Quartic Fields Unramified Outside of {∞, 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  22 2 22  22
D_{4} 12  -750  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}  4  -30  22 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  2 22 22 22
D_{4}  4  -120  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 -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
17. 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
18. 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
19. 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
20. 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
21. 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
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 -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
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 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
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 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
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 -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

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 -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
34. 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
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 -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
40. 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
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} 0_{+} 3_{+}  0 0  0 1^{4} 11_{i} −2∗ 2∗ 2 0_{+} ∗ ∗ 1^{4} 3_{+} 5∗ 5∗ 22 22  4 22 22 4 2
D_{4}  2  -40  22  2 22 22 22 4 2
49. 1_{k} 11_{i} 0_{+} 3_{+}  0 0  0 1^{4} 11_{i} −2∗ 2∗ 2 0_{+} ∗ ∗ 1^{4} 3_{+} 5∗ 5∗ 22 22 22 4 22 22 4 2
D_{4}  2  -10  2 22  22 4 2
50. 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
51. 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
52. 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
53. 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
54. 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
55. 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
56. 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
57. 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
58. 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
59. 1_{k} 11_{−} 3_{k} 0_{+}  0 0 0 1^{4} 11_{−} 2∗ −2∗ 1^{4} 3_{k} 3 3∗  22 22 4 4 2 2 22 22
D_{4}  -6  4 4 2 2 22 22 4 2
60. 1_{k} 11_{−} 3_{k} 0_{+}  0 0 0 1^{4} 11_{−} 2∗ −2∗ 1^{4} 3_{k} 3 3∗ 2 0_{+} ∗ ∗ 22 22 4 4 2 2  22
D_{4}  -24  2 0_{+} ∗ ∗ 4 4 2 2  22 4 2
61. 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

∞  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} 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
63. 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
64. 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
65. 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
66. 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
67. 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
68. 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
69. 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
70. 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
71. 1_{k} 9_{−} 3_{k} 0_{+}  0 0 -4 1^{4} 9_{−} 2∗ −1 1^{3} 3_{k} 3  3 0_{+} 1  3 3 4 4 4 4 22 3
S_{4}  -3  4 4 2 2 3 22 2 2
72. 1_{k} 11_{−} 3_{k} 0_{+}  0 0 -8 1^{4} 11_{−} 2∗ 2∗ 1^{3} 3_{k} 3  3 0_{+} 1  3 3 4 4 2 2 22 3
S_{4}  4  6  2 2 4 4 3 22 2 4
73. 1_{k} 11_{−} 3_{k} 0_{+}  0 -12 -16 1^{4} 11_{−} 2∗ −2∗ 1^{3} 3_{k} 3  3 0_{+} 1  3 3 2 2 4 4 22 3
S_{4}  12  4 4 4 4 3 22 2 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
74. 1_{k} 4_{k} 0_{+} 3_{−}  0 0 0 2^{2} 4_{k} −∗  ∗ 2 0_{+} ∗ ∗ 1^{4} 3_{−} 5 5 22 2 4 4 2 22 22 2
D_{4}  -5  2 0_{+} ∗ ∗  4 22 22 22 4 2 22 22
75. 1_{k} 6_{k} 0_{+} 3_{−}  0 0 0 2^{2} 6_{k} −∗  ∗ 2 0_{+} ∗ ∗ 1^{4} 3_{−} 5 5 22 2 4 4 2 22  2
D_{4}  -20  2 0_{+} ∗ ∗  4 22 22 22 4 2  22
76. 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
77. 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
78. 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
79. 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
80. 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
81. 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
82. 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

∞  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_{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
84. 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
85. 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
86. 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
87. 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
88. 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
89. 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
90. 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
91. 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
92. 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
93. 1_{k} 6_{+} 3_{i} 0_{+}  2 0 2 1^{4} 6_{+} ∗ −∗ 1^{4} 3_{i} 3∗ 3 4 0_{+} ∗ ∗ 22 2 22 4 22 2 4 22
D_{4}  1  4 22 2 4 2  22
94. 1_{k} 8_{+} 3_{i} 0_{+}  0 0 0 1^{4} 8_{+} ∗ −∗ 1^{4} 3_{i} 3∗ 3 4 0_{+} ∗ ∗ 22 2  4 22 2 4 22
D_{4}  -3  22 4 22 2 4 2 22 22
95. 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
96. 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
97. 1_{k} 4_{+} 5_{i} 0_{+}  2 0 6 1^{4} 4_{+} ∗  1^{3} 5_{i} 3∗  4 0_{+} ∗ ∗ 22 4 3 4 3 4 2 3
S_{4}  3  22 2 3 2 4 4 3 3
98. 1_{k} 0_{+} 5_{i} 2_{+} -1 0 4 4 0_{+} ∗  ∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  22 4 3 4 3 2 4 22
S_{4}  -1  3 4 3 4 4 4 3 22
99. 1_{k} 8_{+} 3_{i} 0_{+}  0 0 4 1^{4} 8_{+} ∗  1^{3} 3_{i} 3∗  4 0_{+} ∗ ∗ 3 4 3 4 3 4 2 22
S_{4}  -6  3 2 22 4 2 4 3 3
100. 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
101. 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
102. 1_{k} 6_{+} 5_{i} 0_{+}  2 -3 2 2^{2} 6_{+} ∗  ∗ 1^{3} 5_{i} 3∗  4 0_{+} ∗ ∗ 3 2 3 4 3 4 2 3
S_{4} 2  7  3 4 3 2 2 4 22 22
103. 1_{k} 6_{+} 5_{i} 0_{+} -2 0 -4 1^{4} 6_{+} ∗ −1 1^{3} 5_{i} 3∗  4 0_{+} ∗ ∗ 3 4 3 2 3 2 4 3
S_{4}  2  3 4 3 4 4 4 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} 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
105. 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
106. 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
107. 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
108. 1_{k} 8_{+} 5_{i} 0_{+}  0 -6 -4 1^{4} 8_{+} ∗ −∗ 1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 3 4 3 4 3 4 4 3
S_{4}  6  3 2 3 4 4 2 22 22
109. 1_{k} 8_{+} 5_{i} 0_{+}  0 -6 -4 1^{4} 8_{+} ∗  1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 3 4 22 2 22 4 4 3
S_{4}  15  3 4 3 2 2 4 3 3
110. 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
111. 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
112. 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
113. 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
114. 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
115. 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
116. 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
117. 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
118. 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
119. 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
120. 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
121. 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
122. 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
123. 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
124. 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
125. 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
126. 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

∞ 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} 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
128. 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
129. 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

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
130. 1_{k} 11_{i} 0_{+} 0_{+}  0 0 0 1^{4} 11_{i} −2  2 2 0_{+} ∗ ∗ 4 0_{+} ∗ ∗ 2 22 4 22 22 2 4 2
D_{4}  -2  2 0_{+} ∗ ∗  4 22 22 2 4 22 4 22
131. 1_{k} 9_{i} 2_{+} 0_{+}  0 2 0 1^{4} 9_{i} −2 −∗ 2^{2} 2_{+} 1 V 4 0_{+} ∗ ∗ 4  2 22 22 2 4 4
D_{4}  -2  2 22 22 2 4 22 2 22
132. 1_{k} 9_{k} 2_{−} 0_{+}  0 -2 0 1^{4} 9_{k} −2 −∗ 1^{2} 1_{k} 3 3 4 0_{+} ∗ ∗ 4 22 2 22 22 2 4 4
D_{4}  -2  1^{2} 1_{k} 3 3  2 22 22 2 4  2 22
133. 1_{k} 11_{i} 2_{+} 0_{+}  0 0 0 1^{4} 11_{i} −2  2 2^{2} 2_{+} 1 V 4 0_{+} ∗ ∗ 2 22 4  22 2 4 2
D_{4}  -18  4  22 2 4 22 4 22
134. 1_{k} 11_{k} 2_{−} 0_{+}  0 4 0 1^{4} 11_{k} −2 −2∗ 1^{2} 1_{i} 3∗ 3∗ 2 0_{+} ∗ ∗ 4 22 4 22 22 2 2 4
D_{4}  -2  1^{2} 1_{i} 3∗ 3∗  4 22 22 2 2 22 4
135. 1_{k} 11_{i} 2_{+} 0_{+}  0 -4 0 1^{4} 11_{i} −2 −2∗ 2^{2} 2_{+} 1 V 2 0_{+} ∗ ∗ 4 22 4 22  2 2 4
D_{4}  -2  4 22  2 2 22 4 22
136. 1_{k} 11_{i} 0_{+} 2_{+}  0 0 0 1^{4} 11_{i} −2  2 2 0_{+} ∗ ∗ 2^{2} 2_{+} ∗ ∗ 2 22 4  22 2 4 2
D_{4}  2  -50  2 0_{+} ∗ ∗  4 22 22 2 4 22 4 22
137. 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
138. 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
139. 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
140. 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
141. 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
142. 1_{k} 9_{i} 0_{+} 2_{+}  0 -4 -4 1^{4} 9_{i} −2 −∗ 3 0_{+} 1  1^{3} 2_{+} ∗  4 3 4 3 3 2 4 2
S_{4}  -3  4 3 22 4 2 22 4 3
143. 1_{k} 9_{i} 4_{+} 0_{+}  0 -6 -8 1^{4} 9_{i} −2 −∗ 1^{3} 4_{+} 1  4 0_{+} ∗ ∗ 2 3 4 3 3 4 2 2
S_{4}  6  4 3 3 4 2 3 2 3
144. 1_{k} 11_{i} 0_{+} 2_{+}  0 4 -8 1^{4} 11_{i} −2  2 3 0_{+} 1  1^{3} 2_{+} ∗  4 3 2 3 3 4 2 4
S_{4}  2  2  4 3 22 2 4  4 3
145. 1_{k} 11_{i} 0_{+} 2_{+}  0 -4 16 1^{4} 11_{i} −2 −2∗ 3 0_{+} 1  1^{3} 2_{+} ∗  2 3 4 3 3 4 4 4
S_{4}  -18  2 3 22 4 4 22 2 3
146. 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
147. 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

∞  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
148. 1_{k} 11_{i} 4_{+} 0_{+}  0 -12 -8 1^{4} 11_{i} −2  2 1^{3} 4_{+} 1  2 0_{+} ∗ ∗ 4 3 4 3 3 4 4 2
S_{4}  2  18  2 3 3 4 2 3 2 3
149. 1_{k} 11_{i} 4_{+} 0_{+}  0 0 -8 1^{4} 11_{i} −2 −2∗ 1^{3} 4_{+} 1  4 0_{+} ∗ ∗ 4 3 2 3 3 2 4 2
S_{4}  -6  4 3 3 2 2 3 2 3
150. 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
151. 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
152. 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
153. 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
154. 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
155. 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
156. 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
157. 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

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
158. 1_{k} 4_{k} 0_{+} 2_{−}  0 -1 0 2^{2} 4_{k} −1 ∗ 4 0_{+} ∗ ∗ 2^{2} 2_{−} 1 V 4 2 22 22 2 4  2
D_{4}  -1  22 22 4 4 22 2 22 4
159. 1_{k} 10_{i} 0_{+} 0_{+}  0 -2 0 1^{4} 10_{i} −1 2 4 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 2 4 22 22 4 2 22 2
D_{4} -1 2 0_{+} ∗ ∗ 22 4 2 22 4 22 4
160. 1_{k} 6_{i} 0_{+} 2_{+}  0 2 0 2^{2} 6_{i} −1 ∗ 4 0_{+} ∗ ∗ 1^{2} 1_{+} 5 5 4 2 22 22 2 4 22 2
D_{4} -4 1^{2} 1_{+} 5 5 22 22 4 4 22 2 4
161. 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
162. 1_{k} 10_{k} 2_{−} 0_{+}  0 6 0 1^{4} 10_{k} −1 2 2^{2} 2_{−} ∗ ∗ 2 0_{+} ∗ ∗ 2 4 22  4 2 22 2
D_{4}  -9  2 0_{+} ∗ ∗ 22 22 4 2 22 4 22 4
163. 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
164. 1_{k} 10_{k} 0_{+} 2_{−}  0 10 0 1^{4} 10_{k} −1 2 4 0_{+} ∗ ∗ 2^{2} 2_{−} 1 V 2 4 22  4 2 22 2
D_{4}  2  -25  22  4 2 22 4 22 4
165. 1_{k} 10_{i} 0_{+} 2_{+}  0 -2 0 1^{4} 10_{i} −1 2∗ 2 0_{+} ∗ ∗ 1^{2} 1_{−} 5∗ 5∗ 4 4 22 22 4 4 22 2
D_{4}  2  -9  1^{2} 1_{−} 5∗ 5∗  22 2 4 22 4 22 2
166. 1_{k} 10_{k} 0_{+} 2_{−}  0 6 0 1^{4} 10_{k} −1 2∗ 2 0_{+} ∗ ∗ 2^{2} 2_{−} 1 V 4 4  22 4 4 22 2
D_{4}  2  -1  22 22 2 4  4 22 2
167. 1_{k} 10_{i} 2_{+} 2_{+}  0 -18 0 1^{4} 10_{i} −1 2∗ 1^{2} 1_{k} 3 3 1^{2} 1_{−} 5∗ 5∗ 4 4  22 4 4 22 2
D_{4}  4  -9  1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{−} 5∗ 5∗ 22  2 4 22 4 22 2
168. 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

∞  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
169. 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
170. 1_{k} 6_{i} 4_{+} 0_{+}  2 3 -2 2^{2} 6_{i} −1 ∗ 1^{3} 4_{+} ∗  3 0_{+} 1  4 4 3 3 4 4 3 2
S_{4}  -1  3 22 4 2 22 2 3 4
171. 1_{k} 10_{i} 4_{+} 0_{+}  0 0 -16 1^{4} 10_{i} −1 2∗ 1^{3} 4_{+} ∗  3 0_{+} 1  2 4 3 3 2 4 3 4
S_{4}  2  -24  3 22 4 4 22 2 3 2
172. 1_{k} 10_{i} 4_{+} 0_{+}  0 -6 -8 1^{4} 10_{i} −1 2 1^{3} 4_{+} ∗  3 0_{+} 1  4 2 3 3 4 2 3 4
S_{4}  2  15  3 22 2 4  2 3 4

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
173. 2_{−} 4_{−} 2_{+} 0_{+} 0 -1 0 2^{2} 4_{−} 1  {−1 \atop −∗} 2^{2} 2_{+} 1 V 2 0_{+} ∗ ∗ 22 22  22 22 22 22 22
V_{4}  1  2 0_{+} ∗ ∗  22 22 22 22 22  22
174. 2_{−} 0_{+} 2_{+} 2_{−} -1 2 1 2 0_{+} ∗  ∗ 2^{2} 2_{+} 1 V 2^{2} 2_{−} 1 V 22 22 22 22  22 22
V_{4}  1  2 0_{+} ∗  ∗  22 22 22 22 22 22  22
175. 2_{−} 8_{−} 0_{+} 0_{+} 0 0 0 1^{4} 8_{−} 1  {−2 \atop −1} 2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 22 22 22  22 22 22 22
V_{4}  1  2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 22  22 22 22 22 22 22
176. 2_{−} 4_{−} 0_{+} 2_{+} 0 3 0 2^{2} 4_{−} 1  {−1 \atop −∗} 2 0_{+} ∗ ∗ 1^{2} 1_{+} 5 5 22 22 22 22 22 22  22
V_{4}  1  2 0_{+} ∗ ∗ 1^{2} 1_{+} 5 5 22  22 22 22 22  22
177. 2_{−} 6_{−} 2_{+} 0_{+} 0 2 0 2^{2} 6_{−} 1  {∗ \atop 2} 2^{2} 2_{+} 1 V 2 0_{+} ∗ ∗  22 22 22 22 22 22
V_{4}  4  2 0_{+} ∗ ∗ 22 22 22 22 22 22 22 22
178. 2_{−} 6_{+} 2_{−} 0_{+} 0 -2 0 2^{2} 6_{+} 1 {−2 \atop −2∗} 1^{2} 1_{i} 3∗ 3∗ 2 0_{+} ∗ ∗ 22 22 22 22  22 22 22
V_{4} 4 1^{2} 1_{i} 3∗ 3∗ 2 0_{+} ∗ ∗ 22 22 22 22 22 22
179. 0_{+} 6_{−} 0_{+} 2_{−} 0 -6 0 2^{2} 6_{−} 1  {∗ \atop 2} 2 0_{+} ∗ ∗ 2^{2} 2_{−} 1 V 22 22 22 22 22 22 22
V_{4}  4  2 0_{+} ∗ ∗  22  22 22 22 22 22 22
180. 2_{−} 6_{+} 0_{+} 2_{−} 0 6 0 2^{2} 6_{+} 1 {−2 \atop −2∗} 2 0_{+} ∗ ∗ 2^{2} 2_{−} 1 V 22  22 22  22 22 22
V_{4}  4  2 0_{+} ∗ ∗  22  22 22 22  22 22
181. 2_{−} 8_{−} 2_{+} 0_{+} 0 0 0 1^{4} 8_{−} 1 {−2∗ \atop −1} 2^{2} 2_{+} 1 V  22 22 22 22 22 22  22
V_{4} 2  9  22 22 22 22  22 22 22
182. 0_{+} 8_{+} 2_{+} 0_{+} 0 -4 0 1^{4} 8_{+} 1 {−2∗ \atop −∗} 2^{2} 2_{+} 1 V 2 0_{+} ∗ ∗ 22 22 22 22 22  22 22
V_{4}  1  2 0_{+} ∗ ∗ 22 22 22  22 22 22 22
183. 2_{−} 8_{+} 2_{−} 0_{+} 0 4 0 1^{4} 8_{+} 1  {−2 \atop −∗} 1^{2} 1_{k} 3 3 2 0_{+} ∗ ∗ 22  22 22 22 22 22 22
V_{4} 2  1  1^{2} 1_{k} 3 3 2 0_{+} ∗ ∗ 22 22 22 22 22  22 22
184. 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
185. 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
186. 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
187. 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
188. 2_{−} 8_{−} 0_{+} 2_{+} 0 0 0 1^{4} 8_{−} 1 {−2∗ \atop −1} 2 0_{+} ∗ ∗ 1^{2} 1_{−} 5∗ 5∗ 22 22  22 22 22 22 22
V_{4} 2  25  2 0_{+} ∗ ∗ 1^{2} 1_{−} 5∗ 5∗  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
189. 2_{−} 8_{+} 0_{+} 2_{−} 0 -4 0 1^{4} 8_{+} 1  {−2 \atop −∗}  2^{2} 2_{−} 1 V 22 22 22 22 22 22 22 22
V_{4} 2  9  22  22 22 22 22
190. 2_{−} 8_{+} 0_{+} 2_{−} 0 4 0 1^{4} 8_{+} 1 {−2∗ \atop −∗} 2 0_{+} ∗ ∗ 2^{2} 2_{−} 1 V  22 22 22 22  22 22
V_{4} 2  9  2 0_{+} ∗ ∗  22  22  22 22 22 22
191. 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
192. 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
193. 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
194. 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
195. 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
196. 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
197. 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
198. 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
199. 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
200. 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
201. 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
202. 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
203. 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
204. 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
205. 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
206. 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
207. 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
208. 2_{−} 6_{−} 4_{+} 0_{+} -2 6 -4 1^{4} 6_{−} 1  1^{3} 4_{+} 1  3 0_{+} 1  3 3 3 22 22 3 3 3
A_{4}  2  22 3 3 3 22 3 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
209. 2_{−} 11_{−} 0_{+} 0_{+} 0 4  0 1^{4} 11_{−} 2 2 4 0_{+} ∗ ∗ 4 0_{+} ∗ ∗  4 4  4  4 22
C_{4}  2  4 22 4 22 4 4 4 4
210. 0_{+} 11_{+} 0_{+} 0_{+} 0 -4  0 1^{4} 11_{+} 2 2 4 0_{+} ∗ ∗ 4 0_{+} ∗ ∗ 22 4 4  4 22 4
C_{4}  2  4 22 4  4 4 4 4
211. 0_{+} 11_{−} 2_{−} 0_{+} 0 -12  0 1^{4} 11_{−} 2 2 2^{2} 2_{−} ∗ ∗ 4 0_{+} ∗ ∗  4 4 22 4 22 4 22
C_{4}  18  4  4  4 4 4 4
212. 2_{−} 11_{+} 2_{−} 0_{+} 0 12  0 1^{4} 11_{+} 2 2 2^{2} 2_{−} ∗ ∗ 4 0_{+} ∗ ∗ 22 4 4 22 4  4
C_{4}  2  18  4  4 22 4 4 4 4
213. 2_{−} 11_{−} 0_{+} 2_{+} 0 20  0 1^{4} 11_{−} 2 2 4 0_{+} ∗ ∗ 2^{2} 2_{+} ∗ ∗ 22 4 4 22 4 22 4 22
C_{4}  2  50  4 22 4  4 4 4 4
214. 0_{+} 11_{+} 0_{+} 2_{+} 0 -20  0 1^{4} 11_{+} 2 2 4 0_{+} ∗ ∗ 2^{2} 2_{+} ∗ ∗  4 4 22 4  4
C_{4}  2  50  4 22 4 22 4 4 4 4
215. 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
216. 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
217. 2_{−} 9_{−} 0_{+} 0_{+} 0 -2  0 1^{4} 9_{−} 2 −1 4 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 22 4 2 22 4 22 2 22
D_{4} 2 2 4 22 2 4 2 4
218. 2_{−} 11_{−} 0_{+} 0_{+} 0 0  0 1^{4} 11_{−} 2 −2 2 0_{+} ∗ ∗ 4 0_{+} ∗ ∗ 22 2 4 22 2 22 4 22
D_{4}  2  4 22 2 22 4 2 4 2
219. 2_{−} 9_{+} 2_{−} 0_{+} 0 6  0 1^{4} 9_{+} 2 −1 2^{2} 2_{−} ∗ ∗ 2 0_{+} ∗ ∗ 22 4 2  4 22 2 22
D_{4}  2  18  2 22 4 22 2 4 2 4
220. 2_{−} 9_{+} 0_{+} 2_{−} 0 10  0 1^{4} 9_{+} 2 −1 4 0_{+} ∗ ∗ 1^{2} 1_{+} 5 5 22 4 2  4 22 2 22
D_{4}  2  50  1^{2} 1_{−} 5∗ 5∗ 2  4 22 2 4 2 4
221. 2_{−} 11_{−} 2_{+} 0_{+} 0 0  0 1^{4} 11_{−} 2 −2 1^{2} 1_{i} 3∗ 3∗ 4 0_{+} ∗ ∗ 22 2 4  2 22 4 22
D_{4}  2  18  1^{2} 1_{k} 3 3  4  2 22 4 2 4 2
222. 2_{−} 11_{−} 0_{+} 2_{+} 0 0  0 1^{4} 11_{−} 2 −2 2 0_{+} ∗ ∗ 2^{2} 2_{+} ∗ ∗ 22 2 4  2 22 4 22
D_{4}  2  50  4 22 2 22 4 2 4 2
223. 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
224. 2_{−} 11_{−} 2_{+} 2_{+} 0 0  0 1^{4} 11_{−} 2 −2 1^{2} 1_{k} 3 3 2^{2} 2_{+} ∗ ∗ 22 2 4 22 2 22 4 22
D_{4}  4  450  1^{2} 1_{i} 3∗ 3∗  4  2 22 4 2 4 2
225. 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
226. 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
227. 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
228. 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
229. 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
230. 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
231. 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

∞  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
232. 2_{−} 4_{k} 3_{k} 0_{+} 0 -3 0 2^{2} 4_{k} −∗  ∗ 1^{4} 3_{k} 3 3∗ 4 0_{+} ∗ ∗ 2 22 22 4 2 22 4 2
D_{4}  3  4 2 22 4 22  2
233. 2_{−} 6_{k} 3_{k} 0_{+} 0 0 0 2^{2} 6_{k} −∗  ∗ 1^{4} 3_{k} 3 3∗ 4 0_{+} ∗ ∗ 2 22  4 2 22 4 2
D_{4}  12  22 4 2 22 4 22 22 2
234. 2_{−} 10_{i} 1_{i} 0_{+} 0 -2 0 1^{4} 10_{i} −∗ −2 1^{2} 1_{i} 3∗ 3∗ 4 0_{+} ∗ ∗ 4  22 2 2 22 4 4
D_{4} 3 2 0_{+} ∗ ∗ 22 2 2 22 4 22 22 2
235. 2_{−} 10_{k} 1_{k} 0_{+} 0 2 0 1^{4} 10_{k} −∗ −2 1^{2} 1_{k} 3 3 4 0_{+} ∗ ∗ 4 22 22 2 2 22 4 4
D_{4}  3  22 2 2 22 4  22 2
236. 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
237. 0_{+} 10_{i} 3_{k} 0_{+} 0 -6 0 1^{4} 10_{i} −∗ −2∗ 1^{4} 3_{k} 3 3∗ 2 0_{+} ∗ ∗ 4 22 22 4 2 22 2 4
D_{4} 3 22 4 2 22 2 22 22 2
238. 2_{−} 10_{k} 3_{k} 0_{+} 0 6 0 1^{4} 10_{k} −∗ −2∗ 1^{4} 3_{k} 3 3∗ 2 0_{+} ∗ ∗ 4 22 22 4 2  2 4
D_{4} 2 3 22 4 2 2 22 22 2
239. 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
240. 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
241. 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
242. 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
243. 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
244. 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
245. 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
246. 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
247. 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
248. 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
249. 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
250. 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

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
251. 2_{−} 0_{+} 0_{+} 3_{−} -1 1 -1 4 0_{+} ∗ ∗ 4 0_{+} ∗ ∗ 1^{4} 3_{−} 5 5 4  4 4 22 4 22
C_{4} 1 4 4 4 4 22 4
252. 0_{+} 0_{+} 2_{−} 3_{−} -1 -4 4 4 0_{+} ∗ ∗ 2^{2} 2_{−} ∗ ∗ 1^{4} 3_{−} 5 5 4 22 4 4 22 4
C_{4}  1  4 22 4 4 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
253. 0_{+} 4_{−} 0_{+} 3_{−} 0 -5 0 2^{2} 4_{−} ∗ ∗ 4 0_{+} ∗ ∗ 1^{4} 3_{−} 5 5 4 22 4 4  4 22 22
C_{4}  5  4  4 4 4  4
254. 0_{+} 6_{−} 0_{+} 3_{−} 0 -10 0 2^{2} 6_{−} ∗ ∗ 4 0_{+} ∗ ∗ 1^{4} 3_{−} 5 5 4  4 4 22 4  22
C_{4}  20  4  4 4 4 22 22 4
255. 2_{−} 6_{+} 0_{+} 3_{−} 0 10 0 2^{2} 6_{+} ∗ ∗ 4 0_{+} ∗ ∗ 1^{4} 3_{−} 5 5 4 22 4 4  4
C_{4} 2  20  4  4 4 4  22 4
256. 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
257. 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
258. 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
259. 2_{−} 6_{+} 0_{+} 1_{−} 2 4 2 1^{4} 6_{+} ∗ −1 4 0_{+} ∗ ∗ 1^{2} 1_{−} 5∗ 5∗ 4 22 2 2 22 4  22
D_{4} 1 2 0_{+} ∗ ∗ 2 22 4 4 2 22 22 4
260. 2_{−} 8_{−} 0_{+} 1_{+} 0 -4 0 1^{4} 8_{−} ∗ −1 4 0_{+} ∗ ∗ 1^{2} 1_{+} 5 5 4 22 2 2 22 4 22 22
D_{4} 5 2 22 4 4 2 22 4
261. 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
262. 2_{−} 6_{+} 0_{+} 3_{−} -2 4 2 1^{4} 6_{+} ∗ −∗ 2 0_{+} ∗ ∗ 1^{4} 3_{−} 5 5 2 22 4 4 22 2 22 22
D_{4} 4 1 4 22 2 2 4 22 22 2
263. 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
264. 2_{−} 8_{+} 0_{+} 3_{−} 0 0 0 1^{4} 8_{+} ∗ −∗ 2 0_{+} ∗ ∗ 1^{4} 3_{−} 5 5 2 22 4 4 22 2  22
D_{4} 4 5 4 22 2 2 4 22 2
265. 2_{−} 6_{+} 2_{+} 3_{−} -2 4 -18 1^{4} 6_{+} ∗ −∗ 1^{2} 1_{i} 3∗ 3∗ 1^{4} 3_{−} 5 5 2 22 4 4 22 2  22
D_{4} 8 21 1^{2} 1_{k} 3 3 4 2 2 4 22 22 2
266. 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
267. 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
268. 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
269. 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
270. 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
271. 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
272. 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
273. 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

∞  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
274. 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
275. 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
276. 2_{−} 11_{i} 1_{i} 0_{+} 0 -4 0 1^{4} 11_{i} −2∗ −2 1^{2} 1_{i} 3∗ 3∗ 2 0_{+} ∗ ∗ 4 2 4 2 22 22 22 4
D_{4} 6 2 0_{+} ∗ ∗ 4 2 22 22 22 2 4
277. 2_{−} 11_{k} 1_{k} 0_{+} 0 4 0 1^{4} 11_{k} −2∗ −2 1^{2} 1_{k} 3 3 2 0_{+} ∗ ∗ 4 2 4 2  22 22 4
D_{4} 6 2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 4 2 22 22 2 4 22
278. 0_{+} 9_{k} 3_{i} 0_{+} 0 -6 0 1^{4} 9_{k} −2∗ −∗ 1^{4} 3_{i} 3∗ 3 2 0_{+} ∗ ∗ 4 2 2 4 22 22 22 4
D_{4} 6 2 0_{+} ∗ ∗ 2 4 22 22 22 2 2 22
279. 2_{−} 9_{i} 3_{i} 0_{+} 0 6 0 1^{4} 9_{i} −2∗ −∗ 1^{4} 3_{i} 3∗ 3 2 0_{+} ∗ ∗ 4 2 2 4 22  22 4
D_{4}  2  6  2 0_{+} ∗ ∗ 2 4 22  22 2 2 22
280. 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
281. 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
282. 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
283. 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
284. 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
285. 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
286. 2_{−} 11_{i} 3_{i} 0_{+} 0 0 0 1^{4} 11_{i} −2∗ 2∗ 1^{4} 3_{i} 3∗ 3  2 2 4 4 22 22 22 2
D_{4} 2 24 4 4 22 22 22 2 4 22
287. 2_{−} 11_{i} 3_{i} 0_{+} 0 0 0 1^{4} 11_{i} −2∗ 2∗ 1^{4} 3_{i} 3∗ 3 2 0_{+} ∗ ∗ 2 2 4 4 22 22  2
D_{4} 2 6 2 0_{+} ∗ ∗ 4 4 22 22 2 4 22
288. 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
289. 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
290. 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
291. 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
292. 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
293. 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
294. 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
295. 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
296. 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

∞  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
297. 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
298. 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
299. 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
300. 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
301. 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
302. 2_{−} 5_{i} 5_{i} 0_{+} 0 3 -2 1^{2} 3_{+} 2  2 1^{3} 5_{i} 3∗  3 0_{+} 1  4 4 4 4 3 3 3 2
S_{4}  6  1^{2} 2_{i} −∗ −∗  2 4 22 3 3 4 4 3
303. 2_{−} 9_{i} 5_{i} 0_{+} 0 12 -4 1^{4} 9_{i} −2∗ −∗ 1^{3} 5_{i} 3∗  3 0_{+} 1  4 4 2 4 3 3 3 4
S_{4}  4  69  2 2  3 3 2 4 3
304. 2_{−} 9_{i} 5_{i} 0_{+} 0 12 -16 1^{4} 9_{i} −2∗ −∗ 1^{3} 5_{i} 3∗  3 0_{+} 1  2 2 4 2 3 3 3 4
S_{4}  4  24  2 4 22 3 3 4 2 3
305. 2_{−} 11_{i} 5_{i} 0_{+} 0 12 -16 1^{4} 11_{i} −2∗ −2 1^{3} 5_{i} 3∗  3 0_{+} 1  2 4 2 2 3 3 3 2
S_{4}  2  6  2 4 22 3 3 2 2 3
306. 0_{+} 11_{k} 5_{i} 0_{+} 0 -24 56 1^{4} 11_{k} −2∗ −2 1^{3} 5_{i} 3∗  3 0_{+} 1  4 2 4 4 3 3 3 2
S_{4}  -30  2 2 22 3 3 4 4 3
307. 2_{−} 11_{i} 5_{i} 0_{+} 0 12 -8 1^{4} 11_{i} −2∗ 2∗ 1^{3} 5_{i} 3∗  3 0_{+} 1  2 4 4 2 3 3 3 4
S_{4}  2  42  2 2 22 3 3 4 2 3
308. 2_{−} 11_{i} 5_{i} 0_{+} 0 12 -16 1^{4} 11_{i} −2∗ 2∗ 1^{3} 5_{i} 3∗  3 0_{+} 1  4 2 2 4 3 3 3 4
S_{4}  2  60  2 4 22 3 3 2 4 3

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
309. 0_{+} 11_{+} 0_{+} 3_{+} 0 -20 0 1^{4} 11_{+} 2∗  2∗  1^{4} 3_{+} 5∗ 5∗ 4 4 22 4 4 4 4 22
C_{4}  2  10  22 22 22 4  4 4 22
310. 0_{+} 11_{+} 0_{+} 3_{+} 0 -20 0 1^{4} 11_{+} 2∗  2∗ 2 0_{+} ∗ ∗ 1^{4} 3_{+} 5∗ 5∗ 4 4  4 4 4 4 22
C_{4}  2  90  2 0_{+} ∗ ∗  22  4 22 4 4
311. 2_{−} 11_{−} 0_{+} 3_{+} 0 20 0 1^{4} 11_{−} 2∗  2∗ 2 0_{+} ∗ ∗ 1^{4} 3_{+} 5∗ 5∗ 4 4 22 4 4 4 4
C_{4}  4  10  2 0_{+} ∗ ∗  22 22  4  4 4
312. 2_{−} 11_{−} 0_{+} 3_{+} 0 20 0 1^{4} 11_{−} 2∗  2∗  1^{4} 3_{+} 5∗ 5∗ 4 4  4 4 4 4
C_{4} 20  90  22 22 4 22 4 4 22
313. 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
314. 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
315. 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
316. 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
317. 2_{−} 9_{+} 0_{+} 1_{−} 0 6 0 1^{4} 9_{+} 2∗ −1 2 0_{+} ∗ ∗ 1^{2} 1_{−} 5∗ 5∗ 4 4 22 2 4 4 2 22
D_{4}  10  2 0_{+} ∗ ∗  22 22 4 22 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
318. 2_{−} 9_{−} 0_{+} 1_{+} 0 2 0 1^{4} 9_{−} 2∗ −1 2 0_{+} ∗ ∗ 1^{2} 1_{+} 5 5 4 4  2 4 4 2 22
D_{4} 10 2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 22 22 22 4 4 2 22
319. 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
320. 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
321. 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
322. 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
323. 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
324. 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
325. 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
326. 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
327. 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
328. 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
329. 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
330. 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
331. 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
332. 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
333. 2_{−} 11_{−} 0_{+} 3_{+} 0 0 0 1^{4} 11_{−} 2∗ −2∗ 2 0_{+} ∗ ∗ 1^{4} 3_{+} 5∗ 5∗ 2 2  4 2 2 4 22
D_{4} 4 10 2 0_{+} ∗ ∗ 22 22 2 22 2 4 22
334. 2_{−} 11_{−} 0_{+} 3_{+} 0 0 0 1^{4} 11_{−} 2∗ −2∗ 2 0_{+} ∗ ∗ 1^{4} 3_{+} 5∗ 5∗ 2 2 22 4 2 2 4 22
D_{4} 4 40 2 0_{+} ∗ ∗ 22 2 2 4 22
335. 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
336. 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
337. 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
338. 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
339. 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
340. 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

∞  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
341. 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
342. 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
343. 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
344. 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
345. 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
346. 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
347. 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
348. 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
349. 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
350. 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
351. 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
352. 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
353. 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
354. 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
355. 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
356. 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
357. 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
358. 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
359. 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
360. 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
361. 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
362. 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
363. 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

∞  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
364. 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
365. 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
366. 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
367. 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

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
368. 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
369. 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
370. 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
371. 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
372. 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
373. 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
374. 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
375. 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
376. 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
377. 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
378. 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
379. 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