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Author: William A. Stein
1\\ discnewfac.gp
2\\ This is a PARI readable file of discriminants of Hecke
3\\ algebras acting on S_2^new(Gamma_0(N)) for N
4\\ in the range:  1 <= N <= 389.
5\\ Computed by William Stein ([email protected])
6\\ JANUARY 28, 1999.
7
8discnew=vector(389,x,[]);
9
10
11discnew[11] = 1
12discnew[14] = 1
13discnew[15] = 1
14discnew[17] = 1
15discnew[19] = 1
16discnew[20] = 1
17discnew[21] = 1
18discnew[23] = 5
19discnew[24] = 1
20discnew[26] = 2^2
21discnew[27] = 1
22discnew[29] = 2^3
23discnew[30] = 1
24discnew[31] = 5
25discnew[32] = 1
26discnew[33] = 1
27discnew[34] = 1
28discnew[35] = 2^2*17
29discnew[36] = 1
30discnew[37] = 2^2
31discnew[38] = 2^2
32discnew[39] = 2^5
33discnew[40] = 1
34discnew[41] = 2^2*37
35discnew[42] = 1
36discnew[43] = 2^5
37discnew[44] = 1
38discnew[45] = 1
39discnew[46] = 1
40discnew[47] = 19*103
41discnew[48] = 1
42discnew[49] = 1
43discnew[50] = 2^2
44discnew[51] = 2^2*17
45discnew[52] = 1
46discnew[53] = 2^4*37
47discnew[54] = 2^2
48discnew[55] = 2^5
49discnew[56] = 2^2
50discnew[57] = 2^2*3^2
51discnew[58] = 2^2
52discnew[59] = 2^3*31*557
53discnew[61] = 2^4*37
54discnew[62] = 2^4*3
55discnew[63] = 2^4*3
56discnew[64] = 1
57discnew[65] = 2^11*3
58discnew[66] = 2^4
59discnew[67] = 2^4*5^4
60discnew[68] = 2^2*3
61discnew[69] = 2^4*5
62discnew[70] = 1
63discnew[71] = 3^4*257^2
64discnew[72] = 1
65discnew[73] = 2^4*3^2*5*13
66discnew[74] = 2^4*5*13
67discnew[75] = 2^2*3^2
68discnew[76] = 1
69discnew[77] = 2^6*5^3
70discnew[78] = 1
71discnew[79] = 2^2*83*983
72discnew[80] = 2^2
73discnew[81] = 2^2*3
74discnew[82] = 2^5
75discnew[83] = 2^4*197*11497
76discnew[84] = 2^2
77discnew[85] = 2^11*3
78discnew[86] = 2^4*3*5*7
79discnew[87] = 2^4*5*229
80discnew[88] = 2^6*17
81discnew[89] = 2^6*5^3*6689
82discnew[90] = 2^4
83discnew[91] = 2^15*79
84discnew[92] = 2^2
85discnew[93] = 2^4*5*229
86discnew[94] = 2^5
87discnew[95] = 2^12*37*709
88discnew[96] = 2^2
89discnew[97] = 2^6*7^2*2777
90discnew[98] = 2^5
91discnew[99] = 2^4*3^4
92discnew[100] = 1
93discnew[101] = 2^8*17568767
94discnew[102] = 2^4
95discnew[103] = 2^4*5*17*411721
96discnew[104] = 2^2*17
97discnew[105] = 2^4*5
98discnew[106] = 2^4*3^2
99discnew[107] = 2^6*5*7*1667*19079
100discnew[108] = 1
101discnew[109] = 2^10*7^2*7537
102discnew[110] = 2^8*3*11
103discnew[111] = 2^12*37*389
104discnew[112] = 2^6
105discnew[113] = 2^10*3^4*7^2*11^2*107
106discnew[114] = 2^4
107discnew[115] = 2^6*5*17^2*53
108discnew[116] = 2^4*5^2
109discnew[117] = 2^11*3
110discnew[118] = 2^4*3^2
111discnew[119] = 2^8*71*131*311*1459
112discnew[120] = 2^2
113discnew[121] = 2^4*3^2
114discnew[122] = 2^6*13*229
115discnew[123] = 2^15*79
116discnew[124] = 2^2
117discnew[125] = 2^8*5^12*11
118discnew[126] = 2^2
119discnew[127] = 2^6*3^4*7*86235899
120discnew[128] = 2^16
121discnew[129] = 2^12*5^2*71
122discnew[130] = 2^4
123discnew[131] = 2^9*5*46141*75619573
124discnew[132] = 2^2
125discnew[133] = 2^16*5^2*13*229
126discnew[134] = 2^6*3^4*11*43
127discnew[135] = 2^6*3^4*13^2
128discnew[136] = 2^8*5
129discnew[137] = 2^10*5^2*29*401*895241
130discnew[138] = 2^8*5
131discnew[139] = 2^8*3^2*7^2*997*2151701
132discnew[140] = 2^2
133discnew[141] = 2^14*3^2*17
134discnew[142] = 2^8*3^2
135discnew[143] = 2^10*5*7*19*103*5560463
136discnew[144] = 2^2
137discnew[145] = 2^21*37^2
138discnew[146] = 2^12*101*389
139discnew[147] = 2^14*3^2*7^4
140discnew[148] = 2^2*17
141discnew[149] = 2^12*7^2*234893*1252037
142discnew[150] = 2^4
143discnew[151] = 2^6*7^2*11*67^2*257*439867
144discnew[152] = 2^8*31^2
145discnew[153] = 2^12*3^2*17
146discnew[154] = 2^8*5
147discnew[155] = 2^24*29*73*5077
148discnew[156] = 2^2
149discnew[157] = 2^13*61*397*48795779
150discnew[158] = 2^13*3^3*5^2
151discnew[159] = 2^8*19*103*1054013
152discnew[160] = 2^13
153discnew[161] = 2^16*5^3*37*536777
154discnew[162] = 2^4*3^4
155discnew[163] = 2^15*3^2*65657*82536739
156discnew[164] = 2^4*1613
157discnew[165] = 2^17*3*37
158discnew[166] = 2^6*5*229
159discnew[167] = 2^4*5*8269*5103536431379173
160discnew[168] = 2^2
161discnew[169] = 2^8*3*7^4*13^4
162discnew[170] = 2^12*5^2*17
163discnew[171] = 2^16*3^7*11^2
164discnew[172] = 2^5
165discnew[173] = 2^14*5^2*7*29*5608385124289
166discnew[174] = 2^8*5^2
167discnew[175] = 2^12*3^4*5^6*17
168discnew[176] = 2^14*17
169discnew[177] = 2^16*5^3*229
170discnew[178] = 2^16*71
171discnew[179] = 2^12*3^4*7^2*313*137707*536747147
172discnew[180] = 1
173discnew[181] = 2^16*5^2*7*61*397*595051637
174discnew[182] = 2^8*3^2
175discnew[183] = 2^22*37*127*5623
176discnew[184] = 2^14*3^2*17
177discnew[185] = 2^26*3^2*23029*60869
178discnew[186] = 2^8*17
179discnew[187] = 2^28*3*5^2*17*37*8461
180discnew[188] = 2^4*5*13
181discnew[189] = 2^16*3^9*7
182discnew[190] = 2^8*17
183discnew[191] = 2^4*3^3*5*382146223*319500117632677
184discnew[192] = 2^12
185discnew[193] = 2^14*5*11^2*17*103*401*4153*680059
186discnew[194] = 2^20*7^2*137*223
187discnew[195] = 2^14*3^2*79
188discnew[196] = 2^5*7^4
189discnew[197] = 2^18*5^2*61*397*35217676193989
190discnew[198] = 2^10
191discnew[199] = 2^8*3*5^3*29*31*71^2*347*947*37316093
192discnew[200] = 2^8*3^2*5^4
193discnew[201] = 2^18*3^2*37*269*953
194discnew[202] = 2^8*3^4*10273
195discnew[203] = 2^35*3^7*17*29*37*7547
196discnew[204] = 2^2
197discnew[205] = 2^30*3^2*5*13*229^2
198discnew[206] = 2^16*3^2*5^2*13*29*359
199discnew[207] = 2^20*3^4*5^2*11^2
200discnew[208] = 2^14*3^2*17
201discnew[209] = 2^32*3^4*15427*2002061
202discnew[210] = 2^8
203discnew[211] = 2^14*3*5*7^4*41^2*43*229*52184516509
204discnew[212] = 2^4*3^3*7^3
205discnew[213] = 2^20*3^2*5^4*13*89
206discnew[214] = 2^16*3^6
207discnew[215] = 2^14*3*7^4*101*107*321821*1933097
208discnew[216] = 2^8*3^4
209discnew[217] = 2^31*3^8*11*31*557*619
210discnew[218] = 2^19*3^4*5*11^2*23
211discnew[219] = 2^24*3^2*29*73*1189637
212discnew[220] = 2^2
213discnew[221] = 2^40*3^3*5^6*7*37*109^2*229
214discnew[222] = 2^8*3^2
215discnew[223] = 2^18*7^2*19*103*3995922697473293141
216discnew[224] = 2^18*5^2
217discnew[225] = 2^12*3^2*5^5
218discnew[226] = 2^23*3*5^3
219discnew[227] = 2^19*5^3*7^4*13^2*29*31^2*13591*57139*273349
220discnew[228] = 2^4*3*11
221discnew[229] = 2^24*107*17467*39555937*53625889
222discnew[230] = 2^16*3^2*5*7*13*367
223discnew[231] = 2^20*3^4*5^3*7*31*229
224discnew[232] = 2^20*71
225discnew[233] = 2^22*3^7*53*139*653*4127*24989*8388019
226discnew[234] = 2^6*3^2*5^2
227discnew[235] = 2^18*3^2*73*1453*3851*1916279
228discnew[236] = 2^2*3*7^2*107
229discnew[237] = 2^18*19*103*1705391537
230discnew[238] = 2^16*5
231discnew[239] = 2^6*7^2*2833*51817*97423*1174779433*8920940047
232discnew[240] = 2^10
233discnew[241] = 2^23*97*1489*20857*651474368435017
234discnew[242] = 2^18*3^2*5^2*11^8
235discnew[243] = 2^13*3^40
236discnew[244] = 2^4*5077
237discnew[245] = 2^36*3^4*7^8*17
238discnew[246] = 2^12*3^2*5^2
239discnew[247] = 2^30*3^4*5^2*11*31^2*619*57713*2655049
240discnew[248] = 2^22*3*11*79
241discnew[249] = 2^33*389*23029
242discnew[250] = 2^8*5^12
243discnew[251] = 2^14*5^2*29*373*8768135668531*2006012696666681
244discnew[252] = 2^2
245discnew[253] = 2^28*3^4*13^2*2711*3187*170701
246discnew[254] = 2^28*3^4*17*569
247discnew[255] = 2^23*5*13*229*1721
248discnew[256] = 2^31
249discnew[257] = 2^29*29*479*71711*409177*654233*32354821
250discnew[258] = 2^12*3^2*5^2
251discnew[259] = 2^43*3^9*5^3*7^2*17^3*29*37*167
252discnew[260] = 2^6*3*47
253discnew[261] = 2^19*3^4*5^3*23^2*229
254discnew[262] = 2^19*3^3*5*11^2*13
255discnew[263] = 2^10*11*61*397*15631853*34867513*97092067*252746489
256discnew[264] = 2^6*3^2
257discnew[265] = 2^37*3^2*5^4*7^3*11^2*13*17^2*113
258discnew[266] = 2^16*5*7*13*29*67
259discnew[267] = 2^26*3^4*5^2*7^4*13^2*97*241
260discnew[268] = 2^4*3^3*5*7
261discnew[269] = 2^22*3^2*43*151*27767*65657*5550873754172978311
262discnew[270] = 2^8
263discnew[271] = 2^12*3^2*1367*6091*592661*1132673*14171513*172450541
264discnew[272] = 2^28*3^3*5
265discnew[273] = 2^25*79*4357
266discnew[274] = 2^20*3^2*19*37*1321
267discnew[275] = 2^31*3^8*5^12*7^2*11^2*13^2
268discnew[276] = 2^10*5
269discnew[277] = 2^22*5^2*19*29*37*137^2*92767*1530091*25531570859
270discnew[278] = 2^22*3^4*7*17^2*103*107
271discnew[279] = 2^28*3^5*5^2*229*1373^2
272discnew[280] = 2^18*3*11*17
273discnew[281] = 2^22*3*5*181*857*8388019*2647382149*1778899342669
274discnew[282] = 2^23*3^2*37
275discnew[283] = 2^40*349*1297*413713*73199099*5832488839
276discnew[284] = 2^6*3^5*107
277discnew[285] = 2^34*3^3*7
278discnew[286] = 2^16*3^2*31^2
279discnew[287] = 2^28*3*5^2*7^2*61^2*97^2*103*257*211039*1798619
280discnew[288] = 2^20*3^2
281discnew[289] = 2^23*3^16*13^2*17^8
282discnew[290] = 2^20*3^3*7*13^2*23*67
283discnew[291] = 2^32*3^4*5^4*11^2*13*19*457*16657
284discnew[292] = 2^7*5*41^2
285discnew[293] = 2^26*3^2*29*233*2351^2*69763*42711913589792108923
286discnew[294] = 2^12*3^2*7^4
287discnew[295] = 2^36*3^4*7^4*43*37199*8055869
288discnew[296] = 2^18*11*53*83*229
289discnew[297] = 2^30*3^24*47^2
290discnew[298] = 2^21*3*5^2*7*13^2*103*107
291discnew[299] = 2^50*3*5^9*7*17^3*197*5936311524617
292discnew[300] = 2^4*5^4
293discnew[301] = 2^38*19*31*37*103*9739*81509*32366197
294discnew[302] = 2^33*3^4*389*1613
295discnew[303] = 2^35*89*3083683*3678833
296discnew[304] = 2^26*3^4*31^2
297discnew[305] = 2^52*3^4*31*43*977*2777*82219057
298discnew[306] = 2^24*3^4
299discnew[307] = 2^22*3^2*5^5*11^2*13^3*107^2*457*3697*21577*974513*568380457
300discnew[308] = 2^12*3*127
301discnew[309] = 2^24*5*37*81509*109363884517
302discnew[310] = 2^23*3^2*37
303discnew[311] = 2^8*5^2*29*3013091897*2106873009119126062143259000543887593
304discnew[312] = 2^18
305discnew[313] = 2^24*5*41^2*8619587*9614923*130838023*2164322751511
306discnew[314] = 2^14*3*47*53*337*907*176130259
307discnew[315] = 2^24*3^4*5^3*17
308discnew[316] = 2^6*3^4*13^2
309discnew[317] = 2^26*7*367*3217*660603043*14989400036918065702697531
310discnew[318] = 2^16*5^2*17*41
311discnew[319] = 2^34*3^4*23^2*127*1063*1433*2459*2777*6709*65551
312discnew[320] = 2^39
313discnew[321] = 2^32*5^2*21803*24443*826957
314discnew[322] = 2^28*3^3*5*79
315discnew[323] = 2^48*7^2*17^3*19*73*103*353*1453*1627*1697*3851*17299
316discnew[324] = 2^4*3^8
317discnew[325] = 2^49*3^9*5^12*7^4*37^2
318discnew[326] = 2^18*17^2*617*28921*482689
319discnew[327] = 2^37*5*37*139*1023203*1033895651
320discnew[328] = 2^28*3^3*37*197
321discnew[329] = 2^46*5^3*7^4*11*13^2*17*37^3*1447*1609*51607
322discnew[330] = 2^8
323discnew[331] = 2^32*3^2*53^2*229*1399*21911*205493*6363601*584461573862449
324discnew[332] = 2^9*7^3*29^2
325discnew[333] = 2^42*3^7*5^2*7^2*37*389
326discnew[334] = 2^27*5^2*7^3*67*733
327discnew[335] = 2^31*3*5*29*71*83*179^2*887*26393*6262079*23057641
328discnew[336] = 2^16*3^2
329discnew[337] = 2^28*113*593*2791*2963615537*747945736667*4122851467451
330discnew[338] = 2^16*3^2*7^6*13^8
331discnew[339] = 2^41*7^2*13^2*17*71^2*8297*470621
332discnew[340] = 2^6*101
333discnew[341] = 2^44*3*5^3*89*151*1121599*344460847*14444130109
334discnew[342] = 2^12*3^4*5^2
335discnew[343] = 2^27*7^48*13^2*29^3*41^2
336discnew[344] = 2^26*3*229*1999567
337discnew[345] = 2^46*3^2*5^4*79
338discnew[346] = 2^18*7^2*229*2777*2075621
339discnew[347] = 2^27*5*7^2*19^2*331*349*479*617*1797330450291217*918291275915301361
340discnew[348] = 2^8
341discnew[349] = 2^28*13*103*1118857*72318613*6771977049413*1313981654817031
342discnew[350] = 2^24*3^4*5^6
343discnew[351] = 2^32*3^17*5^4*13^2*19*37^2
344discnew[352] = 2^42*17^2
345discnew[353] = 2^34*3^2*5*127^2*229*114641*551801*12611821*7779730837*24314514437
346discnew[354] = 2^28*5^2*11*79
347discnew[355] = 2^51*5^2*19*29*103*62581037*933591331
348discnew[356] = 2^9*3*4079*31547
349discnew[357] = 2^49*3*79*113
350discnew[358] = 2^22*3^3*5^3*7*11^4*17^3
351discnew[359] = 2^24*3^4*2777*16512254293*64542630435970307*2171776478013633068927
352discnew[360] = 2^12*3^2
353discnew[361] = 2^28*3^10*5^11*11^4*19^12
354discnew[362] = 2^26*5^4*17^3*6359*1134769
355discnew[363] = 2^36*3^9*5^7*11^18
356discnew[364] = 2^15*3^2
357discnew[365] = 2^51*3^3*5^4*7^3*47*313^2*353783*9377894173
358discnew[366] = 2^16*3^2*13^2*17
359discnew[367] = 2^22*7*81421*251387*418175501*15354151381*13144405392643360366681
360discnew[368] = 2^40*3^4*5^3*17
361discnew[369] = 2^41*3^6*5^2*23^2*37^3*79
362discnew[370] = 2^28*3^2*11*223
363discnew[371] = 2^62*5^3*7*157*229*64627370911*76723322773093
364discnew[372] = 2^10*5^2*17
365discnew[373] = 2^32*7*11^3*23*199*673*2143*1542194372227*72819251148518000363297
366discnew[374] = 2^28*5^2*157*257*11117*17417
367discnew[375] = 2^24*5^24*101^2
368discnew[376] = 2^33*5^5*41^2*61
369discnew[377] = 2^70*3^3*5^2*7^2*829*991*36497*202817*400031*54126547
370discnew[378] = 2^16*3^8
371discnew[379] = 2^28*59*317*421*278329*5698591*2117788336277*2851210737989187265253
372discnew[380] = 2^15*3
373discnew[381] = 2^32*11^2*15427*81509*98361184089911
374discnew[382] = 2^28*7^2*11*13^2*619*44171
375discnew[383] = 2^16*5*11^2*13*72893*3151861*16141144314299*178236551484825400362837637090811
376discnew[384] = 2^40
377discnew[385] = 2^61*3*37^3*2837
378discnew[386] = 2^32*5^2*14653*22961*9659021
379discnew[387] = 2^51*3^9*5^8*7^2*13^2*71
380discnew[388] = 2^8*7^2*179*1297
381discnew[389] = 2^53*3^4*5^6*31^2*37*389*3881*215517113148241*477439237737571441
382