696] CALCULATION OF THE MINIMUM N.G.F. OF THE BINARY SEVENTHIC. 415 
is thus verified, viz. so soon as, in the calculation, we arrive at this term, we know 
that it is right, and the calculation up to this point is, to a considerable extent, 
verified. And similarly, in continuing the calculation, we arrive at other terms which 
are verified in the like manner. 
Expansions of the Functions E, F, G, H. 
Ind. x 
E 
F 
G 
H 
Ind. x 
E 
F 
G 
H 
0 
1 
1 
1 
1 
16 
45 
36 
20 
6 
2 
1 
1 
1 
0 
18 
61 
47 
26 
7 
4 
3 
3 
2 
1 
20 
85 
66 
35 
10 
6 
5 
4 
3 
1 
22 
111 
84 
44 
11 
8 
9 
8 
5 
2 
24 
113 
58 
16 
10 
13 
11 
7 
2 
26 
141 
71 
17 
12 
22 
18 
11 
4 
28 
183 
90 
23 
14 
30 
24 
14 
4 
30 
225 
110 
26 
Ind. 
x F 
G 
H 
Ind. x 
G 
H 
Ind. x 
H 
32 
284 
136 
33 
70 
2172 
419 
108 
2265 
34 
344 
163 
37 
72 
2432 
472 
110 
2426 
36 
425 
199 
47 
74 
2702 
515 
112 
2623 
38 
508 
235 
52 
76 
3009 
576 . 
114 
2807 
40 
617 
282 
64 
78 
3331 
629 
116 
3026 
42 
729 
331 
72 
80 
3692 
699 
118 
3232 
44 
872 
391 
86 
82 
4070 
760 
120 
3479 
46 
1020 
454 
96 
84 
4494 
843 
122 
3708 
48 
1205 
532 
115 
86 
4935 
913 
124 
3981 
50 
1397 
612 
127 
88 
5427 
1007 
126 
4240 
52 
1632 
709 
149 
90 
5942 
1091 
128 
4541 
54 
1877 
811 
166 
92 
6510 
1197 
130 
4828 
56 
2172 
931 
192 
94 
7104 
1293 
132 
5164 
58 
2480 
1057 
212 
96 
7760 
1416 
134 
5481 
60 
2846 
1206 
245 
98 
8442 
1525 
136 
5850 
62 
3228 
1360 
269 
100 
9192 
1663 
138 
6204 
64 
3677 
1540 
307 
102 
9975 
1790 
140 
6609 
66 
1729 
338 
104 
10829 
1945 
142 
6998 
68 
1945 
382 
106 
2088