314 MR. G. T. BENNETT ON THE RESIDUES OE POWERS OF NUMBERS 
7ji = 8 + 7 ! = — (1 + 2i) (3 + 2i) N {m) = G5 (m) = 48 = 3 
H. E. = 12 X = X + 57Y (mod 65). 
= 1 -f 87 = (2 + i) (2 + 37 ) N {m) =65 $ [m) = 48 = 2'1 2^. 3 
H. E. = 12 X = X + 8Y (mod 65). 
m = 7 47 = — 7 (1 + 27 ) (2 + 37 ) N [m) — 65 {m) = 48 = 2~. 2^ 3 
PI. E. = 12 X = X + 47Y (mod 65). 
= 4 + 7i = (2 + 7 ) (3 + 27 ) N (m) =65 (P (m) = 48 = 2^. 21 3 
H. E. = 12 X = X + 18Y (mod 65). 
Generators 27, 2. 
0 
0 
0 
0 
1 
1 
1 
1 
2 
2 
2 
2 
3 
3 
3 
3 
4 
4 
4 
4 
5 
5 
5 
5 
(12) 
0 
1 
2 
3 
0 
1 
2 
3 
0 
1 
2 
3 
0 
1 
2 
3 
0 
1 
0 
3 
0 
1 
2 
3 
(4) 
1 
27 
14 
53 
2 
54 
28 
41 
4 
43 
5G 
17 
8 
21 
47 
34 
16 
42 
29 
3 
32 
19 
58 
6 ' 
0 
6 
G 
6 
7 
7 
7 
7 
8 
8 
8 
8 
9 
9 
9 
9 
10 
10 
10 
10 
11 
11 
11 
11 
(12) 
0 
1 
2 
3 
0 
1 
2 
3 
0 
1 
2 
3 
0 
1 
2 
3 
0 
1 
2 
3 
0 
1 
2 
3 
(4) 
G1 
38 
51 
12 
G3 
11 
37 
24 
G1 
22 
9 
48 
57 
44 
18 
31 
49 
23 
36 
62 
33 
46 
7 
59 
1 
2 
3 
4 
6 
7 
8 
9 
11 
12 
14 
16 
17 
18 
19 
21 
22 
23 
24 
27 
28 
29 
31 
32 
0 
1 
4 
2 
5 
11 
3 
8 
7 
6 
0 
4 
2 
9 
5 
3 
8 
10 
7 
0 
1 
4 
9 
5 
(V2) 
0 
0 
0 
fj 
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0 
C\ 
0 
2 
1 
3 
2 
0^ 
3 
2 
1 
1 
1 
1 
3 
1 
2 
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3 
0 
(4) 
33 
34 
36 
37 
38 
41 
42 
43 
44 
46 
47 
48 
49 
51 
53 
54 
56 
57 
58 
59 
61 
62 
63 
64 
11 
3 
10 
7 
6 
1 
4 
2 
9 
11 
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8 
10 
6 
0 
1 
2 
9 
5 
11 
8 
10 
r- 
/ 
6 
(12) 
0 
3 
2 
2 
1 
3 
1 
1 
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2 
3 
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2 
0 
2 
3 
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(4) 
