Old Sextic Fields Ramifying Above {2, 19}

Discriminant class: −38

∞  2 19 a_{1} a_{2} a_{3}  Over p = 2  Over p = 19  3 5 7 11 13 17 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_{−} 3_{i} -2  5 4 1^{2} 3_{−} 2∗  2∗ 1^{2} 1_{k} 19 19 33 222 33 222 33 33 33 33
S_{3}  2  34 16 16 1^{2} 3_{−} 2∗  2∗ 1^{2} 1_{k} 19 19 222  222 222  33 33 222
2.  3_{i}  11_{−} 3_{i}  2  9 12 1^{4} 8_{+} 1  {−2 \atop −∗} 1^{4} 3_{i} 19∗ 19 33 4 33 222 33 33 33 33
S_{4}^{−}  2  28 24 10 1^{2} 3_{−} 2∗  2∗ 2 0_{+} ∗  ∗ 4 22 222 4  33 33 4
3.  3_{i}  11_{+} 3_{k}  0  2 0 1^{6} 11_{+} 2∗  1^{4} 3_{k} 19 19∗ 42 6 33 6 22 33 22 42
S_{4} × C_{2}  2  0  0 38  222 42 4 6 33 22 42 6
4.  3_{i}  11_{+} 3_{k} -3 14 -30 1^{4} 11_{+} 2∗  2∗ 2^{2} 2_{+} 1  V 33 222 33 4 33 33 33 33
S_{4}^{−}  2  51 -73 44  1^{2} 1_{k} 19 19 4 22 4 222 22 33 33 222
5.  3_{i}  11_{+} 3_{k}  0 10 0 1^{6} 11_{+} 2∗  1^{4} 3_{k} 19 19∗ 22 6 33 6 22 33 22 22
S_{4} × C_{2}  2  38  0 38  4 22 222 6 33 42 42 6
6.  3_{i}  11_{−} 3_{i}  0 11 0 1^{4} 11_{−} 2∗  2∗ 1^{4} 3_{i} 19∗ 19 33 4 33 4 33 33 33 33
S_{4}^{−}  38  0 38  2 0_{+} ∗  ∗ 222 22 4 4 22 33 33 4
7.  3_{i}  11_{+} 3_{k}  0 -4 0 1^{6} 11_{+} 2∗  2^{2} 2_{+} 1  V 22 6 33 6 22 33  22
D_{6}  6  4  0 38  1^{2} 1_{k} 19 19 222 22 222 6 33 22 22 6
8.  3_{i}  11_{+} 3_{k}  0  2 0 1^{6} 11_{+} 2∗  2^{2} 2_{+} 1  V 42 6 33 6 22 33 22 42
S_{4} × C_{2}  2  -18  0 38  1^{2} 1_{k} 19 19 4 42 4 6 33 42 22 6
9.  3_{i}  13_{+} 3_{k}  0  8 0 1^{4} 10_{i} −1 2∗ 2^{2} 2_{+} 1  V 33 4 33 222 33 33 33 33
S_{4}^{−}  2  35  0 38 1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{k} 19 19 222 22 4 4 22 33 33 222
10.  3_{i}  13_{−} 3_{i}  0 17 0 1^{4} 11_{i} −2∗ 2∗ 1^{4} 3_{i} 19∗ 19 33 222 33 4 33 33 33 33
S_{4}^{−}  2  38  0 38 1^{2} 2_{i} −1 −1 2 0_{+} ∗  ∗ 222 22 222 222 22 33 33 4
11.  3_{i}  13_{−} 3_{i}  0  4 0 1^{4} 10_{k} −1 2∗ 1^{4} 3_{i} 19∗ 19 33 222 33 222 33 33 33 33
S_{4}^{−}  2  19  0 38 1^{2} 3_{k} −2∗ −2∗ 2 0_{+} ∗  ∗ 4 22 4 222 22 33 33 4
12.  3_{i}  13_{−} 3_{i}  0  9 0 1^{4} 11_{i} −2∗ 2∗ 1^{2} 1_{k} 19 19 33 4 33 4 33 33 33 33
S_{4}^{−}  2  6  0 38 1^{2} 2_{i} −1 −1 1^{2} 1_{k} 19 19 4  222 4 22 33 33 222
13.  3_{i}  9_{−} 5_{i}  0  0 0 2^{2} 6_{+} 1 {−2 \atop −2∗} 1^{6} 5_{i} 19  33 4 42 6 22 22 42 42
S_{4} × C_{2}  6  -19  0 38 1^{2} 3_{−} 2∗  2∗  4 42 6 2 42 22 33 4
14.  1_{k}  9_{+} 5_{i}  0  0 0 3^{2} 9_{+} 2∗  1^{6} 5_{i} 19  33 6 22 2 33 33 33 33
A_{4} × C_{2}  -76  0 152  222 22 6 6 33 33 33 6
15.  3_{i}  9_{−} 5_{i}  0 38 0 3^{2} 9_{−} 2∗  1^{6} 5_{i} 19  33 6  222 33 33 33 33
C_{6}  18  152  0 152  222  6 6 33 33 33 6
16.  3_{i}  9_{−} 5_{i} -2 -11 26 3^{2} 9_{−} 2∗  1^{6} 5_{i} 19  3 6 33 222 3 3 3 3
S_{3} × C_{3} 18  174 -388 201  222  6 6 33 3 3 6
17.  3_{i}  11_{−} 5_{i}  0 19 0 1^{4} 11_{−} 2 −2 1^{6} 5_{i} 19  33 222 22 6 42 22 42 22
S_{4} × C_{2}  6  114  0 38 2 0_{+} ∗  ∗  4 42 6 2 22 42 33 222
18.  3_{i}  11_{−} 5_{i}  0 19 0 1^{4} 11_{−} 2 −2 1^{6} 5_{i} 19  33 4 42 6 42 22 22 42
S_{4} × C_{2}  6  -38  0 38 2 0_{+} ∗  ∗  222 22 6 222 42 42 33 4
19.  3_{i}  11_{−} 5_{i} -2 27 -12 1^{4} 8_{+} 1  {−2 \atop −∗} 1^{6} 5_{i} 19  33 222 22 6 22  22 22
D_{6}  36  136 144 182 1^{2} 3_{−} 2∗  2∗  222 22 6 222 22 22 33 222
20.  3_{i}  13_{−} 5_{i}  0 19 0 1^{4} 11_{i} −2∗ 2∗ 1^{6} 5_{i} 19  22 4 33 4 5 5 5 33
S_{5}  6  95 -304 285 1^{2} 2_{i} −1 −1  6 5 4 6 5 5 5 6

Discriminant class: −19

∞  2 19 a_{1} a_{2} a_{3}  Over p = 2  Over p = 19  3 5 7 11 13 17 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
21.  3_{i}  4_{+} 3_{k}  1 2 -1 2^{3} 4_{+} ∗  1^{4} 3_{k} 19 19∗ 4 33 33 33 222 33 22 4
S_{4}^{−}  2 -3 1  2 0_{+} ∗  ∗ 222 4 4 33 33 222 4 33
22.  3_{i}  4_{+} 3_{k} -3 4 -3 2^{3} 4_{+} ∗  1^{2} 1_{i} 19∗ 19∗ 222 33 33 33 222 33  222
S_{3}  4 -3 1  1^{2} 1_{i} 19∗ 19∗ 222 222 222 33 33 222 222 33
23.  3_{i}  6_{−} 3_{i}  1 -1 -4 2^{2} 6_{−} 1  {∗ \atop 2} 2^{2} 2_{+} 1  V 6 22 33 22 6 33 33 6
D_{6}  -1 3 5 2 0_{+} ∗  ∗ 1^{2} 1_{i} 19∗ 19∗ 222 222 222 22  6 6 22
24.  3_{i}  8_{−} 3_{i}  1 -1 -2 1^{4} 8_{−} 1 {−2∗ \atop −1} 1^{4} 3_{i} 19∗ 19 6 42 33 22 6 33 33 6
S_{4} × C_{2}  4 6 2 2 0_{+} ∗  ∗  4 2 222 42  6 6 42
25.  3_{i}  10_{+} 3_{k}  0 9 0 1^{6} 10_{+} ∗  1^{2} 1_{i} 19∗ 19∗ 4 33 33 33 222 33 22 4
S_{4}^{−}  2  25 0 19  1^{2} 1_{i} 19∗ 19∗ 4 4 4 33 33 4 222 33
26.  3_{i}  10_{+} 3_{k}  0 7 0 1^{6} 10_{+} ∗  1^{4} 3_{k} 19 19∗ 222 33 33 33 222 33 22 222
S_{4}^{−}  2  19 0 19  2 0_{+} ∗  ∗ 4 222 222 33 33 4 4 33
27.  3_{i}  12_{−} 3_{i}  0 3 0 1^{4} 10_{i} −1 2∗ 1^{4} 3_{i} 19∗ 19 6 22 33 22 6 33 33 6
S_{4} × C_{2}  4  -19 0 19 1^{2} 2_{i} −∗ −∗  4 2 4 22 22 6 6 42
28.  3_{i}  12_{+} 3_{k}  0 7 0 1^{4} 10_{k} −1 2∗ 1^{2} 1_{i} 19∗ 19∗ 6 42 33 22 6 33 33 6
S_{4} × C_{2}  2  17 0 19 1^{2} 2_{i} −∗ −∗ 1^{2} 1_{k} 19 19 222 2 4 42 22 6 6 22
29.  3_{i}  4_{+} 5_{k} -1 2 -11 2^{3} 4_{+} ∗  1^{6} 5_{k} 19∗  6 3 33 33 6 3 33 6
S_{3} × C_{3}  3  18 33 83  222 222 6 3 3 6 6 3
30.  3_{i}  14_{−} 3_{i}  0 -6 0 1^{4} 11_{i} −2∗ 2∗ 2^{2} 2_{+} 1  V 6 42 33 42 6 33 33 6
S_{4} × C_{2}  2  -10 0 76 1^{2} 3_{i} −2 −2 1^{2} 1_{i} 19∗ 19∗ 4 222 222 42 22 6 6 22
31.  3_{i}  14_{+} 3_{k}  0 20 0 1^{4} 11_{+} 2∗ 2∗ 1^{2} 1_{k} 19 19 6 22 33 42 6 33 33 6
S_{4} × C_{2}  4  138 0 304 1^{2} 3_{+} 2  2 1^{2} 1_{i} 19∗ 19∗ 4 2 4 22 22 6 6 22
32.  3_{i}  14_{−} 3_{i}  0 -4 0 1^{4} 11_{−} 2∗ 2∗ 1^{4} 3_{i} 19∗ 19 6 42 33 42 6 33 33 6
S_{4} × C_{2}  2  -38 0 304 1^{2} 3_{+} 2  2  222 2 4 42 22 6 6 42
33.  3_{i}  14_{−} 3_{i}  0 10 0 1^{4} 11_{i} −2∗ 2∗ 1^{4} 3_{i} 19∗ 19 6 22 33 42 6 33 33 6
S_{4} × C_{2}  2  38 0 76 1^{2} 3_{i} −2 −2  222 2 222 22 22 6 6 42
34.  1_{k}  6_{−} 5_{k}  0 0 0 3^{2} 6_{−} ∗  1^{6} 5_{k} 19∗  6 33 22 22 6 33 33 6
A_{4} × C_{2}  -19 0 19  222 2 6 33 33 6 6 33
35.  3_{i}  6_{+} 5_{k}  3 -1 12 2^{2} 6_{+} 1 {−2 \atop −2∗} 1^{6} 5_{k} 19∗  6 22 22 33 222  22 222
D_{6}  3  52 -20 68 2 0_{+} ∗  ∗  222 222 6  22 222 6 22
36.  3_{i}  8_{+} 5_{k} -2 8 -12 1^{4} 8_{+} 1  {−2 \atop −∗} 1^{6} 5_{k} 19∗  6 42 42 33 222 22 42 4
S_{4} × C_{2}  6  41 -46 68 2 0_{+} ∗  ∗  4 4 6 22 42 222 6 42
37.  3_{i}  14_{+} 5_{k}  0 38 0 1^{4} 11_{−} 2 −2 1^{6} 5_{k} 19∗  6 22 22 33 4 22 42 222
S_{4} × C_{2} 60  456 0 304 1^{2} 3_{−} 2∗ 2∗  4 4 6 22 22 4 6 22
38.  3_{i}  14_{+} 5_{k}  0 0 0 1^{4} 11_{−} 2 −2 1^{6} 5_{k} 19∗  6 42 42 33 4 22 22 4
S_{4} × C_{2} 12  114 0 304 1^{2} 3_{−} 2∗ 2∗  222 222 6  42 4 6 42

Discriminant class: −2

∞  2 19 a_{1} a_{2} a_{3}  Over p = 2  Over p = 19  3 5 7 11 13 17 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
39.  3_{i}  9_{k} 2_{+}  2  1  -2 3^{2} 9_{k} −2  1^{3} 2_{+} 1  3 6 222 33 6 33 6 6
S_{3} × C_{3}  0  4  3  3 0_{+} 1  222 222 3 33 6 6 3 6
40.  3_{i}  11_{i} 2_{−}  0 -5  0 1^{4} 11_{i} −2∗ 2∗ 1^{2} 1_{k} 19 19 33 4 6 42 6 33 6 6
S_{4} × C_{2}  6  0  2 2 0_{+} ∗  ∗ 1^{2} 1_{k} 19 19 4 222 22 42 2 6 33 222
41.  3_{i}  11_{i} 2_{−}  0  0  0 1^{6} 11_{i} −2  1^{2} 1_{i} 19∗ 19∗ 42 6 6 33 222 33 2 4
S_{4} × C_{2}  -2  0  2  1^{2} 1_{i} 19∗ 19∗ 4 4 42 33 6 4 22 6

Discriminant class: −2 (continued)

∞  2 19 a_{1} a_{2} a_{3}  Over p = 2  Over p = 19  3 5 7 11 13 17 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
42.  3_{i}  11_{i} 2_{−}  0  2  0 1^{6} 11_{i} −2  1^{2} 1_{i} 19∗ 19∗ 22 6 6 33 222 33 222 222
D_{6}  4  0  2  1^{2} 1_{i} 19∗ 19∗ 222 222 22 33 6 222 22 6
43.  3_{i}  11_{i} 2_{−}  0  0  0 1^{4} 8_{+} 1 {−2 \atop −∗} 1^{2} 1_{k} 19 19 33 222 6 22 6 33 6 6
D_{6}  5  0  2 1^{2} 3_{i} −2 −2 1^{2} 1_{k} 19 19 222 222 22 22 222 6 33 222
44.  3_{i}  13_{k} 2_{+}  0  1  0 1^{4} 11_{−} 2∗ 2∗ 2^{2} 2_{+} 1  V 33 222 6 42 6 33 6 6
S_{4} × C_{2}  -2  0  2 1^{2} 2_{i} −∗ −∗  4 2 42 22 2 6 33 222
45.  3_{i}  13_{k} 2_{+}  0  4  0 1^{4} 10_{k} −1 2∗ 2^{2} 2_{+} 1  V 33 4 6 22 6 33 6 6
S_{4} × C_{2}  2  3  0  2 1^{2} 3_{+} 2  2  222 2 42 42 2 6 33 222
46.  3_{i}  9_{i} 4_{−} -2 -9  -8 1^{2} 3_{−} 2∗ 2∗ 1^{4} 3_{i} 19∗ 19 33 4 6 22 6 33 6 6
S_{4} × C_{2}  2  24 128 176 1^{2} 3_{i} −2 −2 1^{2} 1_{i} 19∗ 19∗ 4 2 22 42 222 6 33 4
47.  1_{k}  9_{i} 4_{+}  0  4  0 3^{2} 9_{i} −2  1^{3} 2_{+} 1  33 6 2 22 6 33 6 6
A_{4} × C_{2}  -20  0  8  1^{3} 2_{+} 1  222 2 33 33 6 6 33 6
48.  3_{i}  9_{k} 4_{+}  0 -12  0 1^{2} 3_{i} −2 −2 1^{3} 2_{+} 1  33 222 222 33 222  222 222
S_{3}  3  29  0 50 1^{2} 3_{i} −2 −2 1^{3} 2_{+} 1  222 222 33  222 222 33 222
49.  3_{i}  9_{k} 4_{+} -2 -5 18 3^{2} 9_{k} −2  1^{3} 2_{+} 1  33 6 222  6 33 6 6
C_{6}  3  38 -152 209  1^{3} 2_{+} 1  222 222 33 33 6 6 33 6
50.  3_{i}  11_{i} 4_{−}  0 19  0 1^{4} 11_{i} −2∗ 2∗ 1^{4} 3_{i} 19∗ 19 33 222 6 42 6 33 6 6
S_{4} × C_{2}  2  190  0 722 2 0_{+} ∗  ∗ 1^{2} 1_{i} 19∗ 19∗ 222 2 22 22 2 6 33 4
51.  3_{i}  11_{i} 4_{−}  0  0  0 1^{6} 11_{i} −2  1^{4} 3_{k} 19 19∗ 42 6 6 33 222 33 2 4
S_{4} × C_{2}  4  -152  0 722  1^{2} 1_{k} 19 19 222 4 42 33 6 222 42 6
52.  3_{i}  11_{i} 4_{−}  0  0  0 1^{6} 11_{i} −2  1^{4} 3_{k} 19 19∗ 22 6 6 33 222 33 2 222
S_{4} × C_{2}  4  114  0 722  1^{2} 1_{k} 19 19 4 222 22 33 6 4 42 6
53.  3_{i}  11_{k} 4_{+}  0  6  0 1^{4} 8_{−} 1 {−2 \atop −1} 1^{3} 2_{+} 1  33 4 4 33 222 22 4 4
S_{4}^{−}  12  -7  0  8 1^{2} 3_{i} −2 −2 1^{3} 2_{+} 1  4 4 33 22 4 222 33 4
54.  3_{i}  13_{i} 4_{−}  0 38  0 1^{4} 10_{i} −1 2∗ 1^{4} 3_{i} 19∗ 19 33 222 6 22 6 33 6 6
S_{4} × C_{2} 12  551  0 2888 1^{2} 3_{+} 2  2 1^{2} 1_{i} 19∗ 19∗ 4 2 42 22 2 6 33 4
55.  3_{i}  13_{i} 4_{−}  0  0  0 1^{4} 11_{+} 2∗ 2∗ 1^{4} 3_{i} 19∗ 19 33 4 6 42 6 33 6 6
S_{4} × C_{2}  4  266  0 2888 1^{2} 2_{i} −∗ −∗ 1^{2} 1_{i} 19∗ 19∗ 222 2 42 42 2 6 33 4
56.  3_{i}  13_{k} 4_{+}  0 -15  0 1^{4} 11_{−} 2 −2 1^{3} 2_{+} 1  33 4 4 33 4 22 222 4
S_{4}^{−}  6  56  0  8 1^{2} 2_{i} −1 −1 1^{3} 2_{+} 1  222 222 33  4 4 33 4
57.  3_{i}  13_{k} 4_{+}  0  4  0 1^{4} 11_{−} 2 −2 1^{3} 2_{+} 1  33 222 222 33 4 22 4 222
S_{4}^{−}  12  18  0  8 1^{2} 2_{i} −1 −1 1^{3} 2_{+} 1  4 4 33 22 222 4 33 222

Discriminant class: −1

∞  2 19 a_{1} a_{2} a_{3}  Over p = 2  Over p = 19  3 5 7 11 13 17 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
58.  3_{i}  8_{k} 2_{+} -2 2  -2 1^{6} 8_{k} −1  2^{2} 2_{+} 1  V 222 33 6 6 22 33 222 22
D_{6}  0 0  2  2 0_{+} ∗  ∗ 222 22 22 6 6 22 222 33
59.  3_{i}  10_{k} 2_{+} 0 1  0 1^{6} 10_{k} −1  2^{2} 2_{+} 1  V 4 33 6 6 22 33 2 42
S_{4} × C_{2}  3 0  1  2 0_{+} ∗  ∗ 4 42 42 6 6 42 222 33
60.  3_{i}  10_{i} 2_{−} 0 -2  0 1^{4} 10_{i} −1 2∗ 2 0_{+} ∗  ∗ 6 42 6 222 33 33 6 33
S_{4} × C_{2}  -1 0  4  1^{2} 1_{k} 19 19 222 22 42 4 2 33 6 22
61.  3_{i}  10_{k} 2_{+} -2 2  -4 1^{4} 8_{−} 1 {−2∗ \atop −1} 2^{2} 2_{+} 1  V 6 22 6 222 33 33 6 33
D_{6}  1 2  2 1^{2} 2_{i} −1 −1 2 0_{+} ∗  ∗ 222  22 222 222 33 6 22
62.  3_{i}  14_{i} 2_{−} 0 -2  0 1^{4} 11_{−} 2∗  2∗ 2 0_{+} ∗  ∗ 6 22 6 4 33 33 6 33
S_{4} × C_{2}  2 0  4 1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{k} 19 19 4 22 42 222 2 33 6 22

Discriminant class: −1 (continued)

∞  2 19 a_{1} a_{2} a_{3}  Over p = 2  Over p = 19  3 5 7 11 13 17 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
63.  3_{i}  14_{k} 2_{+} 0 8  0 1^{4} 11_{i} −2∗ 2∗ 2^{2} 2_{+} 1  V 6 42 6 4 33 33 6 33
S_{4} × C_{2}  2  22 0 16 1^{2} 3_{−} 2∗  2∗ 2 0_{+} ∗  ∗ 4  22 4 2 33 6 22
64.  3_{i}  6_{k} 4_{+} 0 13  0 3^{2} 6_{k} −1  2^{3} 4_{+} ∗  6 33 222 222 33 33 6 33
C_{6}  50 0 49  222  33 6 6 33 6 33
65.  1_{k}  6_{i} 4_{+} 0 2  0 3^{2} 6_{i} −1  2^{3} 4_{+} ∗  6 33 2 2 33 33 6 33
A_{4} × C_{2}  -5 0  1  222 22 33 6 6 33 6 33
66.  3_{i}  8_{k} 4_{+} -2 10  -8 2^{2} 6_{−} 1  {∗ \atop 2} 1^{4} 3_{i} 19∗ 19 6 42 6 222 33 33 6 33
S_{4} × C_{2}  2  24 14 43 1^{2} 2_{i} −1 −1 1^{2} 1_{k} 19 19 4 22 22 4 222 33 6 42
67.  3_{i}  8_{k} 4_{+} 2 1 18 1^{6} 8_{k} −1  1^{4} 3_{k} 19 19∗ 4 33 6 6 22 33 2 42
S_{4} × C_{2}  4  -1 -76 81  1^{2} 1_{i} 19∗ 19∗ 222 42 42 6 6 22 4 33
68.  3_{i}  8_{k} 4_{+} -2 11 -16 1^{2} 2_{i} −1 −1 2^{3} 4_{+} ∗  6 42 4 6 22 22 4 42
S_{4} × C_{2}  3  46 -40 56 1^{2} 3_{i} −2 −2  4 42 33 2 4 22 6 42
69.  3_{i}  10_{k} 4_{+} 0 -19  0 1^{4} 10_{k} −1 2∗ 1^{4} 3_{i} 19∗ 19 6 22 6 222 33 33 6 33
S_{4} × C_{2}  2  57 0 361  1^{2} 1_{k} 19 19 4 22 42 222 2 33 6 42
70.  3_{i}  10_{k} 4_{+} 0 19  0 1^{6} 10_{k} −1  1^{4} 3_{k} 19 19∗ 222 33 6 6 22 33 2 22
S_{4} × C_{2}  4  133 0 361  1^{2} 1_{i} 19∗ 19∗ 4 22 22 6 6 42 4 33
71.  3_{i}  10_{k} 4_{+} -2 2  -4 1^{4} 8_{−} 1  {−2 \atop −1} 2^{3} 4_{+} ∗  6 22 222 6 22  222 22
D_{6}  6  49 -70 50 1^{2} 2_{i} −1 −1  222 22 33 222 222 22 6 22
72.  3_{i}  14_{k} 4_{+} 0 38  0 1^{4} 11_{+} 2∗  2∗ 1^{4} 3_{i} 19∗ 19 6 42 6 4 33 33 6 33
S_{4} × C_{2}  4  418 0 1444 1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{k} 19 19 222 22 42 4 2 33 6 42
73.  3_{i}  14_{k} 4_{+} 0 8  0 1^{4} 11_{−} 2 −2 2^{3} 4_{+} ∗  6 22 222 6 42 22 4 22
S_{4} × C_{2} 12  72 0 64 1^{2} 3_{i} −2 −2  4 42 33 2 222 42 6 22
74.  3_{i}  14_{k} 4_{+} 0 8  0 1^{4} 11_{−} 2 −2 2^{3} 4_{+} ∗  6 42 4 6 42 22 222 42
S_{4} × C_{2} 12  34 0 64 1^{2} 3_{i} −2 −2  222 22 33 222 4 42 6 42
75.  3_{i}  14_{k} 4_{+} 0 38  0 1^{4} 11_{i} −2∗ 2∗ 1^{4} 3_{i} 19∗ 19 6 22 6 4 33 33 6 33
S_{4} × C_{2}  8  646 0 1444 1^{2} 3_{−} 2∗  2∗ 1^{2} 1_{k} 19 19 222 22 22 222 2 33 6 42

Discriminant class: 1

∞  2 19 a_{1} a_{2}  a_{3}  Over p = 2  Over p = 19  3 5 7 11 13 17 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
76. 2_{−} 10_{+} 2_{−} 0 -1  0 1^{6} 10_{+} 1  1^{2} 1_{i} 19∗ 19∗ 42 33 33 33 22 33 22 42
S_{4}^{+}  3  0  -1  1^{2} 1_{i} 19∗ 19∗ 42 42 42 33 33 42 22 33
77. 2_{−} 12_{−} 2_{+} 0  2  0 1^{4} 10_{i} −1 2∗ 2^{2} 2_{+} 1  V 33 42 33 22 33 33 33 33
S_{4}^{+}  -1  0  -4 1^{2} 2_{i} −1 −1  22 22 42 42 22 33 33 22
78. 2_{−} 4_{+} 4_{−} -1 -5  9 1^{3} 2_{+} ∗  1^{4} 3_{k} 19 19∗ 42 33 33 33 22 33 22 42
S_{4}^{+}  4 -20  4 1^{3} 2_{+} ∗  1^{2} 1_{k} 19 19 22 42 42 33 33 22 42 33
79. 2_{−} 14_{+} 2_{−} 0 -8  0 1^{4} 11_{i} −2∗ 2∗ 1^{2} 1_{k} 19 19 33 42 33 42 33 33 33 33
S_{4}^{+}  22  0 -16 1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{k} 19 19 42  22 42 22 33 33 22
80. 2_{−} 14_{−} 2_{+} 0  2  0 1^{4} 11_{+} 2∗  2∗ 2^{2} 2_{+} 1  V 33 22 33 42 33 33 33 33
S_{4}^{+}  2  2  0  -4 1^{2} 3_{−} 2∗  2∗  42 22 42 22 22 33 33 22
81. 2_{−} 6_{−} 4_{+} 2 -6 -10 3^{2} 6_{−} 1  1^{5} 4_{+} 1  5 22 33 5 33 22 5 5
A_{5}  17 12 -19  5 5 33 5 33 5 5 33
82. 2_{−} 6_{−} 4_{+} 0 -2  0 3^{2} 6_{−} 1  1^{3} 2_{+} 1  33 33 22 22 33 33 33 33
A_{4}  -5  0  -1  1^{3} 2_{+} 1  22 33 33 33 33 33 33
83. 2_{−} 8_{+} 4_{−} 2  2  0 1^{4} 8_{+} 1  {−2 \atop −∗} 1^{4} 3_{i} 19∗ 19 33 42 33 22 33 33 33 33
S_{4}^{+}  -34 -124 -128  1^{2} 1_{i} 19∗ 19∗ 42 22 22 42  33 33 42

Discriminant class: 1 (continued)

∞  2 19 a_{1} a_{2}  a_{3}  Over p = 2  Over p = 19  3 5 7 11 13 17 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
84. 2_{−} 8_{−} 4_{+} 2  5  8 1^{4} 8_{−} 1  {−2 \atop −1} 1^{3} 2_{+} 1  33 42 42 33 22 22 42 42
S_{4}^{+}  3  -15 18 -27  1^{3} 2_{+} 1  42 42 33 22 42 22 33 42
85. 2_{−} 10_{+} 4_{−} 0 -19  0 1^{6} 10_{+} 1  1^{4} 3_{k} 19 19∗ 22 33 33 33 22 33 22 22
S_{4}^{+}  4  133  0 -361  1^{2} 1_{k} 19 19 42 22 22 33 33 42 42 33
86. 2_{−} 12_{+} 4_{−} 0 19  0 1^{4} 10_{k} −1 2∗ 1^{4} 3_{i} 19∗ 19 33 22 33 22 33 33 33 33
S_{4}^{+}  2  57  0 -361 1^{2} 2_{i} −1 −1 1^{2} 1_{i} 19∗ 19∗ 42 22 42 22 22 33 33 42
87. 2_{−} 14_{+} 4_{−} 0 -38  0 1^{4} 11_{−} 2∗  2∗ 1^{4} 3_{i} 19∗ 19 33 42 33 42 33 33 33 33
S_{4}^{+}  2  418  0 -1444 1^{2} 3_{−} 2∗  2∗ 1^{2} 1_{i} 19∗ 19∗ 22 22 42 42 22 33 33 42
88. 2_{−} 14_{−} 4_{+} 0 -8  0 1^{4} 11_{−} 2 −2 1^{3} 2_{+} 1  33 42 42 33 42 22 22 42
S_{4}^{+}  6  34  0 -64 1^{2} 3_{+} 2  2 1^{3} 2_{+} 1  22 22 33  42 42 33 42
89. 2_{−} 14_{−} 4_{+} 0 -8  0 1^{4} 11_{−} 2 −2 1^{3} 2_{+} 1  33 22 22 33 42 22 42 22
S_{4}^{+}  6  72  0 -64 1^{2} 3_{+} 2  2 1^{3} 2_{+} 1  42 42 33 22 22 42 33 22
90. 2_{−} 14_{+} 4_{−} 0 -38  0 1^{4} 11_{i} −2∗ 2∗ 1^{4} 3_{i} 19∗ 19 33 22 33 42 33 33 33 33
S_{4}^{+}  2  646  0 -1444 1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{i} 19∗ 19∗ 22 22 22 22 22 33 33 42

Discriminant class: 2

∞  2 19 a_{1} a_{2}  a_{3}  Over p = 2  Over p = 19  3 5 7 11 13 17 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
91.  2_{−}  9_{−} 2_{+}  0 2  -2 2^{2} 6_{−} 1  {∗ \atop 2} 2^{2} 2_{+} 1  V 6 222 33 222 6 33 33 6
D_{6}  -2 0  -1 1^{2} 3_{+} 2  2 2 0_{+} ∗  ∗ 22 222 22 222  6 6 222
92.  2_{−}  11_{+} 2_{−}  0 -1  0 1^{4} 11_{+} 2∗ 2∗ 2 0_{+} ∗  ∗ 6 222 33 4 6 33 33 6
S_{4} × C_{2}  -2 0  -2 2 0_{+} ∗  ∗ 1^{2} 1_{k} 19 19 42 2 42 222 22 6 6 222
93.  2_{−}  11_{−} 2_{+}  0 0  0 1^{6} 11_{−} 2  2^{2} 2_{+} 1  V 4 6 33 6 222 33 22 4
S_{4} × C_{2}  -2 0  -2  2 0_{+} ∗  ∗ 42 4 42 6 33 4 222 6
94.  2_{−}  11_{−} 2_{+} -2 3  -4 1^{6} 11_{−} 2  2^{2} 2_{+} 1  V 6 6 3 6 6 3 33 6
S_{3} × S_{3}  1 -2  1  2 0_{+} ∗  ∗ 22 222 22 6 33 6 6 6
95.  2_{−}  11_{−} 2_{+}  0 -2  0 1^{6} 11_{−} 2  2^{2} 2_{+} 1  V 222 6 33 6 222 33  222
D_{6}  4 0  -2  2 0_{+} ∗  ∗ 22 222 22 6 33 222 222 6
96.  2_{−}  13_{+} 2_{−}  0 -4  0 1^{4} 10_{k} −1 2∗ 2 0_{+} ∗  ∗ 6 4 33 222 6 33 33 6
S_{4} × C_{2}  3 0  -2 1^{2} 3_{i} −2 −2 1^{2} 1_{k} 19 19 22 2 42 4 22 6 6 222
97.  2_{−}  13_{−} 2_{+}  0 5  0 1^{4} 11_{i} −2∗ 2∗ 2^{2} 2_{+} 1  V 6 4 33 4 6 33 33 6
S_{4} × C_{2}  6 0  -2 1^{2} 2_{i} −∗ −∗ 2 0_{+} ∗  ∗ 42 222 22 4 22 6 6 222
98.  2_{−}  9_{−} 4_{+}  0 -6  0 1^{2} 3_{+} 2  2 2^{3} 4_{+} ∗  6 4 42 6 222 22 42 4
S_{4} × C_{2}  3  -7 0  -8 1^{2} 3_{i} −2 −2  42 4 33 2 42 222 6 4
99.  2_{−}  9_{−} 4_{+}  0 -4  0 3^{2} 9_{−} 2  2^{3} 4_{+} ∗  6 6 22 2 6 33 33 6
A_{4} × C_{2}  -20 0  -8  2 33 6 33 6 6 6
100.  0_{+}  9_{+} 4_{+} -2 -17  34 3^{2} 9_{+} 2  2^{3} 4_{+} ∗  6 6  222 6 33 33 6
C_{6}  30 -32  -7  222 33 6 33 6 6 6
101.  2_{−}  11_{−} 4_{+}  0 -4  0 1^{4} 11_{−} 2 −2 2^{3} 4_{+} ∗  6 222 22 6 4 22 42 222
S_{4} × C_{2}  3  18 0  -8  42 4 33 2 22 4 6 222
102.  2_{−}  11_{−} 4_{+}  0 15  0 1^{4} 11_{−} 2 −2 2^{3} 4_{+} ∗  6 4 42 6 4 22 22 4
S_{4} × C_{2}  3  56 0  -8  22 222 33 222 42 4 6 4
103.  2_{−}  11_{−} 4_{+}  2 -17  0 1^{4} 8_{−} 1 {−2∗ \atop −1} 1^{4} 3_{i} 19∗ 19 6 4 33 222 6 33 33 6
S_{4} × C_{2}  2  137 -86 -185 1^{2} 3_{+} 2  2 1^{2} 1_{k} 19 19 42 2 22 4  6 6 4
104.  2_{−}  11_{−} 4_{+}  0 0  0 1^{6} 11_{−} 2  1^{4} 3_{k} 19 19∗ 4 6 33 6 222 33 22 4
S_{4} × C_{2}  2  -152 0 -722  1^{2} 1_{i} 19∗ 19∗ 22 4 42 6 33 222 4 6

∞  2 19 a_{1} a_{2}  a_{3}  Over p = 2  Over p = 19  3 5 7 11 13 17 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
105.  2_{−}  11_{−} 4_{+}  3 11  8 1^{4} 11_{−} 2∗ 2∗ 1^{4} 3_{i} 19∗ 19 6 4 33 4 6 33 33 6
S_{4} × C_{2}  -50 42 -94 2 0_{+} ∗  ∗ 1^{2} 1_{k} 19 19 22 2 42 4 22 6 6 4
106.  2_{−}  11_{−} 4_{+}  0 0  0 1^{6} 11_{−} 2  1^{4} 3_{k} 19 19∗ 222 6 33 6 222 33 22 222
S_{4} × C_{2}  2  114 0 -722  1^{2} 1_{i} 19∗ 19∗ 42 222 22 6 33 4 4 6
107.  2_{−}  11_{−} 4_{+}  0 12  0 1^{4} 8_{−} 1  {−2 \atop −1} 2^{3} 4_{+} ∗  6 222 22 6 222  22 222
D_{6}  6  29 0 -50 1^{2} 3_{+} 2  2  22 222 33 222 22 222 6 222
108.  2_{−}  13_{−} 4_{+}  0 -19  0 1^{4} 11_{i} −2∗ 2∗ 1^{4} 3_{i} 19∗ 19 6 222 33 4 6 33 33 6
S_{4} × C_{2}  2  190 0 -722 1^{2} 2_{i} −∗ −∗ 1^{2} 1_{k} 19 19 22 2 22 222 22 6 6 4
109.  2_{−}  13_{−} 4_{+}  0 -38  0 1^{4} 10_{i} −1 2∗ 1^{4} 3_{i} 19∗ 19 6 222 33 222 6 33 33 6
S_{4} × C_{2}  2  551 0 -2888 1^{2} 3_{i} −2 −2 1^{2} 1_{k} 19 19 42 2 42 222 22 6 6 4

Discriminant class: 19

∞  2 19 a_{1} a_{2} a_{3}  Over p = 2  Over p = 19  3 5 7 11 13 17 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
110.  2_{−}  8_{k} 3_{k}  2  0 -10 1^{6} 8_{k} −∗  1^{4} 3_{k} 19 19∗ 42 33 6 6 222 33 2 4
S_{4} × C_{2}  -10 -4 -2  22 4 4 6 6 222 42 33
111.  2_{−}  8_{i} 3_{i}  0 -1  2 1^{2} 3_{−} 2∗  2∗ 1^{4} 3_{i} 19∗ 19 33 42 6 222 6 33 6 6
S_{4} × C_{2}  2  0 -8 1^{2} 3_{−} 2∗  2∗ 2 0_{+} ∗  ∗ 42 2 222 4 222 6 33 42
112.  2_{−}  8_{k} 3_{k} -2  3  6 1^{6} 8_{k} −∗  2^{2} 2_{+} 1  V 22 33 6 6 222 33 222 222
D_{6}  -7  8 -3  1^{2} 1_{k} 19 19 22 222 222 6 6 222 22 33
113.  2_{−}  10_{i} 3_{i}  2 -6 -20 1^{4} 8_{+} 1  {−2 \atop −∗} 1^{2} 1_{k} 19 19 33 22 6 222 6 33 6 6
D_{6}  -15 -2 -10 1^{2} 2_{i} −∗ −∗ 1^{2} 1_{k} 19 19 22 222 222 222 222 6 33 22
114.  2_{−}  10_{i} 3_{i}  3  3 -10 1^{4} 10_{i} −1 2∗ 1^{4} 3_{i} 19∗ 19 33 22 6 222 6 33 6 6
S_{4} × C_{2}  -7 13 -1 2 0_{+} ∗  ∗ 2 0_{+} ∗  ∗ 42 2 4 222 2 6 33 42
115.  2_{−}  10_{k} 3_{k}  0 -7  0 1^{6} 10_{k} −∗  1^{4} 3_{k} 19 19∗ 22 33 6 6 222 33 2 222
S_{4} × C_{2}  19  0 -19  42 222 222 6 6 4 42 33
116.  2_{−}  10_{k} 3_{k}  0 -9  0 1^{6} 10_{k} −∗  2^{2} 2_{+} 1  V 42 33 6 6 222 33 2 4
S_{4} × C_{2}  25  0 -19  1^{2} 1_{k} 19 19 42 4 4 6 6 4 22 33
117.  2_{−}  10_{k} 3_{k}  0 -7  0 1^{4} 10_{k} −1 2∗ 2^{2} 2_{+} 1  V 33 42 6 222 6 33 6 6
S_{4} × C_{2}  17  0 -19 2 0_{+} ∗  ∗ 1^{2} 1_{k} 19 19 22 2 4 4 2 6 33 22
118.  2_{−}  14_{i} 3_{i}  0  4  0 1^{4} 11_{+} 2∗  2∗ 1^{4} 3_{i} 19∗ 19 33 42 6 4 6 33 6 6
S_{4} × C_{2}  2  -38  0 -304 1^{2} 3_{i} −2 −2 2 0_{+} ∗  ∗ 22 2 4 4 2 6 33 42
119.  2_{−}  14_{k} 3_{k}  0 -20  0 1^{4} 11_{−} 2∗  2∗ 2^{2} 2_{+} 1  V 33 22 6 4 6 33 6 6
S_{4} × C_{2}  138  0 -304 1^{2} 3_{i} −2 −2 1^{2} 1_{k} 19 19 42 2 4 222 2 6 33 22
120.  2_{−}  14_{i} 3_{i}  0 -10  0 1^{4} 11_{i} −2∗ 2∗ 1^{4} 3_{i} 19∗ 19 33 22 6 4 6 33 6 6
S_{4} × C_{2}  2  38  0 -76 1^{2} 3_{+} 2  2 2 0_{+} ∗  ∗ 22 2 222 222 2 6 33 42
121.  2_{−}  14_{i} 3_{i}  0  6  0 1^{4} 11_{i} −2∗ 2∗ 1^{2} 1_{k} 19 19 33 42 6 4 6 33 6 6
S_{4} × C_{2}  2  -10  0 -76 1^{2} 3_{+} 2  2 1^{2} 1_{k} 19 19 42 222 222 4 2 6 33 22
122.  2_{−}  6_{i} 5_{i}  0  0  0 3^{2} 6_{i} −∗  1^{6} 5_{i} 19  33 33 2 2 6 33 6 6
A_{4} × C_{2}  -19  0 -19  2 6 6 6 6 33 33
123.  0_{+}  6_{k} 5_{i}  0 -19  0 3^{2} 6_{k} −∗  1^{6} 5_{i} 19  33 33 222 222 6 33 6 6
C_{6}  38  0 -19  222 6 6 6 6 33 33
124.  2_{−}  8_{i} 5_{i} -2  8 -12 1^{4} 6_{+} ∗ −∗ 1^{6} 5_{i} 19  5 5 4 6 4 33 4 222
S_{5}  6  22 -8 -8 1^{2} 2_{i} −1 −1  33 4 4 6 4 6 33 22
125.  2_{−}  8_{i} 5_{i}  2  8 12 2^{2} 6_{+} 1 {−2 \atop −2∗} 1^{6} 5_{i} 19  33 42 4 6 222 22 4 4
S_{4} × C_{2}  3  -16  8 -8 1^{2} 2_{i} −∗ −∗  42 4 6 2 4 222 33 42

∞  2 19 a_{1} a_{2} a_{3}  Over p = 2  Over p = 19  3 5 7 11 13 17 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
126.  2_{−}  10_{i} 5_{i}  0 -19  0 1^{4} 8_{+} 1  {−2 \atop −∗} 1^{6} 5_{i} 19  3 22 6 6 6 33 6 6
S_{3} × S_{3}  3  133 -152 57 1^{2} 2_{i} −∗ −∗  22 222 6 222 222 6 3 22
127.  2_{−}  10_{i} 5_{i}  0 -19  0 1^{4} 8_{+} 1  {−2 \atop −∗} 1^{6} 5_{i} 19  33 22 222 6 222  222 222
D_{6}  6  152  0 -304 1^{2} 2_{i} −∗ −∗  22 222 6 222 222 222 33 22
128.  2_{−}  14_{i} 5_{i}  0 -38  0 1^{4} 11_{−} 2 −2 1^{6} 5_{i} 19  33 22 222 6 4 22 4 222
S_{4} × C_{2}  6  456  0 -304 1^{2} 3_{k} −2∗ −2∗  42 4 6 2 222 4 33 22
129.  2_{−}  14_{i} 5_{i}  0  0  0 1^{4} 11_{−} 2 −2 1^{6} 5_{i} 19  33 42 4 6 4 22 222 4
S_{4} × C_{2}  6  114  0 -304 1^{2} 3_{k} −2∗ −2∗  22 222 6 222 4 4 33 42

Discriminant class: 38

∞  2 19 a_{1} a_{2} a_{3}  Over p = 2  Over p = 19  3 5 7 11 13 17 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
130.  2_{−}  9_{i} 3_{i} -2 -1  2 2^{2} 6_{−} 1  {∗ \atop 2} 1^{4} 3_{i} 19∗ 19 6 4 6 22 33 33 6 33
S_{4} × C_{2}  -1 8 -2 1^{2} 3_{k} −2∗ −2∗  42 22 222 42 222 33 6 4
131.  2_{−}  11_{i} 3_{i} -3 0 14 1^{4} 11_{i} −2∗ 2∗ 2^{2} 2_{+} 1  V 6 4 6 42 33 33 6 33
S_{4} × C_{2}  7 -17 -10  1^{2} 1_{i} 19∗ 19∗ 42  222 42 2 33 6 222
132.  2_{−}  11_{k} 3_{k}  0 -2  0 1^{6} 11_{k} −2∗  1^{4} 3_{k} 19 19∗ 4 6 6 33 22 33 2 42
S_{4} × C_{2}  0 0 -38  2 0_{+} ∗  ∗ 22 42 4 33 6 22 4 6
133.  2_{−}  11_{k} 3_{k}  0 -10  0 1^{6} 11_{k} −2∗  1^{4} 3_{k} 19 19∗ 222 6 6 33 22 33 2 22
S_{4} × C_{2}  38 0 -38  2 0_{+} ∗  ∗ 42 22 222 33 6 42 4 6
134.  2_{−}  11_{k} 3_{k}  0 -2  0 1^{6} 11_{k} −2∗  1^{2} 1_{i} 19∗ 19∗ 4 6 6 33 22 33 2 42
S_{4} × C_{2}  -18 0 -38  1^{2} 1_{i} 19∗ 19∗ 42 42 4 33 6 42 222 6
135.  2_{−}  11_{i} 3_{i}  3 10 20 1^{4} 11_{i} −2∗ 2∗ 1^{4} 3_{i} 19∗ 19 6 222 6 42 33 33 6 33
S_{4} × C_{2}  10 -2 -4  22 22 222 22 2 33 6 4
136.  2_{−}  11_{i} 3_{i}  2 1 -12 1^{4} 8_{−} 1 {−2∗ \atop −1} 2^{2} 2_{+} 1  V 6 222 6 22 33 33 6 33
D_{6}  -12 0 -2 1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{i} 19∗ 19∗ 22  222 22 222 33 6 222
137.  2_{−}  11_{k} 3_{k}  0 4  0 1^{6} 11_{k} −2∗  1^{2} 1_{i} 19∗ 19∗ 222 6 6 33 22 33 222 22
D_{6}  4 0 -38  1^{2} 1_{i} 19∗ 19∗ 22 22 222 33 6 22 222 6
138.  2_{−}  13_{i} 3_{i}  0 -4  0 1^{4} 10_{k} −1 2∗ 1^{4} 3_{i} 19∗ 19 6 222 6 22 33 33 6 33
S_{4} × C_{2}  2  19 0 -38 1^{2} 3_{−} 2∗  2∗  42 22 4 22 2 33 6 4
139.  2_{−}  13_{k} 3_{k}  0 -8  0 1^{4} 10_{i} −1 2∗ 1^{2} 1_{k} 19 19 6 4 6 22 33 33 6 33
S_{4} × C_{2}  2  35 0 -38 1^{2} 3_{−} 2∗  2∗ 1^{2} 1_{i} 19∗ 19∗ 22 22 4 42 2 33 6 222
140.  2_{−}  13_{i} 3_{i}  0 -11  0 1^{4} 11_{+} 2∗  2∗ 1^{4} 3_{i} 19∗ 19 6 4 6 42 33 33 6 33
S_{4} × C_{2}  2  38 0 -38 1^{2} 2_{i} −1 −1  22 22 4 42 2 33 6 4
141.  2_{−}  13_{k} 3_{k}  0 5  0 1^{4} 11_{−} 2∗  2∗ 1^{2} 1_{k} 19 19 6 222 6 42 33 33 6 33
S_{4} × C_{2}  30 0 -38 1^{2} 2_{i} −1 −1 1^{2} 1_{k} 19 19 42 22 4 22 2 33 6 222
142.  2_{−}  9_{k} 5_{k}  0 0  0 3^{2} 9_{k} −2∗  1^{6} 5_{k} 19∗  6 6 2 22 33 33 6 33
A_{4} × C_{2}  -76 0 -152  22 6 33 6 33 6 6
143.  2_{−}  9_{k} 5_{k}  0 0 -38 2^{2} 6_{+} 1 {−2 \atop −2∗} 1^{6} 5_{k} 19∗  6 222 222 33 22  222 22
D_{6}  3  -38 -76 323 1^{2} 3_{k} −2∗ −2∗  22 22 6  222 22 6 222
144.  0_{+}  9_{i} 5_{k}  0 -38  0 3^{2} 9_{i} −2∗  1^{6} 5_{k} 19∗  6 6 222  33 33 6 33
C_{6}  152 0 -152  6 33 6 33 6 6
145.  2_{−}  11_{k} 5_{k}  0 0  0 1^{4} 8_{+} 1  {−2 \atop −∗} 1^{6} 5_{k} 19∗  6 4 4 33 22 22 4 42
S_{4} × C_{2}  6  -19 0 -38 1^{2} 3_{k} −2∗ −2∗  42 42 6 22 4 22 6 4
146.  2_{−}  11_{k} 5_{k}  0 0  0 1^{6} 11_{k} −2∗  1^{6} 5_{k} 19∗  6 6 6 3 22 33 222 22
S_{3} × S_{3}  3  -38 -76 -38  22 22 6 33 6 22 6 6

∞  2 19 a_{1} a_{2} a_{3}  Over p = 2  Over p = 19  3 5 7 11 13 17 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
147.  2_{−}  13_{k} 5_{k}  0 -19  0 1^{4} 11_{−} 2 −2 1^{6} 5_{k} 19∗  6 4 4 33 42 22 222 42
S_{4} × C_{2}  6  -38 0 -38 1^{2} 2_{i} −∗ −∗  22 22 6  4 42 6 4
148.  2_{−}  13_{k} 5_{k}  0 -19  0 1^{4} 11_{−} 2 −2 1^{6} 5_{k} 19∗  6 222 222 33 42 22 4 22
S_{4} × C_{2}  6  114 0 -38 1^{2} 2_{i} −∗ −∗  42 42 6 22 222 42 6 222