Sharedwww / Tables / an_s6g0new_51-100_hiprec.gpOpen in CoCalc
Author: William A. Stein
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\\ an_s6g0new_51-100_hiprec.gp
\\ This is a PARI readable nonnormalized basis for S_6(Gamma_0(N)) for N 
\\ in the range:  51 <= N <= 100.
\\ The number of a_n computed is always at least 500.
\\ William Stein ([email protected])

E[51,1] = [x^2+7*x-24, [1,x,9,-7*x-8,5*x-39,9*x,-32*x-112,9*x-168,81,-74*x+120,-9*x+117,-63*x-72,43*x-589,112*x-768,45*x-351,-7*x+472,289,81*x,147*x-559,478*x-528,-288*x-1008,180*x-216,227*x-2403,81*x-1512,-565*x-1004,-890*x+1032,729,-528*x+6272,84*x-1998,-666*x+1080,598*x+1538,233*x+5208,-81*x+1053,289*x,1808*x+528,-567*x-648,934*x+10664,-1588*x+3528,387*x-5301,-1506*x+7632,-249*x-8589,1008*x-6912,1189*x+6023,-1188*x+576,405*x-3159,-3992*x+5448,-438*x+1110,-63*x+4248,20313,2951*x-13560,2601,5886*x-2512,-1908*x-17238,729*x,1251*x-5643,6384*x+11904,1323*x-5031,-2586*x+2016,-6282*x-16986,4302*x-4752,-2358*x-36580,-2648*x+14352,-2592*x-9072,3801*x-9512,-6127*x+28131,1620*x-1944,4408*x+2540,-2023*x-2312,2043*x-21627,-12128*x+43392,-1268*x-77436,729*x-13608,1052*x+18062,4126*x+22416,-5085*x-9036,9940*x-20224,-4752*x-6192,-8010*x+9288,542*x-12598,2878*x-19248,6561,-6846*x-5976,-6938*x-65586,-4752*x+56448,1445*x-11271,-2300*x+28536,756*x-17982,3132*x-21600,11726*x+59820,-5994*x+9720,23664*x+32944,26128*x-18912,5382*x+13842,4176*x-10512,-13673*x+39441,2097*x+46872,-7614*x+16208,20313*x,-729*x+9477,-16137*x+102952,23086*x+95832,2601*x,-26175*x-84601,-15234*x+108240,16272*x+4752,-3882*x-45792,19891*x+149529,-5103*x-5832,-17734*x-123220,-14400*x+30024,8406*x+95976,-15888*x-47488,-20599*x-56727,-14292*x+31752,-28813*x+120957,17430*x+1872,3483*x-47709,26988*x-150768,-9248*x-32368,-13554*x+68688,-2673*x-145418,-20074*x-56592,-2241*x-77301,13752*x-112768,21165*x+93231,9072*x-62208,-5673*x+130649,-43575*x-75432,10701*x+54207,71020*x-147048,19697*x+46995,-10692*x+5184,34352*x-50288,-28316*x+105792,3645*x-28431,2601*x-48552,-45468*x-111354,-35928*x+49032,61630*x+260126,70432*x-307968,-3942*x+9990,-68560*x-30432,13041*x-78201,-567*x+38232,-16206*x+88002,10698*x+25248,182817,-36354*x-242224,-54260*x-331878,26559*x-122040,-120*x+149072,-38988*x+125664,23409,27072*x-114048,-36562*x+11778,52974*x-22608,25255*x-335881,-16392*x+13008,-17172*x-155142,8798*x-175152,102320*x+94800,6561*x,46130*x+454706,49914*x+110544,11259*x-50787,-17020*x-166512,17623*x+223833,57456*x+107136,-63597*x+20004,-21386*x+34680,11907*x-45279,6588*x-247936,-42127*x-82155,-23274*x+18144,-31152*x+546368,-5508*x+56736,-56538*x-152874,-22262*x+281424,9750*x-191730,38718*x-42768,49696*x+191006,-132704*x+567936,-21222*x-329220,-74064*x+452736,-15796*x-303816,-23832*x+129168,-2601*x+33813,-25728*x+64704,-23328*x-81648,135152*x-328152,3814*x-229590,34209*x-85608,-4092*x+892430,69506*x-182736,-55143*x+253179,-142191*x-162504,-55659*x+325977,14580*x-17496,14944*x+184496,121479*x+46632,39672*x+22860,-65770*x+554064,73344*x+159264,-18207*x-20808,-24519*x+305091,98624*x-628200,18387*x-194643,26526*x-285232,31491*x-97155,-109152*x+390528,-76902*x+469418,42438*x+458448,-11412*x-696924,10292*x+477384,-57871*x-92217,6561*x-122472,17760*x-631520,918*x-425616,9468*x+162558,90792*x-165024,12427*x-170221,37134*x+201744,107*x+116885,-140560*x-762240,-45765*x-81324,87466*x-494376,133641*x+929451,89460*x-182016,93872*x-309082,322648*x-691512,-42768*x-55728,-37386*x+353808,74991*x-75045,-72090*x+83592,37962*x-95850,-138660*x+1191264,4878*x-113382,32368*x-221952,-200348*x-1127844,25902*x-173232,-119002*x-1039876,-126707*x-64152,59049,159382*x+688784,101565*x-792207,-61614*x-53784,-154867*x+480955,-124296*x-129216,-62442*x-590274,-54924*x+507960,85104*x-194244,-42768*x+508032,62487*x-330183,170360*x-136152,13005*x-101439,107961*x-741416,-83430*x-1246392,-20700*x+256824,-236640*x-1911680,-448124*x+804288,6804*x-161838,-90884*x+472728,216328*x+1298544,28188*x-194400,55002*x+443322,-290752*x+824448,105534*x+538380,162948*x-760864,-180781*x-1338477,-53946*x+87480,-96201*x+518825,-2023*x+136408,212976*x+296496,206922*x-1091232,-92664*x+4572,235152*x-170208,194352*x+1269278,-171284*x+1479120,48438*x+124578,-412896*x+301824,130914*x+1690968,37584*x-94608,-150006*x+51842,490064*x+832512,-123057*x+354969,-169488*x+312984,246960*x+1153200,18873*x+421848,83521,201444*x-388944,-68526*x+145872,-83302*x-321232,-45438*x-1587852,182817*x,379938*x-91386,-119778*x-1589808,-6561*x+85293,47942*x-1302240,-305359*x+1649631,-145233*x+926568,-59568*x-1587728,149912*x-2880,207774*x+862488,80500*x-288544,-8408*x+1143660,23409*x,329360*x+584468,-151488*x+847872,-235575*x-761409,267712*x-877488,245288*x-892056,-137106*x+974160,-329286*x-2260720,-512666*x+606120,146448*x+42768,110408*x+9728,263176*x-612786,-34938*x-412128,33102*x-251910,-328834*x+827088,179019*x+1345761,-621440*x+2455680,42483*x-161551,-45927*x-52488,459678*x+8276,131796*x+1107120,-159606*x-1108980,-19782*x+1389168,-84576*x+212064,-129600*x+270216,41431*x+1770773,174644*x+1690272,75654*x+863784,100472*x+422952,-313492*x+429900,-142992*x-427392,-17084*x-128338,465183*x-1526328,-185391*x-510543,138142*x-152592,93798*x+50778,-128628*x+285768,-112192*x-392672,-220452*x-755040,-259317*x+1088613,212734*x-1011048,-323624*x-2242332,156870*x+16848,-142051*x-1880143,764432*x-747648,31347*x-429381,-4932*x+559008,-286296*x-1474758,242892*x-1356912,-293348*x+2867844,62026*x-2448528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E[51,2] = [x^3-5*x^2-54*x+256, 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E[52,2] = [x, [1,0,-5,0,-3,0,53,0,-218,0,-702,0,169,0,15,0,-2019,0,-826,0,-265,0,2208,0,-3116,0,2305,0,822,0,860,0,3510,0,-159,0,5969,0,-845,0,144,0,16589,0,654,0,17193,0,-13998,0,10095,0,-23664,0,2106,0,4130,0,-23010,0,-15832,0,-11554,0,-507,0,20090,0,-11040,0,-59025,0,-76558,0,15580,0,-37206,0,81896,0,41449,0,31524,0,6057,0,-4110,0,-31926,0,8957,0,-4300,0,2478,0,-23098,0,153036,0,73908,0,26132,0,795,0,-36996,0,216401,0,-29845,0,-152166,0,-6624,0,-36842,0,-107007,0,331753,0,-720,0,18723,0,-12388,0,-82945,0,-115551,0,-43778,0,-6915,0,-110832,0,-180319,0,-85965,0,-118638,0,-2466,0,69990,0,-452022,0,-400189,0,440142,0,-2580,0,363902,0,118320,0,117024,0,-450400,0,-10530,0,-575544,0,28561,0,180068,0,169200,0,-165148,0,115050,0,596097,0,559604,0,79160,0,-17907,0,1417338,0,122165,0,-810246,0,-449428,0,2535,0,-366741,0,741494,0,-100450,0,43566,0,-432,0,-481344,0,579852,0,109673,0,295125,0,-49767,0,45580,0,382790,0,-341211,0,-903721,0,679288,0,-640752,0,223523,0,186030,0,-734115,0,-51579,0,-409480,0,777333,0,-1478506,0,-767360,0,41994,0,-139594,0,-157620,0,1127472,0,-1550016,0,-30285,0,509913,0,316357,0,-179196,0,-381732,0,70992,0,159630,0,-1587912,0,-1484047,0,-44785,0,2187432,0,-184540,0,-187480,0,-663894,0,1260284,0,-12390,0,7632,0,2656504,0,115490,0,532221,0,69030,0,-1618110,0,373152,0,879217,0,-369540,0,47496,0,1342406,0,-130660,0,2019270,0,861095,0,34662,0,2382378,0,-577044,0,184980,0,1667694,0,-526604,0,-1082005,0,911229,0,-1212232,0,-1301242,0,-60270,0,-3330625,0,760830,0,-603720,0,-1632665,0,33120,0,1972401,0,2838845,0,389545,0,-2337144,0,177075,0,535035,0,1023240,0,-1793823,0,-1658765,0,229674,0,-4030354,0,-31392,0,-1254192,0,-1830772,0,-93615,0,138918,0,-1327780,0,61940,0,1405023,0,111618,0,-3616402,0,3924474,0,-4457952,0,577755,0,-245688,0,5257742,0,218890,0,-1873116,0,145340,0,-124347,0,-4190238,0,4641536,0,554160,0,-1219530,0,-94572,0,901595,0,3680739,0,-7081615,0,-3748074,0,6291204,0,-839096,0,593190,0,3229365,0,-2365249,0,12330,0,-1823808,0,7212974,0,3051564,0,-829089,0,95778,0,2260110,0,4021302,0,-101088,0,2000945,0,-26871,0,7861814,0,-4653795,0,2108769,0,-3376288,0,12900,0,-541980,0,1064770,0,-1819510,0,-11645478,0,2573816,0,5158752,0,6971217,0,1008761,0,-585120,0,69294,0,7662152,0,2252000,0,-4902555,0,-1659618,0,-459108,0,-3128325,0,-4834504,0]];
E[52,3] = [x^3-12*x^2-813*x+11232, 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E[56,3] = [x^2+6*x-336, [1,0,x,0,3*x+50,0,-49,0,-6*x+93,0,6*x+188,0,-39*x+338,0,32*x+1008,0,6*x+1626,0,-45*x-472,0,-49*x,0,72*x-336,0,246*x+2399,0,-114*x-2016,0,114*x+4374,0,-210*x-3736,0,152*x+2016,0,-147*x-2450,0,-390*x-5426,0,572*x-13104,0,-678*x-2686,0,-798*x-7396,0,87*x-1398,0,714*x-4232,0,2401,0,1590*x+2016,0,768*x-3306,0,756*x+15448,0,-202*x-15120,0,-2253*x-12768,0,75*x+51594,0,294*x-4557,0,-234*x-22412,0,-1944*x+6236,0,-768*x+24192,0,-1740*x+39640,0,1716*x-22646,0,923*x+82656,0,-294*x-9212,0,-1956*x+18544,0,126*x-60903,0,3447*x+28232,0,5070*x+87348,0,3690*x+38304,0,-4728*x-23334,0,1911*x-16562,0,-2476*x-70560,0,-2856*x-68960,0,462*x-33606,0,-354*x+5388,0,2451*x-111310,0,-2070*x+119888,0,-1568*x-49392,0,1884*x-144780,0,-8274*x+11558,0,-3086*x-131040,0,8010*x+56786,0,1296*x+55776,0,-7059*x+110058,0,-294*x-79674,0,2040*x-113611,0,1382*x-227808,0,5694*x+211668,0,924*x+91720,0,-2608*x-268128,0,8139*x+173576,0,2205*x+23128,0,-9696*x-215712,0,4092*x-155622,0,-1515*x+176728,0,-8516*x+239904,0,-3900*x-15080,0,16770*x+333612,0,2401*x,0,12804*x+299190,0,13092*x+5712,0,-8982*x+139122,0,-17928*x-398480,0,-7647*x+111714,0,-7914*x+258048,0,-3528*x+16464,0,3066*x+340404,0,10912*x+254016,0,1278*x-188144,0,-35490*x+254007,0,-2973*x+46824,0,6333*x+222882,0,-12054*x-117551,0,750*x-757008,0,-4740*x-538084,0,5505*x+175738,0,51144*x+25200,0,-28758*x-664420,0,10668*x+317784,0,5586*x+98784,0,28356*x+261680,0,30678*x+38626,0,-21008*x-78624,0,-2172*x+176406,0,6150*x+889056,0,17900*x-653184,0,-5586*x-214326,0,-29754*x-817724,0,11304*x-176400,0,-9672*x-179456,0,-5712*x-153876,0,50080*x-584640,0,-47724*x-1174184,0,10290*x+183064,0,-32942*x+576576,0,-59982*x+470964,0,-33876*x-269472,0,17340*x-272829,0,-10029*x+130072,0,-6459*x-660998,0,-7448*x-98784,0,13560*x+446666,0,10152*x+508112,0,30280*x-657216,0,38880*x+359864,0,-1386*x+56650,0,-33957*x+532224,0,7203*x+120050,0,-7332*x+430144,0,7550*x+1158192,0,86661*x-33576,0,8928*x+81984,0,56928*x+1703520,0,1080*x-546622,0,19110*x+265874,0,-11538*x+176958,0,-69804*x-207432,0,14658*x+608844,0,5034*x-1588608,0,-10515*x-280574,0,37224*x+45024,0,-28028*x+642096,0,51786*x+946948,0,-109776*x-292346,0,-4674*x+75912,0,-63600*x+1239834,0,-9357*x+790864,0,-51824*x-959616,0,33222*x+131614,0,19296*x+1236115,0,-36378*x+155232,0,44055*x+1322178,0,-110400*x-2909424,0,-29424*x-608832,0,54288*x-1057056,0,39102*x+362404,0,-126016*x+823536,0,157182*x+2655300,0,30363*x-2184008,0,132308*x-695520,0,-36648*x-31288,0,12378*x-1534862,0,-4263*x+68502,0,39300*x+405966,0,43572*x+1052136,0,-156084*x+633024,0,-74382*x-858192,0,47151*x-2412722,0,61202*x-2780064,0,-34986*x+207368,0,70674*x-1633060,0,-17754*x+281622,0,-43500*x-1647752,0,38526*x-834958,0,8726*x+2691360,0,-54336*x-1125728,0,-117649,0,48000*x+435456,0,40890*x-2537364,0,94893*x-1136718,0,13416*x+812448,0,-63312*x+1659154,0,63240*x+228080,0,-77910*x-98784,0,68820*x+361200,0,30330*x-1572915,0,-125851*x+685440,0,-13026*x+597428,0,-146412*x+232432,0,-71346*x+1117050,0,-37632*x+161994,0,-125820*x-1376234,0,177504*x+1913184,0,-105378*x-15444,0,-22146*x+2636252,0,86176*x+310464,0,58650*x+930792,0,-37044*x-756952,0,-58566*x+920940,0,55650*x+2799310,0,112464*x-401184,0,124742*x+2734704,0,-6960*x-1044448,0,-64227*x-3593534,0,9898*x+740880,0,-80826*x+148962,0,25584*x+1489072,0,-178677*x-2918142,0,-91836*x-1806328,0,66294*x+2574418,0,-180174*x+1374912,0,110397*x+625632,0,195000*x+4886176,0,185818*x-509040,0,9285*x+5373296,0,-31800*x-2095658,0,117498*x-1833000,0,405534*x+4396710,0,-3675*x-2528106,0,8320*x-1310400,0,-259080*x+581320,0,282*x+393130,0,232992*x+5634720,0,576*x-930048,0,-46320*x+2330424,0,-14406*x+223293,0,-151872*x-4716540,0,-221298*x-5932524,0,222366*x+4302144,0,-289416*x-1954142,0,-119172*x-1871816,0,-72840*x+4398912,0,11466*x+1098188,0,51366*x-4170710,0,-193356*x-3507840,0,267345*x+2044530,0,-185136*x-2946064,0,-290912*x-6023808,0,-167361*x+2431768,0,95256*x-305564,0,157596*x-2569392,0,-165672*x-2999216,0,-157647*x-4851848,0,118908*x-1855746,0,65694*x-651384,0,-11466*x+3276572,0,37632*x-1185408,0,-86034*x-1214604,0,-158376*x-6246496,0,322008*x+1030176,0,305016*x+2134932,0,207504*x+7341948,0,4836*x-87432,0,85260*x-1942360,0,35016*x-590788,0]];
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E[57,3] = [x^2+3*x-36, 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E[57,4] = [x^3-9*x^2-18*x+72, 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E[58,1] = [x^2+14*x+27, 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