320 MR. G. T. BENNETT ON THE RESIDUES OF POWERS OF NUMBERS 
m = 8 + 4^ = - (1 4- i)^ (2 + ^) N (m) = 80 ^ (m) = 32 = 2. 22. 2^ H.E. 
y = Y (mod 4) a: = X + 3 (Y — y) (mod 20). 
Generators 17, 8 + 
i 
3 
1 
1 
0 
3z 
2 
3 
0 i 
1 
0 
0 
0 j 
1+22 
1 
0 
1 
2 + 32' 
0 
3 
1 
3 
3 
2 
0 i 
3 + 22 
2 
2 
1 ' 
4+ i 
1 
1 
0 i 
4 + 32' 
3 
3 
0 i 
5 + 22' 
0 
0 
1 i 
6+ i 
2 
1 
1 
7 
1 
2 
0 1 
7+22 
3 
2 
1 
8 + i 
0 
1 
0 
8 + 32 
1 
3 
0 
9 
2 
0 
0 
10+ i 
3 
1 
1 
10 + 32' 
2 
3 
1 
11 
0 
2 
0 
11 + 22 
1 
2 
1 
12+ .32 
0 
3 
0 
13 
3 
0 
0 
13 + 22'. 
2 
0 
1 I 
14 + 2 
1 
1 
1 ! 
14 + 32 
3 
3 
1 
15 + 22' 
0 
2 
1 
16+ 2 
2 
1 
0 
17 
1 
0 
0 ! 
17 + 22' 
3 
0 
1 
18+ 2 
0 
1 
1 
18 + 32 
1 
3 
1 
19 
2 
2 
0 
1 
0 
0 
0 
1 
0 
0 
1 
5 + 2z' 
0 
1 
0 
8+ i 
0 
1 
1 
18+ i 
0 
2 
0 
11 
0 
2 
1 
15 + 2^' 
0 
3 
0 
12+3^■ 
0 
3 
1 
2 + 3z' 
1 
0 
0 
17 
1 
0 
1 
l+2i 
1 
1 
0 
4+ i 
1 
1 
1 
14+ i 
1 
2 
0 
7 
1 
2 
1 
ll + 2^' 
1 
3 
0 
8 + 3z' 
1 
3 
1 
18 + 3i 
2 
0 
0 
9 
2 
0 
1 
13 + 2i 
2 
1 
0 
16+ i 
2 
1 
1 
6+ i 
2 
2 
0 
19 
2 
0 
1 
3+2?: 
2 
3 
0 
3? 
2 
3 
1 
10 + 3? 
3 
0 
0 
13 
3 
0 
1 
17 + 2i 
3 
1 
0 
i 
3 
1 
1 
10+ i 
3 
2 
0 
3 
3 
2 
1 
7 + 2i 
3 
3 
0 
4 + 3i 
3 
3 
1 
14 + 3i 
(4) (4) (2) 
(4) (4) (2) 
