Old Sextic Fields Ramifying Above {3, 13}

Discriminant class: −39

∞  3 13 a_{1}  a_{2} a_{3}  Over p = 3  Over p = 13 2 5 7 11 17 19 23 29
G  h  a_{4}  a_{5} a_{6} f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
1.  3_{i}  7_{k} 3_{+} -3  9 -13 1^{6} 7_{k} 3∗  1^{2} 1_{+} 13 13 33 33 222  222 222 222 222
S_{3}  4  9  -3  1  1^{2} 1_{+} 13 13 222 222  33 33 222 33 33
2.  3_{i}  3_{k} 5_{+} 1  8  9 3^{2} 3_{k} 3∗  1^{6} 5_{+} 13  33  6 33 6 6 6 6
C_{6}  4  6 -10 25  222 6 33 33  222 33 33
3.  3_{i}  9_{k} 3_{+} 0  18 10 1^{6} 9_{k} 3∗  3^{2} 3_{+} 13  33 33 6 33 222 222 6 6
C_{6}  4  81  90 181  6 222 33 33 33 222 33 33
4.  3_{i}  11_{k} 3_{+} 0  18  0 1^{6} 11_{k} 3∗  1^{2} 1_{+} 13 13  33 222 33 222 222 222 222
S_{3}  4  81  0 156  1^{2} 1_{+} 13 13 222 222 33 33 33 222 33 33
5.  3_{i}  11_{k} 3_{+} 0  9 -21 1^{6} 11_{k} 3∗  1^{2} 1_{+} 13 13 33  222 33 222 222 222 222
S_{3}  4  108 -36 120  1^{2} 1_{+} 13 13 222 222 33  33 222  33
6.  3_{i}  11_{k} 3_{+} 0 -18  0 1^{6} 11_{k} 3∗  1^{2} 1_{+} 13 13 33 33 222 33 222 222 222 222
S_{3}  4  81  0 39  1^{2} 1_{+} 13 13 222 222 33 33  222 33
7.  3_{i}  9_{k} 5_{+} 0  0 -26 1^{6} 9_{k} 3∗  1^{6} 5_{+} 13  33 6  6 6 6 222
C_{6}  156  351 234 208  6 6 33 33 33 222  33
8.  3_{i}  9_{k} 5_{+} 0  0 26 1^{6} 9_{k} 3∗  1^{6} 5_{+} 13  33 33 222 33 6 6 222 6
C_{6}  12  351 936 793  6 6  33 222 33
9.  3_{i}  11_{k} 3_{+} 0  0 -27 1^{6} 11_{k} 3∗  3^{2} 3_{+} 13  22 22 6 22 222 6 222 222
D_{6}  12  0  0 192  6 6 22 33 22 222 22
10.  3_{i}  7_{k} 5_{+} 0  0  0 1^{6} 7_{k} 3∗  1^{6} 5_{+} 13  22 22 222 22 222 6 222 222
D_{6}  36  0  0 351  6 6 22 33 22 222 22 33
11.  3_{i}  11_{k} 5_{+} 0  0  0 1^{6} 11_{k} 3∗  1^{6} 5_{+} 13  22 22 6 22 222 6 222 222
D_{6}  36  0  0 3159  6 222 22 33 22 222 22 33
12.  3_{i}  11_{k} 5_{+} 0  0  0 1^{6} 11_{k} 3∗  1^{6} 5_{+} 13  22 22 6 22 222 222 222 222
D_{6}  72  0  0 39  222 6 22  22 222 22 33
13.  3_{i}  9_{k} 3_{+} 0  6  3 1^{6} 9_{k} 3∗  3^{2} 3_{+} 13  3 3 6 33 222 222 6 6
S_{3} × C_{3}  4  9  9 12  6 222 33 3 3 222 3 3
14.  3_{i}  11_{k} 3_{+} 0  18  3 1^{6} 11_{k} 3∗  3^{2} 3_{+} 13  3 3 6 3 222 222 6 6
S_{3} × C_{3}  4  81  27 90  6 222 3 3 33 222 3 33
15.  3_{i}  11_{k} 3_{+} 0  18 -12 1^{6} 11_{k} 3∗  3^{2} 3_{+} 13  33 3 6 3 222 222 6 6
S_{3} × C_{3}  4  81 -108 75  6 222 3 3 3 222 3 3
16.  3_{i}  11_{k} 3_{+} 0 -18 -15 1^{6} 11_{k} 3∗  3^{2} 3_{+} 13  3 33 6 3 222 222 6 6
S_{3} × C_{3}  4  81 135 144  6 222 3 33 3 222 33 3
17.  3_{i}  7_{k} 5_{+} -3  -6  4 1^{6} 7_{k} 3∗  1^{6} 5_{+} 13  3 33 6 33 6 6 6 6
S_{3} × C_{3} 12  96 -144 64  222 6 33 3 33 222 3 3
18.  3_{i}  9_{k} 5_{+} 0  0 52 1^{6} 9_{k} 3∗  1^{6} 5_{+} 13  33 3 6  6 6 6 222
S_{3} × C_{3} 12  351 1170 1651  6 6 33 3 3 222 33 3
19.  3_{i}  9_{k} 5_{+} 0  0 65 1^{6} 9_{k} 3∗  1^{6} 5_{+} 13  3 3 222 33 6 6 222 6
S_{3} × C_{3} 12  351 117 1066  6 6  33 3 222 3 33
20.  3_{i}  11_{k} 5_{+} 0  0 -78 1^{6} 11_{k} 3∗  1^{6} 5_{+} 13  33 33 6 33 6 6 6 222
S_{3} × C_{3} 12  351 -1872 4017  6 6 3 33 3 222  3
21.  3_{i}  11_{k} 5_{+} 0  0 -78 1^{6} 11_{k} 3∗  1^{6} 5_{+} 13  3 6 33 6 6 6 222
S_{3} × C_{3} 12  351 -1170 2496  6 6 3 3 3 222 33 3
22.  3_{i}  11_{k} 5_{+} 0  0 39 1^{6} 11_{k} 3∗  1^{6} 5_{+} 13  3 3 222 3 6 6 222 6
S_{3} × C_{3} 12  351 585 624  6 6 33 33 33 222 3

Discriminant class: −39 (continued)

∞  3 13 a_{1}  a_{2} a_{3}  Over p = 3  Over p = 13 2 5 7 11 17 19 23 29
G  h  a_{4}  a_{5} a_{6} f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
23.  3_{i}  11_{k} 5_{+} 0  0 39 1^{6} 11_{k} 3∗  1^{6} 5_{+} 13  3 33 6 3 6 6 6 6
S_{3} × C_{3} 12  351 819 858  222 6 3 3  222 3 33
24.  3_{i}  11_{k} 5_{+} 0  0 -78 1^{6} 11_{k} 3∗  1^{6} 5_{+} 13  33 33 6 3 6 6 6 6
S_{3} × C_{3} 12  351 468 1677  222 6 3 3 33 222 3 3
25.  3_{i}  11_{k} 5_{+} 0  0  0 1^{6} 11_{k} 3∗  1^{6} 5_{+} 13  33 3 222 3 6 6 222 6
S_{3} × C_{3} 12  351 1638 1911  6 6 33 33 3 222 3 33
26.  3_{i}  11_{k} 5_{+} 0  0  0 1^{6} 11_{k} 3∗  1^{6} 5_{+} 13  33 3 6 33 6 6 6 222
S_{3} × C_{3} 48  351 234 39  6 6 3 3 33 222 33 33
27.  3_{i}  11_{k} 5_{+} 0  0 39 1^{6} 11_{k} 3∗  1^{6} 5_{+} 13  3  6 3 6 6 6 6
S_{3} × C_{3} 12  351 -1989 3198  222 6 3 33 33 222 33 3
28.  3_{i}  11_{k} 5_{+} 0  0 -117 1^{6} 11_{k} 3∗  1^{6} 5_{+} 13  3 33 222 3 6 6 222 6
S_{3} × C_{3} 12  351 117 3432  6 6 33  3 222 33 33
29.  3_{i}  11_{k} 5_{+} 0  0 -39 1^{6} 11_{k} 3∗  1^{6} 5_{+} 13  42 42 6 42 4 2 222 4
S_{4} × C_{2} 24  117 -117 39  222 6 22 22 22 222 22 33

Discriminant class: −3

∞  3 13 a_{1} a_{2} a_{3}  Over p = 3  Over p = 13 2 5 7 11 17 19 23 29
G  h  a_{4} a_{5} a_{6} f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
30.  3_{i}  3_{k} 4_{+} -1  5  6 3^{2} 3_{k} 3∗  1^{3} 2_{+} 1  6 222 33 6 6 33 6 6
C_{6}  15  4  1  1^{3} 2_{+} 1  33 6 33 222 222 6 33
31.  3_{i}  7_{k} 4_{+}  3  6 -19 1^{6} 7_{k} 3∗  1^{3} 2_{+} 1  222 222  222 222 33 222 222
S_{3}  3  -33 42 196  1^{3} 2_{+} 1  33 33 222 33 222 222 222 33
32.  3_{i}  9_{k} 4_{+}  0  0 91 1^{6} 9_{k} 3∗  1^{3} 2_{+} 1  6 6  6 6 33 222 6
C_{6}  21  0  0 2197  1^{3} 2_{+} 1  33 33 222  6 222 6
33.  3_{i}  9_{k} 4_{+}  0  0 26 1^{6} 9_{k} 3∗  1^{3} 2_{+} 1  222 6 33 222 6 33 6 222
C_{6}  3  0  0 2197  1^{3} 2_{+} 1  33 33 6 33 6 222 222 33
34.  3_{i}  11_{k} 4_{+} -3  6 71 1^{6} 11_{k} 3∗  1^{3} 2_{+} 1  222 222 33 222 222  222 222
S_{3}  12  -111 -120 1600  1^{3} 2_{+} 1  33 222  222 222 222 33
35.  3_{i}  11_{k} 4_{+}  0  0  0 1^{6} 11_{k} 3∗  1^{3} 2_{+} 1  222 222 33 222 222 33 222 222
S_{3}  3  0  0 507  1^{3} 2_{+} 1  33  222 33 222 222 222 33
36.  3_{i}  7_{k} 2_{+}  0  3  0 1^{6} 7_{k} 3∗  1^{2} 1_{+} 13 13 6 6 22 222 222 22 222 222
D_{6}  -6  0  3  1^{2} 1_{+} 13 13 22 22 222 33 6 222 6 33
37.  3_{i}  11_{k} 2_{+}  0 -18  0 1^{6} 11_{k} 3∗  1^{2} 1_{+} 13 13 222 6 22 6 222 22 222 222
D_{6}  81  0 48  1^{2} 1_{+} 13 13 22 22 6 33 6 222 6 33
38.  3_{i}  11_{k} 2_{+}  0  9 -30 1^{6} 11_{k} 3∗  1^{2} 1_{+} 13 13 6 222 22 6 222 22 222 222
D_{6}  3  81 -135 225  1^{2} 1_{+} 13 13 22 22 6  6 222 222 33
39.  3_{i}  11_{k} 2_{+}  0 -9  6 1^{6} 11_{k} 3∗  1^{2} 1_{+} 13 13 6 6 22 6 222 22 222 222
D_{6}  81 -27  9  1^{2} 1_{+} 13 13 22 22 6 33 222 222 6
40.  3_{i}  7_{k} 2_{+}  0  0  -5 1^{6} 7_{k} 3∗  1^{3} 2_{+} 1  6 222 33 6 6 3 6 6
S_{3} × C_{3}  0  0 13  33 3 6 3 222 222 6 3
41.  3_{i}  9_{k} 2_{+}  0  0  -7 1^{6} 9_{k} 3∗  1^{3} 2_{+} 1  6 6  6 6 3 222 6
S_{3} × C_{3}  0  0 13  3 0_{+} 1  3 3 222 33 6 222 6 33
42.  3_{i}  9_{k} 2_{+}  0  0  2 1^{6} 9_{k} 3∗  1^{3} 2_{+} 1  222 6 33 222 6 3 6 222
S_{3} × C_{3}  0  0 13  3 0_{+} 1  3 3 6 3 6 222 222 3
43.  3_{i}  11_{k} 2_{+}  0  0  6 1^{6} 11_{k} 3∗  1^{3} 2_{+} 1  222 6 3 222 6 3 6 222
S_{3} × C_{3}  0  0 117  3 0_{+} 1  3 33 6 3 6 222 222 3

Discriminant class: −3 (continued)

∞  3 13 a_{1} a_{2} a_{3}  Over p = 3  Over p = 13 2 5 7 11 17 19 23 29
G  h  a_{4} a_{5} a_{6} f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
44.  3_{i}  11_{k} 2_{+}  0  0 -15 1^{6} 11_{k} 3∗  1^{3} 2_{+} 1  6 222 3 6 6 3 6 6
S_{3} × C_{3}  0  0 117  3 0_{+} 1  33 33 6 3 222 222 6 3
45.  3_{i}  11_{k} 2_{+}  0  0  3 1^{6} 11_{k} 3∗  1^{3} 2_{+} 1  6 6 33 6 6 33 222 6
S_{3} × C_{3}  0  0 39  3 0_{+} 1  33 3 222  6 222 6 33
46.  3_{i}  11_{k} 2_{+}  0  0 -12 1^{6} 11_{k} 3∗  1^{3} 2_{+} 1  222 6 3 222 6 33 6 222
S_{3} × C_{3}  0  0 39  33 3 6 33 6 222 222 3
47.  3_{i}  11_{k} 2_{+}  0  0  9 1^{6} 11_{k} 3∗  1^{3} 2_{+} 1  6 222 3 6 6 33 6 6
S_{3} × C_{3}  0  0 39  3 0_{+} 1  3 6 33 222 222 6 3
48.  3_{i}  11_{k} 2_{+}  0  0 21 1^{6} 11_{k} 3∗  1^{3} 2_{+} 1  6 6 33 6 6 3 222 6
S_{3} × C_{3}  0  0 117  3 33 222 33 6 222 6 33
49.  3_{i}  9_{k} 4_{+}  0  0 13 1^{6} 9_{k} 3∗  1^{3} 2_{+} 1  6 6 33 6 222 33 6 6
S_{3} × C_{3}  3  0  0 169  1^{3} 2_{+} 1  3 33 6 3 6 222 6 3
50.  3_{i}  11_{k} 4_{+}  0  0 156 1^{6} 11_{k} 3∗  1^{3} 2_{+} 1  222 6 3 222 6 3 6 222
S_{3} × C_{3}  3  0  0 6591  1^{3} 2_{+} 1  3 3 6 3 6 222 222 33
51.  3_{i}  11_{k} 4_{+}  0  0 -39 1^{6} 11_{k} 3∗  1^{3} 2_{+} 1  6 6 33 6 6 3 222 6
S_{3} × C_{3}  3  0  0 6591  1^{3} 2_{+} 1  3 3 222 33 6 222 6
52.  3_{i}  11_{k} 4_{+}  0  0 39 1^{6} 11_{k} 3∗  1^{3} 2_{+} 1  6 6 3 6 222 33 6 6
S_{3} × C_{3}  3  0  0 507  1^{3} 2_{+} 1  3  6 3 6 222 6 3
53.  3_{i}  11_{k} 4_{+}  0  0 117 1^{6} 11_{k} 3∗  1^{3} 2_{+} 1  6 222 3 6 6 3 6 6
S_{3} × C_{3}  3  0  0 6591  1^{3} 2_{+} 1  33 3 6 3 222 222 6 33
54.  3_{i}  11_{k} 4_{+}  0  0 39 1^{6} 11_{k} 3∗  1^{3} 2_{+} 1  6 6 3 6 222  6 6
S_{3} × C_{3}  3  0  0 1521  1^{3} 2_{+} 1  33 33 6 33 6 222 6 3
55.  3_{i}  11_{k} 4_{+}  3  6  7 1^{6} 11_{k} 3∗  1^{3} 2_{+} 1  4 4 33 4 4 22 222 4
S_{4}^{−}  24  6  3 40  1^{3} 2_{+} 1  33 222 22 222 222 222 33

Discriminant class: 1

∞  3 13 a_{1} a_{2} a_{3}  Over p = 3  Over p = 13 2 5 7 11 17 19 23 29
G  h  a_{4} a_{5} a_{6} f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
56. 2_{−} 10_{−} 4_{+} 0 -12 0 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  42 42 33 42 42 22 22 42
S_{4}^{+}  3  48 0 -25 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  33 22 22 22 22 22 33

Discriminant class: 13

∞  3 13 a_{1} a_{2}  a_{3}  Over p = 3  Over p = 13 2 5 7 11 17 19 23 29
G  h  a_{4} a_{5}  a_{6} f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
57.  0_{+}  8_{+} 3_{+} -3 -12  31 1^{3} 4_{+} 1  3^{2} 3_{+} 13  6 6 6 6  222 33 33
C_{6}  15 -18  3 1^{3} 4_{+} 1  6 222 6 33 6  6 33
58.  0_{+}  8_{+} 5_{+} 0 -39 -26 1^{3} 4_{+} 1  1^{6} 5_{+} 13  222 6 6 222 33 6 33
C_{6}  3  351 234 -468 1^{3} 4_{+} 1  6 6 6 33 6  222 33
59.  0_{+}  8_{+} 5_{+} 0 -39  26 1^{3} 4_{+} 1  1^{6} 5_{+} 13  6 6 222 6 33 6  33
C_{6}  3  351 -585 117 1^{3} 4_{+} 1  6 6 222  6  6
60.  2_{−}  6_{−} 3_{+} 0  0  3 1^{3} 3_{i} 3∗  1^{2} 1_{+} 13 13 6 6 222 222 22 222 22 22
D_{6}  0  0  -1 1^{3} 3_{i} 3∗  1^{2} 1_{+} 13 13 222 222 222 33 6 22 6 33
61.  2_{−}  10_{−} 3_{+} 0  0 -24 1^{3} 5_{i} 3∗  1^{2} 1_{+} 13 13 222 6 222 6 22 222 22 22
D_{6}  0  0  27 1^{3} 5_{i} 3∗  1^{2} 1_{+} 13 13 222 222 6 33 6 22 6 33

Discriminant class: 13 (continued)

∞  3 13 a_{1} a_{2}  a_{3}  Over p = 3  Over p = 13 2 5 7 11 17 19 23 29
G  h  a_{4} a_{5}  a_{6} f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
62.  2_{−}  10_{−} 3_{+} 0  0  3 1^{3} 5_{i} 3∗  1^{2} 1_{+} 13 13 6 6 222 6 22 222 22 22
D_{6}  0  0 -27 1^{3} 5_{i} 3∗  1^{2} 1_{+} 13 13 222 222 6 33 222 22 6
63.  2_{−}  10_{−} 3_{+} 0  0 -15 1^{3} 5_{i} 3∗  1^{2} 1_{+} 13 13 6 222 222 6 22 222 22 22
D_{6}  0  0  27 1^{3} 5_{i} 3∗  1^{2} 1_{+} 13 13 222 222 6  6 22 222 33
64.  2_{−}  10_{−} 3_{+} 3 -6 -23 1^{3} 5_{i} 3∗  3^{2} 3_{+} 13  222 222 6 222 22 6 22 22
D_{6}  9 -36 -48 1^{3} 5_{i} 3∗  6 6 222 33 222 22 222
65.  2_{−}  6_{−} 5_{+} 0  0  0 1^{3} 3_{i} 3∗  1^{6} 5_{+} 13  222 222 222 222 22 6 22 22
D_{6}  3  0  0 -13 1^{3} 3_{i} 3∗  6 6 222 33 222 22 222 33
66.  2_{−}  10_{−} 5_{+} 0  0  0 1^{3} 5_{i} 3∗  1^{6} 5_{+} 13  222 222 6 222 22 222 22 22
D_{6}  18  0  0 -1053 1^{3} 5_{i} 3∗  222 6 222  222 22 222 33
67.  2_{−}  10_{−} 5_{+} 0  0  0 1^{3} 5_{i} 3∗  1^{6} 5_{+} 13  222 222 6 222 22 6 22 22
D_{6}  3  0  0 -117 1^{3} 5_{i} 3∗  6 222 222 33 222 22 222 33
68.  2_{−}  6_{−} 3_{+} 1  3  2 1^{3} 5_{i} 3∗  3^{2} 3_{+} 13  6 222 6 6 22 6 22 22
S_{3} × S_{3}  2 -3  -3 1^{2} 1_{i} 3∗ 3∗  6 6 6 33 6 22 222 33
69.  2_{−}  8_{−} 3_{+} 0  0  -1 1^{3} 5_{i} 3∗  3^{2} 3_{+} 13  6 6 6 6 22 6 22 22
S_{3} × S_{3}  0  0  -3 1^{3} 3_{i} 3∗  6 6 6 3 222 22 6
70.  2_{−}  8_{−} 3_{+} 0  0  -8 1^{3} 5_{i} 3∗  3^{2} 3_{+} 13  222 6 6 6 22 6 22 22
S_{3} × S_{3}  0  0  3 1^{3} 3_{i} 3∗  6 6 6 3 6 22 6 33
71.  2_{−}  4_{−} 5_{+} 0  0 -13 1^{3} 3_{i} 3∗  1^{6} 5_{+} 13  6 6 222 222 22 6 22 22
S_{3} × S_{3}  3  0  0  13 1^{2} 1_{i} 3∗ 3∗  6 6 222 3 6 22 6 3
72.  2_{−}  10_{−} 3_{+} 0  0  -9 1^{3} 5_{i} 3∗  3^{2} 3_{+} 13  6 6 6 222 22 6 22 22
S_{3} × S_{3}  0  0  -9 1^{3} 5_{i} 3∗  6 6 222 3 6 22 6 33
73.  2_{−}  6_{−} 5_{+} 0  0 -13 1^{3} 5_{i} 3∗  1^{6} 5_{+} 13  6 6 6 6 22 222 22 22
S_{3} × S_{3}  3  0  0  39 1^{2} 1_{i} 3∗ 3∗  222 6 6 33 222 22 6 33
74.  2_{−}  6_{−} 5_{+} 0  0 -26 1^{3} 5_{i} 3∗  1^{6} 5_{+} 13  222 6 6 6 22 6 22 22
S_{3} × S_{3}  3  0  0 117 1^{2} 1_{i} 3∗ 3∗  6 222 6 3 6 22 6 3
75.  2_{−}  8_{−} 5_{+} 0  0 -13 1^{3} 5_{i} 3∗  1^{6} 5_{+} 13  6 6 6 6 22 6 22 22
S_{3} × S_{3}  3  0  0 -117 1^{3} 3_{i} 3∗  6 222 6 3 222 22 6 33
76.  2_{−}  8_{−} 5_{+} 0  0  65 1^{3} 5_{i} 3∗  1^{6} 5_{+} 13  6 222 6 6 22 6 22 22
S_{3} × S_{3}  3  0  0 117 1^{3} 3_{i} 3∗  6 222 6 33 6 22 222 3
77.  2_{−}  8_{−} 5_{+} 0  0 -26 1^{3} 5_{i} 3∗  1^{6} 5_{+} 13  222 6 6 6 22 222 22 22
S_{3} × S_{3}  3  0  0 -39 1^{3} 3_{i} 3∗  222 6 6 33 6 22 6 3
78.  2_{−}  8_{−} 5_{+} 0  0 -13 1^{3} 5_{i} 3∗  1^{6} 5_{+} 13  6 222 6 6 22 222 22 22
S_{3} × S_{3}  3  0  0 -39 1^{3} 3_{i} 3∗  222 6 6  6 22 222 3
79.  2_{−}  10_{−} 5_{+} 0  0 -117 1^{3} 5_{i} 3∗  1^{6} 5_{+} 13  6 6 6 222 22 222 22 22
S_{3} × S_{3}  3  0  0 1053 1^{3} 5_{i} 3∗  222 6 222 33 6 22 6 3
80.  2_{−}  10_{−} 5_{+} 0  0 -39 1^{3} 5_{i} 3∗  1^{6} 5_{+} 13  6 6 6 222 22 6 22 22
S_{3} × S_{3}  3  0  0 117 1^{3} 5_{i} 3∗  6 222 222 3 6 22 6 3
81.  2_{−}  10_{−} 5_{+} 0  0 -39 1^{3} 5_{i} 3∗  1^{6} 5_{+} 13  6 222 222 6 22 6 22 22
S_{3} × S_{3}  6  0  0 -351 1^{3} 5_{i} 3∗  6 6 6 33 6 22 222 3
82.  2_{−}  10_{−} 5_{+} 0  0 -78 1^{3} 5_{i} 3∗  1^{6} 5_{+} 13  222 6 222 6 22 6 22 22
S_{3} × S_{3}  3  0  0 -351 1^{3} 5_{i} 3∗  6 6 6 3 6 22 6 3
83.  2_{−}  10_{−} 5_{+} 0  0 -39 1^{3} 5_{i} 3∗  1^{6} 5_{+} 13  6 6 222 6 22 6 22 22
S_{3} × S_{3}  3  0  0 351 1^{3} 5_{i} 3∗  6 6 6 3 222 22 6 33
84.  2_{−}  10_{−} 5_{+} 3 -6 -17 1^{3} 5_{i} 3∗  1^{6} 5_{+} 13  4 4 6 4 42 2 22 42
S_{4} × C_{2}  6  18 27 -66 1^{3} 5_{i} 3∗  222 6 222 22 222 22 222 33