[Introduction] - Groups of Genus: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Groups of Level:
7
8
9
10
11
12
13
14
15
16
18
20
21
24
26
27
28
30
32
33
34
35
36
39
40
41
42
43
45
48
49
50
51
52
54
55
56
60
64
66
72
84
96
^ | Level 7 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/7Z) Matrix Generators |
---|---|---|---|---|---|---|---|---|---|
7A3 | Γ(7) | 168 | 1 | 1 | 0 | 0 | [ 6, 0, 0, 6 ] | ||
^ | Level 8 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/8Z) Matrix Generators |
8A3 | 96 | 1 | 1 | 0 | 0 | [ 3, 0, 0, 3 ] , [ 7, 0, 0, 7 ] | |||
8B3 | 96 | 1 | 3 | 0 | 0 | [ 3, 4, 0, 3 ] , [ 5, 4, 0, 5 ] , [ 7, 0, 0, 7 ] | |||
^ | Level 9 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/9Z) Matrix Generators |
9A3 | 108 | 1 | 36 | 0 | 3 | [ 1, 3, 2, 7 ] , [ 8, 0, 0, 8 ] | |||
^ | Level 10 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/10Z) Matrix Generators |
10A3 | 60 | 1 | 10 | 0 | 0 | [ 7, 0, 4, 3 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 5 ] | |||
10B3 | 60 | 1 | 15 | 0 | 0 | [ 6, 5, 5, 1 ] , [ 7, 4, 0, 3 ] , [ 9, 0, 0, 9 ] | |||
10C3 | 90 | 1 | 45 | 4 | 0 | [ 3, 4, 0, 7 ] , [ 9, 0, 0, 9 ] , [ 9, 2, 9, 1 ] | |||
10D3 | 120 | 1 | 20 | 0 | 6 | [ 9, 0, 0, 9 ] , [ 9, 3, 3, 0 ] | |||
^ | Level 11 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/11Z) Matrix Generators |
11A3 | 110 | 2 | 55 | 6 | 2 | [ 8, 2, 2, 2 ] , [ 8, 10, 10, 3 ] , [ 10, 0, 0, 10 ] | |||
^ | Level 12 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/12Z) Matrix Generators |
12A3 | 48 | 1 | 1 | 0 | 0 | [ 1, 6, 6, 1 ] , [ 1, 9, 9, 10 ] , [ 5, 0, 6, 5 ] , [ 7, 0, 6, 7 ] , [ 10, 9, 9, 1 ] , [ 11, 0, 0, 11 ] | |||
12B3 | 48 | 1 | 4 | 0 | 0 | [ 4, 9, 3, 4 ] , [ 5, 0, 0, 5 ] , [ 7, 0, 0, 7 ] , [ 10, 3, 3, 1 ] , [ 11, 0, 0, 11 ] | |||
12C3 | 48 | 1 | 12 | 0 | 0 | [ 5, 0, 0, 5 ] , [ 5, 8, 8, 1 ] , [ 7, 0, 0, 7 ] , [ 10, 3, 3, 1 ] , [ 11, 0, 0, 11 ] | |||
12D3 | 72 | 1 | 3 | 0 | 0 | [ 1, 0, 6, 1 ] , [ 5, 0, 0, 5 ] , [ 7, 0, 0, 7 ] , [ 7, 0, 6, 7 ] , [ 7, 6, 3, 1 ] , [ 7, 6, 9, 1 ] , [ 11, 0, 0, 11 ] | |||
12E3 | 72 | 1 | 9 | 0 | 0 | [ 2, 11, 5, 4 ] , [ 4, 1, 7, 2 ] , [ 5, 0, 0, 5 ] , [ 7, 0, 0, 7 ] , [ 7, 6, 6, 7 ] , [ 8, 11, 5, 10 ] , [ 11, 6, 6, 11 ] | |||
12F3 | 72 | 1 | 9 | 0 | 0 | [ 1, 4, 10, 5 ] , [ 1, 6, 6, 1 ] , [ 5, 0, 0, 5 ] , [ 5, 8, 2, 1 ] , [ 7, 6, 6, 7 ] | |||
12G3 | 72 | 1 | 9 | 0 | 0 | [ 5, 0, 0, 5 ] , [ 7, 0, 0, 7 ] , [ 7, 6, 6, 7 ] , [ 9, 4, 8, 9 ] , [ 9, 8, 4, 9 ] | |||
12H3 | 72 | 1 | 18 | 4 | 0 | [ 0, 11, 1, 0 ] , [ 1, 6, 6, 1 ] , [ 5, 0, 6, 5 ] , [ 7, 0, 6, 7 ] , [ 11, 0, 0, 11 ] | |||
12I3 | 72 | 1 | 18 | 4 | 0 | [ 5, 0, 0, 5 ] , [ 7, 0, 0, 7 ] , [ 7, 2, 2, 11 ] , [ 10, 9, 3, 10 ] | |||
12J3 | 72 | 1 | 18 | 4 | 0 | [ 4, 3, 9, 4 ] , [ 4, 9, 3, 4 ] , [ 5, 0, 0, 5 ] , [ 7, 0, 0, 7 ] , [ 9, 8, 4, 9 ] | |||
12K3 | 96 | 1 | 4 | 0 | 0 | [ 1, 0, 8, 1 ] , [ 5, 0, 0, 5 ] , [ 5, 0, 8, 5 ] , [ 7, 0, 0, 7 ] , [ 11, 0, 8, 11 ] | |||
12L3 | 96 | 1 | 12 | 0 | 0 | [ 1, 8, 10, 9 ] , [ 5, 4, 8, 9 ] , [ 7, 0, 6, 7 ] , [ 9, 4, 2, 1 ] , [ 9, 8, 4, 5 ] | |||
12M3 | 96 | 1 | 24 | 8 | 0 | [ 1, 9, 9, 10 ] , [ 4, 5, 11, 8 ] , [ 10, 3, 3, 1 ] , [ 11, 0, 0, 11 ] | |||
12N3 | 144 | 1 | 3 | 0 | 0 | [ 1, 6, 0, 1 ] , [ 7, 0, 6, 7 ] , [ 7, 6, 6, 7 ] , [ 11, 0, 0, 11 ] , [ 11, 6, 0, 11 ] | |||
12O3 | 144 | 1 | 6 | 0 | 0 | [ 1, 0, 3, 1 ] , [ 1, 0, 6, 1 ] , [ 11, 0, 0, 11 ] , [ 11, 0, 6, 11 ] | |||
12P3 | 144 | 1 | 18 | 8 | 0 | [ 2, 1, 7, 10 ] , [ 5, 6, 6, 5 ] , [ 8, 7, 1, 4 ] , [ 11, 0, 0, 11 ] | |||
^ | Level 13 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/13Z) Matrix Generators |
13A3 | 78 | 1 | 78 | 6 | 0 | [ 6, 4, 6, 2 ] , [ 9, 6, 8, 4 ] , [ 12, 0, 0, 12 ] | |||
13B3 | 91 | 1 | 91 | 3 | 4 | [ 5, 1, 0, 8 ] , [ 9, 9, 1, 4 ] , [ 12, 0, 0, 12 ] , [ 12, 12, 3, 2 ] | |||
13C3 | 91 | 1 | 91 | 7 | 1 | [ 1, 1, 12, 0 ] , [ 3, 6, 7, 10 ] , [ 4, 2, 11, 9 ] , [ 12, 0, 0, 12 ] | |||
^ | Level 14 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/14Z) Matrix Generators |
14A3 | 42 | 1 | 21 | 0 | 0 | [ 0, 5, 11, 7 ] , [ 1, 9, 11, 2 ] , [ 2, 13, 5, 5 ] , [ 8, 7, 7, 1 ] , [ 13, 7, 7, 6 ] | |||
14B3 | 42 | 2 | 7 | 0 | 0 | [ 7, 10, 2, 13 ] , [ 7, 12, 4, 7 ] , [ 9, 6, 12, 5 ] , [ 9, 12, 10, 1 ] , [ 13, 0, 0, 13 ] | |||
14C3 | 56 | 1 | 28 | 0 | 2 | [ 1, 7, 7, 8 ] , [ 1, 12, 8, 13 ] , [ 9, 2, 0, 11 ] , [ 13, 0, 0, 13 ] | |||
14D3 | 84 | 1 | 84 | 4 | 0 | [ 1, 12, 1, 13 ] , [ 1, 12, 8, 13 ] , [ 9, 2, 0, 11 ] , [ 13, 0, 0, 13 ] | |||
14E3 | 84 | 2 | 14 | 0 | 6 | [ 4, 5, 7, 9 ] , [ 5, 8, 2, 9 ] , [ 7, 12, 4, 7 ] , [ 9, 6, 12, 5 ] , [ 13, 0, 0, 13 ] | |||
14F3 | 84 | 2 | 21 | 8 | 0 | [ 5, 8, 2, 9 ] , [ 7, 9, 10, 7 ] , [ 8, 7, 7, 1 ] , [ 9, 6, 12, 5 ] , [ 13, 0, 0, 13 ] | |||
^ | Level 15 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/15Z) Matrix Generators |
15A3 | 60 | 1 | 20 | 0 | 0 | [ 4, 0, 0, 4 ] , [ 4, 6, 3, 1 ] , [ 6, 5, 10, 11 ] , [ 6, 10, 5, 1 ] , [ 13, 0, 6, 7 ] | |||
15B3 | 60 | 1 | 20 | 0 | 3 | [ 6, 5, 10, 6 ] , [ 9, 10, 5, 9 ] , [ 10, 12, 2, 4 ] , [ 11, 0, 0, 11 ] , [ 11, 10, 10, 1 ] | |||
15C3 | 60 | 1 | 30 | 4 | 0 | [ 4, 0, 0, 4 ] , [ 6, 10, 5, 6 ] , [ 7, 0, 9, 13 ] , [ 10, 12, 12, 4 ] , [ 11, 0, 0, 11 ] | |||
15D3 | 60 | 2 | 20 | 0 | 3 | [ 4, 0, 0, 4 ] , [ 4, 6, 3, 1 ] , [ 5, 13, 8, 9 ] , [ 11, 0, 0, 11 ] , [ 13, 0, 6, 7 ] | |||
15E3 | 72 | 1 | 6 | 0 | 0 | [ 4, 0, 0, 4 ] , [ 4, 6, 3, 1 ] , [ 7, 3, 3, 10 ] , [ 11, 0, 0, 11 ] | |||
15F3 | 72 | 1 | 18 | 0 | 0 | [ 4, 0, 0, 4 ] , [ 5, 12, 12, 2 ] , [ 13, 1, 1, 14 ] , [ 13, 6, 6, 4 ] | |||
15G3 | 80 | 1 | 40 | 0 | 2 | [ 1, 0, 5, 1 ] , [ 4, 0, 10, 4 ] , [ 4, 3, 3, 10 ] , [ 11, 0, 10, 11 ] | |||
15H3 | 90 | 1 | 45 | 10 | 0 | [ 2, 10, 7, 13 ] , [ 2, 11, 5, 13 ] , [ 4, 0, 0, 4 ] , [ 4, 12, 9, 1 ] , [ 11, 0, 0, 11 ] | |||
15I3 | 144 | 1 | 36 | 8 | 0 | [ 4, 9, 9, 13 ] , [ 14, 0, 0, 14 ] , [ 14, 8, 11, 1 ] | |||
^ | Level 16 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/16Z) Matrix Generators |
16A3 | 48 | 1 | 3 | 0 | 0 | [ 1, 8, 0, 1 ] , [ 1, 12, 8, 1 ] , [ 5, 8, 8, 13 ] , [ 7, 10, 4, 15 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 0, 9 ] , [ 13, 6, 4, 13 ] | |||
16B3 | 48 | 1 | 3 | 0 | 0 | [ 1, 8, 0, 1 ] , [ 1, 12, 8, 1 ] , [ 3, 10, 4, 3 ] , [ 7, 10, 12, 15 ] , [ 9, 0, 0, 9 ] , [ 9, 6, 4, 1 ] , [ 9, 8, 0, 9 ] | |||
16C3 | 48 | 1 | 6 | 0 | 0 | [ 5, 12, 12, 13 ] , [ 7, 12, 12, 7 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 9 ] , [ 12, 9, 7, 12 ] , [ 15, 0, 0, 15 ] | |||
16D3 | 48 | 1 | 6 | 0 | 0 | [ 1, 8, 0, 1 ] , [ 1, 12, 8, 1 ] , [ 5, 8, 0, 13 ] , [ 7, 10, 12, 15 ] , [ 9, 0, 0, 9 ] , [ 9, 6, 4, 1 ] , [ 9, 8, 0, 9 ] | |||
16E3 | 48 | 1 | 12 | 0 | 0 | [ 1, 8, 8, 1 ] , [ 5, 0, 8, 13 ] , [ 5, 12, 12, 13 ] , [ 8, 11, 13, 4 ] , [ 9, 8, 8, 9 ] , [ 15, 4, 12, 15 ] | |||
16F3 | 48 | 1 | 12 | 0 | 0 | [ 1, 8, 8, 1 ] , [ 2, 11, 1, 6 ] , [ 9, 8, 8, 9 ] , [ 11, 6, 6, 15 ] , [ 11, 14, 14, 15 ] , [ 13, 12, 12, 5 ] , [ 15, 0, 0, 15 ] , [ 15, 2, 2, 11 ] | |||
16G3 | 48 | 2 | 24 | 2 | 0 | [ 0, 11, 13, 0 ] , [ 1, 8, 8, 1 ] , [ 3, 0, 12, 11 ] , [ 9, 0, 8, 9 ] , [ 9, 4, 4, 9 ] , [ 15, 4, 12, 15 ] | |||
16H3 | 96 | 1 | 3 | 0 | 0 | [ 1, 8, 8, 1 ] , [ 7, 4, 4, 7 ] , [ 9, 8, 8, 9 ] , [ 9, 12, 12, 9 ] , [ 11, 12, 4, 3 ] , [ 13, 12, 4, 5 ] , [ 15, 0, 0, 15 ] | |||
16I3 | 96 | 1 | 3 | 0 | 0 | [ 7, 12, 4, 7 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 9 ] , [ 13, 0, 0, 5 ] , [ 15, 4, 12, 15 ] , [ 15, 8, 8, 15 ] | |||
16J3 | 96 | 1 | 6 | 0 | 0 | [ 1, 8, 0, 1 ] , [ 1, 12, 0, 1 ] , [ 9, 12, 0, 9 ] , [ 13, 2, 0, 5 ] , [ 13, 10, 0, 5 ] , [ 15, 4, 0, 15 ] | |||
16K3 | 96 | 1 | 12 | 8 | 0 | [ 1, 8, 8, 1 ] , [ 1, 12, 12, 1 ] , [ 9, 8, 8, 9 ] , [ 9, 12, 12, 9 ] , [ 12, 5, 3, 4 ] , [ 15, 0, 0, 15 ] , [ 15, 4, 4, 15 ] | |||
16L3 | 96 | 1 | 12 | 8 | 0 | [ 0, 11, 13, 0 ] , [ 1, 8, 8, 1 ] , [ 3, 0, 0, 11 ] , [ 8, 11, 13, 8 ] , [ 9, 0, 0, 9 ] , [ 15, 8, 8, 15 ] | |||
16M3 | 96 | 1 | 12 | 8 | 0 | [ 1, 8, 8, 1 ] , [ 5, 4, 4, 13 ] , [ 7, 8, 8, 7 ] , [ 8, 7, 9, 8 ] , [ 9, 8, 8, 9 ] , [ 13, 4, 4, 5 ] , [ 15, 8, 8, 15 ] | |||
16N3 | 96 | 1 | 24 | 0 | 0 | [ 5, 4, 12, 13 ] , [ 6, 15, 1, 0 ] , [ 7, 8, 8, 7 ] , [ 9, 8, 8, 9 ] , [ 11, 2, 14, 7 ] | |||
16O3 | 96 | 1 | 24 | 0 | 0 | [ 1, 4, 8, 1 ] , [ 1, 8, 0, 1 ] , [ 3, 6, 4, 3 ] , [ 7, 0, 8, 7 ] , [ 9, 4, 0, 9 ] , [ 11, 10, 4, 11 ] , [ 11, 14, 12, 11 ] | |||
16P3 | 96 | 1 | 24 | 4 | 0 | [ 0, 5, 3, 8 ] , [ 1, 0, 8, 1 ] , [ 1, 8, 8, 1 ] , [ 9, 4, 12, 9 ] , [ 9, 12, 12, 9 ] , [ 15, 0, 0, 15 ] , [ 15, 8, 0, 15 ] | |||
16Q3 | 96 | 1 | 24 | 4 | 0 | [ 1, 0, 8, 1 ] , [ 1, 8, 8, 1 ] , [ 1, 12, 4, 1 ] , [ 4, 13, 11, 12 ] , [ 12, 13, 11, 12 ] , [ 15, 0, 0, 15 ] , [ 15, 4, 4, 15 ] | |||
16R3 | 96 | 1 | 24 | 8 | 0 | [ 0, 3, 5, 0 ] , [ 1, 6, 6, 5 ] , [ 5, 4, 4, 13 ] , [ 9, 8, 8, 9 ] , [ 15, 0, 0, 15 ] | |||
16S3 | 96 | 1 | 24 | 8 | 0 | [ 5, 4, 4, 13 ] , [ 9, 6, 6, 13 ] , [ 9, 8, 8, 9 ] , [ 14, 3, 9, 2 ] , [ 15, 0, 0, 15 ] | |||
^ | Level 18 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/18Z) Matrix Generators |
18A3 | 36 | 1 | 3 | 0 | 0 | [ 7, 0, 0, 13 ] , [ 9, 10, 8, 9 ] , [ 10, 9, 9, 1 ] , [ 11, 6, 6, 5 ] , [ 13, 6, 6, 7 ] | |||
18B3 | 36 | 1 | 6 | 0 | 0 | [ 1, 12, 6, 1 ] , [ 7, 9, 15, 4 ] , [ 7, 12, 0, 13 ] , [ 17, 6, 12, 17 ] , [ 17, 16, 10, 1 ] | |||
18C3 | 36 | 2 | 9 | 0 | 0 | [ 1, 8, 8, 11 ] , [ 7, 0, 0, 13 ] , [ 10, 9, 9, 1 ] , [ 11, 6, 6, 5 ] , [ 13, 6, 6, 7 ] | |||
18D3 | 54 | 1 | 27 | 4 | 0 | [ 5, 0, 12, 11 ] , [ 7, 0, 12, 13 ] , [ 7, 12, 0, 13 ] , [ 11, 10, 4, 7 ] , [ 15, 10, 17, 15 ] | |||
18E3 | 54 | 2 | 27 | 2 | 0 | [ 5, 0, 12, 11 ] , [ 7, 0, 12, 13 ] , [ 7, 12, 0, 13 ] , [ 15, 10, 17, 15 ] , [ 15, 14, 16, 9 ] | |||
18F3 | 72 | 1 | 6 | 0 | 0 | [ 10, 9, 9, 1 ] , [ 13, 0, 0, 7 ] , [ 13, 12, 6, 7 ] , [ 17, 0, 0, 17 ] | |||
18G3 | 72 | 1 | 12 | 0 | 0 | [ 1, 0, 6, 1 ] , [ 1, 9, 9, 10 ] , [ 7, 0, 2, 13 ] , [ 17, 0, 0, 17 ] | |||
18H3 | 72 | 1 | 12 | 0 | 0 | [ 1, 0, 6, 1 ] , [ 1, 15, 15, 10 ] , [ 7, 9, 15, 4 ] , [ 17, 0, 0, 17 ] | |||
18I3 | 72 | 1 | 24 | 0 | 0 | [ 1, 0, 12, 1 ] , [ 1, 9, 13, 10 ] , [ 7, 9, 17, 4 ] , [ 17, 0, 0, 17 ] | |||
18J3 | 81 | 1 | 81 | 7 | 0 | [ 11, 10, 4, 7 ] , [ 11, 12, 12, 5 ] , [ 13, 12, 12, 7 ] , [ 15, 2, 4, 3 ] , [ 15, 4, 11, 3 ] | |||
18K3 | 108 | 1 | 54 | 4 | 0 | [ 1, 12, 0, 1 ] , [ 13, 0, 12, 7 ] , [ 17, 0, 0, 17 ] , [ 17, 2, 17, 1 ] | |||
^ | Level 20 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/20Z) Matrix Generators |
20A3 | 48 | 1 | 6 | 0 | 0 | [ 6, 5, 5, 1 ] , [ 9, 4, 4, 13 ] , [ 11, 0, 10, 11 ] , [ 11, 6, 6, 7 ] , [ 11, 10, 0, 11 ] | |||
20B3 | 48 | 1 | 24 | 0 | 0 | [ 1, 10, 5, 11 ] , [ 11, 0, 0, 11 ] , [ 13, 16, 16, 9 ] , [ 16, 5, 15, 11 ] , [ 19, 0, 0, 19 ] | |||
20C3 | 48 | 1 | 24 | 0 | 0 | [ 9, 16, 8, 1 ] , [ 11, 0, 0, 11 ] , [ 13, 16, 16, 9 ] , [ 16, 5, 15, 11 ] , [ 19, 0, 0, 19 ] | |||
20D3 | 60 | 1 | 20 | 6 | 0 | [ 6, 15, 15, 1 ] , [ 9, 0, 0, 9 ] , [ 11, 0, 0, 11 ] , [ 13, 0, 8, 17 ] , [ 16, 15, 5, 16 ] , [ 17, 16, 0, 13 ] | |||
20E3 | 60 | 1 | 30 | 0 | 0 | [ 1, 0, 10, 1 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 5 ] , [ 11, 0, 5, 11 ] , [ 11, 0, 10, 11 ] , [ 17, 0, 4, 13 ] | |||
20F3 | 60 | 1 | 30 | 4 | 0 | [ 1, 0, 10, 1 ] , [ 1, 10, 5, 11 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 5 ] , [ 11, 0, 10, 11 ] , [ 17, 0, 4, 13 ] | |||
20G3 | 72 | 1 | 18 | 0 | 0 | [ 1, 0, 10, 1 ] , [ 5, 12, 12, 17 ] , [ 9, 0, 0, 9 ] , [ 11, 0, 0, 11 ] , [ 13, 2, 17, 15 ] | |||
20H3 | 72 | 1 | 18 | 0 | 0 | [ 1, 0, 10, 1 ] , [ 1, 4, 17, 9 ] , [ 3, 16, 6, 19 ] , [ 5, 12, 12, 17 ] , [ 9, 0, 0, 9 ] | |||
20I3 | 72 | 1 | 18 | 0 | 0 | [ 1, 0, 10, 1 ] , [ 5, 6, 4, 5 ] , [ 13, 12, 12, 5 ] , [ 17, 8, 8, 5 ] , [ 19, 4, 14, 3 ] | |||
20J3 | 72 | 1 | 18 | 0 | 0 | [ 1, 0, 10, 1 ] , [ 1, 4, 12, 9 ] , [ 3, 16, 6, 19 ] , [ 5, 12, 12, 17 ] , [ 9, 0, 0, 9 ] | |||
20K3 | 72 | 1 | 36 | 4 | 0 | [ 1, 12, 14, 9 ] , [ 5, 12, 12, 17 ] , [ 9, 0, 0, 9 ] , [ 11, 0, 0, 11 ] , [ 13, 2, 7, 15 ] | |||
20L3 | 72 | 1 | 36 | 4 | 0 | [ 1, 10, 5, 11 ] , [ 11, 0, 0, 11 ] , [ 13, 16, 16, 9 ] , [ 19, 0, 0, 19 ] , [ 19, 6, 3, 1 ] | |||
20M3 | 72 | 2 | 18 | 4 | 0 | [ 1, 4, 17, 9 ] , [ 1, 14, 7, 19 ] , [ 11, 0, 10, 11 ] , [ 13, 16, 16, 9 ] , [ 15, 12, 2, 7 ] , [ 19, 0, 0, 19 ] | |||
20N3 | 80 | 1 | 10 | 0 | 8 | [ 1, 10, 10, 1 ] , [ 1, 15, 15, 6 ] , [ 9, 0, 10, 9 ] , [ 9, 8, 8, 5 ] , [ 11, 0, 10, 11 ] | |||
20O3 | 80 | 1 | 40 | 8 | 2 | [ 1, 15, 15, 6 ] , [ 3, 10, 11, 17 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 5 ] , [ 11, 0, 0, 11 ] | |||
20P3 | 90 | 1 | 45 | 4 | 0 | [ 1, 0, 10, 1 ] , [ 1, 0, 15, 1 ] , [ 3, 14, 5, 17 ] , [ 9, 0, 0, 9 ] , [ 11, 0, 10, 11 ] , [ 19, 2, 9, 1 ] | |||
20Q3 | 96 | 2 | 24 | 8 | 0 | [ 5, 12, 12, 17 ] , [ 16, 5, 15, 11 ] , [ 19, 0, 0, 19 ] , [ 19, 6, 3, 1 ] | |||
20R3 | 144 | 1 | 18 | 0 | 0 | [ 1, 10, 0, 1 ] , [ 9, 0, 10, 9 ] , [ 11, 0, 10, 11 ] , [ 13, 16, 16, 9 ] | |||
20S3 | Γ1(20) | 144 | 1 | 36 | 0 | 0 | [ 1, 0, 10, 1 ] , [ 1, 0, 15, 1 ] , [ 7, 4, 9, 11 ] , [ 13, 16, 16, 9 ] | ||
20T3 | 144 | 1 | 36 | 8 | 0 | [ 1, 0, 10, 1 ] , [ 11, 2, 9, 9 ] , [ 13, 16, 16, 9 ] , [ 17, 8, 8, 5 ] , [ 19, 0, 0, 19 ] | |||
^ | Level 21 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/21Z) Matrix Generators |
21A3 | 48 | 1 | 24 | 0 | 0 | [ 1, 0, 18, 1 ] , [ 8, 0, 0, 8 ] , [ 8, 0, 3, 8 ] , [ 13, 0, 0, 13 ] , [ 15, 14, 7, 15 ] , [ 16, 0, 0, 4 ] | |||
21B3 | 56 | 2 | 28 | 0 | 2 | [ 1, 7, 14, 15 ] , [ 4, 6, 3, 10 ] , [ 6, 7, 14, 20 ] , [ 7, 18, 12, 7 ] , [ 8, 14, 7, 15 ] , [ 13, 0, 0, 13 ] , [ 13, 6, 15, 7 ] , [ 15, 14, 7, 1 ] | |||
21C3 | 84 | 1 | 28 | 12 | 0 | [ 1, 14, 14, 8 ] , [ 7, 15, 6, 13 ] , [ 8, 0, 0, 8 ] , [ 10, 18, 15, 4 ] , [ 13, 0, 0, 13 ] , [ 13, 17, 11, 8 ] , [ 15, 7, 14, 15 ] | |||
21D3 | 96 | 1 | 32 | 0 | 0 | [ 1, 0, 7, 1 ] , [ 1, 0, 9, 1 ] , [ 8, 0, 0, 8 ] , [ 8, 0, 7, 8 ] , [ 13, 0, 0, 13 ] , [ 13, 0, 14, 13 ] | |||
^ | Level 24 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/24Z) Matrix Generators |
24A3 | 36 | 1 | 3 | 0 | 0 | [ 1, 0, 12, 1 ] , [ 1, 8, 20, 17 ] , [ 1, 16, 4, 17 ] , [ 7, 0, 0, 7 ] , [ 13, 0, 12, 13 ] , [ 13, 12, 6, 13 ] , [ 13, 12, 18, 13 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 12, 19 ] , [ 19, 18, 21, 1 ] | |||
24B3 | 48 | 1 | 12 | 0 | 0 | [ 1, 0, 12, 1 ] , [ 1, 4, 6, 1 ] , [ 1, 16, 0, 1 ] , [ 7, 0, 12, 7 ] , [ 13, 0, 0, 13 ] , [ 13, 12, 6, 13 ] , [ 17, 12, 18, 17 ] , [ 19, 0, 12, 19 ] , [ 19, 4, 18, 19 ] , [ 19, 6, 21, 13 ] | |||
24C3 | 48 | 1 | 12 | 0 | 0 | [ 1, 0, 12, 1 ] , [ 1, 4, 6, 1 ] , [ 1, 16, 0, 1 ] , [ 7, 0, 12, 7 ] , [ 13, 0, 0, 13 ] , [ 13, 12, 6, 13 ] , [ 17, 12, 18, 17 ] , [ 19, 0, 12, 19 ] , [ 19, 4, 18, 19 ] , [ 19, 6, 15, 1 ] | |||
24D3 | 48 | 2 | 12 | 4 | 0 | [ 1, 8, 20, 17 ] , [ 1, 9, 21, 22 ] , [ 1, 12, 12, 1 ] , [ 7, 0, 0, 7 ] , [ 13, 0, 12, 13 ] , [ 16, 15, 9, 16 ] , [ 17, 0, 0, 17 ] , [ 17, 4, 16, 1 ] , [ 19, 0, 12, 19 ] , [ 19, 12, 0, 19 ] | |||
24E3 | 48 | 2 | 12 | 4 | 0 | [ 1, 8, 8, 17 ] , [ 1, 9, 21, 22 ] , [ 1, 12, 12, 1 ] , [ 4, 3, 21, 4 ] , [ 7, 0, 0, 7 ] , [ 13, 0, 12, 13 ] , [ 16, 15, 9, 4 ] , [ 17, 0, 0, 17 ] , [ 17, 4, 4, 1 ] , [ 19, 12, 0, 19 ] | |||
24F3 | 64 | 1 | 16 | 0 | 4 | [ 1, 16, 0, 1 ] , [ 1, 21, 9, 22 ] , [ 5, 16, 0, 5 ] , [ 11, 0, 12, 11 ] , [ 13, 0, 12, 13 ] , [ 13, 12, 0, 13 ] , [ 19, 12, 12, 19 ] | |||
24G3 | 64 | 1 | 16 | 0 | 4 | [ 1, 16, 0, 1 ] , [ 1, 21, 9, 22 ] , [ 13, 0, 12, 13 ] , [ 13, 12, 0, 13 ] , [ 13, 20, 0, 13 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 12, 19 ] | |||
24H3 | 72 | 1 | 9 | 8 | 0 | [ 1, 0, 12, 1 ] , [ 7, 4, 16, 23 ] , [ 7, 12, 6, 7 ] , [ 7, 22, 1, 17 ] , [ 13, 0, 12, 13 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 12, 19 ] , [ 23, 0, 0, 23 ] , [ 23, 18, 9, 5 ] | |||
24I3 | 72 | 1 | 9 | 8 | 0 | [ 1, 0, 12, 1 ] , [ 1, 16, 4, 17 ] , [ 5, 18, 3, 11 ] , [ 7, 6, 21, 1 ] , [ 13, 0, 12, 13 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 12, 19 ] , [ 23, 0, 0, 23 ] , [ 23, 18, 3, 17 ] | |||
24J3 | 72 | 1 | 12 | 6 | 0 | [ 1, 0, 12, 1 ] , [ 1, 8, 20, 17 ] , [ 1, 12, 12, 1 ] , [ 7, 0, 0, 7 ] , [ 7, 20, 20, 23 ] , [ 15, 20, 4, 15 ] , [ 16, 17, 23, 8 ] , [ 17, 0, 0, 17 ] , [ 23, 0, 0, 23 ] | |||
24K3 | 72 | 1 | 18 | 0 | 0 | [ 1, 0, 12, 1 ] , [ 1, 0, 18, 1 ] , [ 7, 0, 18, 7 ] , [ 11, 20, 14, 19 ] , [ 11, 20, 17, 7 ] , [ 13, 0, 12, 13 ] , [ 13, 4, 10, 5 ] , [ 17, 0, 12, 17 ] , [ 23, 20, 11, 19 ] | |||
24L3 | 72 | 1 | 18 | 0 | 0 | [ 1, 0, 12, 1 ] , [ 1, 0, 18, 1 ] , [ 5, 8, 20, 13 ] , [ 7, 0, 18, 7 ] , [ 7, 16, 13, 23 ] , [ 7, 16, 22, 23 ] , [ 13, 0, 12, 13 ] , [ 17, 0, 12, 17 ] , [ 17, 8, 2, 1 ] , [ 17, 8, 17, 1 ] | |||
24M3 | 72 | 1 | 18 | 4 | 0 | [ 1, 0, 12, 1 ] , [ 1, 0, 18, 1 ] , [ 1, 10, 4, 17 ] , [ 11, 0, 12, 11 ] , [ 13, 0, 12, 13 ] , [ 17, 0, 9, 17 ] , [ 17, 12, 18, 17 ] , [ 19, 12, 18, 19 ] , [ 23, 0, 0, 23 ] , [ 23, 2, 23, 1 ] | |||
24N3 | 72 | 1 | 18 | 4 | 0 | [ 1, 0, 6, 1 ] , [ 1, 0, 12, 1 ] , [ 7, 4, 16, 23 ] , [ 7, 22, 1, 17 ] , [ 13, 0, 12, 13 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 12, 19 ] , [ 23, 0, 0, 23 ] , [ 23, 18, 9, 5 ] | |||
24O3 | 72 | 1 | 18 | 4 | 0 | [ 1, 0, 6, 1 ] , [ 1, 0, 12, 1 ] , [ 1, 6, 15, 19 ] , [ 1, 16, 4, 17 ] , [ 13, 0, 12, 13 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 12, 19 ] , [ 23, 0, 0, 23 ] , [ 23, 18, 9, 5 ] | |||
24P3 | 72 | 1 | 18 | 8 | 0 | [ 0, 5, 19, 0 ] , [ 1, 12, 12, 1 ] , [ 5, 8, 8, 13 ] , [ 7, 0, 0, 7 ] , [ 13, 0, 0, 13 ] , [ 15, 20, 16, 15 ] , [ 17, 0, 0, 17 ] , [ 21, 8, 4, 21 ] , [ 23, 0, 0, 23 ] | |||
24Q3 | 72 | 1 | 18 | 8 | 0 | [ 1, 0, 12, 1 ] , [ 1, 6, 3, 19 ] , [ 7, 0, 0, 7 ] , [ 7, 18, 9, 13 ] , [ 9, 8, 4, 9 ] , [ 13, 0, 12, 13 ] , [ 13, 14, 5, 11 ] , [ 17, 0, 0, 17 ] , [ 19, 8, 2, 11 ] , [ 23, 0, 0, 23 ] | |||
24R3 | 72 | 1 | 36 | 6 | 0 | [ 1, 0, 12, 1 ] , [ 1, 12, 12, 1 ] , [ 3, 20, 4, 3 ] , [ 4, 3, 21, 4 ] , [ 5, 8, 8, 13 ] , [ 7, 0, 0, 7 ] , [ 17, 0, 0, 17 ] , [ 21, 8, 4, 21 ] , [ 23, 0, 0, 23 ] | |||
24S3 | 72 | 2 | 9 | 8 | 0 | [ 1, 0, 12, 1 ] , [ 1, 12, 18, 1 ] , [ 9, 8, 10, 9 ] , [ 9, 8, 22, 9 ] , [ 13, 0, 12, 13 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 12, 19 ] , [ 23, 2, 23, 1 ] | |||
24T3 | 72 | 2 | 18 | 8 | 0 | [ 1, 0, 12, 1 ] , [ 1, 6, 3, 19 ] , [ 7, 0, 0, 7 ] , [ 7, 18, 9, 13 ] , [ 13, 0, 12, 13 ] , [ 13, 14, 5, 11 ] , [ 17, 0, 0, 17 ] , [ 19, 4, 22, 11 ] , [ 19, 8, 2, 11 ] , [ 23, 0, 0, 23 ] | |||
24U3 | 96 | 1 | 12 | 0 | 0 | [ 1, 0, 6, 1 ] , [ 1, 0, 12, 1 ] , [ 1, 0, 18, 1 ] , [ 1, 16, 0, 1 ] , [ 5, 20, 12, 5 ] , [ 7, 12, 6, 7 ] , [ 19, 12, 6, 19 ] | |||
24V3 | 96 | 1 | 12 | 0 | 0 | [ 1, 0, 12, 1 ] , [ 1, 8, 0, 1 ] , [ 5, 16, 6, 5 ] , [ 7, 0, 0, 7 ] , [ 13, 0, 0, 13 ] , [ 13, 0, 6, 13 ] , [ 19, 0, 12, 19 ] , [ 19, 8, 6, 19 ] , [ 19, 8, 18, 19 ] | |||
24W3 | 96 | 1 | 24 | 0 | 0 | [ 1, 0, 6, 1 ] , [ 1, 0, 12, 1 ] , [ 1, 8, 0, 1 ] , [ 11, 0, 6, 11 ] , [ 13, 0, 18, 13 ] , [ 17, 0, 9, 17 ] , [ 19, 0, 21, 19 ] | |||
24X3 | 96 | 1 | 48 | 0 | 0 | [ 1, 0, 6, 1 ] , [ 1, 0, 12, 1 ] , [ 1, 8, 0, 1 ] , [ 5, 0, 6, 5 ] , [ 13, 0, 15, 13 ] , [ 17, 0, 9, 17 ] , [ 19, 0, 18, 19 ] | |||
24Y3 | 96 | 1 | 48 | 0 | 0 | [ 1, 0, 6, 1 ] , [ 1, 0, 12, 1 ] , [ 1, 8, 0, 1 ] , [ 7, 0, 12, 7 ] , [ 17, 0, 0, 17 ] , [ 17, 0, 9, 17 ] , [ 23, 0, 3, 23 ] | |||
24Z3 | 96 | 1 | 48 | 0 | 0 | [ 1, 0, 12, 1 ] , [ 1, 0, 18, 1 ] , [ 1, 16, 0, 1 ] , [ 5, 8, 0, 5 ] , [ 11, 20, 6, 11 ] , [ 13, 4, 12, 13 ] , [ 13, 12, 12, 13 ] , [ 13, 12, 18, 13 ] | |||
24AA3 | 96 | 1 | 48 | 0 | 0 | [ 1, 0, 6, 1 ] , [ 1, 0, 12, 1 ] , [ 1, 0, 18, 1 ] , [ 1, 12, 12, 1 ] , [ 1, 16, 0, 1 ] , [ 7, 0, 18, 7 ] , [ 17, 8, 0, 17 ] | |||
24AB3 | 96 | 1 | 48 | 16 | 0 | [ 4, 1, 7, 20 ] , [ 4, 19, 13, 20 ] , [ 7, 0, 0, 7 ] , [ 12, 5, 19, 12 ] , [ 13, 8, 8, 5 ] , [ 17, 0, 0, 17 ] , [ 22, 15, 3, 1 ] | |||
24AC3 | 144 | 1 | 3 | 0 | 0 | [ 1, 0, 9, 1 ] , [ 1, 0, 12, 1 ] , [ 1, 0, 18, 1 ] , [ 5, 12, 3, 17 ] , [ 5, 12, 9, 17 ] , [ 7, 12, 9, 19 ] , [ 13, 0, 0, 13 ] , [ 13, 0, 12, 13 ] | |||
^ | Level 26 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/26Z) Matrix Generators |
26A3 | 84 | 1 | 28 | 0 | 6 | [ 3, 6, 20, 23 ] , [ 13, 16, 4, 15 ] , [ 22, 21, 13, 3 ] , [ 25, 0, 0, 25 ] | |||
^ | Level 27 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/27Z) Matrix Generators |
27A3 | 36 | 1 | 12 | 0 | 0 | [ 1, 0, 18, 1 ] , [ 1, 18, 6, 1 ] , [ 10, 0, 9, 19 ] , [ 13, 0, 12, 25 ] , [ 19, 0, 0, 10 ] , [ 25, 24, 4, 19 ] , [ 26, 0, 0, 26 ] | |||
27B3 | 81 | 2 | 81 | 13 | 0 | [ 0, 1, 26, 0 ] , [ 1, 25, 1, 26 ] , [ 5, 3, 3, 2 ] , [ 7, 21, 21, 13 ] , [ 19, 9, 9, 10 ] , [ 19, 18, 0, 10 ] | |||
27C3 | 108 | 1 | 36 | 0 | 3 | [ 1, 0, 15, 1 ] , [ 1, 0, 18, 1 ] , [ 19, 0, 0, 10 ] , [ 19, 0, 9, 10 ] , [ 25, 6, 25, 19 ] , [ 26, 0, 0, 26 ] | |||
^ | Level 28 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/28Z) Matrix Generators |
28A3 | 42 | 2 | 21 | 0 | 0 | [ 1, 7, 0, 1 ] , [ 1, 14, 0, 1 ] , [ 9, 12, 24, 1 ] , [ 9, 20, 12, 5 ] , [ 13, 0, 0, 13 ] , [ 15, 14, 0, 15 ] , [ 21, 12, 4, 21 ] , [ 21, 24, 16, 13 ] | |||
28B3 | 42 | 2 | 21 | 2 | 0 | [ 1, 7, 14, 15 ] , [ 1, 14, 0, 1 ] , [ 9, 19, 24, 1 ] , [ 9, 20, 12, 5 ] , [ 13, 0, 0, 13 ] , [ 15, 14, 0, 15 ] , [ 21, 12, 4, 21 ] , [ 21, 24, 16, 13 ] | |||
28C3 | 48 | 1 | 24 | 0 | 0 | [ 1, 0, 14, 1 ] , [ 13, 24, 16, 21 ] , [ 15, 0, 14, 15 ] , [ 15, 14, 21, 1 ] , [ 17, 0, 20, 5 ] , [ 17, 24, 8, 13 ] , [ 25, 8, 12, 5 ] | |||
28D3 | 56 | 2 | 28 | 4 | 2 | [ 9, 20, 12, 5 ] , [ 13, 0, 0, 13 ] , [ 15, 0, 0, 15 ] , [ 15, 7, 14, 1 ] , [ 21, 12, 4, 21 ] , [ 21, 24, 16, 13 ] , [ 22, 21, 21, 1 ] | |||
28E3 | 64 | 1 | 32 | 0 | 4 | [ 1, 7, 7, 22 ] , [ 13, 0, 0, 13 ] , [ 13, 24, 16, 21 ] , [ 15, 0, 0, 15 ] , [ 17, 24, 8, 13 ] | |||
^ | Level 30 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/30Z) Matrix Generators |
30A3 | 30 | 1 | 5 | 0 | 0 | [ 1, 15, 15, 16 ] , [ 7, 21, 15, 28 ] , [ 11, 0, 0, 11 ] , [ 11, 10, 10, 1 ] , [ 13, 6, 12, 1 ] , [ 19, 0, 0, 19 ] , [ 21, 10, 20, 21 ] , [ 22, 15, 27, 13 ] | |||
30B3 | 36 | 1 | 6 | 0 | 0 | [ 1, 10, 10, 11 ] , [ 7, 18, 18, 25 ] , [ 11, 0, 0, 11 ] , [ 16, 15, 15, 1 ] , [ 21, 10, 20, 21 ] , [ 27, 10, 2, 3 ] , [ 29, 0, 0, 29 ] | |||
30C3 | 36 | 1 | 12 | 0 | 0 | [ 11, 0, 0, 11 ] , [ 11, 10, 10, 1 ] , [ 13, 6, 6, 19 ] , [ 13, 18, 0, 7 ] , [ 16, 15, 25, 1 ] , [ 19, 0, 0, 19 ] , [ 21, 10, 20, 21 ] | |||
30D3 | 45 | 1 | 15 | 3 | 0 | [ 1, 0, 15, 1 ] , [ 7, 0, 12, 13 ] , [ 7, 6, 0, 13 ] , [ 11, 0, 0, 11 ] , [ 11, 10, 10, 1 ] , [ 13, 6, 12, 1 ] , [ 19, 0, 0, 19 ] , [ 21, 10, 20, 21 ] | |||
30E3 | 45 | 2 | 15 | 3 | 0 | [ 1, 0, 15, 1 ] , [ 1, 18, 6, 19 ] , [ 7, 0, 12, 13 ] , [ 11, 0, 0, 11 ] , [ 11, 10, 10, 1 ] , [ 19, 0, 0, 19 ] , [ 19, 24, 16, 25 ] , [ 21, 20, 10, 21 ] | |||
30F3 | 48 | 1 | 24 | 0 | 0 | [ 1, 0, 20, 1 ] , [ 7, 18, 18, 25 ] , [ 11, 0, 20, 11 ] , [ 16, 15, 15, 1 ] , [ 19, 0, 10, 19 ] , [ 19, 6, 23, 1 ] | |||
30G3 | 48 | 1 | 24 | 0 | 0 | [ 1, 0, 20, 1 ] , [ 7, 18, 18, 25 ] , [ 11, 0, 20, 11 ] , [ 16, 15, 15, 1 ] , [ 19, 0, 10, 19 ] , [ 19, 6, 8, 1 ] | |||
30H3 | 60 | 1 | 30 | 8 | 0 | [ 1, 15, 15, 16 ] , [ 7, 0, 24, 13 ] , [ 11, 0, 0, 11 ] , [ 11, 10, 25, 1 ] , [ 19, 0, 0, 19 ] , [ 21, 10, 20, 21 ] , [ 25, 12, 12, 19 ] | |||
30I3 | 72 | 1 | 18 | 8 | 0 | [ 1, 12, 24, 19 ] , [ 5, 12, 12, 17 ] , [ 13, 6, 6, 19 ] , [ 13, 16, 1, 29 ] , [ 16, 15, 15, 1 ] , [ 19, 0, 0, 19 ] | |||
30J3 | 72 | 1 | 18 | 8 | 0 | [ 1, 12, 9, 19 ] , [ 5, 12, 12, 17 ] , [ 13, 6, 6, 19 ] , [ 13, 16, 16, 29 ] , [ 16, 15, 15, 1 ] , [ 19, 0, 0, 19 ] | |||
30K3 | Γ0(30) | 72 | 1 | 72 | 0 | 0 | [ 1, 0, 15, 1 ] , [ 1, 0, 20, 1 ] , [ 7, 18, 18, 25 ] , [ 11, 0, 20, 11 ] , [ 19, 0, 10, 19 ] , [ 19, 6, 8, 1 ] | ||
30L3 | 72 | 2 | 18 | 8 | 0 | [ 1, 15, 15, 16 ] , [ 11, 0, 0, 11 ] , [ 13, 6, 6, 19 ] , [ 13, 10, 13, 17 ] , [ 19, 0, 0, 19 ] , [ 21, 10, 5, 21 ] | |||
^ | Level 32 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/32Z) Matrix Generators |
32A3 | 48 | 1 | 6 | 0 | 0 | [ 1, 16, 16, 1 ] , [ 5, 28, 20, 29 ] , [ 9, 22, 18, 5 ] , [ 11, 2, 30, 23 ] , [ 13, 22, 10, 17 ] , [ 17, 4, 4, 1 ] , [ 17, 16, 16, 17 ] , [ 21, 4, 28, 13 ] , [ 25, 24, 8, 9 ] , [ 27, 30, 26, 23 ] , [ 28, 23, 17, 14 ] , [ 29, 8, 16, 21 ] | |||
32B3 | 48 | 1 | 6 | 0 | 0 | [ 1, 16, 16, 1 ] , [ 5, 28, 20, 29 ] , [ 9, 22, 18, 5 ] , [ 11, 2, 30, 23 ] , [ 13, 22, 10, 17 ] , [ 17, 4, 4, 1 ] , [ 17, 16, 16, 17 ] , [ 21, 4, 28, 13 ] , [ 25, 24, 8, 9 ] , [ 27, 30, 26, 23 ] , [ 29, 8, 16, 21 ] , [ 30, 5, 27, 28 ] | |||
32C3 | 48 | 1 | 12 | 0 | 0 | [ 1, 16, 16, 1 ] , [ 5, 28, 20, 29 ] , [ 9, 22, 2, 5 ] , [ 11, 2, 30, 23 ] , [ 13, 22, 10, 17 ] , [ 17, 4, 20, 1 ] , [ 17, 16, 16, 17 ] , [ 21, 4, 28, 13 ] , [ 25, 24, 8, 9 ] , [ 27, 30, 10, 23 ] , [ 29, 8, 0, 21 ] , [ 30, 5, 27, 28 ] | |||
32D3 | 48 | 1 | 12 | 4 | 0 | [ 0, 5, 19, 0 ] , [ 1, 8, 8, 1 ] , [ 1, 16, 16, 1 ] , [ 9, 6, 6, 29 ] , [ 9, 8, 8, 25 ] , [ 13, 6, 6, 25 ] , [ 13, 18, 18, 25 ] , [ 17, 16, 16, 17 ] , [ 21, 4, 4, 13 ] , [ 31, 0, 0, 31 ] | |||
32E3 | 48 | 1 | 24 | 4 | 0 | [ 1, 8, 24, 1 ] , [ 1, 16, 16, 1 ] , [ 1, 24, 8, 1 ] , [ 11, 6, 6, 15 ] , [ 11, 14, 30, 15 ] , [ 12, 9, 23, 4 ] , [ 15, 2, 18, 11 ] , [ 17, 16, 16, 17 ] , [ 25, 24, 24, 9 ] , [ 27, 18, 10, 15 ] , [ 29, 28, 28, 5 ] , [ 31, 16, 16, 31 ] | |||
32F3 | 48 | 1 | 24 | 4 | 0 | [ 1, 8, 24, 1 ] , [ 1, 16, 16, 1 ] , [ 1, 24, 8, 1 ] , [ 9, 4, 12, 9 ] , [ 11, 6, 6, 15 ] , [ 11, 14, 30, 15 ] , [ 12, 9, 23, 4 ] , [ 15, 2, 18, 11 ] , [ 17, 16, 16, 17 ] , [ 25, 24, 24, 9 ] , [ 29, 28, 28, 5 ] , [ 31, 16, 16, 31 ] | |||
32G3 | 48 | 1 | 24 | 4 | 0 | [ 1, 8, 24, 1 ] , [ 1, 16, 16, 1 ] , [ 1, 24, 8, 1 ] , [ 11, 6, 22, 15 ] , [ 11, 14, 14, 15 ] , [ 15, 2, 2, 11 ] , [ 15, 30, 22, 27 ] , [ 17, 16, 16, 17 ] , [ 24, 5, 19, 24 ] , [ 25, 24, 24, 9 ] , [ 29, 28, 28, 5 ] , [ 31, 16, 16, 31 ] | |||
32H3 | 48 | 1 | 24 | 4 | 0 | [ 1, 8, 24, 1 ] , [ 1, 16, 16, 1 ] , [ 1, 24, 8, 1 ] , [ 9, 4, 12, 9 ] , [ 11, 6, 22, 15 ] , [ 11, 14, 14, 15 ] , [ 15, 2, 2, 11 ] , [ 17, 16, 16, 17 ] , [ 24, 5, 19, 24 ] , [ 25, 24, 24, 9 ] , [ 29, 28, 28, 5 ] , [ 31, 16, 16, 31 ] | |||
32I3 | 48 | 2 | 24 | 2 | 0 | [ 1, 16, 16, 1 ] , [ 9, 16, 16, 25 ] , [ 9, 24, 8, 25 ] , [ 10, 25, 27, 10 ] , [ 17, 0, 0, 17 ] , [ 19, 30, 10, 31 ] , [ 21, 0, 0, 29 ] , [ 21, 28, 20, 13 ] , [ 24, 29, 11, 16 ] , [ 25, 0, 0, 9 ] , [ 31, 0, 0, 31 ] , [ 31, 8, 24, 31 ] | |||
32J3 | 96 | 1 | 6 | 0 | 0 | [ 1, 16, 0, 1 ] , [ 5, 16, 16, 13 ] , [ 9, 12, 16, 25 ] , [ 13, 30, 8, 21 ] , [ 17, 0, 0, 17 ] , [ 17, 4, 16, 17 ] , [ 17, 24, 0, 17 ] , [ 25, 0, 0, 9 ] , [ 25, 24, 0, 9 ] , [ 25, 28, 16, 9 ] , [ 31, 2, 8, 15 ] | |||
32K3 | 96 | 1 | 6 | 0 | 0 | [ 1, 16, 0, 1 ] , [ 5, 16, 0, 13 ] , [ 13, 30, 8, 21 ] , [ 17, 0, 0, 17 ] , [ 17, 4, 16, 17 ] , [ 17, 24, 0, 17 ] , [ 19, 26, 24, 11 ] , [ 21, 12, 16, 29 ] , [ 25, 0, 0, 9 ] , [ 25, 24, 0, 9 ] , [ 25, 28, 16, 9 ] | |||
32L3 | 96 | 1 | 6 | 16 | 0 | [ 1, 16, 16, 1 ] , [ 4, 1, 15, 28 ] , [ 13, 0, 0, 5 ] , [ 17, 0, 0, 17 ] , [ 17, 8, 8, 17 ] , [ 17, 12, 12, 1 ] , [ 25, 0, 0, 9 ] , [ 29, 4, 4, 5 ] , [ 31, 0, 0, 31 ] | |||
32M3 | 96 | 1 | 12 | 0 | 0 | [ 5, 12, 4, 29 ] , [ 5, 30, 18, 25 ] , [ 8, 25, 7, 6 ] , [ 9, 8, 24, 25 ] , [ 11, 26, 6, 23 ] , [ 17, 0, 0, 17 ] , [ 17, 16, 16, 17 ] , [ 21, 20, 12, 13 ] , [ 21, 28, 20, 13 ] , [ 28, 29, 3, 18 ] , [ 30, 13, 19, 20 ] | |||
32N3 | 96 | 1 | 12 | 16 | 0 | [ 9, 6, 22, 29 ] , [ 9, 8, 8, 25 ] , [ 9, 16, 16, 25 ] , [ 14, 27, 1, 18 ] , [ 17, 0, 0, 17 ] , [ 17, 16, 16, 17 ] , [ 21, 4, 4, 13 ] , [ 31, 16, 16, 31 ] | |||
32O3 | 96 | 1 | 24 | 0 | 0 | [ 1, 16, 16, 1 ] , [ 7, 8, 24, 23 ] , [ 9, 8, 24, 25 ] , [ 11, 2, 30, 23 ] , [ 11, 4, 28, 19 ] , [ 17, 16, 16, 17 ] , [ 21, 4, 28, 13 ] , [ 27, 2, 30, 7 ] , [ 30, 13, 3, 12 ] | |||
32P3 | 96 | 1 | 24 | 4 | 0 | [ 17, 0, 0, 17 ] , [ 17, 16, 16, 17 ] , [ 19, 4, 28, 11 ] , [ 23, 12, 20, 23 ] , [ 25, 8, 24, 9 ] , [ 25, 16, 16, 9 ] , [ 28, 27, 29, 4 ] , [ 31, 8, 24, 31 ] , [ 31, 20, 12, 15 ] | |||
32Q3 | 96 | 1 | 24 | 4 | 0 | [ 13, 0, 16, 5 ] , [ 17, 0, 0, 17 ] , [ 17, 16, 16, 17 ] , [ 20, 3, 5, 12 ] , [ 23, 12, 4, 23 ] , [ 25, 8, 24, 9 ] , [ 25, 16, 16, 9 ] , [ 31, 8, 24, 31 ] , [ 31, 20, 28, 15 ] | |||
^ | Level 33 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/33Z) Matrix Generators |
33A3 | 36 | 1 | 12 | 0 | 0 | [ 1, 22, 22, 23 ] , [ 4, 24, 12, 31 ] , [ 23, 0, 0, 23 ] , [ 23, 22, 22, 1 ] , [ 25, 6, 9, 22 ] , [ 32, 0, 0, 32 ] | |||
33B3 | 44 | 2 | 44 | 0 | 2 | [ 1, 0, 22, 1 ] , [ 1, 15, 24, 31 ] , [ 23, 0, 0, 23 ] , [ 32, 0, 0, 32 ] , [ 32, 6, 18, 23 ] | |||
33C3 | Γ0(33) | 48 | 1 | 48 | 0 | 0 | [ 1, 0, 22, 1 ] , [ 4, 24, 12, 31 ] , [ 23, 0, 0, 23 ] , [ 25, 6, 9, 22 ] , [ 32, 0, 0, 32 ] | ||
^ | Level 34 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/34Z) Matrix Generators |
34A3 | 36 | 1 | 18 | 0 | 0 | [ 1, 0, 8, 1 ] , [ 1, 17, 17, 18 ] , [ 15, 0, 8, 25 ] , [ 21, 0, 14, 13 ] , [ 27, 0, 5, 29 ] , [ 33, 0, 0, 33 ] | |||
34B3 | 36 | 1 | 18 | 0 | 0 | [ 1, 0, 8, 1 ] , [ 1, 17, 17, 18 ] , [ 15, 0, 8, 25 ] , [ 21, 0, 14, 13 ] , [ 27, 0, 22, 29 ] , [ 33, 0, 0, 33 ] | |||
34C3 | Γ0(34) | 54 | 1 | 54 | 2 | 0 | [ 1, 0, 8, 1 ] , [ 1, 0, 17, 1 ] , [ 15, 0, 8, 25 ] , [ 21, 0, 14, 13 ] , [ 27, 0, 22, 29 ] , [ 33, 0, 0, 33 ] | ||
^ | Level 35 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/35Z) Matrix Generators |
35A3 | Γ0(35) | 48 | 1 | 48 | 0 | 0 | [ 1, 0, 25, 1 ] , [ 6, 0, 0, 6 ] , [ 6, 28, 6, 34 ] , [ 15, 14, 11, 22 ] , [ 16, 0, 0, 11 ] , [ 29, 0, 0, 29 ] | ||
^ | Level 36 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/36Z) Matrix Generators |
36A3 | 48 | 1 | 4 | 0 | 0 | [ 1, 0, 12, 1 ] , [ 1, 18, 18, 1 ] , [ 13, 27, 19, 34 ] , [ 19, 18, 0, 19 ] , [ 25, 0, 0, 13 ] , [ 31, 0, 34, 7 ] , [ 35, 0, 0, 35 ] | |||
36B3 | 48 | 1 | 16 | 0 | 0 | [ 1, 0, 20, 1 ] , [ 10, 9, 27, 10 ] , [ 13, 0, 0, 25 ] , [ 19, 0, 0, 19 ] , [ 19, 9, 27, 28 ] , [ 25, 0, 24, 13 ] , [ 35, 0, 0, 35 ] | |||
36C3 | 48 | 1 | 16 | 0 | 3 | [ 10, 9, 27, 10 ] , [ 13, 0, 0, 25 ] , [ 19, 0, 0, 19 ] , [ 19, 9, 27, 28 ] , [ 25, 0, 24, 13 ] , [ 25, 12, 8, 1 ] , [ 35, 0, 0, 35 ] | |||
36D3 | 54 | 1 | 27 | 4 | 0 | [ 1, 0, 18, 1 ] , [ 15, 14, 16, 27 ] , [ 19, 0, 18, 19 ] , [ 23, 0, 30, 11 ] , [ 25, 0, 12, 13 ] , [ 25, 12, 0, 13 ] , [ 29, 28, 4, 25 ] , [ 33, 10, 17, 15 ] | |||
36E3 | 54 | 1 | 27 | 6 | 0 | [ 1, 0, 18, 1 ] , [ 11, 8, 35, 19 ] , [ 15, 14, 16, 27 ] , [ 15, 28, 35, 15 ] , [ 19, 0, 18, 19 ] , [ 23, 0, 30, 11 ] , [ 25, 0, 12, 13 ] , [ 25, 12, 0, 13 ] | |||
36F3 | 72 | 1 | 6 | 12 | 0 | [ 1, 9, 9, 10 ] , [ 1, 18, 18, 1 ] , [ 9, 10, 35, 27 ] , [ 13, 0, 0, 25 ] , [ 19, 18, 0, 19 ] , [ 25, 12, 12, 13 ] , [ 35, 0, 0, 35 ] | |||
36G3 | 72 | 1 | 12 | 0 | 0 | [ 1, 0, 12, 1 ] , [ 1, 0, 18, 1 ] , [ 1, 18, 9, 19 ] , [ 13, 0, 0, 25 ] , [ 19, 0, 18, 19 ] , [ 25, 0, 20, 13 ] , [ 35, 0, 0, 35 ] | |||
36H3 | 72 | 1 | 12 | 12 | 0 | [ 1, 24, 12, 1 ] , [ 10, 27, 27, 1 ] , [ 13, 0, 24, 25 ] , [ 19, 0, 0, 19 ] , [ 28, 9, 27, 28 ] , [ 29, 12, 12, 5 ] , [ 29, 28, 4, 25 ] | |||
36I3 | 108 | 1 | 54 | 4 | 0 | [ 1, 0, 18, 1 ] , [ 13, 0, 24, 25 ] , [ 19, 0, 18, 19 ] , [ 25, 12, 12, 13 ] , [ 25, 24, 3, 13 ] , [ 29, 24, 24, 5 ] , [ 35, 34, 4, 7 ] | |||
36J3 | 144 | 1 | 12 | 0 | 0 | [ 1, 0, 18, 1 ] , [ 1, 0, 24, 1 ] , [ 1, 18, 18, 1 ] , [ 13, 0, 4, 25 ] , [ 25, 0, 24, 13 ] , [ 35, 0, 0, 35 ] | |||
36K3 | 144 | 1 | 24 | 0 | 0 | [ 1, 0, 12, 1 ] , [ 1, 0, 18, 1 ] , [ 1, 0, 27, 1 ] , [ 13, 0, 0, 25 ] , [ 25, 0, 8, 13 ] , [ 35, 0, 0, 35 ] | |||
^ | Level 39 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/39Z) Matrix Generators |
39A3 | Γ0(39) | 56 | 1 | 56 | 0 | 2 | [ 1, 0, 13, 1 ] , [ 4, 0, 24, 10 ] , [ 13, 3, 30, 28 ] , [ 14, 0, 0, 14 ] , [ 31, 33, 3, 7 ] , [ 37, 27, 3, 37 ] | ||
^ | Level 40 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/40Z) Matrix Generators |
40A3 | 48 | 2 | 24 | 4 | 0 | [ 1, 20, 20, 1 ] , [ 9, 0, 0, 9 ] , [ 9, 16, 28, 1 ] , [ 12, 17, 15, 8 ] , [ 21, 0, 20, 21 ] , [ 21, 15, 15, 26 ] , [ 25, 32, 32, 17 ] , [ 39, 0, 0, 39 ] | |||
40B3 | 48 | 2 | 24 | 4 | 0 | [ 1, 20, 20, 1 ] , [ 9, 0, 0, 9 ] , [ 9, 16, 8, 1 ] , [ 12, 17, 15, 8 ] , [ 21, 0, 20, 21 ] , [ 21, 15, 15, 26 ] , [ 25, 32, 32, 17 ] , [ 39, 0, 0, 39 ] | |||
40C3 | 72 | 1 | 18 | 8 | 0 | [ 1, 20, 20, 1 ] , [ 6, 15, 5, 6 ] , [ 9, 0, 0, 9 ] , [ 21, 0, 0, 21 ] , [ 25, 32, 32, 17 ] , [ 31, 20, 20, 31 ] , [ 31, 30, 30, 11 ] , [ 39, 38, 26, 11 ] | |||
40D3 | 72 | 1 | 18 | 8 | 0 | [ 1, 20, 20, 1 ] , [ 6, 15, 5, 26 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 16, 1 ] , [ 16, 5, 35, 16 ] , [ 21, 0, 0, 21 ] , [ 25, 32, 32, 17 ] , [ 31, 20, 20, 31 ] | |||
40E3 | 72 | 1 | 36 | 0 | 0 | [ 1, 10, 30, 21 ] , [ 1, 20, 20, 1 ] , [ 6, 7, 9, 24 ] , [ 6, 15, 25, 36 ] , [ 9, 0, 0, 9 ] , [ 11, 10, 30, 31 ] , [ 21, 20, 20, 21 ] , [ 25, 32, 32, 17 ] | |||
40F3 | Γ0(40) | 72 | 1 | 36 | 0 | 0 | [ 1, 10, 30, 21 ] , [ 1, 20, 20, 1 ] , [ 1, 32, 24, 9 ] , [ 6, 15, 25, 36 ] , [ 9, 0, 0, 9 ] , [ 11, 10, 30, 31 ] , [ 21, 20, 20, 21 ] , [ 25, 32, 32, 17 ] | ||
40G3 | 72 | 1 | 36 | 4 | 0 | [ 1, 20, 20, 1 ] , [ 6, 15, 5, 26 ] , [ 9, 0, 0, 9 ] , [ 14, 23, 21, 6 ] , [ 21, 0, 0, 21 ] , [ 25, 32, 32, 17 ] , [ 31, 20, 20, 31 ] , [ 31, 30, 10, 11 ] | |||
40H3 | 72 | 1 | 36 | 4 | 0 | [ 1, 20, 20, 1 ] , [ 6, 15, 5, 26 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 16, 1 ] , [ 21, 0, 0, 21 ] , [ 25, 32, 32, 17 ] , [ 31, 20, 20, 31 ] , [ 31, 30, 10, 11 ] | |||
40I3 | 72 | 2 | 18 | 4 | 0 | [ 1, 20, 20, 1 ] , [ 1, 32, 34, 9 ] , [ 6, 15, 25, 16 ] , [ 9, 0, 20, 9 ] , [ 11, 10, 30, 31 ] , [ 17, 8, 8, 25 ] , [ 21, 20, 20, 21 ] , [ 21, 30, 30, 1 ] | |||
40J3 | 144 | 1 | 18 | 0 | 0 | [ 1, 20, 20, 1 ] , [ 6, 15, 25, 36 ] , [ 11, 10, 30, 31 ] , [ 16, 15, 25, 26 ] , [ 21, 20, 20, 21 ] , [ 33, 16, 16, 9 ] , [ 38, 7, 17, 0 ] | |||
^ | Level 41 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/41Z) Matrix Generators |
41A3 | Γ0(41) | 42 | 1 | 42 | 2 | 0 | [ 3, 3, 26, 40 ] , [ 19, 15, 36, 22 ] , [ 30, 25, 19, 35 ] , [ 30, 39, 28, 5 ] , [ 40, 0, 0, 40 ] | ||
^ | Level 42 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/42Z) Matrix Generators |
42A3 | 42 | 2 | 14 | 0 | 3 | [ 1, 14, 14, 29 ] , [ 1, 30, 18, 37 ] , [ 7, 12, 18, 7 ] , [ 7, 24, 30, 13 ] , [ 13, 0, 0, 13 ] , [ 15, 14, 28, 15 ] , [ 15, 28, 14, 15 ] , [ 22, 21, 7, 1 ] , [ 29, 0, 0, 29 ] , [ 37, 6, 12, 19 ] | |||
42B3 | 48 | 2 | 16 | 0 | 3 | [ 13, 0, 0, 13 ] , [ 13, 6, 8, 7 ] , [ 15, 14, 28, 15 ] , [ 20, 27, 15, 35 ] , [ 25, 8, 26, 5 ] , [ 29, 0, 0, 29 ] , [ 29, 28, 28, 1 ] , [ 31, 24, 36, 13 ] | |||
42C3 | 63 | 2 | 21 | 9 | 0 | [ 1, 0, 21, 1 ] , [ 7, 12, 18, 7 ] , [ 7, 24, 30, 13 ] , [ 13, 0, 0, 13 ] , [ 13, 12, 24, 19 ] , [ 15, 14, 28, 15 ] , [ 29, 0, 0, 29 ] , [ 29, 14, 35, 1 ] , [ 37, 6, 12, 19 ] | |||
42D3 | 64 | 1 | 32 | 0 | 4 | [ 1, 0, 28, 1 ] , [ 1, 21, 21, 22 ] , [ 1, 30, 30, 19 ] , [ 13, 0, 21, 13 ] , [ 13, 18, 6, 31 ] , [ 37, 12, 18, 7 ] , [ 41, 0, 0, 41 ] | |||
42E3 | 64 | 1 | 32 | 0 | 4 | [ 1, 0, 28, 1 ] , [ 1, 21, 21, 22 ] , [ 1, 30, 30, 19 ] , [ 13, 0, 0, 13 ] , [ 13, 18, 6, 31 ] , [ 29, 0, 0, 29 ] , [ 37, 12, 18, 7 ] | |||
42F3 | 84 | 2 | 21 | 16 | 0 | [ 1, 21, 21, 22 ] , [ 7, 12, 18, 7 ] , [ 13, 0, 0, 13 ] , [ 17, 20, 17, 25 ] , [ 23, 6, 12, 5 ] , [ 25, 18, 36, 31 ] , [ 29, 0, 0, 29 ] , [ 33, 2, 25, 27 ] , [ 37, 30, 0, 25 ] | |||
^ | Level 43 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/43Z) Matrix Generators |
43A3 | Γ0(43) | 44 | 1 | 44 | 0 | 2 | [ 8, 19, 11, 37 ] , [ 24, 21, 24, 30 ] , [ 41, 32, 12, 1 ] , [ 42, 0, 0, 42 ] | ||
^ | Level 45 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/45Z) Matrix Generators |
45A3 | 45 | 1 | 45 | 5 | 0 | [ 1, 30, 15, 1 ] , [ 16, 0, 15, 31 ] , [ 19, 0, 0, 19 ] , [ 19, 27, 9, 1 ] , [ 22, 18, 21, 7 ] , [ 26, 20, 35, 1 ] , [ 36, 5, 25, 6 ] , [ 37, 36, 0, 28 ] , [ 41, 30, 30, 11 ] | |||
45B3 | 60 | 1 | 20 | 0 | 6 | [ 1, 27, 9, 19 ] , [ 1, 35, 30, 16 ] , [ 10, 9, 36, 19 ] , [ 16, 15, 0, 31 ] , [ 19, 0, 0, 19 ] , [ 19, 18, 36, 1 ] , [ 28, 36, 0, 37 ] , [ 31, 0, 0, 16 ] , [ 41, 5, 30, 41 ] | |||
45C3 | 60 | 2 | 20 | 0 | 3 | [ 1, 27, 9, 19 ] , [ 1, 40, 0, 1 ] , [ 10, 9, 21, 19 ] , [ 14, 21, 39, 20 ] , [ 16, 15, 0, 31 ] , [ 19, 0, 0, 19 ] , [ 19, 18, 36, 1 ] , [ 28, 36, 0, 37 ] , [ 31, 0, 0, 16 ] | |||
45D3 | Γ0(45) | 72 | 1 | 24 | 0 | 0 | [ 8, 24, 24, 44 ] , [ 18, 14, 34, 29 ] , [ 31, 0, 30, 16 ] , [ 31, 30, 15, 16 ] , [ 32, 3, 0, 38 ] , [ 34, 30, 0, 4 ] , [ 37, 27, 27, 10 ] | ||
^ | Level 48 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/48Z) Matrix Generators |
48A3 | 48 | 2 | 8 | 6 | 0 | [ 0, 1, 47, 0 ] , [ 1, 16, 16, 17 ] , [ 1, 24, 24, 1 ] , [ 13, 45, 45, 34 ] , [ 17, 0, 0, 17 ] , [ 17, 16, 16, 1 ] , [ 25, 12, 12, 25 ] , [ 25, 24, 0, 25 ] , [ 37, 12, 24, 13 ] , [ 47, 0, 0, 47 ] | |||
48B3 | 48 | 2 | 24 | 6 | 0 | [ 0, 1, 47, 24 ] , [ 1, 16, 16, 17 ] , [ 1, 24, 24, 1 ] , [ 13, 45, 45, 34 ] , [ 17, 0, 0, 17 ] , [ 25, 12, 12, 25 ] , [ 25, 24, 0, 25 ] , [ 32, 17, 47, 16 ] , [ 37, 12, 24, 13 ] , [ 47, 0, 0, 47 ] | |||
48C3 | 72 | 1 | 6 | 12 | 0 | [ 1, 0, 24, 1 ] , [ 13, 20, 38, 29 ] , [ 17, 0, 0, 17 ] , [ 17, 32, 32, 1 ] , [ 23, 0, 24, 23 ] , [ 25, 0, 24, 25 ] , [ 25, 20, 2, 17 ] , [ 33, 32, 16, 33 ] , [ 39, 34, 35, 33 ] , [ 41, 24, 36, 41 ] | |||
48D3 | 72 | 1 | 12 | 6 | 0 | [ 1, 0, 24, 1 ] , [ 1, 32, 32, 17 ] , [ 3, 46, 23, 33 ] , [ 5, 24, 24, 29 ] , [ 17, 0, 0, 17 ] , [ 17, 0, 36, 17 ] , [ 17, 16, 34, 1 ] , [ 17, 32, 32, 1 ] , [ 25, 0, 0, 25 ] , [ 25, 0, 24, 25 ] , [ 35, 24, 36, 11 ] | |||
48E3 | 72 | 1 | 12 | 12 | 0 | [ 1, 0, 24, 1 ] , [ 17, 0, 0, 17 ] , [ 17, 32, 32, 1 ] , [ 23, 0, 24, 23 ] , [ 25, 0, 24, 25 ] , [ 25, 20, 2, 17 ] , [ 33, 32, 16, 33 ] , [ 37, 0, 0, 13 ] , [ 39, 34, 35, 33 ] , [ 41, 24, 36, 41 ] | |||
48F3 | 72 | 1 | 18 | 12 | 0 | [ 1, 0, 24, 1 ] , [ 9, 20, 46, 33 ] , [ 13, 20, 38, 29 ] , [ 17, 0, 0, 17 ] , [ 23, 0, 24, 23 ] , [ 25, 0, 24, 25 ] , [ 25, 4, 46, 17 ] , [ 25, 20, 2, 17 ] , [ 39, 34, 35, 33 ] , [ 41, 24, 36, 41 ] | |||
48G3 | 72 | 1 | 36 | 6 | 0 | [ 1, 0, 24, 1 ] , [ 3, 46, 23, 33 ] , [ 5, 24, 24, 29 ] , [ 17, 0, 0, 17 ] , [ 17, 0, 36, 17 ] , [ 19, 22, 7, 41 ] , [ 19, 38, 23, 41 ] , [ 25, 0, 0, 25 ] , [ 25, 0, 24, 25 ] , [ 35, 24, 36, 11 ] , [ 35, 38, 29, 37 ] | |||
48H3 | 72 | 1 | 36 | 12 | 0 | [ 1, 0, 24, 1 ] , [ 9, 20, 46, 33 ] , [ 17, 0, 0, 17 ] , [ 23, 0, 24, 23 ] , [ 25, 0, 24, 25 ] , [ 25, 4, 46, 17 ] , [ 25, 20, 2, 17 ] , [ 37, 0, 0, 13 ] , [ 39, 34, 35, 33 ] , [ 41, 24, 36, 41 ] | |||
48I3 | 96 | 1 | 24 | 0 | 0 | [ 1, 0, 16, 1 ] , [ 1, 24, 24, 1 ] , [ 10, 9, 39, 40 ] , [ 16, 3, 21, 34 ] , [ 19, 42, 6, 31 ] , [ 22, 39, 9, 16 ] , [ 25, 0, 0, 25 ] , [ 26, 9, 39, 32 ] , [ 37, 36, 12, 13 ] | |||
48J3 | Γ0(48) | 96 | 1 | 24 | 0 | 0 | [ 1, 0, 16, 1 ] , [ 1, 24, 24, 1 ] , [ 13, 6, 42, 1 ] , [ 16, 45, 27, 46 ] , [ 17, 0, 0, 17 ] , [ 19, 42, 6, 31 ] , [ 22, 39, 9, 40 ] , [ 25, 0, 0, 25 ] , [ 37, 36, 12, 13 ] | ||
48K3 | 96 | 1 | 48 | 0 | 0 | [ 1, 0, 16, 1 ] , [ 1, 24, 24, 1 ] , [ 10, 9, 39, 16 ] , [ 19, 42, 6, 31 ] , [ 22, 39, 9, 40 ] , [ 25, 0, 0, 25 ] , [ 37, 36, 12, 13 ] , [ 38, 39, 9, 32 ] , [ 43, 30, 18, 7 ] | |||
48L3 | 96 | 1 | 48 | 0 | 0 | [ 1, 0, 16, 1 ] , [ 1, 24, 24, 1 ] , [ 13, 6, 42, 1 ] , [ 17, 0, 0, 17 ] , [ 19, 42, 6, 31 ] , [ 22, 39, 9, 40 ] , [ 25, 0, 0, 25 ] , [ 37, 36, 12, 13 ] , [ 43, 30, 18, 7 ] | |||
48M3 | 144 | 1 | 9 | 32 | 0 | [ 1, 0, 24, 1 ] , [ 17, 0, 0, 17 ] , [ 25, 0, 24, 25 ] , [ 33, 28, 26, 9 ] , [ 33, 32, 16, 33 ] , [ 41, 24, 12, 41 ] , [ 45, 28, 38, 45 ] , [ 47, 0, 0, 47 ] , [ 47, 2, 47, 1 ] | |||
^ | Level 49 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/49Z) Matrix Generators |
49A3 | 168 | 1 | 8 | 0 | 0 | [ 22, 28, 21, 29 ] , [ 25, 39, 38, 26 ] , [ 36, 0, 21, 15 ] , [ 48, 0, 0, 48 ] | |||
^ | Level 50 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/50Z) Matrix Generators |
50A3 | 60 | 1 | 30 | 0 | 0 | [ 7, 48, 18, 45 ] , [ 19, 0, 20, 29 ] , [ 26, 25, 25, 1 ] , [ 31, 0, 30, 21 ] , [ 31, 40, 40, 21 ] , [ 41, 0, 40, 11 ] , [ 43, 40, 48, 47 ] | |||
^ | Level 51 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/51Z) Matrix Generators |
51A3 | 54 | 1 | 18 | 6 | 0 | [ 1, 0, 42, 1 ] , [ 10, 34, 22, 29 ] , [ 18, 17, 34, 18 ] , [ 32, 34, 25, 25 ] , [ 35, 0, 0, 35 ] , [ 35, 17, 17, 1 ] , [ 38, 17, 14, 13 ] , [ 50, 34, 34, 16 ] | |||
^ | Level 52 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/52Z) Matrix Generators |
52A3 | 56 | 1 | 56 | 4 | 2 | [ 5, 20, 16, 33 ] , [ 13, 16, 4, 41 ] , [ 14, 39, 39, 1 ] , [ 17, 0, 24, 49 ] , [ 27, 0, 0, 27 ] , [ 27, 26, 13, 1 ] , [ 37, 40, 16, 37 ] | |||
52B3 | 112 | 1 | 14 | 0 | 16 | [ 17, 28, 48, 21 ] , [ 25, 0, 26, 25 ] , [ 27, 0, 26, 27 ] , [ 27, 13, 39, 40 ] , [ 27, 26, 0, 27 ] , [ 45, 24, 32, 9 ] | |||
^ | Level 54 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/54Z) Matrix Generators |
54A3 | 72 | 1 | 12 | 0 | 0 | [ 1, 0, 36, 1 ] , [ 1, 27, 27, 28 ] , [ 7, 18, 42, 31 ] , [ 7, 18, 46, 49 ] , [ 35, 0, 0, 17 ] , [ 37, 0, 36, 19 ] , [ 37, 0, 48, 19 ] | |||
54B3 | 72 | 1 | 24 | 0 | 0 | [ 1, 0, 36, 1 ] , [ 19, 0, 12, 37 ] , [ 19, 9, 49, 46 ] , [ 31, 45, 19, 52 ] , [ 37, 0, 0, 19 ] , [ 46, 45, 27, 37 ] , [ 53, 0, 0, 53 ] | |||
54C3 | 72 | 1 | 24 | 0 | 9 | [ 1, 0, 18, 1 ] , [ 16, 15, 25, 37 ] , [ 19, 0, 18, 37 ] , [ 28, 45, 9, 1 ] , [ 34, 27, 15, 31 ] , [ 37, 0, 36, 19 ] , [ 37, 18, 24, 19 ] , [ 53, 0, 0, 53 ] | |||
^ | Level 55 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/55Z) Matrix Generators |
55A3 | 55 | 2 | 55 | 3 | 4 | [ 1, 22, 44, 34 ] , [ 17, 52, 14, 17 ] , [ 18, 25, 42, 37 ] , [ 21, 11, 22, 43 ] , [ 23, 11, 0, 12 ] , [ 34, 0, 0, 34 ] , [ 54, 0, 0, 54 ] | |||
^ | Level 56 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/56Z) Matrix Generators |
56A3 | 56 | 2 | 28 | 6 | 2 | [ 1, 28, 28, 1 ] , [ 9, 40, 52, 1 ] , [ 9, 48, 40, 33 ] , [ 15, 0, 0, 15 ] , [ 15, 7, 42, 1 ] , [ 22, 49, 21, 1 ] , [ 29, 28, 0, 29 ] , [ 41, 0, 0, 41 ] , [ 49, 24, 16, 41 ] , [ 49, 40, 32, 49 ] | |||
56B3 | 56 | 2 | 28 | 6 | 2 | [ 1, 28, 28, 1 ] , [ 9, 48, 40, 33 ] , [ 15, 0, 0, 15 ] , [ 15, 7, 14, 29 ] , [ 22, 49, 21, 1 ] , [ 23, 47, 10, 1 ] , [ 29, 28, 0, 29 ] , [ 41, 0, 0, 41 ] , [ 49, 24, 16, 41 ] , [ 49, 40, 32, 49 ] | |||
56C3 | 56 | 2 | 28 | 6 | 2 | [ 1, 28, 28, 1 ] , [ 9, 40, 24, 1 ] , [ 9, 48, 40, 33 ] , [ 15, 0, 0, 15 ] , [ 15, 7, 14, 29 ] , [ 22, 49, 21, 1 ] , [ 29, 28, 0, 29 ] , [ 41, 0, 0, 41 ] , [ 49, 24, 16, 41 ] , [ 49, 40, 32, 49 ] | |||
56D3 | 56 | 2 | 28 | 6 | 2 | [ 1, 28, 28, 1 ] , [ 9, 40, 24, 1 ] , [ 9, 48, 40, 33 ] , [ 15, 0, 0, 15 ] , [ 15, 7, 42, 1 ] , [ 22, 49, 21, 1 ] , [ 29, 28, 0, 29 ] , [ 41, 0, 0, 41 ] , [ 49, 24, 16, 41 ] , [ 49, 40, 32, 49 ] | |||
^ | Level 60 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/60Z) Matrix Generators |
60A3 | 60 | 2 | 20 | 6 | 3 | [ 1, 20, 20, 41 ] , [ 13, 0, 48, 37 ] , [ 16, 15, 45, 16 ] , [ 21, 40, 20, 21 ] , [ 31, 0, 0, 31 ] , [ 37, 36, 0, 13 ] , [ 41, 0, 0, 41 ] , [ 46, 15, 15, 1 ] , [ 49, 0, 0, 49 ] , [ 49, 8, 48, 25 ] | |||
60B3 | 72 | 1 | 24 | 12 | 0 | [ 1, 30, 45, 31 ] , [ 13, 36, 36, 49 ] , [ 19, 0, 0, 19 ] , [ 19, 6, 3, 1 ] , [ 31, 0, 0, 31 ] , [ 41, 0, 0, 41 ] , [ 41, 20, 20, 1 ] , [ 41, 40, 40, 1 ] , [ 56, 45, 15, 11 ] | |||
60C3 | 72 | 2 | 6 | 12 | 0 | [ 1, 15, 15, 46 ] , [ 1, 20, 20, 41 ] , [ 1, 30, 30, 1 ] , [ 9, 11, 28, 21 ] , [ 13, 36, 36, 49 ] , [ 21, 20, 40, 21 ] , [ 31, 0, 30, 31 ] , [ 41, 0, 0, 41 ] , [ 59, 0, 0, 59 ] | |||
60D3 | 72 | 2 | 18 | 12 | 0 | [ 1, 15, 15, 46 ] , [ 1, 20, 50, 41 ] , [ 1, 30, 30, 1 ] , [ 9, 11, 58, 51 ] , [ 13, 36, 36, 49 ] , [ 21, 20, 40, 21 ] , [ 31, 0, 30, 31 ] , [ 41, 0, 0, 41 ] , [ 59, 0, 0, 59 ] | |||
^ | Level 64 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/64Z) Matrix Generators |
64A3 | 96 | 1 | 12 | 0 | 0 | [ 1, 32, 32, 1 ] , [ 5, 36, 28, 61 ] , [ 9, 8, 56, 57 ] , [ 17, 16, 48, 49 ] , [ 17, 50, 46, 45 ] , [ 27, 2, 46, 39 ] , [ 29, 26, 46, 17 ] , [ 33, 0, 0, 33 ] , [ 33, 32, 32, 33 ] , [ 35, 18, 46, 31 ] , [ 36, 63, 9, 30 ] , [ 53, 4, 28, 13 ] , [ 58, 61, 59, 8 ] , [ 59, 50, 30, 7 ] | |||
64B3 | Γ0(64) | 96 | 1 | 12 | 0 | 0 | [ 1, 32, 32, 1 ] , [ 5, 36, 28, 61 ] , [ 9, 8, 56, 57 ] , [ 17, 16, 48, 49 ] , [ 17, 50, 46, 45 ] , [ 27, 2, 46, 39 ] , [ 29, 26, 14, 17 ] , [ 33, 0, 0, 33 ] , [ 33, 32, 32, 33 ] , [ 35, 18, 46, 31 ] , [ 36, 63, 9, 30 ] , [ 53, 4, 28, 13 ] , [ 58, 61, 59, 8 ] , [ 59, 50, 30, 7 ] | ||
^ | Level 66 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/66Z) Matrix Generators |
66A3 | 66 | 2 | 33 | 12 | 0 | [ 1, 44, 44, 23 ] , [ 11, 26, 41, 7 ] , [ 23, 0, 0, 23 ] , [ 23, 55, 55, 34 ] , [ 26, 7, 7, 7 ] , [ 34, 33, 33, 1 ] , [ 45, 11, 22, 45 ] , [ 65, 0, 0, 65 ] | |||
^ | Level 72 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/72Z) Matrix Generators |
72A3 | 144 | 1 | 12 | 0 | 0 | [ 1, 24, 0, 1 ] , [ 1, 36, 0, 1 ] , [ 13, 56, 0, 61 ] , [ 19, 45, 36, 55 ] , [ 25, 53, 0, 49 ] , [ 29, 50, 36, 5 ] , [ 37, 18, 0, 37 ] , [ 37, 36, 0, 37 ] , [ 49, 0, 0, 25 ] , [ 49, 64, 0, 25 ] , [ 55, 36, 36, 55 ] | |||
^ | Level 84 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/84Z) Matrix Generators |
84A3 | 84 | 2 | 28 | 18 | 0 | [ 13, 0, 0, 13 ] , [ 15, 7, 14, 57 ] , [ 22, 21, 21, 1 ] , [ 29, 0, 0, 29 ] , [ 29, 28, 28, 1 ] , [ 37, 12, 24, 1 ] , [ 37, 48, 12, 61 ] , [ 49, 12, 60, 49 ] , [ 49, 24, 72, 13 ] , [ 57, 28, 56, 57 ] , [ 71, 0, 0, 71 ] | |||
^ | Level 96 | Name | Index | con | len | c2 | c3 | > | SL(2,Z/96Z) Matrix Generators |
96A3 | 144 | 1 | 12 | 36 | 0 | [ 1, 0, 48, 1 ] , [ 13, 20, 26, 77 ] , [ 25, 0, 72, 73 ] , [ 25, 20, 38, 65 ] , [ 33, 64, 32, 33 ] , [ 41, 72, 12, 89 ] , [ 49, 0, 48, 49 ] , [ 49, 48, 24, 49 ] , [ 65, 0, 0, 65 ] , [ 65, 32, 32, 1 ] , [ 71, 38, 77, 25 ] , [ 95, 0, 0, 95 ] |