FOR ANY COMPOSITE MODULUS, REAL OF COMPLEX. 
309 
VI = 7 N (7) = 49 (P (7) = 48 = 2^.3. H. E. = 48. x 
y = Y (mod 7). 
Generator 2 + i. 
0 
1 
1 
2 + i 
2 
3 + 4i 
3 
2+4-i: 
4 
3t' 
5 
4 + 6'( 
6 
2 + 2t‘ 
7 
2 + 6i 
8 
5 
9 
3 + 5^• 
10 
l + 6t 
11 
3 + 6^- 
12 
i 
13 
6 + 2i 
14 
3 + 3i 
15 
3 + 2i 
16 
4 
17 
l + 4( 
18 
o + 2i 
19 
l + 2i 
20 
5i 
21 
2 H" 3'i 
22 
i+i 
23 
l+3i 
(48) 
24 
6 
i 
12 i 
25 
5 
2i 
44 
26 
4 + 3-i 
3i 
4 
27 
0 “)“ 3^ 
28 ' 
28 
4i 
hi 
20 
29 
3 + i 
6i 
36 
30 
o + 5i 
1 
0 
31 
5 ‘i 
14" 
22 
32 
o 
l + 2'( 
19 
33 
4 4“ 2'i 
l + 3i 
23 
34 
6 + i 
l + 4i 
17 
35 
4 + i 
l-hSi 
37 
36 
6i 
l + 6( 
10 
37 
l + 5i 
2 
32 
38 
4 + 4(. 
24”^ 
1 
39 
4 4“ 5i 
2 4” 2i 
6 
40 
3 
2 + 3i 
21 
41 
6 4~ 3(1' 
2 + 4i 
3 
42 
2 + 5i 
2 + hi 
42 
43 
6 + 5t 
2 + 6i: 
7 
44 
2i 
3 
40 
45 
5 + 4'i 
3 + z: 
29 i 
46 
64 6 i 
3 + 2t 
15 ' 
47 
6 + 4i 
3 + 3i 
14 
(48) (48) 
= X (mod 7) 
3 + 4i 
2 
3 + 5i 
9 
3 + 6i 
11 
4 
16 
4 + i 
35 
4 4" 2t 
33 
4 + 3i 
26 
4 + 4i 
38 
4< + hi 
39 
4 + 6i 
5 
5 
8 
5 + 7 
31 
5 + 27 
18 
5 + 37 
27 
5 4" 4ii 
45 
5+57 
30 
5 + 67 
25 
6 
24 
6 + 7 
34 
6 4" 2't 
13 
b 4” 
41 
6+47 
47 
6+57 
43 
6 + 67 
46 
(48) 
m 7 d- t = - 7 (1 + ^■) (2 + if N {m) = 50 * {ui) = 20 = 2^ 5 H. E. = 20 
a: = X + 43Y (mod 50). 
m = 1 + 7i = — 7 (I + i) (1 4" 2i)^ N (w) = 50 fl> {m) = 20 = 2^.5 H. E. = 20 
cc = X + 7Y (mod 50). 
Generator 3. 
0 1 
2 
3 
4 
5 
(j 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 ; 
1 
1 3 
9 
27 
31 
43 
29 
37 
11 
33 
49 
47 
41 
23 
19 
7 
21 
13 
39 
17 
1 3 
7 
9 
11 
13 
17 
19 
21 
23 
27 
29 
31 
33 
37 
39 
41 
43 
47 
49 
0 1 
15 
2 
8 
17 
19 
14 
16 
13 
0 
6 
4 
9 
7 
18 
12 
5 
11 
10 
I 
( 20 ) 
