Quartic Fields Ramifying Above {2, 3, 5}

Discriminant class: −30

∞  2 3 5  a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G  h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
1. 1_{k} 11_{−} 3_{i} 3_{−}  0 0  0 1^{4} 11_{−} 2 −2 1^{4} 3_{i} 3∗ 3 1^{4} 3_{−} 5 5 2 22  2 22 22 22
D_{4}  4  -120  4 22 22 4 22 4 22
2. 1_{k} 11_{−} 3_{i} 3_{−}  0 0  0 1^{4} 11_{−} 2 −2 1^{4} 3_{i} 3∗ 3 1^{4} 3_{−} 5 5 2 22 22 22 2 22 22 22
D_{4}  4  -270  22 4 22 22 4 22 4 22
3. 1_{k} 11_{−} 3_{i} 3_{−}  0 0  0 1^{4} 11_{−} 2 −2 1^{4} 3_{i} 3∗ 3 1^{4} 3_{−} 5 5 2 22  22 2 22  22
D_{4} 12  -750  4 22 22 4 22 4 22
4. 1_{k} 11_{−} 3_{i} 3_{−}  0 0  0 1^{4} 11_{−} 2 −2 1^{4} 3_{i} 3∗ 3 1^{4} 3_{−} 5 5 2 22 22  2 22  22
D_{4}  4  -30  22 4 22 22 4 22 4 22
5. 1_{k} 9_{−} 3_{i} 1_{−}  0 -6 -8 1^{4} 9_{−} 2 −1 1^{3} 3_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 4 3 3 3 2 3 3 3
S_{4}  -6  2 0_{+} ∗ ∗ 22 4 3 3 4 22 2 22
6. 1_{k} 5_{−} 3_{i} 3_{−}  0 0 -20 1^{2} 3_{i} −2 −2 1^{3} 3_{i} 3∗  1^{4} 3_{−} 5 5 4 3 3 3 4 3 3 3
S_{4}  2  -45  1^{2} 2_{i} −1 −1  22 4 3 3 2 22 4 22
7. 1_{k} 3_{−} 5_{i} 3_{−}  -1 -9 24 1^{2} 3_{−} 2∗ 2∗ 1^{3} 5_{i} 3∗  1^{4} 3_{−} 5 5 2 3 22 3 4 3 3 22
S_{4}  2  -24  2 0_{+} ∗  ∗  3 4 3 22 2 3 4 3
8. 1_{k} 3_{−} 5_{i} 3_{−}  -1 -9 -6 1^{2} 3_{−} 2∗ 2∗ 1^{3} 5_{i} 3∗  1^{4} 3_{−} 5 5 4 3 3  4 3 22 3
S_{4}  2  6  2 0_{+} ∗  ∗  3 2 22 3 4 3 4 3
9. 1_{k} 11_{+} 3_{i} 1_{+}  0 -12 -16 1^{4} 11_{+} 2  2 1^{3} 3_{i} 3∗  1^{2} 1_{+} 5 5 4 3 3 3 4 3 3 3
S_{4}  4  60  22 2 3 3 4 22 2 22
10. 1_{k} 11_{−} 3_{i} 1_{−}  0 0 -16 1^{4} 11_{−} 2 −2 1^{3} 3_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 2 3 3 3 4 3 3 3
S_{4}  18  2 0_{+} ∗ ∗ 22 4 3 3 2 22 2 22
11. 1_{k} 9_{+} 5_{i} 1_{+}  0 12 -32 1^{4} 9_{+} 2 −1 1^{3} 5_{i} 3∗  1^{2} 1_{+} 5 5 4 3 22 3 2 3 3 22
S_{4}  -120  3 2 3 22 4 3 2 3
12. 1_{k} 9_{−} 5_{i} 1_{−}  0 0 -12 1^{4} 9_{−} 2 −1 1^{3} 5_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 2 22 3 3 2 22 3 3
S_{4}  -27  2 0_{+} ∗ ∗ 3 2 3 3 4 3 4 3
13. 1_{k} 9_{+} 5_{i} 1_{+}  0 -24 -4 1^{4} 9_{+} 2 −1 1^{3} 5_{i} 3∗  1^{2} 1_{+} 5 5 2 3 3 22 4 3 22 3
S_{4}  -3  3 4 22 3 4 3 4 3
14. 1_{k} 5_{−} 5_{i} 3_{−}  2 9 28 1^{2} 3_{i} −2 −2 1^{3} 5_{i} 3∗  1^{4} 3_{−} 5 5 4 22 3 3 2 22 3 3
S_{4}  2  -4  1^{2} 2_{i} −1 −1  3 2 3 3 2 3 2 3
15. 1_{k} 9_{−} 3_{i} 3_{−}  0 -30 -80 1^{4} 9_{−} 2 −1 1^{3} 3_{i} 3∗  1^{4} 3_{−} 5 5 2 3 3 3 4 3 3 3
S_{4}  4  -30  2 3 3 4  4 22
16. 1_{k} 11_{+} 5_{i} 1_{+}  0 12 -32 1^{4} 11_{+} 2  2 1^{3} 5_{i} 3∗  1^{2} 1_{+} 5 5 2 22 3 3 4 22 3 3
S_{4}  4  -30  3 4 3 3 2 3 4 3
17. 1_{k} 11_{−} 5_{i} 1_{−}  0 0 -72 1^{4} 11_{−} 2  2 1^{3} 5_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 4 3 3 22 4 3  3
S_{4}  2  -162  2 0_{+} ∗ ∗ 3 2 22 3 4 3 4 3
18. 1_{k} 11_{−} 5_{i} 1_{−}  0 -24 64 1^{4} 11_{−} 2 −2 1^{3} 5_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 4 3 22 3 2 3 3
S_{4}  114  2 0_{+} ∗ ∗ 3 4 3  4 3 2 3
19. 1_{k} 11_{−} 5_{i} 1_{−}  0 0 24 1^{4} 11_{−} 2  2 1^{3} 5_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 2 3 22 3 2 3 3 22
S_{4}  2  -162  2 0_{+} ∗ ∗ 3 4 3 22 2 3 2 3
20. 1_{k} 11_{−} 5_{i} 1_{−}  0 12 -40 1^{4} 11_{−} 2 −2 1^{3} 5_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 2 22 3 3 4 22 3 3
S_{4}  6  2 0_{+} ∗ ∗ 3 4 3 3 4 3 2 3
21. 1_{k} 11_{−} 5_{i} 1_{−}  0 -24 -16 1^{4} 11_{−} 2 −2 1^{3} 5_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 4 3 3 22 2 3 22 3
S_{4}  114  2 0_{+} ∗ ∗ 3 4 22 3 2 3 2 3
22. 1_{k} 11_{−} 3_{i} 3_{−}  0 0 -40 1^{4} 11_{−} 2  2 1^{3} 3_{i} 3∗  1^{4} 3_{−} 5 5 2 3 3 3 2 3 3 3
S_{4}  8  30  22 4 3 3 4 22 4

Discriminant class: −30 (continued)

∞  2 3 5  a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G  h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
23. 1_{k} 11_{−} 3_{i} 3_{−}  0 -60 240 1^{4} 11_{−} 2 −2 1^{3} 3_{i} 3∗  1^{4} 3_{−} 5 5 4 3 3 3 2 3 3 3
S_{4}  4  -180  22 2 3 3 2 22 4 22
24. 1_{k} 9_{−} 5_{i} 3_{−}  0 0 180 1^{4} 9_{−} 2 −1 1^{3} 5_{i} 3∗  1^{4} 3_{−} 5 5 4 3 3 22 2 3 22 3
S_{4}  4  405  3 4 22 3 2 3 2 3
25. 1_{k} 9_{−} 5_{i} 3_{−}  0 -60 -320 1^{4} 9_{−} 2 −1 1^{3} 5_{i} 3∗  1^{4} 3_{−} 5 5 4 22 3 3 2 22 3 3
S_{4}  4  -120  3 2 3 3 4 3 4 3
26. 1_{k} 9_{−} 5_{i} 3_{−}  0 -60 -80 1^{4} 9_{−} 2 −1 1^{3} 5_{i} 3∗  1^{4} 3_{−} 5 5 4 3  3 4 3 3 22
S_{4}  4  1320  3 4 3 22 4 3 4 3
27. 1_{k} 11_{−} 5_{i} 3_{−}  0 -60 -160 1^{4} 11_{−} 2 −2 1^{3} 5_{i} 3∗  1^{4} 3_{−} 5 5 2 3 3 22 4 3 22 3
S_{4}  4  420  3 4  3 4 3 4 3
28. 1_{k} 11_{−} 5_{i} 3_{−}  0 0 240 1^{4} 11_{−} 2 −2 1^{3} 5_{i} 3∗  1^{4} 3_{−} 5 5 4 3 22 3 4 3 3 22
S_{4}  4  -270  3 2 3 22 4 3 4 3
29. 1_{k} 11_{−} 5_{i} 3_{−}  0 -60 -80 1^{4} 11_{−} 2 −2 1^{3} 5_{i} 3∗  1^{4} 3_{−} 5 5 4  3 3 4 22 3 3
S_{4}  4  780  3 4 3 3 4 3 2 3
30. 1_{k} 11_{−} 5_{i} 3_{−}  0 -60 400 1^{4} 11_{−} 2  2 1^{3} 5_{i} 3∗  1^{4} 3_{−} 5 5 2 3 22 3 4 3 3 22
S_{4}  8  -1470  3 2 3 22 2 3 4 3
31. 1_{k} 11_{−} 5_{i} 3_{−}  0 -60 -320 1^{4} 11_{−} 2  2 1^{3} 5_{i} 3∗  1^{4} 3_{−} 5 5 2 3 3 22 2 3 22 3
S_{4}  8  -30  3 2 22 3 2 3 2 3
32. 1_{k} 11_{−} 5_{i} 3_{−}  0 0 -120 1^{4} 11_{−} 2  2 1^{3} 5_{i} 3∗  1^{4} 3_{−} 5 5 4 22 3 3 4  3 3
S_{4}  8  270  3 4 3 3 2 3 4 3

Discriminant class: −15

∞ 2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
33. 1_{k} 6_{+} 3_{k} 1_{−}  2 -3 -10 2^{2} 6_{+} 1 {−2 \atop −2∗} 1^{4} 3_{k} 3 3∗ 1^{2} 1_{−} 5∗ 5∗ 4 4 4 22 22  2 22
D_{4}  -5  4 4 2 22 22 4 22 2
34. 1_{k} 6_{−} 3_{k} 1_{+}  2 -3 -4 1^{2} 3_{k} −2∗ −2∗ 1^{4} 3_{k} 3 3∗ 1^{2} 1_{+} 5 5 4 4 4 22 22 22 2 22
D_{4}  -2  1^{2} 3_{k} −2∗ −2∗  2 0_{+} ∗ ∗ 4 4 2  4 22 2
35. 1_{k} 6_{+} 1_{i} 3_{+}  2 -1 -12 1^{2} 3_{−} 2∗  2∗ 1^{2} 1_{i} 3∗ 3∗ 1^{4} 3_{+} 5∗ 5∗ 4 4 2 22 22 22 4 22
D_{4} 2  6  1^{2} 3_{−} 2∗  2∗ 2 0_{+} ∗ ∗  2 2 2 22 22 4 22 2
36. 1_{k} 6_{−} 1_{k} 3_{+}  2 -1 -2 2^{2} 6_{−} 1  {∗ \atop 2} 1^{2} 1_{k} 3 3 1^{4} 3_{+} 5∗ 5∗ 4 4 2 22 22 22 4 22
D_{4} 2  -9  2 2 2 22  4 22 2
37. 1_{k} 8_{−} 3_{k} 1_{+}  0 -6 12 1^{4} 8_{−} 1 {−2∗ \atop −1} 1^{4} 3_{k} 3 3∗ 1^{2} 1_{+} 5 5 4 4 4 22  2 22
D_{4} 2  -6  2 0_{+} ∗ ∗ 4 4 2 22  4 22 2
38. 1_{k} 8_{+} 3_{k} 1_{−}  0 6 0 1^{4} 8_{+} 1 {−2∗ \atop −∗} 1^{4} 3_{k} 3 3∗ 1^{2} 1_{−} 5∗ 5∗ 4 4 4 22  22 2 22
D_{4} 2  -15  4 4 2  22 4 22 2
39. 1_{k} 4_{−} 3_{k} 3_{+} -2 9 -8 2^{2} 4_{−} 1  {−1 \atop −∗} 1^{4} 3_{k} 3 3∗ 1^{4} 3_{+} 5∗ 5∗ 2 2 4  22 22 4 22
D_{4} 4  1  4 4 2 22  2 22 2
40. 1_{k} 4_{−} 3_{k} 3_{+}  2 -6 -22 1^{2} 2_{i} −1 −1 1^{4} 3_{k} 3 3∗ 1^{4} 3_{+} 5∗ 5∗ 2 2 4 22 22 22 4 22
D_{4} 4  1  1^{2} 2_{i} −1 −1  4 4 2 22 22 2 22 2
41. 1_{k} 8_{+} 1_{i} 3_{+}  0 -10 -20 1^{4} 8_{+} 1  {−2 \atop −∗} 1^{2} 1_{i} 3∗ 3∗ 1^{4} 3_{+} 5∗ 5∗ 4 4 2 22 22 22 4
D_{4} 4  -10  2 0_{+} ∗ ∗  2 2 2 22  4 22 2
42. 1_{k} 8_{−} 1_{k} 3_{+}  0 -10 0 1^{4} 8_{−} 1 {−2∗ \atop −1} 1^{2} 1_{k} 3 3 1^{4} 3_{+} 5∗ 5∗ 4 4 2 22 22 22 4
D_{4} 4  -15  2 2 2 22 22 4 22 2
43. 1_{k} 8_{−} 3_{k} 3_{+}  0 0 0 1^{4} 8_{−} 1 {−2∗ \atop −1} 1^{4} 3_{k} 3 3∗ 1^{4} 3_{+} 5∗ 5∗ 2 2 4  22 22 4 22
D_{4} 8  -135  4 4 2 22 22 2  2

∞ 2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
44. 1_{k} 8_{−} 3_{k} 3_{+}  0 0 0 1^{4} 8_{−} 1  {−2 \atop −1} 1^{4} 3_{k} 3 3∗ 1^{4} 3_{+} 5∗ 5∗ 2 2 4 22 22 22 4 22
D_{4} 8  -15  4 4 2 22  2  2
45. 1_{k} 6_{−} 3_{k} 1_{+}  2 6 0 1^{4} 6_{−} 1  1^{3} 3_{k} 3  1^{2} 1_{+} 5 5 4 4 4 3 3 3 4 3
S_{4}  -6  2 0_{+} ∗ ∗ 2 4 4 22 3 4 3 2
46. 1_{k} 6_{−} 3_{k} 3_{+}  2 -6 -22 1^{4} 6_{−} 1  1^{3} 3_{k} 3  1^{4} 3_{+} 5∗ 5∗ 2 4 2 3 3 3 2 3
S_{4} 2  -29  4 4 4 22 3 2 3 4
47. 1_{k} 6_{−} 3_{k} 3_{+}  2 -6 -2 1^{4} 6_{−} 1  1^{3} 3_{k} 3  1^{4} 3_{+} 5∗ 5∗ 4 2 4 3 3 3 4 3
S_{4} 2  11  4 2 2  3 4 3 4

Discriminant class: −10

∞  2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G  h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
48. 1_{k} 11_{i} 2_{+} 3_{+}  0 0  0 1^{4} 11_{i} −2∗ 2∗ 1^{2} 1_{k} 3 3 1^{4} 3_{+} 5∗ 5∗ 22 22  4 22 22 4 2
D_{4}  8  -360  1^{2} 1_{i} 3∗ 3∗  22 22 2 22  22 4 2
49. 1_{k} 11_{i} 2_{+} 3_{+}  0 0  0 1^{4} 11_{i} −2∗ 2∗ 1^{2} 1_{k} 3 3 1^{4} 3_{+} 5∗ 5∗ 22 22 22 4 22 22 4 2
D_{4}  8  -90  1^{2} 1_{i} 3∗ 3∗  22 2 22 22 22 4 2
50. 1_{k} 3_{i} 4_{+} 3_{+}  2 -6 -12 1^{2} 3_{i} −2 −2 1^{3} 4_{+} ∗  1^{4} 3_{+} 5∗ 5∗ 3 22 3 4 3 3 2 4
S_{4}  2  -24  2 0_{+} ∗  ∗  22 3 4 3 3 3 4 2
51. 1_{k} 9_{k} 4_{+} 1_{−}  0 -12 -4 1^{4} 9_{k} −2∗ −∗ 1^{3} 4_{+} ∗  1^{2} 1_{−} 5∗ 5∗ 3 22 3 4 3 3 4 2
S_{4}  45  22 3 4 3 3 3 2 4
52. 1_{k} 11_{i} 4_{+} 1_{+}  0 0 -24 1^{4} 11_{i} −2∗ −2 1^{3} 4_{+} ∗  1^{2} 1_{+} 5 5 3 22 3 4 3 3 4 4
S_{4}  18  2 0_{+} ∗ ∗  3 2 3 3 3 4 4
53. 1_{k} 11_{i} 4_{+} 1_{+}  0 0 -16 1^{4} 11_{i} −2∗ 2∗ 1^{3} 4_{+} ∗  1^{2} 1_{+} 5 5 3 22 3 2 3 3 2 4
S_{4}  2  -42  2 0_{+} ∗ ∗ 22 3 4 3 3 3 4 2
54. 1_{k} 9_{i} 4_{+} 3_{+}  0 0 -20 1^{4} 9_{i} −2∗ −∗ 1^{3} 4_{+} ∗  1^{4} 3_{+} 5∗ 5∗ 3 22 3 2 3 3 4 4
S_{4}  4  -15  22 3 2 3 3 3 4 4
55. 1_{k} 11_{i} 4_{+} 3_{+}  0 0 -200 1^{4} 11_{i} −2∗ −2 1^{3} 4_{+} ∗  1^{4} 3_{+} 5∗ 5∗ 3 22 3 2 3 3 4 2
S_{4}  4  -510  22 3 4 3 3 3 2 4
56. 1_{k} 11_{i} 4_{+} 3_{+}  0 0 -160 1^{4} 11_{i} −2∗ 2∗ 1^{3} 4_{+} ∗  1^{4} 3_{+} 5∗ 5∗ 3  3 4 3 3 2 2
S_{4}  4  390  22 3 2 3 3 3 2 2

Discriminant class: −6

∞  2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G  h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
57. 1_{k} 11_{+} 1_{k} 2_{−}  0 -4 0 1^{4} 11_{+} 2∗ 2∗ 1^{2} 1_{k} 3 3 2^{2} 2_{−} 1 V 22 22 2 4 4 4 22
D_{4} 2 -6 2 2 2 4 22 4 2
58. 1_{k} 11_{−} 1_{i} 2_{−}  0 4 0 1^{4} 11_{−} 2∗ 2∗ 1^{2} 1_{i} 3∗ 3∗ 2^{2} 2_{−} 1 V 22 22 2 4 4 4 22 22
D_{4} 4 -6 2 0_{+} ∗ ∗ 2 2 2 4 22 4 2
59. 1_{k} 11_{+} 1_{i} 2_{+}  0 -8 0 1^{4} 11_{+} 2∗ 2∗ 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{−} 5∗ 5∗ 22 22 2 4 4 4 22
D_{4} 2 -24 2 0_{+} ∗ ∗ 1^{2} 1_{−} 5∗ 5∗ 2 2 2 4 22 22 4 2
60. 1_{k} 11_{−} 1_{k} 2_{+}  0 8 0 1^{4} 11_{−} 2∗ 2∗ 1^{2} 1_{k} 3 3 1^{2} 1_{−} 5∗ 5∗ 22 22 2 4 4 4 22 22
D_{4}  4  -24  1^{2} 1_{−} 5∗ 5∗ 2 2 2 4 22 22 4 2
61. 1_{k} 9_{+} 3_{k} 2_{−}  0 -6 0 1^{4} 9_{+} 2∗ −1 1^{4} 3_{k} 3 3∗ 2^{2} 2_{−} 1 V  4 2 4 4 22 22
D_{4}  4  -6  4 4 2 4 22 22 2 2

∞  2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G  h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
62. 1_{k} 9_{−} 3_{k} 2_{+}  0 12 0 1^{4} 9_{−} 2∗ −1 1^{4} 3_{k} 3 3∗ 1^{2} 1_{−} 5∗ 5∗ 22  4 2 4 4 22 22
D_{4}  4  -24  1^{2} 1_{−} 5∗ 5∗ 4 4 2 4  22 2 2
63. 1_{k} 9_{+} 3_{k} 2_{−}  0 6 0 1^{4} 9_{+} 2∗ −1 1^{4} 3_{k} 3 3∗ 2^{2} 2_{−} 1 V 22 22 4 2 4 4 22 22
D_{4}  4  -6  4 4 2 4 22  2 2
64. 1_{k} 9_{−} 3_{k} 2_{+}  0 -12 0 1^{4} 9_{−} 2∗ −1 1^{4} 3_{k} 3 3∗ 1^{2} 1_{−} 5∗ 5∗  22 4 2 4 4 22 22
D_{4}  4  -24  1^{2} 1_{−} 5∗ 5∗ 4 4 2 4  2 2
65. 1_{k} 11_{−} 3_{k} 2_{+}  0 0 0 1^{4} 11_{−} 2∗ −2∗ 1^{4} 3_{k} 3 3∗ 1^{2} 1_{+} 5 5 22 22 4 4 2 2 22 22
D_{4}  4  -150  1^{2} 1_{+} 5 5 4 4 2 2  22 4 2
66. 1_{k} 11_{−} 3_{k} 2_{+}  0 0 0 1^{4} 11_{−} 2∗ −2∗ 1^{4} 3_{k} 3 3∗ 1^{2} 1_{−} 5∗ 5∗ 22 22 4 4 2 2  22
D_{4}  4  -600  1^{2} 1_{−} 5∗ 5∗ 4 4 2 2 22 22 4 2

Discriminant class: −5

∞  2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G  h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
67. 1_{k} 4_{k} 2_{+} 3_{−}  0 0 0 2^{2} 4_{k} −∗  ∗ 2^{2} 2_{+} 1 V 1^{4} 3_{−} 5 5 22 2 4 4 2 22  2
D_{4}  2  -45  4  22 22 4 2 22 22
68. 1_{k} 10_{i} 2_{+} 1_{+}  0 -4 0 1^{4} 10_{i} −∗ −2∗ 2^{2} 2_{+} 1 V 1^{2} 1_{+} 5 5 22 4 4 4 2  22 4
D_{4}  -20  4 22  22 2 4 22
69. 1_{k} 10_{k} 2_{−} 1_{+}  0 4 0 1^{4} 10_{k} −∗ −2∗ 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{+} 5 5 22 4 4 4 2 22 22 4
D_{4}  -20  1^{2} 1_{i} 3∗ 3∗  4 22 22  2 4 22 22
70. 1_{k} 10_{k} 2_{+} 1_{−}  0 2 0 1^{4} 10_{k} −∗ −2∗ 2^{2} 2_{+} 1 V 1^{2} 1_{−} 5∗ 5∗ 22 4 4 4 2 22  4
D_{4}  -5  2 0_{+} ∗ ∗ 4 22  2 4 22
71. 1_{k} 10_{i} 2_{−} 1_{−}  0 -2 0 1^{4} 10_{i} −∗ −2∗ 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{−} 5∗ 5∗ 22 4 4 4 2  4
D_{4}  -5  1^{2} 1_{i} 3∗ 3∗ 2 0_{+} ∗ ∗ 4 22 22 22 2 4 22 22
72. 1_{k} 6_{k} 2_{+} 3_{−}  0 0 0 2^{2} 6_{k} −∗  ∗ 2^{2} 2_{+} 1 V 1^{4} 3_{−} 5 5 22 2 4 4 2 22 22 2
D_{4}  2  -180  4  22 22 4 2  22
73. 1_{k} 10_{k} 2_{+} 3_{−}  0 20 0 1^{4} 10_{k} −∗ −2 2^{2} 2_{+} 1 V 1^{4} 3_{−} 5 5 22 4 2 2 2 22 22 4
D_{4}  4  -20  2 22 22 22 4 4 22 22
74. 1_{k} 10_{k} 2_{+} 3_{−}  0 -10 0 1^{4} 10_{k} −∗ −2 2^{2} 2_{+} 1 V 1^{4} 3_{−} 5 5  4 2 2 2 22  4
D_{4}  4  -5  2 22 22 22 4 4 22 22
75. 1_{k} 10_{i} 2_{−} 3_{−}  0 -20 0 1^{4} 10_{i} −∗ −2 1^{2} 1_{k} 3 3 1^{4} 3_{−} 5 5  4 2 2 2 22 22 4
D_{4}  4  -20  1^{2} 1_{k} 3 3  2 22 22 22 4 4 22 22
76. 1_{k} 10_{i} 2_{−} 3_{−}  0 10 0 1^{4} 10_{i} −∗ −2 1^{2} 1_{k} 3 3 1^{4} 3_{−} 5 5 22 4 2 2 2 22  4
D_{4}  4  -5  1^{2} 1_{k} 3 3  2 22 22 22 4 4 22 22
77. 1_{k} 4_{k} 4_{+} 1_{−}  0 0 -8 2^{2} 4_{k} −∗  ∗ 1^{3} 4_{+} 1  1^{2} 1_{−} 5∗ 5∗ 3 4 4 4 4 3 3 4
S_{4}  3  2 0_{+} ∗ ∗ 4 3 22 3 2 2 3 3
78. 1_{k} 10_{i} 4_{+} 1_{+}  0 -18 8 1^{4} 10_{i} −∗ −2 1^{3} 4_{+} 1  1^{2} 1_{+} 5 5 3 2 4 4 4 3 3 4
S_{4}  75  2 3 22 3 4 2 3 3
79. 1_{k} 10_{k} 4_{+} 1_{−}  0 -6 -8 1^{4} 10_{k} −∗ −2∗ 1^{3} 4_{+} 1  1^{2} 1_{−} 5∗ 5∗ 3 4 2 2 2 3 3 2
S_{4}  -21  2 0_{+} ∗ ∗ 4 3 22 3 4 2 3 3
80. 1_{k} 6_{k} 4_{+} 3_{−}  0 0 60 1^{2} 3_{+} 2  2 1^{3} 4_{+} 1  1^{4} 3_{−} 5 5 3 2 2 4 4 3 3 4
S_{4}  2  -45  1^{2} 3_{k} −2∗ −2∗  4 3 22 3 4 4 3 3
81. 1_{k} 6_{k} 4_{+} 3_{−} -2 9 2 2^{2} 6_{k} −∗  ∗ 1^{3} 4_{+} 1  1^{4} 3_{−} 5 5 3 4 4 2 2 3 3 2
S_{4}  2  -19  2 3  3 4 4 3 3
82. 1_{k} 10_{k} 4_{+} 3_{−}  0 -30 -80 1^{4} 10_{k} −∗ −2 1^{3} 4_{+} 1  1^{4} 3_{−} 5 5 3 2 4 2 2 3 3 2
S_{4}  4  -45  4 3 22 3 2 4 3 3

∞  2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G  h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
83. 1_{k} 10_{k} 4_{+} 3_{−}  0 0 -80 1^{4} 10_{k} −∗ −2∗ 1^{3} 4_{+} 1  1^{4} 3_{−} 5 5 3 4 2 4 4 3 3 4
S_{4}  4  120  2 3 22 3 2 4 3 3

Discriminant class: −3

∞ 2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
84. 1_{k} 6_{+} 3_{i} 2_{+} -2 0 16 1^{4} 6_{+} ∗ −∗ 1^{4} 3_{i} 3∗ 3 2^{2} 2_{+} ∗ ∗ 22 2  4 22 2 4 22
D_{4} 2 -26 22 4 22 2 4 2 22
85. 1_{k} 8_{+} 3_{i} 2_{+}  0 0 0 1^{4} 8_{+} ∗ −∗ 1^{4} 3_{i} 3∗ 3 2^{2} 2_{+} ∗ ∗ 22 2 22 4 22 2 4 22
D_{4} 2  -75  4 22 2 4 2 22 22
86. 1_{k} 4_{+} 3_{i} 2_{+}  2 0 -6 1^{4} 4_{+} ∗  1^{3} 3_{i} 3∗  2^{2} 2_{+} ∗ ∗ 3 4 3 2 3 4 4 22
S_{4} 2  -6  3 4 22 2 4 2 3 3
87. 1_{k} 4_{+} 3_{i} 2_{+} -2 0 10 1^{4} 4_{+} ∗  1^{4} 3_{i} 3∗ 3 1^{3} 2_{+} ∗  3 4 3 4 3 4 4 3
S_{4}  -5  22 2 3 4 2 4 3 3
88. 1_{k} 8_{−} 1_{k} 2_{+}  0 -4 -4 1^{4} 8_{−} ∗  1^{2} 1_{k} 3 3 1^{3} 2_{+} ∗  3 4 3 4 3 4 4 3
S_{4}  2  2 0_{+} ∗ ∗  22 4 3 2 4 2 3 3
89. 1_{k} 2_{+} 5_{i} 2_{+} -1 0 -8 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  2^{2} 2_{+} ∗ ∗ 3 4 22 4 22 4 2 3
S_{4} 2  -16  3 4 3 4 2 4 3 3
90. 1_{k} 6_{+} 3_{i} 2_{+}  2 3 -6 2^{2} 6_{+} ∗  ∗ 1^{3} 3_{i} 3∗  1^{3} 2_{+} ∗  3 4 22 2 3 4 2 3
S_{4} 2  -15  3 4 3 4 4 4 3 22
91. 1_{k} 6_{+} 3_{i} 2_{+}  0 6 16 1^{4} 6_{+} ∗ −1 1^{3} 3_{i} 3∗  1^{3} 2_{+} ∗  3 4 22 4 3 2 4 3
S_{4}  -3  3 4 3 4 4 2 3 22
92. 1_{k} 4_{+} 5_{i} 2_{+}  0 -6 -28 1^{4} 4_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  22 4 22 2 3 2 4 3
S_{4}  -3  3 2 22 4 2 2 3 3
93. 1_{k} 4_{−} 5_{i} 2_{−}  2 -9 10 2^{2} 4_{−} ∗  ∗ 1^{3} 5_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 3 4 3 2 3 4 4 3
S_{4} 2  5  1^{2} 1_{+} 5 5 3 4 3 2 4 4 22 22
94. 1_{k} 4_{+} 5_{i} 2_{+}  0 -6 -2 1^{4} 4_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  3 2 22 4 3 4 2 22
S_{4}  -3  22 4 3 4 4 2 22 3
95. 1_{k} 8_{+} 3_{i} 2_{+}  0 6 -24 1^{4} 8_{+} ∗  1^{4} 3_{i} 3∗ 3 1^{3} 2_{+} ∗  3 2 3 2 3 2 2 3
S_{4}  -3  22 4 3 4 4 4 3 3
96. 1_{k} 8_{+} 3_{i} 2_{+}  0 -6 -12 1^{4} 8_{+} ∗ −∗ 1^{3} 3_{i} 3∗  1^{3} 2_{+} ∗  3 2 22 4 3 4 4 3
S_{4}  -18  3 2 3 2 2 4 3 22
97. 1_{k} 8_{−} 3_{i} 2_{−}  0 -12 -20 1^{4} 8_{−} ∗  1^{3} 3_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 3 2 3 4 3 2 4 22
S_{4} 2  6  1^{2} 1_{+} 5 5 3 4 22 4 4 4 3 3
98. 1_{k} 8_{+} 3_{i} 2_{+}  0 -6 -12 1^{4} 8_{+} ∗  1^{3} 3_{i} 3∗  1^{3} 2_{+} ∗  22 4 3 2 22 2 4 3
S_{4}  27  3 2 3 2 4 2 22 3
99. 1_{k} 6_{+} 5_{i} 2_{+} -2 0 -10 1^{4} 6_{+} ∗ −1 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  22 2 3 2 3 4 4
S_{4}  5  3 4 3 4 4 4 3 22
100. 1_{k} 6_{+} 5_{i} 2_{+}  2 0 4 1^{4} 6_{+} ∗ −∗ 1^{3} 5_{i} 3∗  2^{2} 2_{+} ∗ ∗ 3 2 3 2 3 4 2 3
S_{4} 2  -106  3 2 3 4 2 2 22 22
101. 1_{k} 6_{+} 5_{i} 2_{+}  0 -6 -40 1^{2} 3_{k} −2∗ −2∗ 1^{3} 5_{i} 3∗  2^{2} 2_{+} ∗ ∗ 3 4 3 4 3 2 4 3
S_{4} 2  24  1^{2} 3_{i} −2 −2  3 2 3 2 4 2  22
102. 1_{k} 6_{+} 5_{i} 2_{+}  0 -6 -32 1^{4} 6_{+} ∗ −∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  22 4 3 4 3 4 2 22
S_{4}  -3  3 2 3 2 2 2 3 22
103. 1_{k} 6_{+} 5_{i} 2_{+} -2 0 20 1^{4} 6_{+} ∗ −∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  3 2 3 2 22 4 4 3
S_{4}  -10  22 2 22 2 4 4 3 22

∞ 2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
104. 1_{k} 6_{+} 5_{i} 2_{+}  0 -6 -32 1^{2} 3_{k} −2∗ −2∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  3 4 3 2 22 4 4 3
S_{4}  -48  1^{2} 3_{i} −2 −2  22 4 22 4 2 2 3 22
105. 1_{k} 8_{+} 5_{i} 2_{+}  0 30 -40 1^{4} 8_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  3 2 3 4 3 2 4 3
S_{4}  -75  3 2 22 2 4 2 22 3
106. 1_{k} 8_{+} 5_{i} 2_{+}  0 -6 -40 1^{4} 8_{+} ∗  1^{3} 5_{i} 3∗  2^{2} 2_{+} ∗ ∗ 22 4 3 4 3 2 4 3
S_{4} 2  69  22 4 3 2 4 4 3 3
107. 1_{k} 8_{−} 5_{i} 2_{−}  0 -18 -60 1^{4} 8_{−} ∗ −1 1^{3} 5_{i} 3∗  1^{2} 1_{+} 5 5 3 2 3 4 3 2 2 3
S_{4} 2  -54  1^{2} 1_{−} 5∗ 5∗ 3 4 3 4 2 4 22 22
108. 1_{k} 8_{+} 5_{i} 2_{+}  0 -6 92 1^{4} 8_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  3 4 3 4  4 2
S_{4}  -93  3 4 3 4 2 4 3 3
109. 1_{k} 8_{+} 5_{i} 2_{+}  0 -24 -16 1^{4} 8_{+} ∗ −∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  3 4 3 2 22 2 2 3
S_{4}  -3  4 22 4 4 4 3
110. 1_{k} 8_{−} 5_{i} 2_{−}  0 12 -20 1^{4} 8_{−} ∗  1^{3} 5_{i} 3∗  1^{2} 1_{+} 5 5 22 2 3 2 3 4 4 3
S_{4} 2  6  1^{2} 1_{−} 5∗ 5∗ 22 4 3 2 2 2 3 3
111. 1_{k} 8_{+} 5_{i} 2_{+}  0 -6 -20 1^{4} 8_{+} ∗  1^{3} 5_{i} 3∗  2^{2} 2_{+} ∗ ∗ 3 2 22 4 22 2 4 3
S_{4} 2  -21  3 2 3 4 2 2 3 3

Discriminant class: −2

∞  2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G  h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
112. 1_{k} 9_{k} 2_{−} 2_{+}  0 10 0 1^{4} 9_{k} −2 −∗ 1^{2} 1_{k} 3 3 2^{2} 2_{+} ∗ ∗ 4  2 22 22 2 4 4
D_{4}  2  -50  1^{2} 1_{k} 3 3  2 22 22 2 4 22 2 22
113. 1_{k} 9_{i} 2_{+} 2_{+}  0 -10 0 1^{4} 9_{i} −2 −∗ 2^{2} 2_{+} 1 V 2^{2} 2_{+} ∗ ∗ 4 22 2 22 22 2 4 4
D_{4}  2  -50  2 22 22 2 4  2 22
114. 1_{k} 11_{i} 2_{−} 2_{−}  0 -20 0 1^{4} 11_{i} −2 −2∗ 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{+} 5 5 4 22 4 22  2 2 4
D_{4}  2  -50  1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{−} 5∗ 5∗ 4 22 22 2 2 22 4
115. 1_{k} 11_{k} 2_{+} 2_{−}  0 20 0 1^{4} 11_{k} −2 −2∗ 2^{2} 2_{+} 1 V 1^{2} 1_{−} 5∗ 5∗ 4 22 4 22 22 2 2 4
D_{4}  2  -50  1^{2} 1_{+} 5 5 4 22  2 2 22 4 22
116. 1_{k} 11_{i} 2_{+} 2_{+}  0 0 0 1^{4} 11_{i} −2  2 2^{2} 2_{+} 1 V 2^{2} 2_{+} ∗ ∗ 2 22 4 22 22 2 4 2
D_{4}  2  -450  4  22 2 4 22 4 22
117. 1_{k} 5_{i} 4_{+} 2_{+} -2 3 8 1^{2} 3_{+} 2  2 1^{3} 4_{+} 1  2^{2} 2_{+} ∗ ∗ 4 3 4 3 3 2 2 4
S_{4}  2  -4  1^{2} 2_{i} −1 −1  2 3 3 4 4 3 4 3
118. 1_{k} 5_{i} 4_{+} 2_{+}  0 -9 -24 1^{2} 3_{+} 2  2 1^{3} 4_{+} 1  1^{3} 2_{+} ∗  4 22 4 22 3 4 4 4
S_{4}  -18  1^{2} 2_{i} −1 −1  4 3 3 2 4 3 2 3
119. 1_{k} 9_{k} 4_{+} 2_{−}  0 -18 -80 1^{4} 9_{k} −2 −∗ 1^{3} 4_{+} 1  1^{2} 1_{−} 5∗ 5∗ 4 3 2 3 3 4 2 4
S_{4}  2  -114  1^{2} 1_{+} 5 5 4 3 3 2 4 3 4 3
120. 1_{k} 9_{i} 4_{+} 2_{+}  0 -6 -8 1^{4} 9_{i} −2 −∗ 1^{3} 4_{+} 1  1^{3} 2_{+} ∗  4 3 2 3 22 2 2 4
S_{4}  -138  4 22 3 2 2 3 4 22
121. 1_{k} 11_{i} 4_{+} 2_{+}  0 -36 -48 1^{4} 11_{i} −2  2 1^{3} 4_{+} 1  1^{3} 2_{+} ∗  2 3 2 3 22 4 4 2
S_{4}  2  252  2 22 3 2 2 3 2 22
122. 1_{k} 11_{i} 4_{+} 2_{+}  0 -24 -64 1^{4} 11_{i} −2  2 1^{3} 4_{+} 1  1^{3} 2_{+} ∗  2 22 4 22 3 4 2 2
S_{4}  8  222  2 3 3 4 4 3 2 3
123. 1_{k} 11_{i} 4_{+} 2_{+}  0 -36 -48 1^{4} 11_{i} −2 −2∗ 1^{3} 4_{+} 1  1^{3} 2_{+} ∗  4 3 2 3 22 4 4 4
S_{4}  -18  4  3 2 2 3 4 22
124. 1_{k} 11_{k} 4_{+} 2_{−}  0 12 -80 1^{4} 11_{k} −2 −2∗ 1^{3} 4_{+} 1  1^{2} 1_{−} 5∗ 5∗ 2 3 4 3 3 2 4 4
S_{4}  2  -84  1^{2} 1_{+} 5 5 4 3 3 4 4 3 4 3

∞  2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G  h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
125. 1_{k} 11_{i} 4_{+} 2_{+}  0 -24 -80 1^{4} 11_{i} −2  2 1^{3} 4_{+} 1  2^{2} 2_{+} ∗ ∗ 2 3 2 3 3 4 4 4
S_{4}  4  -66  2 3 3 2 4 3 4 3
126. 1_{k} 11_{i} 4_{+} 2_{+}  0 -36 -72 1^{4} 11_{i} −2  2 1^{3} 4_{+} 1  1^{3} 2_{+} ∗  4  2 22 3 2 4 4
S_{4}  4  162  4 3 3 4 2 3 2 3

Discriminant class: −1

∞  2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G  h  a_{4}  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
127. 1_{k} 4_{k} 2_{−} 2_{+}  0 3 0 2^{2} 4_{k} −1 ∗ 2^{2} 2_{−} ∗ ∗ 1^{2} 1_{+} 5 5 4 2 22 22 2 4 22 2
D_{4}  -9  1^{2} 1_{+} 5 5 22  4 4 22 2 22 4
128. 1_{k} 6_{i} 2_{−} 2_{−}  0 -6 0 2^{2} 6_{i} −1 ∗ 2^{2} 2_{−} ∗ ∗ 2^{2} 2_{−} 1 V 4 2 22 22 2 4  2
D_{4}  -36  22  4 4 22 2  4
129. 1_{k} 10_{i} 2_{−} 2_{−}  0 30 0 1^{4} 10_{i} −1 2 2^{2} 2_{−} ∗ ∗ 2^{2} 2_{−} 1 V 2 4 22 22 4 2 22 2
D_{4}  2  -225  22 22 4 2 22 4 22 4
130. 1_{k} 10_{i} 2_{+} 2_{+}  0 -18 0 1^{4} 10_{i} −1 2∗ 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{−} 5∗ 5∗ 4 4  22 4 4 22 2
D_{4}  4  -9  1^{2} 1_{k} 3 3 1^{2} 1_{−} 5∗ 5∗ 22  2 4 22 4 22 2
131. 1_{k} 10_{k} 2_{+} 2_{−}  0 6 0 1^{4} 10_{k} −1 2∗ 1^{2} 1_{k} 3 3 2^{2} 2_{−} 1 V 4 4 22 22 4 4 22 2
D_{4}  4  -81  1^{2} 1_{i} 3∗ 3∗  2 4  4 22 2

Discriminant class: 1

∞ 2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
132. 0_{+} 4_{−} 2_{+} 2_{−} -2 -7 8 2^{2} 4_{−} 1  {−1 \atop −∗} 2^{2} 2_{+} 1 V 2^{2} 2_{−} 1 V 22  22 22 22 22 22 22
V_{4}  1  22 22 22 22 22  22
133. 2_{−} 4_{−} 2_{−} 2_{−} 0 1 0 1^{2} 2_{i} −∗ −∗ 1^{2} 1_{k} 3 3 2^{2} 2_{−} 1 V 22 22 22 22 22  22 22
V_{4} 2 4 1^{2} 2_{i} −∗ −∗ 1^{2} 1_{k} 3 3 22 22 22 22 22 22
134. 2_{−} 4_{−} 2_{+} 2_{+} 0 -7 0 1^{2} 2_{i} −1 −1 2^{2} 2_{+} 1 V 1^{2} 1_{−} 5∗ 5∗ 22 22 22  22 22 22 22
V_{4} 2  16  1^{2} 2_{i} −1 −1  1^{2} 1_{−} 5∗ 5∗ 22 22 22 22  22  22
135. 2_{−} 4_{−} 2_{−} 2_{−} 0 -5 0 2^{2} 4_{−} 1  {−1 \atop −∗} 1^{2} 1_{i} 3∗ 3∗ 2^{2} 2_{−} 1 V  22 22 22 22 22 22 22
V_{4} 2  25  1^{2} 1_{i} 3∗ 3∗  22 22  22 22 22
136. 2_{−} 6_{−} 2_{+} 2_{+} 2 11 10 2^{2} 6_{−} 1  {∗ \atop 2} 2^{2} 2_{+} 1 V 1^{2} 1_{+} 5 5 22  22 22 22 22
V_{4} 4  55  1^{2} 1_{+} 5 5 22 22 22 22 22  22 22
137. 2_{−} 6_{−} 2_{+} 2_{+} 0 2 0 1^{2} 3_{k} −2∗ −2∗ 2^{2} 2_{+} 1 V 1^{2} 1_{−} 5∗ 5∗ 22 22 22 22  22 22
V_{4} 2 16 1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{−} 5∗ 5∗ 22 22 22 22 22 22
138. 2_{−} 6_{−} 2_{−} 2_{−} -2 13 -12 1^{2} 3_{i} −2 −2 1^{2} 1_{k} 3 3 2^{2} 2_{−} 1 V 22 22 22  22 22 22
V_{4} 2  6  1^{2} 3_{i} −2 −2 1^{2} 1_{k} 3 3  22 22 22 22 22 22 22 22
139. 0_{+} 6_{+} 2_{+} 2_{+} -2 -13 14 2^{2} 6_{+} 1 {−2 \atop −2∗} 2^{2} 2_{+} 1 V 1^{2} 1_{+} 5 5 22 22 22 22  22  22
V_{4}  19  1^{2} 1_{+} 5 5 22 22 22 22 22 22 22 22
140. 2_{−} 6_{+} 2_{−} 2_{+} 0 -2 0 1^{2} 3_{−} 2∗  2∗ 1^{2} 1_{k} 3 3 1^{2} 1_{−} 5∗ 5∗ 22 22 22 22 22 22 22
V_{4} 4  16  1^{2} 3_{−} 2∗  2∗ 1^{2} 1_{k} 3 3 1^{2} 1_{−} 5∗ 5∗ 22 22 22 22  22 22 22
141. 2_{−} 6_{+} 2_{+} 2_{−} 0 -10 0 2^{2} 6_{+} 1 {−2 \atop −2∗} 2^{2} 2_{+} 1 V 2^{2} 2_{−} 1 V  22  22  22 22 22
V_{4} 2  100  22 22 22 22 22 22 22

Discriminant class: 1 (continued)

∞ 2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
142. 2_{−} 6_{+} 2_{+} 2_{−} 2 5 4 1^{2} 3_{+} 2  2 2^{2} 2_{+} 1 V 2^{2} 2_{−} 1 V 22 22 22  22  22
V_{4} 4  34  1^{2} 3_{+} 2  2  22 22 22  22 22 22 22
143. 2_{−} 6_{−} 2_{−} 2_{−} 0 10 0 2^{2} 6_{−} 1  {∗ \atop 2} 1^{2} 1_{i} 3∗ 3∗ 2^{2} 2_{−} 1 V 22 22  22 22 22 22
V_{4} 4  100  1^{2} 1_{i} 3∗ 3∗  22  22 22 22 22
144. 2_{−} 8_{+} 2_{+} 2_{−} 0 20 0 1^{4} 8_{+} 1 {−2∗ \atop −∗} 2^{2} 2_{+} 1 V 2^{2} 2_{−} 1 V 22  22 22  22 22
V_{4} 4  25  22 22  22  22 22
145. 0_{+} 8_{−} 2_{−} 2_{+} 0 -8 0 1^{4} 8_{−} 1 {−2∗ \atop −1} 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{−} 5∗ 5∗ 22 22 22 22 22 22 22 22
V_{4} 2  1  1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{−} 5∗ 5∗ 22 22  22  22 22
146. 2_{−} 8_{−} 2_{+} 2_{+} 0 0 0 1^{4} 8_{−} 1  {−2 \atop −1} 2^{2} 2_{+} 1 V 1^{2} 1_{+} 5 5 22 22  22 22  22
V_{4} 4  225  1^{2} 1_{+} 5 5  22 22 22 22 22 22 22
147. 2_{−} 8_{−} 2_{−} 2_{−} 0 16 0 1^{4} 8_{−} 1  {−2 \atop −1} 1^{2} 1_{i} 3∗ 3∗ 2^{2} 2_{−} 1 V 22  22  22 22 22 22
V_{4} 4  49  1^{2} 1_{i} 3∗ 3∗  22 22  22 22  22
148. 0_{+} 8_{+} 2_{−} 2_{−} 0 -20 0 1^{4} 8_{+} 1  {−2 \atop −∗} 1^{2} 1_{k} 3 3 2^{2} 2_{−} 1 V 22 22  22 22 22 22 22
V_{4} 2  25  1^{2} 1_{k} 3 3  22 22 22 22 22 22 22
149. 2_{−} 8_{−} 2_{+} 2_{+} 0 8 0 1^{4} 8_{−} 1 {−2∗ \atop −1} 2^{2} 2_{+} 1 V 1^{2} 1_{−} 5∗ 5∗  22 22 22 22 22 22
V_{4} 8 1 1^{2} 1_{−} 5∗ 5∗ 22 22 22 22 22 22
150. 2_{−} 8_{+} 2_{−} 2_{+} 0 12 0 1^{4} 8_{+} 1 {−2∗ \atop −∗} 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{+} 5 5 22 22 22 22 22  22
V_{4} 4  81  1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{+} 5 5 22 22  22 22 22
151. 0_{+} 8_{−} 2_{+} 2_{−} 0 -16 0 1^{4} 8_{−} 1  {−2 \atop −1} 2^{2} 2_{+} 1 V 2^{2} 2_{−} 1 V  22 22  22 22 22 22
V_{4} 2  49  22 22 22 22 22 22 22 22
152. 2_{−} 8_{+} 2_{−} 2_{+} 0 -12 0 1^{4} 8_{+} 1  {−2 \atop −∗} 1^{2} 1_{k} 3 3 1^{2} 1_{+} 5 5  22 22 22 22 22  22
V_{4} 8  81  1^{2} 1_{k} 3 3 1^{2} 1_{+} 5 5 22 22 22 22 22 22 22 22

Discriminant class: 2

∞  2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G  h  a_{4}  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
153. 2_{−} 11_{+} 2_{−} 2_{+} 0 60  0 1^{4} 11_{+} 2 2 2^{2} 2_{−} ∗ ∗ 2^{2} 2_{+} ∗ ∗  4 4  4 22 4
C_{4} 20  450  4  4  4 4 4 4
154. 0_{+} 11_{−} 2_{−} 2_{+} 0 -60  0 1^{4} 11_{−} 2 2 2^{2} 2_{−} ∗ ∗ 2^{2} 2_{+} ∗ ∗ 22 4 4  4  4 22
C_{4}  2  450  4  4 22 4 4 4 4
155. 2_{−} 9_{−} 2_{−} 2_{−} 0 30  0 1^{4} 9_{−} 2 −1 2^{2} 2_{−} ∗ ∗ 1^{2} 1_{+} 5 5 22 4 2 22 4 22 2 22
D_{4} 4 450 1^{2} 1_{−} 5∗ 5∗ 2 22 4 22 2 4 2 4
156. 2_{−} 11_{−} 2_{+} 2_{+} 0 0  0 1^{4} 11_{−} 2 −2 1^{2} 1_{i} 3∗ 3∗ 2^{2} 2_{+} ∗ ∗ 22 2 4 22 2 22 4 22
D_{4}  4  450  1^{2} 1_{k} 3 3  4  2 22 4 2 4 2
157. 2_{−} 3_{−} 4_{+} 2_{+} -1 -3  2 1^{2} 3_{−} 2∗ 2∗ 1^{3} 4_{+} ∗  1^{3} 2_{+} ∗  3 4 4 3 4 22 4 22
S_{4}  10  2 0_{+} ∗ ∗  4 3 2 3 4 4 2 4
158. 0_{+} 9_{+} 4_{+} 2_{+} 0 -24 -44 1^{4} 9_{+} 2 −1 1^{3} 4_{+} ∗  1^{3} 2_{+} ∗  3 2 4 3 2 22 4 22
S_{4}  -3  2 3 4 3 4 4 4 4
159. 2_{−} 9_{−} 4_{+} 2_{+} 0 -6 -8 1^{4} 9_{−} 2 −1 1^{3} 4_{+} ∗  1^{3} 2_{+} ∗  3 4 2 3 4  2
S_{4}  2  42  4 3 4 3 2 2 4 2
160. 2_{−} 11_{−} 4_{+} 2_{+} 0 24 -32 1^{4} 11_{−} 2 −2 1^{3} 4_{+} ∗  1^{3} 2_{+} ∗  3 2 2 3 2 22 4
S_{4}  6  162  2 3 4 3 4 2 4 4
161. 2_{−} 11_{−} 4_{+} 2_{+} 0 -24 -64 1^{4} 11_{−} 2 −2 1^{3} 4_{+} ∗  1^{3} 2_{+} ∗  3 4 4 3 4 22 2 22
S_{4}  2  402  4 3 4 3 2 4 4 2
162. 2_{−} 11_{−} 4_{+} 2_{+} 0 24 -32 1^{4} 11_{−} 2 2 1^{3} 4_{+} ∗  1^{3} 2_{+} ∗  3 4 2 3 4 22 4
S_{4}  8  72  4 3 2 3 4 2 2 4

∞  2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G  h  a_{4}  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
163. 2_{−} 11_{−} 4_{+} 2_{+} 0 36 -144 1^{4} 11_{−} 2 2 1^{3} 4_{+} ∗  1^{3} 2_{+} ∗  3 2 4 3 2 22 2 22
S_{4} 16  162  2 3 2 3 2 4 2 2

Discriminant class: 3

∞  2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G  h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
164. 2_{−} 4_{k} 3_{k} 2_{+} 0 -15 0 2^{2} 4_{k} −∗  ∗ 1^{4} 3_{k} 3 3∗ 2^{2} 2_{+} ∗ ∗ 2 22  4 2 22 4 2
D_{4}  2  75  22 4 2 22 4 22  2
165. 2_{−} 6_{k} 3_{k} 2_{+} 0 0 0 2^{2} 6_{k} −∗  ∗ 1^{4} 3_{k} 3 3∗ 2^{2} 2_{+} ∗ ∗ 2 22 22 4 2 22 4 2
D_{4} 2 300 4 2 22 4 22 22 2
166. 2_{−} 10_{i} 1_{i} 2_{+} 0 10 0 1^{4} 10_{i} −∗ −2 1^{2} 1_{i} 3∗ 3∗ 2^{2} 2_{+} ∗ ∗ 4 22 22 2 2 22 4 4
D_{4} 2 75 2 0_{+} ∗ ∗ 22 2 2 22 4 22 2
167. 2_{−} 10_{k} 1_{k} 2_{+} 0 -10 0 1^{4} 10_{k} −∗ −2 1^{2} 1_{k} 3 3 2^{2} 2_{+} ∗ ∗ 4  22 2 2 22 4 4
D_{4} 2 75 22 2 2 22 4 22 22 2
168. 2_{−} 10_{i} 3_{k} 2_{−} 0 30 0 1^{4} 10_{i} −∗ −2∗ 1^{4} 3_{k} 3 3∗ 1^{2} 1_{+} 5 5 4 22 22 4 2 22 2 4
D_{4} 8 75 1^{2} 1_{−} 5∗ 5∗ 22 4 2 22 2 22 22 2
169. 0_{+} 10_{k} 3_{k} 2_{−} 0 -30 0 1^{4} 10_{k} −∗ −2∗ 1^{4} 3_{k} 3 3∗ 1^{2} 1_{+} 5 5 4 22 22 4 2  2 4
D_{4}  2  75  1^{2} 1_{−} 5∗ 5∗ 22 4 2  2 22 22 2
170. 2_{−} 4_{k} 3_{k} 2_{+} 2 3 4 2^{2} 4_{k} −∗  ∗ 1^{3} 3_{k} 3  1^{3} 2_{+} ∗  4 3 3 4 2 3 2 4
S_{4}  5  3 4 2 3 2 3 3 4
171. 2_{−} 6_{k} 3_{k} 2_{+} 0 6 -16 2^{2} 6_{k} −∗  ∗ 1^{3} 3_{k} 3  1^{3} 2_{+} ∗  2 3 3 2 4 3 4 4
S_{4}  12  3 4 4 3 4 3 3 2
172. 2_{−} 6_{k} 3_{k} 2_{+} 2 3 4 1^{2} 3_{k} −2∗ −2∗ 1^{3} 3_{k} 3  1^{3} 2_{+} ∗  4 3 3 4 4 3 4 2
S_{4}  20  1^{2} 3_{+} 2  2  3 2 4 3 4 3 3 4
173. 2_{−} 10_{k} 3_{k} 2_{+} 0 -6 -8 1^{4} 10_{k} −∗ −2∗ 1^{3} 3_{k} 3  1^{3} 2_{+} ∗  2 3 3 4 4 3 4 2
S_{4}  4  27  3 2 2 3 4 3 3 2
174. 2_{−} 10_{k} 3_{k} 2_{+} 0 6 -16 1^{4} 10_{k} −∗ −2 1^{3} 3_{k} 3  1^{3} 2_{+} ∗  2 3 3 4 2 3 2 4
S_{4}  2  27  3 4 4 3 2 3 3 2
175. 2_{−} 10_{k} 3_{k} 2_{+} 0 6 -24 1^{4} 10_{k} −∗ −2∗ 1^{3} 3_{k} 3  1^{3} 2_{+} ∗  4 3 3 2 2 3 2 2
S_{4}  4  27  3 2 4 3 2 3 3 4
176. 0_{+} 10_{i} 3_{k} 2_{+} 0 -24 -16 1^{4} 10_{i} −∗ −2 1^{3} 3_{k} 3  1^{3} 2_{+} ∗  4 3 3 2 4 3 4 4
S_{4}  72  3 4 2 3 4 3 3 4

Discriminant class: 5

∞ 2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G h  a_{4}  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
177. 2_{−} 4_{−} 2_{−} 3_{−} 0 15 0 2^{2} 4_{−} ∗ ∗ 2^{2} 2_{−} ∗ ∗ 1^{4} 3_{−} 5 5 4  4 4  4  22
C_{4} 4  45  4 22 4 4 4 22  4
178. 0_{+} 6_{+} 2_{−} 3_{−} 0 -30 0 2^{2} 6_{+} ∗ ∗ 2^{2} 2_{−} ∗ ∗ 1^{4} 3_{−} 5 5 4  4 4  4 22
C_{4} 2  180  4 22 4 4 4 22 22 4
179. 2_{−} 6_{−} 2_{−} 3_{−} 0 30 0 2^{2} 6_{−} ∗ ∗ 2^{2} 2_{−} ∗ ∗ 1^{4} 3_{−} 5 5 4 22 4 4 22 4 22 22
C_{4} 4 180 4 22 4 4 4 22 4
180. 2_{−} 6_{+} 2_{−} 1_{+} -2 -4 2 1^{4} 6_{+} ∗ −1 2^{2} 2_{−} ∗ ∗ 1^{2} 1_{+} 5 5 4 22 2 2 22 4 22 22
D_{4} 2  13  2  4 4 2 22 22 4

∞ 2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G h  a_{4}  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
181. 2_{−} 8_{−} 2_{−} 1_{−} 0 12 0 1^{4} 8_{−} ∗ −1 2^{2} 2_{−} ∗ ∗ 1^{2} 1_{−} 5∗ 5∗ 4 22 2 2 22 4  22
D_{4} 2 45 2 0_{+} ∗ ∗ 2 4 4 2 22 4
182. 2_{−} 6_{+} 2_{+} 3_{−} -2 4 -18 1^{4} 6_{+} ∗ −∗ 1^{2} 1_{k} 3 3 1^{4} 3_{−} 5 5 2 22 4 4 22 2  22
D_{4} 8 21 1^{2} 1_{i} 3∗ 3∗ 4 2 2 4 22 22 2
183. 2_{−} 8_{+} 2_{+} 3_{−} 0 0 0 1^{4} 8_{+} ∗ −∗ 1^{2} 1_{i} 3∗ 3∗ 1^{4} 3_{−} 5 5 2 22 4 4 22 2 22 22
D_{4} 8  45  1^{2} 1_{k} 3 3  4  2 2 4 22  2
184. 2_{−} 4_{+} 4_{+} 1_{−} 0 0 -2 1^{4} 4_{+} ∗  1^{3} 4_{+} ∗  1^{2} 1_{−} 5∗ 5∗ 4 3 2 4 3 2 3 3
S_{4}  3  2 0_{+} ∗ ∗ 4 3 4 4 4 3 22 2
185. 2_{−} 2_{+} 4_{+} 3_{−} -1 6 -6 1^{3} 2_{+} ∗  1^{3} 4_{+} ∗  1^{4} 3_{−} 5 5 4 3 2 4 3 4 3 3
S_{4} 8  6  2 3 2 2 4 3 22 4
186. 2_{−} 8_{+} 4_{+} 1_{−} 0 0 -12 1^{4} 8_{+} ∗  1^{3} 4_{+} ∗  1^{2} 1_{−} 5∗ 5∗ 2 3 4 4 3 2 3 3
S_{4}  18  2 0_{+} ∗ ∗ 2 3 2 4 2 3 22 4
187. 2_{−} 8_{−} 4_{+} 1_{+} 0 6 -4 1^{4} 8_{−} ∗  1^{3} 4_{+} ∗  1^{2} 1_{+} 5 5 4 3 4 2 3 2 3 3
S_{4}  27  4 3 4 2 4 3 22 4
188. 2_{−} 4_{+} 4_{+} 3_{−} 2 -6 -12 1^{4} 4_{+} ∗  1^{3} 4_{+} ∗  1^{4} 3_{−} 5 5 2 3 2 2 3 4 3 3
S_{4} 4  21  4 3 4 4 2 3 22 4
189. 2_{−} 8_{+} 4_{+} 3_{−} 0 0 -20 1^{4} 8_{+} ∗  1^{3} 4_{+} ∗  1^{4} 3_{−} 5 5 4 3 4 2 3 4 3 3
S_{4} 4  30  2 3 2 4 4 3  2
190. 0_{+} 8_{−} 4_{+} 3_{−} 0 -30 -40 1^{4} 8_{−} ∗  1^{3} 4_{+} ∗  1^{4} 3_{−} 5 5 2 3 4 4 3 4 3 3
S_{4} 2  45  4 3 4 2 2 3 22 2

Discriminant class: 6

∞  2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G  h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
191. 2_{−} 3_{k} 3_{i} 2_{−} -1 0 2 1^{2} 3_{k} −2∗ −2∗ 1^{4} 3_{i} 3∗ 3 2^{2} 2_{−} 1 V 4 4 4 2 22 22 22 2
D_{4} 2 4 4 4 22 4 2 22
192. 2_{−} 3_{i} 3_{i} 2_{+} 0 -3 0 1^{2} 3_{i} −2 −2 1^{4} 3_{i} 3∗ 3 1^{2} 1_{−} 5∗ 5∗ 4 4 4 2 22  22 2
D_{4}  2  6  2 0_{+} ∗  ∗  1^{2} 1_{−} 5∗ 5∗ 4 4 22 22 22 4 2 22
193. 2_{−} 5_{i} 3_{i} 2_{+} 0 3 0 1^{2} 3_{+} 2  2 1^{4} 3_{i} 3∗ 3 1^{2} 1_{−} 5∗ 5∗ 4 4 4 2  22 22 2
D_{4}  4  6  1^{2} 2_{i} −∗ −∗  1^{2} 1_{−} 5∗ 5∗ 4 4 22  22 4 2 22
194. 2_{−} 5_{k} 3_{i} 2_{−} 0 -6 0 1^{2} 3_{−} 2∗  2∗ 1^{4} 3_{i} 3∗ 3 2^{2} 2_{−} 1 V 4 4 4 2  22 2
D_{4}  4  24  1^{2} 2_{i} −1 −1  4 4 22 22  4 2 22
195. 2_{−} 9_{k} 1_{k} 2_{+} 0 -2 0 1^{4} 9_{k} −2∗ −∗ 1^{2} 1_{k} 3 3 1^{2} 1_{+} 5 5 2 4 4 4 22  22 4
D_{4} 2 6 2 0_{+} ∗ ∗ 1^{2} 1_{+} 5 5 4 2 22 22 4 2
196. 2_{−} 9_{k} 1_{i} 2_{−} 0 -4 0 1^{4} 9_{k} −2∗ −∗ 1^{2} 1_{i} 3∗ 3∗ 2^{2} 2_{−} 1 V 2 4 4 4 22  4
D_{4} 2 24 4 2 22 22 22 4 2 22
197. 2_{−} 9_{i} 1_{k} 2_{−} 0 4 0 1^{4} 9_{i} −2∗ −∗ 1^{2} 1_{k} 3 3 2^{2} 2_{−} 1 V 2 4 4 4 22 22  4
D_{4} 2 24 2 0_{+} ∗ ∗ 4 2 22 4 2
198. 2_{−} 9_{i} 1_{i} 2_{+} 0 2 0 1^{4} 9_{i} −2∗ −∗ 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{+} 5 5 2 4 4 4 22 22 22 4
D_{4} 2 6 1^{2} 1_{+} 5 5 4 2 22 22 4 2 22
199. 2_{−} 11_{i} 1_{k} 2_{−} 0 -20 0 1^{4} 11_{i} −2∗ −2 1^{2} 1_{k} 3 3 2^{2} 2_{−} 1 V 4 2 4 2 22 22 22 4
D_{4} 2 150 2 0_{+} ∗ ∗ 4 2 22 22 2 4 22
200. 2_{−} 11_{k} 1_{i} 2_{−} 0 20 0 1^{4} 11_{k} −2∗ −2 1^{2} 1_{i} 3∗ 3∗ 2^{2} 2_{−} 1 V 4 2 4 2  22 22 4
D_{4} 2 150 4 2 22 22 22 2 4
201. 2_{−} 11_{i} 1_{k} 2_{−} 0 16 0 1^{4} 11_{i} −2∗ 2∗ 1^{2} 1_{k} 3 3 2^{2} 2_{−} 1 V 4 4 2 4 22 22 22 2
D_{4}  4  24  2 0_{+} ∗ ∗  2 2 22 22 22 4 4

∞  2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G  h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
202. 0_{+} 11_{i} 1_{i} 2_{−} 0 -16 0 1^{4} 11_{i} −2∗ 2∗ 1^{2} 1_{i} 3∗ 3∗ 2^{2} 2_{−} 1 V 4 4 2 4 22 22 22 2
D_{4} 2 24 2 2 22 22 4 4 22
203. 2_{−} 11_{i} 1_{i} 2_{+} 0 8 0 1^{4} 11_{i} −2∗ 2∗ 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{−} 5∗ 5∗ 4 4 2 4 22 22 22 2
D_{4} 12 6 1^{2} 1_{−} 5∗ 5∗ 2 2 22 4 4 22
204. 0_{+} 11_{i} 1_{k} 2_{+} 0 -8 0 1^{4} 11_{i} −2∗ 2∗ 1^{2} 1_{k} 3 3 1^{2} 1_{−} 5∗ 5∗ 4 4 2 4 22 22 22 2
D_{4} 2 6 2 0_{+} ∗ ∗ 1^{2} 1_{−} 5∗ 5∗ 2 2 22 22 4 4
205. 2_{−} 9_{k} 3_{i} 2_{−} 0 30 0 1^{4} 9_{k} −2∗ −∗ 1^{4} 3_{i} 3∗ 3 2^{2} 2_{−} 1 V 4 2 2 4 22 22 22 4
D_{4} 8 150 2 4 22 22 22 2 2 22
206. 0_{+} 9_{i} 3_{i} 2_{−} 0 -30 0 1^{4} 9_{i} −2∗ −∗ 1^{4} 3_{i} 3∗ 3 2^{2} 2_{−} 1 V 4 2 2 4 22  22 4
D_{4}  2  150  2 4 22  22 2 2 22
207. 2_{−} 11_{i} 3_{i} 2_{+} 0 12 0 1^{4} 11_{i} −2∗ −2 1^{4} 3_{i} 3∗ 3 1^{2} 1_{+} 5 5 2 4 2 2  22  4
D_{4} 16  6  1^{2} 1_{+} 5 5 2 4 22 22 22 4 4 22
208. 0_{+} 11_{k} 3_{i} 2_{+} 0 -12 0 1^{4} 11_{k} −2∗ −2 1^{4} 3_{i} 3∗ 3 1^{2} 1_{+} 5 5 2 4 2 2 22 22  4
D_{4} 2 6 1^{2} 1_{+} 5 5 2 4 22 22 22 4 4 22
209. 2_{−} 11_{i} 3_{i} 2_{+} 0 0 0 1^{4} 11_{i} −2∗ 2∗ 1^{4} 3_{i} 3∗ 3 1^{2} 1_{+} 5 5 2 2 4 4 22 22 22 2
D_{4} 8 600 1^{2} 1_{+} 5 5 4 4 22 22 2 4 22
210. 2_{−} 11_{i} 3_{i} 2_{+} 0 0 0 1^{4} 11_{i} −2∗ 2∗ 1^{4} 3_{i} 3∗ 3 1^{2} 1_{−} 5∗ 5∗ 2 2 4 4 22 22  2
D_{4} 16 150 1^{2} 1_{−} 5∗ 5∗ 4 4 22 22 22 2 4 22
211. 2_{−} 11_{k} 3_{i} 2_{−} 0 24 0 1^{4} 11_{k} −2∗ −2 1^{4} 3_{i} 3∗ 3 2^{2} 2_{−} 1 V 2 4 2 2 22 22 22 4
D_{4} 8 24 2 4 22 22 22 4 4 22
212. 0_{+} 11_{i} 3_{i} 2_{−} 0 -24 0 1^{4} 11_{i} −2∗ −2 1^{4} 3_{i} 3∗ 3 2^{2} 2_{−} 1 V 2 4 2 2  22 22 4
D_{4}  2  24  2 4 22 22 22 4 4 22

Discriminant class: 10

∞  2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G  h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
213. 2_{−} 11_{+} 2_{−} 3_{+} 0 60 0 1^{4} 11_{+} 2∗  2∗ 1^{2} 1_{k} 3 3 1^{4} 3_{+} 5∗ 5∗ 4 4  4 4 4 4 22
C_{4} 32  810  1^{2} 1_{k} 3 3  4  4 4
214. 2_{−} 11_{+} 2_{−} 3_{+} 0 60 0 1^{4} 11_{+} 2∗  2∗ 1^{2} 1_{i} 3∗ 3∗ 1^{4} 3_{+} 5∗ 5∗ 4 4 22 4 4 4 4 22
C_{4} 16  90  1^{2} 1_{i} 3∗ 3∗  22  22 4 22 4 4 22
215. 0_{+} 11_{−} 2_{−} 3_{+} 0 -60 0 1^{4} 11_{−} 2∗  2∗ 1^{2} 1_{i} 3∗ 3∗ 1^{4} 3_{+} 5∗ 5∗ 4 4  4 4 4 4
C_{4}  4  810  1^{2} 1_{i} 3∗ 3∗  22 4  4 4 22
216. 0_{+} 11_{−} 2_{−} 3_{+} 0 -60 0 1^{4} 11_{−} 2∗  2∗ 1^{2} 1_{k} 3 3 1^{4} 3_{+} 5∗ 5∗ 4 4 22 4 4 4 4
C_{4} 4 90 1^{2} 1_{k} 3 3 22 4 22 4 4
217. 2_{−} 3_{−} 2_{+} 3_{+} 0 5 0 1^{2} 3_{−} 2∗  2∗ 2^{2} 2_{+} 1 V 1^{4} 3_{+} 5∗ 5∗ 4 4 22 2 2 2 4 22
D_{4} 4 10 22 22 22 2 22 4 2 22
218. 2_{−} 3_{+} 2_{−} 3_{+} -1 1 -6 1^{2} 3_{+} 2  2 1^{2} 1_{k} 3 3 1^{4} 3_{+} 5∗ 5∗ 4 4 22 2 2 2 4 22
D_{4} 4 6 2 0_{+} ∗ ∗ 1^{2} 1_{k} 3 3 22 22 22 2 4 2 22
219. 2_{−} 9_{+} 2_{+} 1_{−} 0 -6 0 1^{4} 9_{+} 2∗ −1 2^{2} 2_{+} 1 V 1^{2} 1_{−} 5∗ 5∗ 4 4  2 4 4 2 22
D_{4} 2 90 22 22 4 22 4 2 22
220. 2_{−} 9_{−} 2_{+} 1_{+} 0 18 0 1^{4} 9_{−} 2∗ −1 2^{2} 2_{+} 1 V 1^{2} 1_{+} 5 5 4 4 22 2 4 4 2 22
D_{4} 2 90 2 0_{+} ∗ ∗ 22 4 4 2 22
221. 2_{−} 5_{+} 2_{−} 3_{+} 0 -5 0 1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{k} 3 3 1^{4} 3_{+} 5∗ 5∗ 4 4 22 2 2 2 4
D_{4} 4 10 1^{2} 2_{i} −1 −1 1^{2} 1_{k} 3 3 22 22 22 2 22 4 2 22
222. 2_{−} 5_{−} 2_{+} 3_{+} 0 5 0 1^{2} 3_{i} −2 −2 2^{2} 2_{+} 1 V 1^{4} 3_{+} 5∗ 5∗ 4 4 22 2 2 2 4
D_{4}  4  40  1^{2} 2_{i} −∗ −∗  22 22 22 2  4 2 22

∞  2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G  h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
223. 0_{+} 11_{−} 2_{+} 1_{−} 0 -16 0 1^{4} 11_{−} 2∗ −2∗ 2^{2} 2_{+} 1 V 1^{2} 1_{−} 5∗ 5∗ 4 4 22 4 2 2 2 22
D_{4} 10 22 22 22 2 4 4
224. 2_{−} 11_{−} 2_{+} 1_{+} 0 8 0 1^{4} 11_{−} 2∗  2∗ 2^{2} 2_{+} 1 V 1^{2} 1_{+} 5 5 2 2 22 4 4 4 2 22
D_{4} 4 40 2 0_{+} ∗ ∗ 22 22 22 4 2 4 22
225. 2_{−} 11_{+} 2_{−} 1_{+} 0 -8 0 1^{4} 11_{+} 2∗  2∗ 1^{2} 1_{k} 3 3 1^{2} 1_{+} 5 5 2 2 22 4 4 4 2
D_{4} 4 40 1^{2} 1_{k} 3 3 2 0_{+} ∗ ∗ 22 22 22 4 2 4 22
226. 2_{−} 11_{−} 2_{+} 1_{+} 0 8 0 1^{4} 11_{−} 2∗ −2∗ 2^{2} 2_{+} 1 V 1^{2} 1_{+} 5 5 4 4 22 4 2 2 2 22
D_{4} 2 10 2 0_{+} ∗ ∗ 22 22 22 2 22 4 4
227. 2_{−} 11_{+} 2_{+} 1_{−} 0 -4 0 1^{4} 11_{+} 2∗  2∗ 2^{2} 2_{+} 1 V 1^{2} 1_{−} 5∗ 5∗ 2 2 22 4 4 4 2
D_{4} 4 10 22 22 22 4 22 2 4 22
228. 2_{−} 11_{−} 2_{−} 1_{−} 0 4 0 1^{4} 11_{−} 2∗  2∗ 1^{2} 1_{k} 3 3 1^{2} 1_{−} 5∗ 5∗ 2 2 22 4 4 4 2 22
D_{4} 4 10 1^{2} 1_{k} 3 3 22 22 22 4 22 2 4 22
229. 0_{+} 11_{−} 2_{−} 1_{+} 0 -8 0 1^{4} 11_{−} 2∗ −2∗ 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{+} 5 5 4 4 22 4 2 2 2 22
D_{4} 10 1^{2} 1_{i} 3∗ 3∗ 2 0_{+} ∗ ∗ 22 22 2 22 4 4 22
230. 2_{−} 11_{−} 2_{−} 1_{−} 0 16 0 1^{4} 11_{−} 2∗ −2∗ 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{−} 5∗ 5∗ 4 4 22 4 2 2 2 22
D_{4} 6 10 1^{2} 1_{i} 3∗ 3∗ 22 22 2 4 4 22
231. 0_{+} 9_{−} 2_{−} 3_{+} 0 -20 0 1^{4} 9_{−} 2∗ −1 1^{2} 1_{i} 3∗ 3∗ 1^{4} 3_{+} 5∗ 5∗ 2 2 22 2 4 4 4 22
D_{4} 4 40 1^{2} 1_{i} 3∗ 3∗ 22 22 22 4 22 2 2
232. 2_{−} 9_{+} 2_{−} 3_{+} 0 10 0 1^{4} 9_{+} 2∗ −1 1^{2} 1_{i} 3∗ 3∗ 1^{4} 3_{+} 5∗ 5∗ 2 2 22 2 4 4 4 22
D_{4} 16 10 1^{2} 1_{i} 3∗ 3∗ 22 22 22 4 2 2
233. 0_{+} 9_{+} 2_{+} 3_{+} 0 -10 0 1^{4} 9_{+} 2∗ −1 2^{2} 2_{+} 1 V 1^{4} 3_{+} 5∗ 5∗ 2 2 22 2 4 4 4 22
D_{4} 4 10 22 22 4 2 2 22
234. 2_{−} 9_{−} 2_{+} 3_{+} 0 20 0 1^{4} 9_{−} 2∗ −1 2^{2} 2_{+} 1 V 1^{4} 3_{+} 5∗ 5∗ 2 2 22 2 4 4 4 22
D_{4} 8 40 22 22 4 22 2 2 22
235. 2_{−} 11_{−} 2_{+} 3_{+} 0 0 0 1^{4} 11_{−} 2∗ −2∗ 2^{2} 2_{+} 1 V 1^{4} 3_{+} 5∗ 5∗ 2 2 22 4 2 2 4 22
D_{4} 16 360 22 22 2 22 2 4 22
236. 2_{−} 11_{−} 2_{+} 3_{+} 0 0 0 1^{4} 11_{−} 2∗ −2∗ 2^{2} 2_{+} 1 V 1^{4} 3_{+} 5∗ 5∗ 2 2  4 2 2 4 22
D_{4}  8  90  22 22 22 2  2 4 22

Discriminant class: 15

∞  2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G  h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
237. 2_{−} 2_{i} 3_{i} 3_{+}  -1 6 -1 1^{2} 2_{i} −∗ −∗ 1^{4} 3_{i} 3∗ 3 1^{4} 3_{+} 5∗ 5∗ 22 22 4  2 2 4 2
D_{4}  4  1  2 0_{+} ∗  ∗  4 4 22 2  22 22 22
238. 2_{−} 2_{i} 3_{i} 3_{+}  0 0  0 1^{2} 2_{i} −1 −1 1^{4} 3_{i} 3∗ 3 1^{4} 3_{+} 5∗ 5∗ 22 22 4 22 2 2 4 2
D_{4}  4  15  4 4 22 2 22 22 22 22
239. 2_{−} 10_{i} 3_{i} 1_{+}  0 -12  0 1^{4} 10_{i} −1 2∗ 1^{4} 3_{i} 3∗ 3 1^{2} 1_{+} 5 5  4 22 4 4 2 2
D_{4}  4  60  2 0_{+} ∗ ∗ 4 4 22 4 22 22 22 22
240. 2_{−} 10_{i} 3_{i} 1_{+}  0 12  0 1^{4} 10_{i} −1 2∗ 1^{4} 3_{i} 3∗ 3 1^{2} 1_{+} 5 5 22 22 4 22 4 4 2 2
D_{4}  4  60  2 0_{+} ∗ ∗ 4 4 22 4 22  22 22
241. 2_{−} 10_{k} 3_{i} 1_{−}  0 6  0 1^{4} 10_{k} −1 2∗ 1^{4} 3_{i} 3∗ 3 1^{2} 1_{−} 5∗ 5∗ 22  4 22 4 4 2 2
D_{4}  4  15  4 4 22 4  22 22 22
242. 2_{−} 10_{k} 3_{i} 1_{−}  0 -6  0 1^{4} 10_{k} −1 2∗ 1^{4} 3_{i} 3∗ 3 1^{2} 1_{−} 5∗ 5∗  22 4 22 4 4 2 2
D_{4}  4  15  4 4 22 4  22 22
243. 2_{−} 6_{i} 3_{i} 3_{+}  0 -30  0 1^{2} 3_{−} 2∗  2∗ 1^{4} 3_{i} 3∗ 3 1^{4} 3_{+} 5∗ 5∗ 22 22 4  2 2 4 2
D_{4}  8  240  1^{2} 3_{k} −2∗ −2∗  4 4 22 2 22 22  22

∞  2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G  h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
244. 2_{−} 6_{i} 3_{i} 3_{+}  0 0  0 1^{2} 3_{i} −2 −2 1^{4} 3_{i} 3∗ 3 1^{4} 3_{+} 5∗ 5∗ 22 22 4 22 2 2 4 2
D_{4}  8  60  1^{2} 3_{+} 2  2  4 4 22 2  22  22
245. 2_{−} 10_{k} 1_{k} 3_{+}  0 10  0 1^{4} 10_{k} −1 2∗ 1^{2} 1_{k} 3 3 1^{4} 3_{+} 5∗ 5∗ 22 22 2 22 4 4 4 2
D_{4}  8  15  2 0_{+} ∗ ∗  2 2  4 22 22 22 22
246. 0_{+} 10_{k} 1_{i} 3_{+}  0 -10  0 1^{4} 10_{k} −1 2∗ 1^{2} 1_{i} 3∗ 3∗ 1^{4} 3_{+} 5∗ 5∗ 22 22 2 22 4 4 4 2
D_{4}  2  15  2 2 22 4 22 22 22
247. 2_{−} 10_{i} 1_{i} 3_{+}  0 20  0 1^{4} 10_{i} −1 2∗ 1^{2} 1_{i} 3∗ 3∗ 1^{4} 3_{+} 5∗ 5∗ 22 22 2 22 4 4 4 2
D_{4} 16  60  2 2 22 4  22 22
248. 0_{+} 10_{i} 1_{k} 3_{+}  0 -20  0 1^{4} 10_{i} −1 2∗ 1^{2} 1_{k} 3 3 1^{4} 3_{+} 5∗ 5∗ 22 22 2 22 4 4 4 2
D_{4}  2  60  2 0_{+} ∗ ∗  2 2  4  22 22 22
249. 2_{−} 4_{k} 5_{i} 1_{−}  -2 0  6 2^{2} 4_{k} −1  ∗ 1^{3} 5_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 3 3 4 3 2 4 4 4
S_{4}  15  4 4 3 4 3 22 3 3
250. 2_{−} 6_{i} 5_{i} 1_{+}  -2 9 -4 1^{2} 3_{−} 2∗  2∗ 1^{3} 5_{i} 3∗  1^{2} 1_{+} 5 5 3 3 2 3 4 2 4 4
S_{4}  2  1^{2} 3_{k} −2∗ −2∗  2 0_{+} ∗ ∗ 4 4 3 4 3 22 3 3
251. 2_{−} 6_{i} 5_{i} 1_{+}  -2 9 -6 2^{2} 6_{i} −1  ∗ 1^{3} 5_{i} 3∗  1^{2} 1_{+} 5 5 3 3 4 3 4 4 2 2
S_{4}  3  2 0_{+} ∗ ∗ 2 2 3 2 3 22 3 3
252. 2_{−} 2_{i} 5_{i} 3_{+}  -1 -9  4 1^{2} 2_{i} −∗ −∗ 1^{3} 5_{i} 3∗  1^{4} 3_{+} 5∗ 5∗ 3 3 2 3 4 4 4 2
S_{4}  4  26  2 0_{+} ∗  ∗  4 2 3 4 3  3 3
253. 0_{+} 4_{k} 5_{i} 3_{+}  0 -15 -10 2^{2} 4_{k} −1  ∗ 1^{3} 5_{i} 3∗  1^{4} 3_{+} 5∗ 5∗ 3 3 4 3 4 2 2 4
S_{4}  2  15  2 4 3 2 3 22 3 3
254. 2_{−} 10_{i} 5_{i} 1_{+}  0 -6 -8 1^{4} 10_{i} −1  2 1^{3} 5_{i} 3∗  1^{2} 1_{+} 5 5 3 3 2 3 4 4 4 4
S_{4}  2  159  2 0_{+} ∗ ∗ 2 2 3 2 3 22 3 3
255. 2_{−} 10_{k} 5_{i} 1_{−}  0 -6 -32 1^{4} 10_{k} −1  2 1^{3} 5_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 3 3 2 3 2 4 2 2
S_{4}  6  87  4 4 3 4 3 22 3 3
256. 0_{+} 10_{k} 5_{i} 1_{+}  0 -24 -16 1^{4} 10_{k} −1 2∗ 1^{3} 5_{i} 3∗  1^{2} 1_{+} 5 5 3 3 4 3 4 2 2 2
S_{4}  2  24  2 0_{+} ∗ ∗ 4 4 3 4 3  3 3
257. 2_{−} 10_{k} 5_{i} 1_{−}  0 12 -32 1^{4} 10_{k} −1 2∗ 1^{3} 5_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 3 3 4 3 2 2 4 4
S_{4}  4  60  2 2 3 2 3 22 3 3
258. 2_{−} 6_{i} 5_{i} 3_{+}  0 0 -60 2^{2} 6_{i} −1  ∗ 1^{3} 5_{i} 3∗  1^{4} 3_{+} 5∗ 5∗ 3 3 4 3 2 2 4 2
S_{4}  4  135  4 2 3 4 3 22 3 3
259. 2_{−} 6_{i} 5_{i} 3_{+}  2 9 -32 1^{2} 3_{+} 2  2 1^{3} 5_{i} 3∗  1^{4} 3_{+} 5∗ 5∗ 3 3 2 3 2 4 2 4
S_{4}  4  56  1^{2} 3_{i} −2 −2  2 4 3 2 3 22 3 3
260. 2_{−} 10_{i} 5_{i} 3_{+}  0 90 120 1^{4} 10_{i} −1  2 1^{3} 5_{i} 3∗  1^{4} 3_{+} 5∗ 5∗ 3 3 2 3 4 2 4 2
S_{4}  8  1215  2 4 3 2 3 22 3 3
261. 2_{−} 10_{i} 5_{i} 3_{+}  0 -60 -160 1^{4} 10_{i} −1 2∗ 1^{3} 5_{i} 3∗  1^{4} 3_{+} 5∗ 5∗ 3 3 4 3 2 4 4 2
S_{4}  8  1860  2 4 3 2 3  3 3
262. 0_{+} 10_{k} 5_{i} 3_{+}  0 -60 -160 1^{4} 10_{k} −1  2 1^{3} 5_{i} 3∗  1^{4} 3_{+} 5∗ 5∗ 3 3 2 3 2 2 2 4
S_{4}  4  60  4 2 3 4 3 22 3 3
263. 2_{−} 10_{i} 5_{i} 3_{+}  0 30 -40 1^{4} 10_{i} −1 2∗ 1^{3} 5_{i} 3∗  1^{4} 3_{+} 5∗ 5∗ 3 3 4 3 4 4 2 4
S_{4}  8  15  4 2 3 4 3 22 3 3

Discriminant class: 30

∞  2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G  h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
264. 2_{−} 9_{k} 1_{i} 3_{−} 0 10 0 1^{4} 9_{k} −2 −∗ 1^{2} 1_{i} 3∗ 3∗ 1^{4} 3_{−} 5 5 22 4 22 22 22 2 22 4
D_{4}  4  30  2 0_{+} ∗ ∗  22 2 2 2 4 4 2 2

∞  2 3 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  7 11 13 17 19 23 29 31
G  h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
265. 2_{−} 9_{i} 1_{k} 3_{−} 0 -10 0 1^{4} 9_{i} −2 −∗ 1^{2} 1_{k} 3 3 1^{4} 3_{−} 5 5  4 22 22 22 2 22 4
D_{4}  4  30  22 2 2 2 4 4 2 2
266. 2_{−} 9_{k} 1_{i} 3_{−} 0 -20 0 1^{4} 9_{k} −2 −∗ 1^{2} 1_{i} 3∗ 3∗ 1^{4} 3_{−} 5 5  4 22 22 22 2  4
D_{4}  4  120  2 0_{+} ∗ ∗  22 2 2 2 4 4 2 2
267. 2_{−} 9_{i} 1_{k} 3_{−} 0 20 0 1^{4} 9_{i} −2 −∗ 1^{2} 1_{k} 3 3 1^{4} 3_{−} 5 5 22 4 22 22 22 2  4
D_{4} 4 120 22 2 2 2 4 4 2 2
268. 2_{−} 11_{i} 3_{k} 1_{−} 0 12 0 1^{4} 11_{i} −2 −2∗ 1^{4} 3_{k} 3 3∗ 1^{2} 1_{−} 5∗ 5∗ 22 4 22 22 22 2 22 4
D_{4} 4 30 2 0_{+} ∗ ∗ 22 4 2 2 2 4 4 2
269. 0_{+} 11_{k} 3_{k} 1_{−} 0 -12 0 1^{4} 11_{k} −2 −2∗ 1^{4} 3_{k} 3 3∗ 1^{2} 1_{−} 5∗ 5∗ 22 4 22 22  2 22 4
D_{4}  30  2 0_{+} ∗ ∗ 22 4 2 2 2 4 4 2
270. 2_{−} 11_{k} 3_{k} 1_{+} 0 24 0 1^{4} 11_{k} −2 −2∗ 1^{4} 3_{k} 3 3∗ 1^{2} 1_{+} 5 5 22 4 22 22  2  4
D_{4}  8  120  22 4 2 2 2 4 4 2
271. 0_{+} 11_{i} 3_{k} 1_{+} 0 -24 0 1^{4} 11_{i} −2 −2∗ 1^{4} 3_{k} 3 3∗ 1^{2} 1_{+} 5 5 22 4 22 22 22 2  4
D_{4}  120  22 4 2 2 2 4 4 2
272. 2_{−} 11_{i} 3_{k} 3_{−} 0 0 0 1^{4} 11_{i} −2  2 1^{4} 3_{k} 3 3∗ 1^{4} 3_{−} 5 5 22 2  22 22 2  2
D_{4} 24  270  4 2 2 4 2 4 2
273. 2_{−} 11_{i} 3_{k} 3_{−} 0 0 0 1^{4} 11_{i} −2  2 1^{4} 3_{k} 3 3∗ 1^{4} 3_{−} 5 5 22 2 22 22 22 2 22 2
D_{4}  8  750  22 4 2 2 4 2 4 2
274. 2_{−} 11_{i} 3_{k} 3_{−} 0 0 0 1^{4} 11_{i} −2  2 1^{4} 3_{k} 3 3∗ 1^{4} 3_{−} 5 5 22 2 22  22 2  2
D_{4}  8  120  22 4 2 2 4 2 4 2
275. 2_{−} 11_{i} 3_{k} 3_{−} 0 0 0 1^{4} 11_{i} −2  2 1^{4} 3_{k} 3 3∗ 1^{4} 3_{−} 5 5 22 2  22 2 22 2
D_{4}  8  30  4 2 2 4 2 4 2