The database currently contains 10465 Sato-Tate groups. The statistics below omit the infinite family $\mu(n)$ with trivial identity component since they are generated dynamically in search results.

## Distribution of component groups and identity components

identity component
$\operatorname{SO}(1)$ $\operatorname{SU}(2)$ $\operatorname{SU}(2)^3$ $\operatorname{SU}(2)_2$ $\operatorname{SU}(2)_3$ $\operatorname{SU}(2)\times\operatorname{SU}(2)$ $\operatorname{SU}(2)\times\operatorname{SU}(2)_2$ $\operatorname{SU}(2)\times\operatorname{U}(1)_2$ $\operatorname{SU}(2)\times\operatorname{USp}(4)$ $\operatorname{U}(1)$ $\operatorname{U}(1)^2\times\operatorname{SU}(2)$ $\operatorname{U}(1)^3$ $\operatorname{U}(1)_2$ $\operatorname{U}(1)_3$ $\operatorname{U}(1)\times\operatorname{SU}(2)$ $\operatorname{U}(1)\times\operatorname{SU}(2)^2$ $\operatorname{U}(1)\times\operatorname{SU}(2)_2$ $\operatorname{U}(1)\times\operatorname{U}(1)$ $\operatorname{U}(1)\times\operatorname{U}(1)_2$ $\operatorname{U}(1)\times\operatorname{USp}(4)$ $\operatorname{U}(3)$ $\operatorname{USp}(4)$ $\operatorname{USp}(6)$ Total
component group
$C_1$ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 23
50.00% 100.00% 25.00% 10.00% 9.09% 50.00% 10.00% 3.12% 100.00% 50.00% 20.00% 7.69% 3.12% 0.58% 50.00% 20.00% 3.23% 20.00% 0.82% 50.00% 50.00% 100.00% 100.00% 4.93%
$C_2$ 1 1 2 1 1 2 3 1 2 3 3 2 1 3 5 2 7 1 1 42
50.00% 25.00% 20.00% 9.09% 50.00% 20.00% 9.38% 50.00% 40.00% 23.08% 9.38% 1.17% 50.00% 60.00% 16.13% 40.00% 5.74% 50.00% 50.00% 8.99%
$C_3$ 1 1 1 1 1 1 1 2 1 1 11
25.00% 10.00% 9.09% 10.00% 3.12% 7.69% 3.12% 1.17% 3.23% 0.82% 2.36%
$C_4$ 1 1 1 2 1 2 2 3 2 1 4 20
10.00% 9.09% 10.00% 6.25% 20.00% 15.38% 6.25% 1.75% 6.45% 20.00% 3.28% 4.28%
$C_2^2$ 1 1 1 3 1 3 3 2 1 5 1 12 34
10.00% 9.09% 10.00% 9.38% 20.00% 23.08% 9.38% 1.17% 20.00% 16.13% 20.00% 9.84% 7.28%
$S_3$ 1 1 1 1 2 2 3 2 4 17
25.00% 10.00% 9.09% 10.00% 6.25% 6.25% 1.75% 6.45% 3.28% 3.64%
$C_6$ 1 1 1 3 1 3 4 3 7 24
10.00% 9.09% 10.00% 9.38% 7.69% 9.38% 2.34% 9.68% 5.74% 5.14%
$C_7$ 1 1
0.58% 0.21%
$C_8$ 3 3
1.75% 0.64%
$C_2\times C_4$ 1 1 1 2 1 6 12
3.12% 7.69% 3.12% 1.17% 3.23% 4.92% 2.57%
$D_4$ 1 1 1 3 3 4 3 10 26
10.00% 9.09% 10.00% 9.38% 9.38% 2.34% 9.68% 8.20% 5.57%
$Q_8$ 2 2
1.17% 0.43%
$C_2^3$ 1 1 1 1 1 7 12
3.12% 7.69% 3.12% 0.58% 3.23% 5.74% 2.57%
$C_3^2$ 2 2
1.17% 0.43%
$C_3:C_4$ 2 2
1.17% 0.43%
$C_{12}$ 3 3
1.75% 0.64%
$A_4$ 1 1 1 1 1 5
9.09% 3.12% 3.12% 0.58% 0.82% 1.07%
$D_6$ 1 1 1 4 4 5 4 16 36
10.00% 9.09% 10.00% 12.50% 12.50% 2.92% 12.90% 13.11% 7.71%
$C_2\times C_6$ 1 1 3 1 7 13
3.12% 3.12% 1.75% 3.23% 5.74% 2.78%
$D_7$ 1 1
0.58% 0.21%
$C_4^2$ 1 1
0.58% 0.21%
$\OD_{16}$ 3 3
1.75% 0.64%
$D_8$ 3 3
1.75% 0.64%
$\SD_{16}$ 3 3
1.75% 0.64%
$C_2^2\times C_4$ 1 1
0.82% 0.21%
$C_2\times D_4$ 1 1 2 1 9 14
3.12% 3.12% 1.17% 3.23% 7.38% 3.00%
$D_4:C_2$ 3 3
1.75% 0.64%
$C_2^4$ 1 1
0.82% 0.21%
$C_3\times S_3$ 3 3
1.75% 0.64%
$C_3:S_3$ 2 2
1.17% 0.43%
$C_3\times C_6$ 1 1
0.58% 0.21%
$C_7:C_3$ 1 1
0.58% 0.21%
$C_3:C_8$ 2 2
1.17% 0.43%
$\SL(2,3)$ 2 2
1.17% 0.43%
$C_4\times S_3$ 3 3
1.75% 0.64%
$D_{12}$ 3 3
1.75% 0.64%
$C_3:D_4$ 3 3
1.75% 0.64%
$C_3\times D_4$ 3 3
1.75% 0.64%
$C_3\times Q_8$ 2 2
1.17% 0.43%
$S_4$ 1 2 2 2 4 11
9.09% 6.25% 6.25% 1.17% 3.28% 2.36%
$C_2\times A_4$ 1 1 1 3 6
3.12% 3.12% 0.58% 2.46% 1.28%
$C_2\times D_6$ 1 1 3 1 10 16
3.12% 3.12% 1.75% 3.23% 8.20% 3.43%
$C_2^2\times C_6$ 1 1
0.82% 0.21%
$\He_3$ 1 1
0.58% 0.21%
$\OD_{16}:C_2$ 1 1
0.58% 0.21%
$C_4\wr C_2$ 2 2
1.17% 0.43%
$C_4:D_4$ 1 1
0.58% 0.21%
$D_8:C_2$ 3 3
1.75% 0.64%
$C_2^2\times D_4$ 1 1
0.82% 0.21%
$D_4:C_2^2$ 1 1
0.58% 0.21%
$C_3:C_{12}$ 2 2
1.17% 0.43%
$C_3^2:C_4$ 1 1
0.58% 0.21%
$S_3^2$ 2 2
1.17% 0.43%
$C_3\times A_4$ 1 1
0.58% 0.21%
$C_6\times S_3$ 2 2
1.17% 0.43%
$C_6:S_3$ 1 1
0.58% 0.21%
$C_6^2$ 1 1
0.58% 0.21%
$F_7$ 1 1
0.58% 0.21%
$C_4^2:C_3$ 1 1
0.58% 0.21%
$C_3:D_8$ 2 2
1.17% 0.43%
$Q_8:S_3$ 2 2
1.17% 0.43%
$\GL(2,3)$ 3 3
1.75% 0.64%
$\SL(2,3):C_2$ 2 2
1.17% 0.43%
$S_3\times D_4$ 3 3
1.75% 0.64%
$D_{12}:C_2$ 2 2
1.17% 0.43%
$C_2\times S_4$ 1 1 1 6 9
3.12% 3.12% 0.58% 4.92% 1.93%
$C_2^2\times A_4$ 1 1
0.82% 0.21%
$C_2^2\times D_6$ 1 1
0.82% 0.21%
$C_3^2:C_6$ 2 2
1.17% 0.43%
$C_3^2:S_3$ 1 1
0.58% 0.21%
$D_4:D_4$ 1 1
0.58% 0.21%
$C_6.D_6$ 1 1
0.58% 0.21%
$C_3:D_{12}$ 2 2
1.17% 0.43%
$C_3\times \SL(2,3)$ 1 1
0.58% 0.21%
$C_6\wr C_2$ 2 2
1.17% 0.43%
$F_9$ 1 1
0.58% 0.21%
$\SOPlus(4,2)$ 1 1
0.58% 0.21%
$\PSU(3,2)$ 1 1
0.58% 0.21%
$C_3\times S_4$ 1 1
0.58% 0.21%
$C_3:S_4$ 1 1
0.58% 0.21%
$S_3\times A_4$ 1 1
0.58% 0.21%
$S_3\times D_6$ 1 1
0.58% 0.21%
$C_6:D_6$ 1 1
0.58% 0.21%
$C_4^2:S_3$ 2 2
1.17% 0.43%
$\GU(2,3)$ 1 1
0.58% 0.21%
$C_4^2:C_6$ 1 1
0.58% 0.21%
$\GL(2,3):C_2$ 2 2
1.17% 0.43%
$\SL(2,3):C_2^2$ 1 1
0.58% 0.21%
$C_2^2\times S_4$ 1 1
0.82% 0.21%
$C_3^2:D_6$ 1 1
0.58% 0.21%
$C_3^2:A_4$ 1 1
0.58% 0.21%
$C_3:\GL(2,3)$ 1 1
0.58% 0.21%
$\SL(2,3):S_3$ 1 1
0.58% 0.21%
$D_6:D_6$ 1 1
0.58% 0.21%
$F_9:C_2$ 1 1
0.58% 0.21%
$S_3\times S_4$ 1 1
0.58% 0.21%
$\GL(3,2)$ 1 1
0.58% 0.21%
$C_4^2:D_6$ 1 1
0.58% 0.21%
$\SL(2,3):D_4$ 1 1
0.58% 0.21%
$C_3^2:S_4$ 1 1
0.58% 0.21%
$C_3^2:S_4$ 1 1
0.58% 0.21%
$C_6^2:C_6$ 1 1
0.58% 0.21%
$\PGU(3,2)$ 1 1
0.58% 0.21%
$\PGL(2,7)$ 1 1
0.58% 0.21%
$C_6^2:D_6$ 1 1
0.58% 0.21%
$C_3^2:\GL(2,3)$ 1 1
0.58% 0.21%
Total 2 1 4 10 11 2 10 32 1 2 5 13 32 171 2 5 31 5 122 2 2 1 1 467
0.43% 0.21% 0.86% 2.14% 2.36% 0.43% 2.14% 6.85% 0.21% 0.43% 1.07% 2.78% 6.85% 36.62% 0.43% 1.07% 6.64% 1.07% 26.12% 0.43% 0.43% 0.21% 0.21%

## Distribution of maximal subgroups per identity component

 identity component count proportion identity component count proportion identity component count proportion $\operatorname{SO}(1)$ $\operatorname{SU}(2)$ $\operatorname{SU}(2)^3$ $\operatorname{SU}(2)_2$ $\operatorname{SU}(2)_3$ $\operatorname{SU}(2)\times\operatorname{SU}(2)$ $\operatorname{SU}(2)\times\operatorname{SU}(2)_2$ $\operatorname{SU}(2)\times\operatorname{U}(1)_2$ $\operatorname{SU}(2)\times\operatorname{USp}(4)$ $\operatorname{U}(1)$ 1 1 1 2 2 1 2 2 1 1 2.17% 2.17% 2.17% 4.35% 4.35% 2.17% 4.35% 4.35% 2.17% 2.17% $\operatorname{U}(1)^2\times\operatorname{SU}(2)$ $\operatorname{U}(1)^3$ $\operatorname{U}(1)_2$ $\operatorname{U}(1)_3$ $\operatorname{U}(1)\times\operatorname{SU}(2)$ $\operatorname{U}(1)\times\operatorname{SU}(2)^2$ $\operatorname{U}(1)\times\operatorname{SU}(2)_2$ $\operatorname{U}(1)\times\operatorname{U}(1)$ $\operatorname{U}(1)\times\operatorname{U}(1)_2$ $\operatorname{U}(1)\times\operatorname{USp}(4)$ 2 3 2 12 1 1 2 3 2 1 4.35% 6.52% 4.35% 26.09% 2.17% 2.17% 4.35% 6.52% 4.35% 2.17% $\operatorname{U}(3)$ $\operatorname{USp}(4)$ $\operatorname{USp}(6)$ 1 1 1 2.17% 2.17% 2.17%

## Distribution of trace zero densities and identity components

identity component
$\operatorname{SO}(1)$ $\operatorname{SU}(2)$ $\operatorname{SU}(2)^3$ $\operatorname{SU}(2)_2$ $\operatorname{SU}(2)_3$ $\operatorname{SU}(2)\times\operatorname{SU}(2)$ $\operatorname{SU}(2)\times\operatorname{SU}(2)_2$ $\operatorname{SU}(2)\times\operatorname{U}(1)_2$ $\operatorname{SU}(2)\times\operatorname{USp}(4)$ $\operatorname{U}(1)$ $\operatorname{U}(1)^2\times\operatorname{SU}(2)$ $\operatorname{U}(1)^3$ $\operatorname{U}(1)_2$ $\operatorname{U}(1)_3$ $\operatorname{U}(1)\times\operatorname{SU}(2)$ $\operatorname{U}(1)\times\operatorname{SU}(2)^2$ $\operatorname{U}(1)\times\operatorname{SU}(2)_2$ $\operatorname{U}(1)\times\operatorname{U}(1)$ $\operatorname{U}(1)\times\operatorname{U}(1)_2$ $\operatorname{U}(1)\times\operatorname{USp}(4)$ $\operatorname{U}(3)$ $\operatorname{USp}(4)$ $\operatorname{USp}(6)$ Total
trace zero density
0 2 1 2 2 5 1 10 32 1 1 5 6 2 24 2 3 13 2 35 2 1 1 1 154
100.00% 100.00% 50.00% 20.00% 45.45% 50.00% 100.00% 100.00% 100.00% 50.00% 100.00% 46.15% 6.25% 14.04% 100.00% 60.00% 41.94% 40.00% 28.69% 100.00% 50.00% 100.00% 100.00% 32.98%
1/36 1 1
0.58% 0.21%
1/18 3 3
1.75% 0.64%
1/12 4 1 1 6
2.34% 3.23% 0.82% 1.28%
1/9 4 4
2.34% 0.86%
1/8 1 1 2 4
7.69% 3.23% 1.64% 0.86%
1/6 1 1 1 6 1 1 11
10.00% 9.09% 3.12% 3.51% 3.23% 0.82% 2.36%
3/16 1 1
0.82% 0.21%
2/9 2 2
1.17% 0.43%
1/4 1 1 2 1 4 1 12 22
10.00% 7.69% 6.25% 20.00% 12.90% 20.00% 9.84% 4.71%
7/27 1 1
0.58% 0.21%
7/24 1 3 4
3.23% 2.46% 0.86%
5/16 1 5 6
3.23% 4.10% 1.28%
1/3 1 3 6 1 4 15
25.00% 27.27% 3.51% 3.23% 3.28% 3.21%
37/108 1 1
0.58% 0.21%
11/32 1 1
0.82% 0.21%
13/36 1 1
0.58% 0.21%
10/27 1 1
0.58% 0.21%
3/8 1 1 1 10 13
7.69% 3.12% 3.23% 8.20% 2.78%
19/48 1 1
0.82% 0.21%
13/32 1 1
0.82% 0.21%
5/12 2 2
1.64% 0.43%
7/16 2 2
1.64% 0.43%
4/9 1 1
0.58% 0.21%
1/2 3 1 1 2 7 44 1 7 1 41 1 109
30.00% 50.00% 50.00% 15.38% 21.88% 25.73% 20.00% 22.58% 20.00% 33.61% 50.00% 23.34%
37/72 1 1
0.58% 0.21%
19/36 6 6
3.51% 1.28%
13/24 6 6
3.51% 1.28%
5/9 7 7
4.09% 1.50%
7/12 1 3 12 16
10.00% 9.38% 7.02% 3.43%
11/18 4 4
2.34% 0.86%
5/8 1 5 6
10.00% 15.62% 1.28%
17/27 1 1
0.58% 0.21%
2/3 1 2 1 13 17
25.00% 18.18% 7.69% 7.60% 3.64%
145/216 1 1
0.58% 0.21%
49/72 1 1
0.58% 0.21%
37/54 2 2
1.17% 0.43%
11/16 1 1
3.12% 0.21%
13/18 2 2
1.17% 0.43%
20/27 1 1
0.58% 0.21%
3/4 1 6 1 8
10.00% 18.75% 20.00% 1.71%
19/24 1 1
3.12% 0.21%
13/16 1 1
3.12% 0.21%
5/6 1 7 8
7.69% 4.09% 1.71%
91/108 2 2
1.17% 0.43%
31/36 2 2
1.17% 0.43%
47/54 2 2
1.17% 0.43%
7/8 2 2
6.25% 0.43%
8/9 1 1
0.58% 0.21%
17/18 1 1
0.58% 0.21%
Total 2 1 4 10 11 2 10 32 1 2 5 13 32 171 2 5 31 5 122 2 2 1 1 467
0.43% 0.21% 0.86% 2.14% 2.36% 0.43% 2.14% 6.85% 0.21% 0.43% 1.07% 2.78% 6.85% 36.62% 0.43% 1.07% 6.64% 1.07% 26.12% 0.43% 0.43% 0.21% 0.21%

## Distribution of second trace moments and identity components

identity component
$\operatorname{SO}(1)$ $\operatorname{SU}(2)$ $\operatorname{SU}(2)^3$ $\operatorname{SU}(2)_2$ $\operatorname{SU}(2)_3$ $\operatorname{SU}(2)\times\operatorname{SU}(2)$ $\operatorname{SU}(2)\times\operatorname{SU}(2)_2$ $\operatorname{SU}(2)\times\operatorname{U}(1)_2$ $\operatorname{SU}(2)\times\operatorname{USp}(4)$ $\operatorname{U}(1)$ $\operatorname{U}(1)^2\times\operatorname{SU}(2)$ $\operatorname{U}(1)^3$ $\operatorname{U}(1)_2$ $\operatorname{U}(1)_3$ $\operatorname{U}(1)\times\operatorname{SU}(2)$ $\operatorname{U}(1)\times\operatorname{SU}(2)^2$ $\operatorname{U}(1)\times\operatorname{SU}(2)_2$ $\operatorname{U}(1)\times\operatorname{U}(1)$ $\operatorname{U}(1)\times\operatorname{U}(1)_2$ $\operatorname{U}(1)\times\operatorname{USp}(4)$ $\operatorname{U}(3)$ $\operatorname{USp}(4)$ $\operatorname{USp}(6)$ Total
second trace moment
1 2 1 2 4 2 1 1 1 9 23 1 1 1 1 50
100.00% 100.00% 50.00% 40.00% 18.18% 50.00% 50.00% 7.69% 28.12% 13.45% 20.00% 50.00% 100.00% 100.00% 10.71%
2 1 5 3 1 4 9 1 1 1 3 16 56 1 2 11 2 36 1 1 155
25.00% 50.00% 27.27% 50.00% 40.00% 28.12% 100.00% 50.00% 20.00% 23.08% 50.00% 32.75% 50.00% 40.00% 35.48% 40.00% 29.51% 50.00% 50.00% 33.19%
3 1 4 5 16 2 5 38 1 2 13 1 51 1 140
25.00% 36.36% 50.00% 50.00% 40.00% 38.46% 22.22% 50.00% 40.00% 41.94% 20.00% 41.80% 50.00% 29.98%
4 1 1 2 6 24 1 5 1 16 57
10.00% 20.00% 15.38% 18.75% 14.04% 20.00% 16.13% 20.00% 13.11% 12.21%
5 1 1 6 1 1 7 1 11 29
9.09% 10.00% 18.75% 20.00% 7.69% 4.09% 3.23% 9.02% 6.21%
6 1 17 1 6 25
7.69% 9.94% 3.23% 4.92% 5.35%
8 1 1
3.12% 0.21%
9 1 1 1 1 4
9.09% 3.12% 0.58% 0.82% 0.86%
10 4 1 5
2.34% 0.82% 1.07%
18 1 1
0.58% 0.21%
Total 2 1 4 10 11 2 10 32 1 2 5 13 32 171 2 5 31 5 122 2 2 1 1 467
0.43% 0.21% 0.86% 2.14% 2.36% 0.43% 2.14% 6.85% 0.21% 0.43% 1.07% 2.78% 6.85% 36.62% 0.43% 1.07% 6.64% 1.07% 26.12% 0.43% 0.43% 0.21% 0.21%

## Distribution of fourth trace moments and identity components

identity component
$\operatorname{SO}(1)$ $\operatorname{SU}(2)$ $\operatorname{SU}(2)^3$ $\operatorname{SU}(2)_2$ $\operatorname{SU}(2)_3$ $\operatorname{SU}(2)\times\operatorname{SU}(2)$ $\operatorname{SU}(2)\times\operatorname{SU}(2)_2$ $\operatorname{SU}(2)\times\operatorname{U}(1)_2$ $\operatorname{SU}(2)\times\operatorname{USp}(4)$ $\operatorname{U}(1)$ $\operatorname{U}(1)^2\times\operatorname{SU}(2)$ $\operatorname{U}(1)^3$ $\operatorname{U}(1)_2$ $\operatorname{U}(1)_3$ $\operatorname{U}(1)\times\operatorname{SU}(2)$ $\operatorname{U}(1)\times\operatorname{SU}(2)^2$ $\operatorname{U}(1)\times\operatorname{SU}(2)_2$ $\operatorname{U}(1)\times\operatorname{U}(1)$ $\operatorname{U}(1)\times\operatorname{U}(1)_2$ $\operatorname{U}(1)\times\operatorname{USp}(4)$ $\operatorname{U}(3)$ $\operatorname{USp}(4)$ $\operatorname{USp}(6)$ Total
fourth trace moment
1 2 2
100.00% 0.43%
2 1 1
100.00% 0.21%
3 1 1 1 3
50.00% 100.00% 100.00% 0.64%
5 1 1 2
25.00% 50.00% 0.43%
6 3 1 3 3 1 11
30.00% 50.00% 9.38% 1.75% 50.00% 2.36%
8 1 1 1 3
25.00% 10.00% 9.09% 0.64%
9 4 6 1 11
12.50% 3.51% 20.00% 2.36%
10 1 1
50.00% 0.21%
11 1 1 2
100.00% 50.00% 0.43%
12 3 4 4 1 1 1 14
30.00% 12.50% 2.34% 20.00% 50.00% 50.00% 3.00%
13 1 1
25.00% 0.21%
14 1 3 3 1 8
9.09% 30.00% 9.38% 20.00% 1.71%
15 1 10 5 5 21
7.69% 5.85% 16.13% 4.10% 4.50%
16 2 1 3
20.00% 10.00% 0.64%
17 4 1 1 6
12.50% 20.00% 3.23% 1.28%
18 1 10 5 1 8 25
7.69% 31.25% 2.92% 20.00% 6.56% 5.35%
20 1 2 1 1 5
9.09% 6.25% 50.00% 20.00% 1.07%
21 9 3 1 5 1 19
5.26% 9.68% 20.00% 4.10% 50.00% 4.07%
22 1 1
9.09% 0.21%
23 1 2 3
20.00% 6.45% 0.64%
24 1 1 4 14 3 15 38
25.00% 7.69% 12.50% 8.19% 9.68% 12.30% 8.14%
25 1 1
20.00% 0.21%
26 3 2 1 1 7
30.00% 6.25% 20.00% 3.23% 1.50%
27 3 11 5 13 32
23.08% 6.43% 16.13% 10.66% 6.85%
28 1 1
9.09% 0.21%
30 2 1 10 2 15
20.00% 7.69% 5.85% 1.64% 3.21%
31 2 2
6.45% 0.43%
32 1 10 1 12
10.00% 31.25% 20.00% 2.57%
33 1 4 18 23
7.69% 2.34% 14.75% 4.93%
36 3 1 4
9.38% 20.00% 0.86%
38 1 4 5
9.09% 12.50% 1.07%
39 4 4
3.28% 0.86%
40 1 1
20.00% 0.21%
41 1 1
20.00% 0.21%
42 2 1 7 3 2 15
18.18% 7.69% 4.09% 9.68% 1.64% 3.21%
43 2 2
6.45% 0.43%
45 1 17 10 28
7.69% 9.94% 8.20% 6.00%
46 2 2
6.45% 0.43%
48 1 3 9 10 23
7.69% 9.38% 5.26% 8.20% 4.93%
51 11 7 18
6.43% 5.74% 3.85%
54 1 6 4 11
9.09% 3.51% 3.28% 2.36%
57 3 3
1.75% 0.64%
58 1 1
10.00% 0.21%
59 1 1
3.23% 0.21%
60 2 2
1.17% 0.43%
62 3 1 4
9.38% 20.00% 0.86%
63 1 5 5 11
7.69% 2.92% 4.10% 2.36%
66 2 2
1.17% 0.43%
74 3 3
9.38% 0.64%
75 3 3
2.46% 0.64%
81 2 2
1.17% 0.43%
82 1 1
9.09% 0.21%
84 1 1
0.58% 0.21%
86 1 1
3.23% 0.21%
90 1 8 3 12
7.69% 4.68% 2.46% 2.57%
96 1 1
3.12% 0.21%
99 5 3 8
2.92% 2.46% 1.71%
102 5 3 8
2.92% 2.46% 1.71%
114 1 1
0.58% 0.21%
123 2 2
1.17% 0.43%
126 2 2
1.17% 0.43%
146 1 1
3.12% 0.21%
147 1 1
0.82% 0.21%
162 1 1 2
9.09% 0.58% 0.43%
198 3 1 4
1.75% 0.82% 0.86%
243 1 1
0.58% 0.21%
246 1 1
0.58% 0.21%
486 1 1
0.58% 0.21%
Total 2 1 4 10 11 2 10 32 1 2 5 13 32 171 2 5 31 5 122 2 2 1 1 467
0.43% 0.21% 0.86% 2.14% 2.36% 0.43% 2.14% 6.85% 0.21% 0.43% 1.07% 2.78% 6.85% 36.62% 0.43% 1.07% 6.64% 1.07% 26.12% 0.43% 0.43% 0.21% 0.21%

## Distribution of first $a_2$ moment and identity components

identity component
$\operatorname{SU}(2)^3$ $\operatorname{SU}(2)_2$ $\operatorname{SU}(2)_3$ $\operatorname{SU}(2)\times\operatorname{SU}(2)$ $\operatorname{SU}(2)\times\operatorname{SU}(2)_2$ $\operatorname{SU}(2)\times\operatorname{U}(1)_2$ $\operatorname{SU}(2)\times\operatorname{USp}(4)$ $\operatorname{U}(1)^2\times\operatorname{SU}(2)$ $\operatorname{U}(1)^3$ $\operatorname{U}(1)_2$ $\operatorname{U}(1)_3$ $\operatorname{U}(1)\times\operatorname{SU}(2)$ $\operatorname{U}(1)\times\operatorname{SU}(2)^2$ $\operatorname{U}(1)\times\operatorname{SU}(2)_2$ $\operatorname{U}(1)\times\operatorname{U}(1)$ $\operatorname{U}(1)\times\operatorname{U}(1)_2$ $\operatorname{U}(1)\times\operatorname{USp}(4)$ $\operatorname{U}(3)$ $\operatorname{USp}(4)$ $\operatorname{USp}(6)$ Total
first a2 moment
1 2 8 2 1 2 22 40 1 2 1 1 82
50.00% 80.00% 18.18% 50.00% 15.38% 68.75% 23.39% 20.00% 100.00% 100.00% 100.00% 17.75%
2 1 1 6 1 8 22 1 1 3 8 87 2 3 26 4 91 2 267
25.00% 10.00% 54.55% 50.00% 80.00% 68.75% 100.00% 20.00% 23.08% 25.00% 50.88% 100.00% 60.00% 83.87% 80.00% 74.59% 100.00% 57.79%
3 1 1 1 1 8 4 8 1 34 2 3 26 90
25.00% 10.00% 9.09% 10.00% 25.00% 80.00% 61.54% 3.12% 19.88% 40.00% 9.68% 21.31% 19.48%
4 1 1 1 1 4 2 3 13
9.09% 10.00% 3.12% 3.12% 2.34% 6.45% 2.46% 2.81%
5 1 4 2 7
3.12% 2.34% 1.64% 1.52%
6 1 1 2
9.09% 0.58% 0.43%
9 1 1
0.58% 0.22%
Total 4 10 11 2 10 32 1 5 13 32 171 2 5 31 5 122 2 2 1 1 462
0.87% 2.16% 2.38% 0.43% 2.16% 6.93% 0.22% 1.08% 2.81% 6.93% 37.01% 0.43% 1.08% 6.71% 1.08% 26.41% 0.43% 0.43% 0.22% 0.22%