645*x^22 + 15*x^23 - 10*x^24 + x^25, 17705883633883441908940800000000000000000000000000000000000}, {{1/98283, 1/160103007}, -17453169793242216 + 40533439444285500*x - 22401702078483150*x^2 + 2187948020486625*x^3 - 3804007254484500*x^4 + 77682181068855*x^5 - 12333479154750*x^6 + 42743747198025*x^7 + 37756535273100*x^8 + 7511107216725*x^9 + 4901411607840*x^10 + 1103730189300*x^11 + 405004711500*x^12 + 97621764600*x^13 + 19260731700*x^14 + 4418211510*x^15 + 397775300*x^16 + 102223350*x^17 + 84150*x^18 + 1456875*x^19 - 92880*x^20 + 20025*x^21 - 750*x^22 + 225*x^23 + x^25, -9893933479050235026855468750000000000000000000000000000000000000000}, {{-6659/75872523, 6889/3434066263503}, 64706544639144025902 + 74100290014611376290*x + 30883467634169464755*x^2 + 7720605072102247875*x^3 + 1981288864999234800*x^4 + 387622684042186428*x^5 + 61151511275649720*x^6 + 7957588810843620*x^7 - 459754390817415*x^8 - 18955651287045*x^9 - 74135577746154*x^10 - 3540505607850*x^11 - 3536134755680*x^12 - 183959404760*x^13 - 80232079740*x^14 + 2394219692*x^15 - 944093740*x^16 + 95030100*x^17 - 6050115*x^18 + 3510765*x^19 + 76332*x^20 + 29960*x^21 - 1720*x^22 + 60*x^23 - 5*x^24 + x^25, -2697313161949827576639627542417060659200000000000000000000000000000000000}\ , {{19/220323, 1/537367797}, 3639227675268544 - 6871700197613500*x - 4073287548490020*x^2 + 6509905777832500*x^3 - 4663716441771610*x^4 + 2119148373117825*x^5 - 857633868375560*x^6 + 290527143292610*x^7 - 80077297920750*x^8 + 16861703486235*x^9 - 2877480407760*x^10 + 427961874600*x^11 - 19282001880*x^12 - 10966530300*x^13 + 2176148880*x^14 + 238840920*x^15 - 5595120*x^16 - 37745820*x^17 + 1168340*x^18 + 941980*x^19 - 106470*x^20 - 4345*x^21 + 1960*x^22 - 90*x^23 - 10*x^24 + x^25, -1247347650408586513338178395766259712000000000000000000000000000000}, {{-41/580800, 1/1149984000}, 33692238870648864 - 88775841671216160*x - 259281277725020400*x^2 - 142604271310936680*x^3 - 27404941104082080*x^4 - 615358628749656*x^5 + 411363594229080*x^6 - 153264887756580*x^7 - 68219659651680*x^8 - 3286989535900*x^9 - 1491692929412*x^10 - 228693781950*x^11 + 40762998360*x^12 - 3910580610*x^13 - 2134613310*x^14 - 307406159*x^15 + 160695710*x^16 - 17006535*x^17 - 554960*x^18 - 39760*x^19 + 6612*x^20 + 1500*x^21 - 630*x^22 + 105*x^23 - 10*x^24 + x^25, 3292618605895785616015170339864576000000000000000000000000000000000}, {{34/759027, 2/3436115229}, -3807651143445948205680 - 3252947709972890625600*x - 2011640553561457892700*x^2 - 1763075865553084915300*x^3 - 259613206117657163500*x^4 - 244544319883103416980*x^5 + 7045918209485299100*x^6 - 11364929812074207100*x^7 + 744243673181438700*x^8 + 118411284879106500*x^9 - 82432702895898300*x^10 + 15971700863288700*x^11 - 2077135197419100*x^12 + 67624531831500*x^13 + 16674063254100*x^14 - 2468454950340*x^15 + 31571411400*x^16 + 17822121300*x^17 - 1289378475*x^18 - 28696725*x^19 + 3629385*x^20 + 162655*x^21 - 10925*x^22 - 435*x^23 - 5*x^24 + x^25, -6743282904874568941599068856042651\ 648000000000000000000000000000000000000000000000}, {{10147/534673129, 10201/111269220856803}, -9467125992311490 + 27732446894563875*x - 35579993416307325*x^2 + 26647889502403950*x^3 - 10848965586777975*x^4 + 2682382492478790*x^5 - 1300329885783255*x^6 + 784081387317630*x^7 - 168679991347695*x^8 + 2330874572055*x^9 - 8242089113220*x^10 + 2962345889040*x^11 + 219437970500*x^12 + 86627538140*x^13 - 6229063200*x^14 + 1135070680*x^15 - 44427590*x^16 + 12988845*x^17 - 7371435*x^18 - 190950*x^19 - 42465*x^20 + 6470*x^21 - 925*x^22 - 30*x^23 - 5*x^24 + x^25, -56832277321741223013970753157100208128000000000000000000000000000000}, {{35/10361961, 25/300196372131}, -660694838245779203975168 - 194942074913215052224000*x + 145198569155811891755520*x^2 - 45733075429237658985920*x^3 + 4365489041185534763840*x^4 - 241514169876043063320*x^5 - 186490906128576050300*x^6 + 24983360772617933990*x^7 - 4284374813448685290*x^8 - 44643714817111995*x^9 + 25376474288055720*x^10 - 9286686124214400*x^11 + 637803325725480*x^12 - 53801217278280*x^13 - 2705702297040*x^14 + 399505300500*x^15 - 58354184100*x^16 + 2070246510*x^17 - 4205560*x^18 - 11380880*x^19 + 1492440*x^20 - 47800*x^21 + 1420*x^22 + 30*x^23 - 10*x^24 + x^25, -182923255883099200889731685548032000000000000000000000000\ 00000000000000000000000}, {{305/51344307, 25/1911702582531}, 32500561132334876134440 + 23195952360624307801200*x + 5754250005478675162200*x^2 + 560422507595910440600*x^3 + 47696527584656656600*x^4 + 15990944820671873400*x^5 + 2755035451669804600*x^6 + 316786475717317400*x^7 + 42676381250042580*x^8 + 2420391988986240*x^9 + 433039568228268*x^10 + 122240103828300*x^11 - 3437581676040*x^12 - 1278927088380*x^13 + 138430704600*x^14 - 2860104864*x^15 - 2116427685*x^16 + 284531850*x^17 + 22026645*x^18 - 4502115*x^19 - 266931*x^20 + 32185*x^21 + 2135*x^22 - 195*x^23 - 10*x^24 + x^25, -45679235244455072509943056485580800000000000000000000000000000000000000000}\ , {{5307/2039515921, 8281/2486877619723587}, 3698263962302471055 - 4829783422806024300*x + 3649893796392690825*x^2 - 1768509276795285975*x^3 + 657252226197331125*x^4 - 174865406195068425*x^5 + 40255279360953975*x^6 - 4691944294819725*x^7 + 673195034577150*x^8 + 67082148368325*x^9 - 9305923279710*x^10 + 761801876850*x^11 - 241273557870*x^12 - 61675107490*x^13 + 4017591990*x^14 + 1152682110*x^15 + 532320515*x^16 - 16542090*x^17 - 11409435*x^18 - 405675*x^19 + 77865*x^20 + 17115*x^21 - 1085*x^22 - 225*x^23 + x^25, -888004333152206609593293018079690752000000000000000000000000000000000000}} (* Section five. A degree 9 family: comparison with complete number field tables *) (* Specialization polynomial *) tau311[{u_,v_}] := (t^3 + t^2 + u t + v) t (* The main polynomial *) f9[{u_,v_}] := x^9 - 3 x^8 + 12 u x^7 - 4(u+12 v) x^6 + 42 v x^5 - 6 (4u+1) v x^4 + 4 v (2 u + 3 v) x^3 - 12 v^2 x^2 + 3(4u-1) v^2 x - v^2 (4u-8v-1) (* An octic resolvent *) f8[{u_,v_}] := x^8+x^4 (18 v-6 u^2)+x^2 (8 u^3-36 u v+108 v^2)+(-3 u^4+18 u^2 v-27 v^2) (* fields9 is a 507-element list. Each entry is a quadruple {{u,v},poly,discf,gal}. {u,v} is the specialization point. poly is the polredabs'd form of a largest degree factor of f9[{u,v}]. discf is the field discriminant of poly. gal is i if poly has Galois group 9Ti and else gal is 0 *) fields9 = {{{0, -4/3}, 140 - 171*x + 396*x^2 - 528*x^3 + 180*x^4 + 18*x^5 - 12*x^6 + x^9, -304679870005248, 19}, {{-2, 2/3}, -64 + 144*x + 120*x^3 + 36*x^4 + 81*x^5 - 12*x^6 - 18*x^7 + x^9, -4874877920083968, 16}, {{-1, 1/3}, 6 - 27*x + 36*x^2 - 18*x^3 + 18*x^4 - 12*x^6 + x^9, -1190155742208, 18}, {{1, -1/3}, 1000 + 450*x - 1440*x^2 + 108*x^3 + 36*x^4 - 45*x^5 - 84*x^6 - 18*x^7 + x^9, -4874877920083968, 16}, {{1, 1/3}, -8 + 36*x - 72*x^2 + 96*x^3 - 90*x^4 + 45*x^5 - 9*x^7 + x^9, -4760622968832, 8}, {{3, 1/3}, -160 - 882*x - 1116*x^2 - 456*x^3 + 108*x^4 + 108*x^5 - 12*x^6 - 18*x^7 + x^9, -76169967501312, 19}, {{0, -1/6}, -160 - 882*x - 1116*x^2 - 456*x^3 + 108*x^4 + 108*x^5 - 12*x^6 - 18*x^7 + x^9, -76169967501312, 19}, {{1/2, 1/6}, 564 - 513*x + 252*x^2 - 180*x^3 + 180*x^4 - 54*x^5 - 12*x^6 + x^9, -4874877920083968, 26}, {{0, -4/9}, 132 - 189*x - 756*x^2 - 1188*x^3 - 468*x^4 - 198*x^5 - 36*x^6 + x^9, -43873901280755712, 26}, {{0, -2/9}, -252 + 243*x + 108*x^2 + 108*x^3 - 108*x^4 - 54*x^5 - 36*x^6 + x^9, -43873901280755712, 26}, {{0, -1/9}, 12 - 27*x^2 - 18*x^3 + 9*x^4 + 9*x^5 - 9*x^6 - 9*x^7 + x^9, -167365651248, 12}, {{0, 4/9}, 896 - 1584*x + 864*x^2 - 258*x^3 + 180*x^4 - 54*x^5 - 12*x^6 + x^9, -171382426877952, 18}, {{-16/3, -64/9}, 192 + 324*x - 144*x^2 + 48*x^3 - 36*x^5 - 24*x^6 + x^9, -4874877920083968, 26}, {{-1, -1/9}, -252 + 243*x + 756*x^2 + 270*x^3 - 108*x^4 - 54*x^5 + x^9, -171382426877952, 18}, {{-1/3, 1/9}, -2016 + 6372*x - 5616*x^2 + 1656*x^3 - 864*x^4 + 432*x^5 - 24*x^6 + 36*x^7 + x^9, -19499511680335872, 26}, {{1/3, -1/9}, -22 - 117*x - 90*x^2 - 72*x^3 - 36*x^4 - 18*x^5 - 12*x^6 + x^9, -1190155742208, 26}, {{1/3, 1/9}, 96 - 216*x + 144*x^2 + 24*x^3 - 24*x^6 + x^9, -304679870005248, 26}, {{2/3, 2/9}, 48 - 135*x + 72*x^2 + 48*x^3 - 18*x^5 - 24*x^6 + x^9, -19499511680335872, 26}, {{1, 1/9}, -2736 - 2187*x + 1728*x^2 + 1080*x^3 - 432*x^4 - 162*x^5 + x^9, -43873901280755712, 26}, {{5/3, -1/9}, 924 - 405*x - 1692*x^2 + 12*x^3 + 540*x^4 - 54*x^5 - 60*x^6 + x^9, -4874877920083968, 26}, {{8/3, 16/9}, 12 - 54*x + 72*x^2 - 42*x^3 - 18*x^5 - 6*x^6 + x^9, -4760622968832, 26}, {{8, 16/9}, 12 - 27*x^2 - 18*x^3 + 9*x^4 + 9*x^5 - 9*x^6 - 9*x^7 + x^9, -167365651248, 12}, {{-1/4, -1/3}, 6 - 27*x + 36*x^2 - 18*x^3 + 18*x^4 - 12*x^6 + x^9, -1190155742208, 18}, {{1/4, 1/6}, -1 - 6*x^3 - 3*x^6 + x^9, -1162261467, 4}, {{1/2, 1/12}, 6 - 27*x + 36*x^2 - 18*x^3 + 18*x^4 - 12*x^6 + x^9, -1190155742208, 18}, {{-1/2, 1/18}, 180 + 243*x - 540*x^2 + 108*x^3 - 108*x^4 - 54*x^5 - 36*x^6 + x^9, -43873901280755712, 26}, {{1/6, -1/18}, 924 - 405*x - 1692*x^2 + 12*x^3 + 540*x^4 - 54*x^5 - 60*x^6 + x^9, -4874877920083968, 26}, {{1/3, 1/18}, 96 + 621*x - 288*x^2 + 24*x^3 - 54*x^5 + x^9, -76169967501312, 26}, {{1/2, 1/18}, -1440 - 972*x + 1728*x^2 + 432*x^3 - 432*x^4 - 108*x^5 + x^9, -43873901280755712, 26}, {{1/2, 1/9}, 12 + 162*x + 216*x^2 + 126*x^3 + 36*x^4 - 18*x^6 - 9*x^7 + x^9, -171382426877952, 18}, {{3/8, 1/24}, 140 - 171*x + 396*x^2 - 528*x^3 + 180*x^4 + 18*x^5 - 12*x^6 + x^9, -304679870005248, 19}, {{0, -16/27}, -264 + 1053*x + 144*x^2 + 192*x^3 - 216*x^4 - 54*x^5 - 48*x^6 + x^9, -304679870005248, 26}, {{0, -8/27}, 2 - 6*x + 16*x^3 - 15*x^4 - 3*x^5 - 2*x^6 + 6*x^7 - 3*x^8 + x^9, -82556485632, 16}, {{0, -1/27}, 12 - 54*x + 72*x^2 - 42*x^3 - 18*x^5 - 6*x^6 + x^9, -4760622968832, 26}, {{0, 2/27}, 192 + 324*x - 144*x^2 + 48*x^3 - 36*x^5 - 24*x^6 + x^9, -4874877920083968, 26}, {{0, 4/27}, -60 - 81*x - 84*x^2 - 92*x^3 - 36*x^4 - 30*x^5 - 4*x^6 + x^9, -6687075336192, 26}, {{0, 8/27}, 96 + 81*x - 72*x^2 + 48*x^3 - 18*x^5 - 24*x^6 + x^9, -4874877920083968, 26}, {{0, 32/27}, 4 - 35*x + 104*x^2 - 124*x^3 + 88*x^4 - 40*x^5 + 8*x^6 + 4*x^7 - 4*x^8 + x^9, -2972033482752, 26}, {{-32/3, -512/27}, -60 - 81*x - 84*x^2 - 92*x^3 - 36*x^4 - 30*x^5 - 4*x^6 + x^9, -6687075336192, 26}, {{-32/3, 256/27}, 144 + 405*x - 432*x^2 + 72*x^3 - 54*x^5 + x^9, -43873901280755712, 26}, {{-8/3, -8/27}, 1416 - 567*x - 1872*x^2 + 1200*x^3 - 216*x^4 + 126*x^5 + x^9, -19499511680335872, 26}, {{-8/3, 1/27}, -2 + x^3, -108, 0}, {{-8/3, 16/27}, -120 + 162*x + 648*x^2 + 1260*x^3 + 1152*x^4 + 360*x^5 - 48*x^6 - 36*x^7 + x^9, -43873901280755712, 26}, {{-8/3, 64/27}, -36 + 54*x - 144*x^3 + 54*x^5 - 6*x^6 - 9*x^7 + x^9, -19042491875328, 18}, {{-2/3, -2/27}, 1152 - 3807*x + 2376*x^2 + 144*x^3 - 162*x^5 - 72*x^6 + x^9, -43873901280755712, 26}, {{-2/3, 1/27}, -2 - 2*x^3 + x^6, 5038848, 0}, {{-2/3, 4/27}, -96 - 324*x - 432*x^2 - 162*x^3 + 144*x^4 + 108*x^5 - 12*x^6 - 18*x^7 + x^9, -171382426877952, 18}, {{-1/3, 1/27}, -1 - 2*x^3 + x^6, 373248, 0}, {{1/3, -8/27}, 12 - 54*x + 72*x^2 - 42*x^3 - 18*x^5 - 6*x^6 + x^9, -4760622968832, 26}, {{1/3, -2/27}, 144 + 324*x + 216*x^2 + 144*x^3 - 36*x^6 + x^9, -685529707511808, 26}, {{1/3, -1/27}, 8 + 9*x - 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18*x^6 - 9*x^7 + x^9, -171382426877952, 18}, {{8/75, 4/1125}, -24 - 54*x + 180*x^2 + 138*x^3 - 36*x^5 - 12*x^6 + x^9, -76169967501312, 26}, {{4/25, 8/1125}, -1440 - 972*x + 1728*x^2 + 432*x^3 - 432*x^4 - 108*x^5 + x^9, -43873901280755712, 26}, {{8/25, 32/1125}, 3324 + 2511*x - 4212*x^2 - 2664*x^3 + 468*x^4 + 414*x^5 - 36*x^6 - 36*x^7 + x^9, -43873901280755712, 26}, {{1/3, -1/1125}, -16 - 72*x - 54*x^2 - 3*x^3 + 36*x^4 + 27*x^5 - 6*x^6 - 9*x^7 + x^9, -4760622968832, 18}, {{51/25, -1/1125}, 180 + 243*x - 540*x^2 + 108*x^3 - 108*x^4 - 54*x^5 - 36*x^6 + x^9, -43873901280755712, 26}, {{19/54, 32/729}, -16 - 72*x - 54*x^2 - 3*x^3 + 36*x^4 + 27*x^5 - 6*x^6 - 9*x^7 + x^9, -4760622968832, 18}, {{-1/24, 1/1728}, 11 + 9*x - 27*x^2 - 30*x^3 + 18*x^4 + 27*x^5 - 3*x^6 - 9*x^7 + x^9, -74384733888, 12}, {{5/96, 1/1728}, -264 + 1053*x + 144*x^2 + 192*x^3 - 216*x^4 - 54*x^5 - 48*x^6 + x^9, -304679870005248, 26}, {{23/72, 8/243}, -128 - 144*x + 138*x^3 + 72*x^4 - 27*x^5 - 24*x^6 + x^9, -42845606719488, 18}, {{1/27, 1/2187}, -4 + 6*x + 24*x^2 - 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288*x^2 + 24*x^3 - 54*x^5 + x^9, -76169967501312, 26}, {{-32/75, 128/3375}, 144 + 81*x - 432*x^2 + 144*x^3 - 54*x^5 + x^9, -43873901280755712, 26}, {{-8/75, -16/3375}, 12 - 54*x + 108*x^2 - 90*x^3 - 18*x^4 + 72*x^5 - 6*x^6 - 18*x^7 + x^9, -10711401679872, 26}, {{-1/25, 1/3375}, -24 - 54*x + 180*x^2 + 138*x^3 - 36*x^5 - 12*x^6 + x^9, -76169967501312, 26}, {{7/75, -1/3375}, 96 + 81*x - 72*x^2 + 48*x^3 - 18*x^5 - 24*x^6 + x^9, -4874877920083968, 26}, {{7/75, 8/3375}, -22 - 117*x - 90*x^2 - 72*x^3 - 36*x^4 - 18*x^5 - 12*x^6 + x^9, -1190155742208, 26}, {{16/75, 8/3375}, -716 + 2943*x - 1548*x^2 + 378*x^3 - 396*x^4 + 99*x^5 - 24*x^6 + 18*x^7 + x^9, -4874877920083968, 26}, {{16/75, 32/3375}, 24148 - 10287*x + 252*x^2 + 1626*x^3 - 612*x^4 + 117*x^5 - 18*x^7 + x^9, -43873901280755712, 26}, {{19/75, -1/3375}, -47 - 171*x - 120*x^2 - 24*x^3 + 54*x^4 + 30*x^5 - 3*x^8 + x^9, -60183678025728, 26}, {{1/3, 128/3375}, -4 - 27*x - 54*x^2 - 57*x^3 - 18*x^4 - 9*x^7 + x^9, -2677850419968, 18}, {{32/75, 256/3375}, 9 - 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18*x^3 + 18*x^4 - 12*x^6 + x^9, -1190155742208, 18}, {{7/192, 1/6912}, -4 - 27*x - 54*x^2 - 57*x^3 - 18*x^4 - 9*x^7 + x^9, -2677850419968, 18}, {{-8/147, 4/9261}, 480 + 918*x + 108*x^2 - 378*x^3 + 36*x^4 + 90*x^5 - 12*x^6 + x^9, -685529707511808, 26}, {{-5/147, 1/9261}, -96 - 135*x - 144*x^2 - 192*x^3 - 54*x^5 - 48*x^6 + x^9, -19499511680335872, 26}, {{1/49, 1/9261}, 2 - 6*x + 16*x^3 - 15*x^4 - 3*x^5 - 2*x^6 + 6*x^7 - 3*x^8 + x^9, -82556485632, 16}, {{16/147, 4/9261}, -12 - 54*x - 216*x^2 - 234*x^3 - 36*x^4 - 6*x^6 - 9*x^7 + x^9, -171382426877952, 18}, {{16/147, 64/9261}, -4 + 6*x - 12*x^3 - 12*x^4 - 18*x^5 - 6*x^6 - 3*x^7 + x^9, -235092492288, 18}, {{32/147, 128/9261}, 12 - 36*x + 36*x^2 + 36*x^3 - 105*x^4 + 75*x^5 + 2*x^6 - 6*x^7 - 3*x^8 + x^9, -6687075336192, 16}, {{40/147, -8/9261}, 4 - 12*x + 12*x^4 + 12*x^5 - 3*x^8 + x^9, -330225942528, 19}, {{40/147, 64/9261}, -24 - 54*x + 180*x^2 + 138*x^3 - 36*x^5 - 12*x^6 + x^9, -76169967501312, 26}, {{64/147, 1024/9261}, -60 - 81*x - 108*x^2 - 126*x^3 - 72*x^4 - 72*x^5 - 24*x^6 + x^9, -685529707511808, 26}, {{256/147, 4096/9261}, 4 - 12*x - 8*x^3 + 12*x^4 + 12*x^5 + 4*x^6 - 3*x^8 + x^9, -417942208512, 26}, {{1/75, -1/10125}, -1696 - 1548*x + 1872*x^2 - 384*x^3 - 288*x^4 + 234*x^5 - 48*x^6 + x^9, -43873901280755712, 26}, {{64/225, 256/10125}, 1224 + 729*x + 216*x^2 - 630*x^3 - 108*x^4 - 36*x^6 - 18*x^7 + x^9, -2742118830047232, 26}, {{3/121, 1/11979}, 12 - 27*x^2 - 18*x^3 + 9*x^4 + 9*x^5 - 9*x^6 - 9*x^7 + x^9, -167365651248, 12}, {{32/121, 256/11979}, -2736 - 2187*x + 1728*x^2 + 1080*x^3 - 432*x^4 - 162*x^5 + x^9, -43873901280755712, 26}, {{128/363, 512/11979}, 1416 - 567*x - 1872*x^2 + 1200*x^3 - 216*x^4 + 126*x^5 + x^9, -19499511680335872, 26}, {{-1/60, 1/6750}, -1 - 3*x^3 + x^9, -10460353203, 13}, {{1/4, 64/3375}, -4 - 27*x^3 + 27*x^5 - 9*x^7 + x^9, -74384733888, 12}, {{1/192, -1/13824}, -3 + 4*x^2 - 6*x^4 + x^8, -181398528, 0}, {{64/243, 128/19683}, -3 - 63*x - 324*x^2 + 108*x^3 - 54*x^4 + 18*x^5 + 36*x^6 - 12*x^7 - 3*x^8 + x^9, -240734712102912, 19}, {{64/169, 1024/19773}, -252 + 243*x + 756*x^2 + 270*x^3 - 108*x^4 - 54*x^5 + x^9, -171382426877952, 18}, {{-7/600, 1/27000}, -3 - 6*x^4 + x^8, -573308928, 0}, {{32/147, -256/27783}, 12 - 27*x^2 - 18*x^3 + 9*x^4 + 9*x^5 - 9*x^6 - 9*x^7 + x^9, -167365651248, 12}, {{56/225, -16/30375}, -416 - 171*x + 864*x^2 + 120*x^3 + 72*x^4 - 54*x^5 - 24*x^6 + x^9, -685529707511808, 26}, {{64/225, 512/30375}, -920 - 2223*x - 648*x^2 + 1200*x^3 + 504*x^4 - 54*x^5 - 24*x^6 + x^9, -43873901280755712, 26}, {{4/363, 8/35937}, -4 + 15*x - 12*x^2 + 4*x^3 - 12*x^4 - 6*x^5 - 4*x^6 + x^9, -6687075336192, 26}, {{85/363, -1/35937}, 96 - 216*x + 144*x^2 + 24*x^3 - 24*x^6 + x^9, -304679870005248, 26}, {{256/363, -4096/35937}, -3 + 9*x + 30*x^2 - 26*x^3 - 24*x^4 + 36*x^5 - 14*x^6 + 6*x^7 - 3*x^8 + x^9, -940369969152, 26}, {{-1/125, 1/46875}, -8 + 36*x - 72*x^2 + 96*x^3 - 90*x^4 + 45*x^5 - 9*x^7 + x^9, -4760622968832, 8}, {{8/243, 16/59049}, -8 + 9*x - 12*x^3 - 18*x^5 + x^9, -4760622968832, 26}, {{64/243, 1024/59049}, 1 - 15*x - 72*x^2 + 52*x^3 + 6*x^4 + 18*x^5 - 22*x^6 + 6*x^7 - 3*x^8 + x^9, -940369969152, 26}, {{16/507, 64/59319}, 4 + 3*x - 12*x^2 + 4*x^3 + 12*x^4 - 6*x^5 - 4*x^6 + x^9, -82556485632, 26}, {{64/507, 256/59319}, -640 + 18*x + 900*x^2 - 444*x^3 - 216*x^4 + 180*x^5 - 18*x^7 + x^9, -685529707511808, 26}, {{-5/588, 1/55566}, -1 - 9*x - 27*x^2 - 33*x^3 - 9*x^4 - 12*x^6 - 9*x^7 + x^9, -167365651248, 12}, {{587/1764, 1024/27783}, -4 - 27*x - 54*x^2 - 57*x^3 - 18*x^4 - 9*x^7 + x^9, -2677850419968, 18}, {{384/1225, 4096/128625}, -160 - 882*x - 1116*x^2 - 456*x^3 + 108*x^4 + 108*x^5 - 12*x^6 - 18*x^7 + x^9, -76169967501312, 19}, {{64/867, 512/132651}, -5 + 29*x + 14*x^2 + 6*x^3 - 23*x^4 - 5*x^5 - 6*x^6 + 2*x^7 - x^8 + x^9, -743008370688, 26}, {{-7/2187, 1/177147}, 48 - 135*x + 72*x^2 + 48*x^3 - 18*x^5 - 24*x^6 + x^9, -19499511680335872, 26}, {{-5/1083, 1/185193}, -60 - 81*x - 84*x^2 - 92*x^3 - 36*x^4 - 30*x^5 - 4*x^6 + x^9, -6687075336192, 26}, {{1/1083, 1/185193}, 4 - 12*x - 8*x^3 + 12*x^4 + 12*x^5 + 4*x^6 - 3*x^8 + x^9, -417942208512, 26}, {{64/1083, -512/185193}, 4 - 12*x + 32*x^3 + 12*x^4 + 12*x^5 - 16*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{208/1083, 64/185193}, -16 - 72*x - 54*x^2 - 3*x^3 + 36*x^4 + 27*x^5 - 6*x^6 - 9*x^7 + x^9, -4760622968832, 18}, {{271/1083, 1/185193}, -5 + 29*x + 14*x^2 + 6*x^3 - 23*x^4 - 5*x^5 - 6*x^6 + 2*x^7 - x^8 + x^9, -743008370688, 26}, {{128/361, 8192/185193}, 924 - 405*x - 1692*x^2 + 12*x^3 + 540*x^4 - 54*x^5 - 60*x^6 + x^9, -4874877920083968, 26}, {{19/2028, 1/59319}, -4 - 27*x^3 + 27*x^5 - 9*x^7 + x^9, -74384733888, 12}, {{-128/1587, 512/328509}, 96 - 135*x - 288*x^2 + 192*x^3 - 54*x^5 + x^9, -19499511680335872, 26}, {{16/1587, -64/328509}, 4 - 12*x - 16*x^3 + 12*x^4 + 12*x^5 + 8*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{-1/289, -1/397953}, -128 - 144*x + 138*x^3 + 72*x^4 - 27*x^5 - 24*x^6 + x^9, -42845606719488, 18}, {{128/375, 16384/421875}, -12 - 54*x - 216*x^2 - 234*x^3 - 36*x^4 - 6*x^6 - 9*x^7 + x^9, -171382426877952, 18}, {{256/841, 16384/658503}, 12 - 15*x - 48*x^2 + 36*x^3 + 24*x^4 - 42*x^5 + 16*x^6 + 4*x^7 - 4*x^8 + x^9, -743008370688, 26}, {{16/2883, 64/804357}, 10 + 6*x + 54*x^2 - 22*x^3 + 12*x^4 + 12*x^5 - 4*x^6 - 3*x^8 + x^9, -940369969152, 26}, {{51/4232, 4/109503}, 12 + 162*x + 216*x^2 + 126*x^3 + 36*x^4 - 18*x^6 - 9*x^7 + x^9, -171382426877952, 18}, {{512/1587, 32768/985527}, 64 + 108*x - 24*x^3 - 54*x^5 - 24*x^6 + x^9, -43873901280755712, 26}, {{928/3675, 512/1157625}, 4 + 3*x - 12*x^2 + 4*x^3 + 12*x^4 - 6*x^5 - 4*x^6 + x^9, -82556485632, 26}, {{-8/1125, 16/1265625}, -4 - 27*x - 54*x^2 - 57*x^3 - 18*x^4 - 9*x^7 + x^9, -2677850419968, 18}, {{35/5046, 8/658503}, 2 - 4*x^3 + x^6, 1492992, 0}, {{1024/5043, 32768/1860867}, -16 + 105*x - 48*x^2 + 64*x^3 - 48*x^4 - 6*x^5 - 16*x^6 + x^9, -26748301344768, 26}, {{1024/7203, -32768/3176523}, 48 + 117*x - 16*x^3 + 120*x^4 - 24*x^5 - 24*x^6 + x^9, -26748301344768, 26}, {{-5/23409, 1/10744731}, 152 + 558*x - 576*x^2 - 228*x^3 + 144*x^4 + 144*x^5 - 72*x^6 + x^9, -43873901280755712, 26}, {{5888/23409, 8192/10744731}, 144 + 81*x - 432*x^2 + 144*x^3 - 54*x^5 + x^9, -43873901280755712, 26}, {{1024/3375, 262144/11390625}, -16 - 72*x - 54*x^2 - 3*x^3 + 36*x^4 + 27*x^5 - 6*x^6 - 9*x^7 + x^9, -4760622968832, 18}, {{16/17787, -64/12326391}, 4 - 12*x - 8*x^3 + 12*x^4 + 12*x^5 + 4*x^6 - 3*x^8 + x^9, -417942208512, 26}, {{-11/21675, 1/16581375}, -264 + 1053*x + 144*x^2 + 192*x^3 - 216*x^4 - 54*x^5 - 48*x^6 + x^9, -304679870005248, 26}, {{19/220323, 1/537367797}, 48 + 117*x - 16*x^3 + 120*x^4 - 24*x^5 - 24*x^6 + x^9, -26748301344768, 26}, {{114688/344569, 67108864/1820358027}, 180 + 243*x - 540*x^2 + 108*x^3 - 108*x^4 - 54*x^5 - 36*x^6 + x^9, -43873901280755712, 26}, {{-24, 36}, 10 + 6*x + 54*x^2 - 22*x^3 + 12*x^4 + 12*x^5 - 4*x^6 - 3*x^8 + x^9, -940369969152, 26}, {{-9, -9}, 8 + 9*x - 48*x^2 + 6*x^3 + 60*x^4 + 12*x^5 - 12*x^6 - 6*x^7 + x^9, -417942208512, 19}, {{-6, -18}, -648 + 1944*x - 2016*x^2 + 1072*x^3 - 228*x^4 - 84*x^5 + 68*x^6 - 12*x^7 - 3*x^8 + x^9, -240734712102912, 26}, {{-4, -4}, 4 - 12*x - 8*x^3 + 12*x^4 + 12*x^5 + 4*x^6 - 3*x^8 + x^9, -417942208512, 26}, {{-4, 32/27}, -3 + 9*x + 30*x^2 - 26*x^3 - 24*x^4 + 36*x^5 - 14*x^6 + 6*x^7 - 3*x^8 + x^9, -940369969152, 26}, {{-4, 2}, -4 + 15*x - 12*x^2 + 4*x^3 - 12*x^4 - 6*x^5 - 4*x^6 + x^9, -6687075336192, 26}, {{-3, -3}, 73 - 171*x + 96*x^2 - 24*x^3 - 18*x^4 + 30*x^5 + 24*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{-3, 1}, 4 - 12*x + 12*x^4 + 12*x^5 - 3*x^8 + x^9, -330225942528, 19}, {{-3, 9}, 36 - 108*x + 96*x^3 - 36*x^4 - 36*x^5 + 16*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{-7/3, 1/3}, 12 - 15*x - 48*x^2 + 36*x^3 + 24*x^4 - 42*x^5 + 16*x^6 + 4*x^7 - 4*x^8 + x^9, -743008370688, 26}, {{-56/25, 96/125}, -2 + 6*x + 108*x^2 + 44*x^3 - 24*x^4 - 24*x^5 + 20*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{-2, -2}, 2 - 6*x + 16*x^3 - 15*x^4 - 3*x^5 - 2*x^6 + 6*x^7 - 3*x^8 + x^9, -82556485632, 16}, {{-15/8, 9/16}, -3 + 9*x + 30*x^2 - 26*x^3 - 24*x^4 + 36*x^5 - 14*x^6 + 6*x^7 - 3*x^8 + x^9, -940369969152, 26}, {{-9/5, -729/125}, 48 + 117*x - 16*x^3 + 120*x^4 - 24*x^5 - 24*x^6 + x^9, -26748301344768, 26}, {{-3/2, -3/2}, 9 - 27*x + 72*x^3 - 18*x^4 - 18*x^5 + 24*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{-4/3, -4/3}, -3 + 9*x + 30*x^2 - 26*x^3 - 24*x^4 + 36*x^5 - 14*x^6 + 6*x^7 - 3*x^8 + x^9, -940369969152, 26}, {{-4/3, 8/27}, -47 - 171*x - 120*x^2 - 24*x^3 + 54*x^4 + 30*x^5 - 3*x^8 + x^9, -60183678025728, 26}, {{-63/50, 81/250}, -3 + 8*x^2 + 6*x^4 + x^8, -9172942848, 0}, {{-5/4, 3/2}, -3 - 4*x^2 - 6*x^4 + x^8, -725594112, 0}, {{-7/6, 1/27}, 2 - 4*x^3 + x^6, 1492992, 0}, {{-9/8, -9/8}, 8 + 9*x - 48*x^2 + 6*x^3 + 60*x^4 + 12*x^5 - 12*x^6 - 6*x^7 + x^9, -417942208512, 19}, {{-8/9, -8/9}, 48 + 117*x - 16*x^3 + 120*x^4 - 24*x^5 - 24*x^6 + x^9, -26748301344768, 26}, {{-8/9, 4/27}, 4 + 3*x - 12*x^2 + 4*x^3 + 12*x^4 - 6*x^5 - 4*x^6 + x^9, -82556485632, 26}, {{-3/4, -3/4}, 1 - 6*x + 15*x^2 - 15*x^3 - 3*x^4 + 12*x^5 - 6*x^6 + 3*x^7 - 3*x^8 + x^9, -918330048, 4}, {{-2/3, -2/3}, 4 - 12*x + 32*x^3 + 12*x^4 + 12*x^5 - 16*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{-2/3, -8/27}, 8 + 9*x - 48*x^2 + 6*x^3 + 60*x^4 + 12*x^5 - 12*x^6 - 6*x^7 + x^9, -417942208512, 19}, {{-2/3, 2/27}, -3 - 63*x - 324*x^2 + 108*x^3 - 54*x^4 + 18*x^5 + 36*x^6 - 12*x^7 - 3*x^8 + x^9, -240734712102912, 19}, {{-3/5, 9/125}, 12 - 36*x + 36*x^2 + 36*x^3 - 105*x^4 + 75*x^5 + 2*x^6 - 6*x^7 - 3*x^8 + x^9, -6687075336192, 16}, {{-1/2, -3/2}, -2 + 6*x + 108*x^2 + 44*x^3 - 24*x^4 - 24*x^5 + 20*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{-1/2, -1/2}, 4 + 3*x - 12*x^2 + 4*x^3 + 12*x^4 - 6*x^5 - 4*x^6 + x^9, -82556485632, 26}, {{-1/2, 1/54}, -60 - 81*x - 84*x^2 - 92*x^3 - 36*x^4 - 30*x^5 - 4*x^6 + x^9, -6687075336192, 26}, {{-3/7, -27/343}, -3 + 9*x + 30*x^2 - 26*x^3 - 24*x^4 + 36*x^5 - 14*x^6 + 6*x^7 - 3*x^8 + x^9, -940369969152, 26}, {{-9/25, 3/125}, 9 - 27*x + 18*x^4 + 18*x^5 - 3*x^8 + x^9, -940369969152, 19}, {{-1/3, -1/3}, 4 - 12*x - 16*x^3 + 12*x^4 + 12*x^5 + 8*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{-1/3, -1/27}, 9 - 27*x + 72*x^3 - 18*x^4 - 18*x^5 + 24*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{-16/49, 8/343}, -5 + 29*x + 14*x^2 + 6*x^3 - 23*x^4 - 5*x^5 - 6*x^6 + 2*x^7 - x^8 + x^9, -743008370688, 26}, {{-153/512, 81/4096}, 4 - 12*x - 8*x^3 + 12*x^4 + 12*x^5 + 4*x^6 - 3*x^8 + x^9, -417942208512, 26}, {{-1/4, -1/4}, -3 + 4*x^2 - 6*x^4 + x^8, -181398528, 0}, {{-1053/4489, 6561/300763}, -5 + 29*x + 14*x^2 + 6*x^3 - 23*x^4 - 5*x^5 - 6*x^6 + 2*x^7 - x^8 + x^9, -743008370688, 26}, {{-1/5, -1/125}, 2 - 6*x + 16*x^3 - 15*x^4 - 3*x^5 - 2*x^6 + 6*x^7 - 3*x^8 + x^9, -82556485632, 16}, {{-24/121, 12/1331}, -4 + 6*x - 12*x^3 - 12*x^4 - 18*x^5 - 6*x^6 - 3*x^7 + x^9, -235092492288, 18}, {{-9/49, 81/343}, -4 + 15*x - 12*x^2 + 4*x^3 - 12*x^4 - 6*x^5 - 4*x^6 + x^9, -6687075336192, 26}, {{-45/289, 27/4913}, 4 + 3*x - 12*x^2 + 4*x^3 + 12*x^4 - 6*x^5 - 4*x^6 + x^9, -82556485632, 26}, {{-4/27, 2/729}, 9 - 27*x - 24*x^3 - 18*x^4 - 18*x^5 - 8*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{-1/9, -1/9}, 4 - 12*x - 8*x^3 + 12*x^4 + 12*x^5 + 4*x^6 - 3*x^8 + x^9, -417942208512, 26}, {{-1/9, -1/729}, 73 - 171*x + 96*x^2 - 24*x^3 - 18*x^4 + 30*x^5 + 24*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{-8/75, 8/3375}, 4 - 12*x - 12*x^4 - 12*x^5 - 3*x^8 + x^9, -26748301344768, 19}, {{-1/13, -1/2197}, 4 - 12*x - 8*x^3 + 12*x^4 + 12*x^5 + 4*x^6 - 3*x^8 + x^9, -417942208512, 26}, {{-64/961, 32/29791}, -16 + 105*x - 48*x^2 + 64*x^3 - 48*x^4 - 6*x^5 - 16*x^6 + x^9, -26748301344768, 26}, {{-8/169, 32/59319}, 4 - 12*x - 16*x^3 + 12*x^4 + 12*x^5 + 8*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{-1/33, -1/35937}, 8 + 9*x - 48*x^2 + 6*x^3 + 60*x^4 + 12*x^5 - 12*x^6 - 6*x^7 + x^9, -417942208512, 19}, {{-32/2523, 8/658503}, 124 + 183*x - 108*x^2 - 174*x^3 - 12*x^4 + 27*x^5 - 6*x^7 + x^9, -6687075336192, 26}, {{0, -2/27}, 73 - 171*x + 96*x^2 - 24*x^3 - 18*x^4 + 30*x^5 + 24*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{171/8281, 81/753571}, 124 + 183*x - 108*x^2 - 174*x^3 - 12*x^4 + 27*x^5 - 6*x^7 + x^9, -6687075336192, 26}, {{4/147, -8/9261}, 4 + 3*x - 12*x^2 + 4*x^3 + 12*x^4 - 6*x^5 - 4*x^6 + x^9, -82556485632, 26}, {{51/1849, 9/79507}, 4 - 12*x - 16*x^3 + 12*x^4 + 12*x^5 + 8*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{1/35, 1/42875}, -16 + 105*x - 48*x^2 + 64*x^3 - 48*x^4 - 6*x^5 - 16*x^6 + x^9, -26748301344768, 26}, {{72/1369, 36/50653}, 8 + 9*x - 48*x^2 + 6*x^3 + 60*x^4 + 12*x^5 - 12*x^6 - 6*x^7 + x^9, -417942208512, 19}, {{3/49, -3/343}, -47 - 171*x - 120*x^2 - 24*x^3 + 54*x^4 + 30*x^5 - 3*x^8 + x^9, -60183678025728, 26}, {{1/16, -3/32}, -3 - 4*x^2 - 6*x^4 + x^8, -725594112, 0}, {{1/15, 1/3375}, -4 + 6*x - 12*x^3 - 12*x^4 - 18*x^5 - 6*x^6 - 3*x^7 + x^9, -235092492288, 18}, {{2/27, -16/729}, 10 + 6*x + 54*x^2 - 22*x^3 + 12*x^4 + 12*x^5 - 4*x^6 - 3*x^8 + x^9, -940369969152, 26}, {{2/27, -2/729}, 12 - 36*x + 36*x^2 + 36*x^3 - 105*x^4 + 75*x^5 + 2*x^6 - 6*x^7 - 3*x^8 + x^9, -6687075336192, 16}, {{27/361, 9/6859}, 4 - 12*x - 12*x^4 - 12*x^5 - 3*x^8 + x^9, -26748301344768, 19}, {{29/384, -1/13824}, 4 - 12*x - 8*x^3 + 12*x^4 + 12*x^5 + 4*x^6 - 3*x^8 + x^9, -417942208512, 26}, {{1/11, 1/1331}, -5 + 29*x + 14*x^2 + 6*x^3 - 23*x^4 - 5*x^5 - 6*x^6 + 2*x^7 - x^8 + x^9, -743008370688, 26}, {{32/289, 16/4913}, 4 - 12*x - 8*x^3 + 12*x^4 + 12*x^5 + 4*x^6 - 3*x^8 + x^9, -417942208512, 26}, {{1/9, -1/27}, 2 - 6*x + 16*x^3 - 15*x^4 - 3*x^5 - 2*x^6 + 6*x^7 - 3*x^8 + x^9, -82556485632, 16}, {{21/169, 9/2197}, 9 - 27*x - 24*x^3 - 18*x^4 - 18*x^5 - 8*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{1/8, -1/16}, -3 + 40*x^2 - 6*x^4 + x^8, -11609505792, 0}, {{1/8, -1/432}, -3 + 9*x + 30*x^2 - 26*x^3 - 24*x^4 + 36*x^5 - 14*x^6 + 6*x^7 - 3*x^8 + x^9, -940369969152, 26}, {{1/8, 1/8}, 4 - 12*x - 8*x^3 + 12*x^4 + 12*x^5 + 4*x^6 - 3*x^8 + x^9, -417942208512, 26}, {{51/392, 9/1372}, 10 + 6*x + 54*x^2 - 22*x^3 + 12*x^4 + 12*x^5 - 4*x^6 - 3*x^8 + x^9, -940369969152, 26}, {{24/169, 12/2197}, 73 - 171*x + 96*x^2 - 24*x^3 - 18*x^4 + 30*x^5 + 24*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{1/7, 1/343}, 4 + 3*x - 12*x^2 + 4*x^3 + 12*x^4 - 6*x^5 - 4*x^6 + x^9, -82556485632, 26}, {{4/27, 4/729}, 9 - 27*x + 18*x^4 + 18*x^5 - 3*x^8 + x^9, -940369969152, 19}, {{43/289, 3/4913}, -2 + 6*x + 108*x^2 + 44*x^3 - 24*x^4 - 24*x^5 + 20*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{15/98, -18/343}, 10 + 6*x + 54*x^2 - 22*x^3 + 12*x^4 + 12*x^5 - 4*x^6 - 3*x^8 + x^9, -940369969152, 26}, {{4/25, -6/125}, -2 + 6*x + 108*x^2 + 44*x^3 - 24*x^4 - 24*x^5 + 20*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{1/6, -1/27}, -4 + 6*x - 12*x^3 - 12*x^4 - 18*x^5 - 6*x^6 - 3*x^7 + x^9, -235092492288, 18}, {{1/6, -1/54}, 9 - 27*x + 72*x^3 - 18*x^4 - 18*x^5 + 24*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{9/49, 3/343}, -3 - 63*x - 324*x^2 + 108*x^3 - 54*x^4 + 18*x^5 + 36*x^6 - 12*x^7 - 3*x^8 + x^9, -240734712102912, 19}, {{5/27, -1/81}, -3 + 9*x + 30*x^2 - 26*x^3 - 24*x^4 + 36*x^5 - 14*x^6 + 6*x^7 - 3*x^8 + x^9, -940369969152, 26}, {{3/16, -1/32}, -3 + 6*x^4 + x^8, -143327232, 0}, {{16/81, 8/729}, 2 - 6*x + 16*x^3 - 15*x^4 - 3*x^5 - 2*x^6 + 6*x^7 - 3*x^8 + x^9, -82556485632, 16}, {{1/5, -3/125}, -16 + 105*x - 48*x^2 + 64*x^3 - 48*x^4 - 6*x^5 - 16*x^6 + x^9, -26748301344768, 26}, {{1/5, 1/125}, -4 + 15*x - 12*x^2 + 4*x^3 - 12*x^4 - 6*x^5 - 4*x^6 + x^9, -6687075336192, 26}, {{10/49, -18/343}, 124 + 183*x - 108*x^2 - 174*x^3 - 12*x^4 + 27*x^5 - 6*x^7 + x^9, -6687075336192, 26}, {{5/24, -1/216}, 8 + 9*x - 48*x^2 + 6*x^3 + 60*x^4 + 12*x^5 - 12*x^6 - 6*x^7 + x^9, -417942208512, 19}, {{3/14, 9/686}, -60 - 81*x - 84*x^2 - 92*x^3 - 36*x^4 - 30*x^5 - 4*x^6 + x^9, -6687075336192, 26}, {{297/1369, 729/50653}, 4 - 35*x + 104*x^2 - 124*x^3 + 88*x^4 - 40*x^5 + 8*x^6 + 4*x^7 - 4*x^8 + x^9, -2972033482752, 26}, {{7/32, -1/64}, -3 + 16*x^2 - 6*x^4 + x^8, -46438023168, 0}, {{64/289, -72/4913}, 124 + 183*x - 108*x^2 - 174*x^3 - 12*x^4 + 27*x^5 - 6*x^7 + x^9, -6687075336192, 26}, {{27/121, 81/1331}, 4 - 12*x + 12*x^4 + 12*x^5 - 3*x^8 + x^9, -330225942528, 19}, {{17/75, -1/125}, -60 - 81*x - 84*x^2 - 92*x^3 - 36*x^4 - 30*x^5 - 4*x^6 + x^9, -6687075336192, 26}, {{11/48, -1/96}, -12 + 12*x^2 - 4*x^6 + x^8, -725594112, 0}, {{3/13, 27/2197}, 10 + 6*x + 54*x^2 - 22*x^3 + 12*x^4 + 12*x^5 - 4*x^6 - 3*x^8 + x^9, -940369969152, 26}, {{15/64, 9/256}, -3 + 9*x + 30*x^2 - 26*x^3 - 24*x^4 + 36*x^5 - 14*x^6 + 6*x^7 - 3*x^8 + x^9, -940369969152, 26}, {{19/81, 1/243}, 48 + 117*x - 16*x^3 + 120*x^4 - 24*x^5 - 24*x^6 + x^9, -26748301344768, 26}, {{6/25, 2/125}, 4 - 12*x + 12*x^4 + 12*x^5 - 3*x^8 + x^9, -330225942528, 19}, {{13/54, -2/729}, 10 + 6*x + 54*x^2 - 22*x^3 + 12*x^4 + 12*x^5 - 4*x^6 - 3*x^8 + x^9, -940369969152, 26}, {{31/128, -1/256}, -3 + 10*x^2 - 6*x^4 + x^8, -11609505792, 0}, {{12/49, 6/343}, 9 - 27*x + 72*x^3 - 18*x^4 - 18*x^5 + 24*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{1/4, 1/108}, 1 - 6*x + 15*x^2 - 15*x^3 - 3*x^4 + 12*x^5 - 6*x^6 + 3*x^7 - 3*x^8 + x^9, -918330048, 4}, {{91/361, 9/6859}, 124 + 183*x - 108*x^2 - 174*x^3 - 12*x^4 + 27*x^5 - 6*x^7 + x^9, -6687075336192, 26}, {{37/144, 1/288}, -3 - 4*x^2 - 6*x^4 + x^8, -725594112, 0}, {{7/27, 1/81}, 4 - 12*x + 32*x^3 + 12*x^4 + 12*x^5 - 16*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{63/242, 27/1331}, 2 - 4*x^3 + x^6, 1492992, 0}, {{13/49, 3/343}, -2 + 6*x + 108*x^2 + 44*x^3 - 24*x^4 - 24*x^5 + 20*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{17/64, 1/128}, -3 + 4*x^2 - 6*x^4 + x^8, -181398528, 0}, {{96/361, 144/6859}, -3 + 9*x + 30*x^2 - 26*x^3 - 24*x^4 + 36*x^5 - 14*x^6 + 6*x^7 - 3*x^8 + x^9, -940369969152, 26}, {{4/15, 8/375}, 12 - 15*x - 48*x^2 + 36*x^3 + 24*x^4 - 42*x^5 + 16*x^6 + 4*x^7 - 4*x^8 + x^9, -743008370688, 26}, {{13/48, 1/96}, -27 - 48*x^2 - 18*x^4 + x^8, -11609505792, 0}, {{459/1681, 2187/68921}, 12 - 15*x - 48*x^2 + 36*x^3 + 24*x^4 - 42*x^5 + 16*x^6 + 4*x^7 - 4*x^8 + x^9, -743008370688, 26}, {{5/18, 1/54}, 4 + 3*x - 12*x^2 + 4*x^3 + 12*x^4 - 6*x^5 - 4*x^6 + x^9, -82556485632, 26}, {{9/32, 1/64}, -3 - 6*x^4 + x^8, -573308928, 0}, {{9/32, 3/128}, 9 - 27*x + 18*x^4 + 18*x^5 - 3*x^8 + x^9, -940369969152, 19}, {{2/7, 6/343}, -16 + 105*x - 48*x^2 + 64*x^3 - 48*x^4 - 6*x^5 - 16*x^6 + x^9, -26748301344768, 26}, {{2/7, 8/343}, 4 - 12*x - 8*x^3 + 12*x^4 + 12*x^5 + 4*x^6 - 3*x^8 + x^9, -417942208512, 26}, {{7/24, 1/48}, -27 + 48*x^2 - 18*x^4 + x^8, -11609505792, 0}, {{8/27, 2/81}, 4 - 12*x - 16*x^3 + 12*x^4 + 12*x^5 + 8*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{19/64, 3/128}, -3 - 4*x^2 - 6*x^4 + x^8, -725594112, 0}, {{36/121, 36/1331}, 8 + 9*x - 48*x^2 + 6*x^3 + 60*x^4 + 12*x^5 - 12*x^6 - 6*x^7 + x^9, -417942208512, 19}, {{44/147, 8/343}, -60 - 81*x - 84*x^2 - 92*x^3 - 36*x^4 - 30*x^5 - 4*x^6 + x^9, -6687075336192, 26}, {{3/10, 3/125}, -4 + 6*x - 12*x^3 - 12*x^4 - 18*x^5 - 6*x^6 - 3*x^7 + x^9, -235092492288, 18}, {{3/10, 9/250}, 9 - 27*x - 24*x^3 - 18*x^4 - 18*x^5 - 8*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{11/36, 1/36}, -3 + 4*x^2 - 6*x^4 + x^8, -181398528, 0}, {{37/121, 27/1331}, 124 + 183*x - 108*x^2 - 174*x^3 - 12*x^4 + 27*x^5 - 6*x^7 + x^9, -6687075336192, 26}, {{90/289, 162/4913}, 124 + 183*x - 108*x^2 - 174*x^3 - 12*x^4 + 27*x^5 - 6*x^7 + x^9, -6687075336192, 26}, {{54/169, 72/2197}, 8 + 9*x - 48*x^2 + 6*x^3 + 60*x^4 + 12*x^5 - 12*x^6 - 6*x^7 + x^9, -417942208512, 19}, {{41/128, 9/256}, -3 - 10*x^2 - 6*x^4 + x^8, -11609505792, 0}, {{26/81, 8/243}, 4 - 12*x - 8*x^3 + 12*x^4 + 12*x^5 + 4*x^6 - 3*x^8 + x^9, -417942208512, 26}, {{117/361, 243/6859}, 124 + 183*x - 108*x^2 - 174*x^3 - 12*x^4 + 27*x^5 - 6*x^7 + x^9, -6687075336192, 26}, {{276/841, 864/24389}, -3 + 9*x + 30*x^2 - 26*x^3 - 24*x^4 + 36*x^5 - 14*x^6 + 6*x^7 - 3*x^8 + x^9, -940369969152, 26}, {{174/529, 432/12167}, 10 + 6*x + 54*x^2 - 22*x^3 + 12*x^4 + 12*x^5 - 4*x^6 - 3*x^8 + x^9, -940369969152, 26}, {{1674/5041, 13122/357911}, 4 - 35*x + 104*x^2 - 124*x^3 + 88*x^4 - 40*x^5 + 8*x^6 + 4*x^7 - 4*x^8 + x^9, -2972033482752, 26}, {{639/1922, 2187/59582}, -3 + 8*x^2 + 6*x^4 + x^8, -9172942848, 0}, {{1/3, 1/24}, 1 - 2*x^2 - 2*x^3 - 2*x^5 - 2*x^6 + x^8, -181398528, 0}, {{1/3, 2/27}, 9 - 27*x + 18*x^4 + 18*x^5 - 3*x^8 + x^9, -940369969152, 19}, {{1/3, 1/3}, 10 + 6*x + 54*x^2 - 22*x^3 + 12*x^4 + 12*x^5 - 4*x^6 - 3*x^8 + x^9, -940369969152, 26}, {{771/2312, 729/19652}, 10 + 6*x + 54*x^2 - 22*x^3 + 12*x^4 + 12*x^5 - 4*x^6 - 3*x^8 + x^9, -940369969152, 26}, {{22032/66049, 629856/16974593}, -5 + 29*x + 14*x^2 + 6*x^3 - 23*x^4 - 5*x^5 - 6*x^6 + 2*x^7 - x^8 + x^9, -743008370688, 26}, {{33/98, 27/686}, 9 - 27*x - 24*x^3 - 18*x^4 - 18*x^5 - 8*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{1512/4489, 11664/300763}, 12 - 15*x - 48*x^2 + 36*x^3 + 24*x^4 - 42*x^5 + 16*x^6 + 4*x^7 - 4*x^8 + x^9, -743008370688, 26}, {{57/169, 81/2197}, -648 + 1944*x - 2016*x^2 + 1072*x^3 - 228*x^4 - 84*x^5 + 68*x^6 - 12*x^7 - 3*x^8 + x^9, -240734712102912, 26}, {{87/256, 81/2048}, -3 + 9*x + 30*x^2 - 26*x^3 - 24*x^4 + 36*x^5 - 14*x^6 + 6*x^7 - 3*x^8 + x^9, -940369969152, 26}, {{17/50, 9/250}, -2 + 6*x + 108*x^2 + 44*x^3 - 24*x^4 - 24*x^5 + 20*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{67/196, 27/686}, -3 - 4*x^2 - 6*x^4 + x^8, -725594112, 0}, {{288/841, 972/24389}, -4 + 15*x - 12*x^2 + 4*x^3 - 12*x^4 - 6*x^5 - 4*x^6 + x^9, -6687075336192, 26}, {{576/1681, 2592/68921}, 48 + 117*x - 16*x^3 + 120*x^4 - 24*x^5 - 24*x^6 + x^9, -26748301344768, 26}, {{11/32, 3/64}, -3 - 16*x^2 - 6*x^4 + x^8, -46438023168, 0}, {{216/625, 648/15625}, 4 - 12*x + 12*x^4 + 12*x^5 - 3*x^8 + x^9, -330225942528, 19}, {{42/121, 54/1331}, 36 - 108*x + 96*x^3 - 36*x^4 - 36*x^5 + 16*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{25/72, 1/24}, 4 - 12*x - 8*x^3 + 12*x^4 + 12*x^5 + 4*x^6 - 3*x^8 + x^9, -417942208512, 26}, {{9/25, 6/125}, 9 - 27*x + 18*x^4 + 18*x^5 - 3*x^8 + x^9, -940369969152, 19}, {{9/25, 9/125}, 4 - 12*x - 12*x^4 - 12*x^5 - 3*x^8 + x^9, -26748301344768, 19}, {{18/49, 18/343}, 4 - 12*x - 12*x^4 - 12*x^5 - 3*x^8 + x^9, -26748301344768, 19}, {{10/27, 4/81}, 10 + 6*x + 54*x^2 - 22*x^3 + 12*x^4 + 12*x^5 - 4*x^6 - 3*x^8 + x^9, -940369969152, 26}, {{3/8, 3/64}, 1 - 6*x + 15*x^2 - 15*x^3 - 3*x^4 + 12*x^5 - 6*x^6 + 3*x^7 - 3*x^8 + x^9, -918330048, 4}, {{3/8, 1/16}, -3 + 6*x^4 + x^8, -143327232, 0}, {{112/289, 96/4913}, 124 + 183*x - 108*x^2 - 174*x^3 - 12*x^4 + 27*x^5 - 6*x^7 + x^9, -6687075336192, 26}, {{7/18, 1/18}, -4 + 15*x - 12*x^2 + 4*x^3 - 12*x^4 - 6*x^5 - 4*x^6 + x^9, -6687075336192, 26}, {{9/23, 729/12167}, 4 - 12*x - 8*x^3 + 12*x^4 + 12*x^5 + 4*x^6 - 3*x^8 + x^9, -417942208512, 26}, {{67/169, -81/2197}, 124 + 183*x - 108*x^2 - 174*x^3 - 12*x^4 + 27*x^5 - 6*x^7 + x^9, -6687075336192, 26}, {{48/121, 72/1331}, 4 - 12*x + 32*x^3 + 12*x^4 + 12*x^5 - 16*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{2/5, 6/125}, 48 + 117*x - 16*x^3 + 120*x^4 - 24*x^5 - 24*x^6 + x^9, -26748301344768, 26}, {{123/289, 243/4913}, -60 - 81*x - 84*x^2 - 92*x^3 - 36*x^4 - 30*x^5 - 4*x^6 + x^9, -6687075336192, 26}, {{72/169, 324/2197}, 4 - 12*x - 8*x^3 + 12*x^4 + 12*x^5 + 4*x^6 - 3*x^8 + x^9, -417942208512, 26}, {{7/16, 3/32}, -3 - 40*x^2 - 6*x^4 + x^8, -11609505792, 0}, {{4/9, 2/27}, 4 + 3*x - 12*x^2 + 4*x^3 + 12*x^4 - 6*x^5 - 4*x^6 + x^9, -82556485632, 26}, {{24/49, 36/343}, 4 - 12*x - 16*x^3 + 12*x^4 + 12*x^5 + 8*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{1/2, 1/8}, -3 + 4*x^2 - 6*x^4 + x^8, -181398528, 0}, {{1/2, 1/2}, -4 + 15*x - 12*x^2 + 4*x^3 - 12*x^4 - 6*x^5 - 4*x^6 + x^9, -6687075336192, 26}, {{5/9, 1/9}, -5 + 29*x + 14*x^2 + 6*x^3 - 23*x^4 - 5*x^5 - 6*x^6 + 2*x^7 - x^8 + x^9, -743008370688, 26}, {{3/5, 27/125}, 4 - 12*x - 16*x^3 + 12*x^4 + 12*x^5 + 8*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{16/25, 12/125}, -2 + 6*x + 108*x^2 + 44*x^3 - 24*x^4 - 24*x^5 + 20*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{2/3, 4/27}, -4 + 6*x - 12*x^3 - 12*x^4 - 18*x^5 - 6*x^6 - 3*x^7 + x^9, -235092492288, 18}, {{13/16, 9/32}, -3 - 4*x^2 - 6*x^4 + x^8, -725594112, 0}, {{24/25, -144/125}, -60 - 81*x - 84*x^2 - 92*x^3 - 36*x^4 - 30*x^5 - 4*x^6 + x^9, -6687075336192, 26}, {{1, -3}, 48 + 117*x - 16*x^3 + 120*x^4 - 24*x^5 - 24*x^6 + x^9, -26748301344768, 26}, {{1, 1}, 4 + 3*x - 12*x^2 + 4*x^3 + 12*x^4 - 6*x^5 - 4*x^6 + x^9, -82556485632, 26}, {{11/9, 1/3}, -16 + 105*x - 48*x^2 + 64*x^3 - 48*x^4 - 6*x^5 - 16*x^6 + x^9, -26748301344768, 26}, {{2, 2}, -5 + 29*x + 14*x^2 + 6*x^3 - 23*x^4 - 5*x^5 - 6*x^6 + 2*x^7 - x^8 + x^9, -743008370688, 26}, {{3, 3}, -4 + 6*x - 12*x^3 - 12*x^4 - 18*x^5 - 6*x^6 - 3*x^7 + x^9, -235092492288, 18}, {{3, 27}, 4 - 12*x + 32*x^3 + 12*x^4 + 12*x^5 - 16*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{7, -9}, -2 + 6*x + 108*x^2 + 44*x^3 - 24*x^4 - 24*x^5 + 20*x^6 - 3*x^8 + x^9, -60183678025728, 26}, {{8, 8}, -16 + 105*x - 48*x^2 + 64*x^3 - 48*x^4 - 6*x^5 - 16*x^6 + x^9, -26748301344768, 26}} (* Section six. A degree 52 family: tame-ramification and exceptions to Principle B *) (* One of two main polynomials, this one with 2721 terms *) f52[{u_, v_}] := 25389989167104*u^9*x^46 + 533189772509184*u^9*x^45 + 5027217855086592*u^9*x^44 + 27370408322138112*u^9*x^43 + 89652051749044224*u^9*x^42 + 146627187440025600*u^9*x^41 - 99427197578379264*u^9*x^40 - 1136151235249569792*u^9*x^39 - 2497689404335521792*u^9*x^38 - 1030858950173589504*u^9*x^37 + 7076647000676892672*u^9*x^36 + 16883682656405815296*u^9*x^35 + 8906224230069239808*u^9*x^34 - 29770346268180283392*u^9*x^33 - 65648762230290776064*u^9*x^32 - 28398195083622481920*u^9*x^31 + 89921845773933871104*u^9*x^30 + 161194389044781514752*u^9*x^29 + 43186035694240530432*u^9*x^28 - 189817691772359540736*u^9*x^27 - 257609724548202233856*u^9*x^26 - 22597344258614231040*u^9*x^25 + 271168131103370772480*u^9*x^24 + 271168131103370772480*u^9*x^23 - 22597344258614231040*u^9*x^22 - 257609724548202233856*u^9*x^21 - 189817691772359540736*u^9*x^20 + 43186035694240530432*u^9*x^19 + 161194389044781514752*u^9*x^18 + 89921845773933871104*u^9*x^17 - 28398195083622481920*u^9*x^16 - 65648762230290776064*u^9*x^15 - 29770346268180283392*u^9*x^14 + 8906224230069239808*u^9*x^13 + 16883682656405815296*u^9*x^12 + 7076647000676892672*u^9*x^11 - 1030858950173589504*u^9*x^10 - 2497689404335521792*u^9*x^9 - 1136151235249569792*u^9*x^8 - 99427197578379264*u^9*x^7 + 146627187440025600*u^9*x^6 + 89652051749044224*u^9*x^5 + 27370408322138112*u^9*x^4 + 5027217855086592*u^9*x^3 + 533189772509184*u^9*x^2 + 25389989167104*u^9*x - 228509902503936*u^8*v*x^46 - 6017427432603648*u^8*v*x^45 - 78150386656346112*u^8*v*x^44 - 664354456546443264*u^8*v*x^43 - 4108379537118265344*u^8*v*x^42 - 19320131406870282240*u^8*v*x^41 - 69895694938293927936*u^8*v*x^40 - 191328903927585570816*u^8*v*x^39 - 370652887787191861248*u^8*v*x^38 - 385354605554555092992*u^8*v*x^37 + 324941538380401999872*u^8*v*x^36 + 2278564708207292448768*u^8*v*x^35 + 4684436320107805212672*u^8*v*x^34 + 4304341783998988222464*u^8*v*x^33 - 2754078124304677994496*u^8*v*x^32 - 15133089620914061967360*u^8*v*x^31 - 21819074721210810630144*u^8*v*x^30 - 9012779565546326851584*u^8*v*x^29 + 22205383050928449650688*u^8*v*x^28 + 46942490380431097331712*u^8*v*x^27 + 35680384862742466658304*u^8*v*x^26 - 11300726433330625904640*u^8*v*x^25 - 55359384825557845278720*u^8*v*x^24 - 55359384825557845278720*u^8*v*x^23 - 11300726433330625904640*u^8*v*x^22 + 35680384862742466658304*u^8*v*x^21 + 46942490380431097331712*u^8*v*x^20 + 22205383050928449650688*u^8*v*x^19 - 9012779565546326851584*u^8*v*x^18 - 21819074721210810630144*u^8*v*x^17 - 15133089620914061967360*u^8*v*x^16 - 2754078124304677994496*u^8*v*x^15 + 4304341783998988222464*u^8*v*x^14 + 4684436320107805212672*u^8*v*x^13 + 2278564708207292448768*u^8*v*x^12 + 324941538380401999872*u^8*v*x^11 - 385354605554555092992*u^8*v*x^10 - 370652887787191861248*u^8*v*x^9 - 191328903927585570816*u^8*v*x^8 - 69895694938293927936*u^8*v*x^7 - 19320131406870282240*u^8*v*x^6 - 4108379537118265344*u^8*v*x^5 - 664354456546443264*u^8*v*x^4 - 78150386656346112*u^8*v*x^3 - 6017427432603648*u^8*v*x^2 - 228509902503936*u^8*v*x - 9403699691520*u^8*x^47 - 294335800344576*u^8*x^46 - 20395214075953152*u^8*x^45 - 189091532910145536*u^8*x^44 - 347327411299983360*u^8*x^43 + 3273847003145299968*u^8*x^42 + 20346485926118510592*u^8*x^41 + 34687984599668526336*u^8*x^40 - 67533736713338990592*u^8*x^39 - 377307580659039802368*u^8*x^38 - 394647113373678268416*u^8*x^37 + 992538580307469276672*u^8*x^36 + 3070303854851661189120*u^8*x^35 + 1031688241687778927616*u^8*x^34 - 7693112427135536701440*u^8*x^33 - 11837703791227951888128*u^8*x^32 + 4844659034972439134208*u^8*x^31 + 29616968503088585109504*u^8*x^30 + 19294710972990334451712*u^8*x^29 - 32758484221047111063552*u^8*x^28 - 57313202343056815325184*u^8*x^27 - 389712938955861344256*u^8*x^26 + 72044279647721419825152*u^8*x^25 + 52399486323942187461120*u^8*x^24 - 39288536324933522595840*u^8*x^23 - 75572543379658530723840*u^8*x^22 - 13309446974593414864896*u^8*x^21 + 51535288253627750089728*u^8*x^20 + 39152469107400664080384*u^8*x^19 - 11860653123793865041920*u^8*x^18 - 29332854295034738245632*u^8*x^17 - 8687243438059458958848*u^8*x^16 + 9766048969308251897856*u^8*x^15 + 8376079782759139749888*u^8*x^14 + 101567067981215219712*u^8*x^13 - 2806137264839472654336*u^8*x^12 - 1236956006303295234048*u^8*x^11 + 218582385149044684800*u^8*x^10 + 366765830846130180096*u^8*x^9 + 101753411323297040640*u^8*x^8 - 19349875837952667648*u^8*x^7 - 19939489028153275392*u^8*x^6 - 5182327943698968576*u^8*x^5 - 438728191206271488*u^8*x^4 + 38461072965193728*u^8*x^3 + 6030519145767936*u^8*x^2 - 276116132192256*u^8*x - 2677850419968*u^8 + 914039610015744*u^7*v^2*x^46 + 28944587650498560*u^7*v^2*x^45 + 463722762147987456*u^7*v^2*x^44 + 4972984838225657856*u^7*v^2*x^43 + 39857306554476527616*u^7*v^2*x^42 + 253097872693229518848*u^7*v^2*x^41 + 1319598984979729612800*u^7*v^2*x^40 + 5777772340454920028160*u^7*v^2*x^39 + 21522191456739061923840*u^7*v^2* x^38 + 68546815303767083974656*u^7*v^2*x^37 + 186238186522071705059328*u^7* v^2*x^36 + 427334589951529622962176*u^7*v^2*x^35 + 810562744203396698603520*u^7*v^2*x^34 + 1213761806869633455882240*u^7*v^2* x^33 + 1262395485632581903319040*u^7*v^2*x^32 + 386720852855711846105088*u^7*v^2*x^31 - 1769332461691027368443904*u^7*v^2* x^30 - 4697109177058242458025984*u^7*v^2*x^29 - 6728884333110796546473984*u^7*v^2*x^28 - 5797591077422255198699520*u^7*v^2* x^27 - 1132337308088580438491136*u^7*v^2*x^26 + 5461728804010495393136640*u^7*v^2*x^25 + 10279047087494065249320960*u^7*v^2* x^24 + 10279047087494065249320960*u^7*v^2*x^23 + 5461728804010495393136640*u^7*v^2*x^22 - 1132337308088580438491136*u^7*v^2* x^21 - 5797591077422255198699520*u^7*v^2*x^20 - 6728884333110796546473984*u^7*v^2*x^19 - 4697109177058242458025984*u^7*v^2* x^18 - 1769332461691027368443904*u^7*v^2*x^17 + 386720852855711846105088*u^7*v^2*x^16 + 1262395485632581903319040*u^7*v^2* x^15 + 1213761806869633455882240*u^7*v^2*x^14 + 810562744203396698603520*u^7*v^2*x^13 + 427334589951529622962176*u^7*v^2* x^12 + 186238186522071705059328*u^7*v^2*x^11 + 68546815303767083974656*u^7*v^2*x^10 + 21522191456739061923840*u^7*v^2* x^9 + 5777772340454920028160*u^7*v^2*x^8 + 1319598984979729612800*u^7*v^2* x^7 + 253097872693229518848*u^7*v^2*x^6 + 39857306554476527616*u^7*v^2* x^5 + 4972984838225657856*u^7*v^2*x^4 + 463722762147987456*u^7*v^2*x^3 + 28944587650498560*u^7*v^2*x^2 + 914039610015744*u^7*v^2*x + 73557828698112*u^7*v*x^47 + 2520713945088000*u^7*v*x^46 + 169422695862239232*u^7*v*x^45 + 2463705635234217984*u^7*v*x^44 + 17248283475515965440*u^7*v*x^43 + 60467889920530931712*u^7*v*x^42 - 20270523231831232512*u^7*v*x^41 - 1465458097398785501184*u^7*v*x^40 - 8520050902274070294528*u^7*v*x^39 - 26487285958968793841664*u^7*v*x^38 - 41702480697048365297664*u^7*v*x^37 + 14287258286392515563520*u^7*v*x^36 + 233068870147997611044864*u^7*v*x^35 + 511545036003304813387776*u^7*v*x^34 + 328502645790874552811520*u^7*v*x^33 - 833525721252277508524032*u^7*v*x^32 - 2273730618919488838483968*u^7*v*x^31 - 1764930625102029970538496*u^7*v* x^30 + 1889157617275107299770368*u^7*v*x^29 + 5628524147436010686234624* u^7*v*x^28 + 4057053006205943147446272*u^7*v*x^27 - 3247230442854432829685760*u^7*v*x^26 - 8773969147066924702949376*u^7*v* x^25 - 5332141858104415330652160*u^7*v*x^24 + 4010023960559591962337280* u^7*v*x^23 + 8896824400633482042703872*u^7*v*x^22 + 4545848712306312238325760*u^7*v*x^21 - 3065803977712843625177088*u^7*v* x^20 - 5804571424249118604681216*u^7*v*x^19 - 2731066037289512868003840* u^7*v*x^18 + 1195152090130641707384832*u^7*v*x^17 + 2300950549244420176785408*u^7*v*x^16 + 1143878779868422865043456*u^7*v* x^15 - 105112029328104030732288*u^7*v*x^14 - 468270889301049027969024*u^7* v*x^13 - 278022649856128987152384*u^7*v*x^12 - 58095804087458203484160*u^7*v*x^11 + 23446070242410640564224*u^7*v*x^10 + 23671604048315945250816*u^7*v*x^9 + 9750713520666655733760*u^7*v*x^8 + 2474603685666216235008*u^7*v*x^7 + 396374952857704906752*u^7*v*x^6 + 31989956224147329024*u^7*v*x^5 - 1359416518116175872*u^7*v*x^4 - 613912482443022336*u^7*v*x^3 - 39484606903492608*u^7*v*x^2 + 1904249187532800*u^7*v*x + 21422803359744*u^7*v + 1166755332096*u^7*x^48 + 53949373415424*u^7*x^47 + 7103898678583296*u^7*x^46 + 184468267083497472*u^7*x^45 + 1842700068367257600*u^7*x^44 + 6849786126161940480*u^7*x^43 - 2443951885172557824*u^7*x^42 - 84171063543636413952*u^7*x^41 - 149119527819032365824*u^7*x^40 + 387894747423210647040*u^7*x^39 + 1591661914712159786496*u^7*x^38 + 268370807820816443904*u^7*x^37 - 6828485220238415049216*u^7*x^36 - 9487773452859477087744*u^7*x^35 + 11768360508393132676608*u^7*x^34 + 39847890069062408397312*u^7*x^33 + 9959657000673487145472*u^7*x^32 - 79579058711644798373376*u^7*x^31 - 90759244180134727254528*u^7*x^30 + 63806556465928747233792*u^7*x^29 + 197405959613536824178176*u^7*x^28 + 65571424261939792802304*u^7*x^27 - 207835209883177829171712*u^7*x^26 - 238269403691816477999616*u^7*x^25 + 48467352374814855306240*u^7*x^24 + 279778262744324902381056*u^7*x^23 + 162591330277479641117184*u^7*x^22 - 128864118337083719852544*u^7*x^21 - 228906369372179648706048*u^7*x^20 - 61409882710688720601600*u^7*x^19 + 124344341163420563612160*u^7*x^18 + 123072494783239213364736*u^7*x^17 + 593509140207134903808*u^7*x^16 - 68711815427199329401344*u^7*x^15 - 39461624226638423078400*u^7*x^14 + 9599179450365099910656*u^7*x^13 + 20743781961435144528384*u^7*x^12 + 6930327898907861865984*u^7*x^11 - 2994020627636769836544*u^7*x^10 - 3169311278632246904832*u^7*x^9 - 747117295769717768448*u^7*x^8 + 249378079102264783872*u^7*x^7 + 209704748665609211904*u^7*x^6 + 56829161237846188032*u^7*x^5 + 6182968751418212352*u^7*x^4 - 108218481327489024*u^7*x^3 - 57213166839422976*u^7*x^2 + 114254951251968*u^7*x + 21422803359744*u^7 - 2132759090036736*u^6*v^3* x^46 - 78912086331359232*u^6*v^3*x^45 - 1480134808485494784*u^6*v^3*x^44 - 18612080778967252992*u^6*v^3*x^43 - 175553189618453839872*u^6*v^3*x^42 - 1320100183365888245760*u^6*v^3*x^41 - 8222193750637770964992*u^6*v^3*x^40 - 43545650157287377993728*u^6*v^3*x^39 - 199944481944021961015296*u^6*v^3* x^38 - 808255480936533936832512*u^6*v^3*x^37 - 2912937497402597709447168*u^6*v^3*x^36 - 9454869732135200273989632*u^6*v^3* x^35 - 27844473371483017888137216*u^6*v^3*x^34 - 74730218975735568625041408*u^6*v^3*x^33 - 183059603219256380397453312*u^6* v^3*x^32 - 408993682186668457360097280*u^6*v^3*x^31 - 831722384473335415894966272*u^6*v^3*x^30 - 1535630589791462409638510592*u^6* v^3*x^29 - 2568105140570691474218287104*u^6*v^3*x^28 - 3882588236327651512006213632*u^6*v^3*x^27 - 5299114424695408467308445696* u^6*v^3*x^26 - 6523102351691030452552335360*u^6*v^3*x^25 - 7238266041811943272029880320*u^6*v^3*x^24 - 7238266041811943272029880320* u^6*v^3*x^23 - 6523102351691030452552335360*u^6*v^3*x^22 - 5299114424695408467308445696*u^6*v^3*x^21 - 3882588236327651512006213632* u^6*v^3*x^20 - 2568105140570691474218287104*u^6*v^3*x^19 - 1535630589791462409638510592*u^6*v^3*x^18 - 831722384473335415894966272*u^6* v^3*x^17 - 408993682186668457360097280*u^6*v^3*x^16 - 183059603219256380397453312*u^6*v^3*x^15 - 74730218975735568625041408*u^6* v^3*x^14 - 27844473371483017888137216*u^6*v^3*x^13 - 9454869732135200273989632*u^6*v^3*x^12 - 2912937497402597709447168*u^6*v^3* x^11 - 808255480936533936832512*u^6*v^3*x^10 - 199944481944021961015296*u^6*v^3*x^9 - 43545650157287377993728*u^6*v^3* x^8 - 8222193750637770964992*u^6*v^3*x^7 - 1320100183365888245760*u^6*v^3* x^6 - 175553189618453839872*u^6*v^3*x^5 - 18612080778967252992*u^6*v^3* x^4 - 1480134808485494784*u^6*v^3*x^3 - 78912086331359232*u^6*v^3*x^2 - 2132759090036736*u^6*v^3*x - 251601209524224*u^6*v^2*x^47 - 9323350301933568*u^6*v^2*x^46 - 609155366270533632*u^6*v^2*x^45 - 11726923065241780224*u^6*v^2*x^44 - 121907045534943412224*u^6*v^2*x^43 - 799248014385456807936*u^6*v^2*x^42 - 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1393003344537273842482833984*v^2* x^20 + 1158207720157148177423508864*v^2*x^19 - 800195710229656959642545664*v^2*x^18 - 1923383866381148337562312704*v^2* x^17 - 1651772020714193268931976928*v^2*x^16 - 853583875033008912052439808*v^2*x^15 - 273656207809267490684123136*v^2* x^14 - 39969047279848364550821376*v^2*x^13 + 7992523635303703588572672*v^2* x^12 + 5602630316439612350900736*v^2*x^11 + 1020101285367759309405696*v^2* x^10 - 125791467710075203590144*v^2*x^9 - 114754958300027957812992*v^2* x^8 - 32150941669683468407808*v^2*x^7 - 5963410040813446717440*v^2*x^6 - 892783443447055503360*v^2*x^5 - 107312946746726467584*v^2*x^4 - 9434839043905376256*v^2*x^3 - 573364669743157248*v^2*x^2 - 11882514930204672*v^2*x - 74979811759104*v^2 + 382205952*v*x^51 - 12747165696*v*x^50 - 3412055052288*v*x^49 - 179673895222272*v*x^48 - 5078048289196032*v*x^47 - 97465393644901632*v*x^46 - 1452069492521313024*v*x^45 - 17550433047264457344*v*x^44 - 166075277406972056448*v*x^43 - 1171580155749842765952*v*x^42 - 6071781317109058145856*v*x^41 - 24125868147321735473892*v*x^40 - 82186279832965987478784*v*x^39 - 268010279194178299189344*v*x^38 - 810373319921588791562592*v*x^37 - 2003558290701388225514568*v*x^36 - 3726103137328819684457088*v*x^35 - 5238401004335612943972096*v*x^34 - 6554102942259285739032576*v*x^33 - 9652611471423069379064196*v*x^32 - 15659967025424914478205024*v*x^31 - 21834140639301939665249184*v*x^30 - 26212203753760330879746336*v*x^29 - 31577750941157845639916640*v*x^28 - 37494565320646897844199840*v*x^27 - 37493316175413553548899424*v*x^26 - 31797496008988879059739392*v*x^25 - 27483197627100932263470288*v*x^24 - 23964486860206360926414912*v*x^23 - 17278565885042918177436672*v*x^22 - 11641836856924300823542272*v*x^21 - 10664828566573945910987904*v*x^20 - 10453233651976136783353344*v*x^19 - 8854269987745725682675968*v*x^18 - 7864876546231539056090112*v*x^17 - 7414784962680574496725056*v*x^16 - 6037801902716835882442752*v*x^15 - 4114561400407346957351424*v*x^14 - 2584211148982172644913664*v*x^13 - 1513852856793801442248192*v*x^12 - 732172233263932873363968*v*x^11 - 250507442508413722449408*v*x^10 - 45597180352622698561536*v*x^9 + 4269332065275868402944*v*x^8 + 5523106315161609391104*v*x^7 + 1761382255901548179456*v*x^6 + 325095881127119548416*v*x^5 + 39968648357110308864*v*x^4 + 3535008519877816320*v*x^3 + 202183657486295040*v*x^2 + 3770413391314944*v*x + 21422803359744*v - 95551488*x^51 - 15129980928*x^50 - 1067066763264*x^49 - 44090784504576*x^48 - 1180674687144960*x^47 - 21390160017351168*x^46 - 265446771676289280*x^45 - 2230803587948277024*x^44 - 12195988629927742784*x^43 - 39224003621644473648*x^42 - 49948806024482451528*x^41 + 96704302671106965277*x^40 + 431087488201682108376*x^39 + 415933319648267749884*x^38 - 287086355368145941016*x^37 - 395834304640937448834*x^36 + 256415887503318478392*x^35 - 1722909420592583998100*x^34 - 4460654032687843287360*x^33 - 443692751817894208131*x^32 + 2726247797931002809936*x^31 - 2759074760187799409856*x^30 + 2289665603302993054560*x^29 + 15967517077897102843168*x^28 + 6365794354228594160352*x^27 + 1619271945677281449888*x^26 + 17006890310843871076864*x^25 + 3223420091167815260976*x^24 - 13462679747580071716416*x^23 - 5316238039299401048960*x^22 - 15068056529168990583168*x^21 - 29723973741467840132160*x^20 - 25123580062748363921024*x^19 - 24669430128685759797504*x^18 - 27934693240065337133568*x^17 - 22720969850153124453408*x^16 - 17128087083562340360448*x^15 - 14182599248387477259264*x^14 - 10154699979750988678656*x^13 - 6296094628474201422336*x^12 - 3966320302358080402944*x^11 - 2367142012157149813248*x^10 - 1198058808345925478400*x^9 - 550697674766541258240*x^8 - 245399829796505281536*x^7 - 94109222074760561664*x^6 - 26455578977667649536*x^5 - 4907321675816163840*x^4 - 544905665635479552*x^3 - 30397767811734528*x^2 - 517321029279744*x - 2677850419968 (* The other main main polynomial, with 829 terms. *) phi52[{u_,v_}] := -50031545098999707 + 2223624226622209200*y + 1423119505038213888*u*y - 1423119505038213888*v*y - 41537300553302867856*y^2 - 86810289807331047168*u*y^2 + 41270465646108202752*v*y^2 + 370841224354541235648*y^3 + 2534101465304712863232*u*y^3 - 439269553888462020096*v*y^3 - 241778779983274699296*y^4 - 47484016237624309507584*u*y^4 + 215892499727278669824*u^2*y^4 - 20767003147594676736*v*y^4 + 2590709996727344037888*u*v*y^4 + 647677499181836009472*v^2*y^4 - 36134374644295472600064*y^5 + 645927958228845882302208*u*y^5 - 11658194985273048170496*u^2*y^5 + 60533020644358222487808*v*y^5 - 117445519851639596384256*u*v*y^5 - 22884604971091539001344*v^2*y^5 + 498750924357350213340672*y^6 - 6829946044053906044922624*u*y^6 + 301170037119553744404480*u^2*y^6 - 881144277370597636699392*v*y^6 + 2568832890088313132679168*u*v*y^6 + 360900295377434176389120*v^2*y^6 - 3610982194804918065871872*y^7 + 58583683114429366938673152*u*y^7 - 4987980313699046387613696*u^2*y^7 + 12281884428929630994432*u^3*y^7 + 6748795480996582412820480*v*y^7 - 36087630732190892320358400*u*v*y^7 - 69597345097267908968448*u^2*v*y^7 - 3023006741366440112160768*v^2*y^7 + 135100728718225940938752*u*v^2*y^7 - 77785268049887662964736*v^3*y^7 + 12385801136412360666365184*y^8 - 419142792270798047516276736*u*y^8 + 59837149033300960179388416*u^2*y^8 - 577248568159692656738304*u^3*y^8 - 22607321274519610855237632*v*y^8 + 365775275957572263437402112*u*v*y^8 + 3074565068708717625606144*u^2*v*y^8 + 7465882481309633111654400*v^2*y^8 - 5694700413547038904418304*u*v^2*y^8 + 3197383912998013935550464*v^3*y^8 + 49313216978401720573808640*y^9 + 2547275125573313745681862656*u*y^9 - 556253550298436361668001792*u^2*y^9 + 12971034610775126955786240*u^3*y^9 - 145782005446654475919446016*v*y^9 - 2849921214580642054963986432*u*v*y^9 - 65365553584588932778033152*u^2*v* y^9 + 157482938515754588445868032*v^2*y^9 + 115868662356347575427137536*u* v^2*y^9 - 63474143382533769604890624*v^3*y^9 - 1119808674625629458539450368*y^10 - 13298793588973745305912848384*u*y^10 + 4180222817166032761981501440*u^2*y^10 - 186685704717150175157551104*u^3* y^10 + 310534559388245484896256*u^4*y^10 + 2985478875419070630137868288*v* y^10 + 17770787009306076954948009984*u*v*y^10 + 893358951450469367814291456*u^2*v*y^10 - 1863207356329472909377536*u^3*v* y^10 - 2676689934592579557541281792*v^2*y^10 - 1516230626302159293819912192*u*v^2*y^10 + 3726414712658945818755072*u^2*v^2* y^10 + 809867914128228346648068096*v^3*y^10 - 3105345593882454848962560*u*v^3*y^10 + 931603678164736454688768*v^4*y^10 + 10052005355622395571048873984*y^11 + 59983200083978692493499629568*u*y^11 - 26118737028595971178484465664*u^2*y^11 + 1943064017258170543811592192*u^3* y^11 - 12421382375529819395850240*u^4*y^11 - 27606143803522060628135313408*v*y^11 - 91262374931865371109180309504*u*v* y^11 - 8839498301151069427678052352*u^2*v*y^11 + 72044017778072952495931392*u^3*v*y^11 + 25085804155338934760446623744*v^2* y^11 + 14338708718383849527016685568*u*v^2*y^11 - 141603759081039941112692736*u^2*v^2*y^11 - 7452832609510150989636698112*v^3* y^11 + 116760994329980302320992256*u*v^3*y^11 - 34779870651483494308380672*v^4*y^11 - 64888646085765432345136988160*y^12 - 233753326943073488372452294656*u*y^12 + 138292173942374683812345937920*u^2* y^12 - 15635225883743767227864711168*u^3*y^12 + 237765960971599959602233344*u^4*y^12 + 184658427034508318682970128384*v* y^12 + 394949337134454678110513135616*u*v*y^12 + 67558496230173278770858819584*u^2*v*y^12 - 1339025020082114530872655872*u^3* v*y^12 - 173138253932725263117799391232*v^2*y^12 - 104347568341137386931650297856*u*v^2*y^12 + 2590479294416743835004567552*u^2* v^2*y^12 + 52597679790366312451056599040*v^3*y^12 - 2114947372473543915800100864*u*v^3*y^12 + 625727137167314652065955840*v^4* y^12 + 338703132466366604062262820864*y^13 + 781186416387005712370563809280*u*y^13 - 628401563167096434017163018240*u^2* y^13 + 101406413829649287392633290752*u^3*y^13 - 2914516356498389327281127424*u^4*y^13 + 2944327674199660893831168*u^5*y^13 - 992346329455476694601811886080*v*y^13 - 1470837257786165723465319972864*u*v* y^13 - 415172712341490887551013093376*u^2*v*y^13 + 15966996966944942287843491840*u^3*v*y^13 - 14721638370998304469155840*u^4*v* y^13 + 956068674609658724995446079488*v^2*y^13 + 607269793234005001669737185280*u*v^2*y^13 - 30419781417192890221631373312* u^2*v^2*y^13 + 29443276741996608938311680*u^3*v^2*y^13 - 295322353142900242028521586688*v^3*y^13 + 24596637359544510888856780800*u* v^3*y^13 - 29443276741996608938311680*u^2*v^3*y^13 - 7229336552798173627787771904*v^4*y^13 + 14721638370998304469155840*u*v^4* y^13 - 2944327674199660893831168*v^5*y^13 - 1499602592130542765402186317824* y^14 - 2191110238229895430486145630208*u*y^14 + 2469519070378388917736602337280*u^2*y^14 - 545004424066372128783030288384* u^3*y^14 + 25793058009187556687609856000*u^4*y^14 - 97162813248588809496428544*u^5*y^14 + 4478849180189098908862996021248*v* y^14 + 4818821581113173169810853330944*u*v*y^14 + 2106809655634973458652435841024*u^2*v*y^14 - 137485403749313120122297122816* u^3*v*y^14 + 485814066242944047482142720*u^4*v*y^14 - 4386903541133670212938855612416*v^2*y^14 - 2897715793005288468021698887680*u* v^2*y^14 + 257880411508614399216649764864*u^2*v^2*y^14 - 971628132485888094964285440*u^3*v^2*y^14 + 1349501900016632138426128269312* v^3*y^14 - 206476843806039664816847585280*u*v^3*y^14 + 971628132485888094964285440*u^2*v^3*y^14 + 60288778037550829034885087232*v^4* y^14 - 485814066242944047482142720*u*v^4*y^14 + 97162813248588809496428544*v^5*y^14 + 5778246602362128651767022354432*y^15 + 4865686588430434240067209789440*u*y^15 - 8419666725287113953186750136320*u^2* y^15 + 2473414500191345379254577659904*u^3*y^15 - 175951518976254695605102706688*u^4*y^15 + 1542827701280622308367532032*u^5* y^15 - 17396448748812188973528967544832*v*y^15 - 14244178132800317660720089006080*u*v*y^15 - 8988768031724278697697912815616* u^2*v*y^15 + 911761485927345664967628029952*u^3*v*y^15 - 7714138506403111541837660160*u^4*v*y^15 + 17084762072559422138171831353344* v^2*y^15 + 11523224309560076883911705100288*u*v^2*y^15 - 1682305717121049973474480619520*u^2*v^2*y^15 + 15428277012806223083675320320*u^3*v^2*y^15 - 5084200970146852734730695081984* v^3*y^15 + 1333133052365081734466487975936*u*v^3*y^15 - 15428277012806223083675320320*u^2*v^3*y^15 - 386637302195122730354532679680* v^4*y^15 + 7714138506403111541837660160*u*v^4*y^15 - 1542827701280622308367532032*v^5*y^15 - 19688602867805605916286894735360* y^16 - 6885539735514626503847093207040*u*y^16 + 24854642967481582737140477853696*u^2*y^16 - 9599791777746387952342356983808* u^3*y^16 + 963618989129879477670943653888*u^4*y^16 - 15699155158832591885907787776*u^5*y^16 + 59051200601353329523008948142080*v* y^16 + 39071064615509786948519747125248*u*v*y^16 + 32631380563711188576726222372864*u^2*v*y^16 - 4847890246327393841847862296576*u^3*v*y^16 + 78523692382481296955050819584* u^4*v*y^16 - 57222109435776518787871191072768*v^2*y^16 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+ 1215616158542258449724473344*u^4*y^45 + 113693084526306873462428270592*v*y^45 - 346215190160964730161155014656*u*v* y^45 + 351351126743008839935025217536*u^2*v*y^45 - 118829021108350983236298473472*u^3*v*y^45 - 336173007294793091748905091072* v^2*y^45 + 46387425146643867274152247296*u*v^2*y^45 + 291768937111430991789932150784*u^2*v^2*y^45 - 9911389647896754424478831738880*v^3*y^45 - 231913275531978067669866774528*u* v^3*y^45 + 57757743370355800666508623872*v^4*y^45 - 39213424469105111281434624*y^46 + 156853697876420445125738496*u*y^46 - 235280546814630667688607744*u^2*y^46 + 156853697876420445125738496*u^3* y^46 - 39213424469105111281434624*u^4*y^46 - 11471096605062631930711769088*v*y^46 + 34582407793968233885233840128*u*v* y^46 - 34751525772748571978332372992*u^2*v*y^46 + 11640214583842970023810301952*u^3*v*y^46 + 41938167708853135947419615232*v^2* y^46 - 13080914464031490638667055104*u*v^2*y^46 - 28928977727555090197669478400*u^2*v^2*y^46 + 2317353615719296441701906776064* v^3*y^46 + 23094165401457690769033789440*u*v^3*y^46 - 5766188833276465483893178368*v^4*y^46 + 743602715858585813929426944*v*y^47 - 2230808147575757441788280832*u*v*y^47 + 2230808147575757441788280832*u^2*v* y^47 - 743602715858585813929426944*u^3*v*y^47 - 3782785557971969123398189056*v^2*y^47 + 1923778768325504588574621696*u*v^2* y^47 + 1859006789646464534823567360*u^2*v^2*y^47 - 450032817773682777239454744576*v^3*y^47 - 1487205431717171627858853888*u*v^3* y^47 + 371801357929292906964713472*v^4*y^47 - 23237584870580806685294592*v*y^48 + 69712754611742420055883776*u*v*y^48 - 69712754611742420055883776*u^2*v*y^48 + 23237584870580806685294592*u^3*v* y^48 + 219227009530067898461061120*v^2*y^48 - 161133047353615881747824640*u*v^2*y^48 - 58093962176452016713236480*u^2*v^2* y^48 + 70595379074490205355259199488*v^3*y^48 + 46475169741161613370589184*u*v^3*y^48 - 11618792435290403342647296*v^4* y^48 - 6120186961799060196950016*v^2*y^49 + 6120186961799060196950016*u*v^2* y^49 - 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-1/125}, -403483909399576745937402219150056841444192163573984867\ 1232000000000000000000000000000000000000000000000000000000000000}, {{16/225, 1/225}, -27169173600498261302158071659996827963325048300669927208832\ 20480000000000000000000000000000000000000000000000000000000000}, {{729/1000, 1/1000}, -18803713057003137153246998637666222336630455204966878045\ 7145139200000000000000000000000000000000000000000000000000000000}, {{-320, 1}, -28315314648884509968532154089277335976017920000000000000000000000\ 00000000000000000000000000000000000000000000000000}, {{1/324, 1/324}, -121750670155010061043983622458408043373300005679923200000000\ 00000000000000000000000000000000000000000000000000}, {{-128/225, 1/225}, -197616745539275180947401805283935049816625802077931399774\ 1450015539200000000000000000000000000000000000000000000000000000000000000}, {{-375/16, 1/16}, -58847306625328839664940187779319629933843251200000000000000\ 000000000000000000000000000000000000000000000000}, {{81/640, 1/640}, -24626703454564010372155897164920461513927744358763724800000\ 0000000000000000000000000000000000000000000000000000000000000}, {{36/625, 1/625}, -12188814497177444618371224166101305733829060932403200000000\ 000000000000000000000000000000000000000000000000000000000000}, {{1215/512, -1/512}, -16942450749251987392609894142998546794978206625337054164\ 450017280000000000000000000000000000000000000000000000000000}, {{-800/81, 1/81}, -14752011007808676547651165803723637894791189474796747820580\ 0147079995064320000000000000000000000000000000000000000000000000000000000000000}\ , {{-324/625, 1/625}, -21957416171030575660822422809326116646291755786436822197\ 127222394880000000000000000000000000000000000000000000000000000000000000000}, {{81/1600, 1/1600}, -780084127819356455575758346630483566965059899673804800000\ 00000000000000000000000000000000000000000000000000000}, {{-256/25, 1/225}, -7361797449710785632856257456687653430425591844243235877683\ 2000000000000000000000000000000000000000000000000000000000000}} (* Section seven. A degree 60 family: non-full monodromy and a prime drop *) (* The main degree 24 polynomial *) f24uv[{u_,v_}] := Resultant[m^4 - 2*m^2*v + v^2 - 8*m*v^2 - 4*u*v^2, -240*m^6 + 352*m^4*v + 16*m^2*(9 + 100*m)*v^2 + 192*m*v^3 + 64*v^4 + (528*m^5 - 768*m^3*v - 48*m*(3 + 58*m)*v^2 - 96*v^3)*x - 12*(37*m^4 - 46*m^2*v - 3*v^2 - 128*m*v^2)*x^2 + (184*m^3 - 152*m*v - 272*v^2)*x^3 + 12*(-3*m^2 + v)*x^4 + x^6,m] (* Its twin (not presented explicitly in the paper) *) f24twinuv[{u_,v_}] := Resultant[m^4 - 2*m^2*v + v^2 - 8*m*v^2 - 4*u*v^2, 64*m^9 - 64*m^3*(1 + 324*m)*v^3 - 3456*m^2*(-9 + 22*m)*v^4 + 6912*(-2 + 27*m)*v^5 + 373248*v^6 - m^4*(192*m^3*v - 192*m*(1 + 18*m)*v^2) + (1728*m^6*v - 6912*m^4*v^2 - 8640*m^2*(-1 + 4*m)*v^3 + 3456*(-1 + 18*m)*v^4 + 186624*v^5)*x + (156*m^6 - 528*m^4*v - 12*m^2*(-49 + 324*m)*v^2 + 216*(-1 + 26*m)*v^3 + 27216*v^4)*x^2 + (12*m^3 - 12*m*v - 216*v^2)*x^4 + x^6,m] (* The main polynomial in symmetrized coordinates *) f24[{p_,q_}] := f24uv[{p/3,p^2 q/27}] (* Its twin in symmetrized coordinates *) f24twin[{p_,q_}] := f24twinuv[{p/3,p^2 q/27}] (* Cases where the degree 24 polynomials highly factor. Only the particular specialization point {153/1849, 129/289} is pursued in any detail in the paper *) pqssmall = {{-12, 2/9}, {-27/5, -27/5}, {-2, -2}, {-9/7, -9/7}, {-1, -1}, {-3159/4489, 201/169}, {-3/5, -3/5}, {-27/49, 21}, {-1/3, -1/3}, {-3/13, -3/13}, {-1/11, -1/11}, {513/8281, 273/361}, {153/1849, 129/289}, {3/35, 3/35}, {216/1369, 37/48}, {1/5, 1/5}, {81/361, 19/27}, {3/11, 3/11}, {96/289, 51/64}, {63/169, 39/49}, {3/7, 3/7}, {4/9, 3/4}, {3/5, 3/5}, {81/121, 11/3}, {9/13, 9/13}, {288/361, 57/64}, {1377/1681, 369/289}, {6/7, 6/7}, {1, 2}, {27/23, 27/23}, {216/169, 39/16}, {3/2, 3/2}, {9/5, 9/5}, {3, 3}, {9, 9}} (* Cases where the degree 24 polynomials factor as 18+6. The tuples are {i where the Galois group is 18Ti, the specialization point {p,q}, p = polredabs[deg 18 factor of f24[{p,q}]], p^t = polredabs[deg 18 factor of f24twin[{p,q}]], discf(p), discf(pt)} *) fields18 = {{971, {1/12, 24}, 23612 + 13050*x - 27*x^2 + 21996*x^3 + 26154*x^4 + 9558*x^5 + 5136*x^6 + 684*x^7 - 2232*x^8 - 414*x^9 + 198*x^10 - 216*x^11 + 90*x^12 - 18*x^13 - 36*x^14 + x^18, -16 + 144*x^2 + 48*x^3 - 459*x^4 - 288*x^5 + 603*x^6 + 450*x^7 - 351*x^8 - 156*x^9 + 225*x^10 - 36*x^11 - 123*x^12 + 36*x^13 + 45*x^14 - 6*x^15 - 9*x^16 + x^18, 37173856807010963956659388416, 16521714136449317314070839296}, {972, {-3/125, 1}, 198 + 972*x + 1782*x^2 + 576*x^3 - 2376*x^4 - 3132*x^5 - 1044*x^6 + 756*x^7 + 1134*x^8 + 894*x^9 + 486*x^10 + 162*x^11 - 12*x^12 - 72*x^13 - 36*x^14 + x^18, -1 + 9*x^2 - 30*x^3 + 18*x^4 - 108*x^5 + 48*x^6 + 54*x^7 + 18*x^8 - 180*x^9 + 36*x^10 - 18*x^11 + 72*x^12 - 36*x^13 + 18*x^14 - 18*x^15 + 9*x^16 + x^18, 2447661353548047009491976192, 271962372616449667721330688}, {972, {-3, 1}, -48 + 576*x^3 - 432*x^4 - 1752*x^6 + 2592*x^7 - 972*x^8 + 48*x^9 + 252*x^10 - 324*x^11 + 45*x^12 - 72*x^13 + 27*x^14 - 12*x^15 + 9*x^16 + x^18, -192 + 2688*x^3 - 3600*x^4 - 1104*x^6 + 2880*x^7 + 540*x^8 - 448*x^9 - 936*x^10 - 216*x^11 + 225*x^12 + 144*x^13 + 27*x^14 - 24*x^15 - 9*x^16 + x^18, 39162581656768752151871619072, 69622367389811114936660656128}, {972, {-7/729, 81/49}, -464 + 414*x + 2430*x^2 - 2070*x^3 - 4302*x^4 + 6093*x^5 + 1311*x^6 - 6084*x^7 + 3384*x^8 - 85*x^9 - 927*x^10 + 1026*x^11 - 606*x^12 + 99*x^13 + 81*x^14 - 72*x^15 + 36*x^16 - 9*x^17 + x^18, 192 - 1728*x + 6624*x^2 - 14208*x^3 + 19440*x^4 - 19152*x^5 + 15816*x^6 - 11808*x^7 + 8208*x^8 - 4888*x^9 + 2340*x^10 - 792*x^11 + 234*x^12 - 54*x^13 + 45*x^14 - 12*x^15 + 9*x^16 + x^18, -2506405226033200137719783620608, -69622367389811114936660656128}, {972, {-8/3, 3/4}, -1372 + 9324*x^2 - 4236*x^3 - 11304*x^4 + 1872*x^5 + 7620*x^6 + 666*x^7 - 2925*x^8 - 2190*x^9 - 675*x^10 + 450*x^11 + 531*x^12 + 144*x^13 - 27*x^14 - 24*x^15 - 9*x^16 + x^18, 88 + 576*x + 1800*x^2 + 3840*x^3 + 6930*x^4 + 10728*x^5 + 12456*x^6 + 9288*x^7 + 3483*x^8 - 134*x^9 - 603*x^10 - 18*x^11 + 237*x^12 + 90*x^13 - 36*x^14 - 18*x^15 + x^18, -297390854456087711653275107328, -8459117637862050464804269719552}, {972, {-1/9, 3/4}, 1734 + 1836*x - 8964*x^2 + 1404*x^3 + 9126*x^4 - 5724*x^5 + 1965*x^6 - 3780*x^7 + 3330*x^8 - 1464*x^9 + 783*x^10 - 504*x^11 + 270*x^12 - 72*x^13 - 9*x^14 + x^18, 2040 + 3456*x + 1152*x^2 - 3144*x^3 + 2484*x^4 - 1512*x^5 + 1950*x^6 - 2376*x^7 + 1476*x^8 - 556*x^9 + 378*x^10 - 324*x^11 + 108*x^12 - 144*x^13 + 90*x^14 + 18*x^16 + x^18, -313300653254150017214972952576, -556978939118488919493285249024}, {972, {3/4, 1}, 306 + 2592*x + 7614*x^2 + 6732*x^3 - 2052*x^4 - 9072*x^5 - 2493*x^6 + 756*x^7 + 810*x^8 + 984*x^9 + 297*x^10 + 108*x^11 - 120*x^12 - 72*x^13 - 27*x^14 - 12*x^15 + x^18, 17400 - 54432*x + 74844*x^2 - 49344*x^3 + 16794*x^4 - 6984*x^5 + 7089*x^6 - 1944*x^7 + 1512*x^8 - 1856*x^9 + 927*x^10 + 144*x^11 + 222*x^12 + 72*x^13 - 9*x^14 - 24*x^15 + x^18, -313300653254150017214972952576, -556978939118488919493285249024}, {972, {3/4, 32/9}, 6624 + 23328*x + 32076*x^2 + 32076*x^3 + 22842*x^4 - 15552*x^5 - 40374*x^6 - 28566*x^7 - 14823*x^8 - 3000*x^9 + 405*x^10 + 144*x^12 - 216*x^13 - 30*x^15 + 9*x^16 + x^18, 3136 - 4032*x + 7416*x^2 - 792*x^3 - 9234*x^4 - 4896*x^5 + 5457*x^6 + 3600*x^7 + 378*x^8 - 220*x^9 + 126*x^10 - 252*x^11 - 18*x^12 + 216*x^13 + 99*x^14 - 24*x^15 - 18*x^16 + x^18, -4758253671297403386452401717248, -8459117637862050464804269719552}, {974, {9/121, 11/27}, 1 - 9*x^2 - 54*x^5 - 33*x^6 - 54*x^7 - 234*x^8 - 234*x^9 - 108*x^10 - 54*x^11 - 33*x^12 - 54*x^13 - 36*x^14 + x^18, -327 - 1296*x - 2268*x^2 - 2178*x^3 - 1647*x^4 - 1728*x^5 - 1959*x^6 - 1476*x^7 - 693*x^8 - 92*x^9 + 234*x^10 + 234*x^11 + 60*x^12 + 9*x^14 - 6*x^15 - 9*x^16 + x^18, -2323366050438185247291211776, -16521714136449317314070839296}, {974, {2/9, 3/4}, -72 + 972*x^2 + 1296*x^3 + 1458*x^4 - 3735*x^6 - 2916*x^7 + 648*x^8 + 720*x^9 - 729*x^10 - 648*x^11 - 72*x^12 - 54*x^14 - 36*x^15 + x^18, 9 - 810*x - 3456*x^2 - 4608*x^3 - 1107*x^4 + 4320*x^5 + 5715*x^6 + 2268*x^7 - 1179*x^8 - 2026*x^9 - 936*x^10 - 36*x^11 + 288*x^12 + 162*x^13 + 27*x^14 - 24*x^15 - 9*x^16 + x^18, 1189563417824350846613100429312, 132173713091594538512566714368}, {974, {2/3, 3/4}, 72 - 324*x^2 - 864*x^3 - 972*x^4 + 5832*x^5 - 351*x^6 + 1944*x^7 - 3186*x^8 + 48*x^9 - 324*x^10 + 540*x^11 + 36*x^12 - 27*x^14 - 12*x^15 + x^18, 1752 + 1296*x - 6156*x^2 - 360*x^3 + 6480*x^4 - 2484*x^5 - 1455*x^6 + 1764*x^7 - 504*x^8 - 884*x^9 + 666*x^10 + 288*x^11 - 378*x^12 - 36*x^13 + 117*x^14 - 18*x^16 + x^18, 1189563417824350846613100429312, 132173713091594538512566714368}, {976, {-3/49, 7/3}, -32 - 432*x - 13968*x^2 - 43488*x^3 + 152136*x^4 - 100548*x^5 - 45348*x^6 + 55980*x^7 + 12240*x^8 - 21398*x^9 - 270*x^10 + 3600*x^11 + 360*x^12 - 558*x^13 - 54*x^14 + 42*x^15 + 18*x^16 - 9*x^17 + x^18, -324 + 3159*x^2 - 3564*x^3 + 324*x^5 + 7344*x^6 - 216*x^8 + 876*x^9 + 567*x^10 + 648*x^11 + 72*x^12 - 27*x^14 - 24*x^15 + x^18, 9516507342594806772904803434496, 4229558818931025232402134859776}, {977, {1/9, 9}, 96 - 576*x^3 - 432*x^4 + 624*x^6 + 432*x^7 - 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155952*x + 204984*x^2 + 56052*x^3 - 94923*x^4 - 27864*x^5 - 75255*x^6 - 50004*x^7 - 10476*x^8 - 3564*x^9 - 990*x^10 - 1296*x^11 - 66*x^12 - 108*x^13 - 108*x^14 + 9*x^16 + x^18, 33989 + 4788*x - 15291*x^2 - 5700*x^3 + 7542*x^4 + 2340*x^5 - 1092*x^6 - 36*x^7 + 1404*x^8 + 444*x^9 - 486*x^10 - 396*x^11 + 18*x^12 + 108*x^13 + 36*x^14 - 12*x^15 - 9*x^16 + x^18, -1218112939852135266931814839615488, -8459117637862050464804269719552}, {977, {-3/25, 5}, 192 - 1872*x^3 - 2970*x^4 + 1671*x^6 - 216*x^7 - 1944*x^8 - 636*x^9 + 288*x^10 - 126*x^12 - 72*x^13 + 54*x^14 - 12*x^15 + 18*x^16 + x^18, 5568 - 37152*x + 110808*x^2 - 185088*x^3 + 182016*x^4 - 99792*x^5 + 25092*x^6 - 2304*x^7 + 3024*x^8 - 1400*x^9 - 306*x^10 + 288*x^12 - 108*x^13 + 27*x^14 + x^18, -2566558951457996941025058427502592, -17823326051791645423785127968768}, {977, {8/81, 3/4}, 5848 - 7416*x + 2754*x^2 + 59988*x^3 - 110628*x^4 + 70200*x^5 - 18831*x^6 + 10728*x^7 + 19656*x^8 - 9236*x^9 - 2412*x^10 - 3024*x^11 - 1218*x^12 + 576*x^13 + 270*x^14 - 24*x^15 - 36*x^16 + x^18, -386 - 1548*x + 9756*x^2 + 54000*x^3 + 101700*x^4 + 62784*x^5 - 54609*x^6 - 96300*x^7 - 20574*x^8 + 36916*x^9 + 19179*x^10 - 5544*x^11 - 4824*x^12 + 360*x^13 + 585*x^14 - 12*x^15 - 36*x^16 + x^18, 51972818767024438055757433156927488, 40102483616531202203516537929728}, {977, {48/121, 11/4}, 144 + 1296*x + 4212*x^2 + 5688*x^3 + 3780*x^4 + 5400*x^5 - 9414*x^6 + 972*x^7 - 9234*x^8 + 2712*x^9 + 216*x^10 + 1836*x^11 + 318*x^12 - 180*x^13 + 63*x^14 - 36*x^15 + 18*x^16 + x^18, 2008 - 2664*x - 27126*x^2 + 40944*x^3 + 87552*x^4 - 224568*x^5 + 192528*x^6 - 124920*x^7 + 82620*x^8 - 42320*x^9 + 16542*x^10 - 6840*x^11 + 2472*x^12 - 612*x^13 + 225*x^14 - 36*x^15 + 18*x^16 + x^18, 80204967233062404407033075859456, 2281385734629330614244496380002304}, {977, {-64/9, 3/4}, -7584 + 46656*x - 71064*x^2 + 20160*x^3 + 36288*x^4 - 27648*x^5 + 1698*x^6 - 3888*x^7 + 9756*x^8 - 4056*x^9 + 459*x^10 - 1116*x^11 + 744*x^12 - 72*x^13 + 36*x^14 - 36*x^15 + x^18, 36928 - 20736*x + 269136*x^2 + 11328*x^3 + 273024*x^4 + 215424*x^5 + 208884*x^6 + 133488*x^7 + 84888*x^8 + 30080*x^9 + 13284*x^10 + 420*x^12 - 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7776*x^2 + 5184*x^3 + 23328*x^4 + 15552*x^5 - 27558*x^6 - 23328*x^7 - 1134*x^8 + 2232*x^9 + 3645*x^10 + 2268*x^11 + 378*x^12 - 108*x^14 - 36*x^15 + x^18, 58176 + 285120*x + 653832*x^2 + 431712*x^3 + 433944*x^4 + 310176*x^5 + 199746*x^6 + 101088*x^7 + 33480*x^8 + 16216*x^9 + 5904*x^10 + 2376*x^11 + 1080*x^12 + 36*x^13 + 135*x^14 - 12*x^15 + 18*x^16 + x^18, -1218112939852135266931814839615488, -2165534115292684918989893048205312}, {977, {3/4, 4/3}, 648 - 16038*x^2 - 17496*x^3 + 4374*x^4 - 2673*x^6 + 972*x^8 + 864*x^9 + 729*x^10 - 648*x^11 + 126*x^12 - 27*x^14 + x^18, 648 + 972*x^2 - 2592*x^3 + 1458*x^4 - 2592*x^5 + 4023*x^6 - 1944*x^7 + 2052*x^8 - 2400*x^9 + 567*x^10 - 432*x^11 + 594*x^12 - 27*x^14 - 24*x^15 + x^18, -1218112939852135266931814839615488, -2165534115292684918989893048205312}, {977, {3/4, 64/81}, -128 - 4608*x - 25632*x^2 - 59520*x^3 - 35136*x^4 + 4608*x^5 + 37248*x^6 + 63072*x^7 + 19224*x^8 + 128*x^9 - 9846*x^10 - 8784*x^11 - 3612*x^12 - 1440*x^13 - 468*x^14 - 84*x^15 + x^18, -14368 - 288*x + 73656*x^2 - 1056*x^3 - 155340*x^4 + 8100*x^5 + 172707*x^6 - 17820*x^7 - 111762*x^8 + 15672*x^9 + 43515*x^10 - 5328*x^11 - 9756*x^12 + 468*x^13 + 1071*x^14 - 12*x^15 - 54*x^16 + x^18, 51972818767024438055757433156927488, 2566558951457996941025058427502592}, {977, {3/4, 8/3}, 1327104 - 6345216*x^2 - 2239488*x^3 + 2239488*x^4 - 710208*x^6 + 13824*x^9 + 23328*x^10 - 5184*x^11 + 720*x^12 - 216*x^14 + x^18, 180 - 1296*x + 5508*x^2 - 15336*x^3 + 31860*x^4 - 49248*x^5 + 59688*x^6 - 55188*x^7 + 42093*x^8 - 26028*x^9 + 16119*x^10 - 7884*x^11 + 4464*x^12 - 1332*x^13 + 540*x^14 - 72*x^15 + 27*x^16 + x^18, -623673825204293256669089197883129856, -4331068230585369837979786096410624}, {977, {3/4, 1024/1125}, 27396 + 81000*x - 59616*x^2 - 448848*x^3 - 558414*x^4 - 242676*x^5 + 42120*x^6 + 84240*x^7 + 4212*x^8 - 34980*x^9 - 19980*x^10 - 3456*x^11 + 1827*x^12 + 864*x^13 + 135*x^14 - 48*x^15 - 9*x^16 + x^18, 991000 - 2446560*x + 2446848*x^2 - 1635072*x^3 + 1007190*x^4 - 528120*x^5 + 315342*x^6 - 157176*x^7 + 41310*x^8 - 19312*x^9 - 1062*x^10 + 11016*x^11 + 4422*x^12 - 72*x^13 + 162*x^14 - 9*x^16 + x^18, -9744903518817082135454518716923904, -69297091689365917407676577542569984}, {977, {8/27, 3/4}, 96808 + 11016*x + 72117*x^2 - 289248*x^3 - 349110*x^4 + 143964*x^5 + 329091*x^6 + 146664*x^7 - 42282*x^8 - 85748*x^9 - 44226*x^10 - 7884*x^11 + 4074*x^12 + 3240*x^13 + 621*x^14 - 132*x^15 - 54*x^16 + x^18, -122992 + 525312*x - 749088*x^2 + 195264*x^3 + 450000*x^4 - 326592*x^5 - 50856*x^6 + 108576*x^7 - 27216*x^8 - 15840*x^9 + 13284*x^10 + 1296*x^11 - 2532*x^12 + 288*x^13 + 378*x^14 - 72*x^15 - 45*x^16 + x^18, 16839193280515917930065408342844506112, 12993204691756109513939358289231872}, {977, {-16/9, 3/4}, 911232 + 720576*x + 26730*x^2 - 11016*x^3 + 307476*x^4 + 688176*x^5 + 104283*x^6 - 563760*x^7 - 237654*x^8 + 153600*x^9 + 87183*x^10 - 18792*x^11 - 14220*x^12 + 1080*x^13 + 1215*x^14 - 24*x^15 - 54*x^16 + x^18, 3686464 - 8600112*x + 7104132*x^2 - 315696*x^3 - 3523752*x^4 + 1703592*x^5 + 573558*x^6 - 484560*x^7 - 58320*x^8 + 57008*x^9 + 14886*x^10 - 4752*x^11 - 2568*x^12 + 396*x^13 + 243*x^14 - 12*x^15 - 18*x^16 + x^18, -155918456301073314167272299470782464, -69297091689365917407676577542569984}, {977, {16/27, 3/4}, 2048704 + 1456704*x + 404244*x^2 - 2032608*x^3 - 2166264*x^4 - 22896*x^5 + 967902*x^6 + 573264*x^7 + 34992*x^8 - 131968*x^9 - 76302*x^10 - 12744*x^11 + 5640*x^12 + 3564*x^13 + 513*x^14 - 156*x^15 - 54*x^16 + x^18, -6912 + 13824*x^3 + 18144*x^4 + 17568*x^6 + 6912*x^7 - 5184*x^8 - 6400*x^9 - 2736*x^10 + 864*x^11 + 894*x^12 + 288*x^13 - 54*x^14 - 48*x^15 - 9*x^16 + x^18, 4209798320128979482516352085711126528, 207891275068097752223029732627709952}, {977, {7/64, 16/49}, 393216 - 1327104*x^2 + 1492992*x^4 - 642816*x^6 + 93312*x^8 + 11520*x^9 - 2592*x^11 - 1872*x^12 + 162*x^14 + x^18, -8544 - 140832*x - 903960*x^2 + 281376*x^3 + 621216*x^4 + 87696*x^5 - 12492*x^6 - 94608*x^7 - 70416*x^8 + 3944*x^9 + 3978*x^10 + 4536*x^11 + 2208*x^12 - 180*x^13 - 81*x^14 - 12*x^15 - 18*x^16 + x^18, -170496831965223669041912259471300624384, -415782550136195504446059465255419904}, {977, {19/676, 208/361}, -115968 + 418176*x + 636336*x^2 - 4264416*x^3 + 2715768*x^4 + 5959008*x^5 - 7406397*x^6 + 1643652*x^7 + 433944*x^8 - 22764*x^9 + 85563*x^10 - 73764*x^11 + 17622*x^12 - 5724*x^13 + 1053*x^14 - 216*x^15 + 54*x^16 + x^18, 162444 + 4471848*x + 9250146*x^2 - 1087488*x^3 - 5543910*x^4 + 1438236*x^5 + 849339*x^6 + 132732*x^7 - 412020*x^8 + 36208*x^9 + 35217*x^10 - 432*x^11 + 342*x^12 - 900*x^13 + 45*x^14 - 12*x^15 + x^18, -42624207991305917260478064867825156096, -1663130200544782017784237861021679616}} (* Cases where the degree 24 polynomials are irreducible. Data presented analogously to fields18 *) fields24 = {{24946, {18/25, 5/6}, 4 - 96*x^2 - 160*x^3 - 180*x^4 + 1152*x^5 + 1584*x^6 + 720*x^7 - 3879*x^8 - 5632*x^9 + 1368*x^10 + 7392*x^11 + 4896*x^12 - 3312*x^13 - 2448*x^14 + 1776*x^15 + 306*x^16 - 384*x^17 - 120*x^18 + 36*x^20 - 16*x^21 + x^24, 128 - 1728*x^4 - 3072*x^5 - 3520*x^6 - 2304*x^7 + 516*x^8 + 7936*x^9 + 19584*x^10 + 18432*x^11 + 1296*x^12 - 19584*x^13 - 22752*x^14 - 8064*x^15 + 1332*x^16 + 2688*x^17 + 1280*x^18 - 72*x^20 - 64*x^21 + x^24, 43703853935830110189947501702144851968, 44752746430290032834506241742996328415232}, {24946, {9/14, 6/7}, -164 - 288*x + 1776*x^2 + 5120*x^3 + 6444*x^4 + 9840*x^5 + 3672*x^6 - 18432*x^7 - 20745*x^8 - 9952*x^9 - 12168*x^10 - 18048*x^11 - 40780*x^12 - 52272*x^13 - 23712*x^14 + 1168*x^15 + 4248*x^16 + 2160*x^17 + 880*x^18 - 144*x^19 - 60*x^20 - 48*x^21 + x^24, -464648 + 46272*x + 15906816*x^2 - 24927552*x^3 - 32836968*x^4 + 147452256*x^5 - 264270416*x^6 + 267617088*x^7 - 177219342*x^8 + 67410432*x^9 - 4911696*x^10 - 7866000*x^11 - 1745640*x^12 + 2798784*x^13 - 814968*x^14 + 181632*x^15 - 756*x^16 + 11088*x^17 - 7328*x^18 + 768*x^19 - 216*x^20 - 48*x^21 + x^24, 209034178555603406305103012268806060472532992, 17338130906115968932570464249623849879833776488448}, {24948, {-72, 3/16}, 4 + 64*x^3 - 42*x^4 - 48*x^5 + 352*x^6 - 432*x^7 - 279*x^8 + 944*x^9 - 768*x^10 + 624*x^11 - 148*x^12 - 1752*x^13 + 2400*x^14 - 784*x^15 - 117*x^16 - 72*x^17 + 16*x^18 + 96*x^19 - 24*x^20 - 8*x^21 + x^24, 235908 - 536976*x + 265464*x^2 + 1296864*x^3 + 989712*x^4 - 697896*x^5 - 1003404*x^6 - 364752*x^7 + 241803*x^8 + 236304*x^9 + 82152*x^10 - 31464*x^11 - 23732*x^12 - 864*x^13 + 7356*x^14 + 304*x^15 - 1116*x^16 - 336*x^17 + 288*x^18 + 72*x^19 + 12*x^20 - 8*x^21 + x^24, 219013030524415738967471652480221184, 1594804218716456652108024690771530612736}, {24948, {-12, -3/4}, 4096 - 12288*x^2 - 16384*x^3 + 3840*x^4 + 35328*x^5 + 35968*x^6 - 3840*x^7 - 43164*x^8 - 34576*x^9 + 9144*x^10 + 28656*x^11 + 10512*x^12 - 6696*x^13 - 5004*x^14 + 736*x^15 + 981*x^16 - 336*x^17 - 272*x^18 + 96*x^19 + 78*x^20 - 8*x^21 - 12*x^22 + x^24, 23716 - 85008*x + 152520*x^2 - 194880*x^3 + 215208*x^4 - 214200*x^5 + 190508*x^6 - 153768*x^7 + 113517*x^8 - 77376*x^9 + 49332*x^10 - 29088*x^11 + 17984*x^12 - 12144*x^13 + 6600*x^14 - 2808*x^15 + 1359*x^16 - 432*x^17 - 28*x^18 - 48*x^19 + 72*x^20 - 12*x^22 + x^24, 4922235242952026704037113243122008064, 78755763887232427264593811889952129024}, {24948, {828/841, 522/529}, 4 - 2304*x^2 + 1760*x^3 + 3576*x^4 - 1920*x^5 + 20480*x^6 - 46224*x^7 + 27540*x^8 + 4944*x^9 - 15072*x^10 + 816*x^11 + 9404*x^12 + 672*x^13 - 3984*x^14 + 264*x^15 - 135*x^16 + 72*x^17 + 128*x^18 + 24*x^19 - 24*x^20 - 40*x^21 + x^24, -2 + 336*x - 14760*x^2 + 54520*x^3 - 47352*x^4 + 81816*x^5 - 52212*x^6 + 7176*x^7 + 17682*x^8 - 66656*x^9 + 65004*x^10 - 52080*x^11 + 31538*x^12 - 6840*x^13 - 5784*x^14 + 8888*x^15 - 6951*x^16 + 3864*x^17 - 1316*x^18 + 360*x^19 - 12*x^20 - 24*x^21 + 12*x^22 + x^24, 3588309492112027467243055554235943878656, 229651807495169757903555555471100408233984}, {24949, {-27, -1/3}, 1 - 6*x^2 + 20*x^3 + 18*x^4 + 48*x^5 + 256*x^6 + 36*x^7 + 513*x^8 - 88*x^9 + 486*x^10 - 24*x^11 + 237*x^12 - 72*x^13 + 276*x^14 - 56*x^15 - 9*x^16 - 36*x^17 + 64*x^18 - 8*x^21 + x^24, 337 + 2148*x + 6462*x^2 + 10188*x^3 + 6603*x^4 - 6300*x^5 - 17792*x^6 - 13464*x^7 + 3726*x^8 + 14124*x^9 + 7506*x^10 - 4356*x^11 - 6597*x^12 - 756*x^13 + 3168*x^14 + 2064*x^15 - 126*x^16 - 612*x^17 - 122*x^18 + 132*x^19 + 63*x^20 - 12*x^21 - 12*x^22 + x^24, 380230955771555102374082730000384, 492779318679935412676811218080497664}, {24949, {108/121, 11/12}, 4096 - 12288*x^2 - 16384*x^3 + 23808*x^4 + 41472*x^5 - 12928*x^6 - 62208*x^7 - 4284*x^8 + 50192*x^9 + 13464*x^10 - 20688*x^11 - 12728*x^12 + 3192*x^13 + 6156*x^14 + 1072*x^15 - 1539*x^16 - 720*x^17 + 152*x^18 + 144*x^19 + 30*x^20 - 8*x^21 - 12*x^22 + x^24, -22364 - 24672*x + 44064*x^2 - 14432*x^3 - 19428*x^4 + 150768*x^5 + 19936*x^6 - 207216*x^7 + 13977*x^8 + 95776*x^9 - 67080*x^10 - 26208*x^11 + 47440*x^12 + 8976*x^13 - 12312*x^14 - 560*x^15 + 1638*x^16 - 1152*x^17 - 584*x^18 + 384*x^19 + 180*x^20 - 32*x^21 - 24*x^22 + x^24, 398701054679114163027006172692882653184, 2066866267456527821131999999239903674105856}, {24949, {162/169, 26/27}, -128 - 768*x^2 + 2816*x^3 + 864*x^4 - 576*x^5 - 13312*x^6 + 10656*x^7 + 7902*x^8 - 17128*x^9 + 21996*x^10 - 18888*x^11 + 11146*x^12 - 6768*x^13 + 2736*x^14 - 320*x^15 - 477*x^16 + 432*x^17 - 124*x^18 + 72*x^19 - 24*x^20 - 8*x^21 + x^24, -1244 - 12912*x - 29880*x^2 - 45344*x^3 + 24120*x^4 + 143496*x^5 + 176972*x^6 - 9864*x^7 - 326943*x^8 - 238280*x^9 + 214392*x^10 + 274032*x^11 - 47834*x^12 - 148248*x^13 - 13716*x^14 + 46184*x^15 + 11700*x^16 - 8568*x^17 - 3316*x^18 + 888*x^19 + 486*x^20 - 40*x^21 - 36*x^22 + x^24, 398701054679114163027006172692882653184, 129179141716032988820749999952493979631616}, {24952, {-9, 1/3}, 32 + 192*x^2 + 360*x^4 + 192*x^5 + 88*x^6 + 576*x^7 - 351*x^8 + 64*x^9 + 360*x^10 - 384*x^11 - 64*x^12 + 432*x^13 - 72*x^14 - 64*x^15 + 162*x^16 - 192*x^17 + 72*x^18 + 24*x^20 - 16*x^21 + x^24, 128 + 864*x^4 - 1536*x^5 + 1760*x^6 - 1152*x^7 + 516*x^8 - 1984*x^9 + 4896*x^10 - 4608*x^11 + 1368*x^12 - 1152*x^13 + 2160*x^14 - 960*x^15 + 360*x^16 - 672*x^17 + 320*x^18 + 36*x^20 - 32*x^21 + x^24, 682872717747345471717929714096013312, 10925963483957527547486875425536212992}, {24952, {9/8, 4/3}, -1 - 16*x^3 + 30*x^4 + 144*x^5 + 192*x^6 - 477*x^8 - 992*x^9 - 1152*x^10 + 96*x^11 + 2028*x^12 + 2688*x^13 + 1728*x^14 + 128*x^15 - 531*x^16 - 288*x^17 + 48*x^19 + 6*x^20 - 16*x^21 + x^24, -16 + 256*x^3 + 216*x^4 - 1168*x^6 - 1728*x^7 + 129*x^8 + 3136*x^9 + 4320*x^10 - 384*x^11 - 5788*x^12 - 3456*x^13 + 912*x^14 + 4288*x^15 + 306*x^16 - 576*x^17 - 384*x^18 + 36*x^20 + x^24, -5462981741978763773743437712768106496, -349630831486640881519580013617158815744}, {24952, {3/8, 24}, -2 + 32*x^3 + 96*x^4 - 96*x^5 - 64*x^6 - 507*x^8 + 1040*x^9 + 672*x^10 - 2496*x^11 - 1252*x^12 - 1488*x^13 - 768*x^14 + 512*x^15 - 588*x^16 + 432*x^17 + 32*x^18 - 96*x^19 + 60*x^20 - 16*x^21 + x^24, -16668 + 19008*x - 27072*x^2 - 35904*x^3 + 144540*x^4 - 319632*x^5 + 484264*x^6 - 549888*x^7 + 511181*x^8 - 360392*x^9 + 181252*x^10 - 58640*x^11 - 6994*x^12 + 29976*x^13 - 20440*x^14 + 40*x^15 + 9727*x^16 - 7064*x^17 + 2240*x^18 - 216*x^19 - 34*x^20 - 32*x^21 + 28*x^22 - 8*x^23 + x^24, -55312690137534983209152306841777078272, -226560778803343291224687848823918912602112}, {24952, {-4, 1/2}, 555552 + 1617408*x + 627264*x^2 - 501120*x^3 + 1029024*x^4 - 15552*x^5 - 914112*x^6 + 334368*x^7 - 178524*x^8 - 325728*x^9 + 203904*x^10 - 72576*x^11 - 18648*x^12 + 53568*x^13 - 15120*x^14 + 4752*x^15 + 7704*x^16 - 3888*x^17 + 3008*x^18 - 720*x^19 + 372*x^20 - 32*x^21 + 24*x^22 + x^24, 486 - 1296*x + 3456*x^2 - 9072*x^3 + 3564*x^4 + 9216*x^5 + 2376*x^6 - 2016*x^7 + 15534*x^8 - 2160*x^9 + 2520*x^10 + 5520*x^11 + 2556*x^12 - 2208*x^13 + 3936*x^14 - 840*x^15 + 495*x^16 + 64*x^17 + 48*x^18 + 48*x^19 + 14*x^20 - 32*x^21 + 24*x^22 - 8*x^23 + x^24, 78387816958351277364413629600802272677199872, 9440032450139303801028660367663288025088}, {24952, {-7/2, 4/49}, 243 + 864*x + 4680*x^2 + 5728*x^3 + 45522*x^4 - 18576*x^5 + 43216*x^6 - 40752*x^7 - 40581*x^8 - 6288*x^9 + 12672*x^10 + 25200*x^11 + 8740*x^12 - 25488*x^13 + 10800*x^14 - 5264*x^15 + 3681*x^16 - 1296*x^17 + 312*x^18 - 144*x^19 + 90*x^20 - 32*x^21 + x^24, 1824 - 16128*x + 47232*x^2 - 36096*x^3 - 64992*x^4 + 132096*x^5 - 47744*x^6 - 80640*x^7 + 119640*x^8 - 79744*x^9 + 31008*x^10 - 4032*x^11 - 10736*x^12 + 11424*x^13 - 1632*x^14 - 1760*x^15 + 540*x^16 - 480*x^17 + 256*x^18 + 96*x^19 - 36*x^20 - 16*x^21 + x^24, 11947541069707556373176898277823848906752, 84960292051253734209257943308969592225792}, {24952, {-8/25, 5/8}, 8 + 192*x^2 + 128*x^3 + 1920*x^4 + 1920*x^5 + 11520*x^6 + 11712*x^7 + 32481*x^8 + 16288*x^9 + 28536*x^10 + 26304*x^11 + 12528*x^12 + 15456*x^13 + 6744*x^14 + 4544*x^15 + 2106*x^16 + 672*x^17 + 888*x^18 - 192*x^19 + 240*x^20 - 32*x^21 + 24*x^22 + x^24, 648 + 2304*x^3 - 1728*x^4 - 13824*x^5 + 7168*x^6 + 38400*x^7 + 31500*x^8 + 36352*x^9 + 78336*x^10 + 92928*x^11 + 54336*x^12 + 11520*x^13 - 4608*x^14 - 3328*x^15 + 1254*x^16 + 768*x^17 + 256*x^18 - 192*x^19 - 48*x^20 + x^24, 40322951110263002759472031687655490060288, 226560778803343291224687848823918912602112}, {24952, {123/128, 1728/1681}, -8 - 2176*x^3 + 1776*x^4 + 13440*x^5 + 156160*x^6 + 221184*x^7 - 82719*x^8 - 110288*x^9 + 110688*x^10 + 68352*x^11 - 37228*x^12 - 59952*x^13 - 12864*x^14 + 3328*x^15 + 10350*x^16 + 1296*x^17 + 352*x^18 - 384*x^19 - 60*x^20 - 16*x^21 + x^24, -80928 + 18432*x + 444672*x^2 - 241920*x^3 - 1369440*x^4 + 19584*x^5 + 1385280*x^6 - 46080*x^7 - 977256*x^8 + 93504*x^9 + 526368*x^10 - 101568*x^11 - 147760*x^12 + 67520*x^13 - 10832*x^14 - 7712*x^15 + 11416*x^16 - 6048*x^17 + 2544*x^18 - 880*x^19 + 208*x^20 - 80*x^21 + 16*x^22 + x^24, -71685246418245338239061389666943093440512, -906243115213373164898751395295675650408448}, {24952, {-2, 1/2}, 54 + 432*x^2 + 1152*x^3 + 4068*x^4 + 8640*x^5 - 872*x^6 - 15264*x^7 + 17565*x^8 + 117568*x^9 + 218256*x^10 + 231072*x^11 + 164640*x^12 + 96576*x^13 + 66648*x^14 + 55712*x^15 + 40332*x^16 + 22848*x^17 + 10560*x^18 + 3552*x^19 + 492*x^20 - 128*x^21 - 48*x^22 + x^24, 3627942 - 1464624*x - 572904*x^2 - 1305024*x^3 + 1530240*x^4 - 1213392*x^5 - 195040*x^6 + 265296*x^7 + 709647*x^8 + 672*x^9 + 11016*x^10 + 90240*x^11 + 96792*x^12 - 12288*x^13 - 2712*x^14 + 7248*x^15 + 3504*x^16 - 1920*x^17 - 120*x^18 + 144*x^19 + 24*x^20 - 48*x^21 + x^24, 627102535666810218915309036806418181417598976, 7927814771886588446534277206046570589773103104}, {24953, {1, 9/8}, -3 + 72*x^2 + 96*x^3 - 360*x^4 - 720*x^5 + 684*x^6 + 2592*x^7 + 828*x^8 - 3984*x^9 - 5076*x^10 + 384*x^11 + 6322*x^12 + 6240*x^13 + 1224*x^14 - 2944*x^15 - 3204*x^16 - 1296*x^17 + 84*x^18 + 288*x^19 + 84*x^20 - 16*x^21 - 12*x^22 + x^24, 11913 - 43092*x + 96768*x^2 - 76308*x^3 + 1764*x^4 + 87048*x^5 - 233124*x^6 + 307152*x^7 - 330939*x^8 + 303552*x^9 - 221112*x^10 + 152280*x^11 - 88644*x^12 + 46584*x^13 - 19584*x^14 + 8784*x^15 - 2979*x^16 + 468*x^17 - 288*x^18 - 36*x^19 + 36*x^20 + 12*x^22 + x^24, -1478337956039806238030433654241492992, -3406090650715713572422119139372399853568}, {24953, {1, 9}, -12 + 72*x^2 - 108*x^4 - 72*x^6 + 225*x^8 + 216*x^9 + 648*x^10 + 384*x^11 + 40*x^12 - 216*x^13 - 504*x^14 - 128*x^15 - 54*x^16 + 72*x^17 + 48*x^18 - 12*x^20 - 8*x^21 + x^24, -432 + 2592*x^2 + 5184*x^3 - 5832*x^4 - 23328*x^5 - 15768*x^6 + 27216*x^7 + 58185*x^8 + 36792*x^9 - 8424*x^10 - 30240*x^11 - 19188*x^12 - 648*x^13 + 6264*x^14 + 4176*x^15 + 270*x^16 - 504*x^17 - 216*x^18 + 36*x^20 - 24*x^21 + x^24, -5913351824159224952121734616965971968, -851522662678928393105529784843099963392}, {24953, {648/625, 25/24}, -2 - 96*x^3 + 24*x^4 + 192*x^5 - 448*x^6 + 288*x^7 - 27*x^8 - 432*x^9 + 1248*x^10 - 1248*x^11 - 148*x^12 + 2352*x^13 - 3072*x^14 + 1632*x^15 - 108*x^16 - 144*x^17 - 160*x^18 + 192*x^19 - 12*x^20 - 48*x^21 + x^24, -682112 + 448512*x + 1603584*x^2 + 248832*x^3 - 2861568*x^4 - 299520*x^5 + 483328*x^6 + 3614208*x^7 - 3522528*x^8 + 1323520*x^9 - 386304*x^10 - 91008*x^11 + 60608*x^12 + 77760*x^13 + 9216*x^14 - 25408*x^15 - 3666*x^16 - 288*x^17 + 1920*x^18 + 96*x^19 - 64*x^21 + x^24, -221250760550139932836609227367108313088, -5945861078914941334900707904534927942329827328}, {24953, {27/25, 5/3}, -32 + 192*x^2 - 360*x^4 - 192*x^5 - 296*x^6 + 576*x^7 + 1473*x^8 + 752*x^9 + 1512*x^10 + 384*x^11 + 200*x^12 - 288*x^13 - 744*x^14 - 320*x^15 + 18*x^16 + 624*x^17 + 168*x^18 - 144*x^20 - 32*x^21 + x^24, -93312 + 209952*x^4 - 373248*x^5 + 427680*x^6 - 279936*x^7 + 41796*x^8 + 160704*x^9 - 396576*x^10 + 373248*x^11 - 73224*x^12 - 124416*x^13 + 107568*x^14 - 29376*x^15 + 2592*x^16 - 6048*x^17 + 2880*x^18 + 108*x^20 - 96*x^21 + x^24, -3266159039931303223517234566700094694883328, -4232942115750968977678335998443322724568793088}, {24953, {54/49, 7/6}, -288 + 5184*x^2 - 11520*x^3 - 6912*x^4 + 63072*x^5 - 83904*x^6 + 9216*x^7 + 25227*x^8 + 25872*x^9 - 41364*x^10 - 2808*x^11 + 22006*x^12 - 23544*x^13 + 2256*x^14 + 23256*x^15 + 3327*x^16 - 4680*x^17 - 1144*x^18 + 360*x^19 + 114*x^20 - 24*x^21 - 12*x^22 + x^24, -93312 + 419904*x^4 - 746496*x^5 + 855360*x^6 - 559872*x^7 + 41796*x^8 + 642816*x^9 - 1586304*x^10 + 1492992*x^11 - 255312*x^12 - 715392*x^13 + 712800*x^14 - 224640*x^15 + 11340*x^16 - 24192*x^17 + 11520*x^18 + 216*x^20 - 192*x^21 + x^24, -209034178555603406305103012268806060472532992, -17338130906115968932570464249623849879833776488448}, {24956, {-2, 1/4}, 1 - 16*x^3 + 108*x^4 - 144*x^5 - 320*x^6 + 1152*x^7 + 1242*x^8 - 13008*x^9 + 34560*x^10 - 55152*x^11 + 61026*x^12 - 49104*x^13 + 29376*x^14 - 13008*x^15 + 4077*x^16 - 576*x^17 - 320*x^18 + 288*x^19 - 54*x^20 - 16*x^21 + x^24, 367 - 1230*x + 3582*x^2 - 5334*x^3 + 3702*x^4 + 4854*x^5 - 10010*x^6 + 1170*x^7 + 13365*x^8 - 18848*x^9 + 9444*x^10 - 864*x^11 + 480*x^12 + 624*x^13 - 2148*x^14 + 2008*x^15 - 1305*x^16 - 270*x^17 + 1138*x^18 - 438*x^19 - 126*x^20 + 102*x^21 - 6*x^22 - 6*x^23 + x^24, 159660499252299073707286834658081243136, 638641997009196294829147338632324972544}, {24956, {-8, 1/64}, 171535 + 1264068*x + 4430304*x^2 + 9360448*x^3 + 13266252*x^4 + 13496832*x^5 + 10510426*x^6 + 6248088*x^7 + 2625786*x^8 + 689484*x^9 + 82170*x^10 - 11880*x^11 + 20646*x^12 + 31536*x^13 + 8478*x^14 - 2748*x^15 - 1269*x^16 - 828*x^17 - 344*x^18 + 288*x^19 + 162*x^20 - 20*x^21 - 18*x^22 + x^24, 939680 - 296448*x - 3637248*x^2 + 2102848*x^3 + 4945440*x^4 - 1983552*x^5 - 2323936*x^6 + 186048*x^7 + 1708416*x^8 - 744480*x^9 - 147744*x^10 + 40032*x^11 + 123744*x^12 - 56592*x^13 - 1152*x^14 + 10464*x^15 - 5526*x^16 + 792*x^17 + 1048*x^18 - 1308*x^19 + 798*x^20 - 304*x^21 + 78*x^22 - 12*x^23 + x^24, 116392503954926024732612102465741226246144, 67042082278037390245984571020266946317778944}, {24956, {-3/25, 5/9}, 199089 - 423864*x + 27324*x^2 - 144504*x^3 + 1680054*x^4 - 1851336*x^5 - 200708*x^6 + 1258848*x^7 - 644319*x^8 + 169776*x^9 - 75924*x^10 - 49896*x^11 + 91254*x^12 - 49464*x^13 + 22320*x^14 - 4536*x^15 - 3474*x^16 + 1296*x^17 + 192*x^18 - 72*x^19 + 36*x^20 - 12*x^22 + x^24, 186624 - 497664*x^3 + 559872*x^4 + 373248*x^6 - 870912*x^7 + 443232*x^8 - 50688*x^9 + 176256*x^10 - 93312*x^11 - 22512*x^12 - 6912*x^13 + 7776*x^14 + 800*x^15 + 297*x^16 - 864*x^17 + 408*x^18 + 54*x^20 + x^24, 1047532535594334222593508922191671036215296, 67042082278037390245984571020266946317778944}, {24956, {-3/4, 2/3}, 22579 - 9372*x + 3744*x^2 - 153548*x^3 + 48000*x^4 + 51624*x^5 + 227500*x^6 + 114372*x^7 + 104589*x^8 - 41856*x^9 + 64638*x^10 + 9972*x^11 + 5826*x^12 - 19332*x^13 + 5130*x^14 + 3672*x^15 - 1782*x^16 - 1044*x^17 + 820*x^18 - 48*x^19 - 8*x^21 - 6*x^22 + x^24, 487188 - 314928*x - 149040*x^2 + 569520*x^3 - 1053504*x^4 + 386208*x^5 + 879544*x^6 - 815904*x^7 + 18036*x^8 + 241176*x^9 - 112824*x^10 + 20520*x^11 + 5208*x^12 - 5976*x^13 + 2916*x^14 - 3008*x^15 + 2097*x^16 - 216*x^17 - 300*x^18 + 72*x^19 + 54*x^20 - 24*x^21 + x^24, 9427792820349008003341580299725039325937664, 4190130142377336890374035688766684144861184}, {24956, {-3, -1/3}, 11 + 48*x - 276*x^2 + 4*x^3 + 3720*x^4 - 17304*x^5 + 50204*x^6 - 113220*x^7 + 214497*x^8 - 351572*x^9 + 501774*x^10 - 619428*x^11 + 653786*x^12 - 582384*x^13 + 431790*x^14 - 262472*x^15 + 128682*x^16 - 50148*x^17 + 15628*x^18 - 4188*x^19 + 1140*x^20 - 328*x^21 + 78*x^22 - 12*x^23 + x^24, 186624 + 580608*x^3 - 435456*x^4 + 410112*x^6 - 186624*x^7 + 443232*x^8 - 440064*x^9 + 286848*x^10 - 139968*x^11 + 167184*x^12 - 79488*x^13 + 28512*x^14 - 22384*x^15 + 10665*x^16 - 2160*x^17 + 1560*x^18 - 432*x^19 + 54*x^20 - 48*x^21 + x^24, 9427792820349008003341580299725039325937664, 67042082278037390245984571020266946317778944}, {24961, {-8/3, 9/16}, 2 - 32*x^3 - 18*x^4 + 48*x^5 + 160*x^6 + 144*x^7 - 363*x^8 - 416*x^9 + 384*x^10 + 48*x^11 - 676*x^12 + 432*x^13 + 1056*x^14 + 16*x^15 - 300*x^16 + 96*x^17 + 64*x^18 - 48*x^19 - 18*x^20 + x^24, 128 - 512*x^3 - 96*x^4 + 768*x^5 + 704*x^6 - 1152*x^7 - 540*x^8 + 864*x^9 + 624*x^10 - 1152*x^11 + 380*x^12 + 288*x^13 - 576*x^14 + 576*x^15 - 270*x^16 + 136*x^18 - 96*x^19 + 78*x^20 - 16*x^21 + 12*x^22 + x^24, 2731490870989381886871718856384053248, 682872717747345471717929714096013312}, {24961, {-6, -3/2}, 128 - 768*x^2 + 1152*x^4 + 768*x^6 - 1455*x^8 + 1296*x^9 + 3168*x^10 + 2304*x^11 + 1300*x^12 - 1296*x^13 - 1344*x^14 - 768*x^15 + 1206*x^16 + 432*x^17 + 608*x^18 - 12*x^20 - 48*x^21 + x^24, 128 + 2304*x^4 - 3072*x^5 + 3520*x^6 - 2304*x^7 + 516*x^8 + 13824*x^10 - 18432*x^11 + 4544*x^12 + 3456*x^13 - 1824*x^14 + 128*x^15 + 2340*x^16 - 3072*x^17 + 1024*x^18 + 96*x^20 - 64*x^21 + x^24, 174815415743320440759790006808579407872, 11188186607572508208626560435749082103808}, {24961, {-3/2, 2/9}, 7558272 + 5038848*x^2 + 3779136*x^4 - 559872*x^5 + 933120*x^6 + 1679616*x^7 + 935793*x^8 + 335664*x^9 + 116640*x^10 - 62208*x^11 + 87156*x^12 + 27216*x^13 - 15552*x^14 + 4374*x^16 - 1008*x^17 - 96*x^18 + 84*x^20 - 16*x^21 + x^24, 9 + 40*x^3 + 48*x^4 + 336*x^5 + 292*x^6 + 144*x^7 + 3432*x^8 + 5944*x^9 + 15024*x^10 + 11136*x^11 + 7834*x^12 - 4128*x^13 - 6288*x^14 - 2552*x^15 + 744*x^16 + 816*x^17 + 268*x^18 - 48*x^19 - 48*x^20 - 8*x^21 + x^24, 92904079358045958357823561008358249098903552, 2039047009230089621022190639415270213419008}, {24962, {-27/25, 5/9}, 3 + 24*x^3 - 9*x^4 + 192*x^6 + 216*x^7 + 720*x^8 + 1392*x^9 + 2016*x^10 + 2688*x^11 + 3103*x^12 + 2952*x^13 + 2592*x^14 + 1528*x^15 + 828*x^16 + 216*x^17 - 72*x^19 - 21*x^20 - 8*x^21 + x^24, 67 - 384*x + 414*x^2 + 580*x^3 - 759*x^4 + 612*x^5 + 1318*x^6 + 1089*x^8 + 2092*x^9 + 1326*x^10 + 1512*x^11 + 1990*x^12 + 1680*x^13 + 1422*x^14 + 1264*x^15 + 927*x^16 + 540*x^17 + 244*x^18 + 84*x^19 + 9*x^20 - 20*x^21 - 12*x^22 + x^24, 1478337956039806238030433654241492992, 831565100272391008892118930510839808}, {24962, {891/1369, 111/121}, 24 - 192*x + 240*x^2 + 576*x^3 + 664*x^4 - 2112*x^5 - 1352*x^6 + 2272*x^7 + 2334*x^8 - 1232*x^9 - 560*x^10 + 768*x^11 - 1676*x^12 - 928*x^13 + 1800*x^14 + 632*x^15 - 770*x^16 - 264*x^17 + 136*x^18 + 64*x^19 + 12*x^20 - 8*x^21 - 8*x^22 + x^24, 1534 + 16656*x - 83232*x^2 + 88144*x^3 + 134440*x^4 - 366304*x^5 + 175512*x^6 + 291264*x^7 - 430832*x^8 + 125696*x^9 + 177224*x^10 - 200600*x^11 + 71092*x^12 + 22496*x^13 - 39156*x^14 + 21992*x^15 - 5793*x^16 - 1072*x^17 + 2100*x^18 - 1256*x^19 + 542*x^20 - 176*x^21 + 48*x^22 - 8*x^23 + x^24, -6145854459726109245461367426864119808, -7965027379805037582117932185215899271168}, {24962, {-4, -9/4}, 3 + 24*x^3 - 9*x^4 - 72*x^5 + 144*x^6 - 576*x^8 + 192*x^9 + 1152*x^10 - 120*x^11 - 1361*x^12 - 648*x^13 + 2016*x^14 - 368*x^15 - 468*x^16 + 48*x^18 + 72*x^19 - 21*x^20 - 8*x^21 + x^24, 859 - 9408*x + 36612*x^2 - 48736*x^3 + 119481*x^4 - 71856*x^5 + 166102*x^6 - 75600*x^7 + 129348*x^8 - 60304*x^9 + 67944*x^10 - 30816*x^11 + 20521*x^12 - 12192*x^13 + 2610*x^14 - 3040*x^15 + 756*x^16 - 144*x^17 + 160*x^18 - 48*x^19 + 9*x^20 - 16*x^21 + 6*x^22 + x^24, 23653407296636899808486938467863887872, 3406090650715713572422119139372399853568}, {24962, {-72/121, 11/16}, 624 + 5184*x + 19296*x^2 + 37056*x^3 + 31392*x^4 - 8640*x^5 - 35760*x^6 - 15264*x^7 + 27252*x^8 + 95808*x^9 + 157680*x^10 + 154848*x^11 + 147172*x^12 + 96264*x^13 + 59040*x^14 + 27440*x^15 + 9666*x^16 + 2664*x^17 - 48*x^18 - 216*x^19 - 138*x^20 - 40*x^21 + x^24, 10452 + 44064*x + 130320*x^2 + 309264*x^3 + 597186*x^4 + 922104*x^5 + 1103316*x^6 + 981504*x^7 + 618309*x^8 + 263664*x^9 + 53316*x^10 - 24624*x^11 - 22440*x^12 - 10512*x^13 - 4536*x^14 + 936*x^15 + 693*x^16 - 48*x^18 - 72*x^19 + 54*x^20 - 24*x^21 + 12*x^22 + x^24, 1513818066984761587743164061943288823808, 3487836826332890698160249998717337450053632}, {24962, {5022/5041, 1917/1922}, 331 - 29760*x + 55692*x^2 + 132288*x^3 - 424158*x^4 + 288336*x^5 + 121268*x^6 - 101808*x^7 - 176997*x^8 + 105072*x^9 + 100008*x^10 - 56400*x^11 - 48732*x^12 + 27504*x^13 + 12696*x^14 - 6672*x^15 - 2295*x^16 + 912*x^17 + 140*x^18 - 48*x^19 + 42*x^20 - 12*x^22 + x^24, -55296728 - 86505216*x + 30084864*x^2 + 7515264*x^3 + 8880*x^4 + 59501760*x^5 - 87857248*x^6 + 39226560*x^7 - 21244380*x^8 + 18651264*x^9 - 7366848*x^10 + 14784*x^11 - 1204080*x^12 + 126528*x^13 + 192576*x^14 - 37920*x^15 + 32034*x^16 - 8256*x^17 + 5792*x^18 - 672*x^19 + 420*x^20 - 48*x^21 + 24*x^22 + x^24, -31860109519220150328471728740863597084672, -214050998840937888056425484563257405923873783808}, {24962, {27/25, 10/9}, -48 + 288*x^2 + 384*x^3 + 288*x^4 + 1152*x^5 + 1632*x^6 - 2304*x^7 - 8388*x^8 - 7104*x^9 + 3024*x^10 + 9600*x^11 + 4648*x^12 - 3264*x^13 - 4140*x^14 - 496*x^15 + 1161*x^16 + 432*x^17 - 192*x^18 - 144*x^19 - 24*x^20 - 16*x^21 - 12*x^22 + x^24, 16192 + 54528*x + 144000*x^2 + 104576*x^3 + 305664*x^4 + 123840*x^5 + 179872*x^6 + 333216*x^7 + 7236*x^8 + 215264*x^9 + 66864*x^10 - 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622080*x^9 + 22149936*x^10 + 1150848*x^11 + 10068408*x^12 + 1181952*x^13 + 2258928*x^14 - 103680*x^15 + 225504*x^16 - 41472*x^17 + 16488*x^18 - 5184*x^19 + 324*x^20 + x^24, 1435227444 - 1418225760*x + 3813575256*x^2 - 13343886000*x^3 + 20598920784*x^4 - 18265378176*x^5 + 11445983676*x^6 - 5917092120*x^7 + 2669784165*x^8 - 1032524512*x^9 + 359127324*x^10 - 125190624*x^11 + 40033464*x^12 - 9438456*x^13 + 1772532*x^14 - 525400*x^15 + 158076*x^16 - 7056*x^17 - 7436*x^18 + 144*x^19 + 552*x^20 - 24*x^21 - 24*x^22 + x^24, 1229946378294701252666978262917411496552940599219585024, 60738092755293889020591519156415382545824227121954816}, {24982, {-49/32, 1024/2401}, 206499456 - 949542912*x + 1966830336*x^2 - 2486101248*x^3 + 1817989920*x^4 - 188536896*x^5 - 551962512*x^6 - 409161456*x^7 + 1152783009*x^8 - 588644496*x^9 - 70907400*x^10 + 82219536*x^11 + 69422652*x^12 - 60629904*x^13 + 12439656*x^14 - 727632*x^15 + 980262*x^16 - 252720*x^17 - 5688*x^18 - 3024*x^19 + 2268*x^20 - 112*x^21 - 24*x^22 + x^24, 16702254852 - 2435237856*x + 105678397872*x^2 - 114920894112*x^3 + 89885954340*x^4 - 22694562288*x^5 + 7061589624*x^6 - 3572775504*x^7 + 3397315833*x^8 - 1299287360*x^9 + 203124696*x^10 - 100878768*x^11 + 25703504*x^12 + 2013408*x^13 + 1657944*x^14 - 288016*x^15 + 3174*x^16 - 28128*x^17 + 2376*x^18 + 48*x^19 - 84*x^20 - 48*x^21 + x^24, 546642834797645001185323672407738442912418044097593344, 85316607656270154124946111956336559296192055655530496}, {24982, {-1/2, 2/3}, 4374 - 104976*x^2 - 155520*x^3 + 927288*x^4 + 3919104*x^5 + 6586488*x^6 + 5668704*x^7 + 2060397*x^8 - 362880*x^9 - 134136*x^10 + 832032*x^11 + 758592*x^12 + 186624*x^13 - 70632*x^14 - 47520*x^15 + 48600*x^16 + 10368*x^17 + 10872*x^18 - 7776*x^19 + 2376*x^20 + x^24, 1755122340 + 1876300128*x + 113535333680*x^2 - 167591767744*x^3 + 95905668168*x^4 - 17667171488*x^5 + 11014103392*x^6 - 27418812768*x^7 + 25640572032*x^8 - 12798019776*x^9 + 3710207808*x^10 - 567121904*x^11 + 37709080*x^12 - 19055808*x^13 + 12874472*x^14 - 3301408*x^15 + 180333*x^16 + 88200*x^17 - 19356*x^18 + 1800*x^19 - 238*x^20 + 8*x^21 + 36*x^22 - 8*x^23 + x^24, 8746285356762320018965178758523815086598688705561493504, 85316607656270154124946111956336559296192055655530496}, {24982, {-19/8, 64/361}, 947808 - 5992704*x + 16671744*x^2 - 24477696*x^3 + 15186960*x^4 + 6111936*x^5 - 11605968*x^6 - 5462640*x^7 + 16106769*x^8 - 6428304*x^9 - 3592728*x^10 + 2004912*x^11 + 1624548*x^12 - 1300464*x^13 + 231336*x^14 - 93648*x^15 + 89910*x^16 - 14256*x^17 - 3624*x^18 - 1008*x^19 + 756*x^20 - 16*x^21 - 24*x^22 + x^24, 535125657600 + 474538549248*x + 760785426432*x^2 + 878573537280*x^3 + 954881851392*x^4 + 447661334016*x^5 + 246733910784*x^6 + 70254138240*x^7 + 26137370628*x^8 + 3839213376*x^9 + 1691629920*x^10 - 89159616*x^11 + 105167808*x^12 - 27760320*x^13 + 6625152*x^14 - 1532736*x^15 + 415044*x^16 - 7776*x^17 + 15408*x^18 - 864*x^19 - 96*x^21 + x^24, 136660708699411250296330918101934610728104511024398336, 248783227925683769428342862464677406907696034291526926336}, {24982, {5/32, 16/25}, -133521534 - 1518688800*x + 3432956400*x^2 + 39992288160*x^3 + 23951426004*x^4 - 28623956688*x^5 - 31731909600*x^6 - 2451322656*x^7 + 6018535143*x^8 + 1454926824*x^9 - 239873724*x^10 - 109269000*x^11 - 12298662*x^12 + 11791440*x^13 + 2909520*x^14 - 661176*x^15 - 310419*x^16 - 53568*x^17 + 576*x^18 + 984*x^19 - 642*x^20 - 232*x^21 - 36*x^22 + x^24, 5795672 - 1352448*x - 72844896*x^2 - 63747744*x^3 + 35245248*x^4 + 125968896*x^5 + 609092744*x^6 - 274653936*x^7 - 516754413*x^8 + 218409504*x^9 + 147920328*x^10 - 18032832*x^11 - 6287904*x^12 - 9431568*x^13 - 914328*x^14 + 582864*x^15 + 50490*x^16 + 46512*x^17 - 10688*x^18 + 2448*x^19 - 384*x^20 - 48*x^21 - 24*x^22 + x^24, 136660708699411250296330918101934610728104511024398336, 341266430625080616499784447825346237184768222622121984}, {24982, {5/8, 64/75}, -1706346 + 44043264*x - 145001016*x^2 - 333079776*x^3 - 988490952*x^4 - 3416059008*x^5 - 4800349440*x^6 - 3471941232*x^7 - 1893805677*x^8 - 759172824*x^9 - 179024904*x^10 - 99810792*x^11 - 35023968*x^12 - 2674944*x^13 - 1877256*x^14 + 231984*x^15 - 169938*x^16 + 56376*x^17 + 14832*x^18 - 1512*x^19 + 1836*x^20 - 48*x^21 + 72*x^22 + x^24, 1697773446 + 389367648*x - 2341192896*x^2 - 3995272368*x^3 - 4742584236*x^4 - 2136551904*x^5 + 150703976*x^6 + 1422504864*x^7 + 1413938421*x^8 + 640238400*x^9 + 144974016*x^10 - 98655840*x^11 - 85237692*x^12 - 44664480*x^13 - 15352560*x^14 - 4144032*x^15 - 1112580*x^16 - 120096*x^17 - 26688*x^18 - 1008*x^19 + 1152*x^20 + 72*x^22 + x^24, 136660708699411250296330918101934610728104511024398336, 3071397875625725548498060030428116134662914003599097856}, {24982, {23/24, 512/529}, -1153884072 - 2627299584*x + 500653728*x^2 + 4499715456*x^3 + 2767735080*x^4 + 125468352*x^5 - 1586285616*x^6 - 2478884256*x^7 - 788851575*x^8 + 392466048*x^9 + 290987748*x^10 + 52040736*x^11 - 9396162*x^12 - 5867136*x^13 - 990864*x^14 + 92256*x^15 - 83421*x^16 - 38016*x^17 + 3520*x^18 + 1728*x^19 + 1038*x^20 - 192*x^21 + 12*x^22 + x^24, 2021238 - 60692544*x + 465051888*x^2 - 1472378256*x^3 + 2453926644*x^4 - 2285064432*x^5 + 994315752*x^6 + 524658816*x^7 - 975029643*x^8 + 484010832*x^9 - 101214720*x^10 + 15709536*x^11 - 21294324*x^12 + 13033008*x^13 - 2838672*x^14 + 33216*x^15 + 10188*x^16 + 64368*x^17 - 15664*x^18 - 2832*x^19 + 1704*x^20 - 192*x^21 - 24*x^22 + x^24, 136660708699411250296330918101934610728104511024398336, 3071397875625725548498060030428116134662914003599097856}, {24982, {2/3, 3/2}, -18 + 432*x^2 - 1536*x^3 + 3456*x^4 - 6912*x^5 + 10360*x^6 - 7776*x^7 - 4707*x^8 + 16512*x^9 - 12744*x^10 - 288*x^11 + 6384*x^12 - 4608*x^13 + 792*x^14 + 672*x^15 - 3024*x^16 - 1152*x^17 - 24*x^18 - 288*x^19 - 144*x^20 + x^24, 9633633 - 2113056*x - 7864560*x^2 + 3200520*x^3 + 37930968*x^4 - 16553376*x^5 - 28823724*x^6 + 2384208*x^7 + 9049608*x^8 + 556808*x^9 - 1130952*x^10 - 20160*x^11 + 200314*x^12 - 138144*x^13 - 98424*x^14 - 11320*x^15 + 21366*x^16 + 1296*x^17 - 788*x^18 + 336*x^19 + 360*x^20 - 136*x^21 - 24*x^22 + x^24, -323936494694900741443154768834215373577729211317092352, -575887101679823540343386255705271775249296375674830848}, {24982, {1/2, 2/3}, 4374 - 104976*x^2 + 264384*x^3 + 43740*x^4 - 1119744*x^5 + 2037528*x^6 - 1469664*x^7 - 284067*x^8 + 1223424*x^9 - 536544*x^10 - 427680*x^11 + 498096*x^12 + 31104*x^13 - 198936*x^14 - 16416*x^15 + 55404*x^16 + 10368*x^17 - 5328*x^18 - 2592*x^19 - 540*x^20 + x^24, -78571482 - 510732864*x - 294206832*x^2 + 530198640*x^3 - 3076884*x^4 + 363394944*x^5 - 351963984*x^6 + 239810688*x^7 - 74831211*x^8 - 92962400*x^9 + 83043648*x^10 - 47745552*x^11 + 9384612*x^12 + 3610128*x^13 - 3696480*x^14 + 1011392*x^15 + 152568*x^16 - 139104*x^17 + 3152*x^18 + 6912*x^19 + 768*x^20 - 48*x^21 - 48*x^22 + x^24, 2186571339190580004741294689630953771649672176390373376, 341266430625080616499784447825346237184768222622121984}, {24982, {-128/529, 23/32}, 22502860634 - 41675725296*x + 42388071168*x^2 - 9458717280*x^3 - 15007302372*x^4 + 13201384896*x^5 - 785964656*x^6 - 4633315488*x^7 + 1936940409*x^8 + 643596944*x^9 - 516781620*x^10 - 3276456*x^11 + 71846916*x^12 - 13949544*x^13 - 5575428*x^14 + 2067688*x^15 + 335322*x^16 - 151704*x^17 - 25684*x^18 + 8784*x^19 + 1632*x^20 - 432*x^21 - 12*x^22 + x^24, 483352592 + 143103744*x - 901382016*x^2 + 2094387840*x^3 - 769605600*x^4 - 1470319488*x^5 + 4411840544*x^6 - 5959924128*x^7 + 5836240278*x^8 - 4508894256*x^9 + 2826614808*x^10 - 1479849984*x^11 + 649742124*x^12 - 240407856*x^13 + 76141296*x^14 - 20545008*x^15 + 4773258*x^16 - 989136*x^17 + 158704*x^18 - 13824*x^19 + 1524*x^20 - 240*x^21 - 24*x^22 + x^24, 546642834797645001185323672407738442912418044097593344, 6910645220157882484120635068463261302991556508097970176}, {24982, {-32/25, 5/8}, 349226721 + 844164504*x + 1136024028*x^2 + 928390248*x^3 + 748032732*x^4 + 478375632*x^5 + 285021504*x^6 + 118587888*x^7 + 52617762*x^8 + 15231240*x^9 + 4467312*x^10 - 635688*x^11 - 155358*x^12 - 186624*x^13 - 9396*x^14 - 31752*x^15 + 5832*x^16 + 648*x^17 + 976*x^18 - 360*x^19 - 40*x^21 + x^24, 6985196208 - 11901869568*x + 14839250112*x^2 - 5566059264*x^3 - 4868567568*x^4 + 6622379136*x^5 - 3351446528*x^6 - 1503663552*x^7 + 1685985588*x^8 - 103166976*x^9 - 144393984*x^10 + 71458560*x^11 - 3076704*x^12 + 5897088*x^13 + 344448*x^14 - 690592*x^15 + 521352*x^16 - 116352*x^17 + 24144*x^18 - 2304*x^19 - 396*x^20 - 96*x^21 + x^24, 1229946378294701252666978262917411496552940599219585024, 27642580880631529936482540273853045211966226032391880704}, {24982, {5/8, 16/25}, 629856 - 10077696*x^2 + 22021632*x^3 - 5213808*x^4 - 40310784*x^5 + 66459744*x^6 - 39051072*x^7 - 9645399*x^8 + 25443072*x^9 - 10025208*x^10 - 4929984*x^11 + 6013224*x^12 + 62208*x^13 - 1586304*x^14 - 98496*x^15 + 253206*x^16 + 41472*x^17 - 15912*x^18 - 5184*x^19 - 648*x^20 + x^24, -5130475451546 + 16052248029888*x - 17139903080928*x^2 + 6862198493328*x^3 + 239694950964*x^4 - 710975076624*x^5 + 1611112840*x^6 + 9029599344*x^7 + 37808071317*x^8 - 10180788016*x^9 + 735591168*x^10 - 1028287632*x^11 + 280672356*x^12 + 17088720*x^13 + 7049232*x^14 - 3852784*x^15 - 734148*x^16 + 103536*x^17 + 23392*x^18 + 8064*x^19 - 960*x^20 - 192*x^21 - 24*x^22 + x^24, 1229946378294701252666978262917411496552940599219585024, 248783227925683769428342862464677406907696034291526926336}, {24982, {-2, -1/2}, 39366 + 314928*x^2 + 373248*x^3 + 1399680*x^4 + 1679616*x^5 + 2900664*x^6 + 1889568*x^7 + 2771901*x^8 + 1337472*x^9 + 2070360*x^10 + 474336*x^11 + 1016496*x^12 + 124416*x^13 + 333720*x^14 - 18144*x^15 + 25272*x^16 - 10368*x^17 + 72*x^18 - 2592*x^19 + 432*x^20 + x^24, 16592512068 + 1380271104*x + 37646368704*x^2 - 14101288704*x^3 + 23366748780*x^4 - 16065690336*x^5 + 5818015728*x^6 + 1994919840*x^7 - 1151041023*x^8 - 238425936*x^9 + 443643048*x^10 + 213743952*x^11 + 39832560*x^12 + 2877120*x^13 + 2695176*x^14 + 148128*x^15 + 211446*x^16 - 8208*x^17 + 3256*x^18 - 3312*x^19 + 516*x^20 - 96*x^21 - 24*x^22 + x^24, 78716568210860880170686608826714335779388198350053441536, 1727661305039470621030158767115815325747889127024492544}} (* Section eight. A degree 96 family: a large degree dessin and Newton polygons*) (* The one parameter slice discussed in the paper. As a check, f96[1] indeed factors as 40^2 + 16 *) f96[t_] :=( (-3869835264 + 123834728448*x - 1878160048128*x^2 + 17986994307072*x^3 - 122178152300544*x^4 + 626540088655872*x^5 - 2520589064601600*x^6 + 8162827596988416*x^7 - 21681369027919872*x^8 + 47950288840949760*x^9 - 89556680876359680*x^10 + 143474999551229952*x^11 - 200876992270295040*x^12 + 250987121290100736*x^13 - 284898502452436992*x^14 + 295558502345637888*x^15 - 277106243726667264*x^16 + 229049096903122944*x^17 - 161987009378324480*x^18 + 95197078307043328*x^19 - 45252388465854976*x^20 + 16964516971136000*x^21 - 4902849972088320*x^22 + 1076315934382080*x^23 - 178485128485440*x^24 + 20121596404224*x^25 + 500924971008*x^26 - 1143902168192*x^27 + 345466405984*x^28 - 57608479936*x^29 + 5718682592*x^30 - 316240512*x^31 + 7411887*x^32)^3- t 1048576*x^6*(-2 + 3*x)^2*(-2 + 2*x + x^2)^6*(6 - 14*x + 7*x^2)^21* (-6 + 18*x - 15*x^2 + 2*x^3)^9) (* js237 is the list of 413 specialization points keeping ramification within {2,3,7} *) js237 = {9938375/37933056, -15625/48384, -548347731625/3170893824, 128787625/169344, 4956477625/1626379776, 2251439055699625/43352064, 13027640977/37340352, 7189057/6858432, 53297461115137/254016, -4354703137/29884728384, 103823/108864, 6570725617/79361856, 389017/34992, 2197/972, 7189057/1296, 103823/5668704, 1532808577/7776, 32/81, -64000/9, 1331/8, 125/4, 84448510979617/1613775332736, 268498407453697/435456, -7189057/27869184, 124475734657/108884466432, 65597103937/109734912, 6359387729183/7289703921024, -125/64, 614125/64, 343/512, -389017/294912, -4913/128, 26730899/224, 1/28, 6859/784, 205379/76832, -1/3024, 1771561/42336, 614125/551124, -256/3969, 1295029/6804, 165017459125/333396, 32000/35721, -157216000/9529569, 12167/17496, 343/243, 912673/648, 2197/81, 343/54, 2/27, -448/81, -26779859008/43046721, -1331/256, -15625/1536, 125/128, 12167/12288, -7022735875/8192, -128787625/402653184, 95443993/244944, 2924207/3111696, 1770243636673/81648, 50653/47628, -42592/1750329, 1630532233/1607077584, 42592/567, 433798093/3857868, 64/63, 183250432/63, 32768/7, 512/343, 6355468/27, 28/27, -1/288, -16/9, 15625/10584, 125/189, 125/27, -6329617441/483729408, -16591834777/169869312, 838561807/45349632, -2401/10368, 4913/2239488, 596183/1492992, 1/4, -2197/12, 4, 1372/3, 12994449551/15179544576, -426957777/1792, -185193/1404928, -181802454625/8064, 166375/229376, 127263527/1056964608, -1/16128, -274625/175616, 125/486, -6859/39366, 297754/729, 250/81, 196/27, 28, 20577/128, 3501153/512, -128625/256, 375/4096, 3993/512, 44217/32768, 27/196, -32/49, 50653/28, 32/7, -1/9408, 256/81, 6859/972, 6272/6561, 4/3, -1/48, 103823/1555848, 50653/15309, 1439069689/546852789, 79507/11907, 38272753/4667544, 304821217/4536, 2924207/9920232, 248858189/771895089, 300763/107163, 16194277/1701, 125/3969, 15625/1701, 128/7, -50653/12348, 27/28, 1024/63, 170368/3087, 915498611/6561, -125/2187, 1/243, 1331/81, 42875/243, -13651919/1594323, -8, 8/9, -1/8, -2505377/512, 7/32768, 250/7, 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1195061/3, 2401, -133128246, -4374, 9/2, -6} (* Section nine. A degree 202 family: degenerations and specialization *) (* f202 has 10484 terms*) f202[{u_,v_}] := ( 1350851717672992089*x^202 - 115272679908095324928*x^201*u + 115272679908095324928*x^201*v - 434073685278921457932*x^201 + 3278867339608044797952*x^200*u^2 - 6557734679216089595904*x^200*u*v + 39251948518149626128608*x^200*u + 3278867339608044797952*x^200*v^2 - 34525768641917717806560*x^200*v + 68313371867444793936042*x^200 - 31088519960728128454656*x^199*u^3 + 93265559882184385363968*x^199*u^2*v - 1183079091884408275083264*x^199*u^2 - 93265559882184385363968*x^199*u*v^2 + 2082536158892720675143680*x^199*u*v - 6566425314253481708564544*x^199*u + 31088519960728128454656*x^199*v^3 - 899457067008312400060416*x^199*v^2 + 5049731432400490142786880*x^199*v - 7012164917905823349140328*x^199 + 12221674409561245498736640*x^198*u^3 - 31768581334869056264601600*x^198*u^2*v + 209646398755821381796917504*x^198*u^2 + 26872139441054376032993280*x^198*u*v^2 - 324690108697392593377835520*x^198*u*v + 719355680684508623688664992*x^198*u - 7325232515746565267128320*x^198*v^3 + 119547826250236957007882496*x^198*v^2 - 479845217666486047348379232*x^198*v + 527370315221279450082382614*x^198 - 8953493748689700994940928*x^197*u^4 + 17906987497379401989881856*x^197*u^3*v - 2341463009842043421555621888*x^197*u^3 + 5321222922286366429604806656*x^197*u^2*v - 24331202400705746786207308800*x^197*u^2 - 17906987497379401989881856*x^197*u*v^3 - 3781423101375233818555908096*x^197*u*v^2 + 33118814243180150607209536512*x^197*u*v - 58038230663618028134933922048*x^197*u + 8953493748689700994940928*x^197*v^4 + 801663188930910810506723328*x^197*v^3 - 10208335497363495775157501952*x^197*v^2 + 33233212478295285003038700288*x^197*v - 30940458193009576259752487184*x^197 + 3207838995054436418618130432*x^196*u^4 - 6131904282760676905007972352*x^196*u^3*v + 292048466569937026699332501504*x^196*u^3 + 236528368421210874200457216*x^196*u^2*v^2 - 584385145977077396908575031296*x^196*u^2*v + 2080886666973724487995633198080*x^196*u^2 + 5091300131221863292150480896*x^196*u*v^3 + 345943622964462842401254162432*x^196*u*v^2 - 2484835587018527763750285394944*x^196*u*v + 3677115796158700485932563753920*x^196*u - 2403763211936833679961096192*x^196*v^4 - 52038910502705754576555835392*x^196*v^3 + 624900429112026412635509624832*x^196*v^2 - 1782664706344070565686197199808*x^196*v + 1471622452297697474565186311136*x^196 - 644651549905658471635746816*x^195*u^5 + 3223257749528292358178734080*x^195*u^4*v - 564923047058957037674063462400*x^195*u^4 - 6446515499056584716357468160*x^195*u^3*v^2 + 1032243022767305620167698939904*x^195*u^3*v - 26718565554107951226670059503616*x^195*u^3 + 6446515499056584716357468160*x^195*u^2*v^3 - 77739518638087306729029107712*x^195*u^2*v^2 + 47339836268947989959976641593344*x^195*u^2*v - 139894948117815218234725322797056*x^195*u^2 - 3223257749528292358178734080*x^195*u*v^4 - 703586794971846519434212540416*x^195*u*v^3 - 23107362267379777004580995874816*x^195*u*v^2 + 146180722025754254223548216810496*x^195*u*v - 190490342966492027246760472169760*x^195*u + 644651549905658471635746816*x^195*v^5 + 314006337901585243669606170624*x^195*v^4 + 2001645828080470904567619059712*x^195*v^3 - 28867948549029372081143586880512*x^195*v^2 + 76741622271919147634311381438752*x^195*v - 58187312901293655002023131433272*x^195 + 208428712586627130561266712576*x^194*u^5 - 1028032193563441521838232961024*x^194*u^4*v + 65217993712343822158607465054208*x^194*u^4 + 2027841648387494781740264718336*x^194*u^3*v^2 - 113940296632091786656611532013568*x^194*u^3*v + 1914528966295447476115515358396416*x^194*u^3 - 1999618909648106519804063514624*x^194*u^2*v^3 + 12667313166243409058746683359232*x^194*u^2*v^2 - 3017544755502844297888026609106944*x^194*u^2*v + 7701329743508070942133176773634816*x^194*u^2 + 985698085454359128933931155456*x^194*u*v^4 + 62677321507745336369676652904448*x^194*u*v^3 + 1200037164670859960366204924510208*x^194*u*v^2 - 7019466607273763008950952138513920*x^194*u*v + 8295686986541198515523261508645936*x^194*u - 194317343216932999593166110720*x^194*v^5 - 26473636327012737074592631750656*x^194*v^4 - 23108459511122022967425235501056*x^194*v^3 + 1023854831789927603675686876664064*x^194*v^2 - 2705962749522076344008289856403376*x^194*v + 1944374826629875096708617285071217*x^194 + 27505132795974761456458530816*x^193*u^6 - 110020531183899045825834123264*x^193*u^5*v - 32976273504966506373854225498112*x^193*u^5 + 137525663979873807282292654080*x^193*u^4*v^2 + 161066446327846845014344854405120*x^193*u^4*v - 5553586921842180149328442652884992*x^193*u^4 - 314061208775465102609288320253952*x^193*u^3*v^2 + 9279728721492574832968320933691392*x^193*u^3*v - 112017678416445662215272587702108160*x^193*u^3 - 137525663979873807282292654080*x^193*u^2*v^4 + 305547683408979301480338089312256*x^193*u^2*v^3 - 1362892738399028334027804235530240*x^193*u^2*v^2 + 157674377251405537628499906101084160*x^193*u^2*v - 357084424914303880977383130574150656*x^193*u^2 + 110020531183899045825834123264*x^193*u*v^5 - 148296158278118143320919507992576*x^193*u*v^4 - 4016663100910970715008893842358272*x^193*u*v^3 - 50412817954654184114753522661163008*x^193*u*v^2 + 282825024866400337469694931557823488*x^193*u*v - 309883035049679747155940693845695936*x^193*u - 27505132795974761456458530816*x^193*v^6 + 28719510821723605809379110027264*x^193*v^5 + 1608210629782279033225521980768256*x^193*v^4 - 2667007663258275392103661334888448*x^193*v^3 - 27264938096787836242316286535520256*x^193*v^2 + 78809654076830388324238516457823936*x^193*v - 55457593085177785801300306347229860*x^193 - 11067568816646983354663726743552*x^192*u^6 + 45934717816477683914013098901504*x^192*u^5*v + 3398623134018216952115379031769088*x^192*u^5 - 67001930467394602767069304848384*x^192*u^4*v^2 - 16511063362300484624254116128882688*x^192*u^4*v + 372118861963800135058428903399358464*x^192*u^4 + 30011920037741239021420765249536*x^192*u^3*v^3 + 31900684728215581232945852558868480*x^192*u^3*v^2 - 594882349472185864138194626505867264*x^192*u^3*v + 5507952107921608137806052195823411200*x^192*u^3 + 18642176776071810717978445479936*x^192*u^2*v^4 - 30633343272531135498142007225745408*x^192*u^2*v^3 + 108789974922784631549623689613934592*x^192*u^2*v^2 - 6948038636527683866745389609689178112*x^192*u^2*v + 14234977827201827171883305742656486400*x^192*u^2 - 22580567978295446874025101361152*x^192*u*v^5 + 14615770139526381033886026131570688*x^192*u*v^4 + 194949468375642926473255126252388352*x^192*u*v^3 + 1762244015257692112065124594273910784*x^192*u*v^2 - 9756341041719630941691719976506631168*x^192*u*v + 10081977159495570288234502868438147496*x^192*u + 6061252632046299342345823322112*x^192*v^6 - 2770671366928559096551134367580160*x^192*v^5 - 74178226846566833767741901379207168*x^192*v^4 + 229730121396719254586698068536229888*x^192*v^3 + 479089479346919287860863316134255616*x^192*v^2 - 1885159010435728410570121137432962280*x^192*v + 1355202438621189657249157315775096886*x^192 + 3960739122620365649730028437504*x^191*u^7 - 27725173858342559548110199062528*x^191*u^6*v + 2144444761646560129249576463892480*x^191*u^6 + 83175521575027678644330597187584*x^191*u^5*v^2 - 9072964409992872617069690876854272*x^191*u^5*v - 256132826968609839244632076603883520*x^191*u^5 - 138625869291712797740550995312640*x^191*u^4*v^3 + 14329792584819951008785289730588672*x^191*u^4*v^2 + 1244080628006746431734233647852552192*x^191*u^4*v - 20438016887664262144407116622097022976*x^191*u^4 + 138625869291712797740550995312640*x^191*u^3*v^4 - 9410748531179384045717345273905152*x^191*u^3*v^3 - 2387825501785540296573409675481972736*x^191*u^3*v^2 + 31266679680195843300615776479003803648*x^191*u^3*v - 232448444683740376922996338025604243456*x^191*u^3 - 83175521575027678644330597187584*x^191*u^2*v^5 + 816462759848770316393559248338944*x^191*u^2*v^4 + 2263834739915342530001483083315937280*x^191*u^2*v^3 - 6862863475911293431514321149095837696*x^191*u^2*v^2 + 263646870945039057922268885620370251776*x^191*u^2*v - 495607135870188295007912664529882733568*x^191*u^2 + 27725173858342559548110199062528*x^191*u*v^6 + 1778303214645809779074754003599360*x^191*u*v^5 - 1059855404985202176562359067289321472*x^191*u*v^4 - 7288610499849918254169271909956452352*x^191*u*v^3 - 52493042260825601693594062413256482816*x^191*u*v^2 + 292665246877048745279070156172284435456*x^191*u*v - 289136140888736728463508605832160842288*x^191*u - 3960739122620365649730028437504*x^191*v^7 - 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It appears as a factor in f202degen *) c25[w_] := 4*w*x^5*(5 - 5*x + x^2)^3*(10 - 10*x + 3*x^2)^2*(15 - 20*x + 6*x^2)^4*(10 - 15*x + 6*x^2) - (-5 + 2*x)*(-5 + 3*x)^2*(50 - 120*x + 105*x^2 - 40*x^3 + 6*x^4)^4* (-625 + 1750*x - 1800*x^2 + 760*x^3 - 40*x^4 - 60*x^5 + 12*x^6) (* The 2947 specialization points for the degree 202 family are the same as those from data52 in Section 6 for the degree 52 family. fields25dgen gives information about specialization of c25. 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37775845*x^13 - 31581995*x^14 + 2806843*x^15 + 4016632*x^16 - 228847*x^17 - 233590*x^18 + 15518*x^19 + 3756*x^20 - 342*x^21 + 207*x^22 - 20*x^23 - 8*x^24 + x^25, 172909019862142987392000000000000000000000000000000000}, {-24, -78732000000 - 164025000000*x - 3579390000000*x^2 - 90396000000*x^3 - 14337000000*x^4 + 47187900000*x^5 + 174336300000*x^6 + 13637070000*x^7 - 19826450000*x^8 - 2369128500*x^9 - 2628685000*x^10 - 347004000*x^11 + 491590500*x^12 + 95023500*x^13 - 7756750*x^14 + 2107917*x^15 - 843200*x^16 - 1354175*x^17 - 168300*x^18 + 61370*x^19 + 22140*x^20 + 870*x^21 - 750*x^22 - 55*x^23 + x^25, 524618774337287167672320000000000000000000000000000000000000}, {25, -17517152700 + 139437174000*x - 165638070550*x^2 + 77826877210*x^3 + 4804691240*x^4 - 49216177435*x^5 + 69190690750*x^6 - 48536498500*x^7 + 14323252220*x^8 + 1522215205*x^9 - 1770587620*x^10 + 71809850*x^11 + 188911180*x^12 - 61409140*x^13 + 2407780*x^14 + 11308490*x^15 - 7509500*x^16 + 1956070*x^17 - 168286*x^18 + 7576*x^19 - 13004*x^20 + 3575*x^21 - 170*x^22 - 26*x^23 - 4*x^24 + x^25, 209847509734914867068928000000000000000000000000000000000}, {2/27, 325926528 - 1728010560*x + 3213736320*x^2 - 2215616640*x^3 + 559376640*x^4 - 785069664*x^5 + 1604097440*x^6 - 1369747920*x^7 + 552611000*x^8 - 72985900*x^9 - 52839064*x^10 + 34909280*x^11 - 24472820*x^12 + 15967580*x^13 - 8275370*x^14 + 2787677*x^15 - 821600*x^16 + 296975*x^17 - 98500*x^18 + 21170*x^19 - 700*x^20 + 370*x^21 - 70*x^22 - 65*x^23 + x^25, -47383813383216168960000000000000000000000000000000000000}, {25/27, -8315162496 - 1962423360*x + 6833688480*x^2 + 8055841200*x^3 - 2453812800*x^4 - 5244261840*x^5 + 711625360*x^6 + 1901385960*x^7 + 90314800*x^8 - 221021240*x^9 + 78270916*x^10 + 55534750*x^11 + 3022720*x^12 - 6506690*x^13 - 2368700*x^14 - 254144*x^15 + 212200*x^16 + 48790*x^17 + 17350*x^18 - 515*x^19 - 368*x^20 - 35*x^21 - 50*x^22 + 10*x^23 + x^25, -4738381338321616896000000000000000000000000000000000}, {-2/25, -77145008 + 257380740*x - 323189420*x^2 + 75809290*x^3 + 187698670*x^4 - 113055482*x^5 - 91437220*x^6 + 128394460*x^7 - 62151040*x^8 + 1561345*x^9 + 33689408*x^10 - 34220300*x^11 + 13267020*x^12 + 2926600*x^13 - 4629120*x^14 + 906408*x^15 + 313920*x^16 - 10350*x^17 - 52980*x^18 - 270*x^19 + 3798*x^20 + 10*x^21 - 60*x^22 - 20*x^23 + x^25, 9097692169577504440320000000000000000000000000000000}, {27/25, 192568980 - 474446700*x - 116850100*x^2 + 574077500*x^3 + 106064000*x^4 - 368314504*x^5 + 12446420*x^6 + 182360180*x^7 - 22109445*x^8 - 32292765*x^9 + 3538917*x^10 - 1394775*x^11 + 4732125*x^12 + 1283535*x^13 - 1082550*x^14 + 282354*x^15 + 84390*x^16 - 69060*x^17 - 4995*x^18 + 825*x^19 + 313*x^20 - 365*x^21 + 130*x^22 + 10*x^23 - 5*x^24 + x^25, 568605760598594027520000000000000000000000000000000}, {-25/2, -222253056 - 556177536*x - 716265216*x^2 + 168497760*x^3 + 437550144*x^4 - 576475872*x^5 - 375702720*x^6 + 504536880*x^7 + 175633440*x^8 - 307323660*x^9 - 67011216*x^10 + 78409399*x^11 + 1328554*x^12 - 4131485*x^13 + 5347544*x^14 - 2022721*x^15 - 1408654*x^16 + 511611*x^17 + 162240*x^18 - 56439*x^19 - 9370*x^20 + 3293*x^21 + 248*x^22 - 95*x^23 - 2*x^24 + x^25, 7107572007482425344000000000000000000000000000000000}, {27/2, -1435701024 - 10340002080*x - 33402501840*x^2 - 44474898560*x^3 - 52852924640*x^4 - 49660077312*x^5 - 36833989760*x^6 - 23990010560*x^7 - 12327227520*x^8 - 5606859120*x^9 - 2200154652*x^10 - 755218080*x^11 - 197015080*x^12 - 43035520*x^13 - 2800140*x^14 - 1586416*x^15 - 310570*x^16 + 34770*x^17 - 32370*x^18 + 6120*x^19 - 168*x^20 + 820*x^21 + 250*x^22 - 60*x^23 - 5*x^24 + x^25, 4442232504676515840000000000000000000000000000000000000}, {5/32, -5933035350 + 19653878475*x - 32173158150*x^2 + 36158638950*x^3 - 29206562850*x^4 + 16339758066*x^5 - 6920679105*x^6 + 2772153000*x^7 - 975423915*x^8 + 289640205*x^9 - 118771974*x^10 + 45333840*x^11 - 18640050*x^12 + 10087170*x^13 - 4338540*x^14 + 1788696*x^15 - 714090*x^16 + 239575*x^17 - 74420*x^18 + 22690*x^19 - 5564*x^20 + 1180*x^21 - 275*x^22 + 40*x^23 - 5*x^24 + x^25, -529555380901875000000000000000000000000000000000000}, {27/32, 3155750880 - 4978688400*x - 683746800*x^2 + 3801747600*x^3 - 2453356800*x^4 + 606344400*x^5 + 352638800*x^6 - 87798400*x^7 - 19640100*x^8 + 44956510*x^9 + 1106026*x^10 + 13014570*x^11 - 9713210*x^12 + 3938095*x^13 + 1174815*x^14 - 1267032*x^15 + 247065*x^16 + 57630*x^17 - 27760*x^18 - 2275*x^19 + 1398*x^20 + 320*x^21 - 235*x^22 + 45*x^23 - 5*x^24 + x^25, -1323888452254687500000000000000000000000000000000000000}, {-5/27, 223961814 + 1297893060*x + 2843503800*x^2 + 3906211290*x^3 + 3026381685*x^4 + 2439933948*x^5 + 813209055*x^6 + 53468115*x^7 - 4273925*x^8 - 140519245*x^9 + 3492001*x^10 + 21259835*x^11 - 5155670*x^12 + 2223605*x^13 - 2780300*x^14 - 399856*x^15 + 742975*x^16 - 140180*x^17 - 62995*x^18 + 22645*x^19 + 497*x^20 - 1475*x^21 + 185*x^22 + 25*x^23 - 10*x^24 + x^25, 5784156907130880000000000000000000000000000000000000000}, {32/27, 75348208800 + 25309624500*x - 17092096500*x^2 + 268812213000*x^3 + 299514321000*x^4 + 129429875700*x^5 + 172577861100*x^6 + 64574855625*x^7 + 47869898150*x^8 + 18664323625*x^9 + 5554646600*x^10 + 4493051400*x^11 + 389275200*x^12 + 207207600*x^13 + 178158200*x^14 - 19216286*x^15 + 4549820*x^16 + 3751990*x^17 - 693700*x^18 + 75520*x^19 + 29976*x^20 - 6660*x^21 + 780*x^22 + 25*x^23 - 10*x^24 + x^25, 231366276285235200000000000000000000000000000000000000000000}, {-27/5, 232020288 + 727444800*x + 738000720*x^2 - 711113040*x^3 - 2386852200*x^4 - 2015025336*x^5 + 361740960*x^6 + 1813449600*x^7 + 1143946440*x^8 - 91102680*x^9 - 387447684*x^10 - 126836340*x^11 + 21715260*x^12 + 18102120*x^13 + 3416970*x^14 + 706326*x^15 + 101595*x^16 - 8895*x^17 - 40920*x^18 - 10680*x^19 + 30*x^20 + 630*x^21 + 50*x^22 - 10*x^23 - 5*x^24 + x^25, 34704941442785280000000000000000000000000000000000000}, {32/5, -12314603520 - 132100531200*x - 271926681600*x^2 - 233488638720*x^3 - 112392398400*x^4 - 14617465008*x^5 + 40432564560*x^6 + 38871275280*x^7 + 15717146880*x^8 + 2352159120*x^9 - 970220470*x^10 - 742904655*x^11 - 220960140*x^12 - 19643855*x^13 + 14691450*x^14 + 7939611*x^15 + 1399720*x^16 - 287385*x^17 - 182130*x^18 - 17425*x^19 + 8004*x^20 + 2055*x^21 - 130*x^22 - 75*x^23 + x^25, 555279063084564480000000000000000000000000000000000000}, {1/81, 70374407310000 + 9068018850000*x - 47382212250000*x^2 - 7807198125000*x^3 + 15297484500000*x^4 + 3417141943000*x^5 - 3131463120000*x^6 - 914558375000*x^7 + 448277007500*x^8 + 165467392500*x^9 - 46156003900*x^10 - 20988466250*x^11 + 3630847500*x^12 + 1968099250*x^13 - 223590500*x^14 - 138962100*x^15 + 10713100*x^16 + 7335400*x^17 - 384600*x^18 - 282050*x^19 + 9080*x^20 + 7500*x^21 - 100*x^22 - 125*x^23 + x^25, -5147278302366225000000000000000000000000000000000000000000}, {80/81, -82347521622 + 56249042380*x + 120588666040*x^2 + 89283164960*x^3 + 39710259810*x^4 + 39631975552*x^5 + 14891706785*x^6 + 10685479085*x^7 + 3771351750*x^8 + 1611526950*x^9 + 706148189*x^10 + 160185395*x^11 + 99520255*x^12 + 22752685*x^13 + 7853835*x^14 + 3374553*x^15 + 81615*x^16 + 295155*x^17 + 33465*x^18 + 6415*x^19 + 5761*x^20 - 895*x^21 + 250*x^22 + 20*x^23 - 5*x^24 + x^25, -2058911320946490000000000000000000000000000000000000000}, {-1/80, -1436625 + 3099375*x + 805500*x^2 - 4408250*x^3 - 1037150*x^4 + 9364020*x^5 - 10744100*x^6 + 5295850*x^7 - 1906515*x^8 + 805035*x^9 + 515064*x^10 - 650340*x^11 + 350780*x^12 + 23120*x^13 + 103800*x^14 - 45868*x^15 - 66295*x^16 - 39195*x^17 - 15540*x^18 - 1410*x^19 - 702*x^20 - 260*x^21 - 20*x^22 - 30*x^23 - 5*x^24 + x^25, 579068809016200312500000000000000000000000000000000}, {81/80, 2880 - 4800*x - 49600*x^2 - 85600*x^3 - 31600*x^4 + 121584*x^5 + 148320*x^6 - 88680*x^7 - 190560*x^8 + 49320*x^9 + 75228*x^10 - 20340*x^11 + 14640*x^12 - 720*x^13 - 23890*x^14 + 14888*x^15 - 850*x^16 - 2920*x^17 + 2210*x^18 - 400*x^19 - 331*x^20 + 95*x^21 + 35*x^22 - 5*x^23 - 5*x^24 + x^25, 2451645281953125000000000000000000000000000000}, {-80, 41210897280 + 154305032000*x + 224692766400*x^2 + 139673025600*x^3 + 2790046800*x^4 - 47891512920*x^5 - 30233084400*x^6 - 10301847900*x^7 - 1972927200*x^8 + 1293117150*x^9 + 1533222360*x^10 + 625342425*x^11 + 110529960*x^12 + 4742525*x^13 - 4019760*x^14 - 4027323*x^15 - 1750000*x^16 - 315555*x^17 - 5160*x^18 + 8875*x^19 + 3672*x^20 + 735*x^21 - 80*x^22 - 45*x^23 + x^25, 4632550472129602500000000000000000000000000000000000000}, {81, -264487032 + 1757371140*x + 2188059480*x^2 - 5000576580*x^3 + 1536530580*x^4 + 1689485778*x^5 - 818393040*x^6 + 74999880*x^7 - 186157590*x^8 + 90886095*x^9 + 104081238*x^10 - 58183890*x^11 - 14217860*x^12 + 12860540*x^13 + 640170*x^14 - 1881110*x^15 + 260360*x^16 + 150570*x^17 - 67770*x^18 + 5370*x^19 + 4248*x^20 - 1480*x^21 + 130*x^22 + 30*x^23 - 10*x^24 + x^25, 5448100626562500000000000000000000000000000000000000}, {3/128, 15097570626 - 62779459845*x + 122905053005*x^2 - 157513212205*x^3 + 145616566730*x^4 - 101771663832*x^5 + 58809364830*x^6 - 29301516465*x^7 + 12848762465*x^8 - 5272044385*x^9 + 1847816024*x^10 - 558302360*x^11 + 166814680*x^12 - 40026560*x^13 + 7340180*x^14 - 1028080*x^15 - 154630*x^16 + 88165*x^17 - 48725*x^18 + 18205*x^19 - 2874*x^20 + 1080*x^21 - 210*x^22 + 25*x^23 - 5*x^24 + x^25, -800504721583995312000000000000000000000000000000000000}, {125/128, -2353320 - 8456670*x - 7323390*x^2 - 289500*x^3 - 5065830*x^4 - 2968419*x^5 - 5821519*x^6 - 32098205*x^7 - 24219654*x^8 - 9451614*x^9 - 7862994*x^10 - 2282673*x^11 + 745645*x^12 + 182147*x^13 + 131982*x^14 + 111316*x^15 - 15442*x^16 - 15045*x^17 + 293*x^18 - 647*x^19 - 84*x^20 + 244*x^21 + 20*x^22 - 21*x^23 - x^24 + x^25, -512323021813756999680000000000000000000000000000}, {-3/125, 2378360 - 9753240*x + 25333016*x^2 - 22552244*x^3 - 48540508*x^4 + 19843408*x^5 + 46473060*x^6 - 8863130*x^7 - 11045160*x^8 + 8704010*x^9 + 3505740*x^10 - 5137330*x^11 - 2104736*x^12 + 2089064*x^13 + 474988*x^14 - 466728*x^15 - 120950*x^16 + 96282*x^17 + 13082*x^18 - 10911*x^19 - 2044*x^20 + 805*x^21 + 122*x^22 - 23*x^23 - 6*x^24 + x^25, 134302406230345514924113920000000000000000000000000}, {128/125, -1014912 - 8772768*x + 10335936*x^2 + 95609088*x^3 - 52128336*x^4 - 320969404*x^5 + 167652872*x^6 + 345094436*x^7 - 167449452*x^8 - 188931861*x^9 + 84041694*x^10 + 58416344*x^11 - 23767048*x^12 - 9999934*x^13 + 4663728*x^14 + 1182048*x^15 - 624642*x^16 - 103316*x^17 + 72442*x^18 + 1696*x^19 - 5352*x^20 + 594*x^21 + 192*x^22 - 44*x^23 - 2*x^24 + x^25, 134302406230345514924113920000000000000000000000000}, {-125/3, -27803918088 + 18718694676*x + 45781124742*x^2 - 76946283177*x^3 + 122995145024*x^4 - 147105749067*x^5 + 128897166090*x^6 - 98994998895*x^7 + 58934899800*x^8 - 30976051935*x^9 + 13396963912*x^10 - 5030687364*x^11 + 1608002532*x^12 - 425239592*x^13 + 91800444*x^14 - 10987770*x^15 - 785444*x^16 + 1341942*x^17 - 494982*x^18 + 152569*x^19 - 33348*x^20 + 6807*x^21 - 1006*x^22 + 141*x^23 - 12*x^24 + x^25, 1813082484109664451475537920000000000000000000000000000}, {128/3, -524514151658592 - 261208111528560*x + 513745557771980*x^2 + 174016560947350*x^3 - 86180819393380*x^4 - 64165842921814*x^5 - 13296425953940*x^6 - 1787930477440*x^7 + 1632884717600*x^8 + 287213724040*x^9 - 21435525454*x^10 - 6655387465*x^11 - 3825312650*x^12 + 1127212175*x^13 + 152824560*x^14 - 17980053*x^15 - 10971990*x^16 - 1026565*x^17 + 848350*x^18 - 61585*x^19 - 14802*x^20 + 1395*x^21 + 120*x^22 + 25*x^23 - 10*x^24 + x^25, 2832941381421350705430528000000000000000000000000000000000000}} (* Section ten. A degree 1200 field: computations in large degree *) (* f1200 is the degree 1200 polynomial discussed in the paper *) f1200 = 18353476449040365514302581061144384422915800697208848682665776891893340892892\ 08456216596017890135166070180990677275387752356196690543162475551314875324112\ 83095096789722698664678777326861847459664428758194878916223268160531460622968\ 18981722726093771579980793744426250879900527159661286733052628802870687279123\ 08461768696150592830190865816242842157310984685467043016898677871512982308777\ 02533642579733677507158756424679424 - 484531778254665649577588140014211748764\ 97713840631360522237650994598419957235103244118134872299568384252778153880070\ 23666220359263033948935455471270855657873710555248679244747519721429152772935\ 14091921634480338829427943803056044636021117479968875569711492954852853023229\ 37391701505796975258940039578614416884943390693578375650717038857548811032953\ 009995696329935646125095807942732951713468881641049690861889911696115367936* x + 64387666078523410297276314878706729432473212005948082948528078492140218\ 52044401106099062149962172189607408951494017515312816009229763522596729122845\ 61205263354218557705171455426086618096733257994748969499274213894469360776470\ 15749700351679667682169456888620614196173336867029381523726116895232366230945\ 11261960545576939835509766875595456543138856278396473555480311883941708841844\ 535651560285248982216874306143492890603552768*x^2 - 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