Sharedwww / Tables / charpoly_s2g1.gpOpen in CoCalc
Author: William A. Stein
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\\ charpoly_s2g1.gp
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\\ This is a table of characteristic polynomials of the
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\\ Hecke operators T_p acting on the space S_2(Gamma_1(N))
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\\ of weight 2 cusp forms for Gamma_1(N).
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\\ William Stein ([email protected]), September, 1998.
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{
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T=matrix(37,97,m,n,0);
9
T[11,2]=x + 2;
10
T[11,3]=x + 1;
11
T[11,5]=x -1;
12
T[11,7]=x + 2;
13
T[11,11]=x -1;
14
T[11,13]=x -4;
15
T[11,17]=x + 2;
16
T[11,19]=x ;
17
T[11,23]=x + 1;
18
T[11,29]=x ;
19
T[11,31]=x -7;
20
T[11,37]=x -3;
21
T[11,41]=x + 8;
22
T[11,43]=x + 6;
23
T[11,47]=x -8;
24
T[11,53]=x + 6;
25
T[11,59]=x -5;
26
T[11,61]=x -12;
27
T[11,67]=x + 7;
28
T[11,71]=x + 3;
29
T[11,73]=x -4;
30
T[11,79]=x + 10;
31
T[11,83]=x + 6;
32
T[11,89]=x -15;
33
T[11,97]=x + 7;
34
35
T[13,2]=x^2 + 3*x + 3;
36
T[13,3]=x^2 + 2*x + 4;
37
T[13,5]=x^2 + 3;
38
T[13,7]=(x )^2;
39
T[13,11]=(x )^2;
40
T[13,13]=x^2 + 5*x + 13;
41
T[13,17]=x^2 -3*x + 9;
42
T[13,19]=x^2 + 6*x + 12;
43
T[13,23]=x^2 -6*x + 36;
44
T[13,29]=x^2 + 3*x + 9;
45
T[13,31]=x^2 + 12;
46
T[13,37]=x^2 -15*x + 75;
47
T[13,41]=x^2 + 9*x + 27;
48
T[13,43]=x^2 + 8*x + 64;
49
T[13,47]=x^2 + 12;
50
T[13,53]=(x + 3)^2;
51
T[13,59]=x^2 -12*x + 48;
52
T[13,61]=x^2 + x + 1;
53
T[13,67]=x^2 -6*x + 12;
54
T[13,71]=x^2 -6*x + 12;
55
T[13,73]=x^2 + 3;
56
T[13,79]=(x -4)^2;
57
T[13,83]=x^2 + 192;
58
T[13,89]=x^2 + 12*x + 48;
59
T[13,97]=x^2 -12*x + 48;
60
61
T[14,2]=x + 1;
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T[14,3]=x + 2;
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T[14,5]=x ;
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T[14,7]=x -1;
65
T[14,11]=x ;
66
T[14,13]=x + 4;
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T[14,17]=x -6;
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T[14,19]=x -2;
69
T[14,23]=x ;
70
T[14,29]=x + 6;
71
T[14,31]=x + 4;
72
T[14,37]=x -2;
73
T[14,41]=x -6;
74
T[14,43]=x -8;
75
T[14,47]=x + 12;
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T[14,53]=x -6;
77
T[14,59]=x + 6;
78
T[14,61]=x -8;
79
T[14,67]=x + 4;
80
T[14,71]=x ;
81
T[14,73]=x -2;
82
T[14,79]=x -8;
83
T[14,83]=x + 6;
84
T[14,89]=x + 6;
85
T[14,97]=x + 10;
86
87
T[15,2]=x + 1;
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T[15,3]=x + 1;
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T[15,5]=x -1;
90
T[15,7]=x ;
91
T[15,11]=x + 4;
92
T[15,13]=x + 2;
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T[15,17]=x -2;
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T[15,19]=x -4;
95
T[15,23]=x ;
96
T[15,29]=x + 2;
97
T[15,31]=x ;
98
T[15,37]=x + 10;
99
T[15,41]=x -10;
100
T[15,43]=x -4;
101
T[15,47]=x -8;
102
T[15,53]=x + 10;
103
T[15,59]=x + 4;
104
T[15,61]=x + 2;
105
T[15,67]=x -12;
106
T[15,71]=x + 8;
107
T[15,73]=x -10;
108
T[15,79]=x ;
109
T[15,83]=x -12;
110
T[15,89]=x + 6;
111
T[15,97]=x -2;
112
113
T[16,2]=x^2 + 2*x + 2;
114
T[16,3]=x^2 + 2*x + 2;
115
T[16,5]=x^2 + 2*x + 2;
116
T[16,7]=x^2 + 4;
117
T[16,11]=x^2 -2*x + 2;
118
T[16,13]=x^2 + 2*x + 2;
119
T[16,17]=(x + 2)^2;
120
T[16,19]=x^2 -6*x + 18;
121
T[16,23]=x^2 + 36;
122
T[16,29]=x^2 -6*x + 18;
123
T[16,31]=(x + 8)^2;
124
T[16,37]=x^2 -6*x + 18;
125
T[16,41]=(x )^2;
126
T[16,43]=x^2 -10*x + 50;
127
T[16,47]=(x -8)^2;
128
T[16,53]=x^2 + 10*x + 50;
129
T[16,59]=x^2 + 6*x + 18;
130
T[16,61]=x^2 + 18*x + 162;
131
T[16,67]=x^2 + 10*x + 50;
132
T[16,71]=x^2 + 100;
133
T[16,73]=x^2 + 16;
134
T[16,79]=(x )^2;
135
T[16,83]=x^2 + 2*x + 2;
136
T[16,89]=x^2 + 16;
137
T[16,97]=(x + 2)^2;
138
139
T[17,2]=(x + 1)*(x^4 + 4*x^3 + 8*x^2 + 4*x + 1);
140
T[17,3]=(x^4 + 4*x^3 + 4*x^2 + 8)*(x );
141
T[17,5]=(x + 2)*(x^4 + 2*x^2 + 4*x + 2);
142
T[17,7]=(x -4)*(x^4 + 4*x^3 + 4*x^2 + 8);
143
T[17,11]=(x^4 + 4*x^3 + 12*x^2 + 16*x + 8)*(x );
144
T[17,13]=(x + 2)*(x^2 + 2)^2;
145
T[17,17]=(x -1)*(x^4 + 2*x^2 + 289);
146
T[17,19]=(x + 4)*(x^4 -8*x^3 + 32*x^2 -32*x + 16);
147
T[17,23]=(x -4)*(x^4 -4*x^3 + 12*x^2 -112*x + 392);
148
T[17,29]=(x -6)*(x^4 + 4*x^3 + 22*x^2 + 12*x + 2);
149
T[17,31]=(x -4)*(x^4 + 12*x^3 + 108*x^2 + 432*x + 648);
150
T[17,37]=(x + 2)*(x^4 + 50*x^2 + 500*x + 1250);
151
T[17,41]=(x + 6)*(x^4 + 4*x^3 + 54*x^2 -140*x + 98);
152
T[17,43]=(x -4)*(x^4 + 8*x^3 + 32*x^2 + 32*x + 16);
153
T[17,47]=(x^4 + 144*x^2 + 3136)*(x );
154
T[17,53]=(x -6)*(x^2 + 2*x + 2)^2;
155
T[17,59]=(x + 12)*(x^4 + 1296);
156
T[17,61]=(x + 10)*(x^4 + 50*x^2 + 500*x + 1250);
157
T[17,67]=(x -4)*(x^2 -8*x + 8)^2;
158
T[17,71]=(x + 4)*(x^4 -20*x^3 + 100*x^2 + 5000);
159
T[17,73]=(x + 6)*(x^4 + 28*x^3 + 294*x^2 + 1372*x + 4802);
160
T[17,79]=(x -12)*(x^4 + 4*x^3 + 12*x^2 + 112*x + 392);
161
T[17,83]=(x + 4)*(x^4 -16*x^3 + 128*x^2 + 64*x + 16);
162
T[17,89]=(x -10)*(x^4 + 132*x^2 + 3844);
163
T[17,97]=(x -2)*(x^4 -24*x^3 + 242*x^2 -1316*x + 4418);
164
165
T[18,2]=x^2 + x + 1;
166
T[18,3]=x^2 + 3*x + 3;
167
T[18,5]=(x )^2;
168
T[18,7]=x^2 + 2*x + 4;
169
T[18,11]=x^2 -3*x + 9;
170
T[18,13]=x^2 + 2*x + 4;
171
T[18,17]=(x + 3)^2;
172
T[18,19]=(x + 1)^2;
173
T[18,23]=x^2 -6*x + 36;
174
T[18,29]=x^2 + 6*x + 36;
175
T[18,31]=x^2 -4*x + 16;
176
T[18,37]=(x + 4)^2;
177
T[18,41]=x^2 + 9*x + 81;
178
T[18,43]=x^2 -x + 1;
179
T[18,47]=x^2 -6*x + 36;
180
T[18,53]=(x -12)^2;
181
T[18,59]=x^2 + 3*x + 9;
182
T[18,61]=x^2 + 8*x + 64;
183
T[18,67]=x^2 + 5*x + 25;
184
T[18,71]=(x + 12)^2;
185
T[18,73]=(x -11)^2;
186
T[18,79]=x^2 -4*x + 16;
187
T[18,83]=x^2 + 12*x + 144;
188
T[18,89]=(x -6)^2;
189
T[18,97]=x^2 + 5*x + 25;
190
191
T[19,2]=(x^6 + 6*x^5 + 18*x^4 + 30*x^3 + 36*x^2 + 27*x + 9)*(x );
192
T[19,3]=(x + 2)*(x^6 + 3*x^5 + 3*x^4 -8*x^3 + 6*x^2 -3*x + 1);
193
T[19,5]=(x -3)*(x^6 + 6*x^5 + 18*x^4 + 30*x^3 + 36*x^2 + 27*x + 9);
194
T[19,7]=(x + 1)*(x^6 + 3*x^4 + 2*x^3 + 9*x^2 + 3*x + 1);
195
T[19,11]=(x -3)*(x^6 + 9*x^4 -18*x^3 + 81*x^2 -81*x + 81);
196
T[19,13]=(x + 4)*(x^6 + 3*x^5 + 24*x^4 + 26*x^3 -114*x^2 + 222*x + 1369);
197
T[19,17]=(x + 3)*(x^6 -3*x^5 + 30*x^3 + 36*x^2 + 9);
198
T[19,19]=(x -1)*(x^6 + 12*x^5 + 78*x^4 + 385*x^3 + 1482*x^2 + 4332*x + 6859);
199
T[19,23]=(x^6 -6*x^5 + 36*x^4 -192*x^3 + 576*x^2 -864*x + 576)*(x );
200
T[19,29]=(x -6)*(x^6 + 3*x^5 + 36*x^4 -57*x^3 -477*x^2 -1998*x + 12321);
201
T[19,31]=(x + 4)*(x^6 -9*x^5 + 75*x^4 -160*x^3 + 513*x^2 + 318*x + 2809);
202
T[19,37]=(x -2)*(x^3 -21*x -17)^2;
203
T[19,41]=(x + 6)*(x^6 -21*x^5 + 162*x^4 -672*x^3 + 3411*x^2 -8991*x + 12321);
204
T[19,43]=(x + 1)*(x^6 + 3*x^5 + 60*x^4 + 8*x^3 -663*x^2 + 5379*x + 26569);
205
T[19,47]=(x + 3)*(x^6 + 3*x^5 + 54*x^4 + 24*x^3 -18*x^2 + 9);
206
T[19,53]=(x -12)*(x^6 + 3*x^5 -84*x^3 + 387*x^2 -1377*x + 2601);
207
T[19,59]=(x + 6)*(x^6 -12*x^5 + 18*x^4 -159*x^3 + 3006*x^2 + 19224*x + 71289);
208
T[19,61]=(x + 1)*(x^6 + 12*x^5 + 24*x^4 -37*x^3 + 984*x^2 -2172*x + 32761);
209
T[19,67]=(x + 4)*(x^6 + 30*x^5 + 348*x^4 + 2528*x^3 + 20928*x^2 + 86496*x + 179776);
210
T[19,71]=(x -6)*(x^6 + 6*x^5 -36*x^4 -1536*x^3 + 8352*x^2 -31968*x + 788544);
211
T[19,73]=(x + 7)*(x^6 + 12*x^5 + 96*x^4 + 512*x^3 + 768*x^2 -3072*x + 4096);
212
T[19,79]=(x -8)*(x^6 + 39*x^5 + 708*x^4 + 7487*x^3 + 51663*x^2 + 242700*x + 654481);
213
T[19,83]=(x -12)*(x^6 + 189*x^4 + 918*x^3 + 35721*x^2 + 86751*x + 210681);
214
T[19,89]=(x -12)*(x^6 + 12*x^5 + 54*x^4 -300*x^3 + 522*x^2 -1539*x + 3249);
215
T[19,97]=(x -8)*(x^6 -18*x^5 + 234*x^4 -1855*x^3 + 9522*x^2 -20574*x + 16129);
216
217
T[20,2]=(x^2 + 2*x + 2)*(x );
218
T[20,3]=(x + 2)*(x )^2;
219
T[20,5]=(x + 1)*(x^2 + 4*x + 5);
220
T[20,7]=(x -2)*(x )^2;
221
T[20,11]=(x )^3;
222
T[20,13]=(x -2)*(x^2 + 2*x + 2);
223
T[20,17]=(x + 6)*(x^2 -6*x + 18);
224
T[20,19]=(x + 4)*(x )^2;
225
T[20,23]=(x -6)*(x )^2;
226
T[20,29]=(x -6)*(x^2 + 16);
227
T[20,31]=(x + 4)*(x )^2;
228
T[20,37]=(x -2)*(x^2 + 14*x + 98);
229
T[20,41]=(x -6)*(x + 8)^2;
230
T[20,43]=(x + 10)*(x )^2;
231
T[20,47]=(x + 6)*(x )^2;
232
T[20,53]=(x + 6)*(x^2 -18*x + 162);
233
T[20,59]=(x -12)*(x )^2;
234
T[20,61]=(x -2)*(x -12)^2;
235
T[20,67]=(x -2)*(x )^2;
236
T[20,71]=(x + 12)*(x )^2;
237
T[20,73]=(x -2)*(x^2 + 22*x + 242);
238
T[20,79]=(x -8)*(x )^2;
239
T[20,83]=(x -6)*(x )^2;
240
T[20,89]=(x + 6)*(x^2 + 256);
241
T[20,97]=(x -2)*(x^2 -26*x + 338);
242
243
T[21,2]=(x + 1)*(x^2 + 2*x + 4)*(x )^2;
244
T[21,3]=(x -1)*(x^2 + 3*x + 3)*(x^2 + x + 1);
245
T[21,5]=(x + 2)*(x^2 -2*x + 4)*(x )^2;
246
T[21,7]=(x + 1)*(x^2 -x + 7)*(x^2 + 5*x + 7);
247
T[21,11]=(x -4)*(x^2 -2*x + 4)*(x )^2;
248
T[21,13]=(x + 2)*(x^2 + 3)*(x -1)^2;
249
T[21,17]=(x + 6)*(x )^4;
250
T[21,19]=(x -4)*(x^2 + x + 1)*(x^2 + 9*x + 27);
251
T[21,23]=(x )^5;
252
T[21,29]=(x + 2)*(x -4)^2*(x )^2;
253
T[21,31]=(x^2 -15*x + 75)*(x^2 + 9*x + 81)*(x );
254
T[21,37]=(x -6)*(x^2 + x + 1)*(x^2 + 3*x + 9);
255
T[21,41]=(x -2)*(x + 10)^2*(x )^2;
256
T[21,43]=(x + 4)*(x -5)^2*(x + 5)^2;
257
T[21,47]=(x^2 -6*x + 36)*(x )^3;
258
T[21,53]=(x -6)*(x^2 + 12*x + 144)*(x )^2;
259
T[21,59]=(x -12)*(x^2 -12*x + 144)*(x )^2;
260
T[21,61]=(x + 2)*(x^2 + 10*x + 100)*(x^2 -12*x + 48);
261
T[21,67]=(x -4)*(x^2 + 11*x + 121)*(x^2 -5*x + 25);
262
T[21,71]=(x + 6)^2*(x )^3;
263
T[21,73]=(x + 6)*(x^2 + 27*x + 243)*(x^2 -3*x + 9);
264
T[21,79]=(x + 16)*(x^2 -x + 1)*(x^2 -13*x + 169);
265
T[21,83]=(x + 12)*(x -6)^2*(x )^2;
266
T[21,89]=(x + 14)*(x^2 + 16*x + 256)*(x )^2;
267
T[21,97]=(x -18)*(x^2 + 192)*(x + 6)^2;
268
269
T[22,2]=(x^2 + 2*x + 2)*(x^4 + x^3 + x^2 + x + 1);
270
T[22,3]=(x^4 + 4*x^3 + 6*x^2 -x + 1)*(x + 1)^2;
271
T[22,5]=(x^4 + 6*x^3 + 16*x^2 + 16*x + 16)*(x -1)^2;
272
T[22,7]=(x^4 -2*x^3 + 4*x^2 -8*x + 16)*(x + 2)^2;
273
T[22,11]=(x^4 + x^3 + 21*x^2 + 11*x + 121)*(x -1)^2;
274
T[22,13]=(x^4 + 4*x^3 + 16*x^2 + 24*x + 16)*(x -4)^2;
275
T[22,17]=(x^4 -2*x^3 + 4*x^2 -3*x + 1)*(x + 2)^2;
276
T[22,19]=(x^4 + 5*x^3 + 40*x^2 + 50*x + 25)*(x )^2;
277
T[22,23]=(x + 1)^2*(x^2 + 2*x -4)^2;
278
T[22,29]=(x^4 -10*x^3 + 60*x^2 -200*x + 400)*(x )^2;
279
T[22,31]=(x^4 + 2*x^3 + 4*x^2 + 8*x + 16)*(x -7)^2;
280
T[22,37]=(x^4 + 18*x^3 + 144*x^2 + 432*x + 1296)*(x -3)^2;
281
T[22,41]=(x^4 + 2*x^3 + 24*x^2 + 133*x + 361)*(x + 8)^2;
282
T[22,43]=(x + 6)^2*(x^2 -3*x -99)^2;
283
T[22,47]=(x^4 + 8*x^3 + 64*x^2 + 192*x + 256)*(x -8)^2;
284
T[22,53]=(x^4 + 4*x^3 + 96*x^2 -256*x + 256)*(x + 6)^2;
285
T[22,59]=(x^4 -5*x^3 + 60*x^2 -550*x + 3025)*(x -5)^2;
286
T[22,61]=(x^4 -8*x^3 + 64*x^2 -192*x + 256)*(x -12)^2;
287
T[22,67]=(x + 7)^2*(x^2 -11*x -1)^2;
288
T[22,71]=(x^4 -8*x^3 + 24*x^2 + 8*x + 16)*(x + 3)^2;
289
T[22,73]=(x^4 + 14*x^3 + 136*x^2 + 1179*x + 17161)*(x -4)^2;
290
T[22,79]=(x^4 + 30*x^3 + 540*x^2 + 5400*x + 32400)*(x + 10)^2;
291
T[22,83]=(x^4 + 19*x^3 + 186*x^2 + 944*x + 3481)*(x + 6)^2;
292
T[22,89]=(x -15)^2*(x^2 + 5*x -25)^2;
293
T[22,97]=(x^4 + 3*x^3 + 144*x^2 + 1782*x + 9801)*(x + 7)^2;
294
295
T[23,2]=(x^2 + x -1)*(x^10 + 7*x^9 + 27*x^8 + 68*x^7 + 124*x^6 + 142*x^5 + 103*x^4 + 28*x^3 + 20*x^2 + 8*x + 1);
296
T[23,3]=(x^2 -5)*(x^10 + 7*x^9 + 27*x^8 + 68*x^7 + 113*x^6 + 131*x^5 + 103*x^4 + 17*x^3 -2*x^2 -3*x + 1);
297
T[23,5]=(x^2 + 2*x -4)*(x^10 + 3*x^9 + 9*x^8 -6*x^7 -18*x^6 -32*x^5 + 124*x^4 -233*x^3 + 489*x^2 -667*x + 529);
298
T[23,7]=(x^2 -2*x -4)*(x^10 + 5*x^9 + 25*x^8 + 81*x^7 + 207*x^6 + 298*x^5 + 170*x^4 -448*x^3 -425*x^2 -46*x + 529);
299
T[23,11]=(x^2 + 6*x + 4)*(x^10 -7*x^9 + 16*x^8 + 31*x^7 -74*x^6 -813*x^5 + 3282*x^4 -6111*x^3 + 11317*x^2 -2208*x + 529);
300
T[23,13]=(x^10 + 3*x^9 + 9*x^8 + 71*x^7 + 125*x^6 + 166*x^5 + 1290*x^4 -684*x^3 + 159*x^2 -18*x + 1)*(x -3)^2;
301
T[23,17]=(x^2 -6*x + 4)*(x^10 + 10*x^9 + 56*x^8 + 65*x^7 -274*x^6 -2003*x^5 + 10880*x^4 -20197*x^3 + 14521*x^2 -1541*x + 529);
302
T[23,19]=(x^10 -2*x^9 -40*x^8 -184*x^7 + 544*x^6 + 8416*x^5 + 52864*x^4 + 180096*x^3 + 450816*x^2 + 635904*x + 541696)*(x + 2)^2;
303
T[23,23]=(x^10 + 12*x^9 -10*x^8 -527*x^7 -32*x^6 + 14103*x^5 -736*x^4 -278783*x^3 -121670*x^2 + 3358092*x + 6436343)*(x -1)^2;
304
T[23,29]=(x^10 -14*x^9 + 86*x^8 + 6*x^7 -2394*x^6 + 13100*x^5 -833*x^4 -184633*x^3 + 1146117*x^2 -1896734*x + 4932841)*(x + 3)^2;
305
T[23,31]=(x^2 -45)*(x^10 -10*x^9 + 56*x^8 -164*x^7 + 375*x^6 -505*x^5 + 56*x^4 + 3862*x^3 -1066*x^2 + 2751*x + 17161);
306
T[23,37]=(x^2 -2*x -4)*(x^10 + 19*x^9 + 174*x^8 + 1117*x^7 + 6956*x^6 + 38345*x^5 + 148800*x^4 + 346183*x^3 + 370815*x^2 + 4462*x + 529);
307
T[23,41]=(x^2 -2*x -19)*(x^10 -7*x^9 + 16*x^8 + 9*x^7 + 1235*x^6 + 4181*x^5 + 15173*x^4 + 27978*x^3 + 23747*x^2 + 9331*x + 1849);
308
T[23,43]=(x^10 + 11*x^9 + 66*x^8 + 341*x^7 + 1826*x^6 + 6875*x^5 + 20449*x^4 + 55297*x^3 + 106843*x^2 + 114103*x + 64009)*(x )^2;
309
T[23,47]=(x^2 -5)*(x^5 + 9*x^4 -5*x^3 -97*x^2 -106*x + 1)^2;
310
T[23,53]=(x^2 + 8*x -4)*(x^10 -29*x^9 + 478*x^8 -5579*x^7 + 55454*x^6 -448645*x^5 + 2974063*x^4 -16104853*x^3 + 83193185*x^2 -312339057*x + 517426009);
311
T[23,59]=(x^2 -4*x -16)*(x^10 + 21*x^9 + 265*x^8 + 1649*x^7 + 3433*x^6 -22111*x^5 -98174*x^4 -33991*x^3 + 1176352*x^2 + 20569*x + 4489);
312
T[23,61]=(x^2 -4*x -76)*(x^10 -3*x^9 + 218*x^8 + 281*x^7 + 7066*x^6 + 46573*x^5 + 215097*x^4 + 359141*x^3 + 236219*x^2 -22103*x + 529);
313
T[23,67]=(x^2 + 10*x + 20)*(x^10 -45*x^9 + 1090*x^8 -17513*x^7 + 203501*x^6 -1799216*x^5 + 12627902*x^4 -70242899*x^3 + 291205025*x^2 -798415652*x + 1113757129);
314
T[23,71]=(x^2 -20*x + 95)*(x^10 + 14*x^9 + 130*x^8 + 566*x^7 + 785*x^6 -197*x^5 + 1686*x^4 + 1560*x^3 + 1204*x^2 + 851*x + 529);
315
T[23,73]=(x^2 -22*x + 101)*(x^10 -19*x^9 + 251*x^8 -2415*x^7 + 15063*x^6 -73963*x^5 + 379118*x^4 -1529101*x^3 + 3411556*x^2 -2470563*x + 982081);
316
T[23,79]=(x^2 + 4*x -76)*(x^10 + 15*x^9 + 115*x^8 + 2715*x^7 + 26304*x^6 + 111816*x^5 + 2966242*x^4 + 21480574*x^3 + 54168013*x^2 -24589507*x + 517426009);
317
T[23,83]=(x^2 + 22*x + 116)*(x^10 -18*x^9 + 192*x^8 -321*x^7 + 1455*x^6 -2914*x^5 + 224*x^4 -17*x^3 + 3804*x^2 + 2346*x + 529);
318
T[23,89]=(x^2 + 12*x + 16)*(x^10 -25*x^9 + 262*x^8 -5615*x^7 + 111566*x^6 -1048455*x^5 + 11505750*x^4 -150274617*x^3 + 1491272689*x^2 -10362512230*x + 78310985281);
319
T[23,97]=(x^2 -22*x + 76)*(x^10 + 34*x^9 + 430*x^8 + 4423*x^7 + 52812*x^6 + 183261*x^5 + 1071940*x^4 + 3733313*x^3 + 17156261*x^2 + 10511161*x + 2374681);
320
321
T[24,2]=(x^2 + 2)*(x^2 + 2*x + 2)*(x );
322
T[24,3]=(x + 1)*(x^2 + 1)*(x^2 + 2*x + 3);
323
T[24,5]=(x + 2)*(x^2 + 4)*(x )^2;
324
T[24,7]=(x + 2)^2*(x )^3;
325
T[24,11]=(x -4)*(x^2 + 8)*(x )^2;
326
T[24,13]=(x + 2)*(x^2 + 16)*(x )^2;
327
T[24,17]=(x -2)*(x^2 + 32)*(x + 2)^2;
328
T[24,19]=(x + 4)*(x^2 + 16)*(x -2)^2;
329
T[24,23]=(x + 8)*(x -4)^2*(x )^2;
330
T[24,29]=(x -6)*(x^2 + 36)*(x )^2;
331
T[24,31]=(x -8)*(x -2)^2*(x )^2;
332
T[24,37]=(x -6)*(x^2 + 64)*(x )^2;
333
T[24,41]=(x + 6)*(x^2 + 128)*(x -2)^2;
334
T[24,43]=(x -4)*(x^2 + 16)*(x + 10)^2;
335
T[24,47]=(x + 12)^2*(x )^3;
336
T[24,53]=(x + 2)*(x^2 + 36)*(x )^2;
337
T[24,59]=(x -4)*(x^2 + 16)*(x^2 + 200);
338
T[24,61]=(x + 2)*(x )^4;
339
T[24,67]=(x + 4)*(x^2 + 144)*(x -14)^2;
340
T[24,71]=(x -8)*(x -12)^2*(x )^2;
341
T[24,73]=(x -10)*(x + 6)^2*(x -2)^2;
342
T[24,79]=(x + 8)*(x -10)^2*(x )^2;
343
T[24,83]=(x + 4)*(x^2 + 8)*(x^2 + 256);
344
T[24,89]=(x + 6)*(x^2 + 32)*(x + 10)^2;
345
T[24,97]=(x -2)*(x + 2)^2*(x + 10)^2;
346
347
T[25,2]=(x^4 + 2*x^3 + 4*x^2 + 3*x + 1)*(x^8 + 5*x^7 + 11*x^6 + 10*x^5 + x^4 + 10*x^3 + 26*x^2 -10*x + 1);
348
T[25,3]=(x^4 + x^3 + x^2 + x + 1)*(x^8 + 5*x^7 + 9*x^6 + 15*x^5 + 51*x^4 + 110*x^3 + 144*x^2 + 80*x + 16);
349
T[25,5]=(x^4 + 5*x^3 + 15*x^2 + 25*x + 25)*(x^8 + 5*x^6 -20*x^5 + 5*x^4 -100*x^3 + 125*x^2 + 625);
350
T[25,7]=(x^8 + 21*x^6 + 121*x^4 + 116*x^2 + 16)*(x^2 + x -1)^2;
351
T[25,11]=(x^4 + 2*x^3 + 24*x^2 -32*x + 16)*(x^4 + 2*x^3 + 4*x^2 + 8*x + 16)^2;
352
T[25,13]=(x^4 -9*x^3 + 36*x^2 -54*x + 81)*(x^8 + 5*x^7 + 4*x^6 -5*x^5 + 21*x^4 + 5*x^3 + 4*x^2 -5*x + 1);
353
T[25,17]=(x^4 -8*x^3 + 24*x^2 + 8*x + 16)*(x^8 + 10*x^7 + 56*x^6 + 125*x^5 + 31*x^4 -550*x^3 -784*x^2 + 880*x + 1936);
354
T[25,19]=(x^4 + 5*x^3 + 40*x^2 + 50*x + 25)*(x^8 + 5*x^7 + 30*x^6 + 40*x^5 -15*x^4 -100*x^3 + 400*x^2 + 200*x + 400);
355
T[25,23]=(x^4 + 11*x^3 + 51*x^2 + 31*x + 961)*(x^8 -5*x^7 -x^6 -15*x^5 + 241*x^4 -60*x^3 -16*x^2 -320*x + 256);
356
T[25,29]=(x^4 -5*x^3 + 10*x^2 + 25)*(x^8 + 5*x^7 + 30*x^6 -5*x^5 + 485*x^4 + 4525*x^3 + 49350*x^2 + 142475*x + 483025);
357
T[25,31]=(x^4 -3*x^3 + 9*x^2 -27*x + 81)*(x^8 + 9*x^7 + 117*x^6 + 917*x^5 + 6855*x^4 + 31178*x^3 + 110532*x^2 + 23496*x + 1936);
358
T[25,37]=(x^4 + 7*x^3 + 19*x^2 + 3*x + 1)*(x^8 -30*x^7 + 406*x^6 -3270*x^5 + 17321*x^4 -61170*x^3 + 141631*x^2 -192665*x + 116281);
359
T[25,41]=(x^4 -8*x^3 + 24*x^2 + 8*x + 16)*(x^8 + 4*x^7 + 52*x^6 + 457*x^5 + 2655*x^4 -7622*x^3 + 9492*x^2 -1624*x + 13456);
360
T[25,43]=(x^8 + 129*x^6 + 4421*x^4 + 56784*x^2 + 246016)*(x^2 + 3*x -9)^2;
361
T[25,47]=(x^4 + 2*x^3 + 4*x^2 + 3*x + 1)*(x^8 + 16*x^6 + 615*x^5 + 4101*x^4 + 9840*x^3 -4864*x^2 -61440*x + 65536);
362
T[25,53]=(x^4 -9*x^3 + 61*x^2 -209*x + 361)*(x^8 + 10*x^7 -6*x^6 -1290*x^5 -8079*x^4 + 29590*x^3 + 722619*x^2 + 4157395*x + 8755681);
363
T[25,59]=(x^4 + 90*x^2 -675*x + 2025)*(x^8 + 15*x^5 + 5635*x^4 + 54150*x^3 + 407000*x^2 + 1333200*x + 4080400);
364
T[25,61]=(x^4 -13*x^3 + 139*x^2 -697*x + 1681)*(x^8 + 9*x^7 -43*x^6 -1068*x^5 + 16405*x^4 + 12978*x^3 + 139032*x^2 -59334*x + 116281);
365
T[25,67]=(x^4 + 2*x^3 + 64*x^2 + 528*x + 1936)*(x^8 -20*x^7 + 116*x^6 + 80*x^5 -2384*x^4 + 6080*x^3 + 74816*x^2 + 198400*x + 246016);
366
T[25,71]=(x^4 -8*x^3 + 34*x^2 -87*x + 841)*(x^8 -6*x^7 + 142*x^6 + 297*x^5 + 3455*x^4 -53922*x^3 + 966712*x^2 -5889104*x + 24245776);
367
T[25,73]=(x^4 -9*x^3 + 81*x^2 -729*x + 6561)*(x^8 -15*x^7 + 49*x^6 + 120*x^5 + 91*x^4 + 30*x^3 + 4*x^2 + 1);
368
T[25,79]=(x^4 -15*x^3 + 100*x^2 -250*x + 625)*(x^8 -15*x^7 + 100*x^6 + 600*x^5 + 12185*x^4 + 79050*x^3 + 1416100*x^2 + 4913000*x + 33408400);
369
T[25,83]=(x^4 -9*x^3 + 31*x^2 + 11*x + 121)*(x^8 + 45*x^7 + 949*x^6 + 11175*x^5 + 70651*x^4 + 199950*x^3 + 329344*x^2 + 284400*x + 99856);
370
T[25,89]=(x^4 + 20*x^3 + 240*x^2 + 1600*x + 6400)*(x^8 + 25*x^7 + 520*x^6 + 5890*x^5 + 47985*x^4 + 258800*x^3 + 888600*x^2 + 1640200*x + 1392400);
371
T[25,97]=(x^4 -8*x^3 + 34*x^2 -77*x + 121)*(x^8 + 60*x^7 + 1636*x^6 + 24990*x^5 + 213086*x^4 + 971040*x^3 + 5529361*x^2 + 63360350*x + 301334881);
372
373
T[26,2]=(x + 1)*(x -1)*(x^2 + 1)*(x^2 + x + 1)*(x^4 + 3*x^3 + 5*x^2 + 6*x + 4);
374
T[26,3]=(x -1)*(x + 3)*(x + 1)^2*(x^2 + 2*x + 4)^2*(x )^2;
375
T[26,5]=(x + 3)*(x^2 + 9)*(x^2 + 3)^2*(x + 1)^3;
376
T[26,7]=(x -1)*(x + 1)*(x^2 + 4*x + 16)*(x^2 + 9)*(x )^4;
377
T[26,11]=(x -6)*(x + 2)*(x^2 + 4*x + 16)*(x )^6;
378
T[26,13]=(x -1)*(x + 1)*(x^2 -7*x + 13)*(x^2 -4*x + 13)*(x^2 + 5*x + 13)^2;
379
T[26,17]=(x^2 + 3*x + 9)*(x + 3)^2*(x -3)^2*(x^2 -3*x + 9)^2;
380
T[26,19]=(x -6)*(x -2)*(x^2 + 36)*(x^2 + 6*x + 12)^2*(x )^2;
381
T[26,23]=(x + 4)*(x^2 -4*x + 16)*(x )*(x + 6)^2*(x^2 -6*x + 36)^2;
382
T[26,29]=(x -2)*(x -6)*(x^2 -x + 1)*(x^2 + 3*x + 9)^2*(x )^2;
383
T[26,31]=(x + 4)*(x^2 + 12)^2*(x )^2*(x -4)^3;
384
T[26,37]=(x -3)*(x + 7)*(x^2 + 9)*(x^2 + 3*x + 9)*(x^2 -15*x + 75)^2;
385
T[26,41]=(x^2 -9*x + 81)*(x^2 + 9*x + 27)^2*(x )^4;
386
T[26,43]=(x + 5)*(x^2 -8*x + 64)*(x^2 + 8*x + 64)^2*(x + 1)^3;
387
T[26,47]=(x -3)*(x -13)*(x^2 + 9)*(x + 8)^2*(x^2 + 12)^2;
388
T[26,53]=(x -12)*(x )*(x + 6)^2*(x + 9)^2*(x + 3)^4;
389
T[26,59]=(x + 6)*(x + 10)*(x^2 + 36)*(x^2 -4*x + 16)*(x^2 -12*x + 48)^2;
390
T[26,61]=(x -8)*(x^2 + 7*x + 49)*(x^2 + x + 1)^2*(x + 8)^3;
391
T[26,67]=(x + 2)*(x -14)*(x^2 + 4*x + 16)*(x^2 + 144)*(x^2 -6*x + 12)^2;
392
T[26,71]=(x + 5)*(x + 3)*(x^2 + 225)*(x^2 -8*x + 64)*(x^2 -6*x + 12)^2;
393
T[26,73]=(x + 10)*(x -2)*(x^2 + 36)*(x -11)^2*(x^2 + 3)^2;
394
T[26,79]=(x -8)*(x -10)^2*(x + 4)^3*(x -4)^4;
395
T[26,83]=(x -12)*(x^2 + 36)*(x^2 + 192)^2*(x )^3;
396
T[26,89]=(x + 6)*(x -6)*(x^2 -6*x + 36)*(x^2 + 36)*(x^2 + 12*x + 48)^2;
397
T[26,97]=(x + 10)*(x -14)*(x^2 + 144)*(x^2 + 2*x + 4)*(x^2 -12*x + 48)^2;
398
399
T[27,2]=(x^12 + 6*x^11 + 21*x^10 + 48*x^9 + 72*x^8 + 54*x^7 + 6*x^6 -9*x^5 -18*x^4 -45*x^3 + 27*x^2 + 27*x + 9)*(x );
400
T[27,3]=(x^12 + 6*x^11 + 18*x^10 + 39*x^9 + 63*x^8 + 81*x^7 + 117*x^6 + 243*x^5 + 567*x^4 + 1053*x^3 + 1458*x^2 + 1458*x + 729)*(x );
401
T[27,5]=(x^12 + 3*x^11 + 3*x^10 -12*x^9 -63*x^8 -63*x^7 + 303*x^6 + 1008*x^5 + 1521*x^4 + 1287*x^3 + 837*x^2 -135*x + 9)*(x );
402
T[27,7]=(x + 1)*(x^12 + 6*x^11 + 12*x^10 -11*x^9 + 18*x^8 + 225*x^7 + 273*x^6 + 225*x^5 + 639*x^4 -758*x^3 + 888*x^2 -816*x + 289);
403
T[27,11]=(x^12 -3*x^11 -15*x^10 -6*x^9 + 261*x^8 + 657*x^7 + 1491*x^6 + 1341*x^5 + 495*x^4 -531*x^3 + 108*x^2 -27*x + 9)*(x );
404
T[27,13]=(x -5)*(x^12 + 6*x^11 + 48*x^10 + 214*x^9 + 747*x^8 + 2223*x^7 + 3729*x^6 + 873*x^5 -3546*x^4 -2675*x^3 + 2994*x^2 + 84*x + 1);
405
T[27,17]=(x^12 -9*x^11 + 72*x^10 -189*x^9 + 621*x^8 -567*x^7 + 2727*x^6 -1701*x^5 + 7047*x^4 + 1458*x^3 + 8019*x^2 -2187*x + 729)*(x );
406
T[27,19]=(x + 7)*(x^12 + 3*x^11 + 39*x^10 -14*x^9 + 846*x^8 + 252*x^7 + 6162*x^6 + 873*x^5 + 33354*x^4 + 21604*x^3 + 11208*x^2 + 2280*x + 361);
407
T[27,23]=(x^12 + 12*x^11 + 48*x^10 -192*x^9 -1440*x^8 -774*x^7 + 22713*x^6 + 32220*x^5 + 170838*x^4 + 288216*x^3 + 322812*x^2 + 264870*x + 106929)*(x );
408
T[27,29]=(x^12 + 6*x^11 + 21*x^10 -96*x^9 + 423*x^8 -10206*x^7 -4044*x^6 + 188802*x^5 + 1278324*x^4 -619236*x^3 + 341037*x^2 -203202*x + 45369)*(x );
409
T[27,31]=(x + 4)*(x^12 -3*x^11 + 84*x^10 -434*x^9 + 1881*x^8 -4365*x^7 + 3810*x^6 + 14481*x^5 -29034*x^4 -6158*x^3 + 73617*x^2 -77262*x + 26569);
410
T[27,37]=(x -11)*(x^12 + 3*x^11 + 66*x^10 + 337*x^9 + 3519*x^8 + 15399*x^7 + 90807*x^6 + 331353*x^5 + 1506987*x^4 + 4411480*x^3 + 12573093*x^2 + 19105509*x + 24334489);
411
T[27,41]=(x^12 -15*x^11 + 93*x^10 -705*x^9 + 4797*x^8 + 8208*x^7 -57801*x^6 -178299*x^5 + 2682513*x^4 + 10695744*x^3 + 16475103*x^2 + 15350931*x + 11229201)*(x );
412
T[27,43]=(x -8)*(x^12 -3*x^11 -60*x^10 + 16*x^9 + 2799*x^8 -963*x^7 + 10965*x^6 + 386325*x^5 -386325*x^4 -4380266*x^3 + 49059204*x^2 -4709391*x + 3308761);
413
T[27,47]=(x^12 + 15*x^11 + 111*x^10 -114*x^9 -927*x^8 -30357*x^7 + 29409*x^6 + 676449*x^5 + 1192761*x^4 + 1182393*x^3 + 4549149*x^2 -17296902*x + 42732369)*(x );
414
T[27,53]=(x )*(x^6 + 9*x^5 -108*x^4 -513*x^3 + 4617*x^2 -2916*x -12393)^2;
415
T[27,59]=(x^12 + 12*x^11 + 192*x^10 + 933*x^9 + 5796*x^8 -36189*x^7 + 256911*x^6 -2031741*x^5 + 2890305*x^4 + 10115676*x^3 + 29313684*x^2 -170448354*x + 176384961)*(x );
416
T[27,61]=(x + 1)*(x^12 -12*x^11 -51*x^10 + 34*x^9 + 19512*x^8 -134964*x^7 + 1238790*x^6 -1547091*x^5 -9276372*x^4 + 81354967*x^3 + 226908411*x^2 -12754653*x + 273670849);
417
T[27,67]=(x -5)*(x^12 + 15*x^11 + 255*x^10 + 2365*x^9 + 23913*x^8 + 86274*x^7 + 660099*x^6 -1780641*x^5 -2980269*x^4 + 7604980*x^3 + 5116533*x^2 -13275069*x + 8288641);
418
T[27,71]=(x^12 -27*x^11 + 504*x^10 -5103*x^9 + 38205*x^8 -147015*x^7 + 400761*x^6 + 231093*x^5 + 604827*x^4 -144342*x^3 + 78003*x^2 + 6561*x + 729)*(x );
419
T[27,73]=(x + 7)*(x^12 -6*x^11 + 210*x^10 + 544*x^9 + 27792*x^8 + 2871*x^7 + 746232*x^6 + 498510*x^5 + 16156512*x^4 -5509508*x^3 + 3782073*x^2 + 619347*x + 185761);
420
T[27,79]=(x -17)*(x^12 + 42*x^11 + 813*x^10 + 9520*x^9 + 78291*x^8 + 487872*x^7 + 2309097*x^6 + 7412832*x^5 + 26778888*x^4 + 15614746*x^3 -6043107*x^2 -1848651*x + 3508129);
421
T[27,83]=(x^12 -39*x^11 + 912*x^10 -17196*x^9 + 256059*x^8 -2898477*x^7 + 25416024*x^6 -170563383*x^5 + 853146414*x^4 -3047714604*x^3 + 7328037465*x^2 -10578532986*x + 6951057129)*(x );
422
T[27,89]=(x^12 -9*x^11 + 261*x^10 -432*x^9 + 36666*x^8 -125712*x^7 + 1737990*x^6 -6160293*x^5 + 61794900*x^4 -218178036*x^3 + 765665784*x^2 -992530584*x + 1062042921)*(x );
423
T[27,97]=(x + 19)*(x^12 -3*x^11 + 102*x^10 -1010*x^9 -11349*x^8 + 185823*x^7 + 35103*x^6 -14303619*x^5 + 112050423*x^4 -381413396*x^3 + 532756806*x^2 + 21154719*x + 66765241);
424
425
T[28,2]=(x + 1)*(x^2 + x + 2)*(x^4 + 2*x^3 + 2*x^2 + 4*x + 4)*(x )^3;
426
T[28,3]=(x^2 + x + 1)*(x^4 + 3*x^2 + 9)*(x + 2)^2*(x )^2;
427
T[28,5]=(x^2 + 3*x + 9)*(x^2 + 3*x + 3)^2*(x )^4;
428
T[28,7]=(x^2 + 4*x + 7)*(x^2 + 7)*(x^4 + 2*x^2 + 49)*(x -1)^2;
429
T[28,11]=(x^2 + 28)*(x^2 -3*x + 9)*(x^4 -x^2 + 1)*(x )^2;
430
T[28,13]=(x + 4)^2*(x -2)^2*(x^2 + 12)^2*(x )^2;
431
T[28,17]=(x^2 + 3*x + 9)*(x -6)^2*(x^2 + 3*x + 3)^2*(x )^2;
432
T[28,19]=(x^2 -x + 1)*(x^4 + 27*x^2 + 729)*(x -2)^2*(x )^2;
433
T[28,23]=(x^2 + 3*x + 9)*(x^2 + 28)*(x^4 -x^2 + 1)*(x )^2;
434
T[28,29]=(x + 2)^2*(x + 6)^4*(x -4)^4;
435
T[28,31]=(x^2 -7*x + 49)*(x^4 + 3*x^2 + 9)*(x + 4)^2*(x )^2;
436
T[28,37]=(x^2 -x + 1)*(x -6)^2*(x -2)^2*(x^2 + 3*x + 9)^2;
437
T[28,41]=(x^2 + 12)^2*(x )^2*(x -6)^4;
438
T[28,43]=(x^2 + 28)*(x + 4)^2*(x -8)^2*(x^2 + 4)^2;
439
T[28,47]=(x^2 -9*x + 81)*(x^4 + 75*x^2 + 5625)*(x + 12)^2*(x )^2;
440
T[28,53]=(x^2 + 3*x + 9)*(x + 10)^2*(x -6)^2*(x^2 -x + 1)^2;
441
T[28,59]=(x^2 + 9*x + 81)*(x^4 + 27*x^2 + 729)*(x + 6)^2*(x )^2;
442
T[28,61]=(x^2 -x + 1)*(x -8)^2*(x^2 + 9*x + 27)^2*(x )^2;
443
T[28,67]=(x^2 -7*x + 49)*(x^2 + 252)*(x^4 -9*x^2 + 81)*(x + 4)^2;
444
T[28,71]=(x^2 + 28)*(x^2 + 196)^2*(x )^4;
445
T[28,73]=(x^2 -x + 1)*(x -2)^2*(x^2 -15*x + 75)^2*(x )^2;
446
T[28,79]=(x^2 -13*x + 169)*(x^2 + 252)*(x^4 -81*x^2 + 6561)*(x -8)^2;
447
T[28,83]=(x -12)^2*(x + 6)^2*(x^2 -192)^2*(x )^2;
448
T[28,89]=(x^2 + 15*x + 225)*(x + 6)^2*(x^2 -27*x + 243)^2*(x )^2;
449
T[28,97]=(x^2 + 300)^2*(x )^2*(x + 10)^4;
450
451
T[29,2]=(x^2 + 5)*(x^2 + 2*x -1)*(x^6 + 2*x^5 + 4*x^4 + x^3 + 2*x^2 -3*x + 1)*(x^12 + 7*x^11 + 23*x^10 + 42*x^9 + 32*x^8 + 7*x^7 + 92*x^6 + 259*x^5 + 289*x^4 + 133*x^3 + 18*x^2 + 1);
452
T[29,3]=(x^2 + 5)*(x^2 -2*x -1)*(x^6 + 5*x^5 + 11*x^4 + 13*x^3 + 9*x^2 + 3*x + 1)*(x^12 + 7*x^11 + 23*x^10 + 49*x^9 + 67*x^8 + 105*x^7 + 211*x^6 -84*x^5 -432*x^4 -280*x^3 + 256*x^2 + 224*x + 64);
453
T[29,5]=(x^6 -x^5 + 15*x^4 + 13*x^3 + x^2 -x + 1)*(x^12 + x^11 -x^10 + 4*x^9 + 6*x^8 -79*x^7 + 196*x^6 + 521*x^5 + 1109*x^4 -717*x^3 + 320*x^2 -10*x + 1)*(x + 1)^2*(x + 3)^2;
454
T[29,7]=(x^2 -8)*(x^6 -x^5 + 15*x^4 + 13*x^3 + x^2 -x + 1)*(x^12 + 11*x^11 + 61*x^10 + 207*x^9 + 451*x^8 + 297*x^7 -385*x^6 -1878*x^5 + 2540*x^4 + 872*x^3 + 11248*x^2 -1056*x + 64)*(x -2)^2;
455
T[29,11]=(x^2 + 5)*(x^2 -2*x -1)*(x^6 + 11*x^5 + 79*x^4 + 365*x^3 + 1089*x^2 + 1927*x + 1681)*(x^12 -7*x^11 -5*x^10 + 161*x^9 -297*x^8 -1015*x^7 + 3403*x^6 -1932*x^5 + 6456*x^4 -12152*x^3 + 11680*x^2 + 2912*x + 10816);
456
T[29,13]=(x^2 + 2*x -7)*(x^6 + 5*x^5 + 25*x^4 + 181*x^3 + 513*x^2 -1075*x + 1849)*(x^12 -9*x^11 + 17*x^10 + 66*x^9 -2*x^8 + 449*x^7 + 2646*x^6 -4115*x^5 + 8125*x^4 -1845*x^3 + 3692*x^2 + 1566*x + 841)*(x + 1)^2;
457
T[29,17]=(x^2 + 20)*(x^2 + 4*x -4)*(x^12 + 71*x^10 + 1870*x^8 + 22695*x^6 + 125672*x^4 + 259120*x^2 + 53824)*(x^3 -4*x^2 -4*x + 8)^2;
458
T[29,19]=(x^6 -x^5 + x^4 -15*x^3 + 29*x^2 + 13*x + 169)*(x^12 + 7*x^11 -7*x^10 -77*x^9 + 77*x^8 + 315*x^7 + 3297*x^6 -11466*x^5 -1176*x^4 + 12936*x^3 + 18816*x^2 + 9408*x + 3136)*(x -6)^2*(x )^2;
459
T[29,23]=(x^2 + 4*x -28)*(x^6 + 7*x^5 + 49*x^4 + 245*x^3 + 1029*x^2 + 2401*x + 2401)*(x^12 + 5*x^11 + 3*x^10 + 115*x^9 + 1279*x^8 + 2899*x^7 + 5299*x^6 + 5090*x^5 + 1580*x^4 -200*x^3 + 1200*x^2 + 96*x + 64)*(x -6)^2;
460
T[29,29]=(x^2 + 6*x + 29)*(x^6 -6*x^5 -13*x^4 + 316*x^3 -377*x^2 -5046*x + 24389)*(x^12 + 15*x^11 + 126*x^10 + 622*x^9 + 1665*x^8 -4109*x^7 -52800*x^6 -119161*x^5 + 1400265*x^4 + 15169958*x^3 + 89117406*x^2 + 307667235*x + 594823321)*(x -1)^2;
461
T[29,31]=(x^2 + 45)*(x^2 -6*x -41)*(x^6 -5*x^5 -3*x^4 -139*x^3 + 1885*x^2 -2075*x + 6889)*(x^12 + 21*x^11 + 207*x^10 + 1393*x^9 + 7933*x^8 + 40551*x^7 + 172733*x^6 + 551362*x^5 + 1169872*x^4 + 1297800*x^3 + 17376*x^2 -911232*x + 817216);
462
T[29,37]=(x^6 -11*x^5 + 79*x^4 -365*x^3 + 1089*x^2 -1927*x + 1681)*(x^12 -7*x^11 -77*x^10 -462*x^9 + 5712*x^8 + 57799*x^7 + 221690*x^6 -343441*x^5 -3193771*x^4 -7248521*x^3 + 9550100*x^2 + 51709504*x + 110103049)*(x + 4)^2*(x )^2;
463
T[29,41]=(x^2 -8*x -56)*(x^2 + 20)*(x^12 + 99*x^10 + 3354*x^8 + 46551*x^6 + 240836*x^4 + 383328*x^2 + 107584)*(x^3 -10*x^2 + 24*x -8)^2;
464
T[29,43]=(x^2 -10*x + 23)*(x^2 + 45)*(x^6 -13*x^5 + 85*x^4 -265*x^3 + 337*x^2 -13*x + 169)*(x^12 -7*x^11 + 53*x^10 -525*x^9 + 5735*x^8 -54047*x^7 + 245659*x^6 -1972348*x^5 + 23501608*x^4 -123964456*x^3 + 297070944*x^2 -156036832*x + 24364096);
465
T[29,47]=(x^2 + 5)*(x^2 -2*x -17)*(x^6 -11*x^5 + 65*x^4 -295*x^3 + 1257*x^2 -2151*x + 57121)*(x^12 + 7*x^11 -103*x^10 + 161*x^9 + 19989*x^8 + 67669*x^7 -350475*x^6 + 4670190*x^5 + 39023448*x^4 -264630072*x^3 + 393855872*x^2 -63183680*x + 11343424);
466
T[29,53]=(x^2 -2*x -71)*(x^6 -3*x^5 -5*x^4 -41*x^3 + 417*x^2 + 9*x + 1)*(x^12 + 10*x^11 + 131*x^10 + 570*x^9 + 339*x^8 + 578*x^7 + 33131*x^6 -26542*x^5 + 97201*x^4 -928*x^3 + 7461*x^2 -23668*x + 9409)*(x + 9)^2;
467
T[29,59]=(x^2 -4*x -28)*(x -6)^2*(x^3 + 28*x^2 + 252*x + 728)^2*(x^6 -22*x^5 + 92*x^4 + 440*x^3 -1616*x^2 -288*x + 1856)^2;
468
T[29,61]=(x^2 + 180)*(x^2 + 4*x -4)*(x^6 -3*x^5 + 37*x^4 -13*x^3 -3*x^2 -117*x + 169)*(x^12 + 7*x^11 + 37*x^10 + 1386*x^9 + 12576*x^8 -16723*x^7 -347290*x^6 + 1785091*x^5 + 5400761*x^4 -63413315*x^3 + 245176194*x^2 -454531742*x + 325694209);
469
T[29,67]=(x^2 -32)*(x^6 -19*x^5 + 235*x^4 -167*x^3 + 1017*x^2 + 767*x + 169)*(x^12 + 37*x^11 + 647*x^10 + 6241*x^9 + 33787*x^8 + 74717*x^7 + 101339*x^6 -155226*x^5 + 3141164*x^4 -61163224*x^3 + 442353712*x^2 + 140215392*x + 415833664)*(x -8)^2;
470
T[29,71]=(x^2 + 12*x + 28)*(x^6 -21*x^5 + 189*x^4 -945*x^3 + 3969*x^2 + 11907*x + 35721)*(x^12 + 21*x^11 + 315*x^10 + 1715*x^9 + 12901*x^8 + 22785*x^7 + 411173*x^6 -1767332*x^5 + 6120688*x^4 + 8854888*x^3 + 1782816*x^2 + 638243424*x + 2671649344)*(x )^2;
471
T[29,73]=(x^6 + 25*x^5 + 373*x^4 + 3473*x^3 + 22425*x^2 + 90085*x + 175561)*(x^12 -14*x^11 + 77*x^10 -616*x^9 + 8113*x^8 -31234*x^7 -180061*x^6 + 1002050*x^5 + 1687021*x^4 -4728990*x^3 + 4875059*x^2 -2070838*x + 625681)*(x -4)^2*(x )^2;
472
T[29,79]=(x^2 + 2*x -1)*(x^2 + 45)*(x^6 + 9*x^5 + 81*x^4 -27*x^3 + 2025*x^2 -2187*x + 729)*(x^12 -49*x^11 + 1243*x^10 -23023*x^9 + 357513*x^8 -4897893*x^7 + 56898577*x^6 -508283370*x^5 + 3236678008*x^4 -13718782952*x^3 + 36243227456*x^2 -51708046208*x + 30056463424);
473
T[29,83]=(x^2 -4*x -28)*(x^6 -17*x^5 + 219*x^4 -1693*x^3 + 8089*x^2 -22139*x + 28561)*(x^12 -5*x^11 + 185*x^10 + 1369*x^9 + 36097*x^8 + 418137*x^7 + 1456973*x^6 -3763292*x^5 + 65368364*x^4 + 28644144*x^3 + 249611008*x^2 + 590546112*x + 419758144)*(x + 6)^2;
474
T[29,89]=(x^2 + 8*x -56)*(x^2 + 20)*(x^6 -7*x^5 + 119*x^4 -1337*x^3 + 6321*x^2 -9555*x + 8281)*(x^12 -7*x^11 + 141*x^10 + 1008*x^9 + 18096*x^8 -404103*x^7 + 3818480*x^6 -18842803*x^5 + 26790541*x^4 + 51450665*x^3 + 22907116*x^2 -274309448*x + 203946961);
475
T[29,97]=(x^2 + 8*x -56)*(x^2 + 180)*(x^6 -x^5 + 211*x^4 -1849*x^3 + 4761*x^2 + 1105*x + 169)*(x^12 -14*x^11 + 247*x^10 + 364*x^9 + 3945*x^8 -302162*x^7 + 3340051*x^6 -19681494*x^5 + 66938013*x^4 -118114444*x^3 + 86045131*x^2 + 25484074*x + 1697809);
476
477
T[30,2]=(x + 1)*(x^2 + x + 2)*(x^2 + 1)*(x^4 + 1);
478
T[30,3]=(x -1)*(x^2 + 1)*(x^4 + 4*x^3 + 8*x^2 + 12*x + 9)*(x + 1)^2;
479
T[30,5]=(x + 1)*(x^2 + 4*x + 5)*(x^4 + 8*x^2 + 25)*(x -1)^2;
480
T[30,7]=(x + 4)*(x^2 + 4)*(x^2 + 2*x + 2)^2*(x )^2;
481
T[30,11]=(x )*(x + 4)^2*(x -2)^2*(x^2 + 2)^2;
482
T[30,13]=(x -2)*(x^2 + 36)*(x + 2)^2*(x )^4;
483
T[30,17]=(x -6)*(x^2 + 4)*(x^4 + 16)*(x -2)^2;
484
T[30,19]=(x + 4)*(x -4)^2*(x^2 + 16)^2*(x )^2;
485
T[30,23]=(x^2 + 16)*(x^4 + 256)*(x )^3;
486
T[30,29]=(x + 6)*(x + 2)^2*(x^2 -50)^2*(x )^2;
487
T[30,31]=(x -8)*(x + 8)^2*(x )^2*(x + 2)^4;
488
T[30,37]=(x -2)*(x^2 + 4)*(x + 10)^2*(x^2 -12*x + 72)^2;
489
T[30,41]=(x + 6)*(x -2)^2*(x -10)^2*(x^2 + 32)^2;
490
T[30,43]=(x + 4)*(x^2 + 16)*(x -4)^2*(x^2 -12*x + 72)^2;
491
T[30,47]=(x^2 + 64)*(x -8)^2*(x )^5;
492
T[30,53]=(x + 6)*(x^2 + 36)*(x^4 + 256)*(x + 10)^2;
493
T[30,59]=(x )*(x + 4)^2*(x + 10)^2*(x^2 -98)^2;
494
T[30,61]=(x + 10)*(x + 2)^2*(x -2)^2*(x + 6)^4;
495
T[30,67]=(x + 4)*(x^2 + 64)*(x -12)^2*(x^2 + 8*x + 32)^2;
496
T[30,71]=(x )*(x -12)^2*(x + 8)^2*(x^2 + 200)^2;
497
T[30,73]=(x -2)*(x^2 + 16)*(x -10)^2*(x^2 + 10*x + 50)^2;
498
T[30,79]=(x -8)*(x^2 + 36)^2*(x )^4;
499
T[30,83]=(x^2 + 16)*(x^4 + 20736)*(x -12)^3;
500
T[30,89]=(x -18)*(x + 6)^2*(x -10)^2*(x^2 -8)^2;
501
T[30,97]=(x^2 + 64)*(x^2 -6*x + 18)^2*(x -2)^3;
502
503
T[31,2]=(x^2 -x -1)*(x^4 + 3*x^3 + 4*x^2 + 2*x + 1)*(x^16 + 6*x^15 + 29*x^14 + 91*x^13 + 246*x^12 + 523*x^11 + 1011*x^10 + 1468*x^9 + 1957*x^8 + 1797*x^7 + 1656*x^6 + 1062*x^5 + 576*x^4 -216*x^3 + 459*x^2 + 324*x + 81)*(x^2 + 2*x -1)^2;
504
T[31,3]=(x^2 + 2*x -4)*(x^4 -x^3 + x^2 -x + 1)*(x^4 -2*x^3 + 5*x^2 + 2*x + 1)*(x^16 + 12*x^15 + 74*x^14 + 321*x^13 + 1092*x^12 + 2967*x^11 + 6433*x^10 + 11361*x^9 + 17306*x^8 + 24459*x^7 + 33043*x^6 + 41628*x^5 + 45837*x^4 + 38859*x^3 + 21989*x^2 + 7068*x + 961);
505
T[31,5]=(x^16 + 3*x^15 + 31*x^14 + 72*x^13 + 576*x^12 + 1239*x^11 + 5944*x^10 + 9366*x^9 + 36937*x^8 + 52026*x^7 + 145524*x^6 + 136584*x^5 + 286866*x^4 + 264222*x^3 + 358641*x^2 + 170748*x + 77841)*(x -1)^2*(x^2 + 3*x + 1)^2*(x^2 + x + 1)^2;
506
T[31,7]=(x^2 + 4*x -1)*(x^4 + 3*x^3 + 9*x^2 + 27*x + 81)*(x^4 + 2*x^3 + 5*x^2 -2*x + 1)*(x^16 -2*x^15 -6*x^14 + 34*x^13 -93*x^12 -167*x^11 + 3353*x^10 -4566*x^9 -4334*x^8 + 34596*x^7 -60867*x^6 + 21447*x^5 + 153882*x^4 -389529*x^3 + 433404*x^2 -251343*x + 68121);
507
T[31,11]=(x^4 + 2*x^3 + 24*x^2 -32*x + 16)*(x^4 -2*x^3 + 21*x^2 + 34*x + 289)*(x^16 + 7*x^15 + 13*x^14 -40*x^13 -390*x^12 -2072*x^11 -4106*x^10 + 8330*x^9 + 86209*x^8 + 306225*x^7 + 739071*x^6 + 1357641*x^5 + 1863765*x^4 + 1808190*x^3 + 1167237*x^2 + 449469*x + 77841)*(x -2)^2;
508
T[31,13]=(x^2 + 2*x -4)*(x^4 -6*x^3 + 36*x^2 -81*x + 81)*(x^4 -2*x^3 + 11*x^2 + 14*x + 49)*(x^16 + 7*x^15 + 18*x^14 -50*x^13 -195*x^12 + 73*x^11 -451*x^10 + 4050*x^9 + 20059*x^8 -9690*x^7 -47919*x^6 -231579*x^5 + 493245*x^4 -1391850*x^3 + 3151062*x^2 -881361*x + 77841);
509
T[31,17]=(x^2 -6*x + 4)*(x^4 + 3*x^3 + 19*x^2 + 7*x + 1)*(x^4 -6*x^3 + 35*x^2 -6*x + 1)*(x^16 + 6*x^15 + 41*x^14 + 2*x^13 -63*x^12 -6979*x^11 -19503*x^10 + 5912*x^9 + 275371*x^8 + 1540602*x^7 + 3381567*x^6 -3532239*x^5 -20522988*x^4 -9214533*x^3 + 70913151*x^2 + 135131976*x + 74805201);
510
T[31,19]=(x^2 -5)*(x^4 + 5*x^3 + 25*x^2 + 125*x + 625)*(x^4 + 6*x^3 + 29*x^2 + 42*x + 49)*(x^16 -16*x^15 + 157*x^14 -1005*x^13 + 4955*x^12 -17674*x^11 + 45106*x^10 -79075*x^9 + 52534*x^8 + 72260*x^7 + 71044*x^6 -568187*x^5 + 107895*x^4 + 911720*x^3 + 121928*x^2 -933353*x + 361201);
511
T[31,23]=(x^2 + 2*x -44)*(x^4 -11*x^3 + 61*x^2 -171*x + 361)*(x^16 -x^15 + 60*x^14 -310*x^13 + 1680*x^12 -7723*x^11 + 37718*x^10 -91020*x^9 + 258445*x^8 -599310*x^7 + 991968*x^6 + 1177317*x^5 + 561960*x^4 -482760*x^3 + 221130*x^2 -27621*x + 77841)*(x + 4)^4;
512
T[31,29]=(x^2 -10*x + 20)*(x^4 -5*x^3 + 60*x^2 -550*x + 3025)*(x^16 + 14*x^15 + 181*x^14 + 1141*x^13 + 5748*x^12 + 12869*x^11 + 13939*x^10 + 2848*x^9 + 707773*x^8 + 1365609*x^7 + 3122946*x^6 + 3992868*x^5 + 5548428*x^4 + 4318758*x^3 + 3623319*x^2 -883872*x + 77841)*(x^2 + 8*x + 8)^2;
513
T[31,31]=(x^4 + 11*x^3 + 61*x^2 + 341*x + 961)*(x^16 -15*x^15 + 158*x^14 -1635*x^13 + 13788*x^12 -99390*x^11 + 688351*x^10 -4312200*x^9 + 24371915*x^8 -133678200*x^7 + 661505311*x^6 -2960927490*x^5 + 12733507548*x^4 -46808661885*x^3 + 140225581598*x^2 -412689211665*x + 852891037441)*(x -1)^2*(x^2 + 10*x + 31)^2;
514
T[31,37]=(x^16 + 8*x^15 + 176*x^14 + 1242*x^13 + 20471*x^12 + 128479*x^11 + 1088869*x^10 + 3571101*x^9 + 20869117*x^8 + 46820571*x^7 + 277619329*x^6 + 346528319*x^5 + 1409594951*x^4 -158428158*x^3 + 4527747446*x^2 + 1215563878*x + 344807761)*(x + 2)^2*(x^2 + x + 1)^2*(x^2 + 4*x -1)^2;
515
T[31,41]=(x^4 -8*x^3 + 64*x^2 -192*x + 256)*(x^4 + 2*x^3 + 75*x^2 -142*x + 5041)*(x^16 + 8*x^15 + 24*x^14 + 74*x^13 -543*x^12 -14527*x^11 -14332*x^10 + 138939*x^9 + 1009576*x^8 -583269*x^7 -255102*x^6 + 110817*x^5 + 80847*x^4 + 41256*x^3 + 12474*x^2 + 1377*x + 81)*(x -7)^2;
516
T[31,43]=(x^2 + 2*x -4)*(x^4 -x^3 + 16*x^2 -66*x + 121)*(x^4 -2*x^3 + 101*x^2 + 194*x + 9409)*(x^16 -23*x^15 + 203*x^14 -430*x^13 -6430*x^12 + 60188*x^11 + 134904*x^10 -6434660*x^9 + 63545739*x^8 -335926675*x^7 + 1040373291*x^6 -1703962259*x^5 + 784151645*x^4 + 814057510*x^3 + 228201527*x^2 + 52975559*x + 7612081);
517
T[31,47]=(x^2 + 4*x -16)*(x^4 -7*x^3 + 24*x^2 -38*x + 361)*(x^16 -14*x^15 + 124*x^14 -769*x^13 + 6981*x^12 -31622*x^11 + 189676*x^10 -794482*x^9 + 7964842*x^8 -22382208*x^7 + 239117571*x^6 -162124668*x^5 + 3315570876*x^4 -2392720506*x^3 + 3685168494*x^2 -4369845996*x + 3306365001)*(x^2 -8*x -16)^2;
518
T[31,53]=(x^2 + 12*x + 16)*(x^4 -21*x^3 + 171*x^2 -81*x + 81)*(x^4 + 6*x^3 + 35*x^2 + 6*x + 1)*(x^16 -6*x^15 -69*x^14 + 603*x^13 -1278*x^12 -71766*x^11 + 2038662*x^10 -24121152*x^9 + 155526156*x^8 -558518247*x^7 + 981605547*x^6 -251413146*x^5 -2622043143*x^4 + 7656192738*x^3 -445529079*x^2 -91711239201*x + 366207732801);
519
T[31,59]=(x^2 -5)*(x^4 -5*x^3 + 85*x^2 + 75*x + 25)*(x^4 -6*x^3 + 77*x^2 + 246*x + 1681)*(x^16 -4*x^15 + 39*x^14 + 191*x^13 -10344*x^12 + 19328*x^11 + 740606*x^10 + 1999413*x^9 -4867133*x^8 -46766253*x^7 + 278477391*x^6 -1116660393*x^5 + 2755747881*x^4 -3585893571*x^3 + 2517526899*x^2 -930024261*x + 167728401);
520
T[31,61]=(x^2 + 6*x -116)*(x^2 -8)^2*(x^2 -4*x -76)^2*(x^8 + 30*x^7 + 288*x^6 + 855*x^5 -1591*x^4 -11295*x^3 -7053*x^2 + 31425*x + 38161)^2;
521
T[31,67]=(x^4 -2*x^3 + 21*x^2 + 34*x + 289)*(x^16 -13*x^15 + 278*x^14 -1215*x^13 + 25715*x^12 -90377*x^11 + 1582339*x^10 -1954980*x^9 + 44237164*x^8 -3609120*x^7 + 968412901*x^6 + 619634861*x^5 + 6283805060*x^4 -825845775*x^3 + 24095669462*x^2 + 12302334469*x + 7485883441)*(x -8)^2*(x^2 + 4*x -1)^2;
522
T[31,71]=(x^2 -4*x -121)*(x^4 + 7*x^3 + 124*x^2 + 18*x + 1)*(x^4 -14*x^3 + 197*x^2 + 14*x + 1)*(x^16 + 14*x^15 + 54*x^14 -571*x^13 -5559*x^12 + 9032*x^11 + 489746*x^10 + 4726947*x^9 + 28094137*x^8 + 115250643*x^7 + 336930426*x^6 + 704589408*x^5 + 1084306581*x^4 + 1300605741*x^3 + 1213526934*x^2 + 751317606*x + 214944921);
523
T[31,73]=(x^2 -8*x -4)*(x^4 -21*x^3 + 306*x^2 -2376*x + 9801)*(x^4 + 2*x^3 + 11*x^2 -14*x + 49)*(x^16 -2*x^15 -132*x^14 + 1990*x^13 + 29370*x^12 -287393*x^11 -329281*x^10 -6608985*x^9 + 153857104*x^8 -565298085*x^7 + 4796602581*x^6 -27314967861*x^5 -18297810810*x^4 + 83971435995*x^3 -414865512693*x^2 + 5777484622731*x + 17441907675201);
524
T[31,79]=(x^2 + 10*x -20)*(x^4 -22*x^3 + 381*x^2 -2266*x + 10609)*(x^16 -18*x^15 + 68*x^14 -760*x^13 -3480*x^12 + 222098*x^11 + 727764*x^10 -12085930*x^9 + 116774239*x^8 -1419091350*x^7 -1496728314*x^6 + 91619946846*x^5 + 184597920495*x^4 -501837917850*x^3 + 2724585336027*x^2 + 30606997844844*x + 84609661119201)*(x )^4;
525
T[31,83]=(x^2 + 12*x -44)*(x^4 + 14*x^3 + 96*x^2 + 319*x + 841)*(x^4 -6*x^3 + 77*x^2 + 246*x + 1681)*(x^16 + 16*x^15 + 19*x^14 -4444*x^13 -37239*x^12 -14762*x^11 + 5596636*x^10 + 70689353*x^9 + 147595087*x^8 -14048403843*x^7 + 37835249526*x^6 + 153588916962*x^5 + 1152938790711*x^4 -8323756330311*x^3 + 13126123170054*x^2 + 29811832434*x + 1446653267361);
526
T[31,89]=(x^2 -10*x -20)*(x^4 -5*x^3 + 60*x^2 -550*x + 3025)*(x^16 -x^15 + 109*x^14 -1181*x^13 + 22521*x^12 + 472472*x^11 + 4432966*x^10 + 21636982*x^9 + 75648667*x^8 + 148772748*x^7 + 364745286*x^6 + 954917388*x^5 + 5138578341*x^4 + 4144588911*x^3 + 36524826639*x^2 + 14623714971*x + 117957215601)*(x^2 + 8*x -56)^2;
527
T[31,97]=(x^2 + 14*x -31)*(x^4 + 3*x^3 + 279*x^2 -2673*x + 9801)*(x^16 -3*x^15 + 281*x^14 + 1913*x^13 + 27081*x^12 + 145946*x^11 + 4350864*x^10 -6270766*x^9 + 128632882*x^8 + 923423649*x^7 + 14261276064*x^6 + 27069810066*x^5 + 314343923886*x^4 -577151681967*x^3 + 4668327599346*x^2 -8735669543583*x + 7131992195241)*(x^2 -16*x + 56)^2;
528
529
T[32,2]=(x^2 + 2*x + 2)*(x^8 + 4*x^7 + 6*x^6 + 4*x^5 + 2*x^4 + 8*x^3 + 24*x^2 + 32*x + 16)*(x^2 + 2)^2*(x )^3;
530
T[32,3]=(x^4 + 2*x^2 + 4*x + 2)*(x^8 + 4*x^7 + 8*x^6 -32*x^4 -24*x^3 + 96*x^2 -16*x + 4)*(x )*(x^2 + 2*x + 2)^2;
531
T[32,5]=(x + 2)*(x^4 + 4*x^3 + 6*x^2 + 28*x + 98)*(x^2 + 2*x + 2)^2*(x^4 + 2*x^2 -4*x + 2)^2;
532
T[32,7]=(x^8 + 8*x^7 + 32*x^6 + 48*x^5 + 56*x^4 + 224*x^3 + 1152*x^2 + 1344*x + 784)*(x )*(x^2 -2*x + 2)^2*(x^2 + 4)^2;
533
T[32,11]=(x^4 + 8*x^3 + 18*x^2 -4*x + 2)*(x^8 -4*x^7 + 8*x^6 -64*x^5 + 224*x^4 + 56*x^3 + 160*x^2 -48*x + 4)*(x )*(x^2 -2*x + 2)^2;
534
T[32,13]=(x -6)*(x^4 -4*x^3 + 6*x^2 -4*x + 2)*(x^8 + 8*x^7 + 36*x^6 + 104*x^5 + 200*x^4 + 448*x^3 + 2520*x^2 -8528*x + 6724)*(x^2 + 2*x + 2)^2;
535
T[32,17]=(x -2)*(x^8 + 64*x^6 + 1056*x^4 + 5120*x^2 + 256)*(x^2 + 8)^2*(x + 2)^4;
536
T[32,19]=(x^4 + 8*x^3 + 18*x^2 + 68*x + 578)*(x^8 -4*x^7 -8*x^6 + 48*x^5 + 32*x^4 -168*x^3 + 832*x^2 -336*x + 196)*(x )*(x^2 -6*x + 18)^2;
537
T[32,23]=(x^4 -12*x^3 + 72*x^2 -24*x + 4)*(x^8 + 8*x^7 + 32*x^6 + 16*x^5 -8*x^4 -32*x^3 + 128*x^2 -64*x + 16)*(x )*(x^2 + 36)^2;
538
T[32,29]=(x + 10)*(x^4 + 4*x^3 + 6*x^2 + 28*x + 98)*(x^8 -12*x^6 + 168*x^5 + 72*x^4 -6256*x^3 + 17272*x^2 + 17360*x + 188356)*(x^2 -6*x + 18)^2;
539
T[32,31]=(x )*(x + 4)^4*(x + 8)^4*(x^2 -8*x + 8)^4;
540
T[32,37]=(x + 2)*(x^4 -4*x^3 + 6*x^2 -4*x + 2)*(x^8 + 8*x^7 -44*x^6 -168*x^5 + 3464*x^4 -20640*x^3 + 59320*x^2 -67056*x + 64516)*(x^2 -6*x + 18)^2;
541
T[32,41]=(x -10)*(x^4 + 12*x^3 + 72*x^2 + 24*x + 4)*(x^8 -8*x^7 + 32*x^6 + 240*x^5 + 968*x^4 -416*x^3 + 1152*x^2 + 7872*x + 26896)*(x )^4;
542
T[32,43]=(x^4 -16*x^3 + 162*x^2 -868*x + 1922)*(x^8 + 12*x^7 + 56*x^6 + 256*x^5 + 1760*x^4 + 4856*x^3 + 5888*x^2 + 12816*x + 31684)*(x )*(x^2 -10*x + 50)^2;
543
T[32,47]=(x^4 + 136*x^2 + 16)*(x^8 + 64*x^6 + 544*x^4 + 1024*x^2 + 256)*(x )*(x -8)^4;
544
T[32,53]=(x -14)*(x^4 -4*x^3 + 54*x^2 + 140*x + 98)*(x^8 -8*x^7 + 100*x^6 -1272*x^5 + 9800*x^4 -47328*x^3 + 147160*x^2 -238800*x + 158404)*(x^2 + 10*x + 50)^2;
545
T[32,59]=(x^4 + 16*x^3 + 114*x^2 + 460*x + 1058)*(x^8 + 20*x^7 + 136*x^6 + 528*x^5 + 5408*x^4 + 20712*x^3 + 44896*x^2 + 211728*x + 643204)*(x )*(x^2 + 6*x + 18)^2;
546
T[32,61]=(x + 10)*(x^4 -4*x^3 + 6*x^2 -4*x + 2)*(x^8 -24*x^7 + 132*x^6 + 648*x^5 + 72*x^4 + 6336*x^3 + 34968*x^2 -24720*x + 42436)*(x^2 + 18*x + 162)^2;
547
T[32,67]=(x^4 + 8*x^3 + 18*x^2 + 68*x + 578)*(x^8 + 36*x^7 + 504*x^6 + 3456*x^5 + 18144*x^4 + 68040*x^3 + 233280*x^2 + 734832*x + 1285956)*(x )*(x^2 + 10*x + 50)^2;
548
T[32,71]=(x^4 + 12*x^3 + 72*x^2 + 24*x + 4)*(x^8 + 24*x^7 + 288*x^6 + 1200*x^5 + 10232*x^4 + 173472*x^3 + 1936512*x^2 + 9060672*x + 21196816)*(x )*(x^2 + 100)^2;
549
T[32,73]=(x + 6)*(x^8 + 32*x^7 + 512*x^6 + 4672*x^5 + 26504*x^4 + 88192*x^3 + 165888*x^2 + 112896*x + 38416)*(x^2 + 16)^2*(x^2 -14*x + 98)^2;
550
T[32,79]=(x^8 + 512*x^6 + 78880*x^4 + 4775936*x^2 + 99361024)*(x^2 + 36)^2*(x )^5;
551
T[32,83]=(x^4 -16*x^3 + 114*x^2 -460*x + 1058)*(x^8 -20*x^7 + 184*x^6 + 304*x^5 -22752*x^4 + 131864*x^3 + 1548544*x^2 -16837456*x + 138250564)*(x )*(x^2 + 2*x + 2)^2;
552
T[32,89]=(x -10)*(x^4 -12*x^3 + 72*x^2 + 552*x + 2116)*(x^8 + 16*x^7 + 128*x^6 + 672*x^5 + 14024*x^4 + 209472*x^3 + 1782272*x^2 + 7786112*x + 17007376)*(x^2 + 16)^2;
553
T[32,97]=(x -18)*(x^2 + 20*x + 28)^2*(x^4 -16*x^3 + 40*x^2 + 288*x -992)^2*(x + 2)^4;
554
555
T[33,2]=(x -1)*(x^4 + 3*x^3 + 4*x^2 + 2*x + 1)*(x^4 + x^3 + 6*x^2 -4*x + 1)*(x^8 + 5*x^6 + 10*x^4 + 25)*(x + 2)^2*(x )^2;
556
T[33,3]=(x + 1)*(x^2 -x + 3)*(x^2 + x + 3)*(x^4 + x^3 + x^2 + x + 1)*(x^4 -x^3 + x^2 -x + 1)*(x^8 + 6*x^7 + 13*x^6 + 10*x^5 + x^4 + 30*x^3 + 117*x^2 + 162*x + 81);
557
T[33,5]=(x + 2)*(x^2 + 11)*(x^4 + x^3 + 6*x^2 -4*x + 1)*(x^4 + 3*x^3 + 4*x^2 + 2*x + 1)*(x^8 -11*x^6 + 46*x^4 + 4*x^2 + 1)*(x -1)^2;
558
T[33,7]=(x -4)*(x^4 + 3*x^3 + 9*x^2 + 27*x + 81)*(x^4 -x^3 + x^2 -x + 1)*(x + 2)^2*(x^4 + 5*x^3 + 5*x^2 -5*x + 5)^2*(x )^2;
559
T[33,11]=(x^2 + 11)*(x^4 + 11*x^3 + 51*x^2 + 121*x + 121)*(x^4 -9*x^3 + 41*x^2 -99*x + 121)*(x^8 + 19*x^6 + 301*x^4 + 2299*x^2 + 14641)*(x -1)^3;
560
T[33,13]=(x + 2)*(x^4 + 9*x^3 + 31*x^2 -11*x + 121)*(x^4 -7*x^3 + 19*x^2 -3*x + 1)*(x -4)^2*(x^4 + 5*x^3 + 5*x^2 -5*x + 5)^2*(x )^2;
561
T[33,17]=(x^4 -12*x^3 + 54*x^2 + 27*x + 81)*(x^4 -2*x^3 + 4*x^2 -3*x + 1)*(x^8 + 250*x^4 + 3125*x^2 + 15625)*(x )^2*(x + 2)^3;
562
T[33,19]=(x^4 + 10*x^3 + 40*x^2 + 25*x + 25)^2*(x^4 -10*x^3 + 50*x^2 -125*x + 125)^2*(x )^5;
563
T[33,23]=(x -8)*(x^2 + 11)*(x + 1)^2*(x^2 + 4*x -1)^2*(x^2 + 2*x -19)^2*(x^4 + 42*x^2 + 121)^2;
564
T[33,29]=(x + 6)*(x^4 + 10*x^3 + 60*x^2 + 200*x + 400)*(x^4 -6*x^3 + 36*x^2 -216*x + 1296)*(x^8 + 160*x^4 + 1600*x^2 + 6400)*(x )^4;
565
T[33,31]=(x + 8)*(x^4 + 12*x^3 + 94*x^2 + 403*x + 961)*(x^4 -8*x^3 + 34*x^2 -77*x + 121)*(x -5)^2*(x -7)^2*(x^4 + 10*x^3 + 40*x^2 + 25*x + 25)^2;
566
T[33,37]=(x -6)*(x^4 + 3*x^3 + 19*x^2 + 7*x + 1)*(x^4 -9*x^3 + 31*x^2 + 11*x + 121)*(x -3)^2*(x + 7)^2*(x^4 + 3*x^3 + 9*x^2 + 27*x + 81)^2;
567
T[33,41]=(x + 2)*(x^4 + 3*x^3 + 19*x^2 + 7*x + 1)*(x^4 -23*x^3 + 249*x^2 -1207*x + 5041)*(x^8 -5*x^6 + 85*x^4 + 75*x^2 + 25)*(x + 8)^2*(x )^2;
568
T[33,43]=(x + 6)^2*(x^2 -8*x + 11)^2*(x^2 -45)^2*(x^4 + 50*x^2 + 125)^2*(x )^3;
569
T[33,47]=(x^2 + 44)*(x^4 + 3*x^3 + 4*x^2 + 2*x + 1)*(x^4 -17*x^3 + 114*x^2 -88*x + 121)*(x^8 -79*x^6 + 3966*x^4 -163724*x^2 + 13845841)*(x -8)^3;
570
T[33,53]=(x -6)*(x^2 + 176)*(x^4 -6*x^3 + 76*x^2 -781*x + 5041)*(x^4 -4*x^3 + 6*x^2 + x + 1)*(x^8 -36*x^6 + 486*x^4 + 729*x^2 + 6561)*(x + 6)^2;
571
T[33,59]=(x + 4)*(x^2 + 11)*(x^4 + 20*x^3 + 190*x^2 + 825*x + 3025)*(x^4 + 6*x^3 + 76*x^2 + 781*x + 5041)*(x^8 + 4*x^6 + 46*x^4 -11*x^2 + 1)*(x -5)^2;
572
T[33,61]=(x -6)*(x^4 -3*x^3 + 54*x^2 + 108*x + 81)*(x^4 + 21*x^3 + 306*x^2 + 2376*x + 9801)*(x -12)^2*(x^4 + 5*x^3 + 125)^2*(x )^2;
573
T[33,67]=(x + 4)*(x + 13)^2*(x + 7)^2*(x^2 + 3*x -9)^2*(x^2 -x -101)^2*(x^2 + x -61)^4;
574
T[33,71]=(x^2 + 275)*(x^4 + 27*x^3 + 324*x^2 + 1458*x + 6561)*(x^4 -15*x^3 + 190*x^2 -1100*x + 3025)*(x^8 -155*x^6 + 9150*x^4 + 60500*x^2 + 9150625)*(x )*(x + 3)^2;
575
T[33,73]=(x + 14)*(x^4 -14*x^3 + 136*x^2 -704*x + 1936)*(x^4 -6*x^3 + 16*x^2 -16*x + 16)*(x -4)^2*(x^4 + 2560*x + 20480)^2*(x )^2;
576
T[33,79]=(x + 4)*(x^4 + 11*x^3 + 121*x^2 + 1331*x + 14641)*(x^4 -5*x^3 + 85*x^2 + 75*x + 25)*(x + 10)^2*(x^4 -25*x^3 + 225*x^2 -855*x + 1805)^2*(x )^2;
577
T[33,83]=(x -12)*(x^4 -21*x^3 + 171*x^2 -81*x + 81)*(x^4 -13*x^3 + 69*x^2 -77*x + 121)*(x^8 + 315*x^6 + 37285*x^4 -546325*x^2 + 70644025)*(x + 6)^2*(x )^2;
578
T[33,89]=(x + 6)*(x^2 + 275)*(x -15)^2*(x^2 + 12*x + 31)^2*(x^2 -10*x + 5)^2*(x^4 + 90*x^2 + 25)^2;
579
T[33,97]=(x -2)*(x^4 -3*x^3 + 54*x^2 + 108*x + 81)*(x^4 + 33*x^3 + 634*x^2 + 6752*x + 44521)*(x + 7)^2*(x -17)^2*(x^4 -3*x^3 + 34*x^2 -232*x + 841)^2;
580
581
T[34,2]=(x -1)*(x^2 + x + 2)*(x^4 + 1)*(x^8 + 4*x^7 + 8*x^6 + 12*x^5 + 17*x^4 + 24*x^3 + 32*x^2 + 32*x + 16)*(x + 1)^2*(x^2 + 1)^2;
582
T[34,3]=(x + 2)*(x^2 + 2*x + 2)*(x^2 + 8)*(x^4 + 2*x^2 -4*x + 2)*(x^4 + 4*x^3 + 4*x^2 + 8)^2*(x )^4;
583
T[34,5]=(x^2 + 8)*(x^2 + 2*x + 2)*(x^2 -4*x + 8)*(x^4 + 8*x^3 + 24*x^2 + 32*x + 32)*(x )*(x + 2)^2*(x^4 + 2*x^2 + 4*x + 2)^2;
584
T[34,7]=(x + 4)*(x^2 + 4*x + 8)*(x^4 + 8*x^2 -32*x + 32)*(x -4)^2*(x^4 + 4*x^3 + 4*x^2 + 8)^2*(x )^4;
585
T[34,11]=(x -6)*(x^2 + 8)*(x^2 -2*x + 2)*(x^2 + 8*x + 32)*(x^4 -4*x^3 + 22*x^2 -12*x + 2)*(x^4 + 4*x^3 + 12*x^2 + 16*x + 8)^2*(x )^2;
586
T[34,13]=(x^4 + 24*x^2 + 16)*(x + 2)^2*(x -4)^2*(x + 6)^2*(x -2)^3*(x^2 + 2)^4;
587
T[34,17]=(x + 1)*(x^2 + 2*x + 17)*(x^2 + 6*x + 17)*(x^2 -8*x + 17)*(x^4 + 16*x^2 + 289)*(x -1)^2*(x^4 + 2*x^2 + 289)^2;
588
T[34,19]=(x^2 + 16)^2*(x^4 -8*x^3 + 32*x^2 -32*x + 16)^3*(x + 4)^5;
589
T[34,23]=(x^2 -8*x + 32)*(x^2 + 32)*(x^4 + 16*x^3 + 96*x^2 + 256*x + 512)*(x -4)^2*(x^4 -4*x^3 + 12*x^2 -112*x + 392)^2*(x )^3;
590
T[34,29]=(x^2 + 8)*(x^2 + 4*x + 8)*(x^2 + 6*x + 18)*(x^4 + 8*x^2 + 32*x + 32)*(x )*(x -6)^2*(x^4 + 4*x^3 + 22*x^2 + 12*x + 2)^2;
591
T[34,31]=(x + 4)*(x^2 -12*x + 72)*(x^2 + 8*x + 32)*(x^4 + 8*x^2 -32*x + 32)*(x -4)^2*(x^4 + 12*x^3 + 108*x^2 + 432*x + 648)^2*(x )^2;
592
T[34,37]=(x + 4)*(x^2 -6*x + 18)*(x^2 + 72)*(x^4 + 8*x^3 + 16*x^2 + 128)*(x + 2)^2*(x^4 + 50*x^2 + 500*x + 1250)^2*(x )^2;
593
T[34,41]=(x -6)*(x^2 + 32)*(x^4 -16*x^3 + 66*x^2 -196*x + 4802)*(x + 6)^2*(x^2 -2*x + 2)^2*(x^4 + 4*x^3 + 54*x^2 -140*x + 98)^2;
594
T[34,43]=(x -8)*(x^2 + 16)*(x^2 + 36)*(x^4 -12*x^3 + 72*x^2 + 216*x + 324)*(x -4)^2*(x + 4)^2*(x^4 + 8*x^3 + 32*x^2 + 32*x + 16)^2;
595
T[34,47]=(x^4 + 96*x^2 + 256)*(x^4 + 144*x^2 + 3136)^2*(x -8)^4*(x )^5;
596
T[34,53]=(x + 6)*(x^2 + 36)*(x^2 + 16)*(x^4 -8*x^3 + 32*x^2 -32*x + 16)*(x -6)^4*(x^2 + 2*x + 2)^4;
597
T[34,59]=(x^2 + 16)*(x^2 + 36)*(x^4 + 4*x^3 + 8*x^2 -8*x + 4)*(x )*(x -12)^2*(x + 12)^2*(x^4 + 1296)^2;
598
T[34,61]=(x + 4)*(x^2 + 18*x + 162)*(x^2 + 72)*(x^2 + 8*x + 32)*(x^4 -16*x^3 + 96*x^2 -256*x + 512)*(x + 10)^2*(x^4 + 50*x^2 + 500*x + 1250)^2;
599
T[34,67]=(x -8)*(x + 12)^2*(x + 2)^2*(x -4)^2*(x + 4)^2*(x^2 + 12*x + 34)^2*(x^2 -8*x + 8)^4;
600
T[34,71]=(x^2 + 32)*(x^4 + 8*x^3 + 16*x^2 + 128)*(x )*(x + 4)^2*(x^2 + 8*x + 32)^2*(x^4 -20*x^3 + 100*x^2 + 5000)^2;
601
T[34,73]=(x -2)*(x^2 -10*x + 50)*(x^2 + 2*x + 2)*(x^4 + 98*x^2 + 1372*x + 4802)*(x + 6)^2*(x^4 + 28*x^3 + 294*x^2 + 1372*x + 4802)^2*(x )^2;
602
T[34,79]=(x -8)*(x^2 + 288)*(x^2 -16*x + 128)*(x^2 + 16*x + 128)*(x^4 + 8*x^3 + 48*x^2 + 128*x + 128)*(x -12)^2*(x^4 + 4*x^3 + 12*x^2 + 112*x + 392)^2;
603
T[34,83]=(x^2 + 16)*(x^2 + 196)*(x^4 -12*x^3 + 72*x^2 -168*x + 196)*(x )*(x + 12)^2*(x + 4)^2*(x^4 -16*x^3 + 128*x^2 + 64*x + 16)^2;
604
T[34,89]=(x + 6)*(x^4 + 228*x^2 + 196)*(x -10)^2*(x -6)^2*(x^4 + 132*x^2 + 3844)^2*(x )^4;
605
T[34,97]=(x -14)*(x^2 + 288)*(x^2 -6*x + 18)*(x^2 + 10*x + 50)*(x^4 + 12*x^3 + 54*x^2 + 108*x + 162)*(x -2)^2*(x^4 -24*x^3 + 242*x^2 -1316*x + 4418)^2;
606
607
T[35,2]=(x^2 + x -4)*(x^2 + 4)*(x^4 -2*x^3 + 5*x^2 -4*x + 1)*(x^4 + 2*x^3 + 5*x^2 -2*x + 1)*(x^4 -x^2 + 1)*(x^4 + 4*x^3 + 5*x^2 + 2*x + 1)*(x )*(x^2 + 2*x + 2)^2;
608
T[35,3]=(x -1)*(x^2 + x -4)*(x^2 + 1)*(x^4 + 25)*(x^4 + 2*x^3 + 5*x^2 -2*x + 1)*(x^4 + 4*x^3 + 5*x^2 + 2*x + 1)*(x^4 -x^2 + 1)*(x^4 + 2*x^3 + 5*x^2 + 4*x + 1);
609
T[35,5]=(x + 1)*(x^2 + 4*x + 5)*(x^4 + 2*x^3 -x^2 + 10*x + 25)*(x^4 + 4*x^3 + 11*x^2 + 20*x + 25)*(x^4 -4*x^3 + 11*x^2 -20*x + 25)*(x^4 + 25)*(x -1)^2*(x^2 + x + 1)^2;
610
T[35,7]=(x -1)*(x^2 + 1)*(x^4 -13*x^2 + 49)*(x^4 -4*x^3 + 8*x^2 -28*x + 49)*(x^4 -2*x^3 -3*x^2 -14*x + 49)*(x^4 + 11*x^2 + 49)*(x + 1)^2*(x^2 + 5*x + 7)^2;
611
T[35,11]=(x^2 -x -4)*(x^4 + 4*x^3 + 20*x^2 -16*x + 16)*(x^4 -2*x^3 + 6*x^2 + 4*x + 4)^2*(x + 3)^3*(x + 1)^4*(x )^4;
612
T[35,13]=(x -5)*(x^2 -5*x + 2)*(x^2 + 1)*(x^4 + 25)*(x^2 + 4)^2*(x^2 + 4*x + 8)^2*(x^2 -4*x + 8)^2*(x^2 + 4*x -4)^2;
613
T[35,17]=(x -3)*(x^2 + 49)*(x^2 + 5*x + 2)*(x^4 + 25)*(x^4 -4*x^3 + 20*x^2 -32*x + 16)*(x^4 + 4*x^3 + 20*x^2 -16*x + 16)*(x^4 -4*x^2 + 16)*(x^4 -8*x^3 + 20*x^2 -16*x + 16);
614
T[35,19]=(x -2)*(x^2 + 6*x -8)*(x^4 -2*x^3 + 6*x^2 + 4*x + 4)*(x^4 + 2*x^3 + 6*x^2 -4*x + 4)*(x^4 + 8*x^2 + 64)*(x^2 -10)^2*(x^2 -6*x + 36)^2*(x )^2;
615
T[35,23]=(x + 6)*(x^2 + 36)*(x^2 + 2*x -16)*(x^4 -14*x^3 + 53*x^2 -4*x + 1)*(x^4 + 4*x^3 + 53*x^2 + 14*x + 1)*(x^4 -9*x^2 + 81)*(x^4 -2*x^3 + 5*x^2 + 2*x + 1)*(x^2 -4*x + 8)^2;
616
T[35,29]=(x -3)*(x^2 -x -38)*(x -5)^2*(x + 7)^4*(x + 1)^4*(x^2 + 9)^6;
617
T[35,31]=(x + 4)*(x -2)^2*(x^2 -6*x + 36)^2*(x^2 + 10)^2*(x^2 + 2*x + 4)^2*(x^4 + 12*x^3 + 44*x^2 -48*x + 16)^2*(x )^2;
618
T[35,37]=(x -2)*(x^2 + 4)*(x^4 -12*x^3 + 72*x^2 -288*x + 576)*(x^4 + 12*x^3 + 72*x^2 + 288*x + 576)*(x^4 -64*x^2 + 4096)*(x -6)^2*(x^2 + 12*x + 72)^2*(x )^4;
619
T[35,41]=(x + 12)*(x^2 -2*x -16)*(x -2)^2*(x^2 + 10*x + 17)^2*(x^2 + 90)^2*(x^4 + 42*x^2 + 9)^2*(x -5)^4;
620
T[35,43]=(x + 10)*(x^2 + 16)*(x^2 -10*x + 8)*(x^2 -10*x + 23)^2*(x^2 + 49)^2*(x^2 + 6*x + 18)^2*(x^4 + 6*x^3 + 18*x^2 -198*x + 1089)^2;
621
T[35,47]=(x -9)*(x^2 + 9)*(x^2 + 5*x -32)*(x^4 -6*x^3 + 90*x^2 -108*x + 36)*(x^4 + 2025)*(x^4 -18*x^3 + 90*x^2 -36*x + 36)*(x^2 + 2*x + 4)^2*(x )^4;
622
T[35,53]=(x -12)*(x^2 + 2*x -16)*(x^2 + 36)*(x^4 -36*x^2 + 1296)*(x^4 -8*x^3 + 56*x^2 -64*x + 64)*(x^2 -2*x + 2)^2*(x^4 -10*x^3 + 50*x^2 -500*x + 2500)^2;
623
T[35,59]=(x^4 + 6*x^3 + 54*x^2 -108*x + 324)*(x^4 -8*x^3 + 120*x^2 + 448*x + 3136)*(x^4 -6*x^3 + 54*x^2 + 108*x + 324)*(x )*(x + 4)^2*(x + 10)^2*(x^2 -90)^2*(x^2 -10*x + 100)^2;
624
T[35,61]=(x -8)*(x^2 -6*x -144)*(x^4 -6*x^3 + 99*x^2 + 378*x + 3969)*(x + 8)^2*(x^2 + 7*x + 49)^2*(x^2 + 40)^2*(x^4 + 12*x^3 + 35*x^2 -156*x + 169)^2;
625
T[35,67]=(x + 4)*(x^2 + 4)*(x^2 -4*x -64)*(x^4 -8*x^3 + 137*x^2 -286*x + 169)*(x^4 + 22*x^3 + 137*x^2 + 104*x + 169)*(x^4 -25*x^2 + 625)*(x^4 + 22*x^3 + 365*x^2 + 2618*x + 14161)*(x^2 + 2*x + 2)^2;
626
T[35,71]=(x )*(x + 8)^2*(x -8)^2*(x^2 + 8*x -56)^2*(x + 2)^4*(