Here are the degree sequences for the factorization of the Shoup polynomials F[n] modulo p[n], where F[n]=a[0]*x^n+a[1]*x^(n-1)+...+a[n-1]*x+a[n] with a[0]=1, a[i+1]=a[i]^2+1 and p[n] is the next prime greater or equal to floor(2^(n-2)*Pi) (p[n] has exactly n bits). For example here is the MuPAD code to generate F[n]:

F := proc(n) local p,DIGITS,a,i;
begin
DIGITS:=ceil(0.31*n+1);
p:=nextprime(floor(PI*2^(n-2)));
a[0]:=1;
for i from 0 to n-1 do a[i+1]:=(a[i]^2+1) mod p end_for;
poly(_plus(a[i]*x^(n-i)$hold(i)=0..n),IntMod(p))
end_proc:

and F[6]=poly(x^6+2*x^5+5*x^4+26*x^3-12*x^2-14*x-15,[x],IntMod(53)).

1: [1]
2: [2]
3: [3]
4: [1, 3]
5: [1, 1, 1, 2]
6: [2, 4]
7: [2, 2, 3]
8: [1, 2, 2, 3]
9: [1, 1, 1, 6]
10: [1, 9]
11: [3, 3, 5]
12: [1, 2, 4, 5]
13: [1, 2, 2, 8]
14: [3, 3, 8]
15: [1, 2, 4, 4, 4]
16: [1, 6, 9]
17: [1, 1, 4, 5, 6]
18: [1, 1, 6, 10]
19: [1, 1, 1, 5, 5, 6]
20: [2, 3, 7, 8]
21: [7, 14]
22: [1, 1, 20]
23: [1, 4, 18]
24: [1, 23]
25: [1, 2, 5, 17]
26: [2, 3, 7, 14]
27: [1, 5, 10, 11]
28: [1, 4, 4, 19]
29: [1, 2, 2, 6, 6, 12]
30: [1, 1, 1, 2, 4, 4, 17]
31: [1, 1, 2, 8, 19]
32: [1, 1, 2, 6, 8, 14]
33: [2, 4, 8, 8, 11]
34: [34]
35: [1, 1, 5, 9, 9, 10]
36: [9, 27]
37: [1, 1, 1, 1, 8, 9, 16]
38: [2, 10, 26]
39: [2, 3, 5, 11, 18]
40: [1, 1, 8, 30]
41: [3, 4, 11, 23]
42: [1, 4, 7, 15, 15]
43: [1, 4, 18, 20]
44: [16, 28]
45: [1, 2, 4, 38]
46: [1, 1, 3, 10, 11, 20]
47: [47]
48: [1, 2, 5, 40]
49: [2, 8, 11, 28]
50: [1, 2, 47]
51: [1, 2, 3, 3, 8, 9, 25]
52: [1, 2, 23, 26]
53: [1, 1, 3, 48]
54: [1, 3, 3, 10, 37]
55: [3, 52]
56: [1, 2, 3, 6, 22, 22]
57: [1, 3, 5, 48]
58: [12, 46]
59: [1, 3, 8, 11, 12, 24]
60: [1, 1, 2, 2, 6, 7, 41]
61: [2, 4, 55]
62: [1, 1, 3, 19, 38]
63: [1, 7, 55]
64: [1, 4, 6, 7, 17, 29]
65: [1, 3, 4, 6, 16, 35]
66: [1, 2, 4, 16, 43]
67: [1, 1, 2, 2, 17, 44]
68: [3, 3, 12, 17, 33]
69: [1, 2, 6, 9, 10, 14, 27]
70: [1, 2, 7, 12, 12, 36]
71: [1, 2, 6, 8, 23, 31]
72: [1, 2, 2, 6, 11, 14, 36]
73: [1, 2, 31, 39]
74: [1, 1, 2, 2, 9, 27, 32]
75: [2, 3, 5, 18, 47]
76: [1, 1, 1, 1, 17, 55]
77: [77]
78: [5, 17, 56]
79: [1, 1, 6, 18, 53]
80: [2, 3, 24, 51]
81: [3, 4, 6, 10, 16, 20, 22]
82: [1, 2, 13, 66]
83: [25, 58]
84: [1, 2, 2, 13, 66]
85: [1, 3, 17, 24, 40]
86: [1, 7, 9, 14, 15, 40]
87: [1, 1, 1, 2, 3, 4, 4, 5, 66]
88: [1, 3, 10, 32, 42]
89: [1, 2, 2, 3, 6, 14, 61]
90: [1, 3, 4, 6, 20, 27, 29]
91: [5, 9, 9, 26, 42]
92: [1, 15, 21, 55]
93: [1, 3, 15, 26, 48]
94: [1, 2, 3, 4, 9, 16, 24, 35]
95: [4, 6, 14, 19, 21, 31]
96: [1, 1, 2, 92]
97: [3, 10, 10, 24, 50]
98: [1, 1, 5, 6, 85]
99: [10, 16, 73]
100: [1, 3, 5, 5, 86]
101: [1, 1, 2, 4, 14, 16, 63]
102: [1, 1, 4, 96]
103: [2, 4, 5, 92]
104: [18, 86]
105: [2, 2, 5, 96]
106: [2, 5, 99]
107: [2, 2, 10, 93]
108: [1, 1, 18, 35, 53]
109: [8, 22, 25, 54]
110: [1, 2, 7, 37, 63]
111: [2, 14, 26, 69]
112: [1, 14, 15, 15, 67]
113: [1, 1, 6, 7, 7, 10, 28, 53]
114: [3, 18, 93]
115: [1, 1, 113]
116: [1, 2, 4, 6, 6, 28, 34, 35]
117: [1, 2, 5, 5, 7, 20, 77]
118: [1, 1, 1, 4, 111]
119: [2, 2, 8, 37, 70]
120: [1, 4, 4, 5, 12, 34, 60]
121: [3, 14, 21, 83]
122: [1, 5, 27, 89]
123: [1, 7, 29, 86]
124: [2, 2, 25, 31, 64]
125: [1, 1, 2, 5, 6, 10, 100]
126: [1, 125]
127: [2, 3, 21, 24, 77]
128: [2, 2, 124]
129: [1, 4, 14, 23, 26, 27, 34]
130: [1, 1, 5, 27, 33, 63]
131: [1, 1, 1, 1, 5, 7, 10, 12, 16, 20, 25, 32]
132: [1, 6, 13, 112]
133: [2, 8, 13, 31, 33, 46]
134: [6, 7, 9, 11, 101]
135: [1, 1, 8, 13, 112]
136: [1, 9, 10, 116]
137: [3, 6, 16, 18, 19, 19, 56]
138: [6, 7, 14, 111]
139: [3, 7, 8, 15, 44, 62]
140: [1, 2, 12, 19, 25, 40, 41]
141: [40, 101]
142: [2, 2, 3, 4, 4, 11, 29, 87]
143: [1, 4, 7, 13, 118]
144: [1, 10, 18, 22, 43, 50]
145: [1, 1, 2, 3, 20, 118]
146: [2, 13, 17, 18, 23, 35, 38]
147: [1, 1, 42, 48, 55]
148: [4, 5, 21, 44, 74]
149: [2, 11, 22, 114]
150: [1, 6, 7, 18, 118]
151: [4, 7, 7, 11, 11, 111]
152: [1, 2, 3, 15, 19, 22, 90]
153: [1, 2, 3, 5, 10, 13, 37, 82]
154: [1, 1, 6, 9, 17, 20, 27, 32, 41]
155: [1, 9, 32, 113]
156: [1, 3, 12, 17, 123]
157: [1, 1, 3, 14, 138]
158: [3, 155]
159: [2, 8, 149]
160: [1, 1, 1, 4, 5, 13, 25, 30, 80]
161: [1, 2, 8, 20, 36, 94]
162: [1, 1, 12, 66, 82]
163: [3, 32, 128]
164: [2, 36, 126]
165: [1, 5, 20, 29, 45, 65]
166: [1, 1, 2, 7, 26, 129]
167: [1, 1, 165]
168: [2, 2, 2, 2, 18, 45, 97]
169: [1, 4, 4, 20, 22, 57, 61]
170: [3, 4, 6, 15, 17, 125]
171: [1, 1, 2, 5, 12, 150]
172: [2, 15, 20, 135]
173: [1, 1, 3, 5, 64, 99]
174: [1, 1, 4, 168]
175: [8, 35, 53, 79]
176: [38, 138]
177: [1, 4, 13, 21, 138]
178: [1, 3, 6, 84, 84]
179: [1, 1, 15, 162]
180: [1, 2, 3, 9, 23, 142]
181: [2, 2, 29, 148]
182: [3, 5, 7, 8, 17, 21, 26, 95]
183: [1, 1, 2, 2, 2, 7, 9, 68, 91]
184: [1, 24, 40, 119]
185: [2, 3, 7, 11, 16, 17, 62, 67]
186: [1, 8, 13, 17, 34, 113]
187: [1, 2, 6, 37, 141]
188: [1, 1, 5, 181]
189: [10, 10, 28, 55, 86]
190: [1, 2, 2, 3, 6, 7, 12, 76, 81]
191: [1, 7, 17, 37, 129]
192: [6, 27, 159]
193: [4, 5, 8, 12, 18, 62, 84]
194: [1, 63, 130]
195: [2, 3, 5, 19, 36, 54, 76]
196: [5, 7, 12, 28, 33, 111]
197: [1, 1, 2, 4, 4, 5, 26, 154]
198: [7, 20, 29, 30, 112]
199: [2, 2, 46, 149]
200: [8, 9, 183]
201: [1, 1, 2, 5, 8, 39, 145]
202: [17, 185]
203: [2, 3, 5, 7, 28, 44, 114]
204: [1, 2, 4, 22, 175]
205: [15, 23, 167]
206: [1, 2, 9, 194]
207: [2, 3, 6, 88, 108]
208: [1, 2, 73, 132]
209: [9, 12, 13, 65, 110]
210: [2, 3, 6, 7, 44, 45, 51, 52]
211: [1, 1, 13, 77, 119]
212: [1, 2, 4, 5, 8, 11, 22, 43, 116]
213: [1, 1, 2, 3, 5, 7, 7, 62, 125]
214: [1, 5, 11, 13, 18, 23, 35, 108]
215: [1, 1, 3, 8, 202]
216: [1, 2, 4, 209]
217: [1, 1, 15, 57, 143]
218: [4, 5, 96, 113]
219: [1, 16, 202]
220: [1, 5, 11, 15, 40, 46, 102]
221: [2, 2, 5, 39, 52, 121]
222: [1, 6, 19, 41, 59, 96]
223: [2, 15, 24, 27, 155]
224: [1, 1, 1, 1, 1, 3, 10, 13, 22, 171]
225: [2, 2, 82, 139]
226: [2, 2, 2, 7, 8, 15, 68, 122]
227: [2, 31, 194]
228: [1, 2, 2, 36, 66, 121]
229: [1, 1, 1, 2, 6, 26, 27, 165]
230: [1, 5, 6, 9, 12, 12, 56, 129]
231: [1, 2, 2, 8, 10, 16, 192]
232: [1, 1, 3, 18, 46, 65, 98]
233: [1, 1, 27, 89, 115]
234: [1, 5, 8, 10, 90, 120]
235: [3, 5, 9, 26, 28, 46, 53, 65]
236: [1, 2, 2, 4, 6, 6, 8, 18, 56, 133]
237: [1, 11, 22, 23, 180]
238: [1, 3, 10, 11, 40, 48, 55, 70]
239: [1, 8, 9, 15, 25, 181]
240: [1, 8, 8, 67, 67, 89]
241: [3, 3, 16, 20, 20, 45, 64, 70]
242: [1, 2, 2, 3, 3, 12, 38, 69, 112]
243: [1, 1, 3, 6, 9, 61, 162]
244: [2, 3, 33, 72, 134]
245: [1, 9, 13, 98, 124]
246: [1, 10, 13, 41, 66, 115]
247: [1, 8, 16, 222]
248: [1, 1, 2, 13, 31, 84, 116]
249: [2, 5, 9, 24, 42, 59, 108]
250: [2, 3, 8, 49, 60, 128]
251: [3, 11, 18, 26, 36, 40, 117]
252: [1, 7, 39, 205]
253: [1, 1, 7, 244]
254: [1, 1, 1, 22, 27, 88, 114]
255: [10, 21, 22, 23, 27, 152]
256: [1, 1, 1, 1, 2, 5, 102, 143]
257: [1, 1, 1, 2, 252]
258: [1, 9, 15, 22, 25, 88, 98]
259: [34, 112, 113]
260: [2, 2, 4, 14, 17, 36, 44, 141]
261: [1, 2, 5, 10, 54, 85, 104]
262: [3, 4, 13, 25, 26, 191]
263: [9, 10, 11, 59, 174]
264: [1, 1, 2, 11, 21, 55, 173]
265: [1, 2, 2, 3, 4, 6, 11, 11, 19, 21, 24, 73, 88]
266: [1, 2, 3, 4, 14, 72, 170]
267: [15, 21, 22, 209]
268: [2, 3, 5, 120, 138]
269: [5, 46, 66, 67, 85]
270: [5, 14, 31, 32, 42, 146]
271: [3, 4, 32, 62, 170]
272: [31, 97, 144]
273: [1, 8, 15, 24, 91, 134]
274: [1, 4, 7, 9, 12, 39, 97, 105]
275: [1, 3, 37, 234]
276: [1, 1, 1, 2, 3, 4, 12, 21, 52, 73, 106]
277: [1, 1, 15, 16, 35, 38, 54, 117]
278: [4, 9, 25, 240]
279: [1, 1, 1, 17, 117, 142]
280: [1, 1, 3, 3, 3, 3, 3, 12, 18, 22, 102, 109]
281: [1, 6, 7, 8, 25, 234]
282: [2, 3, 17, 83, 177]
283: [4, 4, 8, 12, 13, 87, 155]
284: [3, 11, 16, 91, 163]
285: [1, 11, 17, 22, 36, 45, 58, 95]
286: [1, 1, 18, 21, 31, 43, 50, 59, 62]
287: [1, 3, 110, 173]
288: [2, 4, 52, 103, 127]
289: [2, 2, 16, 25, 244]
290: [4, 24, 56, 100, 106]
291: [1, 4, 45, 66, 175]
292: [1, 5, 10, 14, 18, 70, 174]
293: [1, 17, 18, 80, 177]
294: [1, 3, 7, 13, 26, 244]
295: [4, 9, 15, 22, 51, 194]
296: [1, 4, 6, 7, 278]
297: [1, 2, 2, 4, 7, 9, 21, 25, 39, 41, 146]
298: [1, 13, 16, 25, 38, 71, 134]
299: [10, 18, 49, 222]
300: [3, 4, 10, 91, 192]
301: [18, 80, 203]
302: [1, 1, 53, 247]
303: [1, 4, 4, 6, 8, 18, 47, 49, 50, 116]
304: [4, 19, 24, 34, 90, 133]
305: [3, 5, 8, 11, 24, 108, 146]
306: [2, 8, 296]
307: [1, 1, 2, 10, 34, 57, 202]
308: [1, 4, 16, 30, 257]
309: [1, 1, 1, 4, 4, 9, 11, 21, 257]
310: [2, 3, 7, 62, 77, 159]
311: [1, 2, 35, 273]
312: [7, 11, 13, 14, 21, 27, 96, 123]
313: [4, 5, 5, 12, 52, 97, 138]
314: [2, 4, 18, 84, 100, 106]
315: [2, 3, 5, 6, 13, 40, 70, 79, 97]
316: [1, 1, 12, 302]
317: [2, 3, 16, 23, 83, 190]
318: [1, 3, 3, 3, 8, 63, 77, 160]
319: [1, 1, 5, 18, 123, 171]
320: [22, 25, 101, 172]
321: [2, 2, 2, 2, 3, 3, 6, 10, 10, 19, 79, 183]
322: [4, 6, 7, 29, 39, 73, 164]
323: [1, 1, 2, 30, 75, 214]
324: [1, 1, 1, 4, 5, 7, 7, 104, 194]
325: [10, 11, 13, 27, 45, 54, 165]
326: [1, 12, 18, 37, 78, 180]
327: [1, 1, 3, 11, 15, 53, 71, 172]
328: [2, 10, 316]
329: [1, 1, 1, 2, 8, 11, 305]
330: [1, 1, 10, 14, 34, 59, 211]
331: [2, 13, 85, 231]
332: [1, 4, 4, 12, 15, 20, 25, 36, 72, 143]
333: [1, 2, 5, 5, 27, 28, 28, 237]
334: [1, 2, 20, 39, 47, 225]
335: [2, 8, 325]
336: [1, 1, 8, 42, 58, 70, 156]
337: [9, 26, 33, 61, 208]
338: [1, 1, 6, 16, 83, 231]
339: [4, 31, 31, 273]
340: [1, 4, 4, 5, 6, 19, 20, 48, 59, 77, 97]
341: [1, 2, 6, 12, 21, 36, 100, 163]
342: [1, 1, 8, 8, 12, 312]
343: [1, 11, 12, 17, 302]
344: [1, 1, 1, 1, 5, 12, 26, 50, 98, 149]
345: [1, 1, 2, 3, 26, 26, 57, 229]
346: [1, 1, 1, 2, 2, 8, 8, 8, 9, 77, 93, 136]
347: [1, 3, 4, 7, 11, 122, 199]
348: [1, 5, 28, 64, 250]
349: [1, 3, 3, 14, 20, 35, 38, 63, 172]
350: [3, 4, 8, 105, 230]
351: [1, 2, 5, 8, 10, 102, 223]
352: [7, 81, 264]
353: [1, 1, 351]
354: [4, 8, 24, 54, 100, 164]
355: [1, 6, 16, 32, 55, 245]
356: [1, 14, 22, 39, 85, 195]
357: [1, 1, 2, 2, 6, 10, 20, 46, 74, 82, 113]
358: [2, 4, 19, 90, 243]
359: [4, 5, 6, 8, 24, 44, 84, 184]
360: [1, 1, 6, 46, 67, 97, 142]
361: [1, 9, 19, 26, 137, 169]
362: [2, 2, 3, 7, 348]
363: [1, 1, 2, 2, 3, 6, 15, 59, 120, 154]
364: [1, 2, 4, 5, 11, 16, 38, 43, 111, 133]
365: [1, 21, 22, 75, 95, 151]
366: [1, 31, 49, 98, 187]
367: [144, 223]
368: [20, 23, 43, 282]
369: [3, 3, 5, 8, 49, 301]
370: [1, 2, 2, 3, 6, 14, 134, 208]
371: [1, 3, 367]
372: [1, 1, 1, 2, 3, 4, 13, 14, 15, 19, 28, 35, 45, 191]
373: [1, 2, 8, 80, 133, 149]
374: [1, 3, 8, 14, 44, 48, 86, 170]
375: [2, 373]
376: [1, 1, 2, 5, 66, 97, 204]
377: [4, 15, 124, 234]
378: [1, 1, 10, 366]
379: [21, 42, 47, 119, 150]
380: [1, 2, 10, 156, 211]
381: [2, 4, 16, 20, 27, 312]
382: [1, 1, 3, 4, 118, 255]
383: [1, 2, 3, 13, 33, 127, 204]
384: [4, 9, 24, 67, 280]
385: [1, 39, 46, 299]
386: [19, 34, 64, 269]
387: [6, 7, 8, 22, 44, 63, 88, 149]
388: [1, 4, 9, 10, 11, 12, 47, 72, 97, 125]
389: [1, 3, 3, 18, 18, 34, 37, 275]
390: [4, 6, 6, 6, 138, 230]
391: [1, 2, 7, 7, 107, 267]
392: [1, 1, 4, 4, 18, 19, 38, 47, 260]
393: [1, 1, 1, 2, 4, 6, 8, 11, 39, 72, 248]
394: [2, 8, 40, 344]
395: [2, 3, 5, 7, 20, 77, 132, 149]
396: [3, 11, 39, 105, 116, 122]
397: [1, 2, 11, 13, 370]
398: [1, 9, 11, 14, 17, 19, 32, 51, 52, 90, 102]
399: [1, 398]
400: [1, 1, 2, 3, 54, 65, 274]
401: [8, 12, 381]
402: [2, 12, 34, 37, 64, 253]
403: [3, 7, 9, 77, 307]
404: [2, 3, 4, 7, 74, 127, 187]
405: [1, 1, 1, 3, 24, 25, 26, 103, 107, 114]
406: [2, 3, 3, 3, 4, 4, 35, 74, 278]
407: [2, 16, 21, 130, 238]
408: [1, 2, 2, 3, 25, 134, 241]
409: [9, 25, 167, 208]
410: [21, 22, 26, 45, 51, 56, 189]
411: [1, 1, 1, 2, 5, 21, 109, 128, 143]
412: [2, 3, 28, 160, 219]
413: [1, 4, 7, 94, 105, 202]
414: [1, 1, 1, 1, 1, 2, 2, 90, 315]
415: [4, 7, 10, 13, 19, 362]
416: [1, 4, 4, 6, 9, 44, 81, 128, 139]
417: [1, 7, 9, 10, 27, 363]
418: [1, 2, 2, 2, 4, 9, 53, 75, 270]
419: [12, 18, 21, 33, 91, 93, 151]
420: [1, 1, 6, 7, 11, 14, 28, 68, 73, 90, 121]
421: [1, 7, 17, 106, 290]
422: [1, 1, 2, 10, 87, 321]
423: [2, 5, 6, 12, 158, 240]
424: [1, 1, 2, 3, 3, 8, 8, 19, 29, 136, 214]
425: [1, 2, 2, 2, 2, 146, 270]
426: [2, 5, 5, 6, 14, 129, 265]
427: [4, 13, 14, 396]
428: [1, 1, 2, 2, 7, 40, 53, 153, 169]
429: [1, 5, 15, 40, 44, 324]
430: [2, 2, 2, 4, 158, 262]
431: [1, 4, 4, 5, 6, 27, 48, 51, 110, 175]
432: [1, 1, 4, 5, 191, 230]
433: [2, 4, 7, 9, 63, 348]
434: [1, 5, 23, 39, 366]
435: [1, 1, 5, 8, 35, 385]
436: [4, 22, 24, 36, 36, 141, 173]
437: [16, 84, 97, 104, 136]
438: [1, 6, 11, 36, 54, 112, 218]
439: [4, 21, 21, 185, 208]
440: [182, 258]
441: [11, 14, 16, 25, 128, 247]
442: [3, 5, 6, 6, 14, 178, 230]
443: [6, 9, 10, 31, 47, 155, 185]
444: [2, 29, 413]
445: [1, 2, 24, 52, 366]
446: [2, 10, 25, 30, 31, 34, 38, 38, 238]
447: [4, 5, 37, 70, 331]
448: [1, 2, 6, 14, 24, 35, 38, 99, 100, 129]
449: [2, 2, 2, 15, 56, 81, 121, 170]
450: [1, 5, 7, 11, 47, 58, 74, 98, 149]
451: [1, 4, 5, 54, 83, 84, 220]
452: [1, 52, 399]
453: [1, 1, 7, 15, 17, 412]
454: [1, 50, 178, 225]
455: [1, 3, 6, 19, 426]
456: [1, 7, 11, 22, 61, 103, 251]
457: [1, 1, 13, 18, 424]
458: [5, 9, 28, 416]
459: [1, 1, 2, 4, 6, 13, 47, 133, 252]
460: [2, 9, 12, 17, 88, 90, 95, 147]
461: [1, 1, 2, 9, 17, 27, 28, 36, 80, 260]
462: [1, 10, 98, 353]
463: [1, 1, 4, 6, 27, 78, 85, 261]
464: [1, 2, 24, 437]
465: [1, 3, 3, 4, 6, 7, 69, 89, 132, 151]
466: [1, 3, 4, 6, 11, 58, 67, 129, 187]
467: [3, 4, 17, 18, 28, 61, 336]
468: [1, 1, 2, 3, 6, 32, 37, 155, 231]
469: [1, 1, 3, 4, 4, 6, 13, 164, 273]
470: [2, 18, 450]
471: [1, 2, 2, 12, 17, 21, 33, 35, 348]
472: [1, 4, 17, 45, 162, 243]
473: [5, 211, 257]
474: [1, 1, 1, 11, 64, 396]
475: [4, 11, 23, 170, 267]
476: [13, 17, 27, 28, 391]
477: [2, 20, 20, 43, 109, 283]
478: [1, 1, 1, 4, 5, 12, 42, 80, 332]
479: [2, 5, 14, 20, 26, 48, 364]
480: [11, 24, 74, 145, 226]
481: [7, 38, 48, 64, 117, 207]
482: [1, 2, 2, 6, 11, 21, 23, 46, 370]
483: [2, 8, 12, 12, 183, 266]
484: [2, 3, 4, 5, 5, 32, 47, 51, 335]
485: [8, 16, 24, 437]
486: [1, 58, 162, 265]
487: [8, 18, 101, 360]
488: [2, 2, 4, 6, 8, 9, 22, 50, 165, 220]
489: [1, 5, 65, 418]
490: [1, 1, 2, 15, 58, 60, 107, 246]
491: [1, 34, 71, 126, 259]
492: [1, 1, 23, 35, 432]
493: [1, 1, 3, 6, 8, 8, 63, 403]
494: [16, 42, 436]
495: [1, 3, 6, 17, 104, 364]
496: [3, 3, 12, 19, 459]
497: [2, 3, 3, 4, 6, 7, 12, 156, 304]
498: [1, 4, 6, 19, 22, 194, 252]
499: [2, 7, 47, 198, 245]
500: [2, 2, 12, 177, 307]
512: [3, 3, 9, 497] according to Shoup
1024: [1, 2, 2, 5, 42, 42, 44, 49, 77, 120, 198, 443] according to Shoup
2048: [2, 28, 69, 884, 1065] according to Shoup