https://github.com/koffie/mdmagma
Raw File
Tip revision: f69d0e06f67b9ac6f57e7d8e6ba3b3d69e650352 authored by Maarten Derickx on 02 November 2020, 22:43:35 UTC
Quickly lists all non cuspidal places up to diamond operators on X_1(N)
Tip revision: f69d0e0
X1_3_21.txt
N := 7;
X := (u^30 + 31*u^29 + 464*u^28 + 4465*u^27 + 31031*u^26 + 165880*u^25 + 709281*u^24 + 2490694*u^23 + 7318300*u^22 + 18239506*u^21 + 38952134*u^20 + 71820190*u^19 + 114967386*u^18 + 160408924*u^17 + 195578591*u^16 + 208653648*u^15 + 194805329*u^14 + 158995799*u^13 + 113180132*u^12 + 70005937*u^11 + 37425035*u^10 + 17167932*u^9 + 6694271*u^8 + 2192242*u^7 + 593970*u^6 + 130768*u^5 + 22918*u^4 + 3128*u^3 + 324*u^2 + 24*u + 1)*v^24 - (u^35 + 34*u^34 + 563*u^33 + 6047*u^32 + 47340*u^31 + 287781*u^30 + 1413075*u^29 + 5755585*u^28 + 19816707*u^27 + 58480944*u^26 + 149483849*u^25 + 333679727*u^24 + 654831049*u^23 + 1136410680*u^22 + 1753792797*u^21 + 2421045756*u^20 + 3009134601*u^19 + 3392028285*u^18 + 3494306270*u^17 + 3311813831*u^16 + 2899485616*u^15 + 2343991912*u^14 + 1740182484*u^13 + 1174831653*u^12 + 712252857*u^11 + 382406663*u^10 + 179196018*u^9 + 72179427*u^8 + 24579823*u^7 + 6945019*u^6 + 1592996*u^5 + 289146*u^4 + 40326*u^3 + 4170*u^2 + 300*u + 12)*v^23 + (u^40 + 37*u^39 + 671*u^38 + 7944*u^37 + 69001*u^36 + 468538*u^35 + 2587991*u^34 + 11946611*u^33 + 46991655*u^32 + 159803219*u^31 + 475096716*u^30 + 1245762357*u^29 + 2901673653*u^28 + 6039786225*u^27 + 11293223912*u^26 + 19058922749*u^25 + 29162060155*u^24 + 40633276588*u^23 + 51777410163*u^22 + 60579639039*u^21 + 65304866811*u^20 + 65038057981*u^19 + 59951855962*u^18 + 51216320901*u^17 + 40599054759*u^16 + 29911912373*u^15 + 20524970570*u^14 + 13135212275*u^13 + 7829749910*u^12 + 4320626656*u^11 + 2180759303*u^10 + 989532361*u^9 + 395305794*u^8 + 135838601*u^7 + 39148534*u^6 + 9200817*u^5 + 1707715*u^4 + 241086*u^3 + 24738*u^2 + 1722*u + 66)*v^22 + (8*u^40 + 274*u^39 + 4559*u^38 + 49033*u^37 + 382518*u^36 + 2301284*u^35 + 11073468*u^34 + 43570360*u^33 + 141819997*u^32 + 382336281*u^31 + 841682960*u^30 + 1440001241*u^29 + 1585582650*u^28 - 334383143*u^27 - 7306824608*u^26 - 23337919281*u^25 - 51963901384*u^24 - 93903360496*u^23 - 145068540865*u^22 - 196487135253*u^21 - 236810487159*u^20 - 256440637845*u^19 - 251171159470*u^18 - 223511642825*u^17 - 181248132663*u^16 - 134217132294*u^15 - 90935730799*u^14 - 56492570033*u^13 - 32249325008*u^12 - 16931216605*u^11 - 8151935709*u^10 - 3567395652*u^9 - 1396048090*u^8 - 477411363*u^7 - 138647515*u^6 - 33070454*u^5 - 6231417*u^4 - 885757*u^3 - 89797*u^2 - 6016*u - 220)*v^21 - (u^43 + 36*u^42 + 641*u^41 + 7477*u^40 + 63975*u^39 + 427194*u^38 + 2318395*u^37 + 10540307*u^36 + 41164168*u^35 + 141186267*u^34 + 433620247*u^33 + 1211095318*u^32 + 3105378606*u^31 + 7326726443*u^30 + 15837173849*u^29 + 31080064027*u^28 + 54712395508*u^27 + 85107164468*u^26 + 114539006044*u^25 + 128431071801*u^24 + 109229574558*u^23 + 44976698156*u^22 - 61571217646*u^21 - 189732450084*u^20 - 307304594674*u^19 - 383844084095*u^18 - 403209676077*u^17 - 368514747623*u^16 - 297911958944*u^15 - 214946166049*u^14 - 139181705225*u^13 - 81211458501*u^12 - 42842210115*u^11 - 20470146208*u^10 - 8841209701*u^9 - 3421929408*u^8 - 1166080539*u^7 - 340486091*u^6 - 82181270*u^5 - 15681085*u^4 - 2239138*u^3 - 223487*u^2 - 14295*u - 495)*v^20 - (5*u^43 + 167*u^42 + 2728*u^41 + 28854*u^40 + 220865*u^39 + 1297142*u^38 + 6050497*u^37 + 22880176*u^36 + 70787678*u^35 + 178114317*u^34 + 350277385*u^33 + 453243710*u^32 - 77266596*u^31 - 2818219883*u^30 - 11295169537*u^29 - 32016762979*u^28 - 74616867690*u^27 - 149297292469*u^26 - 260133901543*u^25 - 395769126623*u^24 - 523716753939*u^23 - 596402206148*u^22 - 571272670677*u^21 - 435578322309*u^20 - 218921720069*u^19 + 17307669100*u^18 + 208183962993*u^17 + 313339608044*u^16 + 328938072844*u^15 + 280237871134*u^14 + 203379834290*u^13 + 128460474101*u^12 + 71441752817*u^11 + 35235064324*u^10 + 15468053995*u^9 + 6033695657*u^8 + 2069336265*u^7 + 610170106*u^6 + 149296919*u^5 + 28871871*u^4 + 4140934*u^3 + 405540*u^2 + 24460*u + 792)*v^19 + (u^46 + 35*u^45 + 612*u^44 + 7090*u^43 + 60995*u^42 + 414729*u^41 + 2319883*u^40 + 10987402*u^39 + 45046624*u^38 + 162679360*u^37 + 524444761*u^36 + 1523630631*u^35 + 4012991463*u^34 + 9612967968*u^33 + 20971277278*u^32 + 41668800282*u^31 + 75318395681*u^30 + 123415318115*u^29 + 181815808555*u^28 + 236575090323*u^27 + 261531000005*u^26 + 221955353418*u^25 + 88312523572*u^24 - 141714766861*u^23 - 425277535309*u^22 - 678514875986*u^21 - 810457629101*u^20 - 770588417305*u^19 - 577892017008*u^18 - 309792030175*u^17 - 59399689024*u^16 + 108722976719*u^15 + 178316551115*u^14 + 172327540738*u^13 + 128903311273*u^12 + 80058053174*u^11 + 42491094989*u^10 + 19557263699*u^9 + 7858127203*u^8 + 2749733679*u^7 + 825112373*u^6 + 205578466*u^5 + 40411036*u^4 + 5829441*u^3 + 558185*u^2 + 31144*u + 924)*v^18 + (2*u^46 + 66*u^45 + 1059*u^44 + 10934*u^43 + 80938*u^42 + 451802*u^41 + 1934264*u^40 + 6206999*u^39 + 12996445*u^38 + 1764502*u^37 - 137531052*u^36 - 802721948*u^35 - 3138404800*u^34 - 9901616096*u^33 - 26743400131*u^32 - 63504431187*u^31 - 134483590321*u^30 - 256167041448*u^29 - 441205101094*u^28 - 688810141329*u^27 - 974039194507*u^26 - 1241300552888*u^25 - 1410009315382*u^24 - 1399259193272*u^23 - 1168535251860*u^22 - 754044219452*u^21 - 270425030376*u^20 + 136056700095*u^19 + 359151603714*u^18 + 380966552765*u^17 + 265476944390*u^16 + 108804282295*u^15 - 14039578273*u^14 - 74133375368*u^13 - 81359319754*u^12 - 61542663121*u^11 - 36891131771*u^10 - 18374156538*u^9 - 7769717312*u^8 - 2812247638*u^7 - 865707518*u^6 - 220722610*u^5 - 44266116*u^4 - 6437146*u^3 - 600441*u^2 - 30105*u - 792)*v^17 + (3*u^46 + 93*u^45 + 1364*u^44 + 12479*u^43 + 78403*u^42 + 345212*u^41 + 985093*u^40 + 905921*u^39 - 8018527*u^38 - 56368376*u^37 - 220363616*u^36 - 614479784*u^35 - 1221967917*u^34 - 1277275233*u^33 + 2213285598*u^32 + 17066575862*u^31 + 59082293342*u^30 + 153752034566*u^29 + 333284414267*u^28 + 626329336937*u^27 + 1041004855505*u^26 + 1546452397950*u^25 + 2062129733715*u^24 + 2465934882627*u^23 + 2629172622292*u^22 + 2473014120361*u^21 + 2019030490609*u^20 + 1395081508916*u^19 + 780289491062*u^18 + 319773607776*u^17 + 66381726157*u^16 - 16855595506*u^15 - 8846443997*u^14 + 20944562589*u^13 + 37309124309*u^12 + 35499002228*u^11 + 24552929113*u^10 + 13452702949*u^9 + 6061004035*u^8 + 2287326213*u^7 + 725397378*u^6 + 189734451*u^5 + 38924690*u^4 + 5721107*u^3 + 518351*u^2 + 22386*u + 495)*v^16 - (u^47 + 26*u^46 + 345*u^45 + 3237*u^44 + 25019*u^43 + 169936*u^42 + 1016063*u^41 + 5234655*u^40 + 22866070*u^39 + 84256393*u^38 + 262381933*u^37 + 693597967*u^36 + 1563186347*u^35 + 3016034356*u^34 + 5029839189*u^33 + 7528663211*u^32 + 11390626962*u^31 + 21156745662*u^30 + 49447504774*u^29 + 120926346719*u^28 + 271281593270*u^27 + 536902842649*u^26 + 935397040655*u^25 + 1443677331417*u^24 + 1984905669679*u^23 + 2436158266326*u^22 + 2664171280467*u^21 + 2582625021282*u^20 + 2202476635429*u^19 + 1637176357995*u^18 + 1049786600240*u^17 + 574979418902*u^16 + 268899306524*u^15 + 112437209821*u^14 + 50221290611*u^13 + 30126798612*u^12 + 21789061893*u^11 + 14758708895*u^10 + 8413684942*u^9 + 3959207562*u^8 + 1544602362*u^7 + 501843648*u^6 + 134145196*u^5 + 28130972*u^4 + 4187966*u^3 + 368410*u^2 + 12936*u + 220)*v^15 - (u^47 + 24*u^46 + 281*u^45 + 2248*u^44 + 14577*u^43 + 82532*u^42 + 398607*u^41 + 1504823*u^40 + 3704145*u^39 + 903978*u^38 - 45134827*u^37 - 274886825*u^36 - 1063717229*u^35 - 3183019888*u^34 - 7853461269*u^33 - 16479187877*u^32 - 29998072133*u^31 - 48343552389*u^30 - 71271166338*u^29 - 101736013391*u^28 - 150956467588*u^27 - 240987348094*u^26 - 399500222762*u^25 - 645384672513*u^24 - 970545406927*u^23 - 1327572953218*u^22 - 1633053071607*u^21 - 1792775736797*u^20 - 1744272671635*u^19 - 1494054268830*u^18 - 1119939305341*u^17 - 731324325158*u^16 - 415392883345*u^15 - 206696984074*u^14 - 92878310367*u^13 - 40632906780*u^12 - 19149081871*u^11 - 9893891408*u^10 - 5073231413*u^9 - 2327899086*u^8 - 908308885*u^7 - 296531599*u^6 - 79968986*u^5 - 17036906*u^4 - 2570958*u^3 - 220438*u^2 - 5862*u - 66)*v^14 - (u^47 + 22*u^46 + 227*u^45 + 1569*u^44 + 8793*u^43 + 43273*u^42 + 174030*u^41 + 455848*u^40 + 75621*u^39 - 6032290*u^38 - 33471941*u^37 - 106309176*u^36 - 207503965*u^35 - 114804336*u^34 + 919693181*u^33 + 4544050804*u^32 + 13379603631*u^31 + 30296457437*u^30 + 56809022720*u^29 + 91649760370*u^28 + 131507859916*u^27 + 174846768525*u^26 + 226401942307*u^25 + 297594838038*u^24 + 400242952098*u^23 + 536081723300*u^22 + 687805521224*u^21 + 817770829855*u^20 + 879647558302*u^19 + 841900143153*u^18 + 708993000091*u^17 + 521728603274*u^16 + 334302481356*u^15 + 186579759916*u^14 + 91413018034*u^13 + 40285683836*u^12 + 16809116016*u^11 + 7077940598*u^10 + 3059015772*u^9 + 1279213314*u^8 + 478668354*u^7 + 152902803*u^6 + 40802731*u^5 + 8732198*u^4 + 1334175*u^3 + 112425*u^2 + 2094*u + 12)*v^13 + (u^48 + 24*u^47 + 315*u^46 + 2921*u^45 + 20966*u^44 + 121979*u^43 + 594987*u^42 + 2508278*u^41 + 9358682*u^40 + 31253059*u^39 + 93280515*u^38 + 247017594*u^37 + 577261741*u^36 + 1192818919*u^35 + 2208747235*u^34 + 3776707386*u^33 + 6265190137*u^32 + 10637763562*u^31 + 18825124901*u^30 + 33527142621*u^29 + 56902238688*u^28 + 88537609817*u^27 + 124455872612*u^26 + 158883802145*u^25 + 188084238231*u^24 + 213033504245*u^23 + 238449485774*u^22 + 268671366191*u^21 + 302532052182*u^20 + 330166895355*u^19 + 335921953989*u^18 + 308352375822*u^17 + 249918275475*u^16 + 176749564794*u^15 + 108508157868*u^14 + 57826395204*u^13 + 26965765623*u^12 + 11262256101*u^11 + 4402376189*u^10 + 1688157100*u^9 + 636812080*u^8 + 223570405*u^7 + 68567242*u^6 + 17779723*u^5 + 3771596*u^4 + 581889*u^3 + 48688*u^2 + 583*u + 1)*v^12 + (u^47 + 25*u^46 + 296*u^45 + 2091*u^44 + 8892*u^43 + 15551*u^42 - 80343*u^41 - 896803*u^40 - 5187006*u^39 - 23194440*u^38 - 86894678*u^37 - 278366171*u^36 - 768227494*u^35 - 1840503269*u^34 - 3867597531*u^33 - 7223812635*u^32 - 12202179763*u^31 - 19072081318*u^30 - 28332292687*u^29 - 40886421994*u^28 - 57599335081*u^27 - 78099835143*u^26 - 99774767180*u^25 - 118336604918*u^24 - 129984582759*u^23 - 133446204888*u^22 - 130467233539*u^21 - 124684873695*u^20 - 119168634469*u^19 - 113741482224*u^18 - 104888876981*u^17 - 89362414417*u^16 - 67912349970*u^15 - 45105556439*u^14 - 25927069499*u^13 - 12872817525*u^12 - 5566962167*u^11 - 2150964924*u^10 - 775447865*u^9 - 269966703*u^8 - 89006845*u^7 - 26074773*u^6 - 6494506*u^5 - 1348520*u^4 - 209386*u^3 - 17560*u^2 - 120*u)*v^11 + (u^47 + 23*u^46 + 258*u^45 + 1772*u^44 + 7900*u^43 + 22560*u^42 + 29854*u^41 - 93357*u^40 - 869774*u^39 - 3883448*u^38 - 12070552*u^37 - 25583959*u^36 - 24578358*u^35 + 68369554*u^34 + 437543162*u^33 + 1398638003*u^32 + 3346961753*u^31 + 6617653604*u^30 + 11350215387*u^29 + 17506142749*u^28 + 25033291931*u^27 + 33883543882*u^26 + 43622036109*u^25 + 52958278958*u^24 + 59927093320*u^23 + 62784457451*u^22 + 60861083713*u^21 + 54916600332*u^20 + 46949952709*u^19 + 39182088750*u^18 + 32616698079*u^17 + 26711908045*u^16 + 20609908951*u^15 + 14341920398*u^14 + 8742410151*u^13 + 4594669453*u^12 + 2072360503*u^11 + 810357266*u^10 + 283525841*u^9 + 92954889*u^8 + 28975806*u^7 + 8129914*u^6 + 1932870*u^5 + 388187*u^4 + 60448*u^3 + 5118*u^2 + 16*u)*v^10 + (u^47 + 21*u^46 + 230*u^45 + 1593*u^44 + 7826*u^43 + 30358*u^42 + 101324*u^41 + 303584*u^40 + 834659*u^39 + 2237430*u^38 + 6386687*u^37 + 19271746*u^36 + 55269107*u^35 + 138009728*u^34 + 288019907*u^33 + 489660634*u^32 + 647359732*u^31 + 569438054*u^30 + 21895476*u^29 - 1163424575*u^28 - 3021526624*u^27 - 5499474901*u^26 - 8515128753*u^25 - 11859025352*u^24 - 15039419329*u^23 - 17370005395*u^22 - 18267166410*u^21 - 17477270219*u^20 - 15222281226*u^19 - 12226588144*u^18 - 9348490572*u^17 - 7027355696*u^16 - 5187429151*u^15 - 3620678442*u^14 - 2282360069*u^13 - 1254798482*u^12 - 589230575*u^11 - 235035538*u^10 - 80928663*u^9 - 25184376*u^8 - 7425680*u^7 - 2002006*u^6 - 451862*u^5 - 86513*u^4 - 13462*u^3 - 1157*u^2 - u)*v^9 + (3*u^46 + 45*u^45 + 284*u^44 + 1007*u^43 + 2035*u^42 - 280*u^41 - 25721*u^40 - 144619*u^39 - 508765*u^38 - 1293166*u^37 - 2679222*u^36 - 5732072*u^35 - 15404202*u^34 - 45391356*u^33 - 120703107*u^32 - 269654882*u^31 - 500453262*u^30 - 774691330*u^29 - 1005787651*u^28 - 1096678293*u^27 - 983874130*u^26 - 637160627*u^25 - 41777350*u^24 + 762556303*u^23 + 1635541341*u^22 + 2383497430*u^21 + 2835919218*u^20 + 2883623228*u^19 + 2543775447*u^18 + 1994689953*u^17 + 1454704760*u^16 + 1028607274*u^15 + 705996986*u^14 + 452760920*u^13 + 258497252*u^12 + 126323896*u^11 + 51642543*u^10 + 17613717*u^9 + 5185765*u^8 + 1428247*u^7 + 370238*u^6 + 78595*u^5 + 14003*u^4 + 2170*u^3 + 190*u^2)*v^8 + (2*u^46 + 26*u^45 + 159*u^44 + 682*u^43 + 2420*u^42 + 7426*u^41 + 19359*u^40 + 47093*u^39 + 130670*u^38 + 395779*u^37 + 1041829*u^36 + 2119961*u^35 + 3234304*u^34 + 3783905*u^33 + 4690150*u^32 + 11572711*u^31 + 36171360*u^30 + 91385733*u^29 + 180047450*u^28 + 286965416*u^27 + 386171732*u^26 + 455188026*u^25 + 474240198*u^24 + 423208539*u^23 + 300650284*u^22 + 134093797*u^21 - 38628578*u^20 - 178536219*u^19 - 249103083*u^18 - 243461212*u^17 - 194459632*u^16 - 140428058*u^15 - 97080232*u^14 - 63935228*u^13 - 38277679*u^12 - 19676230*u^11 - 8325020*u^10 - 2830262*u^9 - 776955*u^8 - 191929*u^7 - 47624*u^6 - 9301*u^5 - 1455*u^4 - 224*u^3 - 20*u^2)*v^7 + (u^46 + 11*u^45 + 72*u^44 + 368*u^43 + 1612*u^42 + 6048*u^41 + 19865*u^40 + 60314*u^39 + 172015*u^38 + 443601*u^37 + 999693*u^36 + 1977651*u^35 + 3542600*u^34 + 6007885*u^33 + 10034518*u^32 + 16455958*u^31 + 25268693*u^30 + 34270743*u^29 + 38938933*u^28 + 35175141*u^27 + 22813151*u^26 + 4467910*u^25 - 17198613*u^24 - 36998431*u^23 - 47513829*u^22 - 46041670*u^21 - 34769420*u^20 - 16708575*u^19 + 1985466*u^18 + 13265687*u^17 + 15224786*u^16 + 12435965*u^15 + 9003656*u^14 + 6182617*u^13 + 3953224*u^12 + 2183146*u^11 + 972162*u^10 + 333534*u^9 + 83458*u^8 + 16479*u^7 + 3854*u^6 + 653*u^5 + 72*u^4 + 11*u^3 + u^2)*v^6 + (5*u^43 + 48*u^42 + 229*u^41 + 912*u^40 + 3555*u^39 + 11633*u^38 + 27820*u^37 + 47614*u^36 + 54968*u^35 + 23178*u^34 - 70362*u^33 - 259416*u^32 - 675128*u^31 - 1611045*u^30 - 3417299*u^29 - 6107469*u^28 - 8949638*u^27 - 10985150*u^26 - 11857118*u^25 - 11288242*u^24 - 8939497*u^23 - 5631686*u^22 - 2669781*u^21 - 479516*u^20 + 620548*u^19 + 301066*u^18 - 654142*u^17 - 1115839*u^16 - 997518*u^15 - 716723*u^14 - 475643*u^13 - 310254*u^12 - 183430*u^11 - 86663*u^10 - 30735*u^9 - 7112*u^8 - 869*u^7 - 188*u^6 - 25*u^5)*v^5 + (u^43 + 7*u^42 + 32*u^41 + 149*u^40 + 645*u^39 + 1949*u^38 + 4214*u^37 + 7357*u^36 + 10924*u^35 + 15933*u^34 + 25149*u^33 + 36288*u^32 + 38866*u^31 + 25411*u^30 + 15037*u^29 + 87935*u^28 + 308462*u^27 + 601729*u^26 + 887607*u^25 + 1168664*u^24 + 1316294*u^23 + 1218667*u^22 + 992257*u^21 + 724879*u^20 + 418692*u^19 + 193236*u^18 + 134024*u^17 + 129843*u^16 + 100658*u^15 + 65626*u^14 + 37496*u^13 + 21448*u^12 + 12656*u^11 + 6170*u^10 + 2304*u^9 + 548*u^8 + 32*u^7 + 7*u^6 + u^5)*v^4 + (8*u^40 + 46*u^39 + 113*u^38 + 215*u^37 + 308*u^36 + 400*u^35 + 665*u^34 + 963*u^33 + 495*u^32 - 1009*u^31 - 3155*u^30 - 1462*u^29 + 7766*u^28 + 13352*u^27 + 7312*u^26 + 1358*u^25 - 11484*u^24 - 36855*u^23 - 52456*u^22 - 53205*u^21 - 51799*u^20 - 42351*u^19 - 22090*u^18 - 10409*u^17 - 8668*u^16 - 6397*u^15 - 4152*u^14 - 2215*u^13 - 1034*u^12 - 589*u^11 - 289*u^10 - 112*u^9 - 30*u^8)*v^3 + (u^40 + 3*u^39 + 8*u^38 + 17*u^37 + 33*u^36 + 71*u^35 + 147*u^34 + 224*u^33 + 337*u^32 + 473*u^31 + 791*u^30 + 1612*u^29 + 2151*u^28 + 1662*u^27 + 1868*u^26 + 1970*u^25 + 1090*u^24 + 1257*u^23 + 2144*u^22 + 2053*u^21 + 1852*u^20 + 2279*u^19 + 1596*u^18 + 565*u^17 + 406*u^16 + 270*u^15 + 170*u^14 + 94*u^13 + 33*u^12 + 17*u^11 + 8*u^10 + 3*u^9 + u^8)*v^2 + (u^35 + u^34 + 2*u^33 + 3*u^32 + 4*u^31 + 23*u^30 + 41*u^29 - 13*u^28 + 5*u^27 + 24*u^26 - 31*u^25 - 12*u^24 + 31*u^23 - 29*u^21 + 13*u^20 - 17*u^19 - 47*u^18 - 4*u^17 - 3*u^16 - 2*u^15 - u^14 - u^13)*v + u^30 - u^29 + u^27 - u^26 + u^24 - u^22 + u^21 - u^19 + u^18;
Xz := u^24*v^6 + (-z - 1)*u^23*v^9 + (-z - 1)*u^23*v^8 + (-z - 1)*u^23*v^7 + 12*u^23*v^6 - z*u^23*v^5 - z*u^23*v^4 - z*u^23*v^3 + (-18*z - 17)*u^22*v^9 + (-16*z - 15)*u^22*v^8 + (-14*z - 13)*u^22*v^7 + 84*u^22*v^6 + (-9*z + 1)*u^22*v^5 + (-7*z + 1)*u^22*v^4 + (-5*z + 1)*u^22*v^3 + (-161*z - 144)*u^21*v^9 + (-113*z - 98)*u^21*v^8 + (-75*z - 62)*u^21*v^7 + (36*z + 436)*u^21*v^6 + (-20*z + 9)*u^21*v^5 + (-14*z + 7)*u^21*v^4 + (-18*z + 5)*u^21*v^3 + z*u^20*v^11 + 4*z*u^20*v^10 + (-933*z - 799)*u^20*v^9 + (-424*z - 346)*u^20*v^8 + (-135*z - 108)*u^20*v^7 + (378*z + 1762)*u^20*v^6 + (23*z - 15)*u^20*v^5 + (-24*z - 6)*u^20*v^4 + (-61*z + 8)*u^20*v^3 + (-4*z - 4)*u^20*v^2 + (-z - 1)*u^20*v + (18*z - 1)*u^19*v^11 + (61*z - 4)*u^19*v^10 + (-3916*z - 3252)*u^19*v^9 + (-667*z - 536)*u^19*v^8 + (412*z + 240)*u^19*v^7 + (1804*z + 5544)*u^19*v^6 + (67*z - 478)*u^19*v^5 + (-132*z - 181)*u^19*v^4 + (-201*z - 14)*u^19*v^3 + (-19*z - 15)*u^19*v^2 + (-2*z - 1)*u^19*v + (155*z - 18)*u^18*v^11 + (425*z - 61)*u^18*v^10 + (-12764*z - 10322)*u^18*v^9 + (1583*z + 1129)*u^18*v^8 + (3076*z + 1856)*u^18*v^7 + (5168*z + 13652)*u^18*v^6 + (-587*z - 2797)*u^18*v^5 + (-595*z - 758)*u^18*v^4 + (-479*z - 9)*u^18*v^3 + (-26*z - 11)*u^18*v^2 + (-3*z - 2)*u^18*v + (847*z - 155)*u^17*v^11 + (1764*z - 425)*u^17*v^10 +(-33992*z - 26440)*u^17*v^9 + (13718*z + 10159)*u^17*v^8 + (8692*z + 4946)*u^17*v^7 + (9920*z + 26824)*u^17*v^6 + (-3470*z - 9493)*u^17*v^5 + (-1381*z - 1535)*u^17*v^4 + (-776*z + 209)*u^17*v^3 + (-15*z - 4)*u^17*v^2 +(-5*z - 3)*u^17*v + (3288*z - 847)*u^16*v^11 + (4681*z - 1764)*u^16*v^10 + (-76499*z - 55504)*u^16*v^9 + (49964*z + 37015)*u^16*v^8 + (13192*z + 5951)*u^16*v^7 + (13583*z + 43333)*u^16*v^6 + (-9503*z - 22660)*u^16*v^5 + (-1786*z - 1559)*u^16*v^4 + (-1004*z + 731)*u^16*v^3 + (11*z + 15)*u^16*v^2 + (-7*z - 4)*u^16*v + u^15*v^12 + (9623*z - 3279)*u^15*v^11 + (7442*z - 4636)*u^15*v^10 + (-147395*z - 95596)*u^15*v^9 + (129464*z + 93364)*u^15*v^8 + (3769*z - 5851)*u^15*v^7 + (14324*z + 59726)*u^15*v^6 + (-17753*z - 41908)*u^15*v^5 + (-1078*z + 616)*u^15*v^4 + (-1109*z + 1649)*u^15*v^3 + (70*z + 10)*u^15*v^2 + (-9*z - 14)*u^15*v - u^15 + (z + 16)*u^14*v^12 + (22010*z - 9505)*u^14*v^11 + (3082*z - 6982)*u^14*v^10 + (-241341*z - 134315)*u^14*v^9 + (266980*z + 179376)*u^14*v^8 + (-40824*z - 47147)*u^14*v^7 + (14066*z + 74656)*u^14*v^6 + (-25755*z - 62197)*u^14*v^5 + (1414*z + 6478)*u^14*v^4 + (-1002*z + 2459)*u^14*v^3 + (116*z - 154)*u^14*v^2 + (-21*z - 33)*u^14*v - z*u^14 + (15*z + 119)*u^13*v^12 + (40297*z - 21304)*u^13*v^11 + (-18744*z - 992)*u^13*v^10 + (-328718*z - 154659)*u^13*v^9 + (452032*z + 268360)*u^13*v^8 + (-142447*z - 126050)*u^13*v^7 + (21878*z + 95476)*u^13*v^6 + (-29246*z - 75465)*u^13*v^5 + (5608*z + 14162)*u^13*v^4 + (-1135*z + 2028)*u^13*v^3 + (50*z - 386)*u^13*v^2 + (-32*z - 15)*u^13*v + (z + 1)*u^13 + (104*z + 545)*u^12*v^12 + (60094*z - 37768)*u^12*v^11 + (-61768*z + 24139)*u^12*v^10 + (-362098*z - 153982)*u^12*v^9 + (627354*z + 314378)*u^12*v^8 + (-299114*z - 216534)*u^12*v^7 + (55874*z + 132395)*u^12*v^6 + (-27004*z - 81844)*u^12*v^5 + (8346*z + 18680)*u^12*v^4 + (-1928*z + 766)*u^12*v^3 + (44*z - 335)*u^12*v^2 + (-8*z + 2)*u^12*v - u^12 + (441*z + 1716)*u^11*v^12 + (73903*z - 54158)*u^11*v^11 + (-113548*z + 69933)*u^11*v^10 + (-311462*z - 152837)*u^11*v^9 + (705658*z + 295986)*u^11*v^8 + (-455699*z - 262930)*u^11*v^7 + (124520*z + 171563)*u^11*v^6 + (-29010*z - 89371)*u^11*v^5 + (7142*z + 20206)*u^11*v^4 + (-2175*z + 262)*u^11*v^3 + (236*z - 249)*u^11*v^2 + (-20*z - 17)*u^11*v - z*u^11 + (1275*z + 3927)*u^10*v^12 + (75273*z - 64691)*u^10*v^11 + (-150353*z + 119372)*u^10*v^10 + (-196515*z - 169858)*u^10*v^9 + (637912*z + 244562)*u^10*v^8 + (-525613*z - 238813)*u^10*v^7 + (197061*z + 176692)*u^10*v^6 + (-44317*z - 93098)*u^10*v^5 + (6344*z + 22578)*u^10*v^4 + (-1217*z - 321)*u^10*v^3 + (181*z - 336)*u^10*v^2 - 33*z*u^10*v + (z + 1)*u^10 + (2652*z + 6733)*u^9*v^12 + (62692*z - 66873)*u^9*v^11 + (-154325*z + 147973)*u^9*v^10 + (-73333*z - 192105)*u^9*v^9 + (461650*z + 202748)*u^9*v^8 + (-469720*z - 179687)*u^9*v^7 + (222745*z + 139587)*u^9*v^6 + (-60871*z - 79043)*u^9*v^5 + (9394*z + 22496)*u^9*v^4 + (-904*z - 1663)*u^9*v^3 + (29*z - 181)*u^9*v^2 + (-9*z + 17)*u^9*v - u^9 + (4080*z + 8787)*u^8*v^12 + (40655*z - 61864)*u^8*v^11 + (-125028*z + 145550)*u^8*v^10 + (10145*z - 190721)*u^8*v^9 + (264460*z + 172931)*u^8*v^8 + (-331855*z - 128678)*u^8*v^7 + (188206*z + 91973)*u^8*v^6 + (-60925*z - 52589)*u^8*v^5 + (11482*z + 16517)*u^8*v^4 + (-1279*z - 1940)*u^8*v^3 + (66*z + 37)*u^8*v^2 + (-7*z - 3)*u^8*v + (4698*z + 8781)*u^7*v^12 + (17724*z - 51338)*u^7*v^11 + (-77392*z + 120483)*u^7*v^10 + (39605*z - 158897)*u^7*v^9 + (114718*z + 136766)*u^7*v^8 + (-185860*z - 90377)*u^7*v^7 + (123682*z + 56405)*u^7*v^6 + (-45904*z - 30185)*u^7*v^5 + (9865*z + 9536)*u^7*v^4 + (-1201*z - 1205)*u^7*v^3 + (70*z + 33)*u^7*v^2 + (-5*z - 2)*u^7*v + (4047*z + 6706)*u^6*v^12 + (1960*z - 36786)*u^6*v^11 + (-32345*z + 85852)*u^6*v^10 + (29972*z - 113073)*u^6*v^9 + (34516*z + 94646)*u^6*v^8 + (-79855*z - 57608)*u^6*v^7 + (62683*z + 31542)*u^6*v^6 + (-26701*z - 15536)*u^6*v^5 + (6571*z + 4907)*u^6*v^4 + (-904*z - 675)*u^6*v^3 + (59*z + 26)*u^6*v^2 + (-3*z - 1)*u^6*v + (2575*z + 3877)*u^5*v^12 + (-4000*z - 21474)*u^5*v^11 + (-5001*z + 51243)*u^5*v^10 + (9075*z - 68802)*u^5*v^9 + (8418*z + 57598)*u^5*v^8 + (-25787*z - 33111)*u^5*v^7 + (23221*z + 15563)*u^5*v^6 + (-11165*z - 6605)*u^5*v^5 + (3126*z + 1979)*u^5*v^4 + (-501*z - 282)*u^5*v^3 + (41*z + 15)*u^5*v^2 + (-2*z - 1)*u^5*v + (1176*z + 1667)*u^4*v^12+ (-3524*z - 9643)*u^4*v^11 + (3639*z + 24086)*u^4*v^10 + (-2727*z - 33870)*u^4*v^9 + (5160*z + 29597)*u^4*v^8 + (-7884*z - 17235)*u^4*v^7 + (6559*z + 7418)*u^4*v^6 + (-3175*z - 2590)*u^4*v^5 + (918*z + 639)*u^4*v^4 + (-156*z - 69)*u^4*v^3 + 15*z*u^4*v^2 - z*u^4*v + (365*z + 518)*u^3*v^12 + (-1508*z - 3154)*u^3*v^11 + (2831*z + 8296)*u^3*v^10 + (-3639*z - 12330)*u^3*v^9 + (3896*z + 11463)*u^3*v^8 + (-3331*z - 7096)*u^3*v^7 + (2008*z+ 3123)*u^3*v^6 + (-780*z - 1025)*u^3*v^5 + (176*z + 228)*u^3*v^4 + (-18*z - 23)*u^3*v^3 + (69*z + 111)*u^2*v^12 + (-352*z - 704)*u^2*v^11 + (855*z + 1929)*u^2*v^10 + (-1349*z - 2997)*u^2*v^9 + (1521*z + 2932)*u^2*v^8 + (-1225*z - 1919)*u^2*v^7 + (679*z + 882)*u^2*v^6 + (-245*z - 290)*u^2*v^5 + (52*z + 62)*u^2*v^4 + (-5*z - 6)*u^2*v^3 + (6*z + 15)*u*v^12 + (-36*z - 96)*u*v^11 + (104*z + 265)*u*v^10 + (-190*z - 415)*u*v^9 + (237*z + 411)*u*v^8 + (-204*z - 275)*u*v^7 + (119*z + 131)*u*v^6 + (-45*z - 45)*u*v^5 + (10*z + 10)*u*v^4 + (-z - 1)*u*v^3 + v^12 - 6*v^11 + 15*v^10 - 20*v^9 + 15*v^8 - 6*v^7 + v^6;
q := u+1;
t := (v*u) / (u+1);
E := [(1+q)*t+(2-q),0,q*t^2+(1-q)*t,0,0];
P := [-t,t^2];
Q := [0,0];
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