Old Sextic Fields Unramified Outside of {∞, 2, 13}

Discriminant class: −26

∞  2 13 a_{1} a_{2} a_{3}  Over p = 2  Over p = 13  3 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}  9_{i} 3_{−}  0 8 0 1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{−} 13∗ 13∗ 33 33 33 222 33 222 222 222
S_{3}  2  29 0 26 1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{−} 13∗ 13∗  33 222 33 33 222 222 222
2.  3_{i}  9_{i} 5_{−}  0 26 0 3^{2} 9_{i} −2∗  1^{6} 5_{−} 13∗  33  33 6 33 6 6 6
C_{6}  18  104 0 104  33 6 33  222 6 6
3.  3_{i}  11_{i} 5_{−}  0 0 0 1^{4} 8_{−} 1 {−2∗ \atop −1} 1^{6} 5_{−} 13∗  22 33 22 222 33 222 222 6
D_{6}  18  -39 0 416 1^{2} 3_{k} −2∗ −2∗  22 33 6 22 22 6 222 6
4.  3_{i}  9_{i} 5_{−}  2 -7 -6 3^{2} 9_{i} −2∗  1^{6} 5_{−} 13∗  3 33 3 6 3 6 6 6
S_{3} × C_{3} 18  44 -60 27  3 6 3 33 222 6 6
5.  3_{i}  11_{k} 3_{+} -1 -7 2 1^{4} 11_{k} −2 −2∗ 1^{4} 3_{+} 13∗ 13∗ 33 33 33 222 33 4 4 222
S_{4}^{−}  25 29 13 2 0_{+} ∗  ∗  22 33 4 33 33 4 222 4
6.  3_{i}  11_{i} 3_{−}  1 5 6 1^{4} 11_{i} −2 −2∗ 1^{2} 1_{−} 13∗ 13∗ 33 33 33 4 33 4 222 4
S_{4}^{−}  2  17 -5 1 2 0_{+} ∗  ∗ 1^{2} 1_{−} 13∗ 13∗ 22 33 4 33 33 222 222 4
7.  3_{i}  11_{k} 3_{+}  0 4 0 1^{4} 8_{+} 1 {−2∗ \atop −∗} 1^{4} 3_{+} 13∗ 13∗ 33 33 33 4 33 222 4 4
S_{4}^{−}  2  13 0 26 1^{2} 3_{k} −2∗ −2∗  22 33 222 33 33 4 222 222
8.  3_{i}  13_{k} 3_{+}  0 1 0 1^{4} 11_{−} 2∗ −2∗ 2^{2} 2_{−} 1  V 33 33 33 222 33 4 4 222
S_{4}^{−}  2  10 0 26 1^{2} 2_{i} −1 −1 1^{2} 1_{−} 13∗ 13∗ 22 33 222 33 33 4 4 222
9.  3_{i}  13_{k} 3_{+}  0 9 0 1^{4} 11_{−} 2∗ −2∗ 1^{4} 3_{+} 13∗ 13∗ 33 33 33 4 33 4 222 4
S_{4}^{−}  2  26 0 26 1^{2} 2_{i} −1 −1  33 222 33 33 222 4 222
10.  3_{i}  13_{k} 3_{+}  0 -12 0 1^{4} 10_{k} −∗ −2∗ 1^{4} 3_{+} 13∗ 13∗ 33 33 33 222 33 222 222 222
S_{4}^{−}  2  39 0 26 1^{2} 3_{+} 2  2  22 33 4 33 33 222 4 4
11.  3_{i}  13_{k} 3_{+}  0 4 0 1^{4} 10_{k} −∗ −2∗ 2^{2} 2_{−} 1  V 33 33 33 4 33 222 4 4
S_{4}^{−}  2  -9 0 26 1^{2} 3_{+} 2  2 1^{2} 1_{−} 13∗ 13∗ 22 33 4 33 33 4 4 4
12.  1_{k}  9_{k} 5_{−}  0 0 0 3^{2} 9_{k} −2∗  1^{6} 5_{−} 13∗  33 22 33 6 33 6 6 6
A_{4} × C_{2}  2  -52 0 104  22 33 6 33  2 6 6
13.  3_{i}  9_{i} 5_{−} -2 6 6 1^{4} 6_{+} ∗ −1 1^{6} 5_{−} 13∗  42 33 22 222 33 4 4 6
S_{4} × C_{2}  6  5 8 14 1^{2} 3_{i} −2 −2  42 33 6 22 42 6 222 6
14.  3_{i}  11_{i} 5_{−}  0 13 0 1^{4} 9_{+} 2 −1 1^{6} 5_{−} 13∗  22 33 42 4 33 222 4 6
S_{4} × C_{2} 12  104 0 416 1^{2} 2_{i} −∗ −∗  42 33 6 22 22 6 4 6
15.  3_{i}  11_{i} 5_{−}  0 0 0 1^{4} 9_{+} 2∗ −1 1^{6} 5_{−} 13∗  42 33 42 4 33 4 222 6
S_{4} × C_{2} 12  -104 0 416 1^{2} 2_{i} −1 −1  22 33 6 22 42 6 4 6
16.  3_{i}  13_{i} 5_{−} -2 -7 -20 1^{4} 10_{i} −∗ −2∗ 1^{6} 5_{−} 13∗  5 5 33 4 22 4 4 6
S_{5}  6  57 138 157 1^{2} 3_{+} 2  2  5 5 4 22 22 4 6 222

Discriminant class: −13

∞  2 13 a_{1} a_{2} a_{3}  Over p = 2  Over p = 13  3 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
17.  3_{i}  6_{k} 5_{+} 0 13 0 3^{2} 6_{k} −∗  1^{6} 5_{+} 13  6 222 33 33 33 33 6 33
C_{6}  2  26 0 13  6 6 6  33 33
18.  3_{i}  10_{i} 3_{−} 0 3 0 1^{4} 8_{+} 1 {−2∗ \atop −∗} 2^{2} 2_{−} 1  V 6 6 33 22 33 22 222 22
D_{6}  2  -1 0 13 1^{2} 2_{i} −∗ −∗ 1^{2} 1_{+} 13 13  6 222 6 33 22 22 22
19.  3_{i}  6_{k} 5_{+} 2 6 -6 2^{2} 4_{−} 1  {−1 \atop −∗} 1^{6} 5_{+} 13  222 6 22 22 33 22 222 33
D_{6}  6  18 -8 1 1^{2} 2_{i} −∗ −∗  22 6 6 222 22 33 22 33

Discriminant class: −13 (continued)

∞  2 13 a_{1} a_{2} a_{3}  Over p = 2  Over p = 13  3 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
20.  1_{k}  6_{i} 5_{+} 0 0 0 3^{2} 6_{i} −∗  1^{6} 5_{+} 13  6 2 33 33 33 33 6 33
A_{4} × C_{2}  2  -13 0 13  22 6 6 6  22 33 33
21.  3_{i}  8_{k} 3_{+} 0 1 -2 1^{2} 3_{k} −2∗ −2∗ 1^{4} 3_{+} 13∗ 13∗ 6 6 33 42 33 22 4 42
S_{4} × C_{2}  0 4 4 1^{2} 3_{k} −2∗ −2∗ 2 0_{+} ∗  ∗ 22 6 222 6 33 42 22 22
22.  3_{i}  10_{k} 3_{+} 1 2 -8 1^{4} 10_{k} −∗ −2∗ 1^{2} 1_{−} 13∗ 13∗ 6 6 33 42 33 22 4 42
S_{4} × C_{2}  2  14 -10 4  1^{2} 1_{+} 13 13 22 6 4 6 33 42 42 42
23.  3_{i}  10_{k} 3_{+} -1 4 -4 1^{4} 10_{k} −∗ −2∗ 1^{4} 3_{+} 13∗ 13∗ 6 6 33 22 33 22 222 22
S_{4} × C_{2}  2 -2 8  2 0_{+} ∗  ∗ 22 6 4 6 33 22 42 42
24.  3_{i}  14_{k} 3_{+} 0 2 0 1^{4} 11_{i} −2 −2∗ 1^{4} 3_{+} 13∗ 13∗ 6 6 33 22 33 42 4 22
S_{4} × C_{2}  2  -26 0 52 1^{2} 3_{−} 2∗  2∗ 2 0_{+} ∗  ∗ 22 6 4 6 33 42 22 42
25.  3_{i}  14_{i} 3_{−} 0 10 0 1^{4} 11_{k} −2 −2∗ 2^{2} 2_{−} 1  V 6 6 33 42 33 42 222 42
S_{4} × C_{2}  2  38 0 52 1^{2} 3_{−} 2∗  2∗ 1^{2} 1_{+} 13 13 22 6 4 6 33 22 22 42
26.  3_{i}  14_{k} 3_{+} 0 2 0 1^{4} 11_{−} 2∗ −2∗ 1^{2} 1_{−} 13∗ 13∗ 6 6 33 22 33 42 4 22
S_{4} × C_{2}  4  40 0 208 1^{2} 3_{i} −2 −2 1^{2} 1_{−} 13∗ 13∗ 22 6 222 6 33 42 42 22
27.  3_{i}  14_{k} 3_{+} 0 -6 0 1^{4} 11_{−} 2∗ −2∗ 1^{4} 3_{+} 13∗ 13∗ 6 6 33 42 33 42 222 42
S_{4} × C_{2}  2  26 0 52 1^{2} 3_{i} −2 −2 2 0_{+} ∗  ∗  6 222 6 33 22 42 22
28.  3_{i}  10_{k} 5_{+} 0 0 0 1^{4} 8_{−} ∗ −1 1^{6} 5_{+} 13  4 6 22 22 33 42 4 33
S_{4} × C_{2} 24  13 0 52 1^{2} 2_{i} −1 −1  42 6 6 222 42 33 22 33
29.  3_{i}  12_{k} 5_{+} 0 0 0 1^{4} 9_{−} 2∗ −1 1^{6} 5_{+} 13  4 6 42 42 33 42 222 33
S_{4} × C_{2}  6  -26 0 52 1^{2} 3_{i} −2 −2  22 6 6 222 42 33 42 33
30.  3_{i}  12_{k} 5_{+} 0 0 0 1^{4} 9_{+} 2 −1 1^{6} 5_{+} 13  222 6 42 42 33 22 4 33
S_{4} × C_{2}  6  78 0 52 1^{2} 3_{k} −2∗ −2∗  42 6 6 222 22 33 42 33

Discriminant class: −2

∞  2 13 a_{1} a_{2} a_{3}  Over p = 2  Over p = 13  3 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
31.  3_{i}  9_{k} 4_{+} 2 -1 2 3^{2} 9_{k} −2  2^{3} 4_{+} ∗  33 222 6 33 33 33 6 6
C_{6}  34 -28 73  222 6 33 33 222 222 33 6
32.  3_{i}  9_{i} 2_{−} 0 2 2 2^{2} 6_{+} 1 {−2 \atop −2∗} 2^{2} 2_{−} 1  V 33 6 6 22 33 22 222 222
D_{6}  2 0 1 1^{2} 3_{i} −2 −2 2 0_{+} ∗  ∗ 222 6 22 33 6 222 22 222
33.  3_{i}  11_{k} 4_{+} 0 -8 0 1^{4} 8_{−} 1  {−2 \atop −1} 2^{3} 4_{+} ∗  22 6 222 22 33 22 222 6
D_{6}  3  17 0 8 1^{2} 3_{i} −2 −2  222 6 33 22 222 6 22 6
34.  1_{k}  9_{i} 4_{+} 0 2 0 3^{2} 9_{i} −2  2^{3} 4_{+} ∗  33 2 6 33 33 33 6 6
A_{4} × C_{2}  -16 0 8  2 6 33 33 222 2 33 6
35.  3_{i}  11_{i} 2_{−} 0 3 0 1^{4} 11_{i} −2 −2∗ 2^{2} 2_{−} 1  V 33 6 6 42 33 42 222 4
S_{4} × C_{2}  2 0 2  2 0_{+} ∗  ∗ 2 6 42 33 6 222 22 4
36.  3_{i}  13_{k} 2_{+} 0 -3 0 1^{4} 11_{−} 2∗ −2∗ 2 0_{+} ∗  ∗ 33 6 6 22 33 42 4 222
S_{4} × C_{2}  2 0 2 1^{2} 2_{i} −∗ −∗ 1^{2} 1_{−} 13∗ 13∗ 2 6 22 33 6 4 42 222
37.  3_{i}  13_{k} 2_{+} 0 0 0 1^{4} 10_{i} −∗ −2∗ 2 0_{+} ∗  ∗ 33 6 6 42 33 22 4 4
S_{4} × C_{2}  -1 0 2 1^{2} 3_{−} 2∗  2∗ 1^{2} 1_{−} 13∗ 13∗ 2 6 42 33 6 4 42 4
38.  3_{i}  9_{k} 4_{+} 0 2 0 1^{4} 6_{+} ∗ −1 2^{3} 4_{+} ∗  42 6 222 22 33 42 4 6
S_{4} × C_{2}  3  -3 0 8 1^{2} 3_{k} −2∗ −2∗  4 6 33 22 4 6 22 6
39.  3_{i}  11_{k} 4_{+} 2 17 4 1^{4} 8_{−} 1 {−2∗ \atop −1} 1^{4} 3_{+} 13∗ 13∗ 33 6 6 42 33 22 4 4
S_{4} × C_{2}  4  52 8 62 1^{2} 3_{i} −2 −2 1^{2} 1_{+} 13 13 2 6 22 33 6 4 22 222
40.  3_{i}  11_{k} 4_{+} 0 2 0 1^{4} 9_{−} 2 −1 2^{3} 4_{+} ∗  22 6 4 42 33 22 4 6
S_{4} × C_{2}  6  10 0 8 1^{2} 2_{i} −1 −1  4 6 33 22 222 6 42 6

Discriminant class: −2 (continued)

∞  2 13 a_{1} a_{2} a_{3}  Over p = 2  Over p = 13  3 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
41.  3_{i}  11_{k} 4_{+} 0 -7 0 1^{4} 9_{−} 2∗ −1 2^{3} 4_{+} ∗  42 6 4 42 33 42 222 6
S_{4} × C_{2}  6  12 0 8 1^{2} 2_{i} −∗ −∗  222 6 33 22 4 6 42 6
42.  3_{i}  11_{k} 4_{+} -1 10 14 1^{4} 11_{k} −2 −2∗ 1^{4} 3_{+} 13∗ 13∗ 33 6 6 22 33 42 4 222
S_{4} × C_{2}  2  71 65 88  1^{2} 1_{+} 13 13 2 6 42 33 6 4 22 4
43.  3_{i}  13_{k} 4_{+} 0 13 0 1^{4} 11_{−} 2∗ −2∗ 1^{4} 3_{+} 13∗ 13∗ 33 6 6 42 33 42 222 4
S_{4} × C_{2}  4  -78 0 338 1^{2} 2_{i} −∗ −∗ 1^{2} 1_{+} 13 13 222 6 22 33 6 222 42 222
44.  3_{i}  13_{k} 4_{+} 0 0 0 1^{4} 10_{i} −∗ −2∗ 1^{4} 3_{+} 13∗ 13∗ 33 6 6 22 33 22 222 222
S_{4} × C_{2}  4  143 0 338 1^{2} 3_{−} 2∗  2∗ 1^{2} 1_{+} 13 13 2 6 42 33 6 222 42 4
45.  3_{i}  11_{k} 4_{+} 1 -3 6 1^{4} 11_{k} −2∗ −2 2^{3} 4_{+} ∗  5 4 4 5 5 22 6 4
S_{5}  3  -1 -23 27 2 0_{+} ∗  ∗  4 222 22 33 4 6 5 4

Discriminant class: −1

∞  2 13 a_{1} a_{2} a_{3}  Over p = 2  Over p = 13  3 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
46.  3_{i}  6_{k} 4_{+} -2 2 -6 1^{2} 2_{i} −1 −1 1^{3} 2_{+} 1  222 33 222 222 33 222 222 33
S_{3}  3  25 -20 8 1^{2} 2_{i} −1 −1 1^{3} 2_{+} 1  222 33 33 222 222 33 222 33
47.  3_{i}  6_{k} 4_{+} 0 9 0 3^{2} 6_{k} −1  1^{3} 2_{+} 1  6  6 6 33 6 6 33
C_{6}  3  14 0 1  1^{3} 2_{+} 1  222 33 33 6 222  6 33
48.  3_{i}  10_{k} 2_{+} 0 2 0 1^{4} 8_{−} 1 {−2∗ \atop −1} 1^{2} 1_{−} 13∗ 13∗ 6 33 6 222 33 222 222 22
D_{6}  1 0 4 1^{2} 2_{i} −1 −1 1^{2} 1_{−} 13∗ 13∗ 222 33 22 6 6 22 222 22
49.  3_{i}  6_{k} 2_{+} 2 3 4 3^{2} 6_{k} −1  1^{3} 2_{+} 1  6 33 6 6 3 6 6 3
S_{3} × C_{3}  4 2 1  3 0_{+} 1  222 3 3 6 222 33 6 3
50.  1_{k}  6_{i} 4_{+} 0 1 0 3^{2} 6_{i} −1  1^{3} 2_{+} 1  6 22 6 6 33 6 6 33
A_{4} × C_{2}  -4 0 1  1^{3} 2_{+} 1  2 33 33 6 222 22 6 33
51.  3_{i}  10_{k} 4_{+} 0 1 0 1^{4} 8_{−} ∗ −1 1^{3} 2_{+} 1  4 33 222 222 33 4 4 33
S_{4}^{−}  6  9 0 1 1^{2} 2_{i} −∗ −∗ 1^{3} 2_{+} 1  4 33 33 222 4 33 222 33
52.  3_{i}  12_{k} 4_{+} 0 10 0 1^{4} 9_{+} 2∗ −1 1^{3} 2_{+} 1  4 33 4 4 33 4 222 33
S_{4}^{−}  3  42 0 64 1^{2} 3_{k} −2∗ −2∗ 1^{3} 2_{+} 1  222 33 33 222 4 33 4 33
53.  3_{i}  12_{k} 4_{+} 0 4 0 1^{4} 9_{−} 2 −1 1^{3} 2_{+} 1  222 33 4 4 33 222 4 33
S_{4}^{−}  3  40 0 64 1^{2} 3_{i} −2 −2 1^{3} 2_{+} 1  4 33 33 222 222 33 4 33
54.  3_{i}  10_{i} 2_{−} 0 1 0 1^{4} 10_{i} −∗ −2∗ 2^{2} 2_{−} 1  V 6 33 6 4 33 222 4 42
S_{4} × C_{2}  5 0 1 2 0_{+} ∗  ∗  2 33 42 6 6 42 4 42
55.  3_{i}  14_{i} 2_{−} 0 2 0 1^{4} 11_{−} 2∗ −2∗ 2^{2} 2_{−} 1  V 6 33 6 222 33 4 4 22
S_{4} × C_{2}  2  -6 0 4 1^{2} 3_{k} −2∗ −2∗  2 33 22 6 6 42 4 22
56.  3_{i}  14_{k} 2_{+} 0 2 0 1^{4} 11_{k} −2 −2∗ 1^{2} 1_{−} 13∗ 13∗ 6 33 6 4 33 4 222 42
S_{4} × C_{2}  6 0 4 1^{2} 3_{+} 2  2 1^{2} 1_{−} 13∗ 13∗ 2 33 42 6 6 22 222 42
57.  3_{i}  8_{i} 4_{−} -2 8 -8 2^{2} 6_{+} 1 {−2 \atop −2∗} 1^{4} 3_{+} 13∗ 13∗ 6 33 6 4 33 222 4 42
S_{4} × C_{2}  2  10 -10 23 1^{2} 2_{i} −1 −1 1^{2} 1_{−} 13∗ 13∗ 2 33 22 6 6 42 222 22
58.  3_{i}  10_{i} 4_{−} 1 -3 12 1^{4} 10_{i} −∗ −2∗ 1^{4} 3_{+} 13∗ 13∗ 6 33 6 222 33 222 222 22
S_{4} × C_{2}  2  6 -26 62 2 0_{+} ∗  ∗ 1^{2} 1_{−} 13∗ 13∗ 2 33 42 6 6 22 4 42
59.  3_{i}  14_{i} 4_{−} 0 26 0 1^{4} 11_{−} 2∗ −2∗ 1^{4} 3_{+} 13∗ 13∗ 6 33 6 4 33 4 222 42
S_{4} × C_{2}  8  234 0 676 1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{−} 13∗ 13∗ 222 33 22 6 6 22 4 22
60.  3_{i}  14_{i} 4_{−} 0 26 0 1^{4} 11_{i} −2 −2∗ 1^{4} 3_{+} 13∗ 13∗ 6 33 6 222 33 4 4 22
S_{4} × C_{2}  4  -26 0 676 1^{2} 3_{+} 2  2 1^{2} 1_{−} 13∗ 13∗ 2 33 42 6 6 42 222 42

Discriminant class: 1

∞  2 13 a_{1} a_{2} a_{3}  Over p = 2  Over p = 13  3 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
61. 2_{−} 6_{−} 4_{+} 0 -1  0 3^{2} 6_{−} 1  1^{3} 2_{+} 1  33 22 33 33 33 33 33 33
A_{4}  -4 0 -1  1^{3} 2_{+} 1  22 33 33 33  22 33 33
62. 2_{−} 12_{+} 2_{−} 0 -1  0 1^{4} 10_{k} −∗ −2∗ 2^{2} 2_{−} 1  V 33 33 33 42 33 22 42 42
S_{4}^{+}  5 0 -1 1^{2} 2_{i} −∗ −∗  22 33 42 33 33 42 42 42
63. 2_{−} 14_{+} 2_{−} 0 -2  0 1^{4} 11_{−} 2∗ −2∗ 2^{2} 2_{−} 1  V 33 33 33 22 33 42 42 22
S_{4}^{+}  -6 0 -4 1^{2} 3_{−} 2∗ 2∗  22 33 22 33 33 42 42 22
64. 2_{−} 14_{−} 2_{+} 0 -2  0 1^{4} 11_{i} −2 −2∗ 1^{2} 1_{−} 13∗ 13∗ 33 33 33 42 33 42 22 42
S_{4}^{+}  6 0 -4 1^{2} 3_{i} −2 −2 1^{2} 1_{−} 13∗ 13∗ 22 33 42 33 33 22 22 42
65. 2_{−} 8_{+} 4_{−} -3 0 12 1^{4} 8_{+} 1 {−2∗ \atop −∗} 1^{4} 3_{+} 13∗ 13∗ 33 33 33 42 33 22 42 42
S_{4}^{+}  2  -7 -3 -4  1^{2} 1_{−} 13∗ 13∗ 22 33 22 33 33 42 22 22
66. 2_{−} 8_{−} 4_{+} 0 -1  0 1^{4} 8_{−} ∗ −1 1^{3} 2_{+} 1  42 33 22 22 33 42 42 33
S_{4}^{+}  3  9 0 -1 2 0_{+} ∗  ∗ 1^{3} 2_{+} 1  42 33 33 22 42 33 22 33
67. 2_{−} 12_{−} 4_{+} 0 -10  0 1^{4} 9_{+} 2∗ −1 1^{3} 2_{+} 1  42 33 42 42 33 42 22 33
S_{4}^{+}  3  42 0 -64 1^{2} 3_{−} 2∗ 2∗ 1^{3} 2_{+} 1  22 33 33 22 42 33 42 33
68. 2_{−} 12_{+} 4_{−} 0 -13  0 1^{4} 10_{k} −∗ −2∗ 1^{4} 3_{+} 13∗ 13∗ 33 33 33 22 33 22 22 22
S_{4}^{+}  2  65 0 -169 1^{2} 2_{i} −∗ −∗ 1^{2} 1_{−} 13∗ 13∗ 22 33 42 33 33 22 42 42
69. 2_{−} 12_{−} 4_{+} 0 -4  0 1^{4} 9_{−} 2 −1 1^{3} 2_{+} 1  22 33 42 42 33 22 42 33
S_{4}^{+}  3  40 0 -64 1^{2} 3_{+} 2  2 1^{3} 2_{+} 1  42 33 33 22 22 33 42 33
70. 2_{−} 14_{+} 4_{−} 0 -26  0 1^{4} 11_{−} 2∗ −2∗ 1^{4} 3_{+} 13∗ 13∗ 33 33 33 42 33 42 22 42
S_{4}^{+} 4 234 0 -676 1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{−} 13∗ 13∗ 33 22 33 33 22 42 22
71. 2_{−} 14_{+} 4_{−} 0 -26  0 1^{4} 11_{k} −2 −2∗ 1^{4} 3_{+} 13∗ 13∗ 33 33 33 22 33 42 42 22
S_{4}^{+}  2  -26 0 -676 1^{2} 3_{i} −2 −2 1^{2} 1_{−} 13∗ 13∗ 22 33 42 33 33 42 22 42

Discriminant class: 2

∞  2 13 a_{1} a_{2} a_{3}  Over p = 2  Over p = 13  3 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
72.  0_{+}  9_{+} 4_{+} -2 -13 14 3^{2} 9_{+} 2  2^{3} 4_{+} ∗  6 222 33 6 33 6 33 6
C_{6}  26 -28  1  6 33 6  222 6 6
73.  2_{−}  11_{+} 2_{−} -2 3  0 1^{4} 8_{+} 1 {−2∗ \atop −∗} 2^{2} 2_{−} 1  V 6 6 33 222 33 222 22 222
D_{6}  -3 -2 -1 1^{2} 3_{+} 2  2 2 0_{+} ∗  ∗  6 22 6 33 222 222 222
74.  2_{−}  11_{−} 4_{+} 0 8  0 1^{4} 8_{−} 1  {−2 \atop −1} 2^{3} 4_{+} ∗  222 6 22 222 33 222 22 6
D_{6}  3  17 0 -8 1^{2} 3_{+} 2  2  22 6 33 222 22 6 222 6
75.  2_{−}  9_{−} 4_{+} 0 -2  0 3^{2} 9_{−} 2  2^{3} 4_{+} ∗  6 2 33 6 33 6 33 6
A_{4} × C_{2}  -16 0 -8  22 6 33 6  2 6 6
76.  2_{−}  11_{−} 2_{+} 0 3  0 1^{4} 11_{−} 2∗ −2∗ 2 0_{+} ∗  ∗ 6 6 33 222 33 4 42 222
S_{4} × C_{2}  2 0 -2 2 0_{+} ∗  ∗ 1^{2} 1_{−} 13∗ 13∗ 22 6 22 6 33 4 4 222
77.  2_{−}  13_{+} 2_{−} 0 -3  0 1^{4} 11_{k} −2 −2∗ 2^{2} 2_{−} 1  V 6 6 33 4 33 4 22 4
S_{4} × C_{2}  2 0 -2 1^{2} 2_{i} −1 −1 2 0_{+} ∗  ∗ 22 6 42 6 33 222 222 4
78.  2_{−}  13_{−} 2_{+} 0 0  0 1^{4} 10_{k} −∗ −2∗ 2 0_{+} ∗  ∗ 6 6 33 4 33 222 42 4
S_{4} × C_{2}  -1 0 -2 1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{−} 13∗ 13∗ 22 6 42 6 33 4 4 4
79.  2_{−}  9_{−} 4_{+} 0 -2  0 1^{4} 9_{−} 2 −1 2^{3} 4_{+} ∗  222 6 42 4 33 222 42 6
S_{4} × C_{2}  3  10 0 -8  42 6 33 222 22 6 4 6
80.  2_{−}  9_{−} 4_{+} 0 -2  0 1^{4} 6_{+} ∗ −1 2^{3} 4_{+} ∗  4 6 22 222 33 4 42 6
S_{4} × C_{2}  3  -3 0 -8 1^{2} 3_{−} 2∗  2∗  42 6 33 222 42 6 222 6
81.  2_{−}  9_{−} 4_{+} 0 7  0 1^{4} 9_{−} 2∗ −1 2^{3} 4_{+} ∗  4 6 42 4 33 4 22 6
S_{4} × C_{2}  3  12 0 -8 2 0_{+} ∗  ∗  22 6 33 222 42 6 4 6

Discriminant class: 2 (continued)

∞  2 13 a_{1} a_{2} a_{3}  Over p = 2  Over p = 13  3 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
82.  2_{−}  9_{−} 4_{+} 2 -5  8 1^{2} 3_{k} −2∗ −2∗ 1^{4} 3_{+} 13∗ 13∗ 6 6 33 4 33 222 42 4
S_{4} × C_{2}  2  10 -16 -16 1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{+} 13 13 22 6 22 6 33 4 222 222
83.  2_{−}  11_{−} 4_{+} -1 -3 14 1^{4} 11_{−} 2∗ −2∗ 1^{4} 3_{+} 13∗ 13∗ 6 6 33 4 33 4 22 4
S_{4} × C_{2}  2  -59 117 -107 2 0_{+} ∗  ∗ 1^{2} 1_{+} 13 13  6 22 6 33 222 4 222
84.  2_{−}  13_{−} 4_{+} 0 13  0 1^{4} 11_{i} −2 −2∗ 1^{4} 3_{+} 13∗ 13∗ 6 6 33 222 33 4 42 222
S_{4} × C_{2}  2  26 0 -338 1^{2} 2_{i} −1 −1 1^{2} 1_{+} 13 13 22 6 42 6 33 4 222 4
85.  2_{−}  13_{−} 4_{+} 0 0  0 1^{4} 10_{k} −∗ −2∗ 1^{4} 3_{+} 13∗ 13∗ 6 6 33 222 33 222 22 222
S_{4} × C_{2}  2  143 0 -338 1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{+} 13 13 22 6 42 6 33 222 4 4
86.  2_{−}  11_{−} 4_{+} 0 2  8 1^{6} 11_{−} 2  1^{5} 4_{+} ∗  4 6 33 4 5 6 5 222
S_{5}  2  20 16 -8  33 4 33 4 5 6 6 4

Discriminant class: 13

∞  2 13 a_{1} a_{2} a_{3}  Over p = 2  Over p = 13  3 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
87.  0_{+}  0_{+} 5_{+} 1 -5 -4 6 0_{+} ∗  1^{6} 5_{+} 13  33 222 6 6 33 6 33 33
C_{6}  6 3 -1  222 6 6 33 222  6 33
88.  2_{−}  6_{+} 3_{−} 1 2 -1 2^{2} 6_{+} 1 {−2 \atop −2∗} 2^{2} 2_{−} 1  V 33 6 6 222 33 222 22 22
D_{6}  -2 1 -1 2 0_{+} ∗  ∗ 1^{2} 1_{+} 13 13 222 6 222 33 6 22 222 22
89.  2_{−}  4_{−} 5_{+} -1 -5  4 2^{2} 4_{−} 1  {−1 \atop −∗} 1^{6} 5_{+} 13  22 6 222 222 33 222 22 33
D_{6}  3  6 -16 12 2 0_{+} ∗  ∗  222 6 6 22 222 33 222 33
90.  2_{−}  6_{−} 5_{+} 0 0  0 3^{2} 6_{−} ∗  1^{6} 5_{+} 13  33 2 6 6 33 6 33 33
A_{4} × C_{2}  2  -13 0 -13  2 6 6 33 222 22 6 33
91.  2_{−}  8_{−} 3_{+} 3 5  2 1^{4} 8_{−} 1 {−2∗ \atop −1} 1^{4} 3_{+} 13∗ 13∗ 33 6 6 4 33 222 42 42
S_{4} × C_{2}  -4 -6 -2 2 0_{+} ∗  ∗ 2 0_{+} ∗  ∗ 2 6 222 33 6 42 222 22
92.  2_{−}  12_{−} 3_{+} 0 7  0 1^{4} 10_{i} −∗ −2∗ 1^{2} 1_{−} 13∗ 13∗ 33 6 6 4 33 222 42 42
S_{4} × C_{2}  2  9 0 -13 1^{2} 2_{i} −1 −1 1^{2} 1_{+} 13 13 2 6 4 33 6 42 4 42
93.  2_{−}  12_{−} 3_{+} 0 -5  0 1^{4} 10_{i} −∗ −2∗ 1^{4} 3_{+} 13∗ 13∗ 33 6 6 222 33 222 22 22
S_{4} × C_{2}  13 0 -13 1^{2} 2_{i} −1 −1 2 0_{+} ∗  ∗ 2 6 4 33 6 22 4 42
94.  2_{−}  14_{−} 3_{+} 0 6  0 1^{4} 11_{−} 2∗ −2∗ 1^{4} 3_{+} 13∗ 13∗ 33 6 6 4 33 4 22 42
S_{4} × C_{2}  2  26 0 -52 1^{2} 3_{+} 2  2 2 0_{+} ∗  ∗ 222 6 222 33 6 22 4 22
95.  2_{−}  14_{+} 3_{−} 0 -10  0 1^{4} 11_{i} −2 −2∗ 2^{2} 2_{−} 1  V 33 6 6 4 33 4 22 42
S_{4} × C_{2}  2  38 0 -52 1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{+} 13 13 2 6 4 33 6 22 222 42
96.  2_{−}  14_{−} 3_{+} 0 -2  0 1^{4} 11_{−} 2∗ −2∗ 1^{2} 1_{−} 13∗ 13∗ 33 6 6 222 33 4 42 22
S_{4} × C_{2}  2  40 0 -208 1^{2} 3_{+} 2  2 1^{2} 1_{+} 13 13 2 6 222 33 6 42 4 22
97.  2_{−}  14_{−} 3_{+} 0 -2  0 1^{4} 11_{k} −2 −2∗ 1^{4} 3_{+} 13∗ 13∗ 33 6 6 222 33 4 42 22
S_{4} × C_{2}  -26 0 -52 1^{2} 3_{k} −2∗ −2∗ 2 0_{+} ∗  ∗ 2 6 4 33 6 42 222 42
98.  2_{−}  8_{−} 5_{+} 0 0  0 1^{4} 8_{−} ∗ −1 1^{6} 5_{+} 13  42 6 222 222 33 4 42 33
S_{4} × C_{2}  6  13 0 -52  4 6 6 22 4 33 222 33
99.  2_{−}  12_{−} 5_{+} 0 0  0 1^{4} 9_{−} 2∗ −1 1^{6} 5_{+} 13  42 6 4 4 33 4 22 33
S_{4} × C_{2}  6  -26 0 -52 1^{2} 3_{+} 2  2  222 6 6 22 4 33 4 33
100.  2_{−}  12_{−} 5_{+} 0 0  0 1^{4} 9_{+} 2 −1 1^{6} 5_{+} 13  22 6 4 4 33 222 42 33
S_{4} × C_{2}  6  78 0 -52 1^{2} 3_{−} 2∗  2∗  4 6 6 22 222 33 4 33

∞  2 13 a_{1} a_{2} a_{3}  Over p = 2  Over p = 13  3 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
101.  0_{+}  9_{−} 5_{−} 0 -26  0 3^{2} 9_{−} 2∗  1^{6} 5_{−} 13∗  6  6 33 33 33 33 6
C_{6}  2  104 0 -104  222 33 6 6 222 222 33 6
102.  2_{−}  11_{+} 3_{−} 2 -3 -4 1^{4} 8_{−} 1 {−2∗ \atop −1} 1^{2} 1_{−} 13∗ 13∗ 6 33 6 22 33 22 22 222
D_{6}  2  4 0 -26 1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{−} 13∗ 13∗ 222 33 222 6 6 222 22 222
103.  2_{−}  11_{+} 5_{−} 0 0  0 1^{4} 8_{−} 1 {−2∗ \atop −1} 1^{6} 5_{−} 13∗  222 33 222 22 33 22 22 6
D_{6}  6  -39 0 -416 1^{2} 3_{−} 2∗ 2∗  222 33 6 222 222 6 22 6
104.  2_{−}  9_{+} 5_{−} 0 0  0 3^{2} 9_{+} 2∗  1^{6} 5_{−} 13∗  6 22 6 33 33 33 33 6
A_{4} × C_{2}  2  -52 0 -104  2 33 6 6 222 2 33 6
105.  2_{−}  11_{+} 5_{−} -2 -7 32 1^{4} 8_{−} 1 {−2∗ \atop −1} 1^{6} 5_{−} 13∗  6 3 6 22 3 22 22 6
S_{3} × S_{3}  6  -47 86 -103 1^{2} 3_{−} 2∗ 2∗  222 3 6 6 6 6 22 6
106.  2_{−}  9_{−} 3_{+} 0 -4 -2 2^{2} 6_{+} 1 {−2 \atop −2∗} 1^{4} 3_{+} 13∗ 13∗ 6 33 6 42 33 22 42 4
S_{4} × C_{2}  4 0 -1 1^{2} 3_{−} 2∗ 2∗  2 33 222 6 6 4 22 222
107.  2_{−}  11_{−} 3_{+} 1 0 -10 1^{4} 11_{−} 2∗ −2∗ 1^{4} 3_{+} 13∗ 13∗ 6 33 6 42 33 42 22 4
S_{4} × C_{2}  -5 -1 -2  222 33 222 6 6 222 42 222
108.  2_{−}  11_{−} 3_{+} 1 -6 -2 1^{4} 11_{−} 2∗ −2∗ 2^{2} 2_{−} 1  V 6 33 6 22 33 42 42 222
S_{4} × C_{2}  2  15 -9 -4  1^{2} 1_{−} 13∗ 13∗ 2 33 222 6 6 4 42 222
109.  2_{−}  13_{−} 3_{+} 0 12  0 1^{4} 10_{i} −∗ −2∗ 1^{4} 3_{+} 13∗ 13∗ 6 33 6 22 33 22 22 222
S_{4} × C_{2}  39 0 -26 1^{2} 3_{i} −2 −2  2 33 4 6 6 222 42 4
110.  2_{−}  13_{−} 3_{+} 0 1  0 1^{4} 11_{i} −2 −2∗ 1^{4} 3_{+} 13∗ 13∗ 6 33 6 22 33 42 42 222
S_{4} × C_{2}  26 0 -26 1^{2} 2_{i} −∗ −∗  2 33 4 6 6 4 22 4
111.  2_{−}  13_{−} 3_{+} 0 -4  0 1^{4} 10_{i} −∗ −2∗ 2^{2} 2_{−} 1  V 6 33 6 42 33 22 42 4
S_{4} × C_{2}  2  -9 0 -26 1^{2} 3_{i} −2 −2 1^{2} 1_{−} 13∗ 13∗ 2 33 4 6 6 4 42 4
112.  2_{−}  13_{+} 3_{−} 0 -7  0 1^{4} 11_{k} −2 −2∗ 1^{2} 1_{−} 13∗ 13∗ 6 33 6 42 33 42 22 4
S_{4} × C_{2}  2  -30 0 -26 1^{2} 2_{i} −∗ −∗ 1^{2} 1_{−} 13∗ 13∗ 2 33 4 6 6 222 22 4
113.  2_{−}  9_{+} 5_{−} -1 8  4 1^{4} 9_{+} 2∗ −1 1^{6} 5_{−} 13∗  4 33 4 42 33 42 22 6
S_{4} × C_{2}  6  -7 75 64  222 33 6 222 4 6 42 6
114.  2_{−}  9_{+} 5_{−} -2 6 -20 1^{4} 6_{+} ∗ −1 1^{6} 5_{−} 13∗  4 33 222 22 33 42 42 6
S_{4} × C_{2}  6  18 8 -12 1^{2} 3_{+} 2  2  4 33 6 222 4 6 22 6
115.  2_{−}  9_{+} 5_{−} 1 -5 -4 1^{4} 9_{+} 2 −1 1^{6} 5_{−} 13∗  222 33 4 42 33 22 42 6
S_{4} × C_{2}  6  -7 -23 -1 2 0_{+} ∗  ∗  4 33 6 222 222 6 42 6
116.  2_{−}  11_{+} 5_{−} -3 -6  4 1^{4} 11_{+} 2∗ 2∗ 1^{6} 5_{−} 13∗  4 5 6 33 33 5 5 4
S_{5}  6  18 -14 12  6 33 4 6 4 4 22 4