A₈ · Neutral gradings
30 neutral gradings · KL, Fourier, Arthur packets
| Ambient orbit | KL block sizes | Arthur parameters | Parameters in packets | Graded orbits | Local systems |
|---|---|---|---|---|---|
| 111111111 | 1 × 1 | 1 | 1 | 1 | 1 |
| 21111111 | 2 × 2 | 2 | 2 | 2 | 2 |
| 2211111 | 3 × 3 | 3 | 3 | 3 | 3 |
| 3111111 | 5 × 5 | 3 | 3 | 5 | 5 |
| 222111 | 4 × 4 | 4 | 4 | 4 | 4 |
| 22221 | 5 × 5 | 5 | 5 | 5 | 5 |
| 321111 | 10 × 10 | 6 | 6 | 10 | 10 |
| 411111 | 8 × 8 | 2 | 2 | 8 | 8 |
| 32211 | 15 × 15 | 9 | 9 | 15 | 15 |
| 3222 | 16 × 16 | 8 | 8 | 16 | 16 |
| 33111 | 14 × 14 | 6 | 6 | 14 | 14 |
| 42111 | 18 × 18 | 6 | 6 | 18 | 18 |
| 3321 | 26 × 26 | 10 | 10 | 26 | 26 |
| 51111 | 20 × 20 | 2 | 2 | 20 | 20 |
| 333 | 20 × 20, 1 × 1, 1 × 1 | 4 | 6 | 20 | 22 |
| 4221 | 28 × 28 | 10 | 10 | 28 | 28 |
| 4311 | 40 × 40 | 6 | 6 | 40 | 40 |
| 432 | 72 × 72, 1 × 1, 1 × 1 | 12 | 14 | 72 | 74 |
| 5211 | 40 × 40 | 4 | 4 | 40 | 40 |
| 441 | 35 × 35 | 3 | 3 | 35 | 35 |
| 522 | 48 × 48 | 6 | 6 | 48 | 48 |
| 6111 | 32 × 32 | 2 | 2 | 32 | 32 |
| 531 | 86 × 86, 1 × 1, 1 × 1 | 9 | 11 | 86 | 88 |
| 54 | 128 × 128 | 4 | 4 | 128 | 128 |
| 621 | 72 × 72 | 4 | 4 | 72 | 72 |
| 63 | 128 × 128, 2 × 2, 2 × 2 | 4 | 8 | 128 | 132 |
| 711 | 80 × 80 | 2 | 2 | 80 | 80 |
| 72 | 128 × 128 | 4 | 4 | 128 | 128 |
| 81 | 128 × 128 | 2 | 2 | 128 | 128 |
| 9 | 256 × 256, 4 × 4, 4 × 4, 1 × 1, 1 × 1, 1 × 1, 1 × 1, 1 × 1, 1 × 1 | 2 | 12 | 256 | 270 |
Counting conventions
Matrix dimensions are listed separately for each block. Parameters in packets counts distinct IC parameters, without multiplicities or repeated membership. Local systems counts orbit–local-system pairs across all exported series. “Not computed” means that the selected export does not contain that result, rather than a count of zero.