Old Sextic Fields Unramified Outside of {∞, 2, 5}

Discriminant class: −10

∞  2 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5 3 7 11 13 17 19 23 29
G  h  a_{4} a_{5} a_{6} f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
1.  3_{i}  9_{k} 5_{+} -2 5 -10 2^{2} 6_{+} 1 {−2 \atop −2∗} 1^{6} 5_{+} 5∗  6 22 33 22 6 33 22 222
D_{6}  2  15 -12 4 1^{2} 3_{k} −2∗ −2∗  222 22 33 222 22 22  222
2.  3_{i}  11_{k} 5_{+} -1 0 0 1^{4} 11_{k} −2∗ −2 1^{6} 5_{+} 5∗  6 22 33 42 6 33 42 4
S_{4} × C_{2}  2  10 14 16  4 22 33 2 42 42 22 222
3.  3_{i}  13_{k} 5_{+} 0 5 0 1^{4} 11_{−} 2 −2 1^{6} 5_{+} 5∗  6 42 33 22 6 33 42 222
S_{4} × C_{2}  2  10 0 10 1^{2} 2_{i} −∗ −∗  4 42 33 2 22 42  4
4.  3_{i}  13_{k} 5_{+} 0 10 0 1^{4} 10_{k} −∗ −2 1^{6} 5_{+} 5∗  6 42 33 42 6 33 22 4
S_{4} × C_{2}  2  35 0 40 1^{2} 3_{+} 2  2  222 42 33 2 42 22 22 4
5.  3_{i}  13_{k} 5_{+} 0 0 0 1^{4} 10_{k} −∗ −2∗ 1^{5} 5_{+} 5∗  4 5 33 5 6 5 33 6
S_{5}  10 24 40 1^{2} 3_{+} 2  2  4 33 5 222 5 33 5 4
6.  3_{i}  11_{k} 7_{+} 0 0 0 1^{6} 11_{k} −2∗  1^{5} 7_{+} 5∗  4 33 5 5 4 5 22 4
S_{5}  2  10 -12 10  6 5 33 4 5 22 33 4

Discriminant class: −5

∞  2 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5 3 7 11 13 17 19 23 29
G  h  a_{4} a_{5} a_{6} f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
7.  3_{i}  10_{i} 5_{−} -2 0 0 1^{4} 8_{+} 1  {−2 \atop −∗} 1^{6} 5_{−} 5  33 22 6 222 6 6 22 22
D_{6}  2  10 -12 4 1^{2} 2_{i} −∗ −∗  222 222 33  22 222 222 22
8.  3_{i}  10_{i} 5_{−} 0 5 0 1^{4} 10_{i} −∗ −2 1^{6} 5_{−} 5  33 42 6 4 6 6 22 42
S_{4} × C_{2}  2  5 0 5  222 4 33 22 42 222 2 42
9.  3_{i}  14_{i} 5_{−} 0 10 0 1^{4} 11_{−} 2 −2 1^{6} 5_{−} 5  33 42 6 222 6 6 42 22
S_{4} × C_{2}  4  40 0 80 1^{2} 3_{k} −2∗ −2∗  4 4 33 22 22 4 222 42
10.  3_{i}  14_{i} 5_{−} 0 10 0 1^{4} 11_{i} −2∗ −2 1^{6} 5_{−} 5  33 22 6 4 6 6 42 42
S_{4} × C_{2}  2  30 0 20 1^{2} 3_{+} 2  2  4 222 33 22 42 4 2 22
11.  3_{i}  12_{i} 5_{−} -2 5 0 1^{4} 9_{k} −2 −∗ 1^{5} 5_{−} 5  5 5 6 4 222 4 5 33
S_{5}  0 4 2 1^{2} 3_{−} 2∗  2∗  4 6 33 33 22 6 6 33
12.  3_{i}  12_{i} 7_{−} -2 -5 0 1^{4} 9_{i} −2∗ −∗ 1^{5} 7_{−} 5  33 33 6 4 6 4 33 5
S_{5}  20 16 8 1^{2} 3_{+} 2  2  6 4 22 22 33 6 4 5
13.  3_{i}  8_{i} 9_{−} -2 0 0 1^{4} 6_{+} ∗ −∗ 1^{5} 9_{−} 5  33 5 4 6 4 222 33 5
S_{5}  2  25 -30 10 1^{2} 2_{i} −1 −1  4 222 5 5 5 4 4 5
14.  3_{i}  10_{i} 9_{−} 2 0 0 1^{4} 8_{+} ∗ −∗ 1^{5} 9_{−} 5  5 5 4 6 6 4 22 5
S_{5}  4  50 60 220 1^{2} 2_{i} −1 −1  6 4 5 5 33 6 4 33
15.  3_{i}  10_{i} 9_{−} -2 -5 20 1^{4} 8_{+} 1 {−2∗ \atop −∗} 1^{5} 9_{−} 5  5 33 6 6 4 6 5 33
S_{5}  2  0 -56 62 1^{2} 2_{i} −∗ −∗  4 222 22 22 5 6 6 22
16.  3_{i}  10_{i} 9_{−} 2 25 60 1^{4} 8_{+} 1  {−2 \atop −∗} 1^{5} 9_{−} 5  5 5 6 4 6 222 33 22
S_{5}  2  260 384 868 1^{2} 2_{i} −∗ −∗  4 6 22 33 5 4 4 33
17.  3_{i}  12_{i} 9_{−} -2 -25 0 1^{4} 9_{i} −2∗ −∗ 1^{5} 9_{−} 5  22 33 6 222 4 4 5 5
S_{5}  200 320 160 1^{2} 3_{+} 2  2  6 6 33 5 5 6 4 33
18.  3_{i}  12_{i} 9_{−} 2 -5 -20 1^{4} 9_{i} −2∗ −∗ 1^{5} 9_{−} 5  33 33 4 4 6 4 5 5
S_{5}  175 546 517 1^{2} 3_{+} 2  2  4 4 5 5 22 222 222 33
19.  3_{i}  12_{i} 9_{−} -2 -5 20 1^{4} 9_{k} −2 −∗ 1^{5} 9_{−} 5  5 22 4 6 6 4 5 5
S_{5}  25 -46 67 1^{2} 3_{−} 2∗  2∗  4 4 22 5 5 4 6 5

Discriminant class: −2

∞  2 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5 3 7 11 13 17 19 23 29
G  h  a_{4} a_{5} a_{6} f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
20. 3_{i} 9_{k} 4_{+} 0  4 0 1^{2} 3_{i} −2 −2 2^{3} 4_{+} ∗  33 222 33 222 33 33 222 222
S_{3}  -3  0 2 1^{2} 3_{i} −2 −2  222 222 33  222 222  222
21. 3_{i} 11_{k} 4_{+} 0 -1 0 1^{4} 11_{k} −2∗ −2 2^{3} 4_{+} ∗  33 222 33 4 33 33 4 4
S_{4}^{−} 2 0 2 2 0_{+} ∗ ∗ 4 222 33 22 4 4 22 222
22. 3_{i} 13_{k} 4_{+} 0 -4 0 1^{4} 11_{−} 2 −2 2^{3} 4_{+} ∗  33 4 33 222 33 33 4 222
S_{4}^{−}  2  0 8 1^{2} 2_{i} −1 −1  4 4 33 22 222 4  4
23. 3_{i} 13_{k} 4_{+} 0  4 0 1^{4} 10_{i} −∗ −2 2^{3} 4_{+} ∗  33 4 33 4 33 33 222 4
S_{4}^{−}  7  0 2 1^{2} 3_{−} 2∗ 2∗  222 4 33 22 4 222 22 4
24. 3_{i} 11_{k} 6_{+} 0  5 0 1^{4} 11_{k} −2∗ −2 1^{5} 6_{+} ∗  5 6 5 6 5 5 6 4
S_{5}  5 -8 5 2 0_{+} ∗  ∗  222 4 5 5 4 222 5 4
25. 3_{i} 13_{k} 6_{+} -2 10 0 1^{4} 11_{−} 2 −2 1^{5} 6_{+} ∗  5 6 22 6 5 33 4 4
S_{5}  40 16 48 1^{2} 2_{i} −1 −1  4 222 33 22 4 4 5 6
26. 3_{i} 11_{k} 8_{+} -1  5 0 1^{4} 11_{k} −2∗ −2 1^{5} 8_{+} ∗  33 4 22 4 5 33 6 4
S_{5}  50 -10 10 2 0_{+} ∗  ∗  222 4 33 33 6 6 33 4
27. 3_{i} 13_{k} 8_{+} 0 -5 0 1^{4} 11_{−} 2 −2 1^{5} 8_{+} ∗  22 4 5 6 5 33 6 6
S_{5}  65 -104 255 1^{2} 2_{i} −1 −1  6 6 5 33 4 4 33 6

Discriminant class: −1

∞  2 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5 3 7 11 13 17 19 23 29
G  h  a_{4} a_{5} a_{6} f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
28.  3_{i}  10_{k} 4_{+} -2 2 4 1^{4} 8_{−} 1  {−2 \atop −1} 1^{3} 2_{+} ∗  6 222 6 22 33 6 222 22
D_{6}  1 2 2 1^{2} 2_{i} −1 −1 1^{3} 2_{+} ∗  222 22 33 222 222 22 222 22
29.  3_{i}  10_{k} 4_{+} 0 2 0 1^{4} 10_{k} −∗ −2 1^{3} 2_{+} ∗  6 4 6 42 33 6 222 42
S_{4} × C_{2}  3 0 4 2 0_{+} ∗  ∗ 1^{3} 2_{+} ∗  222 42 33 2 4 22 2 42
30.  3_{i}  14_{k} 4_{+} 0 2 0 1^{4} 11_{−} 2 −2 1^{3} 2_{+} ∗  6 4 6 22 33 6 4 22
S_{4} × C_{2}  2  18 0 4 1^{2} 3_{i} −2 −2 1^{3} 2_{+} ∗  4 42 33 2 222 42 222 42
31.  3_{i}  14_{k} 4_{+} 0 2 0 1^{4} 11_{i} −2∗ −2 1^{3} 2_{+} ∗  6 222 6 42 33 6 4 42
S_{4} × C_{2}  -2 0 4 1^{2} 3_{−} 2∗  2∗ 1^{3} 2_{+} ∗  4 22 33 2 4 42 2 22
32.  3_{i}  12_{k} 6_{+} -2 -5 20 1^{4} 9_{+} 2∗ −1 1^{5} 6_{+} 1  4 4 4 33 33 6 6 33
S_{5}  5 -54 63 1^{2} 3_{k} −2∗ −2∗  6 33 5 4 222 5 6 33
33.  3_{i}  12_{k} 6_{+} -2 -5 0 1^{4} 9_{−} 2 −1 1^{5} 6_{+} 1  6 4 4 33 5 4 6 5
S_{5}  20 20 10 1^{2} 3_{i} −2 −2  4 22 5 6 4 33 4 22
34.  3_{i}  8_{k} 8_{+} -2 0 -10 1^{6} 8_{k} −1  1^{5} 8_{+} 1  4 6 4 5 33 4 4 5
S_{5}  4  10 16 18  4 22 5 4 6 33 4 33

Discriminant class: 1

∞  2 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5 3 7 11 13 17 19 23 29
G  h  a_{4} a_{5} a_{6} f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
35. 2_{−} 12_{−} 4_{+} 0 -2 0 1^{4} 10_{i} −∗ −2 1^{3} 2_{+} ∗  33 42 33 42 33 33 22 42
S_{4}^{+} 3 0 -4 1^{2} 2_{i} −∗ −∗ 1^{3} 2_{+} ∗ 22 42 33 22 42 22 22 42
36. 2_{−} 14_{−} 4_{+} 0 -2 0 1^{4} 11_{k} −2∗ −2 1^{3} 2_{+} ∗  33 22 33 42 33 33 42 42
S_{4}^{+} -2 0 -4 1^{2} 3_{k} −2∗ −2∗ 1^{3} 2_{+} ∗ 42 22 33 22 42 42 22 22
37. 2_{−} 14_{−} 4_{+} 0 -2 0 1^{4} 11_{−} 2 −2 1^{3} 2_{+} ∗  33 42 33 22 33 33 42 22
S_{4}^{+}  18 0 -4 1^{2} 3_{+} 2  2 1^{3} 2_{+} ∗  42 42 33 22 22 42  42

Discriminant class: 1 (continued)

∞  2 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5 3 7 11 13 17 19 23 29
G  h  a_{4} a_{5} a_{6} f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
38. 2_{−} 6_{−} 6_{+} -2 0 0 3^{2} 6_{−} 1  1^{5} 6_{+} 1  5 33 33 5 33 5 22 33
A_{5}  -5 -2 -1  5 22 33 33 5 5 5 5
39. 2_{−} 6_{−} 8_{+} -2 5 0 3^{2} 6_{−} 1  1^{5} 8_{+} 1  33 5 22 5 22 5 33 5
A_{5}  0 -10 -5  33 33 22 5 5 33 5 33
40. 2_{−} 6_{−} 8_{+} 0 5 0 2 0_{+} ∗  ∗ 1^{5} 8_{+} 1  5 33 33 33 5 5 33 33
A_{5}  15 -32 -5 1^{2} 3_{+} 2  2  33 5 33 33 33 22 22 5
41. 2_{−} 6_{−} 8_{+} -2 5 0 3^{2} 6_{−} 1  1^{5} 8_{+} 1  5 5 5 33 33 5 5 22
A_{5}  0 10 5  22 33 22 22 5 22 33 5
42. 2_{−} 8_{−} 8_{+} -2 -5 20 1^{2} 2_{i} −1 −1 1^{5} 8_{+} 1  33 5 33 33 5 22 5 33
A_{5}  -45 6 -7 1^{2} 3_{−} 2∗  2∗  33 5 22 5 33 33 33 33

Discriminant class: 2

∞  2 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5 3 7 11 13 17 19 23 29
G  h  a_{4} a_{5} a_{6} f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
43.  2_{−}  11_{−} 4_{+} 0 -4  0 1^{4} 8_{−} 1  {−2 \atop −1} 2^{3} 4_{+} ∗  6 22 6 222 33 6 22 222
D_{6}  -3 0 -2 1^{2} 3_{+} 2  2  22 222 33 222 22 222 222 222
44.  2_{−}  11_{−} 4_{+} 0 4  0 1^{4} 11_{−} 2 −2 2^{3} 4_{+} ∗  6 42 6 222 33 6 42 222
S_{4} × C_{2}  2 0 -8  42 4 33 2 22 4 222 4
45.  2_{−}  13_{−} 4_{+} 0 -4  0 1^{4} 10_{k} −∗ −2 2^{3} 4_{+} ∗  6 42 6 4 33 6 22 4
S_{4} × C_{2}  7 0 -2 1^{2} 3_{k} −2∗ −2∗  22 4 33 2 42 222 2 4
46.  2_{−}  13_{−} 4_{+} 0 1  0 1^{4} 11_{i} −2∗ −2 2^{3} 4_{+} ∗  6 22 6 4 33 6 42 4
S_{4} × C_{2}  2 0 -2 1^{2} 2_{i} −∗ −∗  42 222 33 2 42 4 2 222
47.  2_{−}  11_{−} 6_{+} -2 5  0 1^{6} 11_{−} 2  1^{5} 6_{+} ∗  6 33 4 4 5 6 5 4
S_{5}  2  -5 2  1  5 4 33 6 33 6 4 4
48.  2_{−}  13_{−} 6_{+} -2 -5 20 1^{4} 11_{i} −2  2 1^{5} 6_{+} ∗  4 33 4 6 5 6 33 6
S_{5}  5 10 -45 1^{2} 2_{i} −1 −1  33 4 22 6 33 6 222 4
49.  2_{−}  11_{−} 8_{+} 0 5  0 1^{4} 11_{−} 2  2 1^{5} 8_{+} ∗  6 5 4 6 33 4 5 4
S_{5}  15 -48 -5  5 6 33 4 5 6 4 4
50.  2_{−}  11_{−} 8_{+} -2 -15 20 1^{6} 11_{−} 2  1^{5} 8_{+} ∗  4 22 6 4 5 6 33 4
S_{5}  2  55 22 -9  33 4 5 6 5 6 4 222
51.  2_{−}  13_{−} 8_{+} -2 -15 20 1^{4} 10_{i} −1  2 1^{5} 8_{+} ∗  4 5 222 6 33 4 33 222
S_{5}  105 -78 -259 1^{2} 3_{i} −2 −2  33 4 33 222 22 4 4 4

Discriminant class: 5

∞  2 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5 3 7 11 13 17 19 23 29
G  h  a_{4} a_{5} a_{6} f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
52.  2_{−}  6_{+} 5_{−} 2  0 0 2^{2} 6_{+} 1 {−2 \atop −2∗} 1^{6} 5_{−} 5  6 222 33 222 6 33 222 22
D_{6}  0  2 -1 2 0_{+} ∗  ∗  22 222 33 222 222 222  22
53.  2_{−}  12_{+} 5_{−} 0 -5 0 1^{4} 10_{k} −∗ −2 1^{6} 5_{−} 5  6 4 33 4 6 33 222 42
S_{4} × C_{2}  2  5  0 -5 1^{2} 2_{i} −1 −1  22 4 33 2 4 222 22 42
54.  2_{−}  14_{+} 5_{−} 0 -10 0 1^{4} 11_{−} 2 −2 1^{6} 5_{−} 5  6 4 33 222 6 33 4 22
S_{4} × C_{2}  2  40  0 -80 1^{2} 3_{−} 2∗ 2∗  42 4 33 2 222 4  42

Discriminant class: 5 (continued)

∞  2 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5 3 7 11 13 17 19 23 29
G  h  a_{4} a_{5} a_{6} f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
55.  2_{−}  14_{+} 5_{−} 0 -10 0 1^{4} 11_{k} −2∗ −2 1^{6} 5_{−} 5  6 222 33 4 6 33 4 42
S_{4} × C_{2}  2  30  0 -20 1^{2} 3_{i} −2 −2  42 222 33 2 4 4 22 22
56.  2_{−}  10_{+} 5_{−} -2  0 0 1^{6} 10_{+} ∗  1^{5} 5_{−} 5  6 6 5 6 4 33 4 5
S_{5}  0  4 2  22 222 33 4 4 4 5 5
57.  2_{−}  6_{+} 7_{−} -2  0 0 1^{6} 6_{+} ∗  1^{5} 7_{−} 5  6 4 33 4 222 5 6 33
S_{5}  0 -8 -4  22 6 5 4 6 4 33 22
58.  2_{−}  8_{+} 7_{−} 0 -5 0 2^{2} 6_{k} −∗  ∗ 1^{5} 7_{−} 5  4 6 5 222 6 33 4 33
S_{5}  -10 16 -20 1^{2} 2_{i} −1 −1  33 6 5 6 222 6 33 33
59.  2_{−}  4_{+} 9_{−} -1  0 5 2^{3} 4_{+} ∗  1^{5} 9_{−} 5  6 4 22 6 6 5 4 5
S_{5}  10 -27 -23  33 4 33 222 6 4 33 5
60.  2_{−}  10_{+} 7_{−} 0 -5 0 1^{6} 10_{+} ∗  1^{5} 7_{−} 5  4 222 33 6 4 33 4 33
S_{5}  5 -28 25  5 6 5 4 6 222 33 5
61.  2_{−}  6_{+} 9_{−} -2 -5 0 1^{6} 6_{+} ∗  1^{5} 9_{−} 5  222 6 33 6 4 5 4 33
S_{5}  -5 -8 1  5 6 33 6 6 4 5 5
62.  2_{−}  6_{+} 9_{−} -2  0 0 2^{2} 4_{k} −1  ∗ 1^{5} 9_{−} 5  6 4 33 4 4 33 4 33
S_{5}  0 10 5 1^{2} 2_{i} −∗ −∗  33 4 22 6 4 6 22 5
63.  2_{−}  10_{+} 9_{−} -2  0 0 1^{6} 10_{+} ∗  1^{5} 9_{−} 5  222 4 33 6 6 33 4 5
S_{5}  0 20 10  33 6 5 4 222 6 22 22
64.  2_{−}  10_{+} 9_{−} 2  0 0 1^{6} 10_{+} ∗  1^{5} 9_{−} 5  6 222 5 6 6 5 222 22
S_{5}  0 -100 50  5 4 33 6 4 222 5 33
65.  2_{−}  10_{+} 9_{−} 0 15 -80 1^{6} 10_{+} ∗  1^{5} 9_{−} 5  4 6 5 222 222 22 6 33
S_{5}  2  105 -52 5  5 4 5 4 222 4 5 33

Discriminant class: 10

∞  2 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5 3 7 11 13 17 19 23 29
G  h  a_{4} a_{5} a_{6} f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
66.  2_{−}  11_{−} 5_{+} 0 0  0 1^{4} 8_{+} 1  {−2 \atop −∗} 1^{6} 5_{+} 5∗  33 222 6 22 6 6 222 222
D_{6}  2  5 0 -10 1^{2} 3_{−} 2∗  2∗  22 22 33  222 22 222 222
67.  2_{−}  11_{−} 5_{+} 0 -5  0 1^{4} 11_{−} 2 −2 1^{6} 5_{+} 5∗  33 4 6 22 6 6 4 222
S_{4} × C_{2}  2  10 0 -10 2 0_{+} ∗  ∗  42 42 33 22 222 42 222 4
68.  2_{−}  13_{−} 5_{+} 0 -10  0 1^{4} 10_{i} −∗ −2 1^{6} 5_{+} 5∗  33 4 6 42 6 6 222 4
S_{4} × C_{2}  2  35 0 -40 1^{2} 3_{i} −2 −2  22 42 33 22 4 22 2 4
69.  2_{−}  13_{−} 5_{+} 0 0  0 1^{4} 11_{i} −2∗ −2 1^{6} 5_{+} 5∗  33 222 6 42 6 6 4 4
S_{4} × C_{2}  2  -10 0 -40 1^{2} 2_{i} −1 −1  42 22 33 22 4 42 2 222
70.  2_{−}  13_{−} 5_{+} -2 0  0 1^{4} 11_{i} −2∗ 2∗ 1^{5} 5_{+} 5∗  33 6 6 33 222 4 4 4
S_{5}  -5 6 -2 1^{2} 2_{i} −1 −1  5 33 5 33 4 5 6 6
71.  2_{−}  13_{−} 5_{+} 0 0  0 1^{4} 10_{k} −1 2∗ 1^{5} 5_{+} 5∗  5 6 4 33 6 222 4 6
S_{5}  -5 -16 -10 1^{2} 3_{k} −2∗ −2∗  5 5 5 33 222 33 4 4
72.  2_{−}  9_{−} 7_{+} 0 0 -10 3^{2} 9_{−} 2∗  1^{5} 7_{+} 5∗  5 6 4 22 4 6 4 222
S_{5}  2  -5 -2 15  33 33 22 33 4 5 4 4
73.  2_{−}  11_{−} 7_{+} -1 0 30 1^{4} 11_{−} 2∗  2∗ 1^{5} 7_{+} 5∗  5 222 6 33 6 6 6 4
S_{5}  25 -5 30  22 5 22 33 4 5 6 222
74.  2_{−}  13_{−} 7_{+} 0 -5  0 1^{4} 11_{i} −2∗ 2∗ 1^{5} 7_{+} 5∗  33 6 4 5 4 4 6 6
S_{5}  -75 40 -125 1^{2} 2_{i} −1 −1  33 22 22 22 6 5 4 4