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