C₇ · Neutral gradings
64 neutral gradings · KL, Fourier, Arthur packets
| Ambient orbit | KL block sizes | Arthur parameters | Parameters in packets | Graded orbits | Local systems |
|---|---|---|---|---|---|
| 11111111111111 | 1 × 1 | 1 | 1 | 1 | 1 |
| 2111111111111 | 2 × 2, 1 × 1 | 2 | 3 | 2 | 3 |
| 221111111111 | 4 × 4, 1 × 1 | 3 | 5 | 3 | 5 |
| 22211111111 | 5 × 5, 2 × 2 | 4 | 7 | 4 | 7 |
| 41111111111 | 4 × 4, 2 × 2 | 2 | 4 | 4 | 6 |
| 2222111111 | 7 × 7, 2 × 2 | 5 | 9 | 5 | 9 |
| 3311111111 | 4 × 4 | 3 | 3 | 4 | 4 |
| 4211111111 | 10 × 10, 4 × 4, 1 × 1 | 6 | 13 | 8 | 15 |
| 222221111 | 8 × 8, 3 × 3 | 6 | 11 | 6 | 11 |
| 22222211 | 10 × 10, 3 × 3 | 7 | 13 | 7 | 13 |
| 332111111 | 8 × 8, 4 × 4 | 6 | 9 | 8 | 12 |
| 2222222 | 11 × 11, 4 × 4 | 8 | 15 | 8 | 15 |
| 422111111 | 16 × 16, 8 × 8, 1 × 1 | 10 | 23 | 12 | 25 |
| 611111111 | 8 × 8, 4 × 4 | 2 | 4 | 8 | 12 |
| 33221111 | 16 × 16, 4 × 4 | 9 | 15 | 12 | 20 |
| 42221111 | 23 × 23, 10 × 10, 2 × 2 | 14 | 33 | 16 | 35 |
| 44111111 | 14 × 14, 5 × 5, 1 × 1 | 3 | 8 | 11 | 20 |
| 3322211 | 20 × 20, 8 × 8 | 12 | 21 | 16 | 28 |
| 332222 | 21 × 21, 6 × 6 | 10 | 18 | 15 | 27 |
| 62111111 | 20 × 20, 8 × 8, 2 × 2 | 4 | 12 | 16 | 30 |
| 4222211 | 29 × 29, 14 × 14, 2 × 2 | 18 | 43 | 20 | 45 |
| 422222 | 36 × 36, 16 × 16, 3 × 3 | 22 | 53 | 24 | 55 |
| 333311 | 8 × 8 | 5 | 5 | 8 | 8 |
| 4331111 | 16 × 16, 8 × 8 | 6 | 12 | 16 | 24 |
| 33332 | 12 × 12, 6 × 6 | 6 | 9 | 12 | 18 |
| 4421111 | 27 × 27, 14 × 14, 2 × 2 | 10 | 29 | 20 | 43 |
| 433211 | 40 × 40, 16 × 16, 4 × 4 | 18 | 39 | 32 | 60 |
| 6221111 | 32 × 32, 16 × 16, 2 × 2 | 6 | 20 | 24 | 50 |
| 442211 | 46 × 46, 20 × 20, 4 × 4 | 20 | 56 | 30 | 70 |
| 43322 | 48 × 48, 24 × 24, 3 × 3 | 20 | 46 | 36 | 75 |
| 8111111 | 16 × 16, 8 × 8 | 2 | 4 | 16 | 24 |
| 622211 | 46 × 46, 20 × 20, 4 × 4 | 8 | 28 | 32 | 70 |
| 551111 | 13 × 13 | 2 | 2 | 13 | 13 |
| 44222 | 62 × 62, 31 × 31, 5 × 5 | 30 | 84 | 40 | 98 |
| 641111 | 36 × 36, 15 × 15, 4 × 4 | 6 | 18 | 29 | 55 |
| 4433 | 42 × 42, 15 × 15, 3 × 3 | 6 | 16 | 33 | 60 |
| 62222 | 58 × 58, 28 × 28, 4 × 4 | 10 | 36 | 40 | 90 |
| 44411 | 32 × 32, 16 × 16, 2 × 2 | 4 | 12 | 24 | 50 |
| 4442 | 62 × 62, 28 × 28, 6 × 6 | 14 | 47 | 41 | 96 |
| 821111 | 40 × 40, 16 × 16, 4 × 4 | 4 | 12 | 32 | 60 |
| 55211 | 26 × 26, 13 × 13 | 4 | 6 | 26 | 39 |
| 63311 | 32 × 32, 16 × 16 | 6 | 12 | 32 | 48 |
| 5522 | 40 × 40, 10 × 10 | 6 | 10 | 30 | 50 |
| 6332 | 60 × 60, 24 × 24, 6 × 6 | 8 | 24 | 48 | 90 |
| 64211 | 73 × 73, 40 × 40, 8 × 8, 1 × 1 | 18 | 61 | 54 | 122 |
| 6422 | 123 × 123, 60 × 60, 16 × 16, 1 × 1 | 30 | 111 | 81 | 200 |
| 82211 | 64 × 64, 32 × 32, 4 × 4 | 6 | 20 | 48 | 100 |
| 554 | 40 × 40, 20 × 20 | 4 | 8 | 40 | 60 |
| 8222 | 92 × 92, 40 × 40, 8 × 8 | 8 | 28 | 64 | 140 |
| 6611 | 50 × 50, 20 × 20, 5 × 5 | 3 | 8 | 40 | 75 |
| (10,1,1,1,1) | 32 × 32, 16 × 16 | 2 | 4 | 32 | 48 |
| 644 | 100 × 100, 54 × 54, 10 × 10, 1 × 1 | 10 | 39 | 74 | 165 |
| 8411 | 72 × 72, 30 × 30, 8 × 8 | 4 | 16 | 58 | 110 |
| 662 | 100 × 100, 54 × 54, 10 × 10, 1 × 1 | 6 | 24 | 74 | 165 |
| 833 | 48 × 48, 24 × 24 | 4 | 8 | 48 | 72 |
| (10,2,1,1) | 80 × 80, 32 × 32, 8 × 8 | 4 | 12 | 64 | 120 |
| 77 | 35 × 35 | 2 | 2 | 35 | 35 |
| 842 | 146 × 146, 80 × 80, 16 × 16, 2 × 2 | 12 | 52 | 108 | 244 |
| 86 | 130 × 130, 55 × 55, 15 × 15 | 6 | 18 | 105 | 200 |
| (10,2,2) | 128 × 128, 64 × 64, 8 × 8 | 6 | 20 | 96 | 200 |
| (10,4) | 144 × 144, 60 × 60, 16 × 16 | 4 | 16 | 116 | 220 |
| (12,1,1) | 64 × 64, 32 × 32 | 2 | 4 | 64 | 96 |
| (12,2) | 160 × 160, 64 × 64, 16 × 16 | 4 | 12 | 128 | 240 |
| (14) | 128 × 128, 64 × 64 | 2 | 4 | 128 | 192 |
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.