Low Degree Fields Unramified Outside of {∞, 2, 3, 5, 7}

Discriminant class: −210

∞ 2 3 5 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  Over p = 7  11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
1. 1_{k} 3_{i} 1_{i} 1_{−} 1_{i} 0 210  1^{2} 3_{i} −2 −2 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{i} 7∗ 7∗ 2 2 2 2 2
C_{2} 8 2 2 2
2. 1_{k} 3_{i} 3_{i} 1_{−} 1_{i} 0 18 -16 1^{2} 3_{i} −2 −2 1^{3} 3_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{i} 7∗ 7∗ 2 2 2 2 2 3 3 3
S_{3} 5  3 2 3 2 3 3 2 3
3. 1_{k} 3_{i} 5_{i} 1_{−} 1_{i} 0 -27 -114 1^{2} 3_{i} −2 −2 1^{3} 5_{i} 3∗ 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{i} 7∗ 7∗ 2 2 2 2 2 3 3
S_{3}  2 3 2 3 3 2
4. 1_{k} 3_{i} 5_{i} 1_{−} 1_{i} 0 18 -96 1^{2} 3_{i} −2 −2 1^{3} 5_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{i} 7∗ 7∗ 2 2 2 2 2  3 3
S_{3}  3 2  2  3 2 3
5. 1_{k} 3_{i} 5_{i} 1_{−} 1_{i} 0 -27 -306 1^{2} 3_{i} −2 −2 1^{3} 5_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{i} 7∗ 7∗ 2 2 2 2 2 3 3
S_{3} 3 2 3 2 3 2 3

Discriminant class: −105

∞ 2 3 5 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  Over p = 7  11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
6. 1_{k} 2_{i} 1_{k} 1_{+} 1_{i} 0 105  1^{2} 2_{i} −1 −1 1^{2} 1_{k} 3 3 1^{2} 1_{+} 5 5 1^{2} 1_{i} 7∗ 7∗  2  2 2  2
C_{2} 8  2 2
7. 1_{k} 2_{i} 3_{k} 1_{+} 1_{i} 0 -3 -12 1^{2} 2_{i} −1 −1 1^{3} 3_{k} 3 1^{2} 1_{+} 5 5 1^{2} 1_{i} 7∗ 7∗ 3 3 2 3 2 2 2
S_{3}  3 3 3 3 2 2 3

Discriminant class: −70

∞ 2 3 5 7 a_{1} a_{2} a_{3} Over p = 2 Over p = 3 Over p = 5 Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
8. 1_{k} 3_{−} 0_{+} 1_{+} 1_{k} 0 70 1^{2} 3_{−} 2∗ 2∗ 2 0_{+} ∗ ∗ 1^{2} 1_{+} 5 5 1^{2} 1_{k} 7 7 2 2 2 2 2
C_{2} 4  2
9. 1_{k} 3_{−} 4_{+} 1_{+} 1_{k} 0 -3 -58 1^{2} 3_{−} 2∗ 2∗ 1^{3} 4_{+} ∗  1^{2} 1_{+} 5 5 1^{2} 1_{k} 7 7 2 2 3  2 2 2 3
S_{3}  2  3 3 3 3 3 3

Discriminant class: −42

∞ 2 3 5 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
10. 1_{k} 3_{k} 1_{k} 0_{+} 1_{k} 0 42  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{k} 3 3 2 0_{+} ∗ ∗ 1^{2} 1_{k} 7 7 2  2  2
C_{2} 4  2
11. 1_{k} 3_{k} 3_{k} 0_{+} 1_{k} 0 -6 -16 1^{2} 3_{k} −2∗ −2∗ 1^{3} 3_{k} 3  2 0_{+} ∗ ∗ 1^{2} 1_{k} 7 7 2 3 3 2 3 3 3 2
S_{3} 3 2 3 3 3 3
12. 1_{k} 3_{k} 1_{k} 2_{+} 1_{k} -1 2 -38 1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{k} 3 3 1^{3} 2_{+} ∗  1^{2} 1_{k} 7 7 2 3 3 2 3 3 3 2
S_{3}  3 3 2 3 3 3
13. 1_{k} 3_{k} 3_{k} 2_{+} 1_{k} 0 15 -110 1^{2} 3_{k} −2∗ −2∗ 1^{3} 3_{k} 3  1^{3} 2_{+} ∗  1^{2} 1_{k} 7 7 2  3 2 3  2
S_{3} 3  3 3 2  3 3 3 3

Discriminant class: −42 (continued)

∞ 2 3 5 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
14. 1_{k} 3_{k} 3_{k} 2_{+} 1_{k} 0 15 -30 1^{2} 3_{k} −2∗ −2∗ 1^{3} 3_{k} 3  1^{3} 2_{+} ∗  1^{2} 1_{k} 7 7 2 3  2  3 3 2
S_{3} 3  3  2 3  3 3 3

Discriminant class: −35

∞ 2 3 5 7 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
15. 1_{k} 0_{+} 0_{+} 1_{−} 1_{k} 0 35  2 0_{+} ∗ ∗  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 7 7  2 2  2 2
C_{2} 2  2 2  2 2 2 2
16. 1_{k} 2_{+} 0_{+} 1_{−} 1_{k} 0 2 -2 1^{3} 2_{+} ∗  3 0_{+} 1  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 7 7 3 3 3 2 2 3 2 2
S_{3}  2 2 3 2 2 2 2
17. 1_{k} 0_{+} 4_{+} 1_{−} 1_{k} 0 -12 -19 2 0_{+} ∗ ∗ 1^{3} 4_{+} 1 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 7 7 3 3 3 2 2 2 2
S_{3} 3  2 2 3 2 2 2 2 3
18. 1_{k} 2_{+} 4_{+} 1_{−} 1_{k} 0 -12 -26 1^{3} 2_{+} ∗ 1^{3} 4_{+} 1 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 7 7 3 2 2 3 2 2
S_{3} 3  2 2 3 2 2 2 2 3
19. 1_{k} 2_{+} 4_{+} 1_{−} 1_{k} 0 -12 -44 1^{3} 2_{+} ∗  1^{3} 4_{+} 1  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 7 7  3 3 2 2 3 2 2
S_{3} 3  2 2  2 2 2 2 3

Discriminant class: −30

∞ 2 3 5 7 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
20. 1_{k} 3_{+} 1_{i} 1_{+} 0_{+} 0 30  1^{2} 3_{+} 2 2 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{+} 5 5 2 0_{+} ∗ ∗  2
C_{2} 4  2  2  2  2
21. 1_{k} 3_{+} 3_{i} 1_{+} 0_{+} 0 3 -6 1^{2} 3_{+} 2 2 1^{3} 3_{i} 3∗  1^{2} 1_{+} 5 5 2 0_{+} ∗ ∗ 3 3 3 2 3 3 3
S_{3}  2 3 3 2  2  2
22. 1_{k} 3_{+} 5_{i} 1_{+} 0_{+} 0 18 -24 1^{2} 3_{+} 2 2 1^{3} 5_{i} 3∗  1^{2} 1_{+} 5 5 2 0_{+} ∗ ∗ 3 3  2 3  3 3
S_{3}  2  3 2 3 2 3 2
23. 1_{k} 3_{+} 5_{i} 1_{+} 0_{+} 0 27 -18 1^{2} 3_{+} 2 2 1^{3} 5_{i} 3∗  1^{2} 1_{+} 5 5 2 0_{+} ∗ ∗  3 3 2  3 3 3
S_{3}  2 3 3 2 3 2 3 2
24. 1_{k} 3_{+} 5_{i} 1_{+} 0_{+} 0 -18 -48 1^{2} 3_{+} 2 2 1^{3} 5_{i} 3∗  1^{2} 1_{+} 5 5 2 0_{+} ∗ ∗ 3  3 2 3 3  3
S_{3}  2 3  2 3 2 3 2

Discriminant class: −21

∞ 2 3 5 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
25. 1_{k} 2_{i} 1_{i} 0_{+} 1_{k} 0 21  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{i} 3∗ 3∗  1^{2} 1_{k} 7 7  2  2
C_{2} 4  2 2 2 2 2 2
26. 1_{k} 2_{i} 3_{i} 0_{+} 1_{k} 0 -6 -12 1^{2} 2_{i} −∗ −∗ 1^{3} 3_{i} 3∗ 3 0_{+} 1 1^{2} 1_{k} 7 7 3 2 3 3 2 3 3
S_{3}  3 2 2 2 2 2 2 3
27. 1_{k} 2_{i} 5_{i} 0_{+} 1_{k} 0 18 -12 1^{2} 2_{i} −∗ −∗ 1^{3} 5_{i} 3∗ 3 0_{+} 1 1^{2} 1_{k} 7 7 3 2 3 3 2
S_{3}  2 2 2 2 2 2 3

∞ 2 3 5 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
28. 1_{k} 2_{i} 5_{i} 0_{+} 1_{k} 0 9 -30 1^{2} 2_{i} −∗ −∗ 1^{3} 5_{i} 3∗  1^{2} 1_{k} 7 7 3 2 3 3 3 2 3 3
S_{3}  3 2 2 2 2 2 2
29. 1_{k} 2_{i} 5_{i} 0_{+} 1_{k} 0 9 -12 1^{2} 2_{i} −∗ −∗ 1^{3} 5_{i} 3∗ 3 0_{+} 1 1^{2} 1_{k} 7 7 2 3 3 2 3 3
S_{3}  3 2 2 2 2 2 2 3

Discriminant class: −15

∞ 2 3 5 7 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
30. 1_{k} 0_{+} 1_{k} 1_{−} 0_{+} 0 15  1^{2} 1_{k} 3 3 1^{2} 1_{−} 5∗ 5∗ 2 0_{+} ∗ ∗ 2 2  2  2
C_{2} 2  2 2  2  2 2
31. 1_{k} 0_{+} 3_{k} 1_{−} 0_{+} 0 3 -1 3 0_{+} 1  1^{3} 3_{k} 3  1^{2} 1_{−} 5∗ 5∗ 2 0_{+} ∗ ∗ 2 2 3 3 3 2 3 2
S_{3}  2 2  3 2 3 2 2

Discriminant class: −14

∞ 2 3 5 7 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 5  Over p = 7  11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
32. 1_{k} 3_{+} 0_{+} 0_{+} 1_{i} 0 14  1^{2} 3_{+} 2 2  1^{2} 1_{i} 7∗ 7∗ 2  2  2 2 2
C_{2} 4  2 2 2 2  2
33. 1_{k} 3_{+} 4_{+} 0_{+} 1_{i} 0 -3 -26 1^{2} 3_{+} 2 2 1^{3} 4_{+} 1  3 0_{+} 1  1^{2} 1_{i} 7∗ 7∗ 2  2 3 3 2 2 2
S_{3} 3  2 2 2 2  3 2 3

Discriminant class: −10

∞ 2 3 5 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
34. 1_{k} 3_{k} 0_{+} 1_{−} 0_{+} 0 10  1^{2} 3_{k} −2∗ −2∗ 2 0_{+} ∗ ∗ 1^{2} 1_{−} 5∗ 5∗  2  2 2
C_{2} 2  2  2 2 2
35. 1_{k} 3_{k} 0_{+} 1_{−} 2_{+} -1 5 15 1^{2} 3_{k} −2∗ −2∗ 2 0_{+} ∗ ∗ 1^{2} 1_{−} 5∗ 5∗ 1^{3} 2_{+} 1  3 3 2 3 3 2 2 3
S_{3} 3  3 2 3 3  2 2 2
36. 1_{k} 3_{k} 4_{+} 1_{−} 0_{+} 0 -3 -22 1^{2} 3_{k} −2∗ −2∗ 1^{3} 4_{+} ∗  1^{2} 1_{−} 5∗ 5∗ 3 0_{+} 1  3 2 3 3 2 2
S_{3}  3 2 3 3 3 2 2 2
37. 1_{k} 3_{k} 4_{+} 1_{−} 2_{+} 0 42 -112 1^{2} 3_{k} −2∗ −2∗ 1^{3} 4_{+} ∗  1^{2} 1_{−} 5∗ 5∗ 1^{3} 2_{+} 1  3 3 2 3  2 2 3
S_{3} 3  2 3  3 2 2 2
38. 1_{k} 3_{k} 4_{+} 1_{−} 2_{+} 0 63 -126 1^{2} 3_{k} −2∗ −2∗ 1^{3} 4_{+} ∗  1^{2} 1_{−} 5∗ 5∗ 1^{3} 2_{+} 1  3  2  3 2 2 3
S_{3} 6  3 2  3 3 2 2 2

∞ 2 3 5 7 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 5  Over p = 7  11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71

Discriminant class: −7

∞ 2 3 5 7 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 5  Over p = 7  11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
39. 1_{k} 0_{+} 0_{+} 0_{+} 1_{i} 1 2  2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 1^{2} 1_{i} 7∗ 7∗  2 2 2  2
C_{2}  2  2  2 2
40. 1_{k} 0_{+} 0_{+} 2_{+} 1_{i} -1 2 -3 3 0_{+} 1  2 0_{+} ∗ ∗ 1^{3} 2_{+} ∗  1^{2} 1_{i} 7∗ 7∗ 3 2 2 2 3 3 2 3
S_{3}  2 3 2  2 2 3 3
41. 1_{k} 0_{+} 4_{+} 0_{+} 1_{i} 0 -3 -5 3 0_{+} 1  1^{3} 4_{+} ∗  2 0_{+} ∗ ∗ 1^{2} 1_{i} 7∗ 7∗ 3 2 2 2  2 3
S_{3}  2 3 2 3 2 2 3 3
42. 1_{k} 0_{+} 4_{+} 2_{+} 1_{i} 0 15 -5 3 0_{+} 1  1^{3} 4_{+} ∗  1^{3} 2_{+} ∗  1^{2} 1_{i} 7∗ 7∗  2 2 2 3 3 2 3
S_{3} 3  2  2 3 2 2
43. 1_{k} 0_{+} 4_{+} 2_{+} 1_{i} 0 15 -40  1^{3} 4_{+} ∗  1^{3} 2_{+} ∗  1^{2} 1_{i} 7∗ 7∗ 3 2 2 2 3 3 2
S_{3} 3  2 3 2 3 2 2 3 3

Discriminant class: −6

∞ 2 3 5 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
44. 1_{k} 3_{−} 1_{k} 0_{+} 0_{+} 0 6  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{k} 3 3  2 2 2 2  2
C_{2} 2  2 2 2  2 2 2
45. 1_{k} 3_{−} 3_{k} 0_{+} 0_{+} 0 3 -2 1^{2} 3_{−} 2∗ 2∗ 1^{3} 3_{k} 3  3 0_{+} 1  3 0_{+} 1  3 2 2 2 2  3 2
S_{3}  2 2 2 3  2 2 2
46. 1_{k} 3_{−} 1_{k} 0_{+} 2_{+} -1 -2 -6 1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{k} 3 3 3 0_{+} 1  1^{3} 2_{+} 1  3 2 2 2 2 3 3 2
S_{3} 3  2 2 2 3 3 2 2 2
47. 1_{k} 3_{−} 3_{k} 0_{+} 2_{+} 0 -21 -42 1^{2} 3_{−} 2∗ 2∗ 1^{3} 3_{k} 3 3 0_{+} 1 1^{3} 2_{+} 1 2 2 2 2 3 2
S_{3} 3  2 2 2 3 3 2 2 2
48. 1_{k} 3_{−} 3_{k} 0_{+} 2_{+} 0 -21 -70 1^{2} 3_{−} 2∗ 2∗ 1^{3} 3_{k} 3  1^{3} 2_{+} 1  3 2 2 2 2 3 3 2
S_{3} 3  2 2 2  3 2 2 2

Discriminant class: −5

∞ 2 3 5 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
49. 1_{k} 2_{i} 0_{+} 1_{+} 0_{+} 0 5  1^{2} 2_{i} −∗ −∗  1^{2} 1_{+} 5 5  2 2 2 2  2 2
C_{2} 2  2 2  2
50. 1_{k} 2_{i} 0_{+} 1_{+} 2_{+} -1 5 -13 1^{2} 2_{i} −∗ −∗ 3 0_{+} 1  1^{2} 1_{+} 5 5 1^{3} 2_{+} 1  2 2 2 2 3 3 2 2
S_{3} 3  3 3  2 2 3 3 2
51. 1_{k} 2_{i} 4_{+} 1_{+} 0_{+} 0 -3 -8 1^{2} 2_{i} −∗ −∗ 1^{3} 4_{+} 1  1^{2} 1_{+} 5 5 3 0_{+} 1  2 2 2 2 3 3 2 2
S_{3} 3  3  3 2 2 3 3 2
52. 1_{k} 2_{i} 4_{+} 1_{+} 2_{+} 0 -63 -252 1^{2} 2_{i} −∗ −∗ 1^{3} 4_{+} 1  1^{2} 1_{+} 5 5 1^{3} 2_{+} 1  2 2 2 2  3 2 2
S_{3} 9  3 3 3 2 2  2
53. 1_{k} 2_{i} 4_{+} 1_{+} 2_{+} 0 42 -28 1^{2} 2_{i} −∗ −∗ 1^{3} 4_{+} 1  1^{2} 1_{+} 5 5 1^{3} 2_{+} 1  2 2 2 2 3  2 2
S_{3} 9  3 3 2 2 3 3 2

Discriminant class: −3

∞ 2 3 5 7 a_{1} a_{2}  a_{3} Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
54. 1_{k} 0_{+} 1_{i} 0_{+} 0_{+} 1 1  2 0_{+} ∗ ∗ 1^{2} 1_{i} 3∗ 3∗ 2 0_{+} ∗ ∗  2  2  2 2
C_{2}  2  2 2 2  2
55. 1_{k} 2_{+} 3_{i} 0_{+} 0_{+} 0 0  -2 1^{3} 2_{+} ∗  1^{3} 3_{i} 3∗  2 0_{+} ∗ ∗ 3 0_{+} 1  2 3 2 3 2 2  3
S_{3}  2  2 2 2 3 3 2
56. 1_{k} 0_{+} 5_{i} 0_{+} 0_{+} 0 0  -3 2 0_{+} ∗ ∗ 1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 3 0_{+} 1  2 3 2 3 2 2 3 3
S_{3}  2 3 2 2 2  2
57. 1_{k} 2_{+} 1_{i} 2_{+} 0_{+} -1 -3  -3 1^{3} 2_{+} ∗  1^{2} 1_{i} 3∗ 3∗ 1^{3} 2_{+} ∗  3 0_{+} 1  2 3 2 3 2 2 3
S_{3}  2 3 2 2 2 3 3 2
58. 1_{k} 2_{+} 1_{i} 0_{+} 2_{+} -1 5  1 1^{3} 2_{+} ∗  1^{2} 1_{i} 3∗ 3∗ 2 0_{+} ∗ ∗ 1^{3} 2_{+} 1  2 3 2 3 2 2 3 3
S_{3} 3  2 3 2 2 2  3 2
59. 1_{k} 0_{+} 3_{i} 2_{+} 0_{+} 0 0  -5 2 0_{+} ∗ ∗ 1^{3} 3_{i} 3∗  1^{3} 2_{+} ∗  3 0_{+} 1  2  2 3 2 2 3 3
S_{3}  2 3 2 2 2 3  2
60. 1_{k} 2_{+} 5_{i} 0_{+} 0_{+} 0 0  -6 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗  2 3 2 3 2 2 3
S_{3}  2 3 2 2 2 3 3 2
61. 1_{k} 2_{+} 5_{i} 0_{+} 0_{+} 0 0 -12 1^{3} 2_{+} ∗ 1^{3} 5_{i} 3∗ 2 0_{+} ∗ ∗ 3 0_{+} 1 2 2 2 2 3 3
S_{3}  2 3 2 2 2 3 3 2
62. 1_{k} 0_{+} 3_{i} 0_{+} 2_{+} 0 0 -7 2 0_{+} ∗ ∗ 1^{3} 3_{i} 3∗ 2 0_{+} ∗ ∗ 1^{3} 2_{+} 1 2 3 2 2 2 3 3
S_{3} 3  2 3 2 2 2 3 3 2
63. 1_{k} 2_{+} 3_{i} 2_{+} 0_{+} 0 0 -20 1^{3} 2_{+} ∗  1^{3} 3_{i} 3∗  1^{3} 2_{+} ∗  2 3 2  2 2 3 3
S_{3} 3  2 3 2 2 2  3 2
64. 1_{k} 0_{+} 1_{i} 2_{+} 2_{+} 0 0 -35 2 0_{+} ∗ ∗ 1^{2} 1_{i} 3∗ 3∗ 1^{3} 2_{+} ∗  1^{3} 2_{+} 1  2 3 2 3 2 2  3
S_{3} 3  2  2 2 2 3 3 2
65. 1_{k} 2_{+} 3_{i} 0_{+} 2_{+} 0 0 -14 1^{3} 2_{+} ∗  1^{3} 3_{i} 3∗  2 0_{+} ∗ ∗ 1^{3} 2_{+} 1  2  2 3 2 2 3
S_{3} 3  2 3 2 2 2 3  2
66. 1_{k} 0_{+} 5_{i} 2_{+} 0_{+} 0 0 -15 2 0_{+} ∗ ∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 3 2 3 2 2  3
S_{3} 2  2 3 2 2 2 3  2
67. 1_{k} 0_{+} 5_{i} 2_{+} 0_{+} 0 0 -45 2 0_{+} ∗ ∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  3 0_{+} 1  2 3 2  2 2 3
S_{3}  2  2 2 2 3  2
68. 1_{k} 0_{+} 5_{i} 0_{+} 2_{+} 0 0 -63 2 0_{+} ∗ ∗ 1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 1^{3} 2_{+} 1  2 3 2 3 2 2
S_{3} 6  2 3 2 2 2 3 3 2
69. 1_{k} 0_{+} 5_{i} 0_{+} 2_{+} 0 0 -21 2 0_{+} ∗ ∗ 1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 1^{3} 2_{+} 1  2  2 3 2 2 3 3
S_{3} 3  2  2 2 2 3 3 2
70. 1_{k} 2_{+} 1_{i} 2_{+} 2_{+} -1 -23  57 1^{3} 2_{+} ∗  1^{2} 1_{i} 3∗ 3∗ 1^{3} 2_{+} ∗  1^{3} 2_{+} 1  2  2  2 2 3 3
S_{3} 3  2 3 2 2 2 3  2
71. 1_{k} 2_{+} 5_{i} 2_{+} 0_{+} 0 0 -90 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2  2 3 2 2 3 3
S_{3} 3  2  2 2 2 3 3 2
72. 1_{k} 2_{+} 5_{i} 2_{+} 0_{+} 0 0 -150 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  3 0_{+} 1  2 3 2 3 2 2 3 3
S_{3} 3  2  2 2 2  3 2
73. 1_{k} 2_{+} 5_{i} 2_{+} 0_{+} 0 0 -30 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  3 0_{+} 1  2 3 2  2 2  3
S_{3} 3  2 3 2 2 2 3 3 2
74. 1_{k} 2_{+} 5_{i} 2_{+} 0_{+} 0 0 -60 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  3 0_{+} 1  2  2 3 2 2
S_{3} 3  2 3 2 2 2  3 2
75. 1_{k} 0_{+} 3_{i} 2_{+} 2_{+} 0 0 -175 2 0_{+} ∗ ∗ 1^{3} 3_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} 1  2 3 2 3 2 2 3
S_{3} 3  2 3 2 2 2  3 2
76. 1_{k} 2_{+} 5_{i} 0_{+} 2_{+} 0 0 -252 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 1^{3} 2_{+} 1  2  2 3 2 2  3
S_{3} 6  2 3 2 2 2  3 2

∞ 2 3 5 7 a_{1} a_{2}  a_{3} Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
77. 1_{k} 2_{+} 5_{i} 0_{+} 2_{+} 0 0 -84 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 1^{3} 2_{+} 1  2 3 2  2 2 3
S_{3} 3  2  2 2 2  3 2
78. 1_{k} 2_{+} 5_{i} 0_{+} 2_{+} 0 0 -42 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 1^{3} 2_{+} 1  2 3 2 3 2 2 3 3
S_{3} 3  2  2 2 2 3  2
79. 1_{k} 2_{+} 5_{i} 0_{+} 2_{+} 0 0 -126 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 1^{3} 2_{+} 1  2 3 2  2 2  3
S_{3} 9  2 3 2 2 2 3  2
80. 1_{k} 2_{+} 3_{i} 2_{+} 2_{+} 0 0 -490 1^{3} 2_{+} ∗  1^{3} 3_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} 1  2 3 2 3 2 2 3 3
S_{3} 9  2 3 2 2 2 3 3 2
81. 1_{k} 2_{+} 3_{i} 2_{+} 2_{+} 0 0 -140 1^{3} 2_{+} ∗  1^{3} 3_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} 1  2 3 2  2 2
S_{3} 9  2  2 2 2 3 3 2
82. 1_{k} 2_{+} 3_{i} 2_{+} 2_{+} 0 0 -70 1^{3} 2_{+} ∗  1^{3} 3_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} 1  2  2 3 2 2  3
S_{3} 9  2  2 2 2  2
83. 1_{k} 0_{+} 5_{i} 2_{+} 2_{+} 0 0 -525 2 0_{+} ∗ ∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} 1  2  2  2 2  3
S_{3} 9  2 3 2 2 2  3 2
84. 1_{k} 0_{+} 5_{i} 2_{+} 2_{+} 0 0 -735 2 0_{+} ∗ ∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} 1  2 3 2 3 2 2 3 3
S_{3} 3  2  2 2 2  3 2
85. 1_{k} 0_{+} 5_{i} 2_{+} 2_{+} 0 0 -105 2 0_{+} ∗ ∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} 1  2  2 3 2 2 3
S_{3} 6  2 3 2 2 2 3 3 2
86. 1_{k} 0_{+} 5_{i} 2_{+} 2_{+} 0 0 -315 2 0_{+} ∗ ∗ 1^{3} 5_{i} 3∗ 1^{3} 2_{+} ∗ 1^{3} 2_{+} 1 2 3 2 2 2 3 3
S_{3} 3  2 3 2 2 2 3 3 2
87. 1_{k} 2_{+} 5_{i} 2_{+} 2_{+} 0 0 -2940 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} 1  2 3 2 3 2 2 3 3
S_{3} 18  2  2 2 2 3  2
88. 1_{k} 2_{+} 5_{i} 2_{+} 2_{+} 0 0 -1470 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} 1  2  2  2 2 3
S_{3} 9  2  2 2 2 3 3 2
89. 1_{k} 2_{+} 5_{i} 2_{+} 2_{+} 0 0 -630 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} 1  2 3 2 3 2 2 3
S_{3} 9  2 3 2 2 2  2
90. 1_{k} 2_{+} 5_{i} 2_{+} 2_{+} 0 0 -2100 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} 1  2 3 2 3 2 2  3
S_{3} 9  2 3 2 2 2 3 3 2
91. 1_{k} 2_{+} 5_{i} 2_{+} 2_{+} 0 0 -1050 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} 1  2 3 2 3 2 2
S_{3} 18  2 3 2 2 2 3  2
92. 1_{k} 2_{+} 5_{i} 2_{+} 2_{+} 0 0 -1260 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} 1  2  2 3 2 2 3 3
S_{3} 9  2 3 2 2 2 3 3 2
93. 1_{k} 2_{+} 5_{i} 2_{+} 2_{+} 0 0 -210 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} 1  2 3 2  2 2 3 3
S_{3} 18  2 3 2 2 2  2
94. 1_{k} 2_{+} 5_{i} 2_{+} 2_{+} 0 0 -420 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} 1  2 3 2 3 2 2 3 3
S_{3} 9  2 3 2 2 2 3 3 2

Discriminant class: −2

∞ 2 3 5 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
95. 1_{k} 3_{i} 0_{+} 0_{+} 0_{+} 0 2  1^{2} 3_{i} −2 −2  2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗  2  2 2 2 2
C_{2}  2 2  2  2
96. 1_{k} 3_{i} 0_{+} 2_{+} 0_{+} -1 2 2 1^{2} 3_{i} −2 −2 3 0_{+} 1  1^{3} 2_{+} ∗  2 0_{+} ∗ ∗ 3 2 3 3 2 2 2 2
S_{3}  3  2 2  2 3 2
97. 1_{k} 3_{i} 4_{+} 0_{+} 0_{+} 0 -3 -10 1^{2} 3_{i} −2 −2 1^{3} 4_{+} 1  2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 3 2 3 3 2 2 2 2
S_{3} 3  3 3 2 2 3 2 3 2

∞ 2 3 5 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
98. 1_{k} 3_{i} 4_{+} 2_{+} 0_{+} 0 15 -10 1^{2} 3_{i} −2 −2 1^{3} 4_{+} 1  1^{3} 2_{+} ∗  2 0_{+} ∗ ∗ 3 2 3  2 2 2 2
S_{3} 3  3 2 2 3 2  2
99. 1_{k} 3_{i} 4_{+} 2_{+} 0_{+} 0 -30 -80 1^{2} 3_{i} −2 −2 1^{3} 4_{+} 1  1^{3} 2_{+} ∗  2 0_{+} ∗ ∗  2  3 2 2 2 2
S_{3} 3  3 3 2 2 3 2 3 2

Discriminant class: −1

∞ 2 3 5 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
100. 1_{k} 2_{i} 0_{+} 0_{+} 0_{+} 0 1  1^{2} 2_{i} −1 −1 2 0_{+} ∗ ∗  2 0_{+} ∗ ∗ 2  2 2  2
C_{2}  2 2  2  2 2
101. 1_{k} 2_{i} 4_{+} 0_{+} 0_{+} 0 -3 -4 1^{2} 2_{i} −1 −1 1^{3} 4_{+} ∗  3 0_{+} 1  2 0_{+} ∗ ∗ 2 3 3 2 2 3 2 3
S_{3}  2 2  2 3 2 2

Discriminant class: 1

∞ 2 3 5 7 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
102. 0_{+} 0_{+} 0_{+} 0_{+} 2_{+} -1 -2 1 3 0_{+} 1 3 0_{+} 1 3 0_{+} 1 1^{3} 2_{+} 1 3 3 3 3 3 3
C_{3}  3 3 3 3 3
103. 0_{+} 0_{+} 4_{+} 0_{+} 0_{+} 0 -3 1 3 0_{+} 1  1^{3} 4_{+} 1  3 0_{+} 1  3 0_{+} 1  3 3  3 3 3
C_{3}  3 3 3  3 3 3
104. 0_{+} 0_{+} 4_{+} 0_{+} 2_{+} 0 -21 -28  1^{3} 4_{+} 1  3 0_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3 3  3
C_{3} 3  3 3  3
105. 0_{+} 0_{+} 4_{+} 0_{+} 2_{+} 0 -21 35 3 0_{+} 1  1^{3} 4_{+} 1  1^{3} 2_{+} 1  3 3 3  3 3 3
C_{3} 3  3 3 3 3 3 3 3

Discriminant class: 2

∞ 2 3 5 7 a_{1} a_{2}  a_{3} Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
106. 0_{+} 3_{+} 0_{+} 0_{+} 0_{+} 0 -2  1^{2} 3_{+} 2 2 2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗  2 2  2  2  2
C_{2}  2  2 2 2 2
107. 0_{+} 3_{+} 0_{+} 2_{+} 2_{+} -1 -23 -13 1^{2} 3_{+} 2 2 2 0_{+} ∗ ∗ 1^{3} 2_{+} ∗  1^{3} 2_{+} 1  2 2 3 2 3 2 3 2
S_{3} 3  3 2 3 2 2 2 2 3
108. 0_{+} 3_{+} 4_{+} 2_{+} 0_{+} 0 -30 -40 1^{2} 3_{+} 2 2 1^{3} 4_{+} ∗ 1^{3} 2_{+} ∗ 3 0_{+} 1 2 2 3 2 2 2
S_{3}  3 2 3 2 2 2 2
109. 0_{+} 3_{+} 4_{+} 0_{+} 2_{+} 0 -21 -14 1^{2} 3_{+} 2 2 1^{3} 4_{+} ∗ 2 0_{+} ∗ ∗ 1^{3} 2_{+} 1 2 2 2 3 2 3 2
S_{3} 3  3 2 3 2 2 2 2 3
110. 0_{+} 3_{+} 4_{+} 2_{+} 2_{+} 0 -210 -1120 1^{2} 3_{+} 2 2 1^{3} 4_{+} ∗  1^{3} 2_{+} ∗  1^{3} 2_{+} 1  2 2 3 2 3 2 3 2
S_{3} 3  2  2 2 2 2 3

Discriminant class: 3

∞ 2 3 5 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
111. 0_{+} 2_{i} 1_{k} 0_{+} 0_{+} 0 -3  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{k} 3 3 2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗  2 2  2 2
C_{2}  2 2  2  2
112. 0_{+} 2_{i} 3_{k} 2_{+} 0_{+} 0 -15 -20 1^{2} 2_{i} −∗ −∗ 1^{3} 3_{k} 3  1^{3} 2_{+} ∗  2 0_{+} ∗ ∗ 3 3 2 2 3 2 2 3
S_{3}  2 2 3 2 3 3 2 3

Discriminant class: 5

∞ 2 3 5 7 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
113. 0_{+} 0_{+} 0_{+} 1_{+} 0_{+} 1 -1  2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 1^{2} 1_{+} 5 5 2 0_{+} ∗ ∗  2 2  2  2
C_{2}  2 2 2  2
114. 0_{+} 2_{+} 4_{+} 1_{+} 0_{+} 0 -12 -14 1^{3} 2_{+} ∗  1^{3} 4_{+} ∗  1^{2} 1_{+} 5 5 2 0_{+} ∗ ∗ 3 2 2 3 2 3 3 2
S_{3}  3 2 2 2 3  2 3

Discriminant class: 6

∞ 2 3 5 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
115. 0_{+} 3_{k} 1_{i} 0_{+} 0_{+} 0 -6  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{i} 3∗ 3∗  2 0_{+} ∗ ∗ 2 2 2  2 2
C_{2}  2  2 2
116. 0_{+} 3_{k} 5_{i} 0_{+} 0_{+} 0 -9 -6 1^{2} 3_{k} −2∗ −2∗ 1^{3} 5_{i} 3∗  3 0_{+} 1  2 0_{+} ∗ ∗ 2 2 2 3 3 3 2 2
S_{3}  2  3 3 2 2 3 3

Discriminant class: 7

∞ 2 3 5 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
117. 0_{+} 2_{i} 0_{+} 0_{+} 1_{k} 0 -7  1^{2} 2_{i} −1 −1  2 0_{+} ∗ ∗ 1^{2} 1_{k} 7 7 2 2 2  2
C_{2}  2 2  2 2 2
118. 0_{+} 2_{i} 4_{+} 2_{+} 1_{k} 0 -75 -100 1^{2} 2_{i} −1 −1 1^{3} 4_{+} 1  1^{3} 2_{+} ∗  1^{2} 1_{k} 7 7 2 2 2 3 2  3 3
S_{3} 3  2 2  3 3 2 2 2

Discriminant class: 10

∞ 2 3 5 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
119. 0_{+} 3_{−} 0_{+} 1_{−} 0_{+} 0 -10  1^{2} 3_{−} 2∗ 2∗  1^{2} 1_{−} 5∗ 5∗ 2 0_{+} ∗ ∗ 2  2 2 2 2
C_{2} 2  2  2 2

∞ 2 3 5 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
120. 0_{+} 3_{i} 0_{+} 0_{+} 1_{k} 0 -14  1^{2} 3_{i} −2 −2 2 0_{+} ∗ ∗  1^{2} 1_{k} 7 7  2 2 2 2  2
C_{2}  2  2 2  2

Discriminant class: 15

∞ 2 3 5 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
121. 0_{+} 2_{i} 1_{i} 1_{−} 0_{+} 0 -15  1^{2} 2_{i} −1 −1 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{−} 5∗ 5∗  2  2 2 2 2 2
C_{2} 2  2  2
122. 0_{+} 2_{i} 5_{i} 1_{−} 0_{+} 0 -18 -12 1^{2} 2_{i} −1 −1 1^{3} 5_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 3 0_{+} 1  3 2 3 2 2 2 2 2
S_{3}  2 3 2 3  3 3 3
123. 0_{+} 2_{i} 3_{i} 1_{−} 2_{+} 0 -42 -84 1^{2} 2_{i} −1 −1 1^{3} 3_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 1^{3} 2_{+} 1  3 2 3 2 2 2 2 2
S_{3} 3  2  2 3 3  3 3
124. 0_{+} 2_{i} 5_{i} 1_{−} 2_{+} 0 -63 -168 1^{2} 2_{i} −1 −1 1^{3} 5_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 1^{3} 2_{+} 1  2 3 2 2 2 2 2
S_{3} 3  2 3 2  3 3  3
125. 0_{+} 2_{i} 5_{i} 1_{−} 2_{+} 0 -63 -42 1^{2} 2_{i} −1 −1 1^{3} 5_{i} 3∗  1^{2} 1_{−} 5∗ 5∗ 1^{3} 2_{+} 1  3 2  2 2 2 2 2
S_{3} 3  2 3 2 3 3 3 3

Discriminant class: 21

∞ 2 3 5 7 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 5  Over p = 7  11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
126. 0_{+} 0_{+} 1_{k} 0_{+} 1_{i} 0 -21  2 0_{+} ∗ ∗ 1^{2} 1_{k} 3 3  1^{2} 1_{i} 7∗ 7∗ 2 2  2 2 2 2
C_{2}  2  2  2
127. 0_{+} 2_{+} 3_{k} 0_{+} 1_{i} 0 -6 -2 1^{3} 2_{+} ∗  1^{3} 3_{k} 3  3 0_{+} 1  1^{2} 1_{i} 7∗ 7∗ 2 2 3 2 2 2 2 3
S_{3}  3 3 3 2 3 2  2

Discriminant class: 30

∞ 2 3 5 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
128. 0_{+} 3_{i} 1_{k} 1_{+} 0_{+} 0 -30  1^{2} 3_{i} −2 −2 1^{2} 1_{k} 3 3 1^{2} 1_{+} 5 5  2  2  2
C_{2} 2  2 2 2 2 2 2 2
129. 0_{+} 3_{i} 3_{k} 1_{+} 2_{+} 0 -42 -56 1^{2} 3_{i} −2 −2 1^{3} 3_{k} 3 1^{2} 1_{+} 5 5 1^{3} 2_{+} 1 2 3 3 3 2 2
S_{3} 3  2 2 2 2 2 2 2 3

Discriminant class: 35

∞ 2 3 5 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  Over p = 7  11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
130. 0_{+} 2_{i} 0_{+} 1_{−} 1_{i} 0 -35  1^{2} 2_{i} −∗ −∗ 2 0_{+} ∗ ∗ 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{i} 7∗ 7∗ 2  2
C_{2} 2  2  2 2  2  2

∞ 2 3 5 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  Over p = 7  11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
131. 0_{+} 3_{−} 1_{i} 0_{+} 1_{i} 0 -42  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{i} 3∗ 3∗ 2 0_{+} ∗ ∗ 1^{2} 1_{i} 7∗ 7∗  2  2 2
C_{2} 2  2  2  2 2
132. 0_{+} 3_{−} 5_{i} 0_{+} 1_{i} 0 -27 -30 1^{2} 3_{−} 2∗ 2∗ 1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 1^{2} 1_{i} 7∗ 7∗ 3 3 3  2 3 2 2
S_{3}  3 2 3 3 2 3 2 2
133. 0_{+} 3_{−} 3_{i} 2_{+} 1_{i} 0 -45 -110 1^{2} 3_{−} 2∗ 2∗ 1^{3} 3_{i} 3∗ 1^{3} 2_{+} ∗ 1^{2} 1_{i} 7∗ 7∗ 3 3 3 2 3 2 2
S_{3}  2 3 3 2 3 2 2
134. 0_{+} 3_{−} 5_{i} 2_{+} 1_{i} 0 -45 -30 1^{2} 3_{−} 2∗ 2∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{2} 1_{i} 7∗ 7∗ 3  3 3 2  2 2
S_{3}  3 2 3 3 2  2 2
135. 0_{+} 3_{−} 5_{i} 2_{+} 1_{i} 0 -90 -240 1^{2} 3_{−} 2∗ 2∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{2} 1_{i} 7∗ 7∗ 3 3  3 2 3 2 2
S_{3}  3 2  2 3 2 2

Discriminant class: 70

∞ 2 3 5 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 5  Over p = 7  11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
136. 0_{+} 3_{k} 0_{+} 1_{+} 1_{i} 0 -70  1^{2} 3_{k} −2∗ −2∗  1^{2} 1_{+} 5 5 1^{2} 1_{i} 7∗ 7∗  2  2  2
C_{2} 2  2 2 2  2  2 2

Discriminant class: 105

∞ 2 3 5 7 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
137. 0_{+} 0_{+} 1_{i} 1_{+} 1_{k} 0 -105  1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{+} 5 5 1^{2} 1_{k} 7 7 2  2 2  2 2 2
C_{2} 2  2 2  2 2 2
138. 0_{+} 0_{+} 5_{i} 1_{+} 1_{k} 0 -27 -9 3 0_{+} 1  1^{3} 5_{i} 3∗  1^{2} 1_{+} 5 5 1^{2} 1_{k} 7 7 2 3 2 2 3 2 2 2
S_{3}  2 2  3 2 2 2

Discriminant class: 210

∞ 2 3 5 7 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 5  Over p = 7 11 13 17 19 23 29 31 37
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 41 43 47 53 59 61 67 71
139. 0_{+} 3_{+} 1_{k} 1_{−} 1_{k} 0 -210  1^{2} 3_{+} 2 2 1^{2} 1_{k} 3 3 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 7 7  2 2  2
C_{2} 4  2 2 2  2