Old Sextic Fields Ramifying Above {2, 3}

Discriminant class: −6

∞  2  3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3 5 7 11 13 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_{−} 7_{i}  0 0 0 1^{2} 3_{−} 2∗  2∗ 1^{6} 7_{i} 3  33 33 33 222 222 222 222
S_{3}  2  -3 0 6 1^{2} 3_{−} 2∗  2∗  33 222 222 222 222 33  222
2.  3_{i}  9_{−} 9_{i}  0 12 0 3^{2} 9_{−} 2∗  1^{6} 9_{i} 3  33 33 33 6 222 222 6 33
C_{6}  2  36 0 24  33 222 6 6 6  33 6
3.  3_{i}  11_{+} 7_{k} 0 6 0 1^{6} 11_{+} 2∗  1^{6} 7_{k} 3  22 33 22 6 222 6 222 22
D_{6}  2  12 0 6  6 222 222 222 22 22 6
4.  3_{i}  11_{+} 9_{k} 0 6 0 1^{4} 8_{−} 1 {−2∗ \atop −1} 1^{6} 9_{k} 3  33 22 22 6 6 222 222 33
D_{6}  2  9 0 6 1^{2} 3_{−} 2∗  2∗  22 6 222 222 222  22 6
5.  3_{i}  11_{−} 9_{i}  0 6 4 1^{4} 8_{+} 1  {−2 \atop −∗} 1^{6} 9_{i} 3  22 22 33 222 6 6 222 22
D_{6}  6  9 12 10 1^{2} 3_{−} 2∗  2∗  22 222 6 6 222 22 33 222
6.  3_{i}  9_{+} 11_{k} 0 0 0 2^{2} 6_{−} 1  {∗ \atop 2} 1^{6} 11_{k} 3  22 33 22 6 222 6 222 22
D_{6}  4  0 0 24 1^{2} 3_{−} 2∗  2∗  33 6 222 6 222 22 22 222
7.  3_{i}  11_{+} 11_{k} 0 18 0 1^{4} 8_{−} 1 {−2∗ \atop −1} 1^{6} 11_{k} 3  33 22 22 222 222 6 6 33
D_{6}  4  81 0 96 1^{2} 3_{−} 2∗  2∗  22 222 222 222 6 33 22 222
8.  3_{i}  11_{+} 11_{k} 0 0 0 1^{6} 11_{+} 2∗  1^{6} 11_{k} 3  22  22 6 222 6 222 22
D_{6}  2  0 0 6  33 222 222 6 222 22 22 6
9.  3_{i}  11_{+} 11_{k} 0 0 0 1^{6} 11_{+} 2∗  1^{6} 11_{k} 3  22 33 22 222 222 222 222 22
D_{6}  2  0 0 96  33 6 222 6 222 22 22 6
10.  3_{i}  9_{−} 9_{i}  0 6 2 3^{2} 9_{−} 2∗  1^{6} 9_{i} 3  3 3 3 6 222 222 6 33
S_{3} × C_{3}  2  9 6 7  3 222 6 6 6 33 33 6
11.  3_{i}  11_{−} 7_{i}  0 3 0 1^{4} 11_{−} 2∗  2∗ 1^{6} 7_{i} 3  33 33 33 4 4 222 222 22
S_{4}^{−}  2  6 0 6  33 222 222 4 4 33 22 222
12.  1_{k}  9_{+} 9_{i}  0 -6 0 3^{2} 9_{+} 2∗  1^{6} 9_{i} 3  33 33 33 6 2 2 6 33
A_{4} × C_{2}  0 0 24  33 2 6 6 6 22 33 6
13.  3_{i}  13_{−} 7_{i}  0 6 0 1^{4} 10_{k} −1 2∗ 1^{6} 7_{i} 3  33 33 33 4 4 4 4 22
S_{4}^{−}  2  -12 0 24 1^{2} 3_{k} −2∗ −2∗  33 4 4 222 222 33 22 222
14.  3_{i}  13_{−} 7_{i}  0 9 0 1^{4} 11_{i} −2∗ 2∗ 1^{6} 7_{i} 3  33 33 33 222 222 4 4 22
S_{4}^{−}  2  24 0 24 1^{2} 2_{i} −1 −1  33 4 4 4 4 33 22 222
15.  3_{i}  11_{+} 11_{k} 0 0 -12 1^{4} 8_{−} 1 {−2∗ \atop −1} 1^{6} 11_{k} 3  3 22 22 6 6 6 6 3
S_{3} × S_{3}  2  54 -72 60 1^{2} 3_{−} 2∗  2∗  22 6 222 222 6 33 22 6
16.  3_{i}  3_{+} 11_{k} -3 6 -10 4 0_{+} ∗  ∗ 1^{6} 11_{k} 3  42 33 22 6 4 6 4 22
S_{4} × C_{2}  2  15 -12 4 1^{2} 3_{+} 2  2  33 6 4 6 222 22 42 2
17.  3_{i}  11_{+} 7_{k} 0 0 0 1^{6} 11_{+} 2∗  1^{6} 7_{k} 3  42 33 42 6 4 6 4 22
S_{4} × C_{2}  2  -6 0 6  22 6 222 2 4 22 42 6
18.  3_{i}  9_{+} 9_{k} 0 9 -4 1^{4} 6_{+} ∗ −1 1^{6} 9_{k} 3  33 42 42 6 6 4 4 33
S_{4} × C_{2}  2  9 0 1 1^{2} 3_{+} 2  2  22 6 2 4 222 22 22 6
19.  3_{i}  9_{+} 9_{k} 0 6 0 1^{4} 9_{+} 2∗ −1 1^{6} 9_{k} 3  33 22 42 6 6 222 4 33
S_{4} × C_{2}  2  18 0 24  42 6 2 4 4 22 22 6
20.  3_{i}  9_{+} 9_{k} 0 -3 0 1^{4} 9_{+} 2 −1 1^{6} 9_{k} 3  33 42 22 6 6 4 222 33
S_{4} × C_{2}  2  0 0 6 2 0_{+} ∗  ∗  42 6 2 222 4  22 6
21.  3_{i}  7_{+} 11_{k} 0 9 0 2^{2} 4_{k} −∗  ∗ 1^{6} 11_{k} 3  22 33 42 6 4 6 4 42
S_{4} × C_{2}  2  27 0 24 1^{2} 3_{i} −2 −2  33 6 222 6 4 42 22 2
22.  3_{i}  11_{−} 9_{i}  3 3 -4 1^{4} 11_{−} 2 −2 1^{6} 9_{i} 3  22 42 33 4 6 6 4 42
S_{4} × C_{2}  6  -6 -6 10 2 0_{+} ∗  ∗  22 222 6 6 4 22 33 222

Discriminant class: −6 (continued)

∞  2  3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3 5 7 11 13 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}  9_{+} 11_{k} 0 0 0 2^{2} 6_{i} −1  ∗ 1^{6} 11_{k} 3  42 33 42 6 222 6 222 42
S_{4} × C_{2}  2  -36 0 96 1^{2} 3_{k} −2∗ −2∗  33 6 4 6 4 42 42 2
24.  1_{k}  9_{−} 11_{k} 0 0 -6 2^{2} 6_{+} 1 {−2 \atop −2∗} 1^{6} 11_{k} 3  33 42 42 4 4 6 6 33
S_{4} × C_{2}  -54 36 -3 1^{2} 3_{−} 2∗  2∗  22 222 4 2 6 33 42 4
25.  3_{i}  13_{−} 9_{i}  0 -6 0 1^{4} 10_{i} −∗ −2 1^{6} 9_{i} 3  42 22 33 4 6 6 4 22
S_{4} × C_{2} 12  0 0 96 1^{2} 3_{i} −2 −2  22 4 6 6 4 22 33 222
26.  3_{i}  13_{−} 9_{i}  0 12 0 1^{4} 11_{i} −2∗ −2 1^{6} 9_{i} 3  42 42 33 222 6 6 222 42
S_{4} × C_{2}  6  54 0 96 1^{2} 2_{i} −1 −1  22 4 6 6 222 22 33 222
27.  3_{i}  11_{+} 11_{k} 0 0 0 1^{6} 11_{+} 2∗  1^{6} 11_{k} 3  22 33 42 2 222 2 4 42
S_{4} × C_{2}  2  18 0 6  33 6 4 6 222 22 42 6
28.  1_{k}  11_{−} 11_{k} 0 -9 0 1^{4} 11_{−} 2∗ −2∗ 1^{6} 11_{k} 3  33 42 22 222 4 6 6 33
S_{4} × C_{2}  0 0 96  42 222 4 2 6 33 22 4
29.  3_{i}  11_{+} 11_{k} 0 0 0 1^{6} 11_{+} 2∗  1^{6} 11_{k} 3  42 22 42 6 4 6 4 22
S_{4} × C_{2}  2  -36 0 294  33 2 222 6 222 42 42 6
30.  1_{k}  11_{−} 11_{k} 0 -9 0 1^{4} 11_{−} 2∗ −2∗ 1^{6} 11_{k} 3  33 22 42 4 222 6 6 33
S_{4} × C_{2}  18 0 6  42 222 222 2 6 33 42 222
31.  1_{k}  13_{−} 11_{k} 0 0 0 1^{4} 10_{i} −∗ −2∗ 1^{6} 11_{k} 3  33 42 42 222 4 6 6 33
S_{4} × C_{2}  2  -9 0 6 1^{2} 3_{i} −2 −2  42 222 222 222 6 33 22 4
32.  1_{k}  13_{−} 11_{k} 0 0 0 1^{4} 11_{i} −2 −2∗ 1^{6} 11_{k} 3  33 22 42 222 222 6 6 33
S_{4} × C_{2}  2  -18 0 24 1^{2} 2_{i} −∗ −∗  22 222 4 2 6 33 22 222
33.  1_{k}  13_{−} 11_{k} 0 -18 0 1^{4} 10_{i} −∗ −2∗ 1^{6} 11_{k} 3  33 22 22 4 222 6 6 33
S_{4} × C_{2}  2  36 0 24 1^{2} 3_{i} −2 −2  42 222 4 2 6 33 42 222
34.  3_{i}  13_{+} 11_{k} 0 9 0 1^{4} 11_{k} −2 −2∗ 1^{6} 11_{k} 3  33 42 22 4 4 6 6 33
S_{4} × C_{2}  8  18 0 6 1^{2} 2_{i} −∗ −∗  22 222 222 2 6 33 42 4
35.  3_{i}  11_{+} 11_{k} 0 9 24 1^{4} 11_{+} 2∗  2∗ 1^{6} 11_{k} 3  5 5 33 6 6 6 6 33
S_{5}  2  27 72 123  5 4 4 4 4 22 5 4

Discriminant class: −3

∞  2  3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  5 7 11 13 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
36.  3_{i}  4_{+} 7_{k} 0 3 4 2^{3} 4_{+} ∗  1^{6} 7_{k} 3∗  222 33 222 33 222 33 222 222
S_{3}  3 0 1  33 222  222 222 222 33
37.  3_{i}  4_{+} 11_{k} 0 0 0 2^{3} 4_{+} ∗  1^{6} 11_{k} 3∗  222  222 33 222 33 222 222
S_{3}  0 0 48  33  222 33 222 222 222 33
38.  3_{i}  4_{+} 11_{k} 0 0 0 2^{3} 4_{+} ∗  1^{6} 11_{k} 3∗  222 33 222  222  222 222
S_{3}  0 0 12  33 33 222 33 222 222 222 33
39.  3_{i}  6_{−} 7_{i}  0 6 -2 2^{2} 6_{−} 1  {∗ \atop 2} 1^{6} 7_{i} 3∗  6 33 6 22 222 22 222 222
D_{6}  6 0 1 2 0_{+} ∗  ∗  33 22 222 22 222 6 222 22
40.  3_{i}  4_{−} 9_{i}  0 6 2 2^{2} 4_{−} 1  {−1 \atop −∗} 1^{6} 9_{i} 3∗  6 22 222 33 6 22 222 6
D_{6}  9 6 4 2 0_{+} ∗  ∗  22 33 222 22 222 222 222 33
41.  3_{i}  6_{+} 9_{k} 0 -3 0 2^{2} 6_{+} 1 {−2 \atop −2∗} 1^{6} 9_{k} 3∗  222 22 6 22 6 33 222 222
D_{6}  3  9 18 12 2 0_{+} ∗  ∗  22 22 6 33 222 222 6 22
42.  3_{i}  6_{+} 11_{k} 0 9 12 2^{2} 6_{+} 1 {−2 \atop −2∗} 1^{6} 11_{k} 3∗  6 22 222 22 222 33 6 6
D_{6}  81 54 36 2 0_{+} ∗  ∗  22 22 222  6 6 222 22
43.  3_{i}  4_{+} 9_{k} 0 0 -2 2^{3} 4_{+} ∗  1^{6} 9_{k} 3∗  6 3 6 3 222 33 6 6
S_{3} × C_{3}  0 0 4  33 33 6 33 6 222 6 3

∞  2  3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  5 7 11 13 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}  4_{+} 11_{k} 0 0 6 2^{3} 4_{+} ∗  1^{6} 11_{k} 3∗  6 3 6 33 222  6 6
S_{3} × C_{3}  0 0 12  3 33 6 3 6 222 6 3
45.  3_{i}  4_{+} 11_{k} 0 0 -6 2^{3} 4_{+} ∗  1^{6} 11_{k} 3∗  6 33 6 3 222 33 6 6
S_{3} × C_{3}  0 0 36  3  6 3 6 222 6 3
46.  1_{k}  6_{−} 9_{k} 0 -3 0 3^{2} 6_{−} ∗  1^{6} 9_{k} 3∗  6 33 6 33 2 22 6 6
A_{4} × C_{2}  0 0 3  33 22 6 33 6 2 6 33
47.  3_{i}  10_{+} 7_{k} 0 3 0 1^{6} 10_{+} ∗  1^{6} 7_{k} 3∗  4 33 4 33 4 33 4 222
S_{4}^{−}  2  3 0 3  22 33 222 22 4 222 4 33
48.  3_{i}  6_{+} 11_{k} 0 0 12 1^{6} 6_{+} ∗  1^{6} 11_{k} 3∗  4 22 4 33 4 33 4 222
S_{4}^{−}  2  0 -18 30  33 22 222 33 222 4 4 33
49.  3_{i}  6_{+} 11_{k} 0 9 0 2^{2} 6_{+} ∗  ∗ 1^{6} 11_{k} 3∗  4 33 222 33 4 33 4 222
S_{4}^{−}  4  18 0 12  33 33 4 33 222 222 4 22
50.  3_{i}  6_{+} 11_{k} 0 0 0 2^{2} 4_{k} −1  ∗ 1^{6} 11_{k} 3∗  4 33 4 33 222 33 222 4
S_{4}^{−}  2  -9 0 12 1^{2} 2_{i} −∗ −∗  33 33 4 33 4 4 4 22
51.  3_{i}  8_{+} 11_{k} 0 -9 0 2^{2} 6_{k} −∗  ∗ 1^{6} 11_{k} 3∗  222 33 4 33 4 33 4 4
S_{4}^{−}  2  18 0 12 1^{2} 2_{i} −1 −1  33 33 222 33 4 4 222 22
52.  3_{i}  10_{+} 11_{k} 0 9 0 1^{6} 10_{+} ∗  1^{6} 11_{k} 3∗  222 33 4 22 222 22 4 4
S_{4}^{−}  2  9 0 3  33 33 4 33 222 222 4 33
53.  3_{i}  6_{+} 11_{k} 0 0 0 2^{2} 6_{+} 1 {−2 \atop −2∗} 1^{6} 11_{k} 3∗  6 22 6 22 6 3 6 6
S_{3} × S_{3}  27 -36 12 2 0_{+} ∗  ∗  22 22 6 33 6 6 6 22
54.  3_{i}  8_{−} 9_{i}  0 3 0 1^{4} 8_{−} ∗ −1 1^{6} 9_{i} 3∗  6 42 4 33 6 42 4 6
S_{4} × C_{2}  2  9 0 3  22 33 2 42 222 2 222 33
55.  3_{i}  12_{−} 7_{i}  0 3 0 1^{4} 10_{i} −1 2∗ 1^{6} 7_{i} 3∗  6 33 6 42 4 42 4 2
S_{4} × C_{2}  2  -3 0 3 1^{2} 2_{i} −∗ −∗  33 42 4 22 222 6 2 22
56.  3_{i}  14_{−} 7_{i}  0 6 0 1^{4} 11_{−} 2∗  2∗ 1^{6} 7_{i} 3∗  6 33 6 42 4 22 222 2
S_{4} × C_{2}  4  24 0 48 1^{2} 3_{+} 2  2  33 22 222 42 4 6 2 22
57.  3_{i}  14_{−} 7_{i}  0 -6 0 1^{4} 11_{i} −2∗ 2∗ 1^{6} 7_{i} 3∗  6 33 6 22 222 42 4 2
S_{4} × C_{2}  2  6 0 12 1^{2} 3_{i} −2 −2  33 42 4 42 4 6 2 22
58.  1_{k}  8_{−} 11_{k} 3 -3 -14 1^{4} 8_{−} 1 {−2∗ \atop −1} 1^{6} 11_{k} 3∗  6 42 4 42 4 33 6 6
S_{4} × C_{2}  -12 -6 -2 2 0_{+} ∗  ∗  22 22 4 22 6 6 4 42
59.  3_{i}  12_{−} 9_{i}  0 -6 0 1^{4} 9_{+} 2 −1 1^{6} 9_{i} 3∗  6 42 222 33 6 42 222 6
S_{4} × C_{2}  2  0 0 48 1^{2} 3_{−} 2∗  2∗  42 33 2 22 4 222 222 33
60.  3_{i}  12_{−} 9_{i}  0 12 0 1^{4} 9_{−} 2∗ −1 1^{6} 9_{i} 3∗  6 22 4 33 6 22 4 6
S_{4} × C_{2}  2  -18 0 12 1^{2} 3_{+} 2  2  42 33 2 42 4 2 222 33
61.  3_{i}  12_{+} 9_{k} 0 -3 0 1^{4} 10_{k} −∗ −2 1^{6} 9_{k} 3∗  4 22 6 42 6 33 4 222
S_{4} × C_{2}  6  0 0 12 1^{2} 2_{i} −1 −1  22 42 6 33 4 222 6 22
62.  3_{i}  14_{+} 9_{k} 0 6 0 1^{4} 11_{−} 2 −2 1^{6} 9_{k} 3∗  222 42 6 42 6 33 4 4
S_{4} × C_{2}  6  18 0 12 1^{2} 3_{−} 2∗  2∗  22 22 6 33 4 222 6 22
63.  3_{i}  14_{+} 9_{k} 0 6 0 1^{4} 11_{k} −2∗ −2 1^{6} 9_{k} 3∗  4 42 6 22 6 33 222 4
S_{4} × C_{2} 24  -18 0 12 1^{2} 3_{i} −2 −2  22 42 6 33 222 222 6 22
64.  1_{k}  12_{−} 11_{k} 0 0 0 1^{4} 10_{i} −∗ −2∗ 1^{6} 11_{k} 3∗  6 42 4 22 4 33 6 6
S_{4} × C_{2}  -36 0 48 1^{2} 2_{i} −1 −1  42 22 222  6 6 222 42
65.  1_{k}  12_{−} 11_{k} 0 -9 0 1^{4} 10_{i} −∗ −2∗ 1^{6} 11_{k} 3∗  6 22 222 42 222 33 6 6
S_{4} × C_{2}  9 0 3 1^{2} 2_{i} −1 −1  42 22 4 22 6 6 4 22
66.  1_{k}  14_{−} 11_{k} 0 -18 0 1^{4} 11_{−} 2∗ −2∗ 1^{6} 11_{k} 3∗  6 22 4 42 222 33 6 6
S_{4} × C_{2}  72 0 48 1^{2} 3_{+} 2  2  42 22 222 22 6 6 4 22

∞  2  3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  5 7 11 13 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
67.  3_{i}  14_{+} 11_{k} 0 18 0 1^{4} 11_{i} −2 −2∗ 1^{6} 11_{k} 3∗  6 42 222 42 4 33 6 6
S_{4} × C_{2}  8  72 0 48 1^{2} 3_{k} −2∗ −2∗  22 22 222 22 6 6 4 42
68.  1_{k}  14_{−} 11_{k} 0 -18 0 1^{4} 11_{−} 2∗ −2∗ 1^{6} 11_{k} 3∗  6 42 222 22 4 33 6 6
S_{4} × C_{2}  -54 0 108 1^{2} 3_{+} 2  2  42 22 4 22 6 6 222 42
69.  1_{k}  14_{−} 11_{k} 0 -18 0 1^{4} 11_{k} −2 −2∗ 1^{6} 11_{k} 3∗  6 22 4 22 222 33 6 6
S_{4} × C_{2}  2  54 0 12 1^{2} 3_{k} −2∗ −2∗  22 22 4 22 6 6 222 22

Discriminant class: −2

∞  2  3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  5 7 11 13 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
70.  3_{i}  9_{k} 8_{+} 0 -6 0 1^{2} 3_{i} −2 −2 1^{3} 4_{+} 1  222 222 33 222 33 33 222 222
S_{3}  3  9 0 8 1^{2} 3_{i} −2 −2 1^{3} 4_{+} 1  222 222 33 33 222 222 33 222
71.  3_{i}  9_{k} 8_{+} 0 12 0 3^{2} 9_{k} −2  1^{3} 4_{+} 1  6 6 33 6  6 6
C_{6}  3  36 0 8  1^{3} 4_{+} 1  6 222 33 33 6 222 33 6
72.  3_{i}  11_{i} 6_{−} 0 6 0 1^{4} 8_{+} 1  {−2 \atop −∗} 1^{3} 3_{k} 3  6 6 33 222 22 22 222 222
D_{6}  9 0 8 1^{2} 3_{i} −2 −2 1^{3} 3_{k} 3  6 222 22 22 222 6  222
73.  3_{i}  11_{i} 6_{−} 0 0 0 1^{6} 11_{i} −2  1^{3} 3_{i} 3∗  222 6 22 6 22 33 222 222
D_{6}  0 0 2  1^{3} 3_{i} 3∗  222 6 22  222 222 22 6
74.  3_{i}  11_{k} 8_{+} 0 -6 0 1^{4} 8_{−} 1  {−2 \atop −1} 1^{3} 4_{+} ∗  6 222 22 6 33 22 222 6
D_{6}  9 0 2 1^{2} 3_{i} −2 −2 1^{3} 4_{+} ∗  222 6  22 222 222 22 6
75.  3_{i}  9_{i} 10_{−} 0 0 6 2^{2} 6_{+} 1 {−2 \atop −2∗} 1^{3} 5_{i} 3∗  6 222 22 222 22 33 6 6
D_{6}  0 0 27 1^{2} 3_{i} −2 −2 1^{3} 5_{i} 3∗  222 222 22  6 6 22 222
76.  3_{i}  9_{i} 10_{−} 0 6 -6 2^{2} 6_{+} 1 {−2 \atop −2∗} 1^{3} 5_{i} 3∗  222 6 22 6 22 33 222 222
D_{6}  12 36 17 1^{2} 3_{i} −2 −2 1^{3} 5_{i} 3∗  6 6 22 33 222 222 22 222
77.  3_{i}  11_{i} 10_{−} 0 0 0 1^{6} 11_{i} −2  1^{3} 5_{i} 3∗  222 6 22 222 22  222 222
D_{6}  3  0 0 18  1^{3} 5_{i} 3∗  6 6 22 33 222 222 22 6
78.  3_{i}  11_{i} 10_{−} 0 6 12 1^{6} 11_{i} −2  1^{3} 5_{i} 3∗  222 222 22 6 22 33 222 222
D_{6}  12 -72 44  1^{3} 5_{i} 3∗  6 222 22 33 222 222 22 6
79.  3_{i}  9_{k} 4_{+} -2 3 -2 3^{2} 9_{k} −2  1^{3} 4_{+} 1  6 6 3 6 33 33 6 6
S_{3} × C_{3}  2 0 1  3 0_{+} 1  6 222 3 3 6 222 3 6
80.  1_{k}  9_{i} 8_{+} 0 0 0 3^{2} 9_{i} −2  1^{3} 4_{+} 1  6 6 33 6 22 22 6 6
A_{4} × C_{2}  -12 0 8  1^{3} 4_{+} 1  6 2 33 33 6 2 33 6
81.  3_{i}  11_{k} 8_{+} 0 0 0 1^{4} 11_{k} −2∗ −2 1^{3} 4_{+} 1  4 4 33 222 33 33 222 4
S_{4}^{−}  3  6 0 8 2 0_{+} ∗  ∗ 1^{3} 4_{+} 1  222 4 33 33 222 222 33 222
82.  3_{i}  13_{k} 8_{+} 0 9 0 1^{4} 11_{−} 2 −2 1^{3} 4_{+} 1  222 4 33 4 33 33 4 4
S_{4}^{−}  3  24 0 8 1^{2} 2_{i} −1 −1 1^{3} 4_{+} 1  222 222 33 33 4 222 33 222
83.  3_{i}  13_{k} 8_{+} 0 6 0 1^{4} 10_{i} −∗ −2 1^{3} 4_{+} 1  4 222 33 4 33 33 4 222
S_{4}^{−}  3  3 0 8 1^{2} 3_{−} 2∗  2∗ 1^{3} 4_{+} 1  222 4 33 33 4 222 33 222
84.  3_{i}  11_{i} 6_{−} 2 1 -4 1^{6} 11_{i} −2  1^{3} 5_{i} 3∗  6 6 22 222 22 33 6 6
S_{3} × S_{3}  1 2 3  1^{2} 1_{i} 3∗ 3∗ 6 6 22 33 6 6 22 6
85.  3_{i}  9_{i} 8_{−} 0 0 -2 2^{2} 6_{+} 1 {−2 \atop −2∗} 1^{3} 5_{i} 3∗  6 6 22 6 22 3 6 6
S_{3} × S_{3}  0 0 3 1^{2} 3_{i} −2 −2 1^{3} 3_{i} 3∗  6 6 22 33 6 6 22 222
86.  3_{i}  11_{i} 8_{−} 0 0 -4 1^{6} 11_{i} −2  1^{3} 5_{i} 3∗  6 222 22 6 22 3 6 6
S_{3} × S_{3}  0 0 6  1^{3} 3_{i} 3∗  6 222 22 33 6 6 22 6
87.  3_{i}  11_{i} 10_{−} 0 0 12 1^{6} 11_{i} −2  1^{3} 5_{i} 3∗  6 6 22 6 22 3 6 6
S_{3} × S_{3}  0 0 54  1^{3} 5_{i} 3∗  222 6 22  6 6 22 6

∞  2  3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  5 7 11 13 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
88.  3_{i}  11_{i} 6_{−} 0 3 0 1^{4} 11_{i} −2∗ 2∗ 1^{3} 3_{k} 3  6 6 33 222 22 42 4 2
S_{4} × C_{2}  6 0 2 2 0_{+} ∗  ∗ 1^{3} 3_{k} 3  6 4 42 42 4 6 22 222
89.  3_{i}  11_{i} 6_{−} 0 0 0 1^{6} 11_{i} −2  1^{3} 3_{i} 3∗  4 6 42 6 42 33 4 222
S_{4} × C_{2}  6 0 2  1^{3} 3_{i} 3∗  2 6 22 22 4 222 42 6
90.  3_{i}  9_{k} 8_{+} 0 3 2 1^{4} 6_{+} ∗ −1 1^{3} 4_{+} ∗  6 4 42 6 33 42 4 6
S_{4} × C_{2}  6 0 6 1^{2} 3_{k} −2∗ −2∗ 1^{3} 4_{+} ∗  222 6 22 42 222 2 22 6
91.  3_{i}  13_{i} 6_{−} 0 -3 0 1^{4} 11_{+} 2∗  2∗ 1^{3} 3_{k} 3  6 6 33 4 42 22 222 2
S_{4} × C_{2}  0 0 8 1^{2} 2_{i} −∗ −∗ 1^{3} 3_{k} 3  6 222 22 42 4 6 22 222
92.  3_{i}  13_{i} 6_{−} 0 0 0 1^{4} 10_{i} −1 2∗ 1^{3} 3_{k} 3  6 6 33 4 42 42 4 2
S_{4} × C_{2}  2  3 0 2 1^{2} 3_{+} 2  2 1^{3} 3_{k} 3  6 4 42 22 222 6 22 222
93.  3_{i}  7_{i} 10_{−} 0 -3 0 2^{2} 4_{−} ∗  ∗ 1^{3} 5_{i} 3∗  4 6 22 6 42 33 4 222
S_{4} × C_{2}  3 0 2 1^{2} 3_{k} −2∗ −2∗ 1^{3} 5_{i} 3∗  6 6 42 33 222 222 42 2
94.  3_{i}  7_{i} 10_{−} 0 -3 0 2^{2} 4_{k} −∗  ∗ 1^{3} 5_{i} 3∗  222 6 42 6 42 33 4 4
S_{4} × C_{2}  2  3 0 8 1^{2} 3_{−} 2∗  2∗ 1^{3} 5_{i} 3∗  6 6 22 33 4 4 22 2
95.  3_{i}  11_{k} 8_{+} 0 -3 0 1^{4} 9_{−} 2 −1 1^{3} 4_{+} ∗  6 4 22 6 33 42 222 6
S_{4} × C_{2}  2  12 0 8 1^{2} 2_{i} −1 −1 1^{3} 4_{+} ∗  4 6 22 22 4 222 22 6
96.  3_{i}  11_{k} 8_{+} 0 3 0 1^{4} 9_{−} 2∗ −1 1^{3} 4_{+} ∗  6 222 42 6 33 22 4 6
S_{4} × C_{2}  2  0 0 2 1^{2} 2_{i} −∗ −∗ 1^{3} 4_{+} ∗  4 6 22 42 4 2 22 6
97.  3_{i}  9_{i} 10_{−} 0 6 0 2^{2} 6_{i} −1  ∗ 1^{3} 5_{i} 3∗  4 6 42 6 22 33 222 4
S_{4} × C_{2}  2  12 0 32 1^{2} 3_{+} 2  2 1^{3} 5_{i} 3∗  6 6 42 33 4 4 42 2
98.  3_{i}  11_{i} 10_{−} 0 15 0 1^{4} 11_{i} −2 −2∗ 1^{3} 5_{i} 3∗  6 4 22 4 42 33 6 6
S_{4} × C_{2}  7  48 0 8  1^{3} 5_{i} 3∗  222 222 22 22 6 6 42 4
99.  3_{i}  11_{i} 10_{−} 0 6 0 1^{6} 11_{i} −2  1^{3} 5_{i} 3∗  222 6 42 2 22 22 4 4
S_{4} × C_{2}  -6 0 2  1^{3} 5_{i} 3∗  6 6 42 33 222 222 42 6
100.  1_{k}  11_{k} 10_{−} 0 0 0 1^{4} 8_{−} 1 {−2∗ \atop −1} 1^{3} 5_{i} 3∗  6 4 42 4 42 33 6 6
S_{4} × C_{2}  -27 0 18 1^{2} 3_{i} −2 −2 1^{3} 5_{i} 3∗  222 222 42 22 6 6 42 4
101.  3_{i}  11_{i} 10_{−} 0 6 0 1^{6} 11_{i} −2  1^{3} 5_{i} 3∗  4 2 42 6 42 33 4 222
S_{4} × C_{2}  12 0 2  1^{3} 5_{i} 3∗  6 2 22 33 222 4 42 6
102.  1_{k}  11_{k} 10_{−} 0 -12 0 1^{4} 11_{k} −2 −2∗ 1^{3} 5_{i} 3∗  6 222 42 222 22 33 6 6
S_{4} × C_{2}  30 0 32  1^{3} 5_{i} 3∗  222 222 42 22 6 6 22 222
103.  1_{k}  13_{k} 10_{−} 0 -12 0 1^{4} 10_{i} −∗ −2∗ 1^{3} 5_{i} 3∗  6 222 22 4 22 33 6 6
S_{4} × C_{2}  12 0 32 1^{2} 3_{−} 2∗  2∗ 1^{3} 5_{i} 3∗  4 222 42 22 6 6 42 222
104.  1_{k}  13_{k} 10_{−} 0 -3 0 1^{4} 11_{−} 2∗ −2∗ 1^{3} 5_{i} 3∗  6 222 42 4 22 33 6 6
S_{4} × C_{2}  -24 0 8 1^{2} 2_{i} −∗ −∗ 1^{3} 5_{i} 3∗  4 222 22 22 6 6 42 222
105.  1_{k}  13_{k} 10_{−} 0 -12 0 1^{4} 10_{i} −∗ −2∗ 1^{3} 5_{i} 3∗  6 4 42 222 42 33 6 6
S_{4} × C_{2}  -33 0 2 1^{2} 3_{−} 2∗  2∗ 1^{3} 5_{i} 3∗  4 222 22  6 6 22 4
106.  1_{k}  13_{k} 10_{−} 0 -3 0 1^{4} 11_{−} 2∗ −2∗ 1^{3} 5_{i} 3∗  6 4 22 222 42 33 6 6
S_{4} × C_{2}  -6 0 2 1^{2} 2_{i} −∗ −∗ 1^{3} 5_{i} 3∗  4 222 42 22 6 6 22 4

Discriminant class: −1

∞  2  3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3 5 7 11 13 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
107.  3_{i}  6_{k} 8_{+} 0  6 0 3^{2} 6_{k} −1  2^{3} 8_{+} ∗  33 6 6 33  222 6 33
C_{6}  9  0 1  6  33 6 6  6 33
108.  3_{i}  6_{k} 8_{+} 0  0 -2 1^{2} 2_{i} −1 −1 2^{3} 8_{+} ∗  33 222 222 33 33 222 222 33
S_{3}  9  6 2 1^{2} 2_{i} −1 −1  222 33  222 222  222 33

∞  2  3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3 5 7 11 13 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
109.  3_{i}  8_{k} 6_{+} 0  0 -2 1^{6} 8_{k} −1  2^{3} 6_{+} ∗  22 6 222 33 22 6 222 22
D_{6}  0  0 2  222 33 22 222 222 22 222 33
110.  3_{i}  10_{k} 6_{+} 0  0 -4 1^{4} 8_{−} 1 {−2∗ \atop −1} 2^{3} 6_{+} ∗  33 6 6 22 22 222 222
D_{6}  9 -12 8 1^{2} 2_{i} −1 −1  6 22 22 222 222 33 222 22
111.  3_{i}  6_{k} 10_{+} 0  0 0 2^{2} 4_{−} 1  {−1 \atop −∗} 2^{3} 10_{+} ∗  22 6 222 33 22 6 222 22
D_{6}  0  0 9 1^{2} 2_{i} −1 −1  6 33 22 6 222 22 222
112.  3_{i}  10_{k} 8_{+} 0  0 4 1^{4} 8_{−} 1  {−2 \atop −1} 2^{3} 8_{+} ∗  22 222 6 22 33 6 222 22
D_{6}  3  9 -12 8 1^{2} 2_{i} −1 −1  222 22 33 6 222 22 6 22
113.  3_{i}  8_{k} 10_{+} 0  0 0 1^{6} 8_{k} −1  2^{3} 10_{+} ∗  22 222 222 33 22 6 222 22
D_{6}  0  0 36  6  22 6 222 22 222 33
114.  3_{i}  8_{k} 10_{+} 0  0 6 1^{6} 8_{k} −1  2^{3} 10_{+} ∗  22 6 222  22 222 222 22
D_{6}  0  0 18  6 33 22 6 222 22 222 33
115.  3_{i}  10_{k} 10_{+} 0  0 -12 1^{4} 8_{−} 1 {−2∗ \atop −1} 2^{3} 10_{+} ∗  33 222 222 22 22 6 6 33
D_{6}  2  81 -108 72 1^{2} 2_{i} −1 −1  222 22 22 222 6 33 222 22
116.  3_{i}  6_{k} 8_{+} 0  0 4 3^{2} 6_{k} −1  2^{3} 8_{+} ∗  3 6 6 3 33 222 6 3
S_{3} × C_{3}  9  6 5  6 33 33 6 6  6 3
117.  1_{k}  6_{i} 8_{+} 0  0 0 3^{2} 6_{i} −1  2^{3} 8_{+} ∗  33 6 6 33 22 2 6 33
A_{4} × C_{2}  -3  0 1  6 22 33 6 6 22 6 33
118.  3_{i}  10_{k} 8_{+} 0  0 0 1^{4} 8_{−} ∗ −1 2^{3} 8_{+} ∗  33 4 4 33 33 4 4 33
S_{4}^{−}  2  -3  0 4 1^{2} 2_{i} −∗ −∗  222 33 22 4 222 22 222 33
119.  3_{i}  12_{k} 8_{+} 0  0 0 1^{4} 9_{+} 2∗ −1 2^{3} 8_{+} ∗  33 222 4 33 33 222 4 33
S_{4}^{−}  6  0 4 1^{2} 3_{k} −2∗ −2∗  4 33 22 4 4 22 222 33
120.  3_{i}  12_{k} 8_{+} 0  6 0 1^{4} 9_{−} 2 −1 2^{3} 8_{+} ∗  33 4 222 33 33 4 222 33
S_{4}^{−}  18  0 16 1^{2} 3_{i} −2 −2  4 33 22 222 4  222 33
121.  3_{i}  10_{k} 10_{+} 0  0 0 1^{4} 8_{−} 1 {−2∗ \atop −1} 2^{3} 10_{+} ∗  3 6 6 22 22 6 6 33
S_{3} × S_{3}  81 -216 144 1^{2} 2_{i} −1 −1  6 22 22 222 6 3 222 22
122.  3_{i}  10_{k} 6_{+} 0  3 0 1^{4} 10_{k} −1 2∗ 2^{3} 6_{+} ∗  33 6 6 42 42 4 4 22
S_{4} × C_{2}  0  0 4  6 42 42 222 222 33 2 22
123.  3_{i}  10_{k} 6_{+} 0 -3 0 1^{6} 10_{k} −1  2^{3} 6_{+} ∗  42 6 4 33 42 6 4 22
S_{4} × C_{2}  3  0 1  2 33 22 2 4 22 4 33
124.  3_{i}  4_{k} 10_{+} 0  3 0 2^{2} 4_{k} −1  ∗ 2^{3} 10_{+} ∗  42 6 4 33 22 6 222 42
S_{4} × C_{2}  3  0 4  6 33 42 6 4 42 4 22
125.  3_{i}  6_{k} 10_{+} 0  3 0 2^{2} 6_{k} −∗  ∗ 2^{3} 10_{+} ∗  22 6 4 33 42 6 4 42
S_{4} × C_{2}  12  0 4 2 0_{+} ∗  ∗  6 33 22 6 4 42 222 22
126.  3_{i}  10_{k} 8_{+} 0 -3 0 1^{4} 10_{k} −∗ −2 2^{3} 8_{+} ∗  42 222 6 42 33 6 4 22
S_{4} × C_{2}  3  9  0 1 2 0_{+} ∗  ∗  222 42 33 6 4 22 6 22
127.  3_{i}  14_{k} 6_{+} 0  6 0 1^{4} 11_{i} −2∗ 2∗ 2^{3} 6_{+} ∗  33 6 6 22 22 4 4 22
S_{4} × C_{2}  2  6  0 4 1^{2} 3_{−} 2∗  2∗  6 42 42 4 4 33 2 22
128.  3_{i}  14_{k} 6_{+} 0  6 0 1^{4} 11_{+} 2∗  2∗ 2^{3} 6_{+} ∗  33 6 6 42 42 222 222 22
S_{4} × C_{2}  18  0 4 1^{2} 3_{k} −2∗ −2∗  6 22 22 4 4 33 2 22
129.  1_{k}  8_{i} 10_{+} 0 -6 6 2^{2} 6_{+} 1 {−2 \atop −2∗} 2^{3} 10_{+} ∗  33 4 4 42 42 6 6 33
S_{4} × C_{2}  -6  0 1 1^{2} 2_{i} −1 −1  222 22 42 2 6 33 4 42
130.  3_{i}  8_{k} 10_{+} 0  3 0 2^{2} 6_{−} ∗  ∗ 2^{3} 10_{+} ∗  42 6 222 33 42 6 4 22
S_{4} × C_{2}  -6  0 4 1^{2} 2_{i} −∗ −∗  6 33 42 6 222 22 4 22
131.  3_{i}  8_{k} 10_{+} 0  3 0 1^{6} 8_{k} −1  2^{3} 10_{+} ∗  42 2 4 33 42 6 4 22
S_{4} × C_{2}  3  0 49  6 22 22 6 222 42 4 33

∞  2  3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3 5 7 11 13 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
132.  3_{i}  10_{k} 10_{+} 0 -6 0 1^{6} 10_{k} −1  2^{3} 10_{+} ∗  22 6 4 22 22 2 4 42
S_{4} × C_{2}  12  0 4  6 33 42 6 222 22 4 33
133.  1_{k}  10_{i} 10_{+} 0 -6 0 1^{4} 10_{i} −∗ −2∗ 2^{3} 10_{+} ∗  33 222 222 42 22 6 6 33
S_{4} × C_{2}  3  0 4 2 0_{+} ∗  ∗  4 22 42 2 6 33 4 22
134.  1_{k}  10_{i} 10_{+} 0 -6 0 1^{4} 10_{i} −∗ −2∗ 2^{3} 10_{+} ∗  33 4 4 22 42 6 6 33
S_{4} × C_{2}  3  0 16 2 0_{+} ∗  ∗  4 22 22 222 6 33 222 42
135.  3_{i}  14_{k} 8_{+} 0  0 0 1^{4} 11_{−} 2 −2 2^{3} 8_{+} ∗  22 4 6 42 33 6 4 42
S_{4} × C_{2}  6  -30  0 64 1^{2} 3_{i} −2 −2  222 22 33 6 4 22 6 22
136.  3_{i}  14_{k} 8_{+} 0  0 0 1^{4} 11_{i} −2∗ −2 2^{3} 8_{+} ∗  42 4 6 22 33 6 222 42
S_{4} × C_{2}  3  24  0 64 1^{2} 3_{−} 2∗  2∗  222 42 33 6 222 22 6 22
137.  1_{k}  14_{i} 10_{+} 0 -6 0 1^{4} 11_{−} 2∗ −2∗ 2^{3} 10_{+} ∗  33 4 222 22 42 6 6 33
S_{4} × C_{2}  -6  0 4 1^{2} 3_{k} −2∗ −2∗  4 22 42 2 6 33 222 42
138.  1_{k}  14_{i} 10_{+} 0 -6 0 1^{4} 11_{−} 2∗ −2∗ 2^{3} 10_{+} ∗  33 222 4 42 22 6 6 33
S_{4} × C_{2}  -96  0 64 1^{2} 3_{k} −2∗ −2∗  4 22 22 2 6 33 4 22
139.  3_{i}  14_{k} 10_{+} 0 12 0 1^{4} 11_{k} −2 −2∗ 2^{3} 10_{+} ∗  33 4 222 42 42 6 6 33
S_{4} × C_{2}  4  30  0 16 1^{2} 3_{+} 2  2  222 22 22 2 6 33 4 42
140.  1_{k}  14_{i} 10_{+} 0 -6 0 1^{4} 11_{i} −2 −2∗ 2^{3} 10_{+} ∗  33 222 4 22 22 6 6 33
S_{4} × C_{2}  -42  0 4 1^{2} 3_{+} 2  2  222 22 42 2 6 33 222 22

Discriminant class: 1

∞  2  3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3 5 7 11 13 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
141. 2_{−} 6_{−} 8_{+} 0 0 0 3^{2} 6_{−} 1  1^{3} 4_{+} 1  33 33 33 33 22 22 33 33
A_{4}  -3 0 -1  1^{3} 4_{+} 1  33 22 33 33 33 22 33 33
142. 2_{−} 10_{+} 6_{−} 0 3 0 1^{6} 10_{+} 1  1^{3} 3_{i} 3∗  42 33 42 33 42 33 42 22
S_{4}^{+}  3 0 -1  1^{3} 3_{i} 3∗  22 33 22 22 42 22 42 33
143. 2_{−} 8_{−} 8_{+} 0 0 0 1^{4} 8_{−} ∗ −1 1^{3} 4_{+} ∗  33 42 42 33 33 42 42 33
S_{4}^{+} -3 0 -4 2 0_{+} ∗ ∗ 1^{3} 4_{+} ∗ 22 33 22 42 22 22 22 33
144. 2_{−} 12_{+} 6_{−} 0 -3 0 1^{4} 10_{k} −1 2∗ 1^{3} 3_{k} 3  33 33 33 42 42 42 42 22
S_{4}^{+}  0 0 -4 1^{2} 2_{i} −1 −1 1^{3} 3_{k} 3  33 42 42 22 22 33 22 22
145. 2_{−} 6_{+} 10_{−} 0 -3 0 2^{2} 6_{+} ∗  ∗ 1^{3} 5_{i} 3∗  42 33 22 33 42 33 42 22
S_{4}^{+}  -6 0 -4 2 0_{+} ∗  ∗ 1^{3} 5_{i} 3∗  33 33 42 33 22 22 42 22
146. 2_{−} 6_{+} 10_{−} 0 -3 0 2^{2} 4_{k} −1  ∗ 1^{3} 5_{i} 3∗  42 33 42 33 22 33 22 42
S_{4}^{+}  3 0 -4 1^{2} 2_{i} −1 −1 1^{3} 5_{i} 3∗  33 33 42 33 42 42 42 22
147. 2_{−} 6_{+} 10_{−} 0 -3 -6 1^{6} 6_{+} 1  1^{3} 5_{i} 3∗  42 22 42 33 42 33 42 22
S_{4}^{+}  3 0 -1  1^{3} 5_{i} 3∗  33 22 22 33 22 42 42 33
148. 2_{−} 14_{+} 6_{−} 0 -6 0 1^{4} 11_{i} −2∗ 2∗ 1^{3} 3_{k} 3  33 33 33 22 22 42 42 22
S_{4}^{+}  6 0 -4 1^{2} 3_{k} −2∗ −2∗ 1^{3} 3_{k} 3  33 42 42 42 42 33 22 22
149. 2_{−} 14_{+} 6_{−} 0 -6 0 1^{4} 11_{−} 2∗  2∗ 1^{3} 3_{k} 3  33 33 33 42 42 22 22 22
S_{4}^{+}  2  18 0 -4 1^{2} 3_{−} 2∗  2∗ 1^{3} 3_{k} 3  33 22 22 42 42 33 22 22
150. 2_{−} 8_{+} 10_{−} 0 6 0 1^{4} 8_{+} 1 {−2∗ \atop −∗} 1^{3} 5_{i} 3∗  33 42 42 42 42 33 33 33
S_{4}^{+}  -15 0 -4  1^{3} 5_{i} 3∗  22 22 42 22 33 33 42 42
151. 2_{−} 8_{+} 10_{−} 0 -3 0 2^{2} 6_{k} −∗  ∗ 1^{3} 5_{i} 3∗  22 33 42 33 42 33 42 42
S_{4}^{+}  12 0 -4 1^{2} 2_{i} −∗ −∗ 1^{3} 5_{i} 3∗  33 33 22 33 42 42 22 22
152. 2_{−} 12_{−} 8_{+} 0 3 0 1^{4} 10_{i} −∗ −2 1^{3} 4_{+} 1  42 22 33 42 33 33 42 22
S_{4}^{+}  3  9 0 -1 1^{2} 2_{i} −∗ −∗ 1^{3} 4_{+} 1  22 42 33 33 42 22 33 22

Discriminant class: 1 (continued)

∞  2  3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3 5 7 11 13 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
153. 2_{−} 12_{−} 8_{+} 0 0 0 1^{4} 9_{+} 2∗ −1 1^{3} 4_{+} ∗  33 22 42 33 33 22 42 33
S_{4}^{+} 6 0 -4 1^{2} 3_{−} 2∗ 2∗ 1^{3} 4_{+} ∗ 42 33 22 42 42 22 22 33
154. 2_{−} 12_{−} 8_{+} 0 -6 0 1^{4} 9_{−} 2 −1 1^{3} 4_{+} ∗  33 42 22 33 33 42 22 33
S_{4}^{+}  18 0 -16 1^{2} 3_{+} 2  2 1^{3} 4_{+} ∗  42 33 22 22 42  22 33
155. 2_{−} 10_{+} 10_{−} 0 6 0 1^{6} 10_{+} 1  1^{3} 5_{i} 3∗  22 33 42 22 22 22 42 42
S_{4}^{+}  12 0 -4  1^{3} 5_{i} 3∗  33 33 42 33 22 22 42 33
156. 2_{−} 14_{−} 8_{+} 0 0 0 1^{4} 11_{−} 2 −2 1^{3} 4_{+} 1  22 42 33 42 33 33 42 42
S_{4}^{+} 3 -30 0 -64 1^{2} 3_{+} 2 2 1^{3} 4_{+} 1 22 22 33 33 42 22 33 22
157. 2_{−} 14_{−} 8_{+} 0 0 0 1^{4} 11_{k} −2∗ −2 1^{3} 4_{+} 1  42 42 33 22 33 33 22 42
S_{4}^{+} 3 24 0 -64 1^{2} 3_{k} −2∗ −2∗ 1^{3} 4_{+} 1 22 42 33 33 22 22 33 22
158. 2_{−} 12_{+} 10_{−} 0 6 0 1^{4} 10_{k} −∗ −2∗ 1^{3} 5_{i} 3∗  33 22 22 42 22 33 33 33
S_{4}^{+} 2 3 0 -4 1^{2} 2_{i} −∗ −∗ 1^{3} 5_{i} 3∗ 42 22 42 22 33 33 42 22
159. 2_{−} 12_{+} 10_{−} 0 6 0 1^{4} 10_{k} −∗ −2∗ 1^{3} 5_{i} 3∗  33 42 42 22 42 33 33 33
S_{4}^{+} 2 3 0 -16 1^{2} 2_{i} −∗ −∗ 1^{3} 5_{i} 3∗ 42 22 22 33 33 22 42
160. 2_{−} 14_{+} 10_{−} 0 6 0 1^{4} 11_{k} −2 −2∗ 1^{3} 5_{i} 3∗  33 22 42 22 22 33 33 33
S_{4}^{+} -42 0 -4 1^{2} 3_{i} −2 −2 1^{3} 5_{i} 3∗ 22 22 42 22 33 33 22 22
161. 2_{−} 14_{+} 10_{−} 0 6 0 1^{4} 11_{−} 2∗ −2∗ 1^{3} 5_{i} 3∗  33 22 42 42 22 33 33 33
S_{4}^{+} -96 0 -64 1^{2} 3_{−} 2∗ 2∗ 1^{3} 5_{i} 3∗ 42 22 22 22 33 33 42 22
162. 2_{−} 14_{+} 10_{−} 0 6 0 1^{4} 11_{−} 2∗ −2∗ 1^{3} 5_{i} 3∗  33 42 22 22 42 33 33 33
S_{4}^{+} -6 0 -4 1^{2} 3_{−} 2∗ 2∗ 1^{3} 5_{i} 3∗ 42 22 42 22 33 33 22 42
163. 0_{+} 14_{−} 10_{−} 0 -12 0 1^{4} 11_{i} −2 −2∗ 1^{3} 5_{i} 3∗  33 42 22 42 42 33 33 33
S_{4}^{+}  30 0 -16 1^{2} 3_{i} −2 −2 1^{3} 5_{i} 3∗  22 22 22 22 33 33 42 42

Discriminant class: 2

∞  2  3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3 5 7 11 13 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
164.  0_{+}  9_{+} 8_{+} 0 -12 0 3^{2} 9_{+} 2  2^{3} 8_{+} ∗  6 33 6 6  222 33 6
C_{6}  36 0 -8  33 222 33 6 33 222 6 6
165.  2_{−}  9_{−} 6_{+} 0 0 2 2^{2} 6_{−} 1  {∗ \atop 2} 2^{3} 6_{+} ∗  6 33 6 222 22 222 22 222
D_{6}  0 0 -1 1^{2} 3_{+} 2  2  33 222 22 222 22 6 222 222
166.  2_{−}  11_{−} 6_{+} 0 0 0 1^{6} 11_{−} 2  2^{3} 6_{+} ∗  222 33 222 6 22 6 22 222
D_{6}  0 0 -2  6 22 222 22 222 222 6
167.  2_{−}  11_{−} 8_{+} 0 6 0 1^{4} 8_{−} 1  {−2 \atop −1} 2^{3} 8_{+} ∗  222 22 6 222 33 6 22 222
D_{6}  3  9 0 -8 1^{2} 3_{+} 2  2  22 222 33 6 22 222 6 222
168.  2_{−}  11_{−} 8_{+} 0 6 0 1^{4} 8_{−} 1  {−2 \atop −1} 2^{3} 8_{+} ∗  6 22 222 6 33 222 22 6
D_{6}  9 0 -2 1^{2} 3_{+} 2  2  22 6  222 22 222 222 6
169.  2_{−}  9_{−} 10_{+} 0 -6 6 2^{2} 6_{−} 1  {∗ \atop 2} 2^{3} 10_{+} ∗  222 33 222 6 22 6 22 222
D_{6}  2  12 36 1 1^{2} 3_{+} 2  2  33 6 22 6 22 222 222 222
170.  2_{−}  11_{−} 10_{+} 0 0 0 1^{6} 11_{−} 2  2^{3} 10_{+} ∗  222 33 222 222 22 222 22 222
D_{6}  0 0 -18  33 6 22 6 22 222 222 6
171.  2_{−}  11_{−} 10_{+} 0 -6 12 1^{6} 11_{−} 2  2^{3} 10_{+} ∗  222  222 6 22 6 22 222
D_{6}  12 72 28  33 222 22 6 22 222 222 6
172.  0_{+}  11_{+} 10_{+} 0 -18 -12 1^{4} 8_{+} 1 {−2∗ \atop −∗} 2^{3} 10_{+} ∗  6 22 222 222 22 6 33 6
D_{6}  81 108 18 1^{2} 3_{+} 2  2  22 222 22 222 33 6 222 222
173.  2_{−}  9_{−} 8_{+} 0 0 0 3^{2} 9_{−} 2  2^{3} 8_{+} ∗  6 33 6 6 22 2 33 6
A_{4} × C_{2}  -12 0 -8  33 2 33 6 33 2 6 6

∞  2  3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3 5 7 11 13 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
174.  2_{−}  11_{−} 6_{+} 0 0 -4 1^{6} 11_{−} 2  2^{3} 6_{+} ∗  6 3 6 6 22 6 22 222
S_{3} × S_{3}  0 0 2  33 6 22 222 22 6 222 6
175.  2_{−}  11_{−} 8_{+} 0 -6 4 1^{4} 8_{−} 1  {−2 \atop −1} 2^{3} 8_{+} ∗  6 22 6 6 3 6 22 6
S_{3} × S_{3}  9 -12 -14 1^{2} 3_{+} 2  2  22 6 33 6 22 222 6 6
176.  2_{−}  9_{−} 10_{+} 0 0 -6 2^{2} 6_{−} 1  {∗ \atop 2} 2^{3} 10_{+} ∗  6 3 6 6 22 6 22 222
S_{3} × S_{3}  0 0 -9 1^{2} 3_{+} 2  2  3 6 22 6 22 6 222 222
177.  2_{−}  11_{−} 10_{+} 0 0 -12 1^{6} 11_{−} 2  2^{3} 10_{+} ∗  6 3 6 222 22 222 22 222
S_{3} × S_{3}  0 0 18  3 6 22 6 22 6 222 6
178.  2_{−}  11_{−} 10_{+} 0 0 -12 1^{6} 11_{−} 2  2^{3} 10_{+} ∗  6 33 6 6 22 6 22 222
S_{3} × S_{3}  0 0 -36  3 222 22 6 22 6 222 6
179.  2_{−}  3_{−} 10_{+} 0 3 0 4 0_{+} ∗  ∗ 2^{3} 10_{+} ∗  4 33 222 6 42 6 42 222
S_{4} × C_{2}  3 0 -2 1^{2} 3_{−} 2∗  2∗  33 6 42 6 22 222 4 2
180.  2_{−}  11_{−} 6_{+} 0 3 0 1^{4} 11_{−} 2∗  2∗ 2^{3} 6_{+} ∗  6 33 6 4 42 222 22 2
S_{4} × C_{2}  0 0 -8 2 0_{+} ∗  ∗  33 222 22 4 42 6 2 222
181.  2_{−}  11_{−} 6_{+} 0 0 0 1^{6} 11_{−} 2  2^{3} 6_{+} ∗  4 33 4 6 42 6 42 222
S_{4} × C_{2}  6 0 -2  22 6 22 2 42 222 4 6
182.  2_{−}  9_{−} 8_{+} 0 -3 0 1^{4} 9_{−} 2∗ −1 2^{3} 8_{+} ∗  6 22 4 6 33 222 42 6
S_{4} × C_{2}  0 0 -2 2 0_{+} ∗  ∗  42 6 22 4 42 2 222 6
183.  2_{−}  9_{−} 8_{+} -3 0 10 1^{4} 9_{−} 2 −1 2^{3} 8_{+} ∗  6 42 222 6 33 4 22 6
S_{4} × C_{2}  -18 18 -4  42 6 22 222 42 222 222 6
184.  2_{−}  9_{−} 8_{+} 0 3 4 1^{4} 6_{+} ∗ −1 2^{3} 8_{+} ∗  6 42 4 6 33 4 42 6
S_{4} × C_{2}  -3 0 -1 1^{2} 3_{−} 2∗  2∗  22 6 22 4 22 2 222 6
185.  2_{−}  13_{−} 6_{+} 0 -3 0 1^{4} 11_{i} −2∗ 2∗ 2^{3} 6_{+} ∗  6 33 6 222 22 4 42 2
S_{4} × C_{2}  6 0 -2 1^{2} 2_{i} −∗ −∗  33 4 42 4 42 6 2 222
186.  2_{−}  13_{−} 6_{+} 0 0 0 1^{4} 10_{i} −1 2∗ 2^{3} 6_{+} ∗  6 33 6 4 42 4 42 2
S_{4} × C_{2}  3 0 -2 1^{2} 3_{i} −2 −2  33 4 42 222 22 6 2 222
187.  2_{−}  7_{−} 10_{+} 0 3 0 2^{2} 4_{k} −∗  ∗ 2^{3} 10_{+} ∗  222 33 4 6 42 6 42 4
S_{4} × C_{2}  3 0 -8 1^{2} 3_{k} −2∗ −2∗  33 6 22 6 42 4 222 2
188.  2_{−}  11_{−} 8_{+} 0 -9 0 1^{4} 11_{−} 2 −2 2^{3} 8_{+} ∗  222 42 6 4 33 6 42 4
S_{4} × C_{2}  3  24 0 -8  22 222 33 6 42 222 6 222
189.  2_{−}  9_{−} 10_{+} 0 0 0 1^{2} 3_{+} 2  2 2^{3} 10_{+} ∗  6 42 4 4 42 6 33 6
S_{4} × C_{2}  -27 0 -18 1^{2} 3_{k} −2∗ −2∗  22 222 42 2 33 6 4 4
190.  2_{−}  9_{−} 10_{+} 0 -6 0 2^{2} 6_{i} −1  ∗ 2^{3} 10_{+} ∗  4 33 4 6 22 6 22 4
S_{4} × C_{2}  12 0 -32 1^{2} 3_{i} −2 −2  33 6 42 6 42 4 4 2
191.  2_{−}  13_{−} 8_{+} 0 -6 0 1^{4} 10_{k} −∗ −2 2^{3} 8_{+} ∗  4 22 6 4 33 6 42 222
S_{4} × C_{2}  3  3 0 -8 1^{2} 3_{k} −2∗ −2∗  22 4 33 6 42 222 6 222
192.  2_{−}  13_{−} 8_{+} 0 0 0 1^{4} 11_{i} −2∗ −2 2^{3} 8_{+} ∗  4 42 6 222 33 6 22 4
S_{4} × C_{2}  3  6 0 -8 1^{2} 2_{i} −∗ −∗  22 4 33 6 22 222 6 222
193.  2_{−}  11_{−} 10_{+} 0 3 0 1^{4} 11_{−} 2∗ −2∗ 2^{3} 10_{+} ∗  6 42 222 222 42 6 33 6
S_{4} × C_{2}  -6 0 -2 2 0_{+} ∗  ∗  42 222 42 2 33 6 222 4
194.  2_{−}  11_{−} 10_{+} 0 3 0 1^{4} 11_{−} 2∗ −2∗ 2^{3} 10_{+} ∗  6 22 4 4 22 6 33 6
S_{4} × C_{2}  -24 0 -8 2 0_{+} ∗  ∗  42 222 22 2 33 6 4 222
195.  2_{−}  11_{−} 10_{+} 0 -6 0 1^{6} 11_{−} 2  2^{3} 10_{+} ∗  4 22 4 6 42 6 42 222
S_{4} × C_{2}  12 0 -2  33 2 22 6 22 4 4 6
196.  2_{−}  11_{−} 10_{+} 0 -6 0 1^{6} 11_{−} 2  2^{3} 10_{+} ∗  222 33 4 2 22 2 42 4
S_{4} × C_{2}  -6 0 -2  33 6 42 6 22 222 4 6

∞  2  3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3 5 7 11 13 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
197.  2_{−}  13_{−} 10_{+} 0 12 0 1^{4} 11_{i} −2 −2∗ 2^{3} 10_{+} ∗  6 22 4 222 22 6 33 6
S_{4} × C_{2}  30 0 -32 1^{2} 2_{i} −1 −1  22 222 42 2 33 6 222 222
198.  2_{−}  13_{−} 10_{+} 0 12 0 1^{4} 10_{k} −∗ −2∗ 2^{3} 10_{+} ∗  6 22 222 4 22 6 33 6
S_{4} × C_{2}  12 0 -32 1^{2} 3_{k} −2∗ −2∗  42 222 42 2 33 6 4 222
199.  2_{−}  13_{−} 10_{+} 0 12 0 1^{4} 10_{k} −∗ −2∗ 2^{3} 10_{+} ∗  6 42 4 222 42 6 33 6
S_{4} × C_{2}  -33 0 -2 1^{2} 3_{k} −2∗ −2∗  42 222 22 222 33 6 222 4
200.  0_{+}  13_{+} 10_{+} 0 -15 0 1^{4} 11_{k} −2 −2∗ 2^{3} 10_{+} ∗  6 42 222 4 42 6 33 6
S_{4} × C_{2}  48 0 -32 1^{2} 2_{i} −1 −1  22 222 22 2 33 6 4 4
201.  2_{−}  13_{−} 10_{+} 0 -6 0 1^{4} 10_{i} −1  2 2^{3} 10_{+} ∗  4 5 4 6 5 4 5 4
S_{5}  39 72 40 1^{2} 3_{i} −2 −2  33 6 5 6 5 4 6 6
202.  2_{−}  13_{−} 10_{+} 0 -15 -48 1^{4} 11_{i} −2  2 2^{3} 10_{+} ∗  6 33 6 4 5 6 5 4
S_{5}  -24 0 -8 1^{2} 2_{i} −1 −1  33 6 33 6 22 222 4 222

Discriminant class: 3

∞  2  3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3 5 7 11 13 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
203.  0_{+}  6_{k} 9_{i}  0 -6  0 3^{2} 6_{k} −∗  1^{6} 9_{i} 3  6 6 33 33 222 222 33 6
C_{6}  9 0 -3  6  6 6 33 222 33 33
204.  2_{−}  8_{k} 7_{k} 0 3  0 1^{6} 8_{k} −∗  1^{6} 7_{k} 3  222 6 22 33 222 6 22 222
D_{6}  3 0 -3  222 33 222 222 22 222 22 33
205.  2_{−}  6_{k} 9_{k} 0 0 -4 2^{2} 4_{−} 1  {−1 \atop −∗} 1^{6} 9_{k} 3  6 222 22 33 6 222 22 6
D_{6}  0 0  1 1^{2} 2_{i} −∗ −∗  222 33 222 222 22 222 22 33
206.  2_{−}  10_{i} 7_{i}  0 -3  8 1^{4} 8_{+} 1  {−2 \atop −∗} 1^{6} 7_{i} 3  6 6 33 22 222 222 22 222
D_{6}  -3 0  1 1^{2} 2_{i} −∗ −∗  6 22 222 222 22 6  22
207.  2_{−}  6_{k} 11_{k} 0 0  0 2^{2} 4_{−} 1  {−1 \atop −∗} 1^{6} 11_{k} 3  222 6 22 33 222 6 22 222
D_{6}  0 0 -3 1^{2} 2_{i} −∗ −∗  6 33 222 6 22 222 22
208.  2_{−}  10_{i} 9_{i}  0 -6  0 1^{4} 8_{+} 1  {−2 \atop −∗} 1^{6} 9_{i} 3  222 222 33 22 6 6 22 222
D_{6}  3  9 0 -12 1^{2} 2_{i} −∗ −∗  222 22 6 6 22 222 33 22
209.  2_{−}  8_{k} 11_{k} 0 0  0 1^{6} 8_{k} −∗  1^{6} 11_{k} 3  222 222 22 33 222 6 22 222
D_{6}  0 0 -48  6  222 6 22 222 22 33
210.  2_{−}  8_{k} 11_{k} 0 0  0 1^{6} 8_{k} −∗  1^{6} 11_{k} 3  222 6 22  222 222 22 222
D_{6}  0 0 -12  6 33 222 6 22 222 22 33
211.  0_{+}  10_{i} 11_{k} 0 -18  0 1^{4} 8_{+} 1 {−2∗ \atop −∗} 1^{6} 11_{k} 3  6 222 22 22 222 6 33 6
D_{6}  81 0 -12 1^{2} 2_{i} −∗ −∗  222 22 222 222 33 6 22 22
212.  2_{−}  6_{i} 9_{i}  0 3  0 3^{2} 6_{i} −∗  1^{6} 9_{i} 3  6 6 33 33 2 2 33 6
A_{4} × C_{2}  0 0 -3  6 22 6 6 33 2 33 33
213.  2_{−}  8_{k} 9_{k} 0 0 -2 1^{6} 8_{k} −∗  1^{6} 9_{k} 3  6 6 22 3 6 6 22 6
S_{3} × S_{3}  0 0 -2  222 3 222 222 22 222 22 3
214.  2_{−}  6_{k} 11_{k} 0 0 -6 2^{2} 4_{−} 1  {−1 \atop −∗} 1^{6} 11_{k} 3  6 6 22 3 6 6 22 6
S_{3} × S_{3}  0 0 -3 1^{2} 2_{i} −∗ −∗  6 3 222 6 22 222 22 33
215.  2_{−}  10_{i} 9_{i}  0 6  8 1^{4} 8_{+} 1  {−2 \atop −∗} 1^{6} 9_{i} 3  6 6 3 22 6 6 22 222
S_{3} × S_{3}  9 24  4 1^{2} 2_{i} −∗ −∗  6 22 6 6 22 6 33 22
216.  2_{−}  8_{k} 11_{k} 0 0  6 1^{6} 8_{k} −∗  1^{6} 11_{k} 3  6 222 22 3 6 6 22 6
S_{3} × S_{3}  0 0  6  6 33 222 6 22 222 22 3
217.  2_{−}  8_{k} 11_{k} 0 0  6 1^{6} 8_{k} −∗  1^{6} 11_{k} 3  6 6 22 33 6 222 22 6
S_{3} × S_{3}  0 0 -18  6 3 222 6 22 222 22 3

∞  2  3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3 5 7 11 13 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
218.  2_{−}  10_{i} 7_{i}  0 -3  0 1^{4} 10_{i} −1 2∗ 1^{6} 7_{i} 3  6 6 33 42 4 4 42 2
S_{4} × C_{2}  -3 0 -3 2 0_{+} ∗  ∗  6 42 4 222 22 6 22 22
219.  2_{−}  10_{k} 7_{k} 0 -3  0 1^{6} 10_{k} −∗  1^{6} 7_{k} 3  4 6 42 33 4 6 42 222
S_{4} × C_{2}  3 0 -3  2 33 222 2 42 222 42 33
220.  2_{−}  4_{k} 11_{k} 0 0  0 2^{2} 4_{k} −1  ∗ 1^{6} 11_{k} 3  4 6 42 33 222 6 22 4
S_{4} × C_{2}  -9 0 -12 2 0_{+} ∗  ∗  6 33 4 6 42 4 42 22
221.  2_{−}  6_{k} 11_{k} 0 9  0 2^{2} 6_{k} −∗  ∗ 1^{6} 11_{k} 3  222 6 42 33 4 6 42 4
S_{4} × C_{2}  18 0 -12  6 33 222 6 42 4 22 22
222.  2_{−}  10_{i} 9_{i}  0 3  0 1^{4} 10_{i} −∗ −2 1^{6} 9_{i} 3  4 222 33 42 6 6 42 222
S_{4} × C_{2}  3  0 0 -12  222 42 6 6 42 222 33 22
223.  2_{−}  10_{k} 9_{k} 0 -3  0 1^{4} 8_{−} ∗ −1 1^{6} 9_{k} 3  6 4 42 33 6 4 42 6
S_{4} × C_{2}  2  9 0 -3 1^{2} 2_{i} −1 −1  222 33 2 4 22 2 22 33
224.  2_{−}  14_{i} 7_{i}  0 6  0 1^{4} 11_{i} −2∗ 2∗ 1^{6} 7_{i} 3  6 6 33 22 222 4 42 2
S_{4} × C_{2}  2  6 0 -12 1^{2} 3_{+} 2  2  6 42 4 4 42 6 22 22
225.  2_{−}  14_{i} 7_{i}  0 -6  0 1^{4} 11_{+} 2∗  2∗ 1^{6} 7_{i} 3  6 6 33 42 4 222 22 2
S_{4} × C_{2}  24 0 -48 1^{2} 3_{i} −2 −2  6 22 222 4 42 6 22 22
226.  2_{−}  8_{k} 11_{k} 0 9  0 1^{2} 2_{i} −∗ −∗ 1^{6} 11_{k} 3  6 4 42 42 4 6 33 6
S_{4} × C_{2}  0 0 -12 1^{2} 3_{k} −2∗ −2∗  222 22 4 2 33 6 42 42
227.  2_{−}  8_{k} 11_{k} 0 -9  0 2^{2} 6_{−} ∗  ∗ 1^{6} 11_{k} 3  4 6 22 33 4 6 42 222
S_{4} × C_{2}  18 0 -12 1^{2} 2_{i} −1 −1  6 33 4 6 22 222 42 22
228.  2_{−}  8_{k} 11_{k} 0 -9  0 1^{6} 8_{k} −∗  1^{6} 11_{k} 3  4 2 42 33 4 6 42 222
S_{4} × C_{2}  -9 0 -3  6 22 222 6 22 4 42 33
229.  2_{−}  12_{k} 9_{k} 0 6  0 1^{4} 9_{+} 2 −1 1^{6} 9_{k} 3  6 4 22 33 6 4 22 6
S_{4} × C_{2}  0 0 -48 1^{2} 3_{k} −2∗ −2∗  4 33 2 222 42 222 22 33
230.  2_{−}  12_{k} 9_{k} 0 -12  0 1^{4} 9_{−} 2∗ −1 1^{6} 9_{k} 3  6 222 42 33 6 222 42 6
S_{4} × C_{2}  -18 0 -12 1^{2} 3_{i} −2 −2  4 33 2 4 42 2 22 33
231.  2_{−}  10_{k} 11_{k} 0 9  0 1^{4} 10_{k} −∗ −2∗ 1^{6} 11_{k} 3  6 222 22 42 222 6 33 6
S_{4} × C_{2}  9 0 -3  4 22 4 2 33 6 42 22
232.  2_{−}  10_{k} 11_{k} 0 0  0 1^{4} 10_{k} −∗ −2∗ 1^{6} 11_{k} 3  6 4 42 22 4 6 33 6
S_{4} × C_{2}  -36 0 -48  4 22 222 222 33 6 22 42
233.  2_{−}  10_{k} 11_{k} 0 -9  0 1^{6} 10_{k} −∗  1^{6} 11_{k} 3  222 6 42 22 222 2 42 4
S_{4} × C_{2}  9 0 -3  6 33 4 6 22 222 42 33
234.  2_{−}  14_{i} 9_{i}  0 -6  0 1^{4} 11_{i} −2∗ −2 1^{6} 9_{i} 3  4 4 33 22 6 6 22 4
S_{4} × C_{2}  3  -18 0 -12 1^{2} 3_{+} 2  2  222 42 6 6 22 222 33 22
235.  2_{−}  14_{i} 9_{i}  0 -6  0 1^{4} 11_{−} 2 −2 1^{6} 9_{i} 3  222 4 33 42 6 6 42 4
S_{4} × C_{2}  6  18 0 -12 1^{2} 3_{k} −2∗ −2∗  222 22 6 6 42 222 33 22
236.  2_{−}  14_{k} 11_{k} 0 18  0 1^{4} 11_{i} −2 −2∗ 1^{6} 11_{k} 3  6 222 42 22 222 6 33 6
S_{4} × C_{2}  2  54 0 -12 1^{2} 3_{−} 2∗  2∗  222 22 4 2 33 6 22 22
237.  2_{−}  14_{k} 11_{k} 0 18  0 1^{4} 11_{−} 2∗ −2∗ 1^{6} 11_{k} 3  6 4 22 22 4 6 33 6
S_{4} × C_{2}  2  -54 0 -108 1^{2} 3_{i} −2 −2  4 22 4 2 33 6 22 42
238.  2_{−}  14_{k} 11_{k} 0 18  0 1^{4} 11_{−} 2∗ −2∗ 1^{6} 11_{k} 3  6 222 42 42 222 6 33 6
S_{4} × C_{2}  2  72 0 -48 1^{2} 3_{i} −2 −2  4 22 222 2 33 6 42 22
239.  0_{+}  14_{i} 11_{k} 0 -18  0 1^{4} 11_{k} −2 −2∗ 1^{6} 11_{k} 3  6 4 22 42 4 6 33 6
S_{4} × C_{2}  72 0 -48 1^{2} 3_{−} 2∗  2∗  222 22 222 2 33 6 42 42
240.  2_{−}  12_{k} 11_{k} 0 0 -24 1^{4} 9_{k} −2∗ −∗ 1^{6} 11_{k} 3  6 4 5 33 6 4 5 4
S_{5}  -54 0 36 1^{2} 3_{+} 2  2  6 5 4 6 33 6 22 33

Discriminant class: 6

∞  2  3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  5 7 11 13 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
241.  0_{+}  9_{i} 9_{k} 0 -12  0 3^{2} 9_{i} −2∗  1^{6} 9_{k} 3∗  33 6 6 6 222  33 33
C_{6}  36 0 -24  6 222 6 33 33  6 6
242.  0_{+}  9_{i} 11_{k} 0 -18 24 1^{2} 3_{k} −2∗ −2∗ 1^{6} 11_{k} 3∗  33 222 222 222 222 33 33 33
S_{3}  27 -36 -6 1^{2} 3_{k} −2∗ −2∗  222 222 222  33 33 222 222
243.  2_{−}  11_{i} 7_{i}  0 0  0 1^{4} 8_{−} 1 {−2∗ \atop −1} 1^{6} 7_{i} 3∗  33 6 6 222 222 22 22
D_{6}  -3 0 -6 1^{2} 3_{k} −2∗ −2∗  6 222 222 22 22 33 222 222
244.  2_{−}  11_{k} 7_{k} 0 -6  0 1^{6} 11_{k} −2∗  1^{6} 7_{k} 3∗  22 6 222 6 222 33 22 22
D_{6}  12 0 -6  222 6 222  22 22 222 6
245.  2_{−}  9_{k} 9_{k} 0 0 -10 2^{2} 6_{+} 1 {−2 \atop −2∗} 1^{6} 9_{k} 3∗  22 222 6 222 6 33 22 22
D_{6}  3  0 0  1 1^{2} 3_{k} −2∗ −2∗  222 222 6 33 22 22 6 222
246.  2_{−}  11_{i} 9_{i}  0 -6  0 1^{4} 8_{−} 1 {−2∗ \atop −1} 1^{6} 9_{i} 3∗  33 222 222 6 6 22 22 33
D_{6}  9 0 -6 1^{2} 3_{k} −2∗ −2∗  222 6 222 22 22  222 6
247.  2_{−}  9_{k} 11_{k} 0 0  0 2^{2} 6_{+} 1 {−2 \atop −2∗} 1^{6} 11_{k} 3∗  22 6 222 6 222 33 22 22
D_{6}  0 0 -24 1^{2} 3_{k} −2∗ −2∗  6 6 222 33 22 22 222 222
248.  2_{−}  11_{k} 11_{k} 0 0  0 1^{6} 11_{k} −2∗  1^{6} 11_{k} 3∗  22 222 222 6 222 33 22 22
D_{6}  0 0 -6  6 222 222 33 22 22 222 6
249.  2_{−}  11_{k} 11_{k} 0 0  0 1^{6} 11_{k} −2∗  1^{6} 11_{k} 3∗  22 6 222 222 222  22 22
D_{6}  3  0 0 -96  6 6 222 33 22 22 222 6
250.  0_{+}  9_{i} 11_{k} 0 -18 18 3^{2} 9_{i} −2∗  1^{6} 11_{k} 3∗  3 6 6 6 222 33 3 3
S_{3} × C_{3}  27 -18 -15  6 222 6 33 3 33 6 6
251.  2_{−}  9_{k} 9_{k} 0 6  0 3^{2} 9_{k} −2∗  1^{6} 9_{k} 3∗  33 6 6 6 2 22 33 33
A_{4} × C_{2}  0 0 -24  6 2 6 33 33 22 6 6
252.  2_{−}  11_{k} 11_{k} 0 0  0 1^{4} 11_{k} −2 −2∗ 1^{6} 11_{k} 3∗  33 222 4 222 222 33 33 33
S_{4}^{−}  -18 0 -24 2 0_{+} ∗  ∗  222 222 4 22 33 33 222 222
253.  2_{−}  11_{k} 11_{k} 0 18  0 1^{4} 8_{+} 1 {−2∗ \atop −∗} 1^{6} 11_{k} 3∗  33 4 4 4 4 33 33 33
S_{4}^{−}  4  9 0 -24 1^{2} 3_{k} −2∗ −2∗  222 222 4 22 33 33 4 4
254.  0_{+}  11_{i} 11_{k} 0 -9  0 1^{4} 11_{i} −2 −2∗ 1^{6} 11_{k} 3∗  33 4 222 4 4 33 33 33
S_{4}^{−}  18 0 -6 2 0_{+} ∗  ∗  222 222 222 22 33 33 4 4
255.  2_{−}  13_{k} 11_{k} 0 0  0 1^{4} 10_{k} −∗ −2∗ 1^{6} 11_{k} 3∗  33 4 4 222 4 33 33 33
S_{4}^{−}  2  -9 0 -6 1^{2} 3_{+} 2  2  4 222 222  33 33 222 4
256.  2_{−}  13_{k} 11_{k} 0 18  0 1^{4} 10_{k} −∗ −2∗ 1^{6} 11_{k} 3∗  33 222 222 4 222 33 33 33
S_{4}^{−}  2  36 0 -24 1^{2} 3_{+} 2  2  4 222 4 22 33 33 4 222
257.  2_{−}  13_{k} 11_{k} 0 9  0 1^{4} 11_{−} 2∗ −2∗ 1^{6} 11_{k} 3∗  33 222 4 4 222 33 33 33
S_{4}^{−}  2  18 0 -6 1^{2} 2_{i} −1 −1  4 222 222 22 33 33 4 222
258.  2_{−}  13_{k} 11_{k} 0 9  0 1^{4} 11_{−} 2∗ −2∗ 1^{6} 11_{k} 3∗  33 4 222 222 4 33 33 33
S_{4}^{−}  2  0 0 -96 1^{2} 2_{i} −1 −1  4 222 4 22 33 33 222 4
259.  2_{−}  11_{i} 9_{i}  0 6 -4 1^{4} 8_{−} 1 {−2∗ \atop −1} 1^{6} 9_{i} 3∗  3 6 6 6 6 22 22 33
S_{3} × S_{3}  9 -12 -2 1^{2} 3_{k} −2∗ −2∗  6 6 222 22 22 33 222 6
260.  2_{−}  11_{k} 9_{k} 0 0 -4 1^{6} 11_{k} −2∗  1^{6} 9_{k} 3∗  22 6 6 6 6 3 22 22
S_{3} × S_{3}  0 0 -2  222 6 6 33 22 22 6 6
261.  2_{−}  9_{k} 11_{k} 0 0 -6 2^{2} 6_{+} 1 {−2 \atop −2∗} 1^{6} 11_{k} 3∗  22 6 6 6 6 3 22 22
S_{3} × S_{3}  0 0  3 1^{2} 3_{k} −2∗ −2∗  6 6 6 3 22 22 6 222
262.  2_{−}  11_{k} 11_{k} 0 0 -24 1^{6} 11_{k} −2∗  1^{6} 11_{k} 3∗  22 222 6 6 6 3 22 22
S_{3} × S_{3}  0 0 -6  6 222 6 3 22 22 6 6
263.  2_{−}  11_{k} 11_{k} 0 0 -12 1^{6} 11_{k} −2∗  1^{6} 11_{k} 3∗  22 6 6 222 6 33 22 22
S_{3} × S_{3}  3  0 0 12  6 6 6 3 22 22 6 6

∞  2  3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  5 7 11 13 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
264.  2_{−}  11_{i} 7_{i}  3 6  4 1^{4} 11_{i} −2∗ 2∗ 1^{6} 7_{i} 3∗  33 6 6 222 222 42 42 22
S_{4} × C_{2}  -6 -18  4  6 4 4 42 42 33 2 222
265.  2_{−}  11_{k} 7_{k} 0 0  0 1^{6} 11_{k} −2∗  1^{6} 7_{k} 3∗  42 6 4 6 4 33 42 22
S_{4} × C_{2}  -6 0 -6  2 6 222 22 42 22 4 6
266.  2_{−}  9_{i} 9_{i}  0 -3 -2 1^{4} 6_{+} ∗ −1 1^{6} 9_{i} 3∗  33 4 4 6 6 42 42 33
S_{4} × C_{2}  18 12 -14 1^{2} 3_{i} −2 −2  222 6 2 42 22 22 222 6
267.  2_{−}  13_{i} 7_{i}  0 -3  0 1^{4} 11_{+} 2∗  2∗ 1^{6} 7_{i} 3∗  33 6 6 4 4 22 22 22
S_{4} × C_{2}  6 0 -6 1^{2} 2_{i} −1 −1  6 222 222 42 42 33 2 222
268.  2_{−}  13_{i} 7_{i}  0 -6  0 1^{4} 10_{k} −1 2∗ 1^{6} 7_{i} 3∗  33 6 6 4 4 42 42 22
S_{4} × C_{2}  2  -12 0 -24 1^{2} 3_{−} 2∗  2∗  6 4 4 22 22 33 2 222
269.  2_{−}  7_{k} 11_{k} 0 -9  0 2^{2} 4_{k} −∗  ∗ 1^{6} 11_{k} 3∗  22 6 4 6 4 33 42 42
S_{4} × C_{2}  2  27 0 -24 1^{2} 3_{+} 2  2  6 6 222 33 42 42 222 2
270.  2_{−}  7_{k} 11_{k} 0 0  0 2^{2} 4_{−} ∗  ∗ 1^{6} 11_{k} 3∗  42 6 222 6 4 33 42 22
S_{4} × C_{2}  9 0 -6 1^{2} 3_{i} −2 −2  6 6 4 33 22 22 4 2
271.  2_{−}  11_{k} 9_{k} -3 6 -6 1^{4} 11_{k} −2∗ −2 1^{6} 9_{k} 3∗  42 4 6 222 6 33 22 42
S_{4} × C_{2}  3  -9 27 12  222 4 6 33 22 22 6 222
272.  2_{−}  11_{i} 9_{i}  0 -6  0 1^{4} 9_{+} 2∗ −1 1^{6} 9_{i} 3∗  33 222 4 6 6 22 42 33
S_{4} × C_{2}  2  18 0 -24 1^{2} 2_{i} −1 −1  4 6 2 42 42 22 222 6
273.  2_{−}  11_{i} 9_{i}  0 3  0 1^{4} 9_{+} 2 −1 1^{6} 9_{i} 3∗  33 4 222 6 6 42 22 33
S_{4} × C_{2}  2  0 0 -6 1^{2} 2_{i} −∗ −∗  4 6 2 22 42  222 6
274.  2_{−}  9_{k} 11_{k} 0 0  0 2^{2} 6_{i} −1  ∗ 1^{6} 11_{k} 3∗  42 6 4 6 222 33 22 42
S_{4} × C_{2}  2  -36 0 -96 1^{2} 3_{−} 2∗  2∗  6 6 4 33 42 42 4 2
275.  2_{−}  13_{k} 9_{k} 0 -3  0 1^{4} 11_{−} 2 −2 1^{6} 9_{k} 3∗  22 4 6 4 6 33 42 42
S_{4} × C_{2}  3  0 0 -96 1^{2} 2_{i} −∗ −∗  222 222 6 33 42 22 6 222
276.  2_{−}  13_{k} 9_{k} 0 6  0 1^{4} 10_{k} −∗ −2 1^{6} 9_{k} 3∗  42 222 6 4 6 33 42 22
S_{4} × C_{2}  3  0 0 -96 1^{2} 3_{+} 2  2  222 4 6 33 42 22 6 222
277.  2_{−}  11_{k} 11_{k} 0 0  0 1^{6} 11_{k} −2∗  1^{6} 11_{k} 3∗  22 6 4 2 222 22 42 42
S_{4} × C_{2}  18 0 -6  6 6 4 33 22 22 4 6
278.  2_{−}  11_{k} 11_{k} 0 0  0 1^{6} 11_{k} −2∗  1^{6} 11_{k} 3∗  42 2 4 6 4 33 42 22
S_{4} × C_{2}  -36 0 -294  6 2 222 33 22 42 4 6
279.  2_{−}  13_{k} 9_{k} 0 0 -8 1^{4} 11_{−} 2∗ −2∗ 1^{6} 9_{k} 3∗  5 4 4 6 4 5 33 5
S_{5}  3  -18 0 -8 1^{2} 2_{i} −1 −1  4 6 6 33 5 33 6 222