New 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}  13_{−} 5_{i}  2 -1 -4 1^{4} 10_{i} −∗ −2 1^{3} 5_{i} 3∗  42 42 33 6 32 32 222 42
C_{3}^{2}.D_{4}  -2  4 6 1^{2} 3_{i} −2 −2 2 0_{+} ∗ ∗ 42 6 32 2 6 42 22 6
2. 3_{i}  13_{+} 7_{k} 0 -6 4 1^{4} 10_{k} −∗ −2 1^{3} 4_{+} 1  42 42 22 6 2 32 6 42
C_{3}^{2}.D_{4}  3  9 -12 12 1^{2} 3_{i} −2 −2 1^{3} 3_{k} 3  42 6 32 32 222 42 33 6
3. 3_{i}  13_{−} 7_{i}  0  0 8 1^{4} 10_{i} −∗ −2 1^{3} 4_{+} ∗  42 42 3 222 32 2 6 42
C_{3}^{2}.D_{4}  18 24 24 1^{2} 3_{i} −2 −2 1^{3} 3_{i} 3∗  42 6 32 32 6 42 22 6
4. 1_{k}  11_{+} 9_{i}  0 -6 -12 1^{4} 9_{k} −2 −∗ 1^{6} 9_{i} 3  42 42 22 32 222 6 32 42
C_{3}^{2}.D_{4}  9 36 -12 1^{2} 2_{i} −∗ −∗  42 32 6 6 2 42 3 32
5. 1_{k}  11_{−} 9_{k} 0 -6 -8 1^{4} 9_{i} −2 −∗ 1^{6} 9_{k} 3  42 42 33 2 6 222 32 42
C_{3}^{2}.D_{4}  -18 24 16 1^{2} 2_{i} −∗ −∗  42 32 6 6 32 42 22 32
6. 3_{i}  13_{−} 9_{i}  0 -12 8 1^{4} 10_{i} −∗ −2 1^{3} 5_{i} 3∗  42 42 33 6 32 32 6 42
C_{3}^{2}.D_{4}  54 -72 24 1^{2} 3_{i} −2 −2 1^{3} 4_{+} ∗  42 6 32 32 6 42 22 222
7. 3_{i}  13_{−} 9_{i}  0  6 8 1^{4} 10_{i} −∗ −2 1^{3} 5_{i} 3∗  42 42 3 6 2 32 6 42
C_{3}^{2}.D_{4}  27  0 24 1^{2} 3_{i} −2 −2 1^{3} 4_{+} ∗  42 222 2 32 222 42 22 6
8. 1_{k}  11_{−} 11_{k} 0 -18 24 1^{4} 9_{i} −2 −∗ 1^{6} 11_{k} 3  42 42 3 32 6 6 32 42
C_{3}^{2}.D_{4}  81 -216 132 1^{2} 2_{i} −∗ −∗  42 32 6 6 32 42 22 2
9. 1_{k}  11_{−} 11_{k} 0  0 0 1^{4} 9_{i} −2 −∗ 1^{6} 11_{k} 3  42 42 33 32 222 6 32 42
C_{3}^{2}.D_{4}  -27 -36 -12 1^{2} 2_{i} −∗ −∗  42 2 222 6 2 42 22 32
10. 1_{k}  11_{−} 11_{k} 0 -18 24 1^{4} 9_{i} −2 −∗ 1^{6} 11_{k} 3  42 42 3 32 6 6 2 42
C_{3}^{2}.D_{4}  54 -144 96 1^{2} 2_{i} −∗ −∗  42 32 6 222 32 42 22 32
11. 3_{i}  13_{−} 7_{i}  0  6 4 1^{4} 11_{i} −2 2 1^{3} 4_{+} ∗  5 5 5 32 32 6 32 5
S_{6}  15 12 12 1^{2} 2_{i} −∗ −∗ 1^{3} 3_{i} 3∗  5 32 6 6 6 5 42 32
12. 1_{k}  11_{−} 9_{k} 0 -9 8 1^{4} 11_{−} 2 −2 1^{6} 9_{k} 3  5 5 5 6 6 32 6 5
S_{6}  0  0 4 2 0_{+} ∗  ∗  5 6 32 32 32 5 42 6

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
13. 3_{i}  14_{−} 3_{i}  2 -1  0 1^{4} 11_{i} −2∗ −2 1^{3} 3_{i} 3∗  6 42 32 42 32 22 6 6
C_{3}^{2}.D_{4}  2 -4  2 1^{2} 3_{i} −2 −2 3 0_{+} 1  42 42 32 22 6 6 32 42
14. 3_{i}  14_{+} 5_{k} 2  1 -4 1^{4} 11_{k} −2∗ −2 1^{3} 4_{+} ∗  6 42 32 42 32 33 6 222
C_{3}^{2}.D_{4}  -11 14 33 1^{2} 3_{i} −2 −2 1^{2} 1_{k} 3 3 42 42 32 3 6 6 32 42
15. 1_{k}  14_{−} 7_{k} 0 -6  8 1^{4} 11_{k} −2 −2∗ 1^{6} 7_{k} 3∗  32 42 6 42 6 22 32 32
C_{3}^{2}.D_{4}  -6  0  4 1^{2} 3_{k} −2∗ −2∗  42 42 6 22 32 32 6 42
16. 1_{k}  14_{+} 9_{i}  0 -12 16 1^{4} 11_{i} −2 −2∗ 1^{6} 9_{i} 3∗  32 42 6 42 6 3 32 2
C_{3}^{2}.D_{4}  -18 48 -32 1^{2} 3_{k} −2∗ −2∗  42 42 6 33 32 32 6 42
17. 3_{i}  14_{−} 9_{i}  0  6 -4 1^{4} 11_{i} −2∗ −2 1^{3} 5_{i} 3∗  6 42 32 42 2 22 6 222
C_{3}^{2}.D_{4}  3  81 36 12 1^{2} 3_{i} −2 −2 1^{3} 4_{+} 1  42 42 2 22 222 222 32 42
18. 3_{i}  14_{−} 9_{i}  0 -12 16 1^{4} 11_{i} −2∗ −2 1^{3} 5_{i} 3∗  6 42 32 42 32 22 222 6
C_{3}^{2}.D_{4}  3  54 -144 96 1^{2} 3_{i} −2 −2 1^{3} 4_{+} 1  42 42 32 22 6 6 32 42
19. 3_{i}  14_{−} 9_{i}  0  6 -4 1^{4} 11_{i} −2∗ −2 1^{3} 5_{i} 3∗  222 42 2 42 32 22 6 6
C_{3}^{2}.D_{4}  3  27 -36 12 1^{2} 3_{i} −2 −2 1^{3} 4_{+} 1  42 42 32 22 6 6 2 42

Discriminant class: −3 (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
20. 1_{k}  14_{−} 11_{k} 0 -18 12 1^{4} 11_{k} −2 −2∗ 1^{6} 11_{k} 3∗  32 42 6 42 6 22 2 32
C_{3}^{2}.D_{4}  27 -36 12 1^{2} 3_{k} −2∗ −2∗  42 42 6 22 32 32 6 42
21. 1_{k}  14_{−} 11_{k} 0 -18 12 1^{4} 11_{k} −2 −2∗ 1^{6} 11_{k} 3∗  2 42 222 42 6 22 32 32
C_{3}^{2}.D_{4}  81 -108 -180 1^{2} 3_{k} −2∗ −2∗  42 42 6 22 32 32 222 42
22. 1_{k}  14_{−} 11_{k} 0 -18 12 1^{4} 11_{k} −2 −2∗ 1^{6} 11_{k} 3∗  32 42 6 42 222 22 32 2
C_{3}^{2}.D_{4}  3  81 -108 12 1^{2} 3_{k} −2∗ −2∗  42 42 222 22 2 2 6 42
23. 3_{i}  12_{−} 9_{i}  0  6 -12 1^{4} 9_{k} −2 −∗ 1^{3} 5_{i} 3∗  32 5 6 5 32 22 6 4
S_{6}  21  0  2 1^{2} 3_{k} −2∗ −2∗ 1^{3} 4_{+} 1  5 33 32 5 6 32 32 3
24. 1_{k}  12_{−} 11_{k} 0 -9 -24 1^{4} 10_{i} −∗ −2 1^{6} 11_{k} 3∗  6 5 32 5 6 22 32 4
S_{6}  9 72  3 1^{2} 2_{i} −1 −1  5 3 6 5 32 6 6 33

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
25. 3_{i}  11_{i} 6_{−} 0 0 0 1^{4} 9_{+} 2 −1 2^{3} 6_{−} 1  32 6 42 32 3 42 6 32
C_{3}^{2}.D_{4}  9 -12 4 1^{2} 2_{i} −1 −1  222 2 22 42 6 32 42 32
26. 1_{k}  13_{k} 6_{−} 0 -6 4 1^{4} 10_{k} −1 2 2^{3} 6_{−} 1  6 32 42 6 33 42 32 6
C_{3}^{2}.D_{4}  9 -12 -4 1^{2} 3_{+} 2  2  2 222 22 42 32 6 42 6
27. 3_{i}  11_{k} 8_{+} 0 0 8 1^{4} 9_{−} 2 −1 2^{3} 8_{+} 1  2 6 42 32 22 42 6 32
C_{3}^{2}.D_{4}  9 12 20 1^{2} 2_{i} −1 −1  6 32 33 42 6 32 42 32
28. 1_{k}  13_{i} 8_{+} 0 0 8 1^{4} 10_{i} −1 2 2^{3} 8_{+} 1  222 32 42 6 22 42 32 6
C_{3}^{2}.D_{4}  -18 -24 8 1^{2} 3_{+} 2  2  32 6 3 42 32 6 42 6

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
29. 3_{i}  4_{k} 10_{+} 0  3 -2 2^{2} 4_{k} −∗  ∗ 1^{6} 10_{+} ∗  42 32 6 22 42 32 6 42
C_{3}^{2}.D_{4}  9 -12 4 2 0_{+} ∗  ∗  2 3 42 32 6 42 6 33
30. 3_{i}  6_{k} 10_{+} 0  3 -4 2^{2} 6_{k} −∗  ∗ 1^{6} 10_{+} ∗  42 32 6 3 42 2 222 42
C_{3}^{2}.D_{4}  9 30 52 2 0_{+} ∗  ∗  32 22 42 32 6 42 222 22
31. 3_{i}  14_{k} 6_{+} 0  6 -4 1^{4} 11_{−} 2 −2 1^{3} 3_{k} 3  42 6 2 42 33 32 6 42
C_{3}^{2}.D_{4}  9 -12 12 1^{2} 3_{i} −2 −2 1^{3} 3_{i} 3∗  6 42 3 32 6 42 32 42
32. 3_{i}  14_{k} 6_{+} 2 -1 0 1^{4} 11_{−} 2 −2 1^{3} 5_{i} 3∗  42 6 32 42 3 32 6 42
C_{3}^{2}.D_{4}  10  4 2 1^{2} 3_{i} −2 −2 1^{2} 1_{k} 3 3 6 42 33 32 222 42 32 42
33. 1_{k}  14_{i} 6_{+} 0 -6 4 1^{4} 11_{i} −2  2 2^{3} 6_{+} ∗  42 32 222 42 3 6 32 42
C_{3}^{2}.D_{4}  -9 12 -4 1^{2} 3_{+} 2  2  32 42 33 6 32 42 6 42
34. 1_{k}  8_{i} 10_{+} 0 -6 2 1^{4} 6_{+} ∗ −∗ 1^{6} 10_{+} ∗  42 6 32 22 42 6 32 42
C_{3}^{2}.D_{4}  9 -6 -2 1^{2} 2_{i} −∗ −∗  222 33 42 6 32 42 32 3
35. 1_{k}  10_{i} 10_{+} 0 -6 8 1^{4} 8_{+} ∗ −∗ 1^{6} 10_{+} ∗  42 6 32 33 42 222 2 42
C_{3}^{2}.D_{4}  9 -24 4 1^{2} 2_{i} −∗ −∗  6 22 42 6 32 42 2 22
36. 1_{k}  14_{i} 8_{+} 0  0 16 1^{4} 11_{i} −2  2 2^{3} 8_{+} ∗  42 32 6 42 22 222 32 42
C_{3}^{2}.D_{4}  -18 -48 32 1^{2} 3_{+} 2  2  32 42 22 222 2 42 6 42
37. 3_{i}  14_{k} 8_{+} 0 -6 4 1^{4} 11_{−} 2 −2 1^{3} 5_{i} 3∗  42 6 32 42 33 2 222 42
C_{3}^{2}.D_{4}  27 -36 12 1^{2} 3_{i} −2 −2 1^{3} 3_{k} 3  222 42 3 2 6 42 32 42

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
38. 3_{i}  14_{k} 8_{+} 0  6 12 1^{4} 11_{−} 2 −2 1^{3} 5_{i} 3∗  42 222 32 42 3 32 6 42
C_{3}^{2}.D_{4}  27 36 36 1^{2} 3_{i} −2 −2 1^{3} 3_{k} 3  6 42 33 32 6 42 2 42
39. 3_{i}  14_{k} 8_{+} 0 -6 12 1^{4} 11_{−} 2 −2 1^{3} 4_{+} 1  42 6 32 42 22 2 6 42
C_{3}^{2}.D_{4}  3  9 -36 68 1^{2} 3_{i} −2 −2 1^{3} 4_{+} ∗  6 42 22 2 222 42 32 42
40. 1_{k}  14_{i} 10_{+} 0 -6 20 1^{4} 11_{−} 2∗ −2∗ 1^{6} 10_{+} ∗  33 6 6 42 42 32 32 22
C_{3}^{2}.D_{4}  9 -60 4 1^{2} 3_{k} −2∗ −2∗  6 42 42 32 2 22 6 42
41. 3_{i}  14_{k} 10_{+} 0 -6 4 1^{4} 11_{i} −2∗ 2∗ 1^{6} 10_{+} ∗  22 32 2 42 42 6 6 33
C_{3}^{2}.D_{4}  2  63 60 28 1^{2} 3_{−} 2∗  2∗  2 42 42 6 222 3 32 42
42. 1_{k}  14_{i} 10_{+} 0 -18 12 1^{4} 11_{−} 2∗ −2∗ 1^{6} 10_{+} ∗  22 6 222 42 42 32 32 3
C_{3}^{2}.D_{4}  27 -108 36 1^{2} 3_{k} −2∗ −2∗  222 42 42 32 2 33 6 42
43. 1_{k}  14_{i} 10_{+} 0 -18 12 1^{4} 11_{i} −2  2 2^{3} 10_{+} ∗  42 32 6 42 3 222 2 42
C_{3}^{2}.D_{4}  81 -108 -36 1^{2} 3_{+} 2  2  2 42 33 222 32 42 6 42
44. 1_{k}  14_{i} 10_{+} 0 -18 36 1^{4} 11_{i} −2  2 2^{3} 10_{+} ∗  42 32 6 42 33 6 32 42
C_{3}^{2}.D_{4}  -81 108 36 1^{2} 3_{+} 2  2  32 42 3 6 2 42 6 42
45. 1_{k}  14_{i} 10_{+} 0 -18 36 1^{4} 11_{i} −2  2 2^{3} 10_{+} ∗  42 2 6 42 33 6 32 42
C_{3}^{2}.D_{4}  81 -324 252 1^{2} 3_{+} 2  2  32 42 3 6 32 42 222 42
46. 3_{i}  14_{k} 10_{+} 0 12 -16 1^{4} 11_{i} −2∗ 2∗ 1^{6} 10_{+} ∗  3 32 32 42 42 6 6 22
C_{3}^{2}.D_{4}  2  36 -96 160 1^{2} 3_{−} 2∗  2∗  32 42 42 6 222 22 32 42
47. 3_{i}  10_{k} 10_{+} 0 -6 4 1^{4} 8_{−} ∗  1^{6} 10_{+} ∗  5 4 32 5 3 32 6 42
S_{6}  2  27 -48 28 1^{2} 2_{i} −∗ −∗  6 5 5 6 32 33 4 5
48. 1_{k}  10_{i} 10_{+} 0 -6 8 1^{6} 10_{i} −1  1^{6} 10_{+} ∗  5 4 6 5 33 6 32 42
S_{6}  0 -24 28  32 5 5 32 6 3 4 5
49. 3_{i}  14_{k} 10_{+} 0 12 4 1^{4} 11_{−} 2  2 1^{6} 10_{+} ∗  5 32 6 33 5 32 6 5
S_{6}  2  27 -12 10 1^{2} 3_{i} −2 −2  32 42 5 6 32 5 32 22
50. 1_{k}  14_{i} 10_{+} 0 -6 4 1^{4} 11_{+} 2  2 1^{6} 10_{+} ∗  5 6 32 3 5 6 32 5
S_{6}  -9 -12 52 1^{2} 3_{i} −2 −2  6 42 5 32 6 5 6 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
51. 2_{−} 14_{+} 6_{−} 0 6 4 1^{4} 11_{+} 2  2 2^{3} 6_{−} 1  42 22 42 42 22 42 3 42
C_{3}^{2}.C_{4}  -9 -12 -4 1^{2} 3_{+} 2  2  33 42 33 42 22 42 42 42
52. 2_{−} 14_{+} 6_{−} 0 6 -4 1^{4} 11_{+} 2  2 2^{3} 6_{−} 1  42 22 42 42 22 42 33 42
C_{3}^{2}.C_{4}  9 -12 -4 1^{2} 3_{+} 2  2  3 42 3 42 22 42 42 42
53. 2_{−} 14_{−} 8_{+} 0 0 -8 1^{4} 11_{−} 2  2 2^{3} 8_{+} 1  42 33 42 42 3 42  42
C_{3}^{2}.C_{4}  -18 -48 -16 1^{2} 3_{+} 2  2  22 42 22 42 22 42 42 42
54. 2_{−} 14_{−} 8_{+} 0 6 -12 1^{4} 11_{−} 2  2 2^{3} 8_{+} 1  42 3 42 42 33 42  42
C_{3}^{2}.C_{4}  9 -36 28 1^{2} 3_{+} 2  2  22 42 22 42 22 42 42 42
55. 2_{−}  8_{−} 8_{+} 3 3 2 1^{4} 8_{−} ∗  2^{3} 8_{+} 1  5 5 33 42 5 42 5 5
A_{6}  -3 -3 -1 2 0_{+} ∗  ∗  42 5 5 5 42 5 5 5
56. 2_{−} 10_{−} 8_{+} 0 -3 12 1^{6} 10_{−} 1  2^{3} 8_{+} 1  5 5 3 42 5 42 5 5
A_{6}  -9 0 1  42 5 5 5 42 5 5 5
57. 2_{−} 12_{+} 8_{−} 0 0 8 1^{4} 9_{k} −2 −∗ 1^{3} 5_{i} 3∗  5 5 42 42 5 42 5 5
A_{6} 9 0 -6 1^{2} 3_{i} −2 −2 1^{3} 3_{i} 3∗ 42 5 33 5 42 5 42 5
58. 2_{−} 12_{+} 8_{−} 0 6 -4 1^{4} 9_{−} 2∗ −1 1^{3} 5_{i} 3∗  5 42 5 5 5 42 5 33
A_{6}  -3 -12 -12 1^{2} 3_{−} 2∗  2∗ 1^{3} 3_{i} 3∗  42 42 42 5 42 22 5 42

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
59. 2_{−} 14_{+} 8_{−} 0 0 -12 1^{4} 11_{i} −2∗ 2∗ 1^{3} 5_{i} 3∗  42 5 5 42 5 5 33 5
A_{6} 21 12 -34 1^{2} 3_{k} −2∗ −2∗ 1^{3} 3_{i} 3∗ 5 33 5 42 22 42 33 3
60. 2_{−} 12_{+} 10_{−} 0 6 -12 1^{4} 10_{k} −∗ −2 1^{3} 5_{i} 3∗  5 5 42 42 5 42 5 5
A_{6} -15 36 -40 1^{2} 2_{i} −∗ −∗ 1^{3} 5_{i} 3∗ 42 5 3 5 42 5 42 5
61. 2_{−} 12_{+} 10_{−} 0 -3 12 1^{4} 10_{k} −1 2∗ 1^{3} 5_{i} 3∗  5 42 5 5 5 42 5 3
A_{6} -6 0 2 1^{2} 2_{i} −1 −1 1^{3} 5_{i} 3∗ 42 42 42 5 42 22 5 42
62. 2_{−} 14_{+} 10_{−} 0 6 12 1^{4} 11_{−} 2∗ −2∗ 1^{3} 5_{i} 3∗  42 5 5 42 5 5 3 5
A_{6}  57 36 -4 1^{2} 3_{−} 2∗  2∗ 1^{3} 5_{i} 3∗  5 3 5 42 22 42 3 33

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
63. 2_{−} 11_{−} 6_{+} 0 3 -4 1^{4} 9_{i} −2∗ −∗ 1^{6} 6_{+} ∗  6 42 32 32 42 6 33 6
C_{3}^{2}.D_{4} 0 0 -2 1^{2} 2_{i} −∗ −∗ 42 32 42 6 3 222 32 32
64. 2_{−} 13_{−} 6_{+} 0 0 -4 1^{4} 10_{k} −∗ −2∗ 1^{6} 6_{+} ∗  32 42 6 6 42 32 3 32
C_{3}^{2}.D_{4} -3 -12 -2 1^{2} 3_{k} −2∗ −2∗ 42 6 42 32 33 2 6 6
65. 2_{−} 11_{−} 10_{+} 0 12 -8 1^{4} 9_{i} −2∗ −∗ 1^{6} 10_{+} ∗  6 42 32 2 42 6 3 6
C_{3}^{2}.D_{4} 9 -12 4 1^{2} 2_{i} −∗ −∗ 42 32 42 6 33 6 2 32
66. 2_{−} 11_{−} 10_{+} 0 -6 4 1^{4} 9_{i} −2∗ −∗ 1^{6} 10_{+} ∗  6 42 2 32 42 222 33 6
C_{3}^{2}.D_{4} 9 -12 -44 1^{2} 2_{i} −∗ −∗ 42 32 42 222 3 6 32 2
67. 2_{−} 11_{−} 10_{+} 0 -6 8 1^{4} 9_{i} −2∗ −∗ 1^{6} 10_{+} ∗  222 42 32 32 42 6 3 222
C_{3}^{2}.D_{4} -18 48 -32 1^{2} 2_{i} −∗ −∗ 42 2 42 6 33 6 32 32
68. 2_{−} 13_{−} 10_{+} 0 -6 16 1^{4} 10_{k} −∗ −2∗ 1^{6} 10_{+} ∗  2 42 6 6 42 32 33 2
C_{3}^{2}.D_{4} -45 24 40 1^{2} 3_{k} −2∗ −2∗ 42 222 42 32 3 32 6 6
69. 2_{−} 13_{−} 10_{+} 0 -6 4 1^{4} 10_{k} −∗ −2∗ 1^{6} 10_{+} ∗  32 42 6 222 42 32 33 32
C_{3}^{2}.D_{4} 9 -12 -20 1^{2} 3_{k} −2∗ −2∗ 42 6 42 32 3 32 222 6
70. 2_{−} 13_{−} 10_{+} 0 12 16 1^{4} 10_{k} −∗ −2∗ 1^{6} 10_{+} ∗  32 42 222 6 42 2 3 32
C_{3}^{2}.D_{4}  2  36 96 -32 1^{2} 3_{k} −2∗ −2∗  42 6 42 2 33 32 6 222
71. 2_{−}  9_{−} 8_{+} 0 0 2 3^{2} 9_{−} 2  1^{3} 5_{i} 3∗  32 5 6 4 5 6 42 6
S_{6}  -3 -6 -3  1^{3} 3_{k} 3  42 6 5 6 5 4 6 32
72. 2_{−}  7_{−} 10_{+} 0 3 -4 1^{4} 4_{+} ∗  1^{6} 10_{+} ∗  6 5 4 6 5 32 5 32
S_{6}  0 -6 -2 1^{2} 3_{−} 2∗  2∗  5 6 33 6 42 6 6 6
73. 2_{−} 11_{−} 8_{+} 3 9 14 1^{4} 11_{−} 2∗ −2∗ 1^{3} 5_{i} 3∗  6 5 6 6 33 4 3 6
S_{6}  3 3 3 2 0_{+} ∗  ∗ 1^{3} 3_{k} 3  22 6 42 6 42 32 32 4
74. 2_{−} 11_{−} 8_{+} 0 0 8 1^{6} 11_{−} 2  1^{3} 5_{i} 3∗  6 42 4 32 5 6 42 4
S_{6}  -12 12 -6  1^{3} 3_{k} 3  5 4 5 32 33 4 6 32
75. 2_{−} 11_{−} 8_{+} 0 -6 4 1^{4} 8_{+} ∗  2^{3} 8_{+} ∗  32 5 32 6 42 4 33 6
S_{6}  6 0 -4 1^{2} 3_{−} 2∗  2∗  5 32 5 4 42 32 32 4
76. 2_{−} 11_{−} 8_{+} 0 -6 4 1^{6} 11_{−} 2  1^{3} 4_{+} 1  6 5 6 32 42 4 3 32
S_{6}  6 0 -6  1^{3} 4_{+} ∗  5 6 5 4 42 6 6 4
77. 2_{−}  9_{−} 10_{+} 0 -6 8 1^{4} 9_{−} 2∗ −1 1^{6} 10_{+} ∗  32 5 32 32 33 4 5 4
S_{6}  18 -24 -32 2 0_{+} ∗  ∗  33 6 42 4 5 6 6 6
78. 2_{−}  9_{−} 10_{+} 0 -6 10 3^{2} 9_{−} 2  1^{6} 10_{+} ∗  4 42 32 4 5 6 42 32
S_{6}  -9 6 1  5 32 5 6 42 32 32 32
79. 2_{−}  9_{−} 10_{+} 0 -9 6 1^{4} 6_{−} 1  1^{6} 10_{+} ∗  4 42 6 4 5 32 42 6
S_{6}  0 0 -18 1^{2} 3_{+} 2  2  5 6 5 32 42 6 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
80. 2_{−}  9_{−} 10_{+} 0 3 6 1^{4} 6_{−} 1  2^{3} 10_{+} ∗  6 5 32 4 5 32 42 32
S_{6}  12 -36 -2 1^{2} 3_{+} 2  2  42 32 5 32 5 4 32 6
81. 2_{−} 13_{−} 8_{+} 0 3 8 1^{4} 11_{i} −2∗ −2 1^{3} 5_{i} 3∗  4 42 6 6 5 6 33 32
S_{6}  -27 48 -29 1^{2} 2_{i} −∗ −∗ 1^{3} 3_{k} 3  5 4 5 32 5 32 6 6
82. 2_{−} 13_{−} 8_{+} 0 -6 4 1^{4} 11_{i} −2  2 1^{3} 5_{i} 3∗  4 42 6 32 42 4 42 6
S_{6}  9 -36 -24 1^{2} 2_{i} −1 −1 1^{3} 3_{k} 3  5 6 5 6 42 32 32 6
83. 2_{−} 13_{−} 8_{+} 0 -3 8 1^{4} 11_{i} −2 −2∗ 1^{3} 5_{i} 3∗  6 5 32 6 5 32 5 6
S_{6} 0 0 12 1^{2} 2_{i} −1 −1 1^{3} 3_{k} 3 42 32 5 4 3 32 6 4
84. 2_{−} 11_{−} 10_{+} -3 9 -14 1^{4} 11_{−} 2∗ −2∗ 1^{6} 10_{+} ∗  6 33 6 32 5 4 5 32
S_{6} 21 -9 1 2 0_{+} ∗ ∗ 3 32 42 32 5 6 4 6
85. 2_{−} 11_{−} 10_{+} -3 0 4 1^{4} 11_{−} 2 −2 1^{6} 10_{+} ∗  6 5 4 32 5 6 42 32
S_{6} 12 -36 16 5 6 42 4 5 32 6 32
86. 2_{−} 11_{−} 10_{+} -3 6 8 1^{4} 11_{−} 2 −2 2^{3} 10_{+} ∗  4 42 32 6 42 4 42 32
S_{6} -30 42 -20 5 32 5 32 42 6 6 32
87. 2_{−} 11_{−} 10_{+} 0 -9 -12 1^{4} 9_{i} −2 −∗ 1^{6} 10_{+} ∗  6 5 6 6 5 4 42 32
S_{6}  2  0 0 -18 1^{2} 2_{i} −1 −1  5 4 22 32 3 6 6 4
88. 2_{−} 11_{−} 10_{+} 0 -6 12 1^{4} 8_{+} ∗  2^{3} 10_{+} ∗  32 42 4 6 5 32 42 4
S_{6}  -6 0 4 1^{2} 3_{−} 2∗  2∗  5 4 5 6 3 4 32 6
89. 2_{−} 11_{−} 10_{+} 0 -6 4 1^{6} 11_{−} 2  1^{6} 10_{+} ∗  32 5 4 32 5 6 5 6
S_{6}  18 -12 -26  5 32 3 32 42 32 32 32
90. 2_{−} 13_{−} 10_{+} 0 -6 12 1^{4} 11_{i} −2∗ −2 2^{3} 10_{+} ∗  32 5 6 32 5 6 5 32
S_{6}  3 -36 28 1^{2} 2_{i} −∗ −∗  42 6 5 4 33 6 32 4
91. 2_{−} 13_{−} 10_{+} 0 -6 20 1^{4} 11_{i} −2  2 1^{6} 10_{+} ∗  32 5 4 6 5 32 42 6
S_{6}  -9 12 -20 1^{2} 2_{i} −1 −1  5 32 42 4 5 6 32 6
92. 2_{−} 13_{−} 10_{+} 0 3 8 1^{4} 11_{i} −2∗ 2∗ 1^{6} 10_{+} ∗  32 3 32 6 5 4 5 6
S_{6} 27 -24 -71 1^{2} 2_{i} −∗ −∗ 33 6 42 6 5 32 4 32
93. 2_{−} 13_{−} 10_{+} 0 -9 -24 1^{4} 11_{i} −2 −2∗ 2^{3} 10_{+} ∗  4 42 32 32 5 32 3 6
S_{6} -27 0 -9 1^{2} 2_{i} −1 −1 5 4 5 6 5 6 32 32
94. 2_{−} 13_{−} 10_{+} 0 -6 12 1^{4} 11_{i} −2∗ 2∗ 2^{3} 10_{+} ∗  32 5 32 32 3 4 33 32
S_{6} -15 36 -8 1^{2} 2_{i} −∗ −∗ 22 32 42 32 42 6 6 4
95. 2_{−} 13_{−} 10_{+} 0 12 -16 1^{4} 10_{k} −∗ −2 1^{6} 10_{+} ∗  32 5 32 32 5 4 42 6
S_{6} 2 -9 -96 -2 1^{2} 3_{k} −2∗ −2∗ 5 4 22 6 33 32 32 4
96. 2_{−} 13_{−} 10_{+} 0 -6 16 1^{4} 10_{i} −1 2∗ 1^{6} 10_{+} ∗  6 5 6 6 3 4 5 4
S_{6}  -18 24 4 1^{2} 3_{i} −2 −2  3 32 42 4 5 32 32 32

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
97. 2_{−} 10_{i} 9_{i}  0 -3 4 1^{6} 10_{i} −∗  1^{3} 5_{i} 3∗  4 6 5 42 6 4 5 6
S_{6}  9 0 -9  1^{3} 4_{+} ∗  6 22 32 32 5 32 42 42
98. 2_{−} 12_{i} 9_{i}  0 6 -12 1^{4} 9_{+} 2∗ −1 1^{3} 5_{i} 3∗  6 6 5 5 32 32 33 32
S_{6}  -15 0 2 1^{2} 3_{i} −2 −2 1^{3} 4_{+} ∗  6 3 6 6 22 4 5 3
99. 2_{−} 10_{k} 11_{k} -3 -3 14 1^{4} 10_{k} −1 2∗ 1^{6} 11_{k} 3  32 32 5 5 6 6 3 6
S_{6}  -39 51 -23 2 0_{+} ∗  ∗  32 33 32 32 22 4 5 33
100. 2_{−} 10_{k} 11_{k} 0 -9 24 1^{4} 8_{−} ∗  1^{6} 11_{k} 3  4 32 5 42 32 4 5 32
S_{6}  27 -72 69 1^{2} 2_{i} −1 −1  32 22 6 6 5 6 42 42

∞  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
101. 2_{−} 14_{i} 9_{i}  0 6 24 1^{4} 11_{−} 2 −2 1^{3} 5_{i} 3∗  6 32 42 3 32 4 5 32
S_{6}  30 0 -4 1^{2} 3_{k} −2∗ −2∗ 1^{3} 4_{+} ∗  4 42 6 6 5 32 5 42
102. 2_{−} 14_{i} 9_{i}  0 -6 -16 1^{4} 11_{k} −2 −2∗ 1^{3} 5_{i} 3∗  32 32 33 42 32 4 42 222
S_{6}  6 0 -12 1^{2} 3_{−} 2∗  2∗ 1^{3} 4_{+} ∗  4 5 32 32 5 4 5 3
103. 2_{−} 14_{k} 11_{k} 0 -18 48 1^{4} 11_{i} −2  2 1^{6} 11_{k} 3  32 6 42 33 6 4 5 6
S_{6}  2  -18 0 -12 1^{2} 3_{−} 2∗  2∗  4 42 32 32 5 6 5 42
104. 2_{−} 14_{k} 11_{k} 0 0 -36 1^{4} 11_{k} −2∗ −2 1^{6} 11_{k} 3  6 6 3 42 6 4 42 2
S_{6}  63 -36 6 1^{2} 3_{+} 2  2  4 5 6 6 5 4 5 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
105. 2_{−} 11_{i} 5_{i} -2 1  0 1^{6} 11_{i} −2∗  1^{3} 5_{i} 3∗  5 6 6 6 6 5 42 33
S_{6}  1 -2 -1  3 0_{+} 1  4 32 6 42 42 3 4 4
106. 2_{−} 11_{i} 9_{i} 0 -3  8 1^{4} 11_{i} −2  2 1^{3} 5_{i} 3∗  5 6 4 6 32 42 5 42
S_{6}  9 0  9 2 0_{+} ∗  ∗ 1^{3} 4_{+} 1  32 32 4 5 42 33 32 32
107. 2_{−} 11_{i} 9_{i} 0 -6  4 1^{4} 8_{+} ∗  1^{3} 5_{i} 3∗  5 6 32 6 6 5 5 5
S_{6}  18 24  4 1^{2} 3_{i} −2 −2 1^{3} 4_{+} 1  2 6 6 42 5 42 32 32
108. 2_{−} 9_{k} 11_{k} -3 6 -10 1^{4} 9_{k} −2∗ −∗ 1^{6} 11_{k} 3∗  5 32 6 6 4 22 42 5
S_{6}  6 6 -8  6 6 6 42 5 42 32 4
109. 2_{−} 13_{i} 9_{i} 0 3  8 1^{4} 11_{+} 2∗  2∗ 1^{3} 5_{i} 3∗  42 6 6 4 4 5 33 42
S_{6}  -3 0  3 1^{2} 2_{i} −1 −1 1^{3} 4_{+} 1  4 32 6 22 5 5 4 32
110. 2_{−} 13_{i} 9_{i} 0 -12  4 1^{4} 10_{k} −1  2 1^{3} 5_{i} 3∗  5 6 6 4 6 5 3 42
S_{6}  2  45 -36 -6 1^{2} 3_{−} 2∗  2∗ 1^{3} 4_{+} 1  6 32 32 5 42 33 4 32
111. 2_{−} 13_{i} 9_{i} 0 6 16 1^{4} 10_{i} −∗ −2∗ 1^{3} 5_{i} 3∗  5 6 32 32 4 22 42 5
S_{6} 18 72 -12 1^{2} 3_{+} 2 2 1^{3} 4_{+} 1 32 32 32 42 5 42 6 4
112. 2_{−} 11_{k} 11_{k} 0 -9 12 1^{4} 9_{−} 2 −1 1^{6} 11_{k} 3∗  5 32 32 4 32 5 33 42
S_{6}  2  0 0 -6 1^{2} 2_{i} −∗ −∗  32 6 6 5 42 3 4 6
113. 2_{−} 11_{k} 11_{k} 0 0 12 1^{6} 11_{k} −2∗  1^{6} 11_{k} 3∗  5 32 6 32 32 5 5 5
S_{6}  54 0 -18  222 32 32 42 5 42 6 6
114. 2_{−} 11_{k} 11_{k} 0 0 12 1^{4} 8_{−} ∗  1^{6} 11_{k} 3∗  5 32 32 32 32 5 42 3
S_{6}  27 0 -18 1^{2} 3_{i} −2 −2  4 6 32 42 42 33 4 4
115. 2_{−} 13_{k} 11_{k} 0 -9 24 1^{4} 11_{−} 2∗  2∗ 1^{6} 11_{k} 3∗  42 32 32 4 4 5 3 42
S_{6}  27 -72 -123 1^{2} 2_{i} −1 −1  4 6 32 22 5 5 4 6
116. 2_{−} 13_{k} 11_{k} 0 0 24 1^{4} 11_{−} 2 −2 1^{6} 11_{k} 3∗  5 32 4 32 6 42 5 42
S_{6}  54 0 -72 1^{2} 2_{i} −∗ −∗  6 6 4 5 42 3 6 6