C₅ · Neutral gradings
24 neutral gradings · KL, Fourier, Arthur packets
| Ambient orbit | KL block sizes | Arthur parameters | Parameters in packets | Graded orbits | Local systems |
|---|---|---|---|---|---|
| 1111111111 | 1 × 1 | 1 | 1 | 1 | 1 |
| 211111111 | 2 × 2, 1 × 1 | 2 | 3 | 2 | 3 |
| 22111111 | 4 × 4, 1 × 1 | 3 | 5 | 3 | 5 |
| 2221111 | 5 × 5, 2 × 2 | 4 | 7 | 4 | 7 |
| 4111111 | 4 × 4, 2 × 2 | 2 | 4 | 4 | 6 |
| 222211 | 7 × 7, 2 × 2 | 5 | 9 | 5 | 9 |
| 22222 | 8 × 8, 3 × 3 | 6 | 11 | 6 | 11 |
| 331111 | 4 × 4 | 3 | 3 | 4 | 4 |
| 421111 | 10 × 10, 4 × 4, 1 × 1 | 6 | 13 | 8 | 15 |
| 33211 | 8 × 8, 4 × 4 | 6 | 9 | 8 | 12 |
| 3322 | 12 × 12, 3 × 3 | 6 | 10 | 9 | 15 |
| 42211 | 16 × 16, 8 × 8, 1 × 1 | 10 | 23 | 12 | 25 |
| 4222 | 23 × 23, 10 × 10, 2 × 2 | 14 | 33 | 16 | 35 |
| 61111 | 8 × 8, 4 × 4 | 2 | 4 | 8 | 12 |
| 433 | 12 × 12, 6 × 6 | 4 | 8 | 12 | 18 |
| 4411 | 14 × 14, 5 × 5, 1 × 1 | 3 | 8 | 11 | 20 |
| 442 | 27 × 27, 14 × 14, 2 × 2 | 10 | 29 | 20 | 43 |
| 6211 | 20 × 20, 8 × 8, 2 × 2 | 4 | 12 | 16 | 30 |
| 55 | 10 × 10 | 2 | 2 | 10 | 10 |
| 622 | 32 × 32, 16 × 16, 2 × 2 | 6 | 20 | 24 | 50 |
| 64 | 36 × 36, 15 × 15, 4 × 4 | 6 | 18 | 29 | 55 |
| 811 | 16 × 16, 8 × 8 | 2 | 4 | 16 | 24 |
| 82 | 40 × 40, 16 × 16, 4 × 4 | 4 | 12 | 32 | 60 |
| (10) | 32 × 32, 16 × 16 | 2 | 4 | 32 | 48 |
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.