\\ discnewfac.gp \\ This is a PARI readable file of discriminants of Hecke \\ algebras acting on S_2^new(Gamma_0(N)) for N \\ in the range: 1 <= N <= 389. \\ Computed by William Stein (was@math.berkeley.edu) \\ JANUARY 28, 1999. discnew=vector(389,x,[]); discnew[11] = 1 discnew[14] = 1 discnew[15] = 1 discnew[17] = 1 discnew[19] = 1 discnew[20] = 1 discnew[21] = 1 discnew[23] = 5 discnew[24] = 1 discnew[26] = 2^2 discnew[27] = 1 discnew[29] = 2^3 discnew[30] = 1 discnew[31] = 5 discnew[32] = 1 discnew[33] = 1 discnew[34] = 1 discnew[35] = 2^2*17 discnew[36] = 1 discnew[37] = 2^2 discnew[38] = 2^2 discnew[39] = 2^5 discnew[40] = 1 discnew[41] = 2^2*37 discnew[42] = 1 discnew[43] = 2^5 discnew[44] = 1 discnew[45] = 1 discnew[46] = 1 discnew[47] = 19*103 discnew[48] = 1 discnew[49] = 1 discnew[50] = 2^2 discnew[51] = 2^2*17 discnew[52] = 1 discnew[53] = 2^4*37 discnew[54] = 2^2 discnew[55] = 2^5 discnew[56] = 2^2 discnew[57] = 2^2*3^2 discnew[58] = 2^2 discnew[59] = 2^3*31*557 discnew[61] = 2^4*37 discnew[62] = 2^4*3 discnew[63] = 2^4*3 discnew[64] = 1 discnew[65] = 2^11*3 discnew[66] = 2^4 discnew[67] = 2^4*5^4 discnew[68] = 2^2*3 discnew[69] = 2^4*5 discnew[70] = 1 discnew[71] = 3^4*257^2 discnew[72] = 1 discnew[73] = 2^4*3^2*5*13 discnew[74] = 2^4*5*13 discnew[75] = 2^2*3^2 discnew[76] = 1 discnew[77] = 2^6*5^3 discnew[78] = 1 discnew[79] = 2^2*83*983 discnew[80] = 2^2 discnew[81] = 2^2*3 discnew[82] = 2^5 discnew[83] = 2^4*197*11497 discnew[84] = 2^2 discnew[85] = 2^11*3 discnew[86] = 2^4*3*5*7 discnew[87] = 2^4*5*229 discnew[88] = 2^6*17 discnew[89] = 2^6*5^3*6689 discnew[90] = 2^4 discnew[91] = 2^15*79 discnew[92] = 2^2 discnew[93] = 2^4*5*229 discnew[94] = 2^5 discnew[95] = 2^12*37*709 discnew[96] = 2^2 discnew[97] = 2^6*7^2*2777 discnew[98] = 2^5 discnew[99] = 2^4*3^4 discnew[100] = 1 discnew[101] = 2^8*17568767 discnew[102] = 2^4 discnew[103] = 2^4*5*17*411721 discnew[104] = 2^2*17 discnew[105] = 2^4*5 discnew[106] = 2^4*3^2 discnew[107] = 2^6*5*7*1667*19079 discnew[108] = 1 discnew[109] = 2^10*7^2*7537 discnew[110] = 2^8*3*11 discnew[111] = 2^12*37*389 discnew[112] = 2^6 discnew[113] = 2^10*3^4*7^2*11^2*107 discnew[114] = 2^4 discnew[115] = 2^6*5*17^2*53 discnew[116] = 2^4*5^2 discnew[117] = 2^11*3 discnew[118] = 2^4*3^2 discnew[119] = 2^8*71*131*311*1459 discnew[120] = 2^2 discnew[121] = 2^4*3^2 discnew[122] = 2^6*13*229 discnew[123] = 2^15*79 discnew[124] = 2^2 discnew[125] = 2^8*5^12*11 discnew[126] = 2^2 discnew[127] = 2^6*3^4*7*86235899 discnew[128] = 2^16 discnew[129] = 2^12*5^2*71 discnew[130] = 2^4 discnew[131] = 2^9*5*46141*75619573 discnew[132] = 2^2 discnew[133] = 2^16*5^2*13*229 discnew[134] = 2^6*3^4*11*43 discnew[135] = 2^6*3^4*13^2 discnew[136] = 2^8*5 discnew[137] = 2^10*5^2*29*401*895241 discnew[138] = 2^8*5 discnew[139] = 2^8*3^2*7^2*997*2151701 discnew[140] = 2^2 discnew[141] = 2^14*3^2*17 discnew[142] = 2^8*3^2 discnew[143] = 2^10*5*7*19*103*5560463 discnew[144] = 2^2 discnew[145] = 2^21*37^2 discnew[146] = 2^12*101*389 discnew[147] = 2^14*3^2*7^4 discnew[148] = 2^2*17 discnew[149] = 2^12*7^2*234893*1252037 discnew[150] = 2^4 discnew[151] = 2^6*7^2*11*67^2*257*439867 discnew[152] = 2^8*31^2 discnew[153] = 2^12*3^2*17 discnew[154] = 2^8*5 discnew[155] = 2^24*29*73*5077 discnew[156] = 2^2 discnew[157] = 2^13*61*397*48795779 discnew[158] = 2^13*3^3*5^2 discnew[159] = 2^8*19*103*1054013 discnew[160] = 2^13 discnew[161] = 2^16*5^3*37*536777 discnew[162] = 2^4*3^4 discnew[163] = 2^15*3^2*65657*82536739 discnew[164] = 2^4*1613 discnew[165] = 2^17*3*37 discnew[166] = 2^6*5*229 discnew[167] = 2^4*5*8269*5103536431379173 discnew[168] = 2^2 discnew[169] = 2^8*3*7^4*13^4 discnew[170] = 2^12*5^2*17 discnew[171] = 2^16*3^7*11^2 discnew[172] = 2^5 discnew[173] = 2^14*5^2*7*29*5608385124289 discnew[174] = 2^8*5^2 discnew[175] = 2^12*3^4*5^6*17 discnew[176] = 2^14*17 discnew[177] = 2^16*5^3*229 discnew[178] = 2^16*71 discnew[179] = 2^12*3^4*7^2*313*137707*536747147 discnew[180] = 1 discnew[181] = 2^16*5^2*7*61*397*595051637 discnew[182] = 2^8*3^2 discnew[183] = 2^22*37*127*5623 discnew[184] = 2^14*3^2*17 discnew[185] = 2^26*3^2*23029*60869 discnew[186] = 2^8*17 discnew[187] = 2^28*3*5^2*17*37*8461 discnew[188] = 2^4*5*13 discnew[189] = 2^16*3^9*7 discnew[190] = 2^8*17 discnew[191] = 2^4*3^3*5*382146223*319500117632677 discnew[192] = 2^12 discnew[193] = 2^14*5*11^2*17*103*401*4153*680059 discnew[194] = 2^20*7^2*137*223 discnew[195] = 2^14*3^2*79 discnew[196] = 2^5*7^4 discnew[197] = 2^18*5^2*61*397*35217676193989 discnew[198] = 2^10 discnew[199] = 2^8*3*5^3*29*31*71^2*347*947*37316093 discnew[200] = 2^8*3^2*5^4 discnew[201] = 2^18*3^2*37*269*953 discnew[202] = 2^8*3^4*10273 discnew[203] = 2^35*3^7*17*29*37*7547 discnew[204] = 2^2 discnew[205] = 2^30*3^2*5*13*229^2 discnew[206] = 2^16*3^2*5^2*13*29*359 discnew[207] = 2^20*3^4*5^2*11^2 discnew[208] = 2^14*3^2*17 discnew[209] = 2^32*3^4*15427*2002061 discnew[210] = 2^8 discnew[211] = 2^14*3*5*7^4*41^2*43*229*52184516509 discnew[212] = 2^4*3^3*7^3 discnew[213] = 2^20*3^2*5^4*13*89 discnew[214] = 2^16*3^6 discnew[215] = 2^14*3*7^4*101*107*321821*1933097 discnew[216] = 2^8*3^4 discnew[217] = 2^31*3^8*11*31*557*619 discnew[218] = 2^19*3^4*5*11^2*23 discnew[219] = 2^24*3^2*29*73*1189637 discnew[220] = 2^2 discnew[221] = 2^40*3^3*5^6*7*37*109^2*229 discnew[222] = 2^8*3^2 discnew[223] = 2^18*7^2*19*103*3995922697473293141 discnew[224] = 2^18*5^2 discnew[225] = 2^12*3^2*5^5 discnew[226] = 2^23*3*5^3 discnew[227] = 2^19*5^3*7^4*13^2*29*31^2*13591*57139*273349 discnew[228] = 2^4*3*11 discnew[229] = 2^24*107*17467*39555937*53625889 discnew[230] = 2^16*3^2*5*7*13*367 discnew[231] = 2^20*3^4*5^3*7*31*229 discnew[232] = 2^20*71 discnew[233] = 2^22*3^7*53*139*653*4127*24989*8388019 discnew[234] = 2^6*3^2*5^2 discnew[235] = 2^18*3^2*73*1453*3851*1916279 discnew[236] = 2^2*3*7^2*107 discnew[237] = 2^18*19*103*1705391537 discnew[238] = 2^16*5 discnew[239] = 2^6*7^2*2833*51817*97423*1174779433*8920940047 discnew[240] = 2^10 discnew[241] = 2^23*97*1489*20857*651474368435017 discnew[242] = 2^18*3^2*5^2*11^8 discnew[243] = 2^13*3^40 discnew[244] = 2^4*5077 discnew[245] = 2^36*3^4*7^8*17 discnew[246] = 2^12*3^2*5^2 discnew[247] = 2^30*3^4*5^2*11*31^2*619*57713*2655049 discnew[248] = 2^22*3*11*79 discnew[249] = 2^33*389*23029 discnew[250] = 2^8*5^12 discnew[251] = 2^14*5^2*29*373*8768135668531*2006012696666681 discnew[252] = 2^2 discnew[253] = 2^28*3^4*13^2*2711*3187*170701 discnew[254] = 2^28*3^4*17*569 discnew[255] = 2^23*5*13*229*1721 discnew[256] = 2^31 discnew[257] = 2^29*29*479*71711*409177*654233*32354821 discnew[258] = 2^12*3^2*5^2 discnew[259] = 2^43*3^9*5^3*7^2*17^3*29*37*167 discnew[260] = 2^6*3*47 discnew[261] = 2^19*3^4*5^3*23^2*229 discnew[262] = 2^19*3^3*5*11^2*13 discnew[263] = 2^10*11*61*397*15631853*34867513*97092067*252746489 discnew[264] = 2^6*3^2 discnew[265] = 2^37*3^2*5^4*7^3*11^2*13*17^2*113 discnew[266] = 2^16*5*7*13*29*67 discnew[267] = 2^26*3^4*5^2*7^4*13^2*97*241 discnew[268] = 2^4*3^3*5*7 discnew[269] = 2^22*3^2*43*151*27767*65657*5550873754172978311 discnew[270] = 2^8 discnew[271] = 2^12*3^2*1367*6091*592661*1132673*14171513*172450541 discnew[272] = 2^28*3^3*5 discnew[273] = 2^25*79*4357 discnew[274] = 2^20*3^2*19*37*1321 discnew[275] = 2^31*3^8*5^12*7^2*11^2*13^2 discnew[276] = 2^10*5 discnew[277] = 2^22*5^2*19*29*37*137^2*92767*1530091*25531570859 discnew[278] = 2^22*3^4*7*17^2*103*107 discnew[279] = 2^28*3^5*5^2*229*1373^2 discnew[280] = 2^18*3*11*17 discnew[281] = 2^22*3*5*181*857*8388019*2647382149*1778899342669 discnew[282] = 2^23*3^2*37 discnew[283] = 2^40*349*1297*413713*73199099*5832488839 discnew[284] = 2^6*3^5*107 discnew[285] = 2^34*3^3*7 discnew[286] = 2^16*3^2*31^2 discnew[287] = 2^28*3*5^2*7^2*61^2*97^2*103*257*211039*1798619 discnew[288] = 2^20*3^2 discnew[289] = 2^23*3^16*13^2*17^8 discnew[290] = 2^20*3^3*7*13^2*23*67 discnew[291] = 2^32*3^4*5^4*11^2*13*19*457*16657 discnew[292] = 2^7*5*41^2 discnew[293] = 2^26*3^2*29*233*2351^2*69763*42711913589792108923 discnew[294] = 2^12*3^2*7^4 discnew[295] = 2^36*3^4*7^4*43*37199*8055869 discnew[296] = 2^18*11*53*83*229 discnew[297] = 2^30*3^24*47^2 discnew[298] = 2^21*3*5^2*7*13^2*103*107 discnew[299] = 2^50*3*5^9*7*17^3*197*5936311524617 discnew[300] = 2^4*5^4 discnew[301] = 2^38*19*31*37*103*9739*81509*32366197 discnew[302] = 2^33*3^4*389*1613 discnew[303] = 2^35*89*3083683*3678833 discnew[304] = 2^26*3^4*31^2 discnew[305] = 2^52*3^4*31*43*977*2777*82219057 discnew[306] = 2^24*3^4 discnew[307] = 2^22*3^2*5^5*11^2*13^3*107^2*457*3697*21577*974513*568380457 discnew[308] = 2^12*3*127 discnew[309] = 2^24*5*37*81509*109363884517 discnew[310] = 2^23*3^2*37 discnew[311] = 2^8*5^2*29*3013091897*2106873009119126062143259000543887593 discnew[312] = 2^18 discnew[313] = 2^24*5*41^2*8619587*9614923*130838023*2164322751511 discnew[314] = 2^14*3*47*53*337*907*176130259 discnew[315] = 2^24*3^4*5^3*17 discnew[316] = 2^6*3^4*13^2 discnew[317] = 2^26*7*367*3217*660603043*14989400036918065702697531 discnew[318] = 2^16*5^2*17*41 discnew[319] = 2^34*3^4*23^2*127*1063*1433*2459*2777*6709*65551 discnew[320] = 2^39 discnew[321] = 2^32*5^2*21803*24443*826957 discnew[322] = 2^28*3^3*5*79 discnew[323] = 2^48*7^2*17^3*19*73*103*353*1453*1627*1697*3851*17299 discnew[324] = 2^4*3^8 discnew[325] = 2^49*3^9*5^12*7^4*37^2 discnew[326] = 2^18*17^2*617*28921*482689 discnew[327] = 2^37*5*37*139*1023203*1033895651 discnew[328] = 2^28*3^3*37*197 discnew[329] = 2^46*5^3*7^4*11*13^2*17*37^3*1447*1609*51607 discnew[330] = 2^8 discnew[331] = 2^32*3^2*53^2*229*1399*21911*205493*6363601*584461573862449 discnew[332] = 2^9*7^3*29^2 discnew[333] = 2^42*3^7*5^2*7^2*37*389 discnew[334] = 2^27*5^2*7^3*67*733 discnew[335] = 2^31*3*5*29*71*83*179^2*887*26393*6262079*23057641 discnew[336] = 2^16*3^2 discnew[337] = 2^28*113*593*2791*2963615537*747945736667*4122851467451 discnew[338] = 2^16*3^2*7^6*13^8 discnew[339] = 2^41*7^2*13^2*17*71^2*8297*470621 discnew[340] = 2^6*101 discnew[341] = 2^44*3*5^3*89*151*1121599*344460847*14444130109 discnew[342] = 2^12*3^4*5^2 discnew[343] = 2^27*7^48*13^2*29^3*41^2 discnew[344] = 2^26*3*229*1999567 discnew[345] = 2^46*3^2*5^4*79 discnew[346] = 2^18*7^2*229*2777*2075621 discnew[347] = 2^27*5*7^2*19^2*331*349*479*617*1797330450291217*918291275915301361 discnew[348] = 2^8 discnew[349] = 2^28*13*103*1118857*72318613*6771977049413*1313981654817031 discnew[350] = 2^24*3^4*5^6 discnew[351] = 2^32*3^17*5^4*13^2*19*37^2 discnew[352] = 2^42*17^2 discnew[353] = 2^34*3^2*5*127^2*229*114641*551801*12611821*7779730837*24314514437 discnew[354] = 2^28*5^2*11*79 discnew[355] = 2^51*5^2*19*29*103*62581037*933591331 discnew[356] = 2^9*3*4079*31547 discnew[357] = 2^49*3*79*113 discnew[358] = 2^22*3^3*5^3*7*11^4*17^3 discnew[359] = 2^24*3^4*2777*16512254293*64542630435970307*2171776478013633068927 discnew[360] = 2^12*3^2 discnew[361] = 2^28*3^10*5^11*11^4*19^12 discnew[362] = 2^26*5^4*17^3*6359*1134769 discnew[363] = 2^36*3^9*5^7*11^18 discnew[364] = 2^15*3^2 discnew[365] = 2^51*3^3*5^4*7^3*47*313^2*353783*9377894173 discnew[366] = 2^16*3^2*13^2*17 discnew[367] = 2^22*7*81421*251387*418175501*15354151381*13144405392643360366681 discnew[368] = 2^40*3^4*5^3*17 discnew[369] = 2^41*3^6*5^2*23^2*37^3*79 discnew[370] = 2^28*3^2*11*223 discnew[371] = 2^62*5^3*7*157*229*64627370911*76723322773093 discnew[372] = 2^10*5^2*17 discnew[373] = 2^32*7*11^3*23*199*673*2143*1542194372227*72819251148518000363297 discnew[374] = 2^28*5^2*157*257*11117*17417 discnew[375] = 2^24*5^24*101^2 discnew[376] = 2^33*5^5*41^2*61 discnew[377] = 2^70*3^3*5^2*7^2*829*991*36497*202817*400031*54126547 discnew[378] = 2^16*3^8 discnew[379] = 2^28*59*317*421*278329*5698591*2117788336277*2851210737989187265253 discnew[380] = 2^15*3 discnew[381] = 2^32*11^2*15427*81509*98361184089911 discnew[382] = 2^28*7^2*11*13^2*619*44171 discnew[383] = 2^16*5*11^2*13*72893*3151861*16141144314299*178236551484825400362837637090811 discnew[384] = 2^40 discnew[385] = 2^61*3*37^3*2837 discnew[386] = 2^32*5^2*14653*22961*9659021 discnew[387] = 2^51*3^9*5^8*7^2*13^2*71 discnew[388] = 2^8*7^2*179*1297 discnew[389] = 2^53*3^4*5^6*31^2*37*389*3881*215517113148241*477439237737571441