Sharedwww / Tables / charpoly_s2new.gpOpen in CoCalc
Author: William A. Stein
1
\\ charpoly_s2new.gp
2
\\ This is a table of characteristic polynomials of the
3
\\ Hecke operators T_p acting on the space S_2^{new}(Gamma_0(N))
4
\\ of weight 2 cuspidal newforms for Gamma_0(N).
5
\\ The cases in which S_2 = S_2^{new} are omitted, since
6
\\ they appear in other tables.
7
\\ William Stein ([email protected]), September, 1998.
8
9
{
10
T=matrix(100,97,m,n,0);
11
T[30,2]=x + 1;
12
T[30,3]=x -1;
13
T[30,5]=x + 1;
14
T[30,7]=x + 4;
15
T[30,11]=x ;
16
T[30,13]=x -2;
17
T[30,17]=x -6;
18
T[30,19]=x + 4;
19
T[30,23]=x ;
20
T[30,29]=x + 6;
21
T[30,31]=x -8;
22
T[30,37]=x -2;
23
T[30,41]=x + 6;
24
T[30,43]=x + 4;
25
T[30,47]=x ;
26
T[30,53]=x + 6;
27
T[30,59]=x ;
28
T[30,61]=x + 10;
29
T[30,67]=x + 4;
30
T[30,71]=x ;
31
T[30,73]=x -2;
32
T[30,79]=x -8;
33
T[30,83]=x -12;
34
T[30,89]=x -18;
35
T[30,97]=x -2;
36
37
T[33,2]=x -1;
38
T[33,3]=x + 1;
39
T[33,5]=x + 2;
40
T[33,7]=x -4;
41
T[33,11]=x -1;
42
T[33,13]=x + 2;
43
T[33,17]=x + 2;
44
T[33,19]=x ;
45
T[33,23]=x -8;
46
T[33,29]=x + 6;
47
T[33,31]=x + 8;
48
T[33,37]=x -6;
49
T[33,41]=x + 2;
50
T[33,43]=x ;
51
T[33,47]=x -8;
52
T[33,53]=x -6;
53
T[33,59]=x + 4;
54
T[33,61]=x -6;
55
T[33,67]=x + 4;
56
T[33,71]=x ;
57
T[33,73]=x + 14;
58
T[33,79]=x + 4;
59
T[33,83]=x -12;
60
T[33,89]=x + 6;
61
T[33,97]=x -2;
62
63
T[34,2]=x -1;
64
T[34,3]=x + 2;
65
T[34,5]=x ;
66
T[34,7]=x + 4;
67
T[34,11]=x -6;
68
T[34,13]=x -2;
69
T[34,17]=x + 1;
70
T[34,19]=x + 4;
71
T[34,23]=x ;
72
T[34,29]=x ;
73
T[34,31]=x + 4;
74
T[34,37]=x + 4;
75
T[34,41]=x -6;
76
T[34,43]=x -8;
77
T[34,47]=x ;
78
T[34,53]=x + 6;
79
T[34,59]=x ;
80
T[34,61]=x + 4;
81
T[34,67]=x -8;
82
T[34,71]=x ;
83
T[34,73]=x -2;
84
T[34,79]=x -8;
85
T[34,83]=x ;
86
T[34,89]=x + 6;
87
T[34,97]=x -14;
88
89
T[38,2]=(x + 1)*(x -1);
90
T[38,3]=(x -1)*(x + 1);
91
T[38,5]=(x + 4)*(x );
92
T[38,7]=(x -3)*(x + 1);
93
T[38,11]=(x -2)*(x + 6);
94
T[38,13]=(x + 1)*(x -5);
95
T[38,17]=(x -3)^2;
96
T[38,19]=(x -1)*(x + 1);
97
T[38,23]=(x + 1)*(x -3);
98
T[38,29]=(x -9)*(x + 5);
99
T[38,31]=(x + 8)*(x + 4);
100
T[38,37]=(x -2)*(x + 2);
101
T[38,41]=(x + 8)*(x );
102
T[38,43]=(x -4)*(x -8);
103
T[38,47]=(x -8)*(x );
104
T[38,53]=(x + 1)*(x + 3);
105
T[38,59]=(x -15)*(x -9);
106
T[38,61]=(x -2)*(x + 10);
107
T[38,67]=(x -5)*(x -3);
108
T[38,71]=(x -2)*(x + 6);
109
T[38,73]=(x + 7)*(x -9);
110
T[38,79]=(x + 10)^2;
111
T[38,83]=(x + 6)^2;
112
T[38,89]=(x + 12)*(x );
113
T[38,97]=(x + 2)*(x + 10);
114
115
T[40,2]=x ;
116
T[40,3]=x ;
117
T[40,5]=x -1;
118
T[40,7]=x + 4;
119
T[40,11]=x -4;
120
T[40,13]=x + 2;
121
T[40,17]=x -2;
122
T[40,19]=x -4;
123
T[40,23]=x -4;
124
T[40,29]=x + 2;
125
T[40,31]=x + 8;
126
T[40,37]=x -6;
127
T[40,41]=x + 6;
128
T[40,43]=x + 8;
129
T[40,47]=x -4;
130
T[40,53]=x -6;
131
T[40,59]=x + 4;
132
T[40,61]=x + 2;
133
T[40,67]=x -8;
134
T[40,71]=x ;
135
T[40,73]=x + 6;
136
T[40,79]=x ;
137
T[40,83]=x + 16;
138
T[40,89]=x + 6;
139
T[40,97]=x + 14;
140
141
T[42,2]=x -1;
142
T[42,3]=x + 1;
143
T[42,5]=x + 2;
144
T[42,7]=x + 1;
145
T[42,11]=x + 4;
146
T[42,13]=x -6;
147
T[42,17]=x -2;
148
T[42,19]=x + 4;
149
T[42,23]=x -8;
150
T[42,29]=x + 2;
151
T[42,31]=x ;
152
T[42,37]=x + 10;
153
T[42,41]=x + 6;
154
T[42,43]=x + 4;
155
T[42,47]=x ;
156
T[42,53]=x -6;
157
T[42,59]=x -4;
158
T[42,61]=x -6;
159
T[42,67]=x -4;
160
T[42,71]=x -8;
161
T[42,73]=x -10;
162
T[42,79]=x ;
163
T[42,83]=x + 4;
164
T[42,89]=x + 6;
165
T[42,97]=x + 14;
166
167
T[44,2]=x ;
168
T[44,3]=x -1;
169
T[44,5]=x + 3;
170
T[44,7]=x -2;
171
T[44,11]=x + 1;
172
T[44,13]=x + 4;
173
T[44,17]=x -6;
174
T[44,19]=x -8;
175
T[44,23]=x + 3;
176
T[44,29]=x ;
177
T[44,31]=x -5;
178
T[44,37]=x + 1;
179
T[44,41]=x ;
180
T[44,43]=x + 10;
181
T[44,47]=x ;
182
T[44,53]=x + 6;
183
T[44,59]=x -3;
184
T[44,61]=x + 4;
185
T[44,67]=x + 1;
186
T[44,71]=x -15;
187
T[44,73]=x + 4;
188
T[44,79]=x -2;
189
T[44,83]=x -6;
190
T[44,89]=x + 9;
191
T[44,97]=x + 7;
192
193
T[45,2]=x -1;
194
T[45,3]=x ;
195
T[45,5]=x + 1;
196
T[45,7]=x ;
197
T[45,11]=x -4;
198
T[45,13]=x + 2;
199
T[45,17]=x + 2;
200
T[45,19]=x -4;
201
T[45,23]=x ;
202
T[45,29]=x -2;
203
T[45,31]=x ;
204
T[45,37]=x + 10;
205
T[45,41]=x + 10;
206
T[45,43]=x -4;
207
T[45,47]=x + 8;
208
T[45,53]=x -10;
209
T[45,59]=x -4;
210
T[45,61]=x + 2;
211
T[45,67]=x -12;
212
T[45,71]=x -8;
213
T[45,73]=x -10;
214
T[45,79]=x ;
215
T[45,83]=x + 12;
216
T[45,89]=x -6;
217
T[45,97]=x -2;
218
219
T[46,2]=x + 1;
220
T[46,3]=x ;
221
T[46,5]=x -4;
222
T[46,7]=x + 4;
223
T[46,11]=x -2;
224
T[46,13]=x + 2;
225
T[46,17]=x + 2;
226
T[46,19]=x + 2;
227
T[46,23]=x -1;
228
T[46,29]=x -2;
229
T[46,31]=x ;
230
T[46,37]=x + 4;
231
T[46,41]=x -6;
232
T[46,43]=x -10;
233
T[46,47]=x ;
234
T[46,53]=x + 4;
235
T[46,59]=x -12;
236
T[46,61]=x + 8;
237
T[46,67]=x + 10;
238
T[46,71]=x ;
239
T[46,73]=x -6;
240
T[46,79]=x + 12;
241
T[46,83]=x -14;
242
T[46,89]=x + 6;
243
T[46,97]=x -6;
244
245
T[48,2]=x ;
246
T[48,3]=x -1;
247
T[48,5]=x + 2;
248
T[48,7]=x ;
249
T[48,11]=x + 4;
250
T[48,13]=x + 2;
251
T[48,17]=x -2;
252
T[48,19]=x -4;
253
T[48,23]=x -8;
254
T[48,29]=x -6;
255
T[48,31]=x + 8;
256
T[48,37]=x -6;
257
T[48,41]=x + 6;
258
T[48,43]=x + 4;
259
T[48,47]=x ;
260
T[48,53]=x + 2;
261
T[48,59]=x + 4;
262
T[48,61]=x + 2;
263
T[48,67]=x -4;
264
T[48,71]=x + 8;
265
T[48,73]=x -10;
266
T[48,79]=x -8;
267
T[48,83]=x -4;
268
T[48,89]=x + 6;
269
T[48,97]=x -2;
270
271
T[51,2]=(x^2 + x -4)*(x );
272
T[51,3]=(x -1)*(x + 1)^2;
273
T[51,5]=(x -3)*(x^2 -3*x -2);
274
T[51,7]=(x + 4)*(x )^2;
275
T[51,11]=(x + 3)*(x^2 + x -4);
276
T[51,13]=(x + 1)*(x^2 -5*x + 2);
277
T[51,17]=(x + 1)*(x -1)^2;
278
T[51,19]=(x + 1)*(x^2 -3*x -36);
279
T[51,23]=(x -9)*(x^2 + 9*x + 16);
280
T[51,29]=(x -6)*(x^2 -68);
281
T[51,31]=(x -2)*(x^2 + 2*x -16);
282
T[51,37]=(x + 4)*(x^2 + 2*x -16);
283
T[51,41]=(x + 3)*(x^2 + 3*x -2);
284
T[51,43]=(x + 7)*(x^2 + 3*x -36);
285
T[51,47]=(x + 6)*(x^2 + 14*x + 32);
286
T[51,53]=(x + 6)*(x^2 -8*x -52);
287
T[51,59]=(x -6)*(x^2 -6*x -8);
288
T[51,61]=(x -8)*(x^2 -10*x + 8);
289
T[51,67]=(x + 4)*(x -4)^2;
290
T[51,71]=(x -12)*(x^2 -4*x -64);
291
T[51,73]=(x -2)*(x^2 + 8*x -52);
292
T[51,79]=(x + 10)*(x^2 -6*x -144);
293
T[51,83]=(x + 6)*(x^2 + 10*x + 8);
294
T[51,89]=(x^2 -6*x -8)*(x );
295
T[51,97]=(x + 16)*(x^2 + 14*x + 32);
296
297
T[52,2]=x ;
298
T[52,3]=x ;
299
T[52,5]=x -2;
300
T[52,7]=x + 2;
301
T[52,11]=x + 2;
302
T[52,13]=x + 1;
303
T[52,17]=x -6;
304
T[52,19]=x + 6;
305
T[52,23]=x -8;
306
T[52,29]=x -2;
307
T[52,31]=x -10;
308
T[52,37]=x + 6;
309
T[52,41]=x + 6;
310
T[52,43]=x -4;
311
T[52,47]=x + 2;
312
T[52,53]=x -6;
313
T[52,59]=x + 10;
314
T[52,61]=x + 2;
315
T[52,67]=x -10;
316
T[52,71]=x -10;
317
T[52,73]=x -2;
318
T[52,79]=x + 4;
319
T[52,83]=x + 6;
320
T[52,89]=x + 6;
321
T[52,97]=x -2;
322
323
T[54,2]=(x + 1)*(x -1);
324
T[54,3]=(x )^2;
325
T[54,5]=(x + 3)*(x -3);
326
T[54,7]=(x + 1)^2;
327
T[54,11]=(x -3)*(x + 3);
328
T[54,13]=(x + 4)^2;
329
T[54,17]=(x )^2;
330
T[54,19]=(x -2)^2;
331
T[54,23]=(x -6)*(x + 6);
332
T[54,29]=(x -6)*(x + 6);
333
T[54,31]=(x -5)^2;
334
T[54,37]=(x -2)^2;
335
T[54,41]=(x -6)*(x + 6);
336
T[54,43]=(x + 10)^2;
337
T[54,47]=(x -6)*(x + 6);
338
T[54,53]=(x -9)*(x + 9);
339
T[54,59]=(x -12)*(x + 12);
340
T[54,61]=(x -8)^2;
341
T[54,67]=(x -14)^2;
342
T[54,71]=(x )^2;
343
T[54,73]=(x + 7)^2;
344
T[54,79]=(x -8)^2;
345
T[54,83]=(x + 3)*(x -3);
346
T[54,89]=(x + 18)*(x -18);
347
T[54,97]=(x + 1)^2;
348
349
T[55,2]=(x -1)*(x^2 -2*x -1);
350
T[55,3]=(x^2 -8)*(x );
351
T[55,5]=(x -1)*(x + 1)^2;
352
T[55,7]=(x )*(x + 2)^2;
353
T[55,11]=(x + 1)*(x -1)^2;
354
T[55,13]=(x -2)*(x^2 + 8*x + 8);
355
T[55,17]=(x -6)*(x^2 -8*x + 8);
356
T[55,19]=(x + 4)*(x )^2;
357
T[55,23]=(x -4)*(x^2 -8);
358
T[55,29]=(x -6)*(x^2 -4*x -28);
359
T[55,31]=(x + 8)*(x )^2;
360
T[55,37]=(x + 2)*(x^2 + 4*x -28);
361
T[55,41]=(x -2)*(x -6)^2;
362
T[55,43]=(x -4)*(x + 6)^2;
363
T[55,47]=(x + 12)*(x^2 -8);
364
T[55,53]=(x + 2)*(x^2 -12*x + 4);
365
T[55,59]=(x -4)*(x^2 + 8*x -16);
366
T[55,61]=(x + 10)*(x^2 -4*x -124);
367
T[55,67]=(x + 16)*(x^2 -8*x -56);
368
T[55,71]=(x -8)*(x^2 -128);
369
T[55,73]=(x -14)*(x^2 + 8*x + 8);
370
T[55,79]=(x -8)*(x -4)^2;
371
T[55,83]=(x + 4)*(x + 6)^2;
372
T[55,89]=(x -10)*(x^2 + 4*x -124);
373
T[55,97]=(x -10)*(x^2 + 4*x -28);
374
375
T[56,2]=(x )^2;
376
T[56,3]=(x -2)*(x );
377
T[56,5]=(x -2)*(x + 4);
378
T[56,7]=(x -1)*(x + 1);
379
T[56,11]=(x + 4)*(x );
380
T[56,13]=(x -2)*(x );
381
T[56,17]=(x + 6)*(x + 2);
382
T[56,19]=(x + 2)*(x -8);
383
T[56,23]=(x -8)*(x );
384
T[56,29]=(x -6)*(x -2);
385
T[56,31]=(x -8)*(x -4);
386
T[56,37]=(x + 2)*(x + 6);
387
T[56,41]=(x -2)*(x + 2);
388
T[56,43]=(x -8)*(x + 4);
389
T[56,47]=(x + 8)*(x + 4);
390
T[56,53]=(x + 10)*(x -6);
391
T[56,59]=(x -6)*(x );
392
T[56,61]=(x + 6)*(x -4);
393
T[56,67]=(x + 4)*(x + 12);
394
T[56,71]=(x + 8)*(x );
395
T[56,73]=(x -10)*(x + 14);
396
T[56,79]=(x -16)*(x + 8);
397
T[56,83]=(x -6)*(x -8);
398
T[56,89]=(x + 6)*(x -10);
399
T[56,97]=(x + 2)*(x + 6);
400
401
T[57,2]=(x -1)*(x + 2)^2;
402
T[57,3]=(x + 1)*(x -1)^2;
403
T[57,5]=(x + 2)*(x + 3)*(x -1);
404
T[57,7]=(x -3)*(x + 5)*(x );
405
T[57,11]=(x + 3)*(x -1)*(x );
406
T[57,13]=(x -6)*(x + 6)*(x -2);
407
T[57,17]=(x + 6)*(x + 1)*(x -3);
408
T[57,19]=(x + 1)^3;
409
T[57,23]=(x + 4)*(x -4)^2;
410
T[57,29]=(x + 2)*(x + 10)*(x -2);
411
T[57,31]=(x + 6)*(x -2)*(x -8);
412
T[57,37]=(x + 10)*(x -8)*(x );
413
T[57,41]=(x + 8)*(x + 2)*(x );
414
T[57,43]=(x + 4)*(x + 1)^2;
415
T[57,47]=(x -12)*(x + 9)*(x -3);
416
T[57,53]=(x -10)*(x + 6)^2;
417
T[57,59]=(x + 12)*(x + 8)*(x );
418
T[57,61]=(x + 2)*(x -7)*(x + 1);
419
T[57,67]=(x + 4)*(x -8)^2;
420
T[57,71]=(x + 12)*(x -12)*(x );
421
T[57,73]=(x -10)*(x + 11)^2;
422
T[57,79]=(x -16)*(x )^2;
423
T[57,83]=(x -16)*(x -4)*(x -12);
424
T[57,89]=(x -10)*(x + 2)*(x + 6);
425
T[57,97]=(x + 2)*(x -10)*(x + 10);
426
427
T[58,2]=(x + 1)*(x -1);
428
T[58,3]=(x + 1)*(x + 3);
429
T[58,5]=(x -1)*(x + 3);
430
T[58,7]=(x + 2)^2;
431
T[58,11]=(x + 3)*(x + 1);
432
T[58,13]=(x -3)*(x + 1);
433
T[58,17]=(x + 4)*(x -8);
434
T[58,19]=(x + 8)*(x );
435
T[58,23]=(x -4)*(x );
436
T[58,29]=(x + 1)^2;
437
T[58,31]=(x -3)*(x + 3);
438
T[58,37]=(x -8)*(x + 8);
439
T[58,41]=(x -2)*(x + 2);
440
T[58,43]=(x -7)*(x + 11);
441
T[58,47]=(x -13)*(x -11);
442
T[58,53]=(x -1)*(x + 11);
443
T[58,59]=(x + 4)*(x );
444
T[58,61]=(x + 8)*(x -4);
445
T[58,67]=(x + 12)*(x + 4);
446
T[58,71]=(x + 2)*(x -2);
447
T[58,73]=(x -4)*(x + 12);
448
T[58,79]=(x + 7)*(x -15);
449
T[58,83]=(x -4)*(x );
450
T[58,89]=(x + 6)*(x + 10);
451
T[58,97]=(x + 2)*(x + 6);
452
453
T[62,2]=(x -1)*(x + 1)^2;
454
T[62,3]=(x^2 -2*x -2)*(x );
455
T[62,5]=(x + 2)*(x^2 -12);
456
T[62,7]=(x )*(x -2)^2;
457
T[62,11]=(x^2 + 6*x + 6)*(x );
458
T[62,13]=(x -2)*(x^2 + 2*x -26);
459
T[62,17]=(x + 6)*(x^2 -12);
460
T[62,19]=(x -4)*(x + 4)^2;
461
T[62,23]=(x -8)*(x )^2;
462
T[62,29]=(x -2)*(x^2 + 6*x -18);
463
T[62,31]=(x + 1)*(x -1)^2;
464
T[62,37]=(x -10)*(x^2 -10*x -2);
465
T[62,41]=(x + 6)*(x^2 -12*x + 24);
466
T[62,43]=(x -8)*(x^2 + 2*x -26);
467
T[62,47]=(x + 8)*(x -6)^2;
468
T[62,53]=(x + 6)*(x^2 -6*x + 6);
469
T[62,59]=(x + 12)*(x^2 + 12*x + 24);
470
T[62,61]=(x + 6)*(x^2 + 2*x -26);
471
T[62,67]=(x + 12)*(x -8)^2;
472
T[62,71]=(x -8)*(x^2 -192);
473
T[62,73]=(x -10)*(x + 10)^2;
474
T[62,79]=(x + 8)*(x^2 -4*x -104);
475
T[62,83]=(x -8)*(x^2 -6*x -66);
476
T[62,89]=(x + 6)*(x -6)^2;
477
T[62,97]=(x -2)*(x^2 -4*x -104);
478
479
T[63,2]=(x -1)*(x^2 -3);
480
T[63,3]=(x )^3;
481
T[63,5]=(x -2)*(x^2 -12);
482
T[63,7]=(x + 1)*(x -1)^2;
483
T[63,11]=(x + 4)*(x^2 -12);
484
T[63,13]=(x + 2)*(x -2)^2;
485
T[63,17]=(x -6)*(x^2 -12);
486
T[63,19]=(x -4)*(x + 4)^2;
487
T[63,23]=(x^2 -12)*(x );
488
T[63,29]=(x -2)*(x )^2;
489
T[63,31]=(x )*(x + 4)^2;
490
T[63,37]=(x -6)*(x -2)^2;
491
T[63,41]=(x + 2)*(x^2 -108);
492
T[63,43]=(x + 4)^3;
493
T[63,47]=(x^2 -48)*(x );
494
T[63,53]=(x + 6)*(x^2 -48);
495
T[63,59]=(x + 12)*(x^2 -48);
496
T[63,61]=(x + 2)*(x + 10)^2;
497
T[63,67]=(x -4)*(x + 4)^2;
498
T[63,71]=(x^2 -108)*(x );
499
T[63,73]=(x + 6)*(x -14)^2;
500
T[63,79]=(x + 16)*(x -8)^2;
501
T[63,83]=(x -12)*(x )^2;
502
T[63,89]=(x -14)*(x^2 -12);
503
T[63,97]=(x -18)*(x -14)^2;
504
505
T[64,2]=x ;
506
T[64,3]=x ;
507
T[64,5]=x -2;
508
T[64,7]=x ;
509
T[64,11]=x ;
510
T[64,13]=x + 6;
511
T[64,17]=x -2;
512
T[64,19]=x ;
513
T[64,23]=x ;
514
T[64,29]=x -10;
515
T[64,31]=x ;
516
T[64,37]=x -2;
517
T[64,41]=x -10;
518
T[64,43]=x ;
519
T[64,47]=x ;
520
T[64,53]=x + 14;
521
T[64,59]=x ;
522
T[64,61]=x -10;
523
T[64,67]=x ;
524
T[64,71]=x ;
525
T[64,73]=x + 6;
526
T[64,79]=x ;
527
T[64,83]=x ;
528
T[64,89]=x -10;
529
T[64,97]=x -18;
530
531
T[66,2]=(x + 1)*(x -1)^2;
532
T[66,3]=(x + 1)*(x -1)^2;
533
T[66,5]=(x -2)*(x + 4)*(x );
534
T[66,7]=(x + 4)*(x -2)*(x + 2);
535
T[66,11]=(x -1)*(x + 1)^2;
536
T[66,13]=(x + 4)*(x -4)*(x + 6);
537
T[66,17]=(x + 6)*(x + 2)*(x -2);
538
T[66,19]=(x -4)*(x + 4)*(x );
539
T[66,23]=(x -6)*(x + 6)*(x -4);
540
T[66,29]=(x -10)*(x -6)^2;
541
T[66,31]=(x -8)*(x + 8)*(x );
542
T[66,37]=(x + 10)*(x + 2)*(x -6);
543
T[66,41]=(x -2)*(x + 6)*(x -6);
544
T[66,43]=(x -8)*(x -4)^2;
545
T[66,47]=(x + 2)*(x + 12)*(x + 6);
546
T[66,53]=(x -4)*(x -2)*(x );
547
T[66,59]=(x -12)*(x )^2;
548
T[66,61]=(x -8)*(x + 14)*(x + 8);
549
T[66,67]=(x -4)*(x + 4)*(x + 12);
550
T[66,71]=(x -2)*(x -6)*(x + 12);
551
T[66,73]=(x -2)*(x + 6)^2;
552
T[66,79]=(x + 4)*(x -14)*(x -10);
553
T[66,83]=(x + 12)*(x -4)^2;
554
T[66,89]=(x + 6)*(x -10)^2;
555
T[66,97]=(x + 2)*(x -14)*(x + 14);
556
557
T[68,2]=(x )^2;
558
T[68,3]=x^2 -2*x -2;
559
T[68,5]=x^2 -12;
560
T[68,7]=x^2 + 2*x -2;
561
T[68,11]=x^2 + 6*x + 6;
562
T[68,13]=x^2 -4*x -8;
563
T[68,17]=(x + 1)^2;
564
T[68,19]=x^2 -4*x -8;
565
T[68,23]=x^2 + 6*x + 6;
566
T[68,29]=x^2 -12;
567
T[68,31]=x^2 + 2*x -26;
568
T[68,37]=x^2 -16*x + 52;
569
T[68,41]=(x + 6)^2;
570
T[68,43]=x^2 -4*x -104;
571
T[68,47]=x^2 -48;
572
T[68,53]=x^2 -12*x -12;
573
T[68,59]=x^2 -12*x + 24;
574
T[68,61]=x^2 + 8*x + 4;
575
T[68,67]=x^2 -16*x + 16;
576
T[68,71]=x^2 + 6*x -18;
577
T[68,73]=(x -2)^2;
578
T[68,79]=x^2 + 14*x + 22;
579
T[68,83]=x^2 + 12*x + 24;
580
T[68,89]=x^2 -12*x + 24;
581
T[68,97]=x^2 -4*x -44;
582
583
T[69,2]=(x -1)*(x^2 -5);
584
T[69,3]=(x -1)*(x + 1)^2;
585
T[69,5]=(x^2 + 2*x -4)*(x );
586
T[69,7]=(x + 2)*(x^2 -2*x -4);
587
T[69,11]=(x -4)^3;
588
T[69,13]=(x + 6)*(x^2 -20);
589
T[69,17]=(x -4)*(x^2 + 10*x + 20);
590
T[69,19]=(x -2)*(x^2 -10*x + 20);
591
T[69,23]=(x + 1)*(x -1)^2;
592
T[69,29]=(x -2)*(x^2 -20);
593
T[69,31]=(x -4)*(x^2 + 4*x -16);
594
T[69,37]=(x -2)*(x^2 -20);
595
T[69,41]=(x -2)*(x^2 + 4*x -76);
596
T[69,43]=(x -10)*(x^2 -2*x -44);
597
T[69,47]=(x )*(x + 4)^2;
598
T[69,53]=(x + 12)*(x^2 + 6*x + 4);
599
T[69,59]=(x + 12)*(x^2 -8*x -64);
600
T[69,61]=(x + 6)*(x^2 -20);
601
T[69,67]=(x + 10)*(x^2 -6*x + 4);
602
T[69,71]=(x -8)*(x + 8)^2;
603
T[69,73]=(x + 14)*(x^2 + 4*x -76);
604
T[69,79]=(x -10)*(x^2 -6*x -36);
605
T[69,83]=(x -12)*(x -4)^2;
606
T[69,89]=(x + 16)*(x^2 -2*x -4);
607
T[69,97]=(x + 10)*(x^2 -8*x -4);
608
609
T[70,2]=x -1;
610
T[70,3]=x ;
611
T[70,5]=x + 1;
612
T[70,7]=x + 1;
613
T[70,11]=x -4;
614
T[70,13]=x + 6;
615
T[70,17]=x -2;
616
T[70,19]=x ;
617
T[70,23]=x ;
618
T[70,29]=x -6;
619
T[70,31]=x -8;
620
T[70,37]=x + 10;
621
T[70,41]=x -2;
622
T[70,43]=x -4;
623
T[70,47]=x -8;
624
T[70,53]=x + 2;
625
T[70,59]=x + 8;
626
T[70,61]=x + 14;
627
T[70,67]=x + 12;
628
T[70,71]=x + 16;
629
T[70,73]=x -2;
630
T[70,79]=x + 8;
631
T[70,83]=x -8;
632
T[70,89]=x -10;
633
T[70,97]=x -2;
634
635
T[72,2]=x ;
636
T[72,3]=x ;
637
T[72,5]=x -2;
638
T[72,7]=x ;
639
T[72,11]=x + 4;
640
T[72,13]=x + 2;
641
T[72,17]=x + 2;
642
T[72,19]=x + 4;
643
T[72,23]=x -8;
644
T[72,29]=x + 6;
645
T[72,31]=x -8;
646
T[72,37]=x -6;
647
T[72,41]=x -6;
648
T[72,43]=x -4;
649
T[72,47]=x ;
650
T[72,53]=x -2;
651
T[72,59]=x + 4;
652
T[72,61]=x + 2;
653
T[72,67]=x + 4;
654
T[72,71]=x + 8;
655
T[72,73]=x -10;
656
T[72,79]=x + 8;
657
T[72,83]=x -4;
658
T[72,89]=x -6;
659
T[72,97]=x -2;
660
661
T[74,2]=(x + 1)^2*(x -1)^2;
662
T[74,3]=(x^2 -3*x -1)*(x^2 + x -1);
663
T[74,5]=(x^2 + x -3)*(x^2 -x -11);
664
T[74,7]=(x^2 -2*x -12)*(x^2 + 2*x -4);
665
T[74,11]=(x^2 + 5*x + 5)*(x^2 + x -3);
666
T[74,13]=(x^2 + x -3)*(x^2 -x -11);
667
T[74,17]=(x^2 -20)*(x + 6)^2;
668
T[74,19]=(x^2 -20)*(x -2)^2;
669
T[74,23]=(x^2 + 3*x -27)*(x^2 + x -11);
670
T[74,29]=(x^2 -3*x -27)*(x^2 + 3*x -59);
671
T[74,31]=(x^2 -17*x + 71)*(x^2 -3*x -1);
672
T[74,37]=(x -1)^2*(x + 1)^2;
673
T[74,41]=(x^2 -9*x -9)*(x^2 -17*x + 71);
674
T[74,43]=(x^2 + 6*x + 4)*(x^2 + 6*x -4);
675
T[74,47]=(x^2 -2*x -12)*(x^2 -2*x -4);
676
T[74,53]=(x^2 + 8*x -4)*(x + 6)^2;
677
T[74,59]=(x^2 + 14*x + 44)*(x^2 -14*x + 36);
678
T[74,61]=(x^2 -19*x + 89)*(x^2 + 3*x -79);
679
T[74,67]=(x^2 + 9*x -11)*(x^2 -11*x -51);
680
T[74,71]=(x^2 + 12*x -44)*(x -6)^2;
681
T[74,73]=(x^2 + 21*x + 107)*(x^2 -3*x -29);
682
T[74,79]=(x^2 -3*x -99)*(x^2 + 7*x -147);
683
T[74,83]=(x^2 -20*x + 48)*(x^2 + 20*x + 80);
684
T[74,89]=(x^2 + 12*x + 16)*(x^2 + 4*x -48);
685
T[74,97]=(x^2 -8*x -4)*(x^2 + 4*x -204);
686
687
T[75,2]=(x -2)*(x + 2)*(x -1);
688
T[75,3]=(x + 1)*(x -1)^2;
689
T[75,5]=(x )^3;
690
T[75,7]=(x -3)*(x + 3)*(x );
691
T[75,11]=(x + 4)*(x -2)^2;
692
T[75,13]=(x + 1)*(x -2)*(x -1);
693
T[75,17]=(x -2)*(x + 2)^2;
694
T[75,19]=(x -4)*(x + 5)^2;
695
T[75,23]=(x + 6)*(x -6)*(x );
696
T[75,29]=(x + 2)*(x -10)^2;
697
T[75,31]=(x )*(x + 3)^2;
698
T[75,37]=(x -2)*(x + 2)*(x -10);
699
T[75,41]=(x -10)*(x + 8)^2;
700
T[75,43]=(x + 1)*(x + 4)*(x -1);
701
T[75,47]=(x + 8)*(x -2)*(x + 2);
702
T[75,53]=(x -10)*(x -4)*(x + 4);
703
T[75,59]=(x + 4)*(x + 10)^2;
704
T[75,61]=(x + 2)*(x -7)^2;
705
T[75,67]=(x -3)*(x + 3)*(x + 12);
706
T[75,71]=(x + 8)^3;
707
T[75,73]=(x + 10)*(x -14)*(x + 14);
708
T[75,79]=(x )^3;
709
T[75,83]=(x -6)*(x + 12)*(x + 6);
710
T[75,89]=(x + 6)*(x )^2;
711
T[75,97]=(x + 17)*(x + 2)*(x -17);
712
713
T[76,2]=x ;
714
T[76,3]=x -2;
715
T[76,5]=x + 1;
716
T[76,7]=x + 3;
717
T[76,11]=x -5;
718
T[76,13]=x + 4;
719
T[76,17]=x + 3;
720
T[76,19]=x + 1;
721
T[76,23]=x -8;
722
T[76,29]=x + 2;
723
T[76,31]=x -4;
724
T[76,37]=x -10;
725
T[76,41]=x -10;
726
T[76,43]=x -1;
727
T[76,47]=x + 1;
728
T[76,53]=x + 4;
729
T[76,59]=x -6;
730
T[76,61]=x + 13;
731
T[76,67]=x + 12;
732
T[76,71]=x -2;
733
T[76,73]=x -9;
734
T[76,79]=x -8;
735
T[76,83]=x + 12;
736
T[76,89]=x -12;
737
T[76,97]=x + 8;
738
739
T[77,2]=(x -1)*(x^2 -5)*(x )^2;
740
T[77,3]=(x -1)*(x -2)*(x + 3)*(x^2 -2*x -4);
741
T[77,5]=(x -3)*(x + 1)*(x + 2)^3;
742
T[77,7]=(x + 1)^2*(x -1)^3;
743
T[77,11]=(x -1)*(x + 1)^4;
744
T[77,13]=(x -4)*(x^2 -2*x -4)*(x + 4)^2;
745
T[77,17]=(x -4)*(x -2)*(x + 6)*(x^2 + 2*x -4);
746
T[77,19]=(x -2)*(x + 6)*(x^2 -4*x -16)*(x );
747
T[77,23]=(x -3)*(x + 4)*(x + 5)*(x^2 + 4*x -16);
748
T[77,29]=(x -10)*(x^2 -8*x -4)*(x + 6)^2;
749
T[77,31]=(x -5)*(x -10)*(x -1)*(x^2 + 10*x + 20);
750
T[77,37]=(x + 6)*(x -11)*(x + 5)*(x^2 + 8*x -4);
751
T[77,41]=(x + 2)*(x -4)*(x -6)*(x^2 + 18*x + 76);
752
T[77,43]=(x -12)*(x + 8)*(x -8)^3;
753
T[77,47]=(x -8)*(x + 10)*(x^2 -10*x + 20)*(x );
754
T[77,53]=(x^2 -8*x -4)*(x + 6)^3;
755
T[77,59]=(x -3)*(x + 9)*(x -2)*(x^2 -2*x -4);
756
T[77,61]=(x + 10)*(x + 2)*(x^2 + 10*x + 20)*(x );
757
T[77,67]=(x + 3)*(x -5)*(x -8)*(x^2 -20*x + 80);
758
T[77,71]=(x + 12)*(x -9)*(x -1)*(x^2 + 12*x + 16);
759
T[77,73]=(x + 8)*(x -2)*(x -10)*(x^2 + 6*x + 4);
760
T[77,79]=(x -8)*(x -6)*(x + 10)*(x^2 -80);
761
T[77,83]=(x^2 -4*x -176)*(x )*(x -12)^2;
762
T[77,89]=(x + 15)*(x + 3)*(x + 6)*(x -2)^2;
763
T[77,97]=(x + 1)*(x + 10)*(x + 5)*(x^2 -8*x -164);
764
765
T[78,2]=x + 1;
766
T[78,3]=x + 1;
767
T[78,5]=x -2;
768
T[78,7]=x -4;
769
T[78,11]=x + 4;
770
T[78,13]=x -1;
771
T[78,17]=x -2;
772
T[78,19]=x + 8;
773
T[78,23]=x ;
774
T[78,29]=x -6;
775
T[78,31]=x + 4;
776
T[78,37]=x + 2;
777
T[78,41]=x + 10;
778
T[78,43]=x -4;
779
T[78,47]=x -8;
780
T[78,53]=x + 10;
781
T[78,59]=x -4;
782
T[78,61]=x + 2;
783
T[78,67]=x + 16;
784
T[78,71]=x + 8;
785
T[78,73]=x -2;
786
T[78,79]=x -8;
787
T[78,83]=x -12;
788
T[78,89]=x -14;
789
T[78,97]=x -10;
790
791
T[80,2]=(x )^2;
792
T[80,3]=(x -2)*(x );
793
T[80,5]=(x -1)*(x + 1);
794
T[80,7]=(x -4)*(x + 2);
795
T[80,11]=(x + 4)*(x );
796
T[80,13]=(x -2)*(x + 2);
797
T[80,17]=(x -2)*(x + 6);
798
T[80,19]=(x -4)*(x + 4);
799
T[80,23]=(x + 6)*(x + 4);
800
T[80,29]=(x + 2)*(x -6);
801
T[80,31]=(x -8)*(x -4);
802
T[80,37]=(x -6)*(x -2);
803
T[80,41]=(x -6)*(x + 6);
804
T[80,43]=(x -8)*(x -10);
805
T[80,47]=(x + 4)*(x -6);
806
T[80,53]=(x -6)*(x + 6);
807
T[80,59]=(x -4)*(x + 12);
808
T[80,61]=(x -2)*(x + 2);
809
T[80,67]=(x + 2)*(x + 8);
810
T[80,71]=(x -12)*(x );
811
T[80,73]=(x + 6)*(x -2);
812
T[80,79]=(x + 8)*(x );
813
T[80,83]=(x + 6)*(x -16);
814
T[80,89]=(x + 6)^2;
815
T[80,97]=(x -2)*(x + 14);
816
817
T[81,2]=x^2 -3;
818
T[81,3]=(x )^2;
819
T[81,5]=x^2 -3;
820
T[81,7]=(x -2)^2;
821
T[81,11]=x^2 -12;
822
T[81,13]=(x + 1)^2;
823
T[81,17]=x^2 -27;
824
T[81,19]=(x -2)^2;
825
T[81,23]=x^2 -12;
826
T[81,29]=x^2 -3;
827
T[81,31]=(x -8)^2;
828
T[81,37]=(x + 7)^2;
829
T[81,41]=x^2 -48;
830
T[81,43]=(x -2)^2;
831
T[81,47]=x^2 -48;
832
T[81,53]=(x )^2;
833
T[81,59]=x^2 -192;
834
T[81,61]=(x + 7)^2;
835
T[81,67]=(x + 10)^2;
836
T[81,71]=x^2 -108;
837
T[81,73]=(x + 7)^2;
838
T[81,79]=(x -2)^2;
839
T[81,83]=x^2 -192;
840
T[81,89]=x^2 -27;
841
T[81,97]=(x -2)^2;
842
843
T[82,2]=(x + 1)*(x -1)^2;
844
T[82,3]=(x + 2)*(x^2 -2);
845
T[82,5]=(x + 2)*(x^2 -8);
846
T[82,7]=(x + 4)*(x^2 + 4*x + 2);
847
T[82,11]=(x + 2)*(x^2 -18);
848
T[82,13]=(x -4)*(x )^2;
849
T[82,17]=(x + 2)*(x^2 -4*x -28);
850
T[82,19]=(x -6)*(x^2 + 8*x + 14);
851
T[82,23]=(x + 8)*(x^2 -8*x + 8);
852
T[82,29]=(x^2 -8*x -16)*(x );
853
T[82,31]=(x + 8)*(x^2 + 8*x + 8);
854
T[82,37]=(x -2)*(x^2 -72);
855
T[82,41]=(x + 1)^3;
856
T[82,43]=(x + 12)*(x^2 -8*x -16);
857
T[82,47]=(x -4)*(x^2 + 4*x -46);
858
T[82,53]=(x + 4)*(x -12)^2;
859
T[82,59]=(x -8)*(x^2 + 8*x + 8);
860
T[82,61]=(x + 14)*(x -6)^2;
861
T[82,67]=(x + 2)*(x^2 + 8*x -2);
862
T[82,71]=(x -8)*(x^2 + 4*x + 2);
863
T[82,73]=(x -10)*(x^2 + 16*x + 32);
864
T[82,79]=(x -4)*(x^2 + 12*x + 18);
865
T[82,83]=(x -12)*(x^2 -24*x + 112);
866
T[82,89]=(x + 14)*(x^2 + 12*x + 4);
867
T[82,97]=(x -6)*(x^2 + 4*x -28);
868
869
T[84,2]=(x )^2;
870
T[84,3]=(x -1)*(x + 1);
871
T[84,5]=(x -4)*(x );
872
T[84,7]=(x -1)*(x + 1);
873
T[84,11]=(x + 6)*(x -2);
874
T[84,13]=(x + 6)*(x -2);
875
T[84,17]=(x + 4)*(x );
876
T[84,19]=(x + 4)^2;
877
T[84,23]=(x + 6)*(x -2);
878
T[84,29]=(x + 2)*(x -6);
879
T[84,31]=(x -8)*(x );
880
T[84,37]=(x -2)^2;
881
T[84,41]=(x -12)*(x );
882
T[84,43]=(x + 4)^2;
883
T[84,47]=(x -12)^2;
884
T[84,53]=(x + 6)^2;
885
T[84,59]=(x + 8)*(x );
886
T[84,61]=(x + 10)*(x -6);
887
T[84,67]=(x -8)*(x + 8);
888
T[84,71]=(x -6)*(x -14);
889
T[84,73]=(x + 10)*(x + 2);
890
T[84,79]=(x + 4)*(x -12);
891
T[84,83]=(x + 12)*(x + 4);
892
T[84,89]=(x -12)*(x );
893
T[84,97]=(x + 2)*(x + 10);
894
895
T[85,2]=(x -1)*(x^2 + 2*x -1)*(x^2 -3);
896
T[85,3]=(x -2)*(x^2 + 4*x + 2)*(x^2 -2*x -2);
897
T[85,5]=(x -1)^2*(x + 1)^3;
898
T[85,7]=(x + 2)*(x^2 + 4*x + 2)*(x^2 + 2*x -2);
899
T[85,11]=(x -2)*(x^2 -6*x + 6)*(x^2 + 8*x + 14);
900
T[85,13]=(x -2)*(x^2 -8)*(x + 4)^2;
901
T[85,17]=(x -1)*(x + 1)^4;
902
T[85,19]=(x^2 -8)*(x^2 -4*x -8)*(x );
903
T[85,23]=(x -6)*(x^2 + 6*x -18)*(x^2 + 4*x + 2);
904
T[85,29]=(x + 6)*(x^2 + 4*x -4)*(x^2 -12);
905
T[85,31]=(x + 10)*(x^2 -10*x + 22)*(x^2 -18);
906
T[85,37]=(x -2)*(x^2 + 4*x -68)*(x^2 + 8*x + 4);
907
T[85,41]=(x -10)*(x^2 -12)*(x^2 -4*x -68);
908
T[85,43]=(x -4)*(x^2 -4*x -28)*(x^2 + 8*x + 4);
909
T[85,47]=(x -12)*(x^2 + 4*x -4)*(x^2 -12*x -12);
910
T[85,53]=(x + 10)*(x^2 -12*x + 4)*(x -6)^2;
911
T[85,59]=(x -8)*(x^2 -12*x + 24)*(x^2 + 24*x + 136);
912
T[85,61]=(x + 14)*(x^2 -4*x -44)*(x^2 -4*x -28);
913
T[85,67]=(x -8)*(x^2 + 12*x + 28)*(x + 10)^2;
914
T[85,71]=(x + 2)*(x^2 -18)*(x^2 -6*x -66);
915
T[85,73]=(x + 14)*(x^2 + 8*x -92)*(x^2 + 4*x -4);
916
T[85,79]=(x + 14)*(x^2 + 2*x -242)*(x^2 -8*x + 14);
917
T[85,83]=(x -4)*(x^2 -24*x + 132)*(x^2 + 4*x -124);
918
T[85,89]=(x -6)*(x^2 + 12*x -72)*(x^2 + 16*x + 32);
919
T[85,97]=(x -2)*(x^2 -4*x -44)*(x^2 + 4*x -28);
920
921
T[86,2]=(x + 1)^2*(x -1)^2;
922
T[86,3]=(x^2 + x -5)*(x^2 -x -1);
923
T[86,5]=(x^2 -3*x -3)*(x^2 + 3*x + 1);
924
T[86,7]=(x^2 -20)*(x -2)^2;
925
T[86,11]=(x^2 + 4*x -16)*(x )^2;
926
T[86,13]=(x^2 -20)*(x -2)^2;
927
T[86,17]=(x^2 + x -1)*(x^2 + 9*x + 15);
928
T[86,19]=(x^2 -x -47)*(x^2 -11*x + 29);
929
T[86,23]=(x^2 + 9*x + 15)*(x^2 -3*x -9);
930
T[86,29]=(x^2 + 7*x + 1)*(x^2 -3*x -3);
931
T[86,31]=(x^2 -x -47)*(x^2 -13*x + 41);
932
T[86,37]=(x^2 -x -47)*(x^2 + 5*x + 5);
933
T[86,41]=(x^2 + 5*x -5)*(x^2 -3*x -45);
934
T[86,43]=(x -1)^2*(x + 1)^2;
935
T[86,47]=(x^2 + 9*x -27)*(x^2 -3*x -59);
936
T[86,53]=(x^2 -6*x -12)*(x^2 + 10*x + 20);
937
T[86,59]=(x^2 -16*x + 44)*(x -6)^2;
938
T[86,61]=(x^2 -4*x -76)*(x -2)^2;
939
T[86,67]=(x + 10)^2*(x -2)^2;
940
T[86,71]=(x^2 + 16*x + 44)*(x^2 -84);
941
T[86,73]=(x^2 -4*x -76)*(x -14)^2;
942
T[86,79]=(x^2 + x -1)*(x^2 + 5*x -41);
943
T[86,83]=(x^2 + 10*x -20)*(x^2 + 6*x -12);
944
T[86,89]=(x^2 -2*x -44)*(x^2 -6*x -12);
945
T[86,97]=(x^2 + 11*x -1)*(x^2 + 11*x -17);
946
947
T[87,2]=(x^2 -x -1)*(x^3 -2*x^2 -4*x + 7);
948
T[87,3]=(x -1)^2*(x + 1)^3;
949
T[87,5]=(x^2 -2*x -4)*(x^3 -16*x + 8);
950
T[87,7]=(x^2 + 4*x -1)*(x^3 -4*x^2 -x + 8);
951
T[87,11]=(x^2 -4*x -1)*(x^3 + 8*x^2 + 15*x + 4);
952
T[87,13]=(x^2 + 2*x -19)*(x^3 -4*x^2 -7*x + 26);
953
T[87,17]=(x^3 -4*x^2 -27*x + 94)*(x -3)^2;
954
T[87,19]=(x^2 + 10*x + 20)*(x^3 + 2*x^2 -20*x + 16);
955
T[87,23]=(x^2 + 2*x -44)*(x^3 -6*x^2 -4*x + 32);
956
T[87,29]=(x + 1)^2*(x -1)^3;
957
T[87,31]=(x^2 + 6*x -36)*(x^3 -6*x^2 -4*x + 32);
958
T[87,37]=(x^2 -6*x + 4)*(x^3 -8*x^2 + 8);
959
T[87,41]=(x^3 + 2*x^2 -100*x + 56)*(x -2)^2;
960
T[87,43]=(x^3 + 4*x^2 -96*x -256)*(x -4)^2;
961
T[87,47]=(x^2 + 4*x -41)*(x^3 + 12*x^2 -9*x -216);
962
T[87,53]=(x^2 -18*x + 76)*(x^3 -8*x^2 -104*x + 248);
963
T[87,59]=(x^2 -20)*(x^3 + 20*x^2 + 108*x + 112);
964
T[87,61]=(x^2 + 6*x + 4)*(x^3 -4*x^2 -16*x + 56);
965
T[87,67]=(x^2 + 4*x -121)*(x^3 -57*x + 52);
966
T[87,71]=(x^2 + 6*x + 4)*(x^3 + 14*x^2 -60*x -416);
967
T[87,73]=(x^2 -18*x + 76)*(x^3 + 8*x^2 -8);
968
T[87,79]=(x^2 + 30*x + 220)*(x^3 + 2*x^2 -60*x -224);
969
T[87,83]=(x^2 + 12*x -44)*(x^3 + 8*x^2 -28*x -208);
970
T[87,89]=(x^3 + 8*x^2 -131*x -74)*(x -5)^2;
971
T[87,97]=(x^2 -6*x -236)*(x^3 -4*x^2 -72*x -104);
972
973
T[88,2]=(x )^3;
974
T[88,3]=(x + 3)*(x^2 -x -4);
975
T[88,5]=(x + 3)*(x^2 -3*x -2);
976
T[88,7]=(x + 2)*(x^2 + 2*x -16);
977
T[88,11]=(x + 1)^3;
978
T[88,13]=(x^2 + 2*x -16)*(x );
979
T[88,17]=(x + 6)*(x -2)^2;
980
T[88,19]=(x -4)*(x + 4)^2;
981
T[88,23]=(x -1)*(x^2 -9*x + 16);
982
T[88,29]=(x + 8)*(x^2 + 2*x -16);
983
T[88,31]=(x + 7)*(x^2 + 7*x + 8);
984
T[88,37]=(x + 1)*(x^2 + 11*x + 26);
985
T[88,41]=(x -4)*(x^2 -6*x -8);
986
T[88,43]=(x -6)*(x^2 + 6*x -8);
987
T[88,47]=(x + 8)*(x -8)^2;
988
T[88,53]=(x -2)*(x^2 -8*x -52);
989
T[88,59]=(x + 1)*(x^2 + 5*x -100);
990
T[88,61]=(x -4)*(x^2 + 6*x -8);
991
T[88,67]=(x + 5)*(x^2 -15*x + 52);
992
T[88,71]=(x -3)*(x^2 + 5*x -32);
993
T[88,73]=(x -16)*(x^2 -2*x -16);
994
T[88,79]=(x -2)*(x^2 + 14*x + 32);
995
T[88,83]=(x + 2)*(x^2 -10*x + 8);
996
T[88,89]=(x -15)*(x^2 + 7*x -26);
997
T[88,97]=(x + 7)*(x^2 -27*x + 178);
998
999
T[90,2]=(x + 1)*(x -1)^2;
1000
T[90,3]=(x )^3;
1001
T[90,5]=(x + 1)*(x -1)^2;
1002
T[90,7]=(x + 4)*(x -2)^2;
1003
T[90,11]=(x + 6)*(x -6)*(x );
1004
T[90,13]=(x -2)*(x + 4)^2;
1005
T[90,17]=(x -6)*(x + 6)^2;
1006
T[90,19]=(x + 4)^3;
1007
T[90,23]=(x )^3;
1008
T[90,29]=(x + 6)*(x -6)^2;
1009
T[90,31]=(x -8)*(x + 4)^2;
1010
T[90,37]=(x -2)*(x -8)^2;
1011
T[90,41]=(x -6)*(x )^2;
1012
T[90,43]=(x + 4)*(x -8)^2;
1013
T[90,47]=(x )^3;
1014
T[90,53]=(x + 6)*(x -6)^2;
1015
T[90,59]=(x + 6)*(x -6)*(x );
1016
T[90,61]=(x + 10)*(x -2)^2;
1017
T[90,67]=(x + 4)^3;
1018
T[90,71]=(x -12)*(x + 12)*(x );
1019
T[90,73]=(x -2)*(x + 10)^2;
1020
T[90,79]=(x -8)*(x + 4)^2;
1021
T[90,83]=(x -12)*(x + 12)^2;
1022
T[90,89]=(x + 18)*(x -12)*(x + 12);
1023
T[90,97]=(x -2)^3;
1024
1025
T[92,2]=(x )^2;
1026
T[92,3]=(x + 3)*(x -1);
1027
T[92,5]=(x + 2)*(x );
1028
T[92,7]=(x + 4)*(x -2);
1029
T[92,11]=(x -2)*(x );
1030
T[92,13]=(x + 1)*(x + 5);
1031
T[92,17]=(x -4)*(x + 6);
1032
T[92,19]=(x + 2)*(x -2);
1033
T[92,23]=(x -1)*(x + 1);
1034
T[92,29]=(x + 7)*(x + 3);
1035
T[92,31]=(x + 3)*(x -5);
1036
T[92,37]=(x -8)*(x -2);
1037
T[92,41]=(x -3)*(x + 9);
1038
T[92,43]=(x -8)*(x + 8);
1039
T[92,47]=(x -9)^2;
1040
T[92,53]=(x -6)*(x -2);
1041
T[92,59]=(x + 12)*(x );
1042
T[92,61]=(x -14)*(x + 2);
1043
T[92,67]=(x -8)*(x -14);
1044
T[92,71]=(x + 3)*(x + 15);
1045
T[92,73]=(x + 3)*(x + 7);
1046
T[92,79]=(x + 10)*(x + 6);
1047
T[92,83]=(x -8)*(x -6);
1048
T[92,89]=(x -12)*(x );
1049
T[92,97]=(x + 10)*(x );
1050
1051
T[93,2]=(x^2 + 3*x + 1)*(x^3 -4*x + 1);
1052
T[93,3]=(x + 1)^2*(x -1)^3;
1053
T[93,5]=(x^2 + 4*x -1)*(x^3 + 2*x^2 -5*x -2);
1054
T[93,7]=(x^2 + 4*x -1)*(x^3 -4*x^2 -x + 8);
1055
T[93,11]=(x^2 + 6*x + 4)*(x^3 + 2*x^2 -20*x + 16);
1056
T[93,13]=(x^2 + 2*x -4)*(x^3 -4*x^2 -16*x + 56);
1057
T[93,17]=(x^2 + 4*x -16)*(x^3 + 2*x^2 -24*x -32);
1058
T[93,19]=(x^2 + 8*x + 11)*(x^3 -4*x^2 -45*x + 196);
1059
T[93,23]=(x^2 -2*x -4)*(x^3 + 6*x^2 -4*x -32);
1060
T[93,29]=(x^2 -2*x -4)*(x^3 + 8*x^2 -56*x -392);
1061
T[93,31]=(x + 1)^5;
1062
T[93,37]=(x^2 -2*x -44)*(x^3 -16*x + 8);
1063
T[93,41]=(x^2 -45)*(x^3 + 10*x^2 -17*x -262);
1064
T[93,43]=(x^2 + 6*x -36)*(x^3 -14*x^2 + 4*x + 368);
1065
T[93,47]=(x^2 -4*x -16)*(x^3 -12*x^2 -16*x + 256);
1066
T[93,53]=(x^2 -80)*(x^3 + 10*x^2 -16*x -32);
1067
T[93,59]=(x^3 -26*x^2 + 213*x -556)*(x + 3)^2;
1068
T[93,61]=(x^3 + 2*x^2 -128*x -512)*(x -8)^2;
1069
T[93,67]=(x + 12)^2*(x -4)^3;
1070
T[93,71]=(x^3 + 10*x^2 -147*x -712)*(x -9)^2;
1071
T[93,73]=(x^2 -2*x -4)*(x^3 + 12*x^2 -96*x -728);
1072
T[93,79]=(x^2 -8*x -4)*(x^3 -8*x^2 -4*x + 64);
1073
T[93,83]=(x^2 + 24*x + 124)*(x^3 -20*x^2 + 108*x -112);
1074
T[93,89]=(x^2 + 4*x -76)*(x + 6)^3;
1075
T[93,97]=(x^3 -4*x^2 -27*x + 94)*(x -9)^2;
1076
1077
T[94,2]=(x -1)*(x + 1)^2;
1078
T[94,3]=(x^2 -8)*(x );
1079
T[94,5]=(x^2 -4*x + 2)*(x );
1080
T[94,7]=(x^2 + 4*x -4)*(x );
1081
T[94,11]=(x -2)*(x^2 -8*x + 14);
1082
T[94,13]=(x + 4)*(x^2 + 4*x + 2);
1083
T[94,17]=(x + 2)*(x )^2;
1084
T[94,19]=(x + 2)*(x^2 + 8*x -2);
1085
T[94,23]=(x -4)*(x^2 -8);
1086
T[94,29]=(x -4)*(x^2 -12*x + 18);
1087
T[94,31]=(x -4)*(x^2 -72);
1088
T[94,37]=(x -2)*(x^2 -4*x -68);
1089
T[94,41]=(x -6)*(x^2 + 12*x + 28);
1090
T[94,43]=(x -6)*(x^2 + 8*x -2);
1091
T[94,47]=(x + 1)*(x -1)^2;
1092
T[94,53]=(x -2)*(x^2 -4*x -4);
1093
T[94,59]=(x -12)*(x^2 + 8*x -16);
1094
T[94,61]=(x -2)*(x^2 + 4*x -68);
1095
T[94,67]=(x -2)*(x^2 + 8*x -34);
1096
T[94,71]=(x -8)*(x^2 -12*x + 28);
1097
T[94,73]=(x + 14)*(x -6)^2;
1098
T[94,79]=(x + 16)*(x )^2;
1099
T[94,83]=(x + 16)*(x^2 -8);
1100
T[94,89]=(x + 10)*(x )^2;
1101
T[94,97]=(x + 14)*(x -6)^2;
1102
1103
T[95,2]=(x^3 -x^2 -3*x + 1)*(x^4 + 2*x^3 -6*x^2 -8*x + 9);
1104
T[95,3]=(x^3 -2*x^2 -4*x + 4)*(x^4 -2*x^3 -8*x^2 + 16*x -4);
1105
T[95,5]=(x -1)^3*(x + 1)^4;
1106
T[95,7]=(x^3 -16*x + 16)*(x^4 -4*x^3 -16*x^2 + 48*x + 32);
1107
T[95,11]=(x^3 + 8*x^2 + 8*x -16)*(x^4 -4*x^3 -16*x^2 + 32*x + 48);
1108
T[95,13]=(x^3 -8*x^2 + 12*x -4)*(x^4 -2*x^3 -24*x^2 + 32*x + 20);
1109
T[95,17]=(x^3 -2*x^2 -36*x + 104)*(x^4 -4*x^3 -32*x^2 + 16*x + 48);
1110
T[95,19]=(x + 1)^3*(x -1)^4;
1111
T[95,23]=(x^3 + 4*x^2 -8*x -16)*(x^4 + 8*x^3 -24*x^2 -176*x + 288);
1112
T[95,29]=(x^3 + 10*x^2 + 12*x -40)*(x^4 -4*x^3 -32*x^2 + 16*x + 48);
1113
T[95,31]=(x^3 -4*x^2 -48*x + 64)*(x^4 -4*x^3 -80*x^2 + 512*x -640);
1114
T[95,37]=(x^3 -20*x^2 + 124*x -244)*(x^4 + 6*x^3 -24*x^2 -40*x + 4);
1115
T[95,41]=(x^3 + 2*x^2 -36*x -104)*(x^4 -16*x^3 + 56*x^2 + 32*x -240);
1116
T[95,43]=(x^3 + 4*x^2 -144*x -592)*(x^4 -4*x^3 -16*x^2 + 48*x + 32);
1117
T[95,47]=(x^3 -16*x + 16)*(x^4 + 12*x^3 -64*x^2 -656*x + 1056);
1118
T[95,53]=(x^3 -16*x^2 + 76*x -92)*(x^4 + 10*x^3 -184*x -348);
1119
T[95,59]=(x^3 + 20*x^2 + 112*x + 160)*(x^4 -64*x^2 -224*x -192);
1120
T[95,61]=(x^3 + 2*x^2 -84*x + 232)*(x^4 -20*x^3 + 56*x^2 + 688*x -2656);
1121
T[95,67]=(x^3 -2*x^2 -76*x -116)*(x^4 + 18*x^3 + 8*x^2 -488*x -1076);
1122
T[95,71]=(x^3 + 4*x^2 -80*x -64)*(x^4 + 20*x^3 + 32*x^2 -1024*x -4224);
1123
T[95,73]=(x^3 -2*x^2 -20*x + 8)*(x^4 -28*x^3 + 256*x^2 -784*x + 176);
1124
T[95,79]=(x^3 -192*x -160)*(x^4 + 16*x^3 + 32*x^2 -480*x -1856);
1125
T[95,83]=(x^3 + 32*x^2 + 328*x + 1072)*(x^4 -72*x^2 -112*x + 480);
1126
T[95,89]=(x^3 -2*x^2 -132*x + 680)*(x^4 -4*x^3 -144*x^2 -176*x + 240);
1127
T[95,97]=(x^3 -20*x^2 -60*x + 1748)*(x^4 -30*x^3 + 224*x^2 -8*x -1388);
1128
1129
T[96,2]=(x )^2;
1130
T[96,3]=(x + 1)*(x -1);
1131
T[96,5]=(x -2)^2;
1132
T[96,7]=(x + 4)*(x -4);
1133
T[96,11]=(x + 4)*(x -4);
1134
T[96,13]=(x + 2)^2;
1135
T[96,17]=(x + 6)^2;
1136
T[96,19]=(x -4)*(x + 4);
1137
T[96,23]=(x )^2;
1138
T[96,29]=(x -2)^2;
1139
T[96,31]=(x + 4)*(x -4);
1140
T[96,37]=(x + 2)^2;
1141
T[96,41]=(x -2)^2;
1142
T[96,43]=(x + 4)*(x -4);
1143
T[96,47]=(x -8)*(x + 8);
1144
T[96,53]=(x -10)^2;
1145
T[96,59]=(x -4)*(x + 4);
1146
T[96,61]=(x -6)^2;
1147
T[96,67]=(x -4)*(x + 4);
1148
T[96,71]=(x -16)*(x + 16);
1149
T[96,73]=(x + 6)^2;
1150
T[96,79]=(x + 4)*(x -4);
1151
T[96,83]=(x -12)*(x + 12);
1152
T[96,89]=(x -10)^2;
1153
T[96,97]=(x + 14)^2;
1154
1155
T[98,2]=(x + 1)*(x -1)^2;
1156
T[98,3]=(x -2)*(x^2 -2);
1157
T[98,5]=(x^2 -8)*(x );
1158
T[98,7]=(x )^3;
1159
T[98,11]=(x )*(x + 2)^2;
1160
T[98,13]=(x -4)*(x )^2;
1161
T[98,17]=(x + 6)*(x^2 -2);
1162
T[98,19]=(x + 2)*(x^2 -50);
1163
T[98,23]=(x )*(x + 4)^2;
1164
T[98,29]=(x + 6)*(x -2)^2;
1165
T[98,31]=(x -4)*(x^2 -72);
1166
T[98,37]=(x -2)*(x -10)^2;
1167
T[98,41]=(x + 6)*(x^2 -98);
1168
T[98,43]=(x -8)*(x -2)^2;
1169
T[98,47]=(x -12)*(x^2 -8);
1170
T[98,53]=(x -6)*(x + 2)^2;
1171
T[98,59]=(x -6)*(x^2 -2);
1172
T[98,61]=(x + 8)*(x^2 -8);
1173
T[98,67]=(x + 4)*(x -12)^2;
1174
T[98,71]=(x )*(x + 12)^2;
1175
T[98,73]=(x + 2)*(x^2 -2);
1176
T[98,79]=(x -8)*(x + 4)^2;
1177
T[98,83]=(x -6)*(x^2 -98);
1178
T[98,89]=(x -6)*(x^2 -50);
1179
T[98,97]=(x -10)*(x^2 -98);
1180
1181
T[99,2]=(x -2)*(x -1)*(x + 1)^2;
1182
T[99,3]=(x )^4;
1183
T[99,5]=(x + 4)*(x + 1)*(x -4)*(x -2);
1184
T[99,7]=(x -4)*(x + 2)^3;
1185
T[99,11]=(x -1)*(x + 1)^3;
1186
T[99,13]=(x -4)*(x + 2)^3;
1187
T[99,17]=(x + 2)*(x -2)^3;
1188
T[99,19]=(x + 6)^2*(x )^2;
1189
T[99,23]=(x + 4)*(x + 8)*(x -1)*(x -4);
1190
T[99,29]=(x + 6)*(x )*(x -6)^2;
1191
T[99,31]=(x + 8)*(x -7)*(x -4)^2;
1192
T[99,37]=(x -6)*(x -3)*(x + 6)^2;
1193
T[99,41]=(x + 10)*(x -2)*(x -8)*(x -10);
1194
T[99,43]=(x + 6)*(x )*(x -6)^2;
1195
T[99,47]=(x -8)*(x + 8)^3;
1196
T[99,53]=(x + 6)*(x -6)*(x )^2;
1197
T[99,59]=(x + 4)*(x + 5)*(x -4)^2;
1198
T[99,61]=(x -12)*(x -6)*(x + 6)^2;
1199
T[99,67]=(x + 4)*(x + 7)*(x -8)^2;
1200
T[99,71]=(x -3)*(x )^3;
1201
T[99,73]=(x -4)*(x + 14)*(x + 2)^2;
1202
T[99,79]=(x + 4)*(x + 10)^3;
1203
T[99,83]=(x -6)*(x -12)*(x + 12)^2;
1204
T[99,89]=(x + 15)*(x -6)*(x )^2;
1205
T[99,97]=(x + 7)*(x -2)^3;
1206
1207
T[100,2]=x ;
1208
T[100,3]=x -2;
1209
T[100,5]=x ;
1210
T[100,7]=x + 2;
1211
T[100,11]=x ;
1212
T[100,13]=x + 2;
1213
T[100,17]=x -6;
1214
T[100,19]=x + 4;
1215
T[100,23]=x + 6;
1216
T[100,29]=x -6;
1217
T[100,31]=x + 4;
1218
T[100,37]=x + 2;
1219
T[100,41]=x -6;
1220
T[100,43]=x -10;
1221
T[100,47]=x -6;
1222
T[100,53]=x -6;
1223
T[100,59]=x -12;
1224
T[100,61]=x -2;
1225
T[100,67]=x + 2;
1226
T[100,71]=x + 12;
1227
T[100,73]=x + 2;
1228
T[100,79]=x -8;
1229
T[100,83]=x + 6;
1230
T[100,89]=x + 6;
1231
T[100,97]=x + 2;
1232
1233
}
1234