FOR ANY COMPOSITE MODULUS, REAL OR COMPLEX. 301 
w = 4 + = - z (1 + if (2 + i) N (m) = 20 $ (m) = 8 = 2. 2^ H. E. = 4 
^ = Y (mod 2) a; = X + 3 (Y — y) (mod 10). 
Generators 7, 8 + z. 
i 
0 0 
1 
i 
3 1 
0 1 
8 + i 
1 
0 0 
1 0 
7 
3 
3 0 
1 1 
4 + 2 
4+2 
1 1 
2 0 
9 
6 + 2 
2 1 
2 1 
6 + 2 
7 
1 0 
3 0 
3 
8 + 2 
0 1 
3 1 
i 
9 
2 0 
(4) (2) (4) (2) 
m = 2 + 4z = - z (1 + {f{l + 2z) N (m) = 20 d) (/,i) = 3 = 2. 2^ H. E. = 4 
z/ = Y (mod 2) a: = X + 7 (Y — ^) (mod 10). 
Generators 7, 4 + i-' 
0 0 
1 
i 
1 1 
0 1 
4 + 2 
1 
0 0 
1 0 
7 
2+2 
2 1 
1 1 
i 
3 
3 0 
2 0 
9 
4 + i 
0 1 
2 1 
2+2 
6 + 2 
3 1 
3 0 
3 
7 
1 0 
3 1 
6 + 2 
9 
2 0 
(4) (2) (4) (2) 
m = 5 = - z (2 + z) (1 + 2z) N (m) = 25 ^ (m) = 16 = 2l 2^ H. E. = 4 
X = X (mod 5) y = Y (mod 5). 
Generators 4 + /, 4 + 4z. 
0 0 
1 
i 
3 1 
0 1 
4 + 4/ 
2 / 
0 2 
0 2 
2/ 
3 / 
2 0 
0 3 
2 + 3/ 
1 3 
1 0 
4 + 2 
1 
0 0 
1 1 
2 
1+2 
2 3 
1 2 
3 + 32 ' 
1 + 4/ 
3 2 
1 3 
4/ 
2 
1 1 
2 0 
3/ 
2 + 2/ 
3 0 
2 1 
3 + 2/ 
2 + 
0 3 
2 2 
4 
3 
3 3 
2 3 
1 “hi 
3 + 2 / 
2 1 
‘ 3 0 
2 + 2 / 
3 4“ 3'i 
1 2 
! 3 1 
i 
4 
2 2 
! 3 2 
1 + 4 / 
4 + 2 
1 0 
i 3 3 
3 
4 + 4/ 
0 .1 
(4) (4) 
(4) (4) 
