Quintic Fields Unramified Outside of {∞, 2, 3, 7}

Discriminant class: −42

∞  2 3 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 7  5 11 13 17 19 23 29 31
G  h  a_{4} a_{5}  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} 9_{i} 5_{i} 1_{k} -2 -4 16 1^{4} 9_{i} −2∗ −∗ 1^{3} 5_{i} 3∗  3 0_{+} 1  4 32 5 5 32 5 5 5
S_{5}  -11 2  2 0_{+} ∗ ∗ 1^{2} 1_{k} 7 7 4 3 22 4 3 22 5 22
2. 1_{k} 11_{i} 5_{k} 1_{i} -1 -8 0 1^{4} 11_{i} −2∗ 2∗ 1^{3} 4_{+} 1  1^{2} 1_{i} 7∗ 7∗ 32 4 5 5 4 5 5 5
S_{5} 6 -6 1^{2} 1_{k} 3 3 2 0_{+} ∗ ∗ 4 5 3 32 5 5 5 3
3. 1_{k} 9_{k} 3_{i} 3_{i} -2 -10 12 1^{4} 9_{k} −2∗ −∗ 1^{3} 3_{i} 3∗  1^{4} 3_{i} 7 7∗ 4 32 5 5 4 5 22 5
S_{5} 30 12 2 0_{+} ∗ ∗ 4 22 3 4 5 5 3 22
4. 1_{k} 11_{i} 3_{k} 3_{i}  0 -10 20 1^{4} 11_{i} −2∗ −2 1^{4} 3_{k} 3 3∗ 1^{4} 3_{i} 7 7∗ 4 32 3 3 32 5 5 5
S_{5} 27 4 32 5 5 4 5 5 22 5
5. 1_{k} 11_{k} 3_{i} 3_{i} -2 -10 0 1^{4} 11_{k} −2∗ −2 1^{3} 3_{i} 3∗  1^{4} 3_{i} 7 7∗ 4 4 5 3 4 22 22 5
S_{5}  27 54  2 0_{+} ∗ ∗  4 5 5 4 5 5 22 3
6. 1_{k} 11_{k} 5_{k} 3_{k} -1 -26 106 1^{4} 11_{k} −2∗ −2 1^{3} 4_{+} 1  1^{3} 2_{+} 1  4 4 5 5 2 3 5 22
S_{5}  -97 25  1^{2} 1_{k} 3 3 1^{2} 1_{k} 7 7 4 5 22 4 22 5 22 22
7. 1_{k} 11_{i} 5_{i} 3_{k} -1 -2 -6 1^{4} 11_{i} −2∗ 2∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  4 32 22 5 4 3 5 3
S_{5}  -21 21  2 0_{+} ∗ ∗ 1^{2} 1_{k} 7 7 2 5 3 4 5 22 22 22

Discriminant class: −21

∞  2 3 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 7 5 11 13 17 19 23 29 31
G  h  a_{4} a_{5}  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
8. 1_{k} 10_{k} 3_{i} 3_{i} 0 -10 -8 1^{4} 10_{k} −∗ −2∗ 1^{4} 3_{i} 3∗ 3 1^{4} 3_{i} 7 7∗ 5 3 32 5 5 5 32 3
S_{5}  27 32  5 3 4 4 4 4 4 4
9. 1_{k} 10_{k} 3_{k} 3_{k} 0 -2 -24 1^{4} 10_{k} −∗ −2 1^{3} 3_{k} 3  1^{3} 2_{+} 1  5 5 4 3 5 22 2 5
S_{5}  51 -24  2 0_{+} ∗ ∗ 1^{2} 1_{k} 7 7 5 5 4 32 32 4 2 4
10. 1_{k} 10_{i} 5_{i} 3_{k} -1 -12 8 1^{4} 10_{i} −∗ −2 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  5 5 4 22 5 22 32 22
S_{5}  22 18  1^{2} 1_{k} 7 7 22 3 4 4 32 4 4 4

Discriminant class: −14

∞  2 3 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 7  5 11 13 17 19 23 29 31
G  h  a_{4} a_{5}  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
11. 1_{k} 11_{−} 4_{−} 1_{i}  0 -6 -4 1^{4} 11_{−} 2 −2 1^{3} 3_{i} 3∗  3 0_{+} 1  5 32 5 4 5 5 4 32
S_{5}  -15 -12  1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{i} 7∗ 7∗ 2 4 32 4 4 5 3 4
12. 1_{k} 11_{−} 4_{−} 3_{i}  0 6 4 1^{4} 11_{−} 2 −2 1^{3} 3_{k} 3  1^{3} 2_{+} 1  22 4 5 32 5 3 4 32
S_{5}  -87 -12  1^{2} 1_{k} 3 3 1^{2} 1_{i} 7∗ 7∗ 32 4 4 32 4 5 3 4
13. 1_{k} 11_{−} 4_{−} 3_{i} -1 -2 50 1^{4} 11_{−} 2 2 1^{3} 3_{i} 3∗  1^{3} 2_{+} 1  3 4 22 4 5 5 32 4
S_{5}  -77 -91  1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{i} 7∗ 7∗ 4 32 32 32 32 22 3 32

Discriminant class: −7

∞ 2 3 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 7  5 11 13 17 19 23 29 31
G h  a_{4} a_{5}  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
14. 1_{k} 6_{−} 4_{+} 3_{k} 0 -6 -6 1^{4} 6_{−} 1  1^{5} 4_{+} ∗  1^{4} 3_{k} 7∗ 7 32 5 4 4 32 22 5 32
S_{5}  3 6  5 4 3 4 3 32 2 5
15. 1_{k} 8_{+} 6_{+} 3_{i} 0 -18 -4 1^{4} 8_{+} 1 {−2∗ \atop −∗} 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  4 5 32 4 4 5 5 32
S_{5}  78 48  1^{2} 1_{k} 3 3 1^{2} 1_{i} 7∗ 7∗ 5 32 5 4  4 2 5
16. 1_{k} 8_{−} 6_{+} 3_{k} -1 -14 14 1^{4} 8_{−} 1 {−2∗ \atop −1} 1^{3} 5_{i} 3∗  1^{4} 3_{k} 7∗ 7 4 5 2 4 4 5 5 32
S_{5}  70 14  1^{2} 1_{k} 3 3  5 4 5 4 5 4 4 3

Discriminant class: −6

∞  2 3 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 7 5 11 13 17 19 23 29 31
G  h  a_{4} a_{5}  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
17. 1_{k} 11_{+} 5_{i} 0_{+} 0 -2 -4 1^{4} 11_{+} 2∗ 2∗ 1^{3} 5_{i} 3∗  5 0_{+} 1  5 3 32 32 32 32 3 5
S_{5}  -9 -4  2 0_{+} ∗ ∗  4 4 4 4 22 5 4 32

Discriminant class: −3

∞ 2 3 7 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 7 5 11 13 17 19 23 29 31
G h  a_{4} a_{5}  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
18. 1_{k} 8_{+} 5_{i} 2_{+} -2 -8 20 1^{4} 8_{+} ∗  1^{3} 4_{+} 1  2^{2} 2_{+} 1 V 4 4 5 32 5 32 32 5
S_{5}  -22 20  1^{2} 1_{i} 3∗ 3∗  5 4 22 32 4 4 3 22

Discriminant class: −2

∞  2 3 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 7 5 11 13 17 19 23 29 31
G  h  a_{4} a_{5}  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
19. 1_{k} 11_{k} 4_{+} 2_{−} -1  8 -8 1^{4} 11_{k} −2 −2∗ 1^{3} 4_{+} ∗  2^{2} 2_{−} ∗ ∗ 4 3 32 5 5 32 32 4
S_{5}  -40  8  2 0_{+} ∗ ∗  2 3 5 4 4 5 32 22
20. 1_{k} 3_{k} 6_{−} 4_{+} -1 -8 17 1^{2} 3_{k} −2∗ −2∗ 1^{3} 5_{i} 3∗  1^{5} 4_{+} ∗  4 5 4 5 5 4 32 32
S_{5}  13  2  2 0_{+} ∗  ∗ 1^{2} 1_{i} 3∗ 3∗  2 5 5 4 32 5 4 5
21. 1_{k} 11_{i} 2_{+} 4_{+}  0 -14 84 1^{4} 11_{i} −2  2 2^{2} 2_{+} 1 V 1^{5} 4_{+} ∗  32 3 4 5 3 32 4 4
S_{5}  -175 28  2 22 5 32 32 5 32 5
22. 1_{k} 11_{i} 6_{−} 2_{−} -2 -26 32 1^{4} 11_{i} −2  2 1^{3} 5_{i} 3∗  2^{2} 2_{−} ∗ ∗ 32 3 2 5 5 32 4 4
S_{5}  143 86  1^{2} 1_{i} 3∗ 3∗  4 5 3 32 4 5 4 22
23. 1_{k} 9_{i} 4_{+} 4_{+} -2 -4 -4 1^{4} 9_{i} −2 −∗ 1^{3} 4_{+} ∗  1^{5} 4_{+} ∗  32 3 2 3 5 32 32 32
S_{5}  5 22  2 0_{+} ∗ ∗  32 3 5 32 4 3 4 3
24. 1_{k} 9_{i} 4_{+} 4_{+} -2 -18 52 1^{4} 9_{i} −2 −∗ 1^{3} 4_{+} 1  1^{5} 4_{+} ∗  4 22 4 3 5 32 2 32
S_{5}  -2 -132  32 5 5 4 32 5 4 5
25. 1_{k} 9_{i} 4_{+} 4_{+} -2 -18 52 1^{4} 9_{i} −2 −∗ 1^{3} 4_{+} 1  1^{5} 4_{+} ∗  32 5 4 5 5 4 4 32
S_{5}  61 -258  4 22 3 4 32 5 4 3
26. 1_{k} 9_{k} 4_{−} 4_{+} -1 -8 -4 1^{4} 9_{k} −2 −∗ 1^{3} 3_{i} 3∗  1^{5} 4_{+} ∗  4 5 32 3 22 4 2 4
S_{5}  13 23  1^{2} 1_{i} 3∗ 3∗  4 3 5 4 32 3 4 5
27. 1_{k} 11_{k} 6_{−} 4_{+} -2 -32 24 1^{4} 11_{k} −2 −2∗ 1^{3} 5_{i} 3∗  1^{5} 4_{+} ∗  4 3 4 3 5 32 4 32
S_{5}  474 -804  1^{2} 1_{i} 3∗ 3∗  4 3 5 2 4 3 2 3

∞  2 3 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 7  5 11 13 17 19 23 29 31
G  h  a_{4} a_{5}  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
28. 1_{k} 6_{i} 4_{+} 2_{+} -1 -5 7 2^{2} 6_{i} −1 ∗ 1^{5} 4_{+} ∗  1^{3} 2_{+} 1  5 4 5 5 4 32 3 32
S_{5}  -7  7  2 0_{+} ∗ ∗ 22 3 32 4 5 32 5 4
29. 1_{k} 10_{i} 0_{+} 4_{+} -1 -8 -4 1^{4} 10_{i} −1 2∗ 3 0_{+} 1  1^{5} 4_{+} ∗  3 32 5 5 4 4 5 4
S_{5}  6  2  2 0_{+} ∗ ∗  3 5 4 32 3 4 22 32
30. 1_{k} 4_{i} 4_{+} 4_{+} -1 -8 10 1^{3} 2_{+} ∗  1^{5} 4_{+} ∗  1^{5} 4_{+} ∗  3 4 5 5 32 32 3 4
S_{5}  -1 -5  1^{2} 2_{i} −∗ −∗  22 5 4 32 22 32 5 32
31. 1_{k} 10_{k} 4_{+} 2_{−}  1 10 26 1^{4} 10_{k} −1 2∗ 1^{5} 4_{+} ∗  2^{2} 2_{−} ∗ ∗ 5 32 5 3 32 4 3 32
S_{5}  -1 -1  3 5 2 4 3 4 3 4
32. 1_{k} 2_{i} 6_{+} 4_{+}  0  0 7 3 0_{+} 1  1^{3} 5_{i} 3∗  1^{5} 4_{+} ∗  5 32 5 3 32 2 22 32
S_{5}  -21 -21  1^{2} 2_{i} −1 −1 1^{2} 1_{k} 3 3  3 3 32 32 3 32 3 4
33. 1_{k} 6_{i} 4_{+} 4_{+} -2 -11 38 2^{2} 6_{i} −1 ∗ 1^{5} 4_{+} ∗  1^{5} 4_{+} ∗  5 32 22 3 4 2 5 32
S_{5}  -37  8  5 5 4 32 22 4 5 4
34. 1_{k} 6_{i} 4_{+} 4_{+} -2 -11 24 1^{2} 3_{+} 2  2 1^{3} 3_{k} 3  1^{5} 4_{+} ∗  5 4 5 22 4 32 5 4
S_{5}  12 -48  1^{2} 3_{i} −2 −2 1^{2} 1_{i} 3∗ 3∗  5 5 4 32 3 4 5 32
35. 1_{k} 6_{i} 4_{+} 4_{+} -1 -1 -25 2^{2} 6_{i} −1 ∗ 1^{3} 4_{+} 1  1^{5} 4_{+} ∗  22 4 22 5 4 32 3 32
S_{5}  13 79  2 0_{+} ∗ ∗  5 5 32 4 3 4 5 4
36. 1_{k} 10_{i} 6_{+} 2_{+}  1  4 4 1^{4} 10_{i} −1 2∗ 1^{3} 5_{i} 3∗  1^{2} 1_{k} 7 7 5 4 3 5 4 4 22 32
S_{5}  -92  4  1^{2} 1_{k} 3 3 1^{2} 1_{i} 7∗ 7∗ 5 5 4 32 5 4 5 4
37. 1_{k} 10_{k} 6_{+} 2_{−} -2 -2 16 1^{4} 10_{k} −1 2 1^{3} 5_{i} 3∗  2^{2} 2_{−} ∗ ∗ 3 4 5 5 32 4 22 4
S_{5}  -47 10  1^{2} 1_{k} 3 3  22 22 32 4 3 4 22 4
38. 1_{k} 10_{i} 6_{+} 2_{+} -1 -14 62 1^{4} 10_{i} −1 2 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  5 32 3 22 2 32 5 4
S_{5}  31 -271  1^{2} 1_{k} 3 3 2 0_{+} ∗ ∗ 5 22 32 4 3 2 5 4
39. 1_{k} 10_{i} 6_{+} 2_{+} -2 -2 4 1^{4} 10_{i} −1 2∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  5 32 3 22 4 32 22 4
S_{5}  -41 34  1^{2} 1_{k} 3 3 2 0_{+} ∗ ∗ 3 3 32 32 22 4 5 4
40. 1_{k} 6_{i} 6_{+} 4_{+} -1 -8 52 2^{2} 6_{i} −1 ∗ 1^{3} 5_{i} 3∗  1^{5} 4_{+} ∗  22 2 5 5 4 4 5 2
S_{5}  83 -47  1^{2} 1_{k} 3 3  5 5 4 4 3 4 5 32
41. 1_{k} 10_{i} 4_{+} 4_{+} -1 -8 52 1^{4} 10_{i} −1 2 1^{5} 4_{+} ∗  1^{5} 4_{+} ∗  5 4 3 5 2 4 3 4
S_{5}  -106 58  3 22 32 4 3 4 5 32
42. 1_{k} 10_{i} 4_{+} 4_{+} -2 10 80 1^{4} 10_{i} −1 2 1^{3} 3_{k} 3  1^{5} 4_{+} ∗  5 32 5 5 32 4 22 2
S_{5}  -79 -118  1^{2} 1_{i} 3∗ 3∗  3 3 2 2 5 4 3 32

Discriminant class: 1

∞ 2 3 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 7 5 11 13 17 19 23 29 31
G h  a_{4} a_{5}  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
43. 2_{−} 8_{+} 6_{−} 2_{+} -2 4 0 1^{4} 8_{+} 1 {−2∗ \atop −∗} 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  5 3 3 5 5 22 5 5
A_{5}  -63 126  1^{2} 1_{i} 3∗ 3∗  5 22 5 5 3 22 5 22

Discriminant class: 2

∞  2 3 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 7  5 11 13 17 19 23 29 31
G  h  a_{4} a_{5}  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. 2_{−} 11_{−} 4_{+} 0_{+} -2 -2 8 1^{4} 11_{−} 2 2 1^{5} 4_{+} ∗  5 0_{+} 1  4 4 4 5 4 5 4 22
F_{5}  -1 -10  4 22 4 22 4 4 4 4
45. 2_{−} 11_{+} 4_{+} 2_{−} -2 -8 8 1^{4} 11_{+} 2 2 1^{5} 4_{+} ∗  1^{2} 1_{k} 7 7 4 4 4 22 4 22 4 22
F_{5}  14 -28  1^{2} 1_{k} 7 7 4 5 4 22 4 4 4 4

Discriminant class: 2 (continued)

∞  2 3 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 7  5 11 13 17 19 23 29 31
G  h  a_{4} a_{5}  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
46. 2_{−} 9_{−} 6_{+} 0_{+} -1 -2 6 1^{4} 9_{−} 2 −1 1^{3} 5_{i} 3∗  5 0_{+} 1  4 4 32 5 4 5 4 3
S_{5}  -6 6  1^{2} 1_{k} 3 3  32 5 32 5 4 32 32 2
47. 2_{−} 5_{−} 6_{+} 2_{+} -1 -5 3 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  2^{2} 2_{+} 1 V 32 4 4 5 4 5 32 3
S_{5}  6 -6  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{k} 3 3  32 3 4 22 4 4 4 4
48. 2_{−} 11_{−} 6_{+} 0_{+} -1 4 -12 1^{4} 11_{−} 2 −2 1^{3} 5_{i} 3∗  3 0_{+} 1  32 32 4 5 32 5 4 3
S_{5}  12 -12  1^{2} 1_{k} 3 3  32 3 32 22 2 4 2 4
49. 2_{−} 11_{−} 4_{+} 2_{+} 0 6 -12 1^{4} 11_{−} 2 −2 1^{5} 4_{+} ∗  1^{3} 2_{+} 1  4 4 32 5 2 3 4 5
S_{5}  33 -60  32 3 32 5 4 32 32 2
50. 2_{−} 11_{−} 4_{+} 2_{+} -2 -2 16 1^{4} 11_{−} 2 −2 1^{3} 3_{i} 3∗  2^{2} 2_{+} 1 V 4 4 32 3 4 3 2 5
S_{5} -5 94 1^{2} 1_{k} 3 3 4 5 32 3 32 32 32 4
51. 2_{−} 9_{+} 6_{+} 2_{−} -2 -2 28 1^{4} 9_{+} 2 −1 1^{3} 5_{i} 3∗  1^{2} 1_{i} 7∗ 7∗ 32 4 4 3 4 5 32 5
S_{5} -35 22 1^{2} 1_{k} 3 3 1^{2} 1_{i} 7∗ 7∗ 4 5 32 5 4 4 4 32
52. 2_{−} 9_{−} 6_{+} 2_{+} -2 16 -8 1^{4} 9_{−} 2 −1 1^{3} 5_{i} 3∗  2^{2} 2_{+} 1 V 4 4 2 3 4 22 4 5
S_{5}  37 -14  1^{2} 1_{k} 3 3  32 5 32 3 32 4 4 32
53. 2_{−} 11_{−} 6_{+} 2_{+} -2 -2 24 1^{4} 11_{−} 2 2 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  32 4 32 22 32 5 2 5
S_{5}  15 6  1^{2} 1_{k} 3 3  4 22 4 5 4 32 4 4
54. 2_{−} 11_{−} 6_{+} 2_{+} -1 -14 14 1^{4} 11_{−} 2 2 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  32 4 4 5 4 3 4 5
S_{5}  43 -67  1^{2} 1_{k} 3 3  32 5 4 5 4 4 4 2

Discriminant class: 3

∞  2 3 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 7  5 11 13 17 19 23 29 31
G  h  a_{4} a_{5}  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
55. 2_{−} 2_{i} 5_{i} 2_{+} 1 -2 -5 3 0_{+} 1  1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  32 5 5 4 4 5 4 4
S_{5}  -2 -2  1^{2} 2_{i} −∗ −∗ 2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 5 4 32 22 32 3 22 32
56. 2_{−} 10_{k} 1_{k} 2_{+} 0 -4 0 1^{4} 10_{k} −∗ −2∗ 3 0_{+} 1  1^{3} 2_{+} 1  4 5 5 4 32 5 4 4
S_{5}  10 -8  1^{2} 1_{k} 3 3 2 0_{+} ∗ ∗ 22 32 4 5 32 5 3 4
57. 2_{−} 10_{i} 5_{i} 0_{+} -2  2 4 1^{4} 10_{i} −∗ −2∗ 1^{3} 5_{i} 3∗  4 0_{+} ∗ ∗ 32 5 3 32 4 5 4 32
S_{5}  -5  2  2 0_{+} ∗ ∗  5 4 32 3 32 22 3 4
58. 2_{−} 6_{k} 1_{k} 4_{+} -1 -1 3 2^{2} 6_{k} −∗  ∗ 3 0_{+} 1  1^{5} 4_{+} ∗  4 3 3 32 4 5 32 32
S_{5}  -1 -19  1^{2} 1_{k} 3 3  5 4 32 5 4 3 22 32
59. 2_{−} 4_{k} 3_{k} 4_{+} -2  3 -4 2^{2} 4_{k} −∗  ∗ 1^{3} 3_{k} 3  1^{5} 4_{+} ∗  4 5 5 4 32 5 4 32
S_{5}  5 -6  5 32 32 5 4 22 3 4
60. 2_{−} 10_{k} 3_{i} 2_{−} 2  4 8 1^{4} 10_{k} −∗ −2∗ 1^{3} 3_{i} 3∗  2^{2} 2_{−} ∗ ∗ 32 5 3 32 4 5 32 4
S_{5}  10 -4  2 0_{+} ∗ ∗  22 4 4 3 4 3 3 32
61. 2_{−} 2_{i} 5_{i} 4_{+} -1 -1 3 1^{2} 2_{i} −1 −1 1^{3} 5_{i} 3∗  1^{5} 4_{+} ∗  4 5 3 32 4 5 32 4
S_{5}  6 -12  2 0_{+} ∗  ∗ 2 0_{+} ∗ ∗  5 4 4 3 4 22 22 32
62. 2_{−} 10_{i} 1_{i} 4_{+} -2 10 -32 1^{4} 10_{i} −∗ −2∗ 1^{2} 1_{i} 3∗ 3∗ 1^{5} 4_{+} ∗  32 5 3 4 4 3 4 32
S_{5}  33 -6  2 0_{+} ∗ ∗  5 32 4 3 4 5 5 4
63. 2_{−} 4_{i} 5_{i} 4_{+} -1 -8 -4 1^{3} 2_{+} ∗  1^{3} 4_{+} ∗  1^{5} 4_{+} ∗  32 5 5 2 4 3 4 4
S_{5}  55 -19  1^{2} 2_{i} −1 −1 1^{2} 1_{i} 3∗ 3∗  22 4 2 5 4 5 22 4
64. 2_{−} 10_{k} 5_{k} 2_{+} -1 -8 -20 1^{4} 10_{k} −∗ −2∗ 1^{3} 4_{+} 1  1^{2} 1_{k} 7 7 4 5 5 32 32 22 4 4
S_{5}  2 -2  1^{2} 1_{k} 3 3 1^{2} 1_{i} 7∗ 7∗ 3 4 4 3 32 3 22 4
65. 2_{−} 10_{i} 5_{i} 2_{+} -1 -2 -30 1^{4} 10_{i} −∗ −2∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  4 3 3 4 32 5 32 2
S_{5}  -51 -93  2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 22 32 4 5 2 3 5 32
66. 2_{−} 10_{i} 5_{i} 2_{+} -1 -8 36 1^{4} 10_{i} −∗ −2 1^{3} 4_{+} ∗  1^{2} 1_{k} 7 7 4 5 3 32 32 22 4 32
S_{5}  -54 54  1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{i} 7∗ 7∗ 5 4 4 3 4 3 5 4

∞  2 3 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 7  5 11 13 17 19 23 29 31
G  h  a_{4} a_{5}  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. 2_{−} 10_{i} 5_{i} 2_{+} -1  8 4 1^{4} 10_{i} −∗ −2∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  32 22 5 4 2 5 4 2
S_{5}  2 62  2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 5 4 32 22 4 5 3 2
68. 2_{−} 10_{i} 5_{i} 2_{+} -1 -2 26 1^{4} 10_{i} −∗ −2 1^{3} 4_{+} ∗  1^{3} 2_{+} 1  4 22 3 4 4 22 32 4
S_{5}  19  5  1^{2} 1_{i} 3∗ 3∗ 2 0_{+} ∗ ∗ 5 4 32 3 4 22 5 4
69. 2_{−} 10_{i} 5_{i} 2_{+} -2 10 -8 1^{4} 10_{i} −∗ −2 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  32 5 22 4 4 3 4 32
S_{5}  1 34  2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 3 4 32 5 32 22 5 4
70. 2_{−} 10_{k} 5_{k} 4_{+} -1 -8 52 1^{4} 10_{k} −∗ −2 1^{3} 4_{+} 1  1^{5} 4_{+} ∗  2 3 5 4 4 5 4 4
S_{5}  146 -362  1^{2} 1_{k} 3 3  5 2 2 5 4 5 3 4
71. 2_{−} 10_{i} 5_{i} 4_{+} -1 20 -88 1^{4} 10_{i} −∗ −2 1^{3} 5_{i} 3∗  1^{5} 4_{+} ∗  4 22 5 4 2 3 2 32
S_{5}  118 -782  2 0_{+} ∗ ∗  22 4 4 5 32 3 3 32
72. 2_{−} 10_{i} 5_{i} 4_{+} -2 -4 -32 1^{4} 10_{i} −∗ −2∗ 1^{3} 5_{i} 3∗  1^{5} 4_{+} ∗  32 22 22 4 4 3 4 2
S_{5}  -86 -76  2 0_{+} ∗ ∗  5 4 4 5 4 22 5 4
73. 2_{−} 10_{i} 5_{i} 4_{+} 2 -4 88 1^{4} 10_{i} −∗ −2∗ 1^{3} 5_{i} 3∗  1^{5} 4_{+} ∗  2 22 3 4 32 5 4 4
S_{5}  236 -232  2 0_{+} ∗ ∗  3 32 4 22 4 5 5 2
74. 2_{−} 10_{i} 5_{i} 4_{+} -2 10 108 1^{4} 10_{i} −∗ −2 1^{3} 5_{i} 3∗  1^{5} 4_{+} ∗  4 5 3 2 32 22 2 32
S_{5}  243 162  2 0_{+} ∗ ∗  22 4 32 22 2 5 5 4
75. 2_{−} 10_{i} 5_{i} 4_{+} -2 10 -4 1^{4} 10_{i} −∗ −2∗ 1^{3} 4_{+} ∗  1^{5} 4_{+} ∗  2 3 5 4 32 5 4 2
S_{5}  -37 50  1^{2} 1_{i} 3∗ 3∗  22 4 32 3 32 5 22 4

Discriminant class: 6

∞  2 3 7 a_{1}  a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 7 5 11 13 17 19 23 29 31
G  h  a_{4}  a_{5}  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
76. 2_{−} 5_{i} 5_{k} 2_{−} 0  3 -4 1^{3} 2_{+} ∗  1^{3} 4_{+} ∗  2^{2} 2_{−} ∗ ∗ 5 32 4 4 5 5 3 4
S_{5}  0  -6  1^{2} 3_{i} −2 −2 1^{2} 1_{k} 3 3  32 4 5 3 5 32 2 5
77. 2_{−} 11_{i} 5_{i} 0_{+} -2  4 0 1^{4} 11_{i} −2∗ 2∗ 1^{3} 4_{+} 1  4 0_{+} ∗ ∗ 5 4 32 4 5 3 5 4
S_{5}  -6  12  1^{2} 1_{i} 3∗ 3∗  32 32 3 5 3 32 2 5
78. 2_{−} 3_{k} 3_{k} 4_{+} -1  -1 -4 3 0_{+} 1  1^{3} 3_{k} 3  1^{5} 4_{+} ∗  3 32 4 32 22 5 22 4
S_{5}  -8  -5  1^{2} 3_{k} −2∗ −2∗ 2 0_{+} ∗ ∗  4 4 5 5 22 4 32 3
79. 2_{−} 9_{k} 3_{k} 2_{+} 0  -2 0 1^{4} 9_{k} −2∗ −∗ 1^{3} 3_{k} 3  1^{3} 2_{+} 1  5 4 4 32 22 5 3 4
S_{5}  6 -24  2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 4 4 22 3 5 4 4 3
80. 2_{−} 5_{i} 3_{i} 4_{+} -1  6 -4 1^{3} 2_{+} ∗  1^{4} 3_{i} 3∗ 3 1^{5} 4_{+} ∗  5 4 4 32 5 3 5 2
S_{5}  13  9  1^{2} 3_{i} −2 −2  32 4 3 3 5 4 32 3
81. 2_{−} 9_{i} 1_{i} 4_{+} -1  6 10 1^{4} 9_{i} −2∗ −∗ 3 0_{+} 1  1^{5} 4_{+} ∗  5 4 32 32 5 22 5 2
S_{5}  6  2  1^{2} 1_{i} 3∗ 3∗  4 2 5 5 3 2 4 3
82. 2_{−} 3_{k} 5_{k} 4_{+} -1  -8 17 3 0_{+} 1  1^{3} 4_{+} ∗  1^{5} 4_{+} ∗  5 2 4 2 5 5 3 4
S_{5}  -8  2  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{k} 3 3  4 32 5 22 5 4 4 5
83. 2_{−} 9_{i} 5_{i} 2_{+} -2  10 0 1^{4} 9_{i} −2∗ −∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  22 4 32 32 5 5 5 4
S_{5}  45  18  2 0_{+} ∗ ∗ 32 32 3 22 22 4 32 5
84. 2_{−} 5_{i} 5_{i} 4_{+} 2  10 32 1^{2} 3_{+} 2  2 1^{3} 5_{i} 3∗  1^{5} 4_{+} ∗  5 32 4 32 22 5 3 32
S_{5}  40 -64  1^{2} 2_{i} −∗ −∗  32 4 5 3 5 32 4 5
85. 2_{−} 5_{i} 5_{i} 4_{+} -2  10 -18 1^{2} 3_{+} 2  2 1^{3} 4_{+} 1  1^{5} 4_{+} ∗  22 4 4 32 5 5 5 4
S_{5}  33 -48  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{i} 3∗ 3∗  32 4 3 3 5 32 32 5
86. 2_{−} 5_{i} 5_{i} 4_{+} -2  10 -46 1^{3} 2_{+} ∗  1^{3} 4_{+} 1  1^{5} 4_{+} ∗  3 4 4 32 3 22 5 32
S_{5}  -16 -244  1^{2} 3_{i} −2 −2 1^{2} 1_{i} 3∗ 3∗  4 4 22 5 22 4 4 3
87. 2_{−} 11_{k} 5_{i} 2_{−} -2  -6 24 1^{4} 11_{k} −2∗ −2 1^{3} 5_{i} 3∗  2^{2} 2_{−} ∗ ∗ 5 4 4 4 5 3 22 32
S_{5}  33  18  2 32 5 3 3 4 4 5

∞  2 3 7 a_{1}  a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 7 5 11 13 17 19 23 29 31
G  h  a_{4}  a_{5}  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
88. 2_{−} 11_{i} 5_{k} 2_{−} -1  16 24 1^{4} 11_{i} −2∗ 2∗ 1^{3} 4_{+} ∗  2^{2} 2_{−} ∗ ∗ 22 32 4 32 3 5 5 32
S_{5}  6  -6  1^{2} 1_{k} 3 3  4 4 3 3 3 4 2 22
89. 2_{−} 11_{i} 5_{i} 2_{+} -1  0 -8 1^{4} 11_{i} −2∗ 2∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  22 32 32 4 22 3 3 32
S_{5}  38 -54  2 0_{+} ∗ ∗ 32 4 22 22 5 32 32 5
90. 2_{−} 9_{i} 3_{i} 4_{+} -1  6 -18 1^{4} 9_{i} −2∗ −∗ 1^{3} 3_{i} 3∗  1^{5} 4_{+} ∗  3 32 4 32 22 5 3 32
S_{5}  6 -54  32 2 22 5 3 32 4 22
91. 2_{−} 11_{k} 3_{k} 4_{+} -2  -4 24 1^{4} 11_{k} −2∗ −2 1^{3} 3_{k} 3  1^{5} 4_{+} ∗  5 4 4 4 22 22 3 2
S_{5}  54  36  2 0_{+} ∗ ∗  4 4 3 5 5 32 32 3
92. 2_{−} 11_{i} 3_{i} 4_{+} 0  14 -28 1^{4} 11_{i} −2∗ 2∗ 1^{4} 3_{i} 3∗ 3 1^{5} 4_{+} ∗  3 4 32 4 5 3 5 4
S_{5}  63 -308  32 2 22 5 22 2 2 5
93. 2_{−} 11_{i} 3_{i} 4_{+} -1  6 10 1^{4} 11_{i} −2∗ 2∗ 1^{3} 3_{i} 3∗  1^{5} 4_{+} ∗  5 2 2 32 5 3 3 4
S_{5}  -43 -117  4 32 5 5 22 4 4 5
94. 2_{−} 11_{i} 3_{i} 4_{+} -1  6 10 1^{4} 11_{i} −2∗ −2 1^{3} 3_{i} 3∗  1^{5} 4_{+} ∗  22 32 32 4 5 5 5 4
S_{5}  -1  9  4 32 3 3 5 32 32 5
95. 2_{−} 9_{k} 5_{k} 4_{+} -2  10 -32 1^{4} 9_{k} −2∗ −∗ 1^{3} 4_{+} ∗  1^{5} 4_{+} ∗  5 32 32 32 3 22 3 4
S_{5}  61 -62  1^{2} 1_{k} 3 3  32 32 5 22 22 32 2 5
96. 2_{−} 11_{i} 5_{i} 4_{+} -2 -18 80 1^{4} 11_{i} −2∗ −2 1^{3} 5_{i} 3∗  1^{5} 4_{+} ∗  3 2 4 32 5 3 22 32
S_{5}  131 -1098  4 2 5 3 5 32 2 5
97. 2_{−} 11_{i} 5_{i} 4_{+} -2  24 -32 1^{4} 11_{i} −2∗ 2∗ 1^{3} 5_{i} 3∗  1^{5} 4_{+} ∗  22 32 2 4 5 22 5 32
S_{5}  166  36  32 4 3 22 3 4 2 3
98. 2_{−} 11_{i} 5_{i} 4_{+} -2 -18 24 1^{4} 11_{i} −2∗ 2∗ 1^{3} 5_{i} 3∗  1^{5} 4_{+} ∗  3 32 32 4 22 22 22 32
S_{5}  33 162  4 4 3 5 3 32 32 3
99. 2_{−} 11_{i} 5_{i} 4_{+} -2  24 80 1^{4} 11_{i} −2∗ 2∗ 1^{3} 5_{i} 3∗  1^{5} 4_{+} ∗  5 4 32 2 5 3 22 2
S_{5}  2  -58 372  32 32 22 5 5 32 4 22

Discriminant class: 7

∞  2 3 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 7 5 11 13 17 19 23 29 31
G  h  a_{4} a_{5}  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
100. 2_{−} 10_{i} 4_{−} 1_{k} -1 -8 4 1^{4} 10_{i} −1 2∗ 1^{3} 3_{i} 3∗  3 0_{+} 1  4 32 4 32 5 4 5 5
S_{5}  14 -14  1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{k} 7 7 5 4 4 3 5 3 4 32
101. 2_{−} 2_{i} 6_{−} 3_{k} -2 -5 3 3 0_{+} 1  1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  4 4 32 4 5 4 5 5
S_{5}  12 12  1^{2} 2_{i} −1 −1 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{k} 7 7 22 32 4 5 22 5 4 4
102. 2_{−} 6_{i} 4_{−} 3_{k}  0 6 -4 2^{2} 6_{i} −1 ∗ 1^{3} 3_{k} 3  1^{3} 2_{+} 1  4 32 4 32 5 4 22 3
S_{5}  -3 12  1^{2} 1_{k} 3 3 1^{2} 1_{k} 7 7 5 4 32 3 5 5 4 4
103. 2_{−} 6_{i} 6_{−} 3_{k} -2 -5 10 2^{2} 6_{i} −1 ∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  32 2 32 4 5 32 5 5
S_{5}  19 -44  1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{k} 7 7 22 4 32 3 5 3 4 4
104. 2_{−} 6_{i} 6_{−} 3_{k} -2 -5 4 1^{2} 3_{i} −2 −2 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  32 32 4 32 5 4 3 5
S_{5}  -14 -32  1^{2} 3_{+} 2  2 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{k} 7 7 22 4 4 3 5 22 4 4
105. 2_{−} 10_{i} 4_{+} 3_{i} -1 8 0 1^{4} 10_{i} −1 2∗ 1^{3} 4_{+} ∗  1^{4} 3_{i} 7 7∗ 4 32 4 4 3 4 3 22
S_{5} 24 24 2 0_{+} ∗ ∗ 5 32 4 5 3 22 4 4
106. 2_{−} 10_{k} 4_{−} 3_{i} -2 4 0 1^{4} 10_{k} −1 2∗ 1^{3} 3_{i} 3∗  1^{4} 3_{i} 7 7∗ 32 4 32 4 5 32 22 3
S_{5} 13  6 12  1^{2} 1_{i} 3∗ 3∗  22 4 4 5 5 3 4 2
107. 2_{−} 10_{i} 4_{+} 3_{i}  0 -12 -8 1^{4} 10_{i} −1 2∗ 1^{3} 4_{+} 1  1^{4} 3_{i} 7 7∗ 32 4 4 4 3 32 22 3
S_{5}  54 72  5 32 4 5 22 5 4 32
108. 0_{+} 10_{k} 6_{−} 3_{k} -1 -26 42 1^{4} 10_{k} −1 2∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  4 32 32 4 5 4 5 5
S_{5}  21 -21  1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{k} 7 7 3 2 32 5 3 5 4 2

∞  2 3 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 7 5 11 13 17 19 23 29 31
G  h  a_{4} a_{5}  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
109. 2_{−} 10_{k} 6_{−} 3_{i} -2 4 40 1^{4} 10_{k} −1 2∗ 1^{3} 5_{i} 3∗  1^{4} 3_{i} 7 7∗ 2 4 4 32 5 32 3 5
S_{5}  -68 40  1^{2} 1_{i} 3∗ 3∗  5 4 2 22 5 5 4 2
110. 2_{−} 10_{i} 6_{−} 3_{k}  1 16 112 1^{4} 10_{i} −1 2∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  32 4 32 32 3 32 22 5
S_{5}  448 448  1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{k} 7 7 3 2 32 3 5 22 4 4

Discriminant class: 14

∞  2 3 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 7  5 11 13 17 19 23 29 31
G  h  a_{4} a_{5}  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
111. 2_{−} 5_{k} 6_{+} 1_{k} 2 -2 -10 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  3 0_{+} 1  5 5 5 32 32 4 4 5
S_{5}  -8 -4  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{k} 3 3 1^{2} 1_{k} 7 7 4 32 3 5 4 4 5 5
112. 2_{−} 9_{k} 4_{+} 1_{k} 1  4 8 1^{4} 9_{k} −2 −∗ 1^{5} 4_{+} ∗  3 0_{+} 1  3 5 5 32 32 4 32 22
S_{5}  17  5  1^{2} 1_{k} 7 7 32 4 3 5 4 4 3 5
113. 2_{−} 11_{k} 0_{+} 3_{k} 0 -2 -4 1^{4} 11_{k} −2 −2∗ 3 0_{+} 1  1^{3} 2_{+} 1  5 5 3 4 4 32 4 5
S_{5}  -5 -4  2 0_{+} ∗ ∗ 1^{2} 1_{k} 7 7 4 4 5 3 4 2 3 3
114. 2_{−} 5_{k} 4_{+} 3_{k} 1  4 -10 1^{3} 2_{+} ∗  1^{5} 4_{+} ∗  1^{3} 2_{+} 1  5 3 3 4 32 32 32 22
S_{5}  -1 -31  1^{2} 3_{k} −2∗ −2∗  1^{2} 1_{k} 7 7 4 4 5 22 4 4 22 5
115. 2_{−} 11_{k} 6_{+} 1_{k} 0  0 -8 1^{4} 11_{k} −2 −2∗ 1^{3} 5_{i} 3∗  3 0_{+} 1  5 22 22 4 4 32 4 3
S_{5}  42 -48  1^{2} 1_{k} 3 3 1^{2} 1_{k} 7 7 4 4 5 3 32 32 3 5
116. 2_{−} 11_{i} 6_{+} 1_{i} -1 -14 6 1^{4} 11_{i} −2  2 1^{3} 5_{i} 3∗  1^{2} 1_{i} 7∗ 7∗ 5 3 5 4 4 4 32 5
S_{5}  75 69  1^{2} 1_{k} 3 3 2 0_{+} ∗ ∗ 4 4 3 5 32 32 3 22
117. 2_{−} 9_{i} 4_{+} 3_{i} -2 -2 -4 1^{4} 9_{i} −2 −∗ 1^{3} 3_{i} 3∗  1^{4} 3_{i} 7 7∗ 3 22 5 4 32 4 4 22
S_{5}  -10 -28  1^{2} 1_{k} 3 3  4 32 5 5 4 32 22 3
118. 2_{−} 9_{k} 4_{+} 3_{k} -1  2 22 1^{4} 9_{k} −2 −∗ 1^{3} 4_{+} 1  1^{3} 2_{+} 1  5 22 3 4 4 2 32 22
S_{5}  -34 -94  2 0_{+} ∗ ∗ 1^{2} 1_{k} 7 7 32 4 22 3 4 4 5 5
119. 2_{−} 9_{k} 4_{+} 3_{k} -1  2 22 1^{4} 9_{k} −2 −∗ 1^{3} 4_{+} 1  1^{3} 2_{+} 1  5 5 5 4 32 4 4 5
S_{5}  4  -34 74  2 0_{+} ∗ ∗ 1^{2} 1_{k} 7 7 4 4 22 3 4 4 5 22
120. 2_{−} 9_{k} 4_{+} 3_{k} -1 16 -20 1^{4} 9_{k} −2 −∗ 1^{5} 4_{+} ∗  1^{3} 2_{+} 1  22 3 3 4 4 32 32 5
S_{5}  29 -17  1^{2} 1_{k} 7 7 32 32 22 5 4 2 5 3
121. 2_{−} 11_{i} 4_{+} 3_{i}  1  0 -16 1^{4} 11_{i} −2  2 1^{3} 4_{+} ∗  1^{4} 3_{i} 7 7∗ 5 3 22 32 4 32 32 3
S_{5}  -40 -72  2 4 3 5 32 32 5 5
122. 2_{−} 11_{k} 4_{+} 3_{k} -1  4 4 1^{4} 11_{k} −2 −2∗ 1^{3} 3_{i} 3∗  1^{3} 2_{+} 1  5 5 22 4 2 4 4 3
S_{5}  14 34  1^{2} 1_{k} 3 3 1^{2} 1_{k} 7 7 4 4 5 5 32 32 5 5
123. 2_{−} 11_{i} 4_{+} 3_{i}  2  4 0 1^{4} 11_{i} −2  2 1^{3} 3_{k} 3  1^{4} 3_{i} 7 7∗ 5 5 3 4 4 2 2 3
S_{5}  -78 -348  1^{2} 1_{i} 3∗ 3∗  4 32 5 22 4 32 5 22
124. 2_{−} 9_{k} 6_{+} 3_{k} 0 -18 -32 1^{4} 9_{k} −2 −∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  22 5 3 4 4 4 4 5
S_{5}  78 384  1^{2} 1_{k} 3 3 1^{2} 1_{k} 7 7 2 2 5 5 4 4 22 3
125. 2_{−} 11_{i} 6_{+} 3_{i} -1 -20 12 1^{4} 11_{i} −2 −2∗ 1^{3} 5_{i} 3∗  1^{4} 3_{i} 7 7∗ 22 22 3 2 32 32 4 5
S_{5} 78 66 1^{2} 1_{k} 3 3 4 32 5 3 4 4 3 5
126. 2_{−} 11_{i} 6_{+} 3_{i} -1 -14 14 1^{4} 11_{i} −2 −2∗ 1^{3} 5_{i} 3∗  1^{4} 3_{i} 7 7∗ 22 3 22 4 32 4 32 22
S_{5}  7 -175  1^{2} 1_{k} 3 3  4 32 3 3 4 32 22 22
127. 2_{−} 11_{i} 6_{+} 3_{i} -2 10 24 1^{4} 11_{i} −2  2 1^{3} 5_{i} 3∗  1^{4} 3_{i} 7 7∗ 5 5 5 2 32 32 4 5
S_{5}  33 -174  1^{2} 1_{k} 3 3  4 4 22 5 32 4 3 3

Discriminant class: 21

∞ 2 3 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 7  5 11 13 17 19 23 29 31
G h  a_{4} a_{5}  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
128. 2_{−} 4_{+} 5_{i} 1_{i} -1 2 -2 1^{5} 4_{+} ∗  1^{3} 5_{i} 3∗  3 0_{+} 1  5 32 32 3 4 4 4 32
S_{5}  -1 -1  2 0_{+} ∗ ∗ 1^{2} 1_{i} 7∗ 7∗ 5 5 22 5 32 3 2 5
129. 2_{−} 8_{−} 5_{k} 1_{i} -2 4 0 1^{4} 8_{−} ∗ −1 1^{3} 4_{+} 1  3 0_{+} 1  5 32 4 22 4 4 4 4
S_{5}  -3 6  1^{2} 1_{k} 3 3 1^{2} 1_{i} 7∗ 7∗ 5 5 5 5 4 5 32 3
130. 2_{−} 4_{+} 5_{k} 3_{k} -2 4 -2 1^{4} 4_{+} ∗  1^{3} 4_{+} 1  1^{4} 3_{k} 7∗ 7 5 4 32 22 4 4 32 4
S_{5}  -5 -2  1^{2} 1_{k} 3 3  22 5 3 22 32 5 32 5
131. 2_{−} 4_{−} 5_{i} 3_{k} -1 8 -2 2^{2} 4_{−} ∗ ∗ 1^{3} 5_{i} 3∗  1^{4} 3_{k} 7∗ 7 3 4 32 5 4 32 4 4
S_{5}  8 -4  2 0_{+} ∗ ∗  5 5 5 5 32 5 4 3
132. 2_{−} 4_{+} 5_{i} 3_{i} -1 4 -4 1^{4} 4_{+} ∗  1^{3} 4_{+} ∗  1^{3} 2_{+} 1  5 4 4 3 32 32 32 32
S_{5}  -8 -4  1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{i} 7∗ 7∗ 5 3 5 5 32 3 4 5
133. 2_{−} 4_{+} 5_{i} 3_{i} -1 -10 24 1^{5} 4_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  3 4 4 5 32 4 4 4
S_{5}  -15 3  2 0_{+} ∗ ∗ 1^{2} 1_{i} 7∗ 7∗ 22 22 5 3 32 5 4 5
134. 2_{−} 4_{+} 5_{k} 3_{k} 2 10 18 1^{5} 4_{+} ∗  1^{3} 4_{+} 1  1^{4} 3_{k} 7∗ 7 5 32 4 5 4 2 4 32
S_{5}  12 6  1^{2} 1_{k} 3 3  3 3 22 22 32 3 32 22
135. 2_{−} 8_{+} 3_{k} 3_{k} -2 -2 -4 1^{4} 8_{+} ∗  1^{4} 3_{k} 3 3∗ 1^{4} 3_{k} 7∗ 7 5 32 32 3 4 4 4 32
S_{5}  11 14  5 22 3 5 32 3 4 5
136. 2_{−} 8_{−} 3_{i} 3_{k} 2 -4 4 1^{4} 8_{−} ∗  1^{3} 3_{i} 3∗  1^{4} 3_{k} 7∗ 7 3 4 32 5 32 4 32 32
S_{5}  26 20  2 0_{+} ∗ ∗  5 22 5 22 4 3 32 22
137. 2_{−} 8_{−} 3_{k} 3_{i}  0 -4 -4 1^{4} 8_{−} ∗  1^{4} 3_{k} 3 3∗ 1^{3} 2_{+} 1  5 32 32 3 4 4 32 4
S_{5}  -6 -8  1^{2} 1_{i} 7∗ 7∗ 22 3 5 5 2 22 4 22
138. 2_{−} 6_{+} 5_{i} 3_{i} -2 8 -34 1^{4} 6_{+} ∗ −1 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  3 4 32 3 32 4 32 4
S_{5}  65 -68  2 0_{+} ∗ ∗ 1^{2} 1_{i} 7∗ 7∗ 5 5 5 22 32 3 32 5
139. 2_{−} 6_{+} 5_{i} 3_{i} -1 -2 8 1^{4} 6_{+} ∗ −∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  5 4 4 5 2 4 32 2
S_{5}  -14 14  2 0_{+} ∗ ∗ 1^{2} 1_{i} 7∗ 7∗ 5 22 5 5 4 3 32 22
140. 2_{−} 6_{−} 5_{i} 3_{k} -1 -11 17 2^{2} 6_{−} ∗ ∗ 1^{3} 4_{+} ∗  1^{4} 3_{k} 7∗ 7 3 32 4 22 32 32 4 4
S_{5}  37 -49  1^{2} 1_{i} 3∗ 3∗  5 3 5 5 2 3 32 5
141. 2_{−} 8_{+} 5_{i} 3_{i} -1 16 8 1^{4} 8_{+} ∗ −∗ 1^{3} 4_{+} ∗  1^{3} 2_{+} 1  3 32 32 5 4 4 4 32
S_{5}  64 32  1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{i} 7∗ 7∗ 3 5 22 5 4 22 4 3
142. 2_{−} 8_{−} 5_{i} 3_{k} -2 4 0 1^{4} 8_{−} ∗  1^{3} 4_{+} ∗  1^{4} 3_{k} 7∗ 7 22 4 32 5 4 4 32 4
S_{5}  -36 -72  1^{2} 1_{i} 3∗ 3∗  5 22 3 22 2 5 4 22
143. 2_{−} 8_{−} 5_{i} 3_{k} -1 8 -16 1^{4} 8_{−} ∗  1^{3} 5_{i} 3∗  1^{4} 3_{k} 7∗ 7 5 4 4 5 4 32 4 4
S_{5}  64 -32  2 0_{+} ∗ ∗  3 5 22 3 4 5 2 3
144. 2_{−} 8_{+} 5_{k} 3_{k} -2 -2 -20 1^{4} 8_{+} ∗  1^{3} 4_{+} 1  1^{4} 3_{k} 7∗ 7 5 2 4 22 32 4 4 32
S_{5}  7 -26  1^{2} 1_{k} 3 3  22 3 5 5 2 3 4 5
145. 2_{−} 8_{+} 5_{i} 3_{i}  0 -8 -4 1^{4} 8_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  5 32 32 5 4 32 4 4
S_{5}  18 -16  2 0_{+} ∗ ∗ 1^{2} 1_{i} 7∗ 7∗ 22 3 5 5 4 5 32 5
146. 2_{−} 8_{−} 5_{i} 3_{k} -1 -4 -20 1^{4} 8_{−} ∗ −1 1^{3} 5_{i} 3∗  1^{4} 3_{k} 7∗ 7 5 32 2 22 32 4 4 4
S_{5}  -28 -52  2 0_{+} ∗ ∗  3 5 22 3 32 5 32 5
147. 2_{−} 8_{+} 5_{i} 3_{i} -1 2 -6 1^{4} 8_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  22 4 32 3 4 32 4 4
S_{5}  15 -3  2 0_{+} ∗ ∗ 1^{2} 1_{i} 7∗ 7∗ 5 22 3 22 32 3 4 5

Discriminant class: 42

∞  2 3 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 7  5 11 13 17 19 23 29 31
G  h  a_{4} a_{5}  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. 2_{−} 11_{−} 3_{k} 1_{i} -2  2 0 1^{4} 11_{−} 2∗ −2∗ 1^{3} 3_{k} 3  3 0_{+} 1  4 5 3 5 5 32 5 32
S_{5}  9 -6  2 0_{+} ∗ ∗ 1^{2} 1_{i} 7∗ 7∗ 32 3 4 3 5 4 5 2

∞  2 3 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 7  5 11 13 17 19 23 29 31
G  h  a_{4} a_{5}  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
149. 2_{−} 3_{−} 5_{i} 3_{k} -2  4 -9 3 0_{+} 1  1^{3} 4_{+} 1  1^{4} 3_{k} 7∗ 7 4 5 5 3 5 32 22 4
S_{5}  9 -9  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{i} 3∗ 3∗  32 22 4 5 3 32 5 4
150. 2_{−} 11_{−} 1_{i} 3_{k} -1 -6 -2 1^{4} 11_{−} 2∗ −2∗ 3 0_{+} 1  1^{4} 3_{k} 7∗ 7 32 3 3 3 5 32 5 32
S_{5}  15 17  1^{2} 1_{i} 3∗ 3∗  4 5 32 5 3 4 5 4
151. 2_{−} 11_{−} 3_{i} 3_{k}  0  2 -36 1^{4} 11_{−} 2∗ 2∗ 1^{3} 3_{i} 3∗  1^{4} 3_{k} 7∗ 7 4 5 3 5 5 4 22 4
S_{5}  33 -12  32 5 32 3 3 32 3 32
152. 2_{−} 9_{+} 5_{i} 3_{i} -1 -2 -6 1^{4} 9_{+} 2∗ −1 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  4 5 22 5 3 4 22 32
S_{5}  42 -42  1^{2} 1_{i} 7∗ 7∗ 32 3 4 5 3 32 22 4
153. 2_{−} 9_{+} 5_{i} 3_{i}  0 -4 -24 1^{4} 9_{+} 2∗ −1 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  4 5 3 5 5 4 5 4
S_{5}  36 -48  1^{2} 1_{i} 7∗ 7∗ 2 5 4 5 5 32 3 2
154. 2_{−} 9_{−} 5_{i} 3_{k} -2 -2 -20 1^{4} 9_{−} 2∗ −1 1^{3} 4_{+} 1  1^{4} 3_{k} 7∗ 7 32 22 3 3 5 4 5 4
S_{5}  -35 -26  1^{2} 1_{i} 3∗ 3∗  4 3 32 5 22 4 5 32
155. 2_{−} 11_{−} 5_{i} 3_{k} -2  0 16 1^{4} 11_{−} 2∗ −2∗ 1^{3} 5_{i} 3∗  1^{4} 3_{k} 7∗ 7 4 22 5 5 22 32 5 2
S_{5}  -38 -132  4 3 32 5 5 32 3 32
156. 2_{−} 11_{+} 5_{i} 3_{i} -2 -8 -48 1^{4} 11_{+} 2∗ 2∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  32 5 5 3 22 32 5 4
S_{5}  168 -336  1^{2} 1_{i} 7∗ 7∗ 32 3 32 3 5 4 22 32