| a^b mod 13 | 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 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | | -9 | 1 | 4 | 3 | 12 | 9 | 10 | 1 | 4 | 3 | 12 | 9 | 10 | 1 | 4 | 3 | 12 | 9 | 10 | 1 | 4 | 3 | 12 | 9 | 10 | 1 | 4 | 3 | 12 | 9 | 10 | 1 | 4 | 3 | 12 | 9 | 10 | 1 | 4 | 3 | 12 | 9 | 10 |
| -8 | 1 | 5 | 12 | 8 | 1 | 5 | 12 | 8 | 1 | 5 | 12 | 8 | 1 | 5 | 12 | 8 | 1 | 5 | 12 | 8 | 1 | 5 | 12 | 8 | 1 | 5 | 12 | 8 | 1 | 5 | 12 | 8 | 1 | 5 | 12 | 8 | 1 | 5 | 12 | 8 | 1 | 5 |
| -7 | 1 | 6 | 10 | 8 | 9 | 2 | 12 | 7 | 3 | 5 | 4 | 11 | 1 | 6 | 10 | 8 | 9 | 2 | 12 | 7 | 3 | 5 | 4 | 11 | 1 | 6 | 10 | 8 | 9 | 2 | 12 | 7 | 3 | 5 | 4 | 11 | 1 | 6 | 10 | 8 | 9 | 2 |
| -6 | 1 | 7 | 10 | 5 | 9 | 11 | 12 | 6 | 3 | 8 | 4 | 2 | 1 | 7 | 10 | 5 | 9 | 11 | 12 | 6 | 3 | 8 | 4 | 2 | 1 | 7 | 10 | 5 | 9 | 11 | 12 | 6 | 3 | 8 | 4 | 2 | 1 | 7 | 10 | 5 | 9 | 11 |
| -5 | 1 | 8 | 12 | 5 | 1 | 8 | 12 | 5 | 1 | 8 | 12 | 5 | 1 | 8 | 12 | 5 | 1 | 8 | 12 | 5 | 1 | 8 | 12 | 5 | 1 | 8 | 12 | 5 | 1 | 8 | 12 | 5 | 1 | 8 | 12 | 5 | 1 | 8 | 12 | 5 | 1 | 8 |
| -4 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 |
| -3 | 1 | 10 | 9 | 12 | 3 | 4 | 1 | 10 | 9 | 12 | 3 | 4 | 1 | 10 | 9 | 12 | 3 | 4 | 1 | 10 | 9 | 12 | 3 | 4 | 1 | 10 | 9 | 12 | 3 | 4 | 1 | 10 | 9 | 12 | 3 | 4 | 1 | 10 | 9 | 12 | 3 | 4 |
| -2 | 1 | 11 | 4 | 5 | 3 | 7 | 12 | 2 | 9 | 8 | 10 | 6 | 1 | 11 | 4 | 5 | 3 | 7 | 12 | 2 | 9 | 8 | 10 | 6 | 1 | 11 | 4 | 5 | 3 | 7 | 12 | 2 | 9 | 8 | 10 | 6 | 1 | 11 | 4 | 5 | 3 | 7 |
| -1 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 2 | 1 | 2 | 4 | 8 | 3 | 6 | 12 | 11 | 9 | 5 | 10 | 7 | 1 | 2 | 4 | 8 | 3 | 6 | 12 | 11 | 9 | 5 | 10 | 7 | 1 | 2 | 4 | 8 | 3 | 6 | 12 | 11 | 9 | 5 | 10 | 7 | 1 | 2 | 4 | 8 | 3 | 6 |
| 3 | 1 | 3 | 9 | 1 | 3 | 9 | 1 | 3 | 9 | 1 | 3 | 9 | 1 | 3 | 9 | 1 | 3 | 9 | 1 | 3 | 9 | 1 | 3 | 9 | 1 | 3 | 9 | 1 | 3 | 9 | 1 | 3 | 9 | 1 | 3 | 9 | 1 | 3 | 9 | 1 | 3 | 9 |
| 4 | 1 | 4 | 3 | 12 | 9 | 10 | 1 | 4 | 3 | 12 | 9 | 10 | 1 | 4 | 3 | 12 | 9 | 10 | 1 | 4 | 3 | 12 | 9 | 10 | 1 | 4 | 3 | 12 | 9 | 10 | 1 | 4 | 3 | 12 | 9 | 10 | 1 | 4 | 3 | 12 | 9 | 10 |
| 5 | 1 | 5 | 12 | 8 | 1 | 5 | 12 | 8 | 1 | 5 | 12 | 8 | 1 | 5 | 12 | 8 | 1 | 5 | 12 | 8 | 1 | 5 | 12 | 8 | 1 | 5 | 12 | 8 | 1 | 5 | 12 | 8 | 1 | 5 | 12 | 8 | 1 | 5 | 12 | 8 | 1 | 5 |
| 6 | 1 | 6 | 10 | 8 | 9 | 2 | 12 | 7 | 3 | 5 | 4 | 11 | 1 | 6 | 10 | 8 | 9 | 2 | 12 | 7 | 3 | 5 | 4 | 11 | 1 | 6 | 10 | 8 | 9 | 2 | 12 | 7 | 3 | 5 | 4 | 11 | 1 | 6 | 10 | 8 | 9 | 2 |
| 7 | 1 | 7 | 10 | 5 | 9 | 11 | 12 | 6 | 3 | 8 | 4 | 2 | 1 | 7 | 10 | 5 | 9 | 11 | 12 | 6 | 3 | 8 | 4 | 2 | 1 | 7 | 10 | 5 | 9 | 11 | 12 | 6 | 3 | 8 | 4 | 2 | 1 | 7 | 10 | 5 | 9 | 11 |
| 8 | 1 | 8 | 12 | 5 | 1 | 8 | 12 | 5 | 1 | 8 | 12 | 5 | 1 | 8 | 12 | 5 | 1 | 8 | 12 | 5 | 1 | 8 | 12 | 5 | 1 | 8 | 12 | 5 | 1 | 8 | 12 | 5 | 1 | 8 | 12 | 5 | 1 | 8 | 12 | 5 | 1 | 8 |
| 9 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 | 1 | 9 | 3 |
| 10 | 1 | 10 | 9 | 12 | 3 | 4 | 1 | 10 | 9 | 12 | 3 | 4 | 1 | 10 | 9 | 12 | 3 | 4 | 1 | 10 | 9 | 12 | 3 | 4 | 1 | 10 | 9 | 12 | 3 | 4 | 1 | 10 | 9 | 12 | 3 | 4 | 1 | 10 | 9 | 12 | 3 | 4 |
| 11 | 1 | 11 | 4 | 5 | 3 | 7 | 12 | 2 | 9 | 8 | 10 | 6 | 1 | 11 | 4 | 5 | 3 | 7 | 12 | 2 | 9 | 8 | 10 | 6 | 1 | 11 | 4 | 5 | 3 | 7 | 12 | 2 | 9 | 8 | 10 | 6 | 1 | 11 | 4 | 5 | 3 | 7 |
| 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 | 1 | 12 |
| 13 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 14 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 15 | 1 | 2 | 4 | 8 | 3 | 6 | 12 | 11 | 9 | 5 | 10 | 7 | 1 | 2 | 4 | 8 | 3 | 6 | 12 | 11 | 9 | 5 | 10 | 7 | 1 | 2 | 4 | 8 | 3 | 6 | 12 | 11 | 9 | 5 | 10 | 7 | 1 | 2 | 4 | 8 | 3 | 6 |