Sharedwww / tables / an_s6g0new_1-50_hiprec.gpOpen in CoCalc
Author: William A. Stein
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\\ an_s6g0new_1-50_hiprec.gp
\\ This is a PARI readable nonnormalized basis for S_6(Gamma_0(N)) for N 
\\ in the range:  1 <= N <= 50.
\\ The number of a_n computed is always at least 500.
\\ William Stein ([email protected])

E[37,1] = [x^7+8*x^6-133*x^5-906*x^4+4326*x^3+19928*x^2-40920*x-109600, 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E[39,3] = [x^3-55*x-78, 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E[40,3] = [x, [1,0,-18,0,-25,0,242,0,81,0,656,0,-206,0,450,0,1690,0,-1364,0,-4356,0,2198,0,625,0,2916,0,-2218,0,-1700,0,-11808,0,-6050,0,-846,0,3708,0,-1818,0,10534,0,-2025,0,12074,0,41757,0,-30420,0,32586,0,-16400,0,24552,0,8668,0,-34670,0,19602,0,5150,0,-47566,0,-39564,0,948,0,-63102,0,-11250,0,158752,0,46536,0,-72171,0,-88778,0,-42250,0,39924,0,-104934,0,-49852,0,30600,0,34100,0,-36254,0,53136,0,42486,0,147934,0,108900,0,-18390,0,-145006,0,15228,0,82746,0,-54950,0,-16686,0,408980,0,269285,0,32724,0,-15625,0,-274446,0,-189612,0,202608,0,-330088,0,-72900,0,-48142,0,-111156,0,-217332,0,-135136,0,55450,0,-751626,0,243178,0,368852,0,136890,0,42500,0,319546,0,-586548,0,531916,0,69862,0,295200,0,-343422,0,-328857,0,-110484,0,-1142,0,151250,0,-156024,0,-86684,0,-651418,0,624060,0,21150,0,1108640,0,705672,0,29140,0,-646406,0,-92700,0,431138,0,-131608,0,856188,0,-536756,0,45450,0,178038,0,-894784,0,1210784,0,-17064,0,-263350,0,-411400,0,1135836,0,-348140,0,34886,0,50625,0,-124182,0,-456386,0,-2857536,0,252666,0,-301850,0,-837648,0,65064,0,-1406002,0,590490,0,-1043925,0,280984,0,1598004,0,-548400,0,1441888,0,760500,0,-493830,0,-204732,0,-179658,0,-1071810,0,-814650,0,1888812,0,999394,0,1007604,0,897336,0,410000,0,1022858,0,-137700,0,-1181722,0,-917506,0,-613800,0,-439956,0,1436243,0,652572,0,-512302,0,-216700,0,1912896,0,-452788,0,2549228,0,-764748,0,866750,0,1409458,0,-2662812,0,-2786036,0,1550858,0,-490050,0,377322,0,-1455008,0,331020,0,-2305160,0,-128750,0,2610108,0,2921908,0,-1630632,0,-68526,0,1189150,0,-3367166,0,-1489428,0,-1115200,0,6037900,0,989100,0,837202,0,-1519098,0,-600696,0,-3518510,0,-23700,0,-7361640,0,-3570888,0,-615603,0,-4847130,0,1577550,0,-3582310,0,-147258,0,7885812,0,635530,0,281250,0,456908,0,67060,0,4940028,0,4451286,0,-3968800,0,853254,0,5798250,0,3714620,0,-3646944,0,-1163400,0,333874,0,5941584,0,-2556894,0,350200,0,1804275,0,-554976,0,-3055106,0,866556,0,2097656,0,2219450,0,2000808,0,-3543468,0,1972938,0,977994,0,1056250,0,-8390140,0,2432448,0,1373956,0,5188130,0,-998100,0,-2998072,0,-2940824,0,3382317,0,-1283466,0,2623350,0,-4377204,0,-4952634,0,-1192608,0,-6639336,0,1246300,0,7913146,0,4928040,0,-6185298,0,491934,0,-765000,0,447442,0,-11510972,0,-5751828,0,6910304,0,-852500,0,2639466,0,8184872,0,174276,0,-9574488,0,906350,0,6215242,0,-1257516,0,827856,0,-3748420,0,-1328400,0,229416,0,-10400404,0]];
E[40,4] = [x^2+12*x-480, [1,0,x,0,25,0,3*x+44,0,-12*x+237,0,-6*x+244,0,-12*x+622,0,25*x,0,84*x+578,0,-36*x-716,0,8*x+1440,0,-123*x-1964,0,625,0,138*x-5760,0,-312*x-1202,0,-54*x-1448,0,316*x-2880,0,75*x+1100,0,-216*x-4266,0,766*x-5760,0,156*x+12474,0,-339*x+6808,0,-300*x+5925,0,-885*x-6764,0,156*x-10551,0,-430*x+40320,0,540*x+534,0,-150*x+6100,0,-284*x-17280,0,504*x+34316,0,1104*x+13678,0,615*x-6852,0,-300*x+15550,0,543*x-39448,0,-488*x-59040,0,546*x+26880,0,-1308*x-41574,0,625*x,0,684*x+2096,0,-2508*x-48000,0,-4500*x+8649,0,-711*x+50096,0,2100*x+14450,0,2542*x-149760,0,1464*x-18726,0,1770*x+10088,0,-800*x-25920,0,-900*x-17900,0,4620*x+101554,0,-5214*x+92388,0,4440*x+78006,0,1305*x-57644,0,200*x+36000,0,-405*x+76800,0,1080*x+20414,0,-1674*x-103680,0,-4296*x+111762,0,-3075*x-49100,0,-12036*x+216534,0,2406*x+146392,0,-3360*x-84235,0,10602*x+74880,0,15625,0,-2877*x-185148,0,10876*x-162720,0,102*x+53532,0,-2436*x-83344,0,3450*x-144000,0,4704*x+182890,0,11304*x+104412,0,3856*x-424800,0,-7524*x+186328,0,-7800*x-30050,0,-12423*x+74880,0,-10104*x-135610,0,2586*x-381136,0,25068*x-346854,0,-1350*x-36200,0,-6456*x+176302,0,-5946*x+259200,0,-6876*x-263536,0,-19707*x-75056,0,7900*x-72000,0,13383*x+188028,0,-16656*x+84711,0,-5124*x+37668,0,-7608*x-35074,0,1875*x+27500,0,28268*x+241920,0,9312*x+228740,0,25104*x+159590,0,430*x+529920,0,-5400*x-106650,0,23076*x-100888,0,-16176*x-54720,0,-2706*x+187688,0,-13116*x+486514,0,19150*x-144000,0,-5892*x+112678,0,7968*x+36008,0,-45964*x+260640,0,-6102*x-502168,0,3900*x+311850,0,-23295*x+243012,0,-7080*x-71024,0,-9954*x-241204,0,20328*x+262080,0,-8475*x+170200,0,-4776*x-141472,0,-25878*x-627840,0,57408*x-124324,0,17625*x-398356,0,-7500*x+148125,0,4911*x-885816,0,32160*x+821974,0,-6112*x+328320,0,-6804*x-509094,0,-22125*x-169100,0,-17904*x-1203840,0,19548*x-969600,0,13452*x+893282,0,29115*x-760320,0,3900*x-263775,0,-18984*x-237992,0,58628*x-341280,0,27354*x+273828,0,-27084*x-124976,0,-10750*x+1008000,0,-33240*x-1210590,0,-14526*x-498744,0,-104448*x+1512246,0,-6939*x+1125252,0,13500*x+13350,0,-36294*x+702720,0,14400*x-1016386,0,42270*x+507384,0,-11152*x+849600,0,-3750*x+152500,0,-11736*x-22330,0,-3198*x-32136,0,2676*x-360950,0,25413*x-1352728,0,-7100*x-432000,0,38670*x+773496,0,12432*x+2301107,0,46114*x+2217600,0,3792*x+199606,0,12600*x+857900,0,78168*x-1802880,0,-70650*x-513128,0,17712*x-188608,0,24726*x+2131200,0,27600*x+341950,0,60063*x+1153048,0,-73304*x+626400,0,-108426*x-518368,0,-13464*x-897286,0,15375*x-171300,0,46020*x-2048802,0,-91380*x+605272,0,81660*x-194400,0,-44664*x-1865368,0,-7500*x+388750,0,7454*x+518400,0,-27372*x-1572016,0,-129810*x+74148,0,-31104*x+233118,0,13575*x-986200,0,-58056*x+399154,0,163314*x-2062080,0,-8376*x-197792,0,-80826*x-979112,0,-12200*x-1476000,0,-2421*x+2281136,0,-33936*x+697710,0,174828*x-4377600,0,5304*x+1865858,0,13650*x+672000,0,117520*x+1154880,0,66192*x-1956984,0,36000*x-1341363,0,-43915*x-1612800,0,-32700*x-1039350,0,36855*x-2122780,0,-90252*x+2057778,0,5922*x+801096,0,169464*x+73318,0,15625*x,0,-224568*x+1049476,0,113580*x+3268540,0,-150624*x-1380960,0,100041*x+2178636,0,17100*x+52400,0,-210855*x+3566136,0,122208*x+3455766,0,-112086*x-6094552,0,52308*x+48960,0,-62700*x-1200000,0,17748*x+1417582,0,-54112*x-1169280,0,91296*x+2107218,0,-23988*x-589616,0,-112500*x+216225,0,-42660*x-418824,0,-154092*x+1193290,0,126442*x+2257920,0,106980*x+2235664,0,-17775*x+1252400,0,-31236*x+5425920,0,40632*x+1875156,0,49224*x-2503914,0,-256017*x+3494532,0,52500*x+361250,0,49866*x+2191592,0,276616*x-3611520,0,-148458*x+157880,0,-996*x-4047742,0,63550*x-3744000,0,105636*x+3531664,0,259968*x+2047192,0,186048*x-3399147,0,230025*x-609864,0,36600*x-468150,0,-14362*x-4849920,0,-56004*x-1811982,0,-25548*x+2594376,0,-412168*x+1241280,0,44250*x+252200,0,-42192*x-4667990,0,-543180*x+2234880,0,-321480*x-2825538,0,250161*x-411972,0,-20000*x-648000,0,233667*x+2128232,0,-114000*x-953792,0,253774*x-3098880,0,-147972*x+2637472,0,-22500*x-447500,0,199332*x-2983842,0,-226188*x-1483184,0,-114264*x-1409292,0,-181024*x-3300480,0,115500*x+2538850,0,-2049*x-2165540,0,161428*x-9459360,0,22890*x+6090516,0,33192*x-13274596,0,-130350*x+2309700,0,85008*x+1968960,0,-22692*x+9000212,0]];

E[41,1] = [x^6+5*x^5-91*x^4-345*x^3+1618*x^2+2548*x-1176, 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E[45,4] = [x^2-5*x-30, 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E[45,5] = [x^2-x-102, 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E[45,6] = [x^2+5*x-30, 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E[46,1] = [x^2-6*x-211, 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E[46,4] = [x^3-14*x^2-375*x+4860, 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E[49,3] = [x^2-9*x+6, 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E[49,6] = [x^2-8*x-21, 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E[49,7] = [x^4-596*x^2+23716, 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