Non-symmetric 5 × 5 invertible matrices
The following are all randomly generated 5 × 5 matrices that have both integer entries and integer eigenvalues. These matrices are non-symmetric and invertible. They are grouped based on the maximum integer in absolute value in the matrix. The eigenvalues are sorted, so if you want an invertible matrix that has three repeated eigenvalues, you can search for, for example, "1, 1, 1".
- No entries greater than one in absolute value
- No entries greater than two in absolute value
- No entries greater than three in absolute value
- No entries greater than four in absolute value
- No entries greater than five in absolute value
Also availble are 5 × 5 matrices that are symmetric or invertible or both. While the matrices are in the Matlab format, some of these have been tested in Maple to ensure that they are not the result of numeric error.
Please note, these do not contain upper- or lower-triangular matrices.
Invertible 5 × 5 non-symmetric matrices with no entries greater than one in absolute value
| Eigenvalues | Matrix |
|---|---|
| -1, -1, -1, 1, 2 | [ 1 1 1 -1 0; -1 -1 0 0 1; 1 1 0 1 1; 0 0 0 -1 0; 0 1 1 -1 1] |
| -1, -1, 1, 2, 2 | [ 1 0 0 -1 0; 1 1 1 1 1; 0 1 1 0 -1; -1 1 -1 1 -1; 0 0 0 0 -1] |
| -1, -1, -1, 1, 1 | [ 1 0 -1 1 1; 0 1 -1 1 0; 0 0 -1 1 0; 0 0 0 -1 0; 0 1 -1 1 -1] |
| -1, -1, 1, 1, 1 | [ 1 -1 1 1 -1; 0 -1 1 1 0; 0 0 1 0 0; 0 0 1 -1 0; 0 -1 1 1 1] |
| -2, -1, -1, 1, 1 | [-1 -1 -1 -1 -1; -1 0 0 0 -1; 0 -1 0 1 1; -1 1 -1 -1 0; 0 -1 1 1 0] |
| -2, -1, -1, -1, 1 | [-1 0 0 -1 0; 0 -1 -1 1 -1; 0 0 -1 0 -1; -1 1 -1 0 1; 0 0 0 0 -1] |
| -1, 1, 1, 1, 1 | [ 1 0 0 0 0; -1 -1 -1 -1 0; 1 1 1 0 -1; -1 -1 0 1 1; 1 0 1 1 1] |
| -2, -1, 1, 1, 2 | [ 1 0 0 0 0; 1 -1 1 1 0; 0 1 -1 1 0; -1 1 0 1 1; -1 0 -1 1 1] |
| 1, 1, 1, 1, 1 | [ 1 0 0 1 0; -1 1 0 1 0; 1 0 1 -1 0; 0 0 0 1 0; -1 0 1 -1 1] |
| -2, -1, -1, 1, 2 | [ 1 -1 0 1 0; -1 0 1 1 1; 0 0 -1 0 0; 1 1 1 -1 0; -1 1 -1 1 0] |
| -1, -1, 1, 1, 2 | [-1 0 -1 -1 0; -1 1 1 0 1; -1 0 1 1 1; 1 0 0 0 -1; 1 0 1 -1 1] |
| -2, -2, -1, 1, 2 | [ 0 1 -1 1 -1; 1 -1 1 0 -1; 1 1 0 -1 0; 1 0 -1 -1 -1; -1 -1 0 -1 0] |
| -2, -1, 1, 1, 1 | [ 1 0 1 1 -1; 1 0 0 1 0; 0 0 1 1 -1; 1 1 0 -1 1; 1 1 0 1 -1] |
| -1, -1, -1, 2, 2 | [ 1 1 -1 0 0; 1 0 1 -1 0; -1 0 1 -1 0; -1 -1 -1 0 0; 1 -1 -1 0 -1] |
| -1, 1, 1, 1, 2 | [ 1 0 1 -1 0; 0 1 0 1 -1; 1 0 1 -1 -1; 1 1 -1 0 0; 1 1 -1 -1 1] |
| -3, -1, -1, 1, 1 | [ 0 0 1 1 -1; -1 -1 -1 0 1; 0 -1 0 1 1; 0 0 1 -1 0; -1 1 1 -1 -1] |
| -1, -1, -1, -1, 1 | [-1 0 0 0 0; 0 -1 0 0 1; -1 0 -1 1 0; 0 0 0 1 0; 0 0 1 1 -1] |
| -2, -2, -1, -1, 1 | [-1 -1 1 1 0; -1 -1 1 -1 0; 0 0 -1 -1 1; 1 -1 1 -1 0; 1 -1 1 0 -1] |
| -2, -1, -1, -1, 2 | [-1 -1 -1 1 0; 0 -1 -1 0 1; 0 -1 1 0 -1; 0 1 -1 -1 -1; 0 1 -1 0 -1] |
| -2, -2, -1, 1, 1 | [-1 0 1 -1 -1; 0 0 -1 -1 1; 1 0 -1 -1 1; -1 0 -1 -1 -1; 0 1 -1 -1 0] |
| -1, 1, 1, 2, 2 | [ 1 0 0 -1 -1; 0 1 1 0 1; 0 -1 1 1 -1; 0 0 1 1 1; 0 1 -1 1 1] |
| -2, 1, 1, 1, 2 | [ 1 1 -1 0 0; 0 1 -1 -1 1; 0 -1 1 -1 1; 0 0 0 1 1; 0 1 0 1 -1] |
| -1, -1, -1, -1, -1 | [-1 -1 0 0 1; 0 -1 1 0 1; 0 0 -1 0 -1; 0 1 1 -1 -1; 0 0 0 0 -1] |
| -2, 1, 1, 1, 1 | [ 0 1 -1 -1 0; 1 0 1 -1 0; -1 1 0 -1 0; 0 0 0 1 0; 0 -1 -1 -1 1] |
| -2, -1, 1, 2, 2 | [ 0 1 1 0 -1; 1 -1 0 1 -1; 1 0 1 -1 1; -1 1 -1 1 -1; -1 0 1 1 1] |
| -2, -1, -1, 1, 3 | [ 0 -1 1 1 1; -1 0 -1 -1 1; 1 -1 0 1 -1; 1 0 1 1 1; 0 0 -1 1 -1] |
| -1, -1, -1, -1, 2 | [ 0 1 0 1 1; 1 0 1 0 1; 0 0 -1 -1 0; 0 0 0 -1 0; 1 1 1 -1 0] |
| -2, -1, -1, 2, 2 | [ 0 0 -1 -1 -1; -1 1 -1 1 1; -1 -1 1 1 1; 0 1 0 -1 1; -1 -1 1 1 -1] |
| -2, -2, -2, 1, 2 | [ 0 1 -1 1 1; 1 0 1 -1 -1; -1 0 -1 -1 -1; 0 -1 -1 -1 1; 0 -1 -1 1 -1] |
| -2, -2, 1, 1, 1 | [-1 -1 0 1 1; -1 0 -1 -1 -1; -1 -1 0 -1 1; 1 0 -1 -1 1; 0 0 0 0 1] |
| -3, -1, 1, 1, 2 | [ 0 -1 1 1 -1; 0 1 -1 1 -1; 0 0 -1 0 -1; 1 1 0 1 1; -1 -1 -1 1 -1] |
| -2, -2, -1, -1, 2 | [ 0 1 1 0 0; 1 -1 1 0 1; 1 1 -1 0 1; 1 1 -1 -1 1; 1 1 1 0 -1] |
| -3, -1, 1, 1, 1 | [ 0 1 0 1 1; 1 0 -1 0 -1; 1 -1 0 0 -1; 1 -1 1 -1 -1; 1 -1 -1 0 0] |
| -2, -2, 1, 1, 2 | [ 1 0 1 0 -1; 1 0 0 -1 -1; 1 -1 -1 -1 1; -1 -1 -1 1 -1; -1 -1 0 0 -1] |
| -3, -2, 1, 1, 2 | [-1 1 -1 1 -1; 1 1 0 -1 0; -1 0 -1 -1 -1; 1 -1 -1 -1 1; -1 0 0 1 1] |
| -2, -1, 1, 1, 3 | [ 0 -1 -1 1 0; -1 0 -1 1 0; -1 -1 1 -1 1; 1 1 -1 1 1; 0 0 0 1 0] |
| -2, -2, -1, 2, 2 | [-1 1 1 -1 1; 1 1 1 1 1; 1 1 -1 -1 -1; -1 1 -1 1 -1; 0 1 0 1 -1] |
| -1, -1, 1, 1, 3 | [ 1 0 0 -1 -1; 0 1 0 0 0; 0 1 1 1 1; -1 -1 1 0 1; -1 -1 1 1 0] |
| -2, 1, 1, 2, 2 | [ 1 0 1 1 -1; 1 0 -1 -1 1; 1 -1 1 1 1; 0 0 1 1 1; -1 1 1 -1 1] |
| -2, -2, 1, 2, 2 | [-1 -1 -1 -1 -1; -1 1 1 -1 -1; -1 1 1 1 -1; 0 -1 1 -1 0; -1 -1 1 -1 1] |
| -2, -1, -1, 2, 3 | [ 1 1 -1 1 -1; 1 0 -1 1 1; -1 -1 -1 -1 -1; 1 1 -1 0 1; -1 0 -1 0 1] |
| -3, -1, -1, 2, 2 | [ 1 -1 0 -1 0; -1 -1 -1 1 1; 0 -1 1 0 -1; -1 1 -1 -1 -1; 1 1 -1 -1 -1] |
| -2, -1, 1, 2, 3 | [ 1 0 0 -1 -1; 1 0 -1 -1 1; 0 -1 0 -1 1; -1 -1 -1 1 -1; -1 1 1 -1 1] |
| -1, -1, 1, 2, 3 | [ 1 0 1 0 -1; -1 0 -1 -1 0; 1 -1 1 1 1; 0 -1 1 1 0; -1 1 1 -1 1] |
| -3, -1, 1, 2, 2 | [ 1 1 1 0 1; 1 -1 -1 -1 -1; 1 -1 -1 1 -1; 0 -1 1 1 0; 1 -1 0 -1 1] |
| -3, -2, -1, 1, 2 | [-1 1 0 -1 -1; 0 -1 -1 1 -1; 0 -1 -1 1 1; -1 1 0 1 -1; -1 -1 1 -1 -1] |
| -3, -2, -1, 1, 1 | [-1 -1 -1 1 -1; -1 -1 0 -1 -1; -1 0 -1 -1 -1; 1 0 -1 -1 1; -1 -1 1 1 0] |
Invertible 5 × 5 non-symmetric matrices with no entries greater than two in absolute value
| Eigenvalues | Matrix |
|---|---|
| -4, -1, 1, 1, 3 | [-1 1 1 -2 1; 0 1 1 1 -2; 2 0 -1 -2 0; -2 2 2 0 2; 0 -2 -1 2 1] |
| -4, -2, -1, 2, 3 | [ 0 1 2 -1 -1; 2 -1 0 0 -1; 0 2 2 -1 2; 0 -2 -2 -1 -2; -2 -2 0 -2 -2] |
| -4, -2, -1, 1, 1 | [ 0 0 2 0 -2; 0 -2 -1 0 1; 2 2 -2 0 2; 1 2 -1 1 2; 0 1 1 0 -2] |
| -4, -1, -1, 1, 1 | [-1 -1 1 1 1; 0 -1 0 0 -2; 0 -1 -2 0 -1; 0 -1 1 1 2; 0 -2 -2 0 -1] |
| -3, -2, -1, -1, 1 | [-2 -1 2 1 -1; 0 -1 0 -2 1; 2 1 0 0 1; 2 1 1 -1 1; -1 0 -1 -1 -2] |
| -2, -1, 1, 2, 5 | [ 2 -1 -1 1 0; -1 0 -1 -1 0; -1 -2 1 -1 2; 1 -1 -2 1 -2; -1 0 1 -2 1] |
| -3, -1, -1, 1, 3 | [ 1 2 -2 -2 0; 0 2 -1 -1 0; -2 0 -2 1 0; 0 1 2 -1 0; 0 0 -1 0 -1] |
| -1, -1, -1, 1, 3 | [-1 -2 -1 -1 -1; 0 -1 0 0 0; 0 1 0 1 1; -1 -1 1 2 1; 1 1 2 0 1] |
| -3, -2, 2, 2, 3 | [ 0 -2 -1 -2 -2; -2 2 1 0 0; 1 -1 0 -1 1; -2 0 -1 0 2; 0 0 2 2 0] |
| -2, -1, 2, 2, 2 | [ 2 -2 -1 -1 2; 0 -2 0 0 2; 0 0 2 0 0; 0 0 0 2 0; 0 0 2 -1 -1] |
| -4, -3, -1, 1, 2 | [-1 2 -2 0 0; 2 -2 -1 2 -2; -1 0 -2 0 1; -1 0 2 -2 2; 2 2 1 2 2] |
| -2, -1, -1, -1, 3 | [-2 1 2 -1 -1; 1 -2 -2 1 1; -1 -2 0 0 2; -1 0 -1 1 0; 1 -2 1 -2 1] |
| -2, -2, -2, -1, 3 | [-1 0 1 -1 -2; -1 -2 -2 -1 0; 0 0 -2 0 -1; 0 0 0 2 -2; 0 0 0 -2 -1] |
| -3, -2, -2, -1, 3 | [-2 0 -2 2 -1; 0 2 0 0 -2; -1 2 -1 0 -1; -1 0 1 -2 0; 0 -2 -1 1 -2] |
| -2, -1, 2, 2, 3 | [ 1 0 -2 0 -1; 2 2 -1 0 2; -1 2 -1 0 2; 2 2 -1 2 0; -2 0 2 0 0] |
| -2, -1, 1, 1, 4 | [ 2 -2 -2 -1 1; -2 0 2 1 -1; 0 -2 1 -1 -2; 0 0 0 1 0; 2 -2 -2 -2 -1] |
| -2, -2, -1, 1, 4 | [-2 0 -1 0 1; -1 2 -2 0 -1; -2 -2 0 -1 2; -2 -2 0 0 1; -2 -2 2 -1 0] |
| -1, 1, 2, 2, 4 | [ 2 1 -1 2 2; 0 2 0 0 0; 0 2 1 -2 0; 2 2 -2 2 0; -1 1 1 -2 1] |
| -2, -2, -1, 1, 3 | [-1 0 0 1 0; 1 2 1 0 -1; 1 2 -1 0 -1; 1 -1 -1 0 1; -1 -2 -1 0 -1] |
| -2, 1, 1, 2, 3 | [-2 2 0 0 0; 0 1 0 -1 0; -1 0 2 1 1; 0 0 0 2 0; -2 2 1 2 2] |
| -4, -1, 1, 2, 3 | [ 2 0 2 -1 1; -2 1 -1 2 1; 0 2 -2 -2 0; 0 2 -2 -1 1; 1 2 -2 1 1] |
| -4, -2, -1, -1, 1 | [-2 0 0 1 0; -2 -1 0 2 0; 0 0 -2 -1 0; 1 2 -1 -1 0; 1 -1 2 -1 -1] |
| -2, -1, 1, 3, 4 | [ 0 -2 2 -2 -1; -2 1 -1 1 1; 1 -2 1 1 0; -1 0 1 1 1; -1 0 1 0 2] |
| -3, -2, 1, 1, 3 | [ 1 -1 1 2 0; -2 0 0 1 2; -1 -1 -1 -2 0; 2 1 -1 1 0; 2 1 0 -1 -1] |
| -2, -2, 1, 2, 3 | [-2 -1 2 -2 0; 0 -1 0 2 -1; 0 -2 2 1 -1; 0 2 0 1 1; 0 2 -1 1 2] |
| -3, -3, 1, 2, 3 | [-1 -2 2 2 -2; -2 2 -2 -2 2; 0 0 1 2 2; 2 1 -2 -1 -2; -2 -1 2 -2 -1] |
| -4, -3, -2, 1, 3 | [-2 -2 -1 2 0; -2 1 2 -2 2; 1 2 -2 2 2; 2 1 0 0 2; 1 2 0 0 -2] |
| -3, -1, 1, 3, 3 | [ 1 2 1 2 2; -2 1 2 0 0; 2 2 1 0 0; 2 1 -2 -1 2; 1 2 1 2 1] |
| -2, -2, -1, -1, 3 | [-2 2 -1 1 1; 0 -1 0 -2 -2; 0 -1 -2 2 2; -2 -2 -2 1 2; 2 0 0 2 1] |
| -3, -2, 1, 2, 2 | [-1 0 0 1 2; -2 -1 0 0 -1; 2 -2 1 -2 1; 2 -1 0 1 -2; 2 -1 0 -1 0] |
| -4, -2, -2, 1, 2 | [-2 -1 -2 -1 -1; 1 -2 -1 2 2; 0 2 -1 2 0; -1 2 2 -2 -2; 0 0 -2 0 2] |
| -4, -3, -1, -1, 1 | [-2 2 1 -2 -1; -1 -1 1 1 1; 1 1 -1 -2 -1; -2 1 -1 -2 -2; 1 -1 -2 0 -2] |
| -3, -1, 1, 1, 4 | [ 0 1 -1 -2 -1; 2 -1 0 0 0; 0 0 1 2 2; 0 1 2 0 0; -1 2 2 0 2] |
| -3, -2, -2, -1, 2 | [-1 -1 1 -2 0; -2 0 -2 2 0; 0 1 -2 0 0; -2 1 -2 -1 0; 0 1 1 1 -2] |
| -4, -2, -1, 1, 2 | [ 0 1 2 -1 1; 2 -2 -2 -2 1; -2 -1 -2 -1 -2; -2 -1 -1 -2 1; 0 0 0 0 2] |
| -3, -2, 2, 2, 2 | [ 1 0 0 0 -2; 2 2 1 2 -2; 1 2 0 2 2; -2 2 1 -2 2; 2 1 2 1 0] |
| -3, -1, -1, 2, 4 | [ 2 0 -1 -2 1; 2 0 -1 -2 -2; -2 -1 -1 1 2; -2 -1 -1 -1 2; 0 0 2 0 1] |
| -4, -2, 1, 1, 3 | [-2 2 0 2 2; 2 2 0 1 2; -2 -1 1 0 -2; 2 -1 0 0 1; 1 0 0 0 -2] |
| -4, -2, -2, 2, 3 | [ 2 -2 0 1 -1; -2 -2 2 2 1; 1 -2 -2 -2 -1; 1 2 -2 0 0; -1 2 0 1 -1] |
| -1, -1, 2, 3, 4 | [ 1 -2 1 1 1; -2 2 -2 2 2; -2 -1 1 0 0; 2 1 -2 2 -1; -2 1 0 -2 1] |
| -2, 1, 2, 2, 4 | [ 2 2 2 -1 1; -1 2 1 -2 0; 2 -2 2 1 -1; 1 -2 0 -1 -2; -1 2 -2 -1 2] |
| -3, -1, 1, 2, 4 | [ 2 2 -2 0 1; 1 2 0 0 -2; -1 0 -2 0 -1; 1 2 2 -1 -1; -1 -2 -2 2 2] |
| -4, -2, -1, -1, 2 | [-1 2 -2 2 1; -1 -1 0 -1 1; -2 1 0 -1 -2; 1 -2 0 -2 -2; 0 -2 0 -2 -2] |
| -3, -2, 1, 2, 3 | [ 2 -2 -2 0 0; 0 0 2 2 2; 0 1 1 -1 -1; -1 2 1 -1 2; -1 1 1 2 -1] |
| -4, -1, 1, 2, 4 | [ 0 -1 2 2 -2; -2 -1 2 -1 -1; 0 -1 2 -2 2; 2 0 -2 2 2; -2 0 2 -1 -1] |
| -2, -1, 1, 3, 3 | [-1 -1 0 0 0; -2 1 -2 2 2; 0 -1 1 2 1; 0 -1 2 1 1; 1 1 -1 1 2] |
| -4, 1, 1, 2, 3 | [-2 -2 -2 -2 -2; 0 2 0 1 2; -2 1 1 0 -2; 0 0 0 1 0; -2 0 -1 2 1] |
| -2, -2, -1, -1, -1 | [-2 0 -1 -1 2; 2 -1 1 0 0; 0 0 -1 0 0; 2 1 -1 -2 0; 1 1 1 -1 -1] |
| -4, -3, -1, 1, 3 | [-1 2 2 1 -2; 0 -1 1 1 -1; 2 -2 0 2 -1; 2 2 0 0 2; -2 -2 1 2 -2] |
| -3, -1, -1, 1, 2 | [ 1 2 0 1 1; 0 1 2 0 0; 0 1 0 0 0; 1 -1 1 -2 -2; -2 -2 0 -1 -2] |
| -2, -2, -2, -1, 2 | [ 0 2 -1 -1 -2; 1 -2 -2 0 1; -1 1 1 0 1; -1 -1 1 -2 2; 0 0 0 0 -2] |
| -1, 1, 2, 2, 3 | [ 1 1 0 0 -1; 0 2 0 0 1; -1 1 1 0 -2; 1 -2 -1 2 2; -2 2 0 0 1] |
| -2, -1, -1, 3, 5 | [-1 2 -2 2 1; 2 2 -2 -2 2; -2 0 1 -2 2; 2 0 -2 1 -2; -2 1 1 1 1] |
| -4, -1, -1, 1, 3 | [-1 -1 1 -2 0; -2 0 1 1 0; 0 1 2 1 0; -2 0 2 -2 0; -1 0 2 1 -1] |
| -5, -2, -1, 2, 3 | [-1 -2 2 0 -2; 0 -1 2 1 2; 2 2 -2 2 2; 1 0 0 -1 -2; -1 1 2 0 2] |
| -4, -1, 1, 2, 2 | [ 1 -2 -2 1 -2; -1 0 -1 -2 0; -1 -2 1 -2 0; -1 1 -2 -1 -1; -1 2 -2 -2 -1] |
| -2, -2, -1, 2, 3 | [ 1 -1 2 2 -2; 2 -2 2 2 0; 1 2 1 -2 -1; 0 0 0 -2 0; 0 0 0 0 2] |
| -3, 1, 2, 2, 3 | [ 2 1 0 2 1; 2 -2 0 -1 -2; 1 -1 2 -1 -2; 2 0 0 1 2; 1 -1 0 -2 2] |
| -5, -2, -1, -1, 1 | [-2 2 -2 -1 -2; -1 -2 1 -1 -2; 0 1 0 0 -1; -1 -1 -1 -2 -1; -1 -2 0 -1 -2] |
| -3, -2, -1, 2, 2 | [-1 -2 1 -2 -2; -2 2 2 2 0; -2 0 -2 2 2; -1 -2 2 -2 2; 1 0 2 -1 1] |
| -1, 1, 1, 2, 3 | [ 1 1 2 -2 -1; -1 1 0 -2 0; 0 0 1 0 0; -2 -1 0 1 1; -1 -1 0 -2 2] |
| -4, -2, -1, 2, 5 | [-2 -1 1 -2 -2; -1 0 0 2 1; 0 -1 2 1 0; -2 1 0 2 2; -2 2 1 2 -2] |
| -3, -2, -1, 2, 3 | [-1 2 0 -1 -1; -1 -1 2 1 2; 1 2 -2 -1 -1; 2 2 -2 1 -1; 1 2 1 -2 2] |
| -3, -2, -2, -1, -1 | [-1 -1 -2 1 -1; 0 -2 -2 1 -1; 0 -2 -2 -2 2; -1 2 1 -2 0; -1 1 -1 0 -2] |
| -3, -2, -1, -1, 3 | [-1 -1 -2 0 0; 0 -2 2 1 1; -1 2 1 -1 1; 0 1 2 -2 1; 0 0 2 0 0] |
| -3, -1, -1, 1, 4 | [ 1 1 -2 -1 2; -2 2 1 -1 -2; -2 -2 -2 1 -2; 2 2 1 -2 2; 2 -2 0 1 1] |
| -3, -2, -1, -1, 2 | [ 1 0 2 0 0; -1 -1 1 0 -2; 2 0 -2 0 0; 2 0 2 -1 0; -1 0 2 -2 -2] |
| -1, -1, 2, 2, 3 | [ 1 1 1 0 0; 1 2 -1 0 0; -1 -2 -1 0 2; -1 -1 -2 2 1; 1 -1 1 0 1] |
| -3, -1, 1, 2, 3 | [ 2 1 -2 -2 -1; 1 1 1 1 -2; 0 1 1 1 1; -1 -2 0 -2 -1; 0 -2 -1 -2 0] |
| -3, -2, -2, 1, 2 | [ 2 -1 1 1 1; 0 -2 0 0 0; 0 2 -2 0 0; 2 -2 -1 -1 2; -2 -2 0 2 -1] |
| -3, -1, 1, 3, 4 | [-1 2 1 0 0; 0 2 -2 0 0; 0 -1 2 1 2; 2 -1 1 2 -2; -1 0 2 -2 -1] |
| -3, -2, -2, -1, 4 | [-1 -2 0 0 2; -2 -1 0 0 -1; 2 -2 -2 -2 -2; -1 2 0 -2 0; 2 -2 0 0 2] |
| -2, -2, 1, 2, 4 | [ 2 0 -2 0 2; 2 2 -2 0 2; -1 -2 -1 0 1; 1 1 1 2 -2; 0 0 0 0 -2] |
| -3, -1, -1, -1, 1 | [-2 2 0 0 -1; 0 -1 0 0 1; 0 2 -1 2 -2; 1 0 0 -1 1; -1 2 0 0 0] |
| -3, -3, 1, 1, 2 | [ 1 0 0 0 0; -1 -2 -1 0 -1; -2 0 1 -2 -2; -2 0 -2 -2 1; -2 -2 -1 -1 0] |
| -3, -2, 1, 2, 4 | [ 2 1 -1 0 -2; 0 -1 1 2 -2; -1 -2 0 1 2; 2 2 2 1 -1; -1 -2 2 1 0] |
| -3, -2, -2, 2, 3 | [-2 1 0 1 0; -1 2 2 1 -1; -1 2 -2 -1 2; 1 1 0 2 2; 0 0 0 0 -2] |
| -3, -2, -1, 1, 3 | [-2 2 -2 -1 -2; 2 2 1 0 2; -1 -1 -2 0 -1; 0 2 1 -1 2; 1 0 0 1 1] |
| -3, -1, 1, 3, 5 | [-1 2 1 0 1; 0 1 -2 0 2; 2 -2 2 -1 2; -1 2 0 1 -1; 1 2 2 -2 2] |
| -3, -3, -1, 1, 1 | [-2 -1 1 -2 0; 2 -1 -2 0 0; 1 -1 -2 -2 0; 0 0 -2 -1 0; 0 1 0 -1 1] |
| -2, 1, 2, 2, 2 | [ 2 0 0 0 0; 1 -1 0 2 -1; -2 1 2 2 -1; -2 0 0 2 0; -1 -2 0 0 0] |
| -2, -1, 1, 2, 4 | [ 0 2 2 2 2; 0 0 1 1 -1; 0 2 1 1 -1; 2 1 -1 1 1; 2 1 -1 0 2] |
| -4, -2, 1, 1, 2 | [-1 -1 0 0 0; -2 -2 0 0 -2; 0 -1 1 -2 -2; -2 0 0 2 0; 2 -2 0 0 -2] |
| -2, -2, 1, 3, 3 | [ 0 1 0 1 1; 2 1 2 -1 -2; -2 2 1 -2 0; 0 0 0 -1 -2; 0 0 0 -2 2] |
| -5, -3, -2, 1, 2 | [-2 1 2 0 -1; 1 -1 1 -2 -2; 2 -1 -1 -2 1; 0 -1 -2 -2 1; -1 -2 1 0 -1] |
| -3, -2, -1, 2, 4 | [ 0 -2 -2 1 2; 0 -1 -1 -1 -2; -1 2 1 1 -2; 2 0 0 2 0; 2 -1 -2 0 -2] |
| -3, -3, -2, 1, 2 | [-2 1 -1 0 0; 1 -2 -1 0 0; -2 -2 2 2 2; 1 1 -2 -1 -2; 0 0 0 -2 -2] |
| -3, -1, -1, 2, 3 | [ 1 0 0 2 -2; 2 1 2 -2 2; 2 2 1 -1 2; 0 0 0 -1 0; -2 1 -1 1 -2] |
| -5, -2, 1, 2, 2 | [-2 0 2 0 -1; 0 -2 -2 0 1; 2 -2 -2 0 -2; 2 -1 0 2 -2; 2 -1 -2 0 2] |
| -3, -2, -1, 1, 4 | [-1 2 -2 1 2; 1 0 -2 1 1; -1 -2 1 0 -2; 2 2 -2 -2 2; 2 0 2 0 1] |
| -4, -2, 1, 2, 4 | [-2 2 0 0 0; -1 2 2 -2 -2; -1 0 2 -2 -1; 0 -1 -2 -2 -1; 1 -2 -2 -2 1] |
| -2, -1, 2, 2, 4 | [ 1 -2 2 0 0; 0 0 -1 1 -1; 1 -2 2 -1 -2; 1 2 0 2 -2; 1 -2 0 -1 0] |
| -1, 1, 2, 3, 4 | [ 1 -1 1 0 0; -1 2 0 -1 1; 0 0 2 2 0; -2 -2 2 2 2; -1 0 0 0 2] |
| -3, -3, -1, 2, 3 | [-1 0 0 0 0; -2 -1 -2 0 2; 2 -1 -2 -2 1; 1 2 -2 0 -1; 1 2 0 -1 2] |
| -4, -3, -1, 2, 2 | [-2 0 2 2 0; 0 2 0 0 0; 2 2 -2 1 -2; 2 -1 -1 0 -2; -1 0 0 -1 -2] |
| -3, -1, 1, 2, 5 | [ 1 -2 2 -2 -2; -2 -2 1 -1 -2; -2 -2 1 2 1; -2 0 0 2 1; -2 -2 2 1 2] |
| -4, -2, 1, 2, 3 | [ 2 2 -2 0 1; 2 -1 2 0 1; 0 2 -1 1 0; 0 -1 1 2 -2; 0 1 -1 0 -2] |
| -4, -3, -2, -2, 3 | [-2 0 0 0 0; -1 -1 -2 2 -2; -2 0 -1 -1 1; 1 2 0 -2 -2; 0 -2 2 -2 -2] |
| -3, -1, 2, 2, 3 | [ 0 1 0 2 0; 2 2 -1 2 -1; 0 0 2 1 0; 1 0 2 -2 1; 2 0 -1 1 1] |
| -3, 1, 1, 2, 3 | [ 2 1 2 0 1; 0 -2 2 0 -1; -1 2 1 0 0; 1 2 1 1 1; 2 -1 -2 0 2] |
| -3, -3, -1, 1, 2 | [ 0 1 1 1 0; -1 2 0 0 2; -1 1 -2 1 -1; -1 1 1 -2 2; -2 2 2 2 -2] |
| -3, -2, 1, 1, 4 | [-2 -1 -1 -2 1; -2 1 -1 0 0; 2 -2 -1 -2 2; 0 2 -2 2 2; 2 0 1 0 1] |
| -2, -2, -1, 3, 4 | [-2 0 -2 2 -1; 2 2 2 0 2; -2 1 1 -1 -1; 0 1 -1 1 1; 2 2 -1 2 0] |
| -3, -1, 2, 2, 2 | [ 1 2 -1 2 0; 2 -2 0 2 0; 0 0 2 2 0; 0 -1 -1 -1 -2; -1 2 0 -2 2] |
| -2, -2, 1, 1, 3 | [ 1 0 0 0 -1; -2 2 0 2 2; 1 -1 1 -2 0; -2 2 0 -1 2; 0 0 0 0 -2] |
| -2, 1, 1, 3, 4 | [ 1 -1 1 2 -1; 0 1 0 0 0; 1 0 2 0 2; 2 -1 -1 1 1; 1 -1 2 2 2] |
| -3, -3, -2, 1, 3 | [-2 -1 1 -1 -1; 1 -2 0 -2 -1; -1 -1 -2 2 -2; -2 -2 1 1 -1; 2 1 -2 -2 1] |
| -3, -3, -2, -1, 1 | [ 0 2 2 -2 -2; 0 -2 -2 -2 1; 1 1 -2 -1 -1; -1 -1 1 -2 -1; 1 1 -1 -1 -2] |
| -3, -2, -2, -2, 3 | [-2 0 -1 1 0; 2 -2 -2 1 0; -1 -2 0 -2 0; 0 0 -2 0 0; 2 0 1 0 -2] |
| -4, -1, -1, 1, 2 | [ 2 0 2 -2 -2; 0 -1 0 0 0; 1 -1 -1 0 -2; -2 2 2 -1 1; 2 -1 -2 0 -2] |
| -3, -1, -1, 3, 3 | [-1 2 -1 2 -1; 2 0 -1 -2 -2; 1 0 0 -2 2; 1 -2 -1 1 -2; -2 1 1 0 1] |
| -4, -3, -1, 2, 3 | [-2 -1 2 -1 0; -1 2 -2 2 0; 1 -1 -1 2 -1; -2 0 2 0 -2; 2 0 -2 0 -2] |
| -4, -2, -1, 1, 4 | [-2 -1 1 0 -1; -1 -1 -2 -2 -2; 2 -2 2 1 -1; -1 -2 1 -2 -2; 0 0 0 0 1] |
| -4, -3, -2, 1, 2 | [-1 1 0 2 -2; 2 1 1 -1 2; 0 0 -2 0 1; 2 2 1 -2 0; -2 2 -2 0 -2] |
| -3, 1, 2, 3, 3 | [-1 2 -2 2 2; 2 2 0 -2 -1; -1 -1 2 1 1; 1 1 1 2 -1; 1 1 2 1 1] |
| -3, -2, -2, -1, 1 | [-2 2 0 1 0; 0 -2 0 0 0; 2 -2 -2 2 1; 0 -2 -2 1 2; 2 1 1 2 -2] |
| -5, -2, -1, 1, 3 | [-1 1 -1 1 2; -2 -2 2 0 1; -2 2 0 2 -2; 2 1 1 -2 2; -1 1 -2 2 1] |
| -3, -2, -2, 2, 2 | [-2 0 0 0 0; 0 -1 0 -1 2; 2 0 2 0 0; -2 -2 0 -2 0; -2 2 2 -1 0] |
| -1, 1, 1, 3, 4 | [ 1 2 0 -2 -2; 0 2 -2 -1 2; -2 2 1 -2 -2; 0 -1 0 2 1; -2 2 -2 -2 2] |
| -2, -2, -1, 2, 5 | [ 2 -2 2 -2 0; -2 1 -1 -1 -2; 2 0 1 1 0; 0 -2 -1 -2 1; 2 -2 1 1 0] |
| -1, 1, 2, 2, 2 | [ 0 -2 0 0 1; -1 1 -1 1 1; 1 0 2 -1 -2; 1 2 2 1 -1; 0 0 0 0 2] |
| -4, -3, -2, -1, 2 | [-2 -1 1 1 1; -2 -1 1 -1 -1; -1 1 -1 -2 -2; 1 -1 -2 -2 2; 1 -1 2 2 -2] |
| -3, -2, -2, 1, 3 | [-2 2 0 -1 -1; 1 -1 0 0 -1; -2 2 -2 1 -1; -2 -2 0 2 -2; 1 0 0 -2 0] |
| -2, 1, 2, 3, 3 | [ 1 2 -2 -2 -2; 0 2 -1 2 -1; 0 0 2 1 1; -1 2 0 2 2; 1 -2 1 0 0] |
| -2, -2, -2, -1, -1 | [-1 0 0 0 0; 0 -2 2 0 2; -2 0 -2 -2 0; 2 0 0 -2 0; -1 0 -2 -1 -1] |
| -3, 1, 1, 2, 2 | [ 1 0 2 0 -1; -1 2 0 -1 0; -1 1 -1 -2 1; 0 -2 -2 0 2; -2 0 2 -1 1] |
| -4, -1, 1, 1, 2 | [ 1 2 2 -2 0; 0 1 -2 0 0; 1 -2 -2 -1 0; 1 0 -2 -2 0; 1 0 2 0 1] |
| -4, -3, -2, -1, 3 | [ 1 -2 -1 -1 -1; -2 -2 -1 2 0; 1 -1 -2 -1 0; -2 2 -1 -2 0; 0 2 0 -2 -2] |
| -2, -1, -1, 1, 4 | [-1 -1 0 1 0; -2 1 -1 1 2; 0 2 -2 -2 0; -2 0 -1 2 2; -2 2 1 1 1] |
| -4, -1, 1, 1, 4 | [ 1 0 0 0 0; 1 -1 2 1 1; -2 1 -1 2 -2; 0 0 2 2 -2; -1 2 -2 -1 0] |
| -6, -2, -1, 1, 2 | [-2 0 -2 2 -1; 2 2 2 -2 2; -2 -1 -2 1 -2; 2 -2 -2 -2 2; -1 -1 -2 1 -2] |
| -4, -2, -1, 1, 3 | [-1 -2 2 2 2; -2 2 -2 -2 1; -1 2 -1 -2 -2; 1 -2 -2 -1 0; 0 0 -1 -1 -2] |
| -4, -2, -1, 2, 2 | [ 1 -1 1 1 0; -1 -2 0 1 0; 1 -2 -2 2 0; 1 1 1 -2 0; -1 0 -1 -1 2] |
| -1, -1, 2, 2, 2 | [ 0 0 0 1 0; 0 2 0 0 0; -2 -1 0 1 -2; 2 1 -2 1 -2; 2 0 -1 -1 1] |
| -4, -4, -2, 1, 2 | [ 0 2 2 -1 -2; 2 -2 0 -2 -2; 0 -2 -2 -1 2; -1 0 -1 -1 0; -2 -2 0 -1 -2] |
| 1, 1, 1, 2, 2 | [ 2 0 -2 -1 0; 0 1 -1 2 0; 0 0 1 0 0; 0 0 0 1 0; 1 -1 -2 1 2] |
| -4, -3, -2, 2, 2 | [-1 -1 -2 -1 2; 0 -2 -2 2 2; 2 -1 -2 -1 1; -2 2 0 0 0; 2 2 2 0 0] |
| -5, -3, -1, 1, 2 | [ 1 0 -2 2 -1; 0 -1 0 0 -2; -2 0 -2 1 0; 2 -1 1 -2 1; 2 -2 -2 2 -2] |
| -1, -1, 1, 2, 4 | [ 0 2 -1 0 -1; -1 1 2 -1 1; -1 2 1 -1 1; -1 0 -2 2 2; -2 1 2 -1 1] |
| -2, 1, 2, 2, 3 | [ 1 -1 1 -2 0; 0 2 0 2 -2; 1 0 2 2 -1; -2 1 -1 -1 2; -1 1 -1 0 2] |
| -4, -1, -1, 1, 4 | [-2 0 -2 2 2; 0 1 -2 -2 -2; -1 -1 -1 2 1; 0 0 0 -1 0; 2 -1 2 0 2] |
| -2, -1, 2, 3, 4 | [ 2 2 -2 2 -1; 0 2 0 0 -1; -1 1 0 2 -2; 1 0 1 1 -2; 1 -1 -1 -2 1] |
| -3, -3, -2, -2, 2 | [-2 0 2 -2 0; 2 -2 1 2 2; 1 0 -1 -2 0; -2 0 -2 -1 1; 0 0 2 -2 -2] |
| -2, -2, -2, -1, 1 | [-2 -2 0 2 1; -2 -1 0 2 0; -1 -1 -2 2 -1; 0 -1 0 0 0; 0 -2 0 2 -1] |
| -2, -2, -1, 2, 4 | [ 2 -1 2 -1 1; 1 -1 -2 1 0; 0 -2 2 -2 2; -1 1 -1 -1 2; 0 -1 2 -1 -1] |
| -2, -2, 2, 3, 3 | [ 0 -1 1 2 -1; 0 1 2 0 -2; -2 2 0 2 2; 0 0 1 1 2; -2 -1 0 2 2] |
| -3, -2, 1, 3, 4 | [ 2 1 -2 0 -1; 2 1 0 -2 0; -2 0 1 0 -2; 2 -1 2 -2 0; -2 1 -2 -1 1] |
| -3, -3, -1, 2, 5 | [-2 2 -1 2 2; 1 -2 -2 1 1; -2 -1 2 -1 -1; 0 2 -2 0 -2; 2 1 -1 0 2] |
| -3, -3, 1, 2, 4 | [ 0 1 0 -2 -2; 0 2 2 1 0; 0 0 -2 -2 2; -2 1 -1 2 -2; 0 0 1 -2 -1] |
| -1, 1, 1, 2, 4 | [ 1 0 -1 -2 0; -1 1 -1 -1 1; -2 -2 2 2 -2; 0 0 0 1 0; -1 0 -1 1 2] |
| -1, -1, 2, 2, 4 | [ 1 0 -2 2 0; -2 -1 -2 1 0; 1 0 2 2 0; 2 0 2 2 0; -2 0 -1 2 2] |
| 1, 1, 1, 1, 4 | [ 1 2 1 1 1; 2 2 -1 2 2; -2 2 2 -2 1; 0 -1 0 1 -1; -2 2 1 -2 2] |
| -3, 1, 1, 2, 4 | [ 0 -2 0 0 -1; 0 2 1 -1 -1; 1 1 0 1 2; 0 2 2 2 1; -2 -2 2 2 1] |
| -2, 1, 1, 2, 4 | [ 2 2 -2 2 0; 2 -1 0 -2 0; -2 -1 2 -2 0; 0 0 1 2 0; 1 0 -2 1 1] |
| -3, -2, -2, -2, 1 | [-2 0 0 2 -2; -1 -1 0 2 0; 1 -1 -2 0 -2; 0 0 0 -2 0; -2 2 0 0 -1] |
| -4, -2, -2, -1, 3 | [-1 2 -1 -2 -1; -2 -2 0 2 -2; 2 1 -2 -1 0; -2 2 0 -2 -2; -2 -2 0 -1 1] |
| -4, -3, -2, 2, 3 | [ 1 2 -1 1 2; 0 0 -2 1 0; -1 -2 -1 -2 2; 1 0 -1 -2 -2; 2 -2 0 -2 -2] |
| -3, -3, -2, 2, 2 | [-1 -1 -1 -2 1; 0 -2 -2 2 0; -2 0 0 0 1; -2 1 -1 1 0; 0 0 2 -2 -2] |
| -3, -1, 2, 2, 5 | [ 1 0 1 2 -2; 0 -2 2 0 -2; 0 0 2 0 0; 2 -2 2 2 -1; -2 -2 2 -1 2] |
| -5, -1, 2, 2, 3 | [ 1 -1 -2 -2 2; -1 2 -2 2 -1; -1 -1 -2 -1 1; -2 -1 -2 1 2; 1 0 1 2 -1] |
| -3, -1, -1, 2, 5 | [ 2 -1 1 0 -2; 1 -1 0 -1 2; 0 -1 1 -2 -2; 0 1 -2 1 2; -2 1 -2 2 -1] |
| -3, -1, 1, 1, 3 | [ 2 -1 -1 -1 1; -2 -1 -2 0 -2; -1 -1 0 0 -1; -2 -2 2 -1 2; 0 0 0 0 1] |
| -3, -2, 2, 3, 4 | [ 2 -2 2 1 0; 0 2 2 2 0; 2 2 0 2 0; -1 1 2 -2 0; 2 -2 2 1 2] |
| -2, -1, -1, 2, 4 | [ 2 -1 0 2 0; -2 2 -2 1 2; -2 0 -1 0 2; 2 0 -1 -1 -1; -2 0 1 0 0] |
| -4, -2, -1, -1, 3 | [-2 1 1 -1 -2; -2 -2 2 1 2; 0 2 -1 -1 0; 2 1 -2 -2 -2; 1 2 -1 -1 2] |
| -4, -1, -1, -1, 1 | [-1 -2 -2 0 0; -2 -2 -2 1 0; 0 0 -1 0 0; 0 2 -1 -1 0; 2 -2 1 0 -1] |
| -3, -2, -1, 1, 5 | [ 2 -2 -2 1 0; -2 -1 2 -2 -2; 0 0 -1 -2 -2; 2 0 -2 1 2; -1 -2 0 1 -1] |
| -3, -2, -2, 3, 3 | [ 1 1 0 2 -1; 2 -1 0 2 0; -1 0 -2 -2 0; 2 1 0 -1 1; -2 1 0 2 2] |
| -3, -3, -2, -1, 2 | [-2 0 0 2 -2; -2 -2 -1 -2 -1; -2 -2 -1 -1 2; 0 0 0 -1 0; 0 -2 2 2 -1] |
| -2, -1, 2, 3, 3 | [ 1 2 -2 0 2; 1 1 1 0 -2; -1 -2 2 -1 -2; -2 2 -2 0 2; -2 -2 -2 1 1] |
| -3, -1, 2, 4, 4 | [ 2 1 0 -2 2; 2 -1 2 0 -2; 0 0 2 0 0; -2 -1 0 1 2; 2 -1 -2 2 2] |
| -4, -4, 2, 2, 2 | [ 2 2 2 -2 2; 2 -2 -2 -2 2; 0 0 2 2 2; 1 -2 -1 -2 -2; -1 2 1 -2 -2] |
| -2, 1, 1, 1, 3 | [ 1 0 0 0 0; 2 -2 0 0 0; 0 -1 1 2 0; 2 2 0 2 1; -2 -2 0 1 2] |
| -4, -2, -2, 1, 3 | [ 2 2 2 2 0; 2 -2 -1 0 -2; 0 0 0 0 1; 0 0 -1 -2 0; -1 -2 1 -2 -2] |
| -2, -2, 2, 2, 3 | [ 2 1 -1 1 0; 2 0 -2 -1 2; 2 0 -2 -1 -1; 0 0 0 2 0; 0 2 -2 0 1] |
| -2, 2, 2, 3, 4 | [ 2 -2 -2 0 -2; -1 2 1 1 -1; 0 0 2 0 0; 0 2 0 2 2; 0 -2 -1 2 1] |
| -3, 1, 1, 1, 2 | [-1 2 0 -2 0; 1 0 0 1 0; 0 -1 1 -2 0; -1 2 0 1 0; -1 -1 1 0 1] |
| -4, -1, 1, 3, 4 | [ 2 -2 1 -2 0; -2 -2 0 -2 -2; -1 1 2 2 2; 0 0 2 2 1; 2 -2 2 -2 -1] |
| -3, -2, 2, 3, 3 | [ 2 2 2 -1 0; 0 -2 0 0 0; 2 2 -1 0 -2; -2 1 1 2 1; 2 -1 -1 1 2] |
| -1, -1, 2, 3, 3 | [ 1 2 -1 1 2; 1 2 -2 -1 -2; -2 2 1 0 0; 0 -2 2 1 -2; 1 -1 -2 -1 1] |
| -4, -1, -1, -1, 2 | [-1 1 0 -2 -1; 0 -1 2 -1 -1; 0 1 -2 1 -1; 0 0 0 -2 -2; 0 -2 2 -2 1] |
| -4, -2, -2, -1, 2 | [-1 1 0 -1 -1; 0 -2 0 0 0; -1 -1 -2 -2 -2; -2 0 0 -2 0; -2 1 -2 1 0] |
| -5, -2, -1, 1, 2 | [-1 2 -1 -2 1; 0 1 1 -1 -2; -2 -2 -1 -1 -1; -2 -2 -2 -2 1; 0 -1 0 2 -2] |
| -1, -1, 1, 3, 3 | [ 2 2 0 -2 -1; 0 1 0 1 -1; 1 -2 -1 0 2; -1 2 0 1 -1; 1 -2 0 0 2] |
| -2, 1, 2, 2, 5 | [ 2 2 -2 2 -2; 0 2 2 1 0; 0 2 0 1 -2; 0 0 1 2 -2; 0 0 -2 -1 2] |
| -3, -3, 1, 2, 2 | [-2 0 0 2 1; -1 2 0 0 1; -2 1 2 0 0; 0 -2 0 -1 2; 1 0 0 2 -2] |
| -2, -2, -2, 1, 1 | [-2 0 -1 -2 0; 1 1 -2 2 -1; 0 0 -2 2 0; 0 0 0 -2 0; -2 0 0 2 1] |
| -3, -2, -2, 1, 1 | [-2 -2 0 2 2; 0 -1 1 -2 -2; 2 0 1 0 -2; 0 0 -2 -2 2; 2 0 0 0 -1] |
| -1, -1, 1, 3, 5 | [ 0 2 2 1 2; 1 2 2 -1 2; 1 2 2 -1 -1; 0 0 -1 1 0; 0 1 -1 0 2] |
| -2, -2, -1, 1, 5 | [ 2 2 0 -2 -1; 0 2 0 -2 -2; 0 2 -2 0 0; -1 -2 0 0 1; -2 -2 0 -1 -1] |
| -1, 1, 2, 3, 3 | [ 2 -2 0 1 -2; -1 1 0 1 -2; 0 2 1 2 -1; 1 0 0 2 1; -2 2 0 2 2] |
| -4, -3, 1, 2, 3 | [-2 2 -2 -2 -1; 2 2 0 0 0; -1 1 -1 1 0; -1 1 2 -2 0; -1 -1 1 1 2] |
| -2, -1, 1, 4, 5 | [ 1 2 -1 0 -2; 2 2 0 2 0; -2 -1 1 2 1; 1 2 1 1 1; -2 -1 0 2 2] |
| -4, -2, -1, 1, 5 | [ 1 -2 -2 1 -1; -1 -1 2 0 2; -2 2 0 -2 -2; 2 -2 -1 1 -1; 0 0 -2 -2 -2] |
| -3, -2, -2, -2, -1 | [-2 -1 -1 0 -2; -1 -2 -1 1 0; 2 -2 -2 0 -2; 0 0 0 -2 0; 0 0 0 0 -2] |
| -3, -2, -2, 2, 4 | [ 0 1 1 0 -2; 2 -2 2 1 2; 2 1 -2 -2 -1; 0 -1 1 2 -2; -2 0 -1 -2 1] |
| -4, 2, 2, 2, 3 | [ 2 2 -1 -1 -2; 0 -2 -2 2 -2; 0 -2 1 0 -2; 0 0 0 2 0; 0 -2 -1 0 2] |
| -3, 1, 2, 2, 4 | [ 2 -2 1 -2 -1; 1 2 2 -2 0; -1 1 -2 2 0; 1 -2 2 2 0; -2 2 -2 1 2] |
| -2, -1, -1, -1, -1 | [-1 0 0 2 0; -1 -1 -2 1 0; 0 0 -1 0 0; 0 0 -1 -2 0; 1 2 -1 -2 -1] |
| -1, 2, 2, 2, 2 | [ 0 0 0 -1 2; -1 2 0 2 -1; -2 1 2 -1 0; -2 0 0 1 2; 0 0 0 0 2] |
| -2, -2, 2, 2, 2 | [ 2 0 2 2 -2; 0 -2 0 0 -2; 0 1 -2 2 -2; 0 1 0 2 0; 0 0 0 0 2] |
| -5, -3, -2, 2, 3 | [ 2 -2 0 -2 -2; -2 -2 -1 -2 -1; -2 2 -1 0 -2; -1 -2 -2 -2 2; -2 -1 -1 1 -2] |
| -2, -2, -1, 3, 3 | [ 1 0 0 -2 -2; -2 1 -2 -2 -2; 2 -2 -1 2 0; -1 -2 -1 2 0; -2 2 -1 -2 -2] |
| -4, -2, 1, 2, 2 | [-1 0 -2 2 -1; -2 2 -1 -2 -1; -1 0 -1 -1 -2; 0 0 -1 -1 1; -2 0 -2 2 0] |
| -5, -2, -2, -1, 1 | [-2 -2 1 0 0; -2 -2 0 0 -1; 2 2 -2 1 1; -2 0 0 -2 -1; 2 -2 1 0 -1] |
| -2, -2, -2, -2, 1 | [-1 2 -1 2 0; 0 -2 2 0 -2; -2 2 -1 -2 1; 0 0 0 -2 0; -2 2 1 1 -1] |
| -2, -1, -1, 3, 3 | [ 1 0 1 -2 -2; 0 0 0 2 1; 2 0 2 -2 0; 0 1 1 1 2; 0 1 -2 2 -2] |
| -2, -2, 2, 3, 4 | [ 0 2 2 -1 2; 1 0 0 -2 0; 0 1 2 1 -1; 0 -2 2 1 2; 1 -2 -2 1 2] |
| -1, 1, 1, 4, 4 | [ 2 1 2 2 1; -2 2 2 -1 -1; 0 -1 2 -1 -2; 2 -2 -2 1 0; 0 -1 -2 -1 2] |
| -4, 1, 1, 2, 6 | [-2 2 0 -2 0; 2 2 -1 2 -2; 2 -2 2 -1 2; -2 2 -1 2 -2; 0 -2 1 1 2] |
| -4, -3, -1, 1, 1 | [-2 -1 0 -2 -1; 1 0 -1 -1 1; 1 -2 -2 0 -2; -1 -1 -2 -1 -1; -2 0 -1 -1 -1] |
| -2, -2, 1, 1, 4 | [ 1 0 0 0 0; 2 -2 0 0 -2; -1 0 1 -1 -2; 0 0 0 0 -2; 2 0 -2 -2 2] |
| -3, 1, 2, 3, 4 | [ 2 -2 2 0 -2; -1 1 2 0 1; 2 2 0 0 -1; 1 -2 -1 2 1; 0 2 -1 0 2] |
| -4, -3, 1, 1, 2 | [-2 -2 1 0 -2; -1 2 -1 0 -2; 2 -2 -2 0 -1; 2 1 2 1 -1; -2 2 -1 0 -2] |
| 1, 1, 2, 2, 3 | [ 1 0 0 0 0; 0 2 -1 1 0; 2 -1 2 1 0; -2 2 -2 2 0; 1 1 0 -2 2] |
| -3, 1, 2, 2, 2 | [ 2 0 -1 0 -1; -1 2 2 -1 1; 2 0 -1 0 -2; -2 0 1 2 1; -2 0 -2 0 -1] |
| -3, -2, -1, 3, 3 | [ 1 2 2 2 2; 0 -1 -1 1 1; 2 -2 1 -2 -2; 0 0 1 -2 -1; 2 0 -2 0 1] |
| -4, -1, -1, 2, 3 | [-1 2 0 1 1; 0 1 2 2 -2; 0 2 2 1 2; 0 0 -2 -2 1; 0 -2 2 0 -1] |
| -4, -4, 1, 1, 2 | [-2 2 2 -2 0; 2 -2 1 -2 0; -1 0 1 -1 0; -2 -2 -2 -2 0; -1 2 -2 0 1] |
| -3, -1, -1, 3, 4 | [-2 1 -2 1 1; 1 0 2 -2 2; -2 1 1 2 2; -2 -1 0 2 1; -2 1 2 2 1] |
| -4, 1, 1, 2, 4 | [ 0 1 0 0 -2; 2 2 0 -1 1; 1 -1 1 0 2; -1 -2 0 2 1; -2 1 2 1 -1] |
| -3, 2, 2, 2, 3 | [ 2 0 -2 2 -2; 0 2 0 0 0; -1 -2 1 -2 -2; -1 2 -1 0 -2; -1 1 -2 -1 1] |
| -4, -3, -1, 1, 4 | [-1 1 0 -1 1; 0 -2 0 2 -1; 2 2 1 -2 2; 0 2 0 1 -2; 2 -2 2 -2 -2] |
| -5, -4, -2, 2, 3 | [ 0 -2 2 2 1; -2 -1 2 -2 2; 2 2 -2 -2 1; 2 -1 0 -1 0; 0 2 2 1 -2] |
| -4, -2, -1, 2, 4 | [ 0 0 2 -1 2; 1 -2 2 -1 2; 1 2 -2 -1 2; 2 1 -2 2 -1; 1 2 1 -1 1] |
| -2, -2, -2, 2, 3 | [-1 -2 -2 0 0; -2 2 -1 0 0; -1 2 2 0 0; 2 1 -1 -2 0; -1 -2 1 0 -2] |
| -3, -3, -1, 2, 2 | [ 0 0 1 -2 2; -2 -2 -1 0 2; 0 0 -1 -1 -2; -2 0 -2 -1 0; 0 1 -1 -1 1] |
| -2, 2, 2, 2, 3 | [ 2 0 0 0 0; 0 0 2 0 -1; 1 2 1 0 1; 1 1 1 2 -2; 1 0 2 0 2] |
| -1, -1, -1, 2, 3 | [ 1 2 -2 -2 0; -1 -1 -1 -1 0; -1 0 1 -1 0; -1 -2 0 2 0; 0 1 -1 0 -1] |
| -1, 1, 1, 1, 4 | [ 2 2 0 0 -1; 0 1 0 0 0; 2 1 1 -1 -1; -2 2 -1 0 2; -2 0 0 1 2] |
| -1, -1, 1, 1, 5 | [ 0 0 -1 2 0; -1 1 -1 1 -2; 0 -2 1 1 2; -1 2 -1 2 -2; 1 -2 1 -2 1] |
| -3, -1, -1, -1, 2 | [-1 0 0 0 0; 1 0 1 2 1; 0 0 -2 -1 -1; -1 0 2 1 2; 1 2 1 2 -2] |
| -1, -1, 1, 1, 4 | [ 2 1 1 -1 -1; 0 -1 0 0 0; 2 2 1 -2 1; 1 -2 -1 0 2; -1 0 -1 1 2] |
| -2, -2, -2, 2, 2 | [-1 1 -2 -1 2; 1 0 -1 1 1; 0 0 -2 0 0; 0 0 1 2 0; 1 2 -2 0 -1] |
| -3, -1, 2, 2, 4 | [ 2 1 2 2 -2; 0 2 0 0 0; 2 0 -1 2 -2; 2 0 2 0 -1; 0 0 -1 2 1] |
| -3, -2, -2, 1, 4 | [ 2 -2 1 2 2; -2 -1 -2 2 1; 2 -1 0 -2 -2; 2 0 0 -1 -1; 0 0 0 0 -2] |
| -3, -3, -1, 1, 3 | [ 1 -2 2 -2 0; -1 -1 1 1 -1; -1 2 -1 0 -2; -1 2 -1 0 1; -2 1 -2 2 -2] |
| -2, -1, 3, 3, 3 | [ 2 1 1 -1 -1; -2 2 0 2 2; -1 2 2 -1 -1; 0 2 -2 1 2; -2 2 0 0 -1] |
| -5, -1, -1, 1, 1 | [-2 -2 -1 0 -1; -2 -1 1 0 -1; -1 0 -1 0 0; -2 -2 -1 1 -2; -2 -2 -1 0 -2] |
| -4, -3, -1, 3, 4 | [ 1 1 -2 1 1; 2 2 2 2 2; -2 2 -1 2 -2; 1 1 2 -1 -2; 1 -1 -1 -1 -2] |
| -3, -1, 2, 3, 3 | [ 2 -2 -2 2 -2; 0 -1 1 2 -1; 1 1 2 1 1; 0 2 2 -1 0; -1 -1 1 -1 2] |
| -4, -2, -2, 1, 1 | [-2 -1 -1 -1 1; -1 -1 1 -1 1; -2 1 -1 0 0; -2 0 -1 0 -1; 1 0 1 -1 -2] |
| -5, -1, 1, 1, 3 | [ 0 1 2 2 -2; 1 -1 1 0 1; 1 -1 2 -2 2; 1 -1 -1 -2 2; -1 2 1 1 0] |
| -4, -3, -2, -1, 1 | [-2 0 1 -1 1; 2 -1 -2 2 -1; 1 0 -2 -1 1; 0 2 -2 -2 2; -1 -1 2 -1 -2] |
| -2, -2, -2, 1, 4 | [ 2 1 0 -2 2; 0 -2 0 0 0; -1 2 -2 -1 -2; -2 -2 0 0 0; 2 -2 0 1 1] |
| -4, -2, -2, -1, 1 | [-1 1 -1 -2 -1; 1 -2 -2 0 1; -2 -2 -2 0 2; 1 1 0 -2 -1; 1 0 0 -2 -1] |
| -2, -2, -2, 1, 3 | [ 1 0 0 2 0; 0 -2 1 -1 -1; -2 0 -1 2 0; 1 0 2 2 1; 2 0 -1 -2 -2] |
| -2, -2, -1, -1, 4 | [-1 1 0 2 1; 0 1 0 2 -1; 1 -2 -2 1 0; 0 2 0 2 -2; 0 -2 0 0 -2] |
| -1, -1, -1, 1, 4 | [ 0 1 -2 0 0; 1 2 1 1 2; 0 0 -1 0 0; 0 0 1 -1 0; -1 2 1 2 2] |
| -5, -3, -2, 2, 4 | [-2 1 1 -2 1; 1 -2 1 -2 0; 2 2 2 2 2; -2 -2 2 -2 -2; 2 2 1 0 0] |
| -4, -2, 1, 1, 1 | [ 1 -2 2 0 -2; 0 1 0 0 0; 0 2 -2 1 2; 0 1 -2 -1 -2; 0 1 2 -2 -2] |
| -4, -2, 1, 1, 4 | [-1 -2 2 -1 -2; -1 0 2 -1 -2; 1 1 2 1 -2; -1 -1 0 -2 2; 0 0 -1 2 1] |
| -4, -2, 2, 3, 4 | [-2 2 -2 -2 2; 2 2 0 2 -2; -2 -2 -1 2 -2; -2 2 0 2 2; 0 2 0 2 2] |
| -5, -1, 1, 2, 3 | [ 1 1 0 0 -2; 1 -1 -1 -1 -2; -2 -1 -1 2 -2; 2 2 2 1 2; -2 -2 -2 1 0] |
| -4, -4, -1, 1, 2 | [-2 -2 0 -2 1; -1 0 -1 -2 -2; 0 1 -2 1 -2; -1 -2 2 0 2; 0 -1 -2 -1 -2] |
| -3, -2, -1, -1, -1 | [-1 0 0 0 0; -2 -1 0 -1 1; 1 -1 -2 0 -2; 2 -2 0 -2 -1; 1 -2 0 -1 -2] |
| -1, 2, 2, 3, 3 | [ 2 1 -1 -1 0; 0 1 2 -2 0; -2 1 2 -2 0; -1 1 -1 2 0; -2 -1 -2 -2 2] |
| -4, -2, 1, 3, 4 | [-1 0 0 -2 -2; 0 1 1 -1 1; -2 2 2 1 -1; -1 -2 2 0 -2; -2 2 -2 -2 0] |
| -4, 1, 2, 2, 3 | [ 2 2 1 -2 0; 1 0 -1 2 0; -2 -2 1 2 0; -2 1 2 -1 0; -2 1 -1 -2 2] |
| -4, -3, -1, 2, 4 | [-2 -1 -2 1 2; 2 2 2 2 0; 0 0 -2 0 2; 1 2 0 -2 1; 2 0 2 2 2] |
| -2, -1, 3, 3, 4 | [ 2 -1 0 -1 0; -2 0 -2 2 -1; -2 -1 2 0 -2; -2 1 -2 1 -1; -2 -2 -2 1 2] |
| -3, -2, -1, -1, 4 | [ 1 0 -1 -2 1; 2 -1 -2 -1 -1; -2 -1 -1 2 -1; -2 0 2 0 1; 0 0 0 0 -2] |
| -4, -2, 2, 2, 3 | [-2 -2 2 -2 -1; -2 1 0 1 1; 2 2 1 -2 -2; 0 1 -2 1 0; 2 2 -1 -2 0] |
| -5, -1, 1, 2, 4 | [ 1 -1 -1 2 -2; 1 1 0 -1 2; -1 1 -1 -2 -2; -1 -2 -2 2 -2; -2 2 -1 -2 -2] |
| -2, 1, 2, 3, 4 | [ 2 -1 -2 0 1; 2 2 1 1 2; -2 1 1 1 1; -1 1 2 1 -1; 2 0 2 0 2] |
| -4, -3, 2, 2, 3 | [ 1 -1 2 -2 -1; 0 0 2 2 2; 2 2 -1 2 -1; 0 1 2 -1 -2; 0 1 -1 -1 1] |
| -3, -3, -2, 1, 5 | [-2 1 -2 1 0; -1 0 -1 -2 -2; -2 -2 1 2 0; 0 -2 2 -1 2; 1 -2 1 2 0] |
| -3, -3, -2, 2, 3 | [-1 -2 2 -2 0; -1 -2 -1 -2 -2; 2 -2 -1 0 2; 0 1 0 2 1; 1 -1 1 2 -1] |
| -1, 1, 1, 2, 6 | [ 2 1 -2 2 -2; 1 2 -1 2 -2; 0 0 2 0 0; 2 2 -2 1 -2; -2 -2 0 2 2] |
| 1, 1, 1, 2, 3 | [ 2 -1 -1 1 -2; 1 0 -2 -1 0; 0 0 2 0 0; 0 0 2 2 -1; 0 0 -2 -1 2] |
| -2, -1, 2, 4, 4 | [ 2 -2 2 -2 2; -2 2 2 -2 2; 0 1 2 2 2; 0 -1 2 2 -2; 1 -1 1 1 -1] |
| -1, 1, 1, 3, 3 | [ 1 -2 2 2 -2; -2 1 -1 -2 1; 2 0 2 1 -1; 0 0 0 1 0; 2 2 1 1 2] |
| -4, -3, 1, 3, 4 | [ 1 1 -1 2 -2; 2 2 1 -2 2; -1 -1 2 -2 2; 2 -2 0 -2 -1; -2 2 -1 -1 -2] |
Invertible 5 × 5 non-symmetric matrices with no entries greater than three in absolute value
| Eigenvalues | Matrix |
|---|---|
| -3, 1, 2, 3, 3 | [ 1 -3 0 -2 1; 0 3 0 0 0; -3 -2 -3 -1 2; 2 0 0 3 1; 2 1 0 2 2] |
| -2, -1, -1, 2, 3 | [ 3 2 1 -1 -1; 3 0 -2 -1 -2; 2 1 2 -1 0; 2 1 3 -2 0; 1 0 0 -1 -2] |
| -2, -1, 1, 3, 3 | [ 1 0 -2 2 -3; -1 2 1 0 1; 2 3 -3 3 -3; 2 2 -2 3 -1; 3 3 -3 0 1] |
| -3, -2, 1, 2, 5 | [ 0 0 1 -3 -3; -2 3 -2 -3 -3; 3 -2 3 1 -2; -3 2 -2 0 -2; 0 0 0 0 -3] |
| -4, -3, -2, 1, 4 | [-1 0 0 2 2; 1 -1 -3 2 3; -1 -2 -2 -1 0; 3 -2 -3 2 3; 1 0 0 1 -2] |
| -3, -1, -1, 2, 2 | [ 2 0 0 0 0; 1 -1 0 0 0; 0 -3 -1 -3 -3; 1 -2 1 0 -2; 0 -1 -1 -3 -1] |
| -4, -3, -1, 1, 3 | [-2 -2 -3 -2 2; 0 0 0 0 -1; -2 -3 -3 0 -1; 0 -1 3 -1 1; 0 -3 0 0 2] |
| -4, -1, 1, 2, 3 | [ 3 -2 1 1 -2; 0 -1 -3 3 3; -2 2 -3 0 0; 0 0 -3 2 -1; 0 3 0 -3 0] |
| -3, -2, 2, 3, 4 | [ 3 0 2 2 -2; 0 3 1 1 -1; 2 0 0 2 0; 2 -3 -1 -3 -1; -1 0 2 -2 1] |
| -1, -1, 2, 2, 4 | [ 0 3 2 -3 -1; 2 1 0 3 1; 0 -2 0 -3 3; 2 2 0 2 1; 2 2 0 0 3] |
| -3, -2, -1, 1, 3 | [ 2 -1 -3 0 -3; -2 -3 0 0 -2; 2 1 0 0 0; 2 3 -3 -1 0; -3 0 0 0 0] |
| -4, -2, -1, 3, 4 | [-2 1 3 1 -3; 0 -1 2 1 1; 0 3 3 2 -1; -3 -3 2 -1 1; -3 3 1 0 1] |
| -4, -3, -2, -1, 2 | [-1 -1 0 3 -1; 3 -3 0 1 3; 2 3 -3 -1 -2; -2 3 0 0 -3; -1 1 0 -3 -1] |
| -5, -2, 1, 2, 3 | [ 3 3 0 3 -2; 0 -1 0 -3 -3; 0 -2 1 3 -3; 0 1 1 -2 0; 0 -3 -1 2 -2] |
| -3, -2, -1, 2, 3 | [ 3 0 0 3 3; -2 3 0 -1 -2; -2 0 -3 -1 -1; -2 0 -1 -2 0; 0 0 -1 0 -2] |
| -5, 2, 2, 3, 4 | [ 1 -1 2 1 0; -3 3 2 -2 0; 0 3 -3 0 2; 0 0 0 2 0; -2 -1 2 3 3] |
| -4, 1, 2, 3, 6 | [ 2 -2 0 2 0; 1 3 -3 1 2; 1 1 -2 -2 3; 2 2 -3 3 3; 1 1 2 1 2] |
| -2, -1, 1, 1, 4 | [-2 -3 -1 3 -2; 0 2 2 1 1; 2 0 1 -2 -2; 2 -2 -2 3 0; 2 0 0 -2 -1] |
| -3, -2, -1, 3, 3 | [ 0 -3 0 0 0; -1 2 0 0 0; 2 3 -3 -2 3; -3 -2 0 -2 0; 1 -1 0 0 3] |
| -3, -3, 1, 2, 2 | [ 0 1 2 0 -1; 1 2 -2 2 2; 0 0 2 -2 0; 0 0 0 -3 0; -2 0 -1 -1 -2] |
| -5, -3, -2, 1, 4 | [-2 -3 -3 -1 0; 0 -1 -2 0 -1; 0 -3 -2 -2 0; 0 -1 -1 -3 1; 0 -3 -3 3 3] |
| -3, -2, -1, 1, 4 | [-1 2 -2 3 -1; -3 -2 -3 0 -2; -1 -2 0 -3 1; 3 1 3 0 3; -3 0 -3 3 2] |
| -5, -2, -1, 1, 2 | [-3 2 -1 1 -3; 1 1 -1 1 -3; -3 0 -1 0 0; -1 3 -1 -3 0; -1 1 -3 -3 1] |
| -6, -2, 1, 2, 6 | [ 3 3 0 -2 0; 2 -2 2 3 1; 3 2 3 2 1; 1 3 0 -3 3; 2 1 1 2 0] |
| -3, -1, 1, 1, 3 | [-2 -1 3 2 -1; 3 2 2 -1 -3; 0 0 1 1 3; 0 0 3 2 -2; 0 0 0 -1 -2] |
| -4, -1, -1, 1, 3 | [-3 -2 0 0 0; -1 -1 -3 -2 -1; 0 0 3 3 0; 0 0 0 1 0; -1 0 -2 0 -2] |
| -5, -2, 1, 2, 5 | [-2 0 0 3 -3; 0 -2 1 3 3; 3 3 2 -1 1; 3 3 0 1 1; 3 3 2 -2 2] |
| -3, -1, 1, 1, 1 | [ 1 3 0 -2 0; 0 -2 0 0 -1; 3 1 1 -3 0; 0 1 0 -3 -3; 0 3 0 0 2] |
| -3, -2, -2, -1, 1 | [-2 1 1 -1 1; -2 -3 -2 1 1; 2 1 0 -2 1; -2 -1 -2 -2 3; -1 1 1 -1 0] |
| -5, -3, -2, -1, 2 | [-2 0 -1 1 1; 0 -3 1 -3 -2; 0 0 -2 -3 -1; 1 -3 1 -2 -1; 2 -1 -1 1 0] |
| -6, -4, 1, 2, 4 | [ 1 -1 2 -1 0; -2 2 3 -2 2; 2 2 -2 2 0; -2 -2 2 -3 3; -2 1 3 1 -1] |
| -5, -3, 2, 3, 4 | [ 1 -2 3 -1 1; 0 -1 3 -3 -3; 3 1 0 0 -3; -3 -3 1 3 -3; 0 0 -3 3 -2] |
| -3, -2, -2, 4, 5 | [ 2 0 -2 3 0; 2 1 -1 -2 3; 0 -3 -2 -2 -3; 2 -1 -1 0 -1; 0 3 0 -2 1] |
| -1, 1, 2, 3, 4 | [ 2 0 2 3 3; -1 3 2 3 3; 1 -1 0 2 2; 0 1 2 3 3; -2 2 0 -1 1] |
| -2, -1, 1, 2, 4 | [-2 -2 0 -3 1; 0 3 0 1 3; 0 -1 2 -1 -3; 0 -2 1 2 -1; 0 0 -1 -2 -1] |
| -1, 1, 2, 3, 3 | [ 3 0 1 2 -2; -2 3 2 3 -3; 0 0 -2 -3 3; -3 0 3 3 -1; -3 0 2 1 1] |
| -4, -1, -1, -1, 2 | [-3 -2 0 2 0; 0 -1 0 0 0; 2 -2 -2 2 -1; 2 3 -1 1 -1; -1 2 1 -3 0] |
| -1, -1, -1, 1, 3 | [-1 0 0 0 0; 1 -1 -3 -3 -3; 3 0 1 0 0; 0 0 3 3 0; 3 0 2 2 -1] |
| -5, -3, -1, -1, 2 | [-3 3 1 -3 2; -2 0 2 -3 2; 0 2 -2 0 0; -3 0 1 0 0; 2 -1 -2 3 -3] |
| -4, -3, -3, -3, 2 | [-3 -3 0 -2 1; 1 0 3 0 1; -1 3 -3 1 -2; -1 3 0 -2 -2; 0 0 -3 3 -3] |
| -5, -1, 1, 1, 3 | [-2 0 -3 -3 0; 1 -1 3 -3 0; 0 0 1 0 0; -3 0 -1 -2 0; -1 -3 3 2 3] |
| -5, 1, 3, 4, 6 | [ 3 -3 -3 0 -3; -3 3 -2 -1 3; -2 -2 -2 3 -3; -1 -1 2 3 1; -2 -2 1 3 2] |
| -7, -4, -2, 1, 1 | [-3 -3 -1 1 -2; 0 1 0 0 0; -1 3 -3 -2 1; 3 -3 -2 -3 1; -3 -3 2 1 -3] |
| -2, -2, -1, 1, 3 | [ 1 0 -3 -1 -2; -2 1 2 2 -2; -2 1 0 0 -2; 2 -2 -2 -3 2; -3 2 3 3 0] |
| -4, -2, 2, 2, 5 | [ 2 -1 -3 -1 1; 0 3 1 3 2; 0 -1 1 2 -1; 0 3 3 0 -1; 0 -1 -1 -2 -3] |
| -3, -3, 2, 3, 4 | [-3 -2 0 -3 1; 2 3 3 1 2; 2 -1 0 -2 -2; -2 1 -3 0 1; -2 1 -3 -2 3] |
| -2, -2, 2, 3, 4 | [ 3 3 2 0 -3; 0 -1 -2 0 2; 1 -1 2 -1 3; 2 -3 0 0 2; 0 1 3 -2 1] |
| -2, -1, 1, 2, 3 | [-2 -1 1 1 -1; -2 3 -1 -3 -1; -3 3 -1 -2 -2; 3 -1 2 3 2; -3 -3 0 -3 0] |
| -4, -2, -1, 1, 3 | [-1 -3 3 1 -1; -1 -1 -3 1 1; 2 -3 2 2 -2; -1 3 -1 -1 1; 0 -3 3 1 -2] |
| -5, 1, 1, 2, 3 | [ 1 -3 0 -1 -1; 1 0 -3 -2 -3; -2 -1 0 -1 0; 3 0 -2 0 -3; -2 -3 -1 -3 1] |
| -3, -2, 2, 4, 4 | [ 2 2 -2 2 1; 1 -1 2 0 1; -1 3 1 2 -1; 2 -2 2 2 0; 3 -1 1 -2 1] |
| -4, -3, -2, 1, 2 | [ 2 3 1 0 -3; -1 -3 -2 -3 1; 0 -1 1 0 1; 3 3 2 -3 -3; -1 1 -2 -3 -3] |
| -3, -3, -2, 1, 3 | [ 1 3 2 0 1; 1 -3 3 0 1; 0 0 -3 0 0; 1 -2 -2 3 -2; -1 -2 -1 0 -2] |
| -3, -2, 1, 3, 4 | [ 3 2 -3 3 0; -1 0 -2 2 0; -1 -1 2 2 -1; 1 1 2 0 -1; -1 -1 1 0 -2] |
| -4, -3, 1, 3, 5 | [ 2 3 0 -2 -1; -1 -3 3 1 0; 0 0 3 0 0; -3 3 -3 3 -1; -1 -3 -2 -3 -3] |
| -2, -2, -1, 2, 3 | [ 0 0 0 2 0; 0 -2 0 0 0; 2 3 2 -1 0; 3 -1 0 1 0; -2 2 1 0 -1] |
| -2, -1, 2, 4, 4 | [ 2 3 1 0 0; 2 3 0 3 1; 2 1 0 1 -2; -2 -2 2 0 1; 0 3 -2 1 2] |
| -4, 1, 1, 4, 6 | [ 1 -2 -3 -1 3; -3 0 -3 1 3; 2 -3 3 3 -2; -1 2 1 1 -1; 0 1 -2 -3 3] |
| -4, -3, -2, 1, 3 | [ 2 3 0 -1 -2; 1 -1 3 3 1; 0 2 -2 -2 2; 0 -1 0 -1 -1; -1 -3 1 -3 -3] |
| -4, -3, 1, 2, 3 | [-2 -2 -1 -2 -1; -2 -2 1 2 1; 2 3 2 0 1; -2 -3 -3 -1 -3; -2 2 1 -1 2] |
| -2, -2, 1, 1, 3 | [ 1 0 -2 0 0; -3 -2 -2 -2 0; 0 3 2 1 -3; 0 1 3 0 -1; -3 -2 -3 -1 0] |
| -5, -3, -2, -1, 1 | [-2 1 0 2 0; 3 -1 1 -1 0; 2 1 -2 1 0; 3 0 -1 -2 0; -3 -1 1 -2 -3] |
| -1, 1, 1, 1, 5 | [ 1 2 -2 2 0; 0 1 3 -3 0; -1 3 3 2 -3; -1 3 2 3 -3; 0 0 -1 1 -1] |
| -4, -3, -3, -1, 4 | [-3 -2 -1 1 1; 0 2 3 3 2; 0 1 -2 2 -3; 0 1 3 -1 3; 0 0 0 0 -3] |
| -3, -3, -2, 2, 3 | [-1 -2 -3 2 2; 3 3 -3 -2 3; -1 0 0 -3 -1; 0 0 0 -3 0; 1 2 -1 1 -2] |
| -4, -2, -1, 1, 2 | [ 2 1 1 -2 0; 1 -1 -1 3 -1; 3 1 -3 0 -3; -2 2 -2 -1 2; 3 -1 3 0 -1] |
| -3, -3, -2, 3, 5 | [ 2 0 2 -2 2; 1 1 -2 1 2; 3 0 3 0 -2; 0 0 0 -3 0; -2 3 -2 0 -3] |
| -4, -1, 2, 3, 6 | [ 3 0 -3 3 -3; -3 3 1 -3 -1; 1 0 -1 -3 3; 1 -3 -3 0 2; 0 -3 0 1 1] |
| -3, -1, 1, 2, 6 | [ 0 -2 -2 0 0; 0 -1 2 1 3; -3 2 3 1 0; -3 1 1 2 0; 2 2 2 -2 1] |
| -5, -3, -1, 1, 2 | [-1 0 0 0 0; 2 0 -1 1 1; 3 -3 -1 2 0; 0 0 3 -2 3; -1 3 -1 1 -2] |
| -3, -3, -2, -1, 2 | [-2 2 -1 0 0; -1 0 1 3 0; -2 2 1 3 0; 0 0 0 -3 0; -2 0 -1 2 -3] |
| -5, -1, 2, 4, 5 | [ 3 0 -2 0 2; -3 2 -3 3 3; -3 -3 2 3 3; 1 -2 2 -1 0; 1 0 3 3 -1] |
| -3, -1, 3, 4, 5 | [-1 1 0 1 -1; 3 1 -3 0 -1; -1 -1 3 -2 -1; 2 -2 -3 2 -1; -1 0 -3 0 3] |
| -5, -4, -2, 3, 3 | [-2 0 2 0 -2; -2 3 3 -1 -3; 2 0 -3 2 3; 2 0 3 0 1; 3 0 3 3 -3] |
| -4, -1, 1, 3, 4 | [ 3 0 0 0 0; -2 2 -3 1 -1; -1 -3 -2 1 -1; 2 2 0 -1 0; -1 -1 0 -2 1] |
| -3, -2, -1, 3, 4 | [ 2 0 -3 0 3; -3 1 -3 3 -2; 0 0 -3 0 0; 0 2 -1 0 2; 2 0 2 0 1] |
| -3, -1, -1, -1, 4 | [-1 -3 1 -1 -2; 0 2 0 3 2; -2 -2 -3 0 0; 1 1 1 -1 0; -3 0 -3 3 1] |
| -2, -2, -2, 2, 2 | [-2 -2 -2 3 3; 0 -2 0 1 0; -3 0 2 1 0; 0 0 0 -2 0; -2 2 0 -2 2] |
| -4, -1, 2, 2, 3 | [-3 2 -2 -1 0; -2 3 -2 -2 2; 2 -3 3 2 -1; -2 0 2 0 -2; -2 -1 3 -2 -1] |
| -3, 1, 1, 2, 2 | [-1 0 -3 -2 3; 0 2 -3 2 -3; 0 0 -1 0 3; 2 0 0 3 -2; 0 0 2 0 0] |
| -4, -2, 1, 1, 3 | [-1 -3 0 -2 -2; -1 3 0 1 -3; -1 0 1 -2 -1; 2 -2 0 -3 -3; -1 -1 0 -1 -1] |
| -4, -2, 2, 3, 4 | [-1 1 -3 3 1; 0 -2 -2 2 1; 0 0 3 0 0; 3 3 -1 1 2; -1 -1 -1 1 2] |
| -2, -1, 1, 3, 4 | [ 0 -2 1 0 -2; -2 -1 -1 -3 0; -2 -1 3 3 0; 1 -1 0 1 0; -1 3 1 3 2] |
| -1, -1, 1, 2, 3 | [-1 3 -2 2 -1; -3 2 1 -1 -1; -2 -2 2 -3 1; 1 -3 0 -1 2; -1 1 -3 3 2] |
| -5, -4, -1, 1, 2 | [-2 3 -3 1 -3; -2 1 3 1 -3; -3 3 -2 1 -3; 2 -3 3 -3 -3; 1 -2 2 -1 -1] |
| -2, -1, 2, 2, 3 | [ 3 1 -2 0 -3; 1 2 2 -3 -2; -1 -3 -3 -2 2; 0 0 0 2 0; 1 -3 -1 -3 0] |
| -2, -1, 2, 3, 5 | [ 1 2 1 -2 2; 2 0 0 -2 2; 1 -1 2 -1 1; -3 -1 -2 3 0; -1 0 1 2 1] |
| -4, -3, -2, -2, -2 | [-2 -1 -3 -3 -1; 0 -2 -1 -3 -1; 0 0 -3 -2 2; 0 0 3 -3 -1; 0 0 3 -1 -3] |
| -3, -1, 2, 4, 5 | [ 2 -3 2 -3 1; -2 3 2 -3 1; 1 1 1 3 1; 1 -1 -1 3 -1; 3 1 3 0 -2] |
| -3, -2, 1, 2, 3 | [ 1 0 -1 0 0; 3 2 -1 1 2; 0 0 -3 0 -3; 3 0 3 0 0; 3 0 -2 -1 1] |
| -5, -2, 1, 3, 5 | [-3 2 -3 -2 0; 2 -2 3 -2 3; 0 0 3 0 0; 1 -1 -2 3 3; 0 1 -3 3 1] |
| -1, 1, 3, 3, 4 | [ 3 -1 2 2 3; 0 3 0 0 0; 1 -3 2 1 1; -1 3 2 3 2; 0 -3 0 0 -1] |
| -4, 1, 1, 2, 3 | [ 3 0 0 0 0; -3 0 -1 -3 -1; -3 2 -2 1 0; 1 -2 3 0 0; -1 0 2 2 2] |
| -3, -2, -2, 1, 5 | [-2 1 -2 -2 -1; 3 -1 1 -2 2; 3 -1 3 2 -1; -2 -2 2 2 -1; 0 0 0 0 -3] |
| -5, -2, -1, 2, 3 | [-2 2 0 1 0; -1 2 -1 2 0; 1 1 -1 1 1; 3 1 3 -3 -2; 3 -3 3 -2 1] |
| -3, -1, -1, 1, 1 | [-3 3 -2 2 0; 0 -1 0 0 0; 2 1 1 0 -2; 2 -1 0 1 -2; -2 3 1 -1 -1] |
| -4, -2, 1, 3, 4 | [ 1 -3 2 -1 0; 0 -2 -2 -1 -2; 3 -3 0 0 -2; 0 -2 3 1 0; 0 -2 0 -2 2] |
| -3, -1, 1, 2, 3 | [-1 0 0 0 -2; 2 1 -1 -2 -3; 3 1 -1 1 0; 1 -3 1 0 1; -3 3 0 3 3] |
| -4, -3, -2, 2, 4 | [ 1 -1 -2 -3 0; -3 -1 2 3 0; 0 2 -1 1 -3; 1 2 -1 1 0; 3 -1 -3 1 -3] |
| -4, -2, -1, 1, 4 | [ 3 0 -3 -1 3; 2 -1 -1 3 1; -3 -2 1 2 -3; -3 0 -1 -3 1; -2 -2 0 3 -2] |
| -3, -1, -1, 1, 3 | [-1 1 2 -2 -1; 3 -2 2 3 -2; 0 0 -1 0 0; -1 -1 2 2 -2; 1 1 -3 -3 1] |
| -3, 2, 3, 4, 5 | [ 3 -1 -2 -2 2; 0 2 0 0 -3; -2 -3 3 -2 3; -3 -2 -3 0 1; 0 0 0 0 3] |
| -2, -1, 2, 4, 5 | [ 3 1 0 -1 1; 3 2 0 -3 3; -1 -1 3 -1 1; 3 -3 2 -1 0; 0 1 3 -2 1] |
| -4, -4, -3, -1, -1 | [-2 0 -1 0 1; 1 -3 -3 0 -2; 0 -1 -2 1 1; -1 0 2 -3 -2; 2 0 -3 0 -3] |
| -4, -2, 2, 4, 5 | [-2 1 2 1 -1; -2 -2 -2 0 2; 3 1 3 0 2; 1 -3 -3 3 1; -1 2 3 1 3] |
| -1, -1, 2, 3, 5 | [ 2 -1 -2 2 -2; -1 -1 0 -1 1; -1 1 3 0 -2; 2 1 -3 2 2; -1 -1 -3 -2 2] |
| -2, -1, -1, 3, 4 | [ 0 -2 2 -2 1; 0 2 0 2 0; -1 -2 -2 1 -1; 0 3 0 1 0; 3 2 -2 1 2] |
| -4, -2, 1, 3, 6 | [ 3 0 -2 -1 0; -2 -1 1 1 3; 0 -1 2 2 3; 0 3 3 -3 3; 0 -1 1 3 3] |
| -3, 1, 2, 2, 3 | [ 1 -1 -1 1 -3; 1 -1 -1 3 3; 0 -3 2 -3 0; 0 3 1 1 -2; 0 0 0 0 2] |
| -5, -2, 1, 2, 4 | [-1 3 3 3 1; 3 1 -1 -2 -3; 0 0 1 1 0; 0 0 3 -1 0; 2 -3 2 -1 0] |
| -3, -2, 2, 4, 5 | [-2 2 2 3 0; 2 3 3 1 -1; -2 2 2 -1 1; 2 3 3 3 0; 2 -1 3 3 0] |
| -3, -1, 1, 2, 5 | [ 0 -3 -2 3 -2; 3 3 -2 -1 -2; 3 -3 2 -2 0; 3 -2 -1 -1 -1; -3 -3 -2 3 0] |
| -1, -1, 1, 2, 5 | [ 1 -3 -3 2 3; -2 -2 -2 -3 -1; 0 2 3 -3 1; 2 -1 2 2 -1; 2 3 2 3 2] |
| -3, -2, 1, 2, 4 | [ 1 3 -1 -2 -1; 3 1 0 -2 -3; 0 2 3 -2 0; 3 2 -1 -3 0; 0 -2 -1 2 0] |
| -6, -3, -2, 1, 5 | [ 0 0 -2 0 2; -3 -1 1 -1 -3; -3 -2 -2 3 3; -3 -2 2 0 2; 0 -2 3 3 -2] |
| -5, -1, -1, 1, 2 | [-2 -1 -1 0 0; 2 -2 0 -3 -2; 2 -1 -1 -3 -2; -2 -2 -1 -2 2; -2 0 3 3 3] |
| -4, -3, 1, 4, 5 | [ 1 -2 0 0 0; -3 -1 -3 -2 3; 2 -1 1 -3 3; -2 3 -2 -1 2; 3 3 1 3 3] |
| -4, -3, 2, 3, 4 | [ 3 1 0 0 3; 0 -3 3 0 -3; -3 0 -1 -3 3; -1 -1 -2 2 -1; 3 0 1 3 1] |
| -5, -2, -1, 2, 6 | [-1 0 0 2 -2; 2 -3 -2 1 1; -1 -3 2 3 -1; 1 0 0 3 -3; 0 3 -3 -3 -1] |
| -6, -4, -1, 1, 4 | [ 2 -1 -3 0 -2; 2 -1 -2 3 -3; -2 -3 -2 -3 3; 1 3 2 -3 3; -1 1 1 3 -2] |
| -4, 2, 2, 3, 4 | [ 0 -3 2 2 3; -2 -1 1 1 -1; 0 0 3 0 0; 2 3 -3 3 -3; 0 0 -1 0 2] |
| -5, -2, 1, 4, 5 | [-1 3 3 -1 2; -3 1 0 -3 0; 3 -2 1 0 -3; -1 -3 -3 -1 -2; 3 -1 -3 -2 3] |
| -4, -2, -1, 1, 1 | [-2 -1 -2 0 2; -1 0 1 0 -1; -1 2 -3 -2 3; -1 0 1 1 0; 1 -2 -1 0 -1] |
| -3, -2, -1, 2, 5 | [ 2 -1 -1 0 -2; -1 1 1 0 3; 0 -1 -2 1 1; 3 1 0 -3 2; 1 3 1 0 3] |
| -2, 1, 2, 3, 3 | [ 0 -3 -2 2 2; 1 2 0 -3 3; -1 0 2 3 -3; 1 -1 0 0 3; -1 0 -1 0 3] |
| -4, -3, -1, 2, 4 | [ 2 2 -1 1 -3; 2 2 1 -1 3; 1 0 -3 2 2; -1 0 2 0 1; 2 2 1 2 -3] |
| -2, -1, 1, 5, 6 | [-1 3 0 -2 1; -1 3 -3 -2 0; 0 -3 3 2 3; 2 0 3 2 -3; 0 3 2 -2 2] |
| -4, -3, -2, 2, 3 | [-3 1 -2 1 -1; 3 1 3 -2 0; -3 -2 -3 -2 -3; 3 3 -2 1 3; -1 -3 0 2 0] |
| -4, -3, 1, 2, 4 | [-1 -2 2 -1 3; -1 0 0 2 0; 2 -2 -1 -1 3; -2 -2 -2 1 3; 1 -2 1 3 1] |
| -3, -3, -2, -1, 6 | [ 3 1 1 1 1; 3 -3 3 3 -1; 3 -1 -2 0 1; 3 1 3 1 1; 3 0 2 2 -2] |
| -4, -3, 2, 2, 3 | [-3 0 0 0 -3; 0 -3 0 3 -3; 2 -3 2 3 1; 3 0 0 2 0; -2 0 0 0 2] |
| -2, -1, 1, 2, 5 | [ 0 1 2 0 2; 3 2 -2 1 -2; 3 2 2 0 3; -2 -2 0 0 0; 3 1 2 -1 1] |
| -5, -2, -1, 1, 4 | [-1 1 3 3 1; -3 0 -2 -1 -3; -2 -1 -3 -3 -2; 2 -3 -1 -2 -1; 3 -3 3 -1 3] |
| -2, -1, 2, 3, 3 | [ 2 2 1 0 -2; 3 -3 -3 0 3; -3 2 2 0 0; -3 1 -1 3 3; 0 1 1 0 1] |
| -2, -1, 2, 2, 5 | [ 0 -1 -2 1 -1; 1 2 -2 -3 -3; -2 0 3 -3 0; 1 -1 -2 0 -1; -3 2 3 -2 1] |
| -3, 1, 2, 4, 5 | [ 2 1 2 1 0; -1 2 -1 1 1; -1 -2 3 3 0; 2 1 3 -1 1; -1 1 1 2 3] |
| -2, -1, 1, 3, 5 | [ 3 -2 2 0 -2; -3 2 3 0 1; -2 0 3 2 2; -1 -3 0 -2 3; 0 -1 3 0 0] |
| -6, -4, -1, 2, 3 | [ 3 -3 0 -2 -1; 0 -3 1 2 -2; 0 0 -3 2 3; 0 1 0 -2 -1; 0 -2 3 -2 -1] |
| -3, -2, 1, 3, 3 | [ 3 0 -2 0 0; 0 3 1 0 1; 0 0 -2 0 0; 2 0 2 0 -3; 0 0 -3 -1 -2] |
| -4, -3, -2, -1, 3 | [ 2 3 1 -3 3; 0 -1 -1 0 0; 0 0 -2 0 0; -2 -1 -2 -3 -3; 0 1 1 0 -3] |
| -4, 1, 2, 3, 4 | [-3 -2 0 0 -2; 0 3 0 0 -1; -1 -1 2 0 0; 2 1 3 1 2; -3 -1 0 0 3] |
| -3, -2, 2, 2, 3 | [ 2 3 0 0 -1; 0 -2 0 0 0; 0 -1 2 -3 -2; 0 -2 0 2 0; -1 0 -2 -3 -2] |
| 1, 1, 1, 3, 5 | [ 3 0 0 0 0; -1 1 0 2 0; -3 -1 1 2 1; 2 0 0 3 -2; 3 0 0 -2 3] |
| -3, -2, -2, 3, 4 | [ 1 0 0 3 0; -2 -2 0 3 -2; 3 2 -2 -2 2; 2 0 0 0 0; -2 -3 0 0 3] |
| -4, -4, -2, -1, 2 | [-3 1 1 -3 -2; 2 0 1 3 2; 3 3 -2 -3 -3; 1 1 0 -1 1; -2 0 0 -3 -3] |
| -3, -1, 1, 3, 5 | [ 1 -1 -3 3 3; 2 0 3 3 1; 1 3 2 0 1; 2 -1 1 2 3; 1 -1 3 2 0] |
| -3, -1, 1, 1, 2 | [ 0 -3 1 -1 -1; 0 1 0 0 0; -1 3 0 2 2; -1 0 2 0 3; -1 -1 -2 2 -1] |
| -2, -1, -1, 1, 3 | [ 3 -1 -2 3 -2; 1 2 2 -3 2; 1 -3 0 -2 1; -1 -3 0 -2 0; -3 -3 -2 2 -3] |
| -3, -2, -2, 1, 2 | [ 1 0 0 2 -1; 0 -3 0 0 0; -3 2 -2 0 -2; 0 2 0 1 0; -3 -1 0 1 -1] |
| -4, -3, -1, 1, 7 | [ 2 2 0 0 2; 3 0 2 0 3; 0 3 -2 0 2; 2 -3 -3 -3 -3; 2 1 3 0 3] |
| -3, -2, -1, 1, 2 | [ 3 1 2 1 -3; 2 1 2 0 -2; 2 2 -3 3 2; -3 -3 3 -2 1; 3 3 -3 1 -2] |
| -3, -2, -1, 1, 1 | [ 0 -1 0 -1 3; 1 -1 -2 -1 -3; 1 -1 1 1 1; -2 1 0 -1 2; 0 -1 -1 -1 -3] |
| -5, -1, 1, 2, 2 | [-1 -3 3 1 0; -3 -2 1 2 2; 0 -1 3 0 1; 3 -2 -1 -3 1; -3 -2 -1 2 2] |
| -4, -1, 1, 3, 7 | [ 1 -3 -3 -2 2; -2 -2 -3 -2 -2; -2 1 1 -1 2; 0 -2 -3 3 3; 2 -3 -3 2 3] |
| -6, -2, -1, 3, 4 | [-2 -3 3 0 -3; 2 -3 2 -3 -2; 2 -2 3 -1 -3; -3 -3 1 3 -2; -2 -3 1 0 -3] |
| -2, -1, 2, 3, 4 | [ 2 0 0 0 0; -2 3 -3 -1 -3; -1 0 -2 0 0; -1 2 0 0 0; -1 -2 -1 3 3] |
| -3, -3, 2, 3, 5 | [ 3 0 0 0 0; 2 2 0 2 3; -2 1 -3 3 3; -1 3 0 -1 1; 3 3 0 -3 3] |
| -4, -3, -1, 1, 2 | [-3 2 2 -3 0; 2 -2 1 -3 0; -2 2 1 -3 0; -1 1 -2 -1 1; 1 3 -2 0 0] |
| -4, -3, -2, -2, 3 | [-2 1 3 1 0; 0 -2 -2 -2 0; 1 -1 -2 3 -2; -1 -3 1 0 0; 1 3 0 -1 -2] |
| -2, -1, 1, 2, 6 | [-2 3 0 -1 0; 1 -1 -2 -2 -2; -1 1 3 3 0; 1 -1 3 3 0; -1 2 1 2 3] |
| -3, -1, 2, 3, 6 | [ 3 1 -1 -3 1; 0 -1 0 -2 2; -1 3 3 0 2; -3 -2 2 1 0; -3 2 2 0 1] |
| -3, -2, 1, 1, 3 | [ 1 3 2 0 2; 0 1 2 0 -2; 0 3 0 0 3; -2 1 0 -2 0; 0 3 3 0 0] |
| -4, -4, -1, 1, 2 | [ 1 0 -3 0 -3; 1 -3 -1 1 0; -1 1 -1 2 -1; -2 2 0 -1 -3; 1 -2 -1 -3 -2] |
| -3, -2, -1, 3, 5 | [ 0 3 3 2 -1; 3 0 1 0 -3; -1 -1 -2 -1 1; 0 0 -2 3 0; -2 -2 2 0 1] |
| -5, -3, 1, 1, 2 | [ 0 -2 0 -1 0; -3 -3 -2 3 -3; 3 -2 -3 -3 2; 0 0 0 1 1; 0 0 0 0 1] |
| -3, -2, 2, 2, 6 | [-2 -3 -3 -2 1; 0 3 3 3 0; 1 3 0 -3 -1; -1 3 0 3 1; 1 -1 2 1 1] |
| -2, -1, 1, 1, 2 | [-1 -2 -1 3 1; 3 -2 0 0 3; -3 0 3 1 2; 0 0 0 1 0; 3 0 -1 2 0] |
| -5, -4, 1, 3, 4 | [ 1 2 3 2 1; 0 1 -3 -2 3; 3 -2 -2 -3 -1; 0 0 -3 -1 3; 3 3 -3 -3 0] |
| -3, -2, -1, 5, 6 | [ 2 2 2 2 -2; 3 1 0 2 -1; 3 0 0 -3 -3; 2 2 -3 2 0; -2 0 0 2 0] |
| -4, -1, 1, 2, 5 | [ 3 2 -2 2 0; 3 1 -2 0 0; 3 -1 -2 1 -2; 1 2 2 0 2; -1 2 -2 3 1] |
| -2, -1, -1, 1, 2 | [-2 -3 -3 2 3; -1 0 -1 -2 -1; 1 1 1 0 -1; 0 0 -3 0 1; 0 0 -3 1 0] |
| -3, -2, -2, 2, 3 | [ 2 3 0 2 0; 0 -2 -1 0 -1; 3 -3 0 0 2; -3 -1 1 -3 0; 3 -3 3 0 1] |
| -3, -2, -1, 3, 7 | [ 0 0 -1 3 -3; -3 0 2 0 -2; -3 0 -2 -3 3; 3 -3 -1 3 -2; -1 -3 -1 -2 3] |
| -5, -1, 1, 2, 4 | [ 0 0 -1 0 0; 0 2 2 0 -3; 2 0 3 0 0; -2 1 3 -2 -3; -2 -3 3 -2 -2] |
| -6, -1, -1, 1, 4 | [-2 -2 -3 -3 3; 0 -1 0 0 0; 0 3 1 -3 2; 0 2 -3 1 2; 1 3 2 3 -2] |
| -2, -2, -1, 1, 4 | [-2 0 0 1 0; -3 3 -1 3 -3; -2 1 -1 0 -3; 0 0 0 1 0; 3 -3 1 0 -1] |
| -4, -2, 1, 2, 3 | [-2 -1 0 1 -1; 3 3 -2 2 1; 0 -3 -3 3 0; 0 -3 0 1 -3; -3 -1 2 -2 1] |
| -6, -1, 1, 3, 4 | [-3 0 -3 -1 2; 1 0 -2 -1 1; -3 0 -2 3 3; -3 -1 -1 3 1; 2 3 -1 2 3] |
| -3, -2, -1, 2, 4 | [-1 -2 0 0 0; 0 -2 2 1 3; -1 2 2 -1 2; 3 -1 -2 3 0; 2 -1 2 1 -2] |
| -4, -3, 1, 3, 4 | [-1 -1 2 1 1; 0 3 -2 3 2; -1 -2 -3 3 -2; 2 -3 3 0 -1; 3 3 1 -3 2] |
| -3, -3, -1, 1, 2 | [ 2 0 0 0 0; -3 1 0 0 0; -3 1 -3 -2 0; -2 3 0 -1 0; 2 -2 -2 1 -3] |
| -2, -1, 3, 3, 4 | [ 3 1 -3 1 -1; -1 -1 -3 0 0; 0 -2 2 -1 0; 2 2 -2 0 0; 1 2 -1 -1 3] |
| -1, 2, 3, 3, 5 | [ 2 -3 2 -2 -1; 0 3 -1 2 2; 0 -1 3 1 1; -3 3 1 1 1; 3 -2 -2 3 3] |
| -5, -3, 1, 2, 3 | [-2 3 -1 2 -3; 1 -1 -1 -3 1; 0 -2 1 -2 0; 3 -3 1 -1 1; -2 -1 -2 -3 1] |
| -4, -2, -1, 1, 6 | [ 1 3 3 2 3; 1 3 1 -2 1; -1 2 -1 -3 3; 0 -3 -3 -1 -3; 0 1 2 1 -2] |
| -2, 1, 1, 3, 4 | [ 0 0 -3 0 3; 1 3 3 0 -1; 2 0 -1 1 -3; -3 -3 2 3 0; -1 -2 -3 0 2] |
| -5, -2, -1, 3, 4 | [-3 0 2 -1 -3; 2 0 -1 2 0; 2 1 2 3 -2; 0 0 0 3 0; -1 1 -3 -2 -3] |
| -5, -2, -1, 1, 5 | [-2 3 3 -3 3; 0 1 3 -3 3; 3 -3 3 -2 2; -1 -1 -1 -1 2; -1 3 1 0 -3] |
| -6, -4, -2, 1, 1 | [-2 -2 -3 3 -2; 3 -3 3 1 -3; -3 3 -2 2 1; 0 2 0 -1 -3; 2 -2 2 0 -2] |
| -5, -2, 2, 2, 3 | [-1 -3 -1 -1 0; -2 0 2 2 -3; -2 3 0 -1 0; 0 1 0 2 -1; -2 -2 2 2 -1] |
| -4, -2, -2, 1, 2 | [ 3 0 -2 0 1; 2 -3 -2 0 -1; 3 1 -2 0 2; 3 3 0 -2 2; 3 -2 2 0 -1] |
| -6, -4, -2, -1, 2 | [-3 2 -2 0 3; 0 0 -1 -2 3; -1 -1 -3 3 -2; -2 -2 0 -2 1; 0 1 -1 3 -3] |
| -2, 1, 2, 2, 5 | [ 2 3 -1 0 0; 1 2 2 0 1; 0 1 1 -2 -2; -1 -2 1 1 -2; 1 3 -2 -1 2] |
| -5, -2, 2, 4, 5 | [-2 2 3 0 -1; 1 3 1 -1 2; 3 -3 0 -3 -1; -2 1 -1 0 3; -3 3 2 3 3] |
| -5, -3, 2, 3, 3 | [ 0 3 -3 2 0; 3 0 0 -3 0; 0 0 -3 0 0; 2 -2 -3 0 0; -3 2 3 -1 3] |
| -2, -1, 2, 2, 4 | [ 2 2 2 -2 -1; 2 -2 2 1 1; -1 3 3 1 -1; 1 -2 0 0 -2; 0 0 0 0 2] |
| -4, -2, -1, 1, 5 | [-2 2 2 3 2; -1 -1 0 1 3; 0 3 3 -1 3; 0 -2 -1 1 -2; 1 2 1 -3 -2] |
| -5, -1, -1, 3, 3 | [-1 -2 -1 1 3; -2 2 2 -1 0; 0 0 2 -3 -3; -2 1 -3 -2 2; 2 -1 2 2 -2] |
| -2, -1, 1, 1, 3 | [ 1 0 0 0 0; 2 1 3 0 3; 3 -1 0 2 -2; 3 2 2 -3 -1; -2 -1 -1 2 3] |
| -4, -3, 1, 2, 2 | [ 2 0 0 0 0; 0 2 1 -2 1; -2 3 -3 -2 0; 2 2 -2 0 -2; 0 1 0 0 -3] |
| -3, -2, 1, 3, 6 | [ 3 3 -3 2 2; 0 1 2 2 0; -3 3 -2 -3 2; 3 -3 -1 0 -2; -2 -1 2 0 3] |
| -7, -3, -1, 1, 1 | [-3 0 0 -2 -1; -1 1 2 -3 -1; 0 0 -3 -2 -1; -3 0 1 -3 -3; -1 0 -2 -3 -1] |
| -6, -2, -1, 1, 2 | [-3 -1 -1 -3 0; 2 -2 -1 -3 -2; -1 -2 0 -3 -1; -3 2 0 0 2; 2 -3 0 3 -1] |
| -3, -1, 1, 1, 6 | [ 2 -3 1 0 1; -2 3 2 0 2; -1 2 2 0 -1; 2 0 -3 -3 -1; -1 2 1 0 0] |
| -2, 1, 2, 2, 4 | [ 2 0 0 0 0; -3 3 2 0 2; 1 -3 2 -3 -3; 1 0 0 -2 0; 3 1 -2 3 2] |
| -2, -1, 1, 3, 6 | [ 0 3 0 2 3; 3 1 -3 2 -3; -1 2 2 -3 1; 3 2 -3 1 -3; 0 0 -1 1 3] |
| -4, 1, 1, 1, 2 | [-3 1 2 1 -1; 1 0 1 3 1; 1 -1 3 -3 2; 0 0 0 1 0; -1 1 -1 -3 0] |
| -4, -2, 3, 3, 5 | [ 3 3 0 -3 -2; 0 1 -1 -2 0; 0 -3 -1 -3 3; 0 -2 -2 1 -1; 0 -3 3 -3 1] |
| -2, -1, -1, 1, 4 | [-2 1 1 0 0; -3 1 2 2 -2; 3 3 2 -2 2; 0 0 0 -1 0; 3 3 3 1 1] |
| -5, -1, 1, 3, 7 | [-3 -2 2 -2 -2; 3 0 1 -1 2; 3 1 3 0 3; -3 -1 0 3 -2; -1 1 3 -3 2] |
| -6, -2, -1, 1, 3 | [ 0 3 1 3 -1; 2 -2 1 -3 -1; -3 3 -2 3 3; -1 -2 0 -3 1; -1 1 3 -3 2] |
| -6, -3, -1, 1, 3 | [-1 1 -2 -2 -3; 1 -2 -1 1 1; 2 -2 -3 2 2; -1 3 -2 0 -2; -3 0 3 -3 0] |
| -4, -2, 1, 3, 5 | [ 3 1 1 0 2; 0 1 0 0 0; -1 3 -1 -2 -2; 0 -3 -3 3 2; 1 -1 -1 2 -3] |
| -6, -3, -1, 1, 2 | [-3 1 0 1 2; 0 -2 0 0 2; 2 2 2 0 -2; 2 1 0 -1 -2; 3 3 0 1 -3] |
| -3, -3, -1, 2, 3 | [ 1 0 2 2 -2; 0 -3 0 -2 -2; 2 0 2 -3 2; 0 0 0 1 -2; -2 0 -1 1 -3] |
| -3, -2, 3, 4, 6 | [-2 -2 -1 3 1; -1 3 3 0 3; 0 3 2 1 -2; -1 3 0 3 3; -1 2 -3 1 2] |
| -1, 1, 1, 3, 4 | [ 2 0 2 0 0; 3 3 0 2 2; -2 0 0 3 3; 1 0 3 2 -1; 0 0 0 0 1] |
| -3, -2, 1, 1, 5 | [ 3 0 -1 3 0; 0 -1 -3 3 0; -2 2 -1 2 0; 3 1 3 0 0; -3 0 -2 2 1] |
| -5, -4, -1, 2, 4 | [ 0 2 -1 -2 3; -1 3 -3 0 3; 1 1 -3 1 2; -2 1 1 -3 0; 3 3 0 -3 -1] |
| -3, -2, -2, -1, 3 | [-2 0 0 0 0; -3 -1 -1 1 1; 0 0 -2 0 0; 0 0 0 -3 1; 1 0 -1 0 3] |
| -3, -2, -1, -1, 2 | [-3 1 -2 0 0; 3 -1 3 0 0; 3 1 2 0 0; -3 -1 0 -2 0; -1 2 1 -1 -1] |
| -3, -1, 1, 3, 4 | [-3 0 0 -3 -3; -1 3 2 -2 3; -3 -2 -1 2 -3; 1 3 3 2 -1; -3 -1 -1 0 3] |
| -4, -2, -1, 2, 4 | [ 3 -2 -3 -1 -2; -2 -1 2 0 -1; -1 1 -2 -1 -3; 1 -2 3 1 -2; -3 2 0 -1 -2] |
| -3, -2, -2, 1, 3 | [ 1 0 1 1 1; -2 -1 1 -2 0; 0 0 -2 3 3; 1 -2 2 -1 -3; -1 2 -2 -2 0] |
| -5, -3, -1, 2, 4 | [-3 0 1 2 -2; 1 2 1 -1 1; -2 0 -3 1 2; 2 0 2 -2 -2; -3 0 -2 -2 3] |
| -5, -1, 1, 3, 4 | [ 1 1 -1 2 1; -2 -3 -1 2 1; -3 -3 1 -1 3; 2 2 1 1 -1; 1 0 2 0 2] |
| -4, -2, -1, 2, 3 | [ 0 1 -1 1 2; -2 0 -1 -3 2; -3 0 -1 -2 2; -1 -2 2 1 3; 3 -3 3 2 -2] |
| 1, 1, 1, 2, 3 | [ 2 0 0 -1 -2; -1 1 -2 0 -2; -3 0 1 3 1; 0 0 0 3 2; 2 0 0 2 1] |
| -5, -4, -3, 1, 4 | [-1 0 -2 3 -2; -1 -3 0 3 -2; -2 -2 0 -3 -1; 2 3 0 0 -1; 1 -2 0 -3 -3] |
| -4, -1, 1, 1, 2 | [ 1 0 0 -1 2; -3 -3 1 1 2; 3 3 -1 -2 -1; 0 0 0 1 0; 0 2 2 -1 1] |
| -5, -4, -2, -1, 4 | [-2 0 -3 -1 -2; 0 -2 -3 -1 -2; -2 -1 -2 1 2; 1 1 3 -3 -2; -3 -1 1 0 1] |
| -5, -3, -1, 1, 3 | [-2 0 -3 3 -3; -1 2 1 3 1; 1 -3 -2 -3 1; 1 2 -1 0 -1; -1 -3 3 -3 -3] |
| -1, 1, 2, 3, 5 | [ 0 -1 0 0 3; -3 2 0 0 -1; -2 -3 3 2 -2; 0 -1 2 3 3; 0 0 0 0 2] |
| -4, -3, -1, 2, 5 | [ 1 0 2 0 -3; -3 -3 -1 0 -3; 1 0 0 0 3; -3 -1 3 -1 -3; -3 0 3 0 2] |
| -3, -3, 1, 3, 6 | [ 2 2 -3 2 2; -2 0 3 -2 -3; 0 0 -3 0 0; 2 -3 -2 3 -1; 2 -3 -3 0 2] |
| -4, -1, 1, 2, 4 | [ 3 1 -2 0 -1; -2 3 -3 2 -3; -3 -2 -3 -1 -3; 3 0 -2 0 -1; 3 2 -1 1 -1] |
| -5, -4, -1, 1, 3 | [-2 -1 -3 2 -2; -3 0 -3 0 2; 0 -3 -1 -2 1; 3 -3 0 -3 -2; 0 -1 -1 -2 0] |
| -5, -3, -2, -2, 3 | [-3 0 -2 3 0; 0 -3 1 -2 -3; 0 1 -1 0 -3; 0 -2 -1 -3 3; 0 -1 -1 0 1] |
| -4, -1, 2, 2, 6 | [ 3 -3 0 -2 -1; -1 3 -1 1 3; 3 3 -3 3 3; -3 -1 1 0 -2; -2 -1 2 -1 2] |
| -5, -4, -2, 1, 3 | [-3 0 1 -1 -2; 1 -2 3 3 0; 3 3 -1 -1 -1; -3 3 1 0 2; 3 -3 -1 1 -1] |
| -3, -2, -1, 2, 2 | [-2 2 0 -2 -2; 2 -1 -2 1 1; 1 -2 1 0 1; -1 -2 -2 1 0; -1 0 -3 2 -1] |
| -5, -2, -1, 4, 6 | [-3 -2 -3 -1 1; -3 -2 0 -3 3; -3 -1 3 -3 3; 0 2 -3 1 3; -2 0 2 1 3] |
| -2, -1, 1, 3, 3 | [ 3 1 0 1 -2; -2 -2 0 1 1; -1 3 3 2 2; 0 2 0 -1 -1; -2 -3 0 1 1] |
| -3, -1, 2, 3, 7 | [ 2 1 -2 3 1; -3 2 2 1 -3; -3 3 3 0 0; 2 -2 0 3 0; -1 -3 0 -2 -2] |
| -1, 1, 1, 3, 5 | [ 3 2 -1 -1 -2; 3 0 1 2 -3; 0 0 1 0 0; -2 2 1 3 2; -1 3 1 1 2] |
| -5, -3, -2, 2, 3 | [-3 -3 2 2 0; -2 2 1 0 -1; 0 -1 -2 -3 1; 0 3 -2 -1 -1; 2 -2 3 0 -1] |
| -2, 2, 2, 2, 3 | [-2 -1 0 1 -2; 0 2 0 0 1; -2 3 2 -2 -3; 0 3 0 2 -2; 0 0 0 0 3] |
| -2, -2, 1, 2, 3 | [ 0 1 2 0 -1; 0 3 3 1 3; 2 3 1 2 0; 0 -2 -3 0 -3; -2 -1 -3 0 -2] |
| -3, -3, -3, 2, 3 | [-3 0 0 0 0; -1 -3 0 0 0; 2 0 2 0 3; -3 3 -3 3 -1; 2 -2 0 0 -3] |
| -4, -1, -1, 3, 4 | [-1 3 2 -3 3; 0 -1 0 0 -3; 0 2 2 3 -1; 0 -3 3 2 2; 0 -3 -2 -2 -1] |
| -3, -2, -1, -1, 1 | [-3 -3 -1 -2 1; 0 -2 0 0 0; 0 2 -2 0 1; 0 -1 0 1 3; 0 -3 -1 0 0] |
| -3, -3, -1, -1, 1 | [-2 -3 0 2 -1; 0 -3 0 -1 0; 1 0 1 1 3; 0 1 1 0 1; -1 3 -1 1 -3] |
| -3, -1, 2, 2, 3 | [ 2 0 0 0 0; 1 3 -1 0 -1; 2 0 -3 0 0; -3 -1 -3 -1 3; 3 0 1 0 2] |
| -3, -3, -1, 1, 3 | [ 2 0 1 -3 -2; -3 -3 3 -2 0; 1 0 2 -3 -2; 0 0 0 -1 -1; 0 0 0 0 -3] |
| -1, -1, -1, 2, 3 | [-1 3 -3 0 0; 3 0 3 1 0; 0 -2 1 0 0; 2 -1 2 3 0; 1 1 -1 -1 -1] |
| -3, -1, -1, 1, 2 | [-3 0 0 0 0; -3 -1 3 -2 -2; 0 -3 2 -1 -1; -1 -3 -3 2 3; -3 -1 2 -1 -2] |
| -5, -3, -1, 2, 6 | [-1 -1 0 0 0; 0 3 3 -3 -3; 0 0 2 0 0; -1 -3 -1 -2 3; 1 -3 -3 2 -3] |
| -4, -3, -3, -2, -1 | [-1 -1 2 2 2; -1 -3 -2 -1 -2; 1 -1 -3 1 0; 1 -1 1 -3 0; -2 2 -1 -1 -3] |
| -3, -3, 1, 1, 2 | [-1 2 -2 -3 -2; 3 0 2 -1 2; 0 -3 -1 -2 -2; 0 0 0 1 0; 0 3 -2 0 -1] |
Invertible 5 × 5 non-symmetric matrices with no entries greater than four in absolute value
| Eigenvalues | Matrix |
|---|---|
| -3, -2, 2, 4, 8 | [ 3 -4 1 4 3; -2 4 0 -2 1; 1 2 1 -2 -4; 2 -1 1 -1 1; 4 0 0 4 2] |
| -6, -3, -2, 1, 2 | [-3 -3 -2 -1 3; 0 -2 0 -3 0; 0 0 -3 -4 0; -4 4 1 2 -4; 4 0 1 -3 -2] |
| -6, -3, -2, 3, 5 | [-2 0 -4 4 2; 2 3 4 0 -2; 0 2 3 -4 -2; 3 2 3 -4 -4; -1 -2 4 -4 -3] |
| -5, -2, -1, 2, 5 | [-2 -2 1 -2 -3; -3 3 -3 2 -3; 2 0 1 2 0; -2 2 -4 -2 3; 3 -3 -2 4 -1] |
| -6, -3, 1, 2, 2 | [-3 -2 1 0 1; 2 -4 4 0 1; 3 1 -2 0 -4; 4 -2 1 2 -1; -4 3 -1 0 3] |
| -4, -2, -1, 2, 2 | [-3 3 -1 -2 0; -3 -4 -3 1 0; 2 -3 0 4 0; 0 0 0 2 0; -4 -3 -1 1 2] |
| -5, -3, -2, 1, 2 | [-3 2 4 -2 4; 0 2 4 1 -4; 0 0 -3 0 1; -3 -2 2 1 0; 0 0 -2 2 -4] |
| -2, -2, -2, 2, 2 | [ 0 1 -4 2 3; 1 3 2 3 -4; -2 -2 2 -2 -4; -1 -1 2 -3 -2; -1 -1 2 -1 -4] |
| -4, -3, -2, 3, 5 | [ 4 0 0 1 0; 0 -2 -4 1 -2; -2 -4 -2 0 1; 4 -4 -4 0 -1; -2 1 4 -1 -1] |
| -6, -5, -4, -2, 5 | [-4 -4 2 -2 0; -3 -1 -4 4 0; -1 -3 -3 -2 -1; -4 1 -2 -3 -1; -1 -4 0 3 -1] |
| -4, -2, 1, 3, 4 | [ 4 4 2 4 1; -4 2 -1 1 -2; 0 -2 -4 -2 -3; 4 -4 1 -3 -1; 0 0 0 0 3] |
| -5, -2, 1, 2, 6 | [ 1 2 -2 1 0; -1 1 2 3 -2; 0 2 -4 2 -2; 1 3 0 0 1; 0 -1 -3 -2 4] |
| -5, -5, -1, 2, 6 | [ 3 0 2 0 2; -1 -4 0 2 0; 2 2 -3 -3 4; 1 3 1 1 1; 4 4 3 1 0] |
| -4, -3, 1, 2, 3 | [ 1 0 0 0 0; 1 3 4 3 2; 4 0 -4 4 0; -3 0 0 -3 0; 0 0 -2 -2 2] |
| -5, -2, -1, 3, 4 | [ 4 2 -2 -4 -4; 0 2 3 -2 3; 0 -1 -2 -4 0; 0 1 -1 -1 -1; 0 4 -2 4 -4] |
| -4, -3, 2, 3, 6 | [ 1 1 -2 2 4; -1 3 -2 2 4; -3 -4 2 -2 4; 3 0 -1 -3 2; 0 1 1 -2 1] |
| -7, 2, 3, 5, 6 | [ 3 3 -1 4 -3; 4 3 -2 0 2; -2 2 4 0 -2; 1 -1 -1 2 1; -4 0 -4 4 -3] |
| -4, -3, -1, 2, 3 | [-4 3 0 1 0; 0 1 3 1 1; 0 2 2 0 0; -2 -4 -1 2 -3; 0 -4 -3 -1 -4] |
| -6, -2, -1, 1, 3 | [ 3 -4 3 0 -1; 0 -4 2 4 -1; 0 -4 -2 -2 3; 0 3 -1 -3 -2; 0 -1 1 2 1] |
| -3, -1, 3, 6, 6 | [ 1 4 3 0 2; 4 4 4 -4 2; 4 4 3 -4 1; 4 -3 2 -1 -4; -4 2 -4 4 4] |
| -4, -3, -1, 3, 4 | [ 0 3 0 0 2; 4 -4 -2 4 -2; -2 -4 1 0 -1; 0 -2 -2 -1 -3; -1 -3 1 1 3] |
| -6, -3, 1, 1, 6 | [-2 -4 -3 1 3; -4 1 4 2 3; 0 2 -3 -2 0; -4 0 4 3 3; 0 2 4 4 0] |
| -6, -2, 1, 4, 5 | [ 0 0 -1 -2 2; 2 -1 -2 -2 2; -1 -3 -2 1 3; -4 -3 -4 2 3; 0 3 3 0 3] |
| -2, -1, 1, 4, 5 | [ 4 -1 3 -2 0; 4 -2 4 -4 2; -2 0 1 -4 4; -2 0 -2 3 0; -2 1 1 1 1] |
| -7, -5, -2, 1, 4 | [-2 -1 0 1 4; 0 0 4 1 3; -1 4 -2 0 -2; 1 -4 -2 -3 -1; 3 4 2 -4 -2] |
| -7, -2, 1, 2, 7 | [-1 0 -1 3 2; -4 3 -3 -3 0; -4 -2 -3 3 3; -2 -4 4 -1 1; -2 2 4 3 3] |
| -3, -2, 4, 6, 7 | [ 0 2 -2 -3 4; -4 3 0 4 2; 0 4 3 -1 1; -4 3 -2 4 2; 4 -1 2 2 2] |
| -2, -2, 2, 4, 5 | [-2 0 2 1 -2; -1 3 -1 3 -1; -2 1 2 -1 4; 0 0 -2 2 2; -2 1 4 -1 2] |
| -2, -1, 1, 3, 4 | [-3 1 1 -4 -1; 1 3 -1 1 1; 0 0 -1 1 4; 3 4 -3 4 3; 0 -1 1 1 2] |
| -5, -4, -4, 1, 4 | [-1 3 1 1 -2; 0 -4 -3 4 4; 0 0 1 -3 -3; 2 0 -3 -2 0; -2 0 -3 0 -2] |
| -4, -3, 1, 2, 6 | [ 0 3 0 -1 -4; 4 2 0 -4 -4; 3 3 2 -2 2; -3 3 0 0 3; -2 -1 0 4 -2] |
| -4, -1, 2, 3, 6 | [-1 -1 0 -2 0; -3 2 0 1 -4; 1 -4 3 4 -2; -4 0 0 3 -3; 0 -1 0 -2 -1] |
| -8, -5, -1, 1, 2 | [-4 2 2 -4 -4; 2 -2 -2 -3 3; 0 0 -1 -1 0; 0 -4 -4 -3 -4; -2 4 -1 2 -1] |
| -3, 1, 2, 3, 4 | [ 0 -3 -3 2 -2; -2 4 2 0 -4; -1 -3 2 0 -2; 4 1 3 -2 4; 1 0 1 -1 3] |
| -4, -2, -2, 5, 6 | [ 4 -1 -1 -2 3; -4 4 4 0 -2; -2 4 -2 1 0; -2 -2 0 -1 0; 0 2 0 0 -2] |
| -4, -2, -1, 1, 3 | [-3 0 -3 1 1; -3 2 0 1 1; -1 -2 1 3 2; -3 4 1 -1 1; 2 -4 -1 3 -2] |
| -3, 1, 3, 5, 8 | [ 3 -3 -4 0 2; -1 3 1 -1 0; -4 1 3 -2 2; 0 -2 0 2 0; 2 0 4 2 3] |
| -3, -2, 1, 2, 2 | [ 0 2 1 4 2; 1 0 -3 -1 -3; 0 -1 3 0 1; 1 -2 3 -2 2; -1 3 -4 4 -1] |
| -4, -4, 1, 2, 3 | [-1 3 -3 -2 -4; -2 4 -4 0 3; 0 0 3 0 0; 0 0 -3 -4 0; 0 0 1 1 -4] |
| -4, -3, 1, 3, 5 | [ 2 -1 3 -2 4; 1 -4 -1 -1 3; 2 -2 3 1 -1; -2 1 -4 2 -2; 1 0 -1 -1 -1] |
| -4, -3, -2, 1, 3 | [-3 1 0 -1 0; 4 3 -1 1 2; 4 2 0 1 1; 4 2 2 -1 -3; 0 0 0 0 -4] |
| -6, 1, 1, 2, 5 | [ 1 2 2 -1 1; 0 2 -1 -1 3; 0 0 0 -2 2; 0 0 0 2 4; 0 3 1 4 -2] |
| -6, -3, -1, 1, 2 | [-1 0 0 -4 4; -1 -1 -3 2 2; 4 4 -2 0 4; 2 4 2 0 -1; 3 3 3 0 -3] |
| -5, -2, -1, 1, 5 | [-4 0 2 1 0; -3 3 4 1 -4; 0 2 -3 2 0; 3 2 -4 0 0; -4 -1 1 2 2] |
| -5, -3, -2, -1, 2 | [-2 2 0 2 -4; 4 2 0 -2 -2; -4 -1 -2 2 1; 3 0 -3 -3 -3; 0 1 -3 0 -4] |
| -5, -2, 2, 4, 5 | [ 1 -4 4 4 -2; -2 0 -3 2 -2; 4 -2 -2 -4 0; 3 -3 1 2 -4; 0 2 3 0 3] |
| -7, -3, -2, 4, 7 | [ 3 0 0 0 3; 1 -4 2 0 1; -2 -4 4 1 3; 4 0 2 -1 4; 4 4 4 4 -3] |
| -3, -2, 2, 5, 6 | [ 2 -3 -3 3 4; -4 3 0 3 1; 0 -3 1 3 0; -4 2 4 4 0; 0 4 -4 -4 -2] |
| -6, -2, -1, 2, 4 | [-1 -1 -2 3 4; -2 -1 1 2 2; -4 3 0 3 3; -2 4 2 -3 -3; -3 4 -1 -3 2] |
| -5, -1, 2, 4, 4 | [-1 2 2 -3 -2; -3 4 0 -4 -4; 2 0 0 -2 -2; 2 0 -4 0 -4; -4 0 -1 -3 1] |
| -5, -4, -4, -1, 3 | [-3 2 -1 0 -1; 2 -2 0 0 2; 1 -2 -4 0 4; -4 2 -2 -4 1; 4 3 1 0 2] |
| -2, -1, 1, 3, 5 | [-2 1 -1 0 3; 0 0 -3 1 3; 0 4 1 -4 0; 0 -2 -2 3 2; 0 1 -2 4 4] |
| -3, -2, 3, 4, 6 | [ 2 -3 1 0 -4; 3 2 3 0 2; -1 0 3 3 1; 1 2 3 -3 -1; -3 4 -3 0 4] |
| -4, -3, -2, 3, 6 | [-4 4 0 -1 -4; 0 -1 3 -2 -1; 0 1 2 -1 -4; -4 0 -3 1 1; 0 1 -4 -1 2] |
| -4, -1, 2, 3, 5 | [ 1 0 -2 0 -2; 1 0 -4 0 1; -4 -4 4 0 3; 4 2 2 3 -2; 3 4 -4 0 -3] |
| -2, -2, 1, 2, 4 | [ 4 -1 -3 0 3; -3 2 -2 0 -3; 0 0 -2 0 0; 1 0 -3 -3 -4; -4 -3 -1 1 2] |
| -5, -4, -2, 1, 5 | [ 0 1 3 0 1; -1 2 3 -4 3; -1 -1 -4 -4 0; -3 0 -3 0 -1; 0 4 3 -4 -3] |
| -5, -3, -1, 1, 6 | [-2 3 0 -3 -3; 3 0 1 -1 -1; 1 -1 -3 1 1; -3 -1 2 4 3; -2 -2 -1 -2 -1] |
| -4, -1, 1, 2, 5 | [ 3 0 -4 0 0; -3 4 -1 -2 -3; 2 0 -3 0 0; -3 -1 -4 3 -3; 1 -2 -1 2 -4] |
| -6, -1, 2, 3, 5 | [ 3 -4 -4 -4 -3; 0 0 -3 -2 -2; -1 -4 -3 -2 -3; 4 1 1 1 4; -4 2 -2 4 2] |
| -4, -2, -1, 4, 5 | [ 1 -2 2 4 0; -3 -2 4 1 -4; -1 -2 4 4 -4; 4 2 -2 1 0; -2 -1 -2 -2 -2] |
| 1, 2, 3, 4, 6 | [ 4 -1 1 -1 0; -2 2 -4 2 4; 4 2 3 2 -1; -4 3 -4 3 3; 4 -1 -1 3 4] |
| -7, -6, -3, -2, 2 | [-3 -1 -2 3 4; 3 -3 1 -4 0; -1 -1 -4 3 4; -2 -1 4 -4 4; 2 -4 -1 3 -2] |
| -2, -1, 1, 1, 4 | [ 2 2 -4 -4 0; 0 4 0 0 0; 0 4 -2 -1 0; 1 -4 -1 -2 0; 0 -1 -2 2 1] |
| -5, -4, 2, 4, 6 | [-4 2 -2 2 -2; 0 3 3 3 3; 4 2 3 -3 -1; -1 2 -4 -2 0; -2 2 -1 0 3] |
| -5, -2, -1, 1, 3 | [-3 3 -3 -4 -4; 4 -2 1 0 2; -3 4 3 -2 -3; -1 0 3 0 1; 3 2 2 -2 -2] |
| -4, -1, 1, 3, 5 | [-1 0 2 0 -4; -2 2 3 1 -4; 4 -2 3 -2 -2; -4 1 -4 1 1; -2 -1 3 1 -1] |
| -6, -3, -1, 2, 5 | [ 4 -2 2 -4 1; 0 -2 2 -1 -4; 4 0 -4 1 3; 2 2 3 -4 1; 3 -3 -3 0 3] |
| -6, -4, -1, 2, 3 | [ 1 -2 4 -4 3; 0 0 -4 2 -2; 2 -2 0 4 -1; -4 -2 1 -4 1; -4 2 0 4 -3] |
| -1, -1, 2, 3, 4 | [ 0 -2 0 -2 3; 4 2 -3 2 0; 0 0 3 0 0; -2 -1 -4 1 2; 2 2 4 4 1] |
| -3, -2, 2, 4, 7 | [ 0 2 -2 -1 3; 4 4 -4 3 1; 0 -2 0 -2 2; -4 -1 -3 0 3; 3 0 1 -3 4] |
| -3, -3, -1, 4, 5 | [ 1 -4 -4 -1 3; 0 0 -1 -3 2; -4 1 0 4 -1; 0 -2 -1 4 -3; 0 1 -1 1 -3] |
| -4, -4, -3, -2, 2 | [-1 2 0 -1 -2; -2 -1 -4 -1 -4; -3 -2 -4 1 -1; -3 -2 0 -3 -2; 0 0 0 0 -2] |
| -1, 1, 2, 4, 6 | [ 3 -1 -4 0 0; -2 4 2 0 0; 0 1 3 -2 2; -1 3 -1 4 -2; -2 1 2 4 -2] |
| -4, -3, -2, -2, 2 | [ 0 3 1 -3 0; -1 -2 3 -1 -4; 0 1 -4 3 4; -1 2 -1 -1 2; -2 2 2 4 -2] |
| -4, -4, 1, 2, 7 | [ 0 -3 4 -3 -4; -4 -3 -2 4 0; 1 -2 3 4 0; -4 1 -2 0 0; -1 4 1 1 2] |
| -6, -2, -1, 1, 4 | [ 1 0 0 0 0; -3 4 0 -4 -4; 2 -4 -1 -4 -4; -1 1 1 -4 2; 1 -1 -1 2 -4] |
| -4, -3, -2, 3, 3 | [ 3 0 0 -4 -2; 1 -4 -3 0 0; 4 0 -2 -4 1; -3 0 0 -1 1; 1 0 0 -2 1] |
| -4, -2, -1, 2, 3 | [ 1 -3 0 -1 2; -3 1 4 -1 -3; 2 -4 0 1 2; 1 -1 1 -4 1; 1 -3 1 1 0] |
| -5, -3, -1, 1, 4 | [-3 1 2 -1 -2; 2 -4 0 -3 -2; -2 2 3 -1 -1; 3 -1 -2 3 1; -2 2 2 2 -3] |
| -6, 1, 2, 3, 5 | [ 2 2 4 -4 2; 1 3 2 2 0; -1 0 1 -4 -2; 0 1 -1 -4 -1; 1 0 -4 -4 3] |
| -5, -1, 1, 4, 6 | [-2 -1 -2 -2 1; -2 4 -4 4 3; 3 4 3 4 -3; 0 2 -2 -4 -2; 4 3 -4 -2 4] |
| -5, -3, -2, -2, 4 | [ 3 2 1 -4 -1; -2 -2 1 3 -4; 0 1 -4 -3 4; -2 -1 -3 -2 4; -1 1 0 0 -3] |
| -4, -4, -1, 1, 6 | [ 3 2 2 3 -1; -1 -4 2 4 -3; 4 2 -4 1 -2; -2 -2 4 1 0; -3 -3 0 -3 2] |
| -4, -3, -2, 2, 3 | [-2 3 4 -4 -4; -3 -4 4 2 -3; 2 0 3 0 2; -3 0 -2 -2 -3; -1 -3 -4 4 1] |
| -6, -4, 2, 4, 5 | [-1 4 3 2 3; 4 0 3 -3 -3; 2 -3 -4 2 3; 2 0 0 4 -2; 3 0 2 1 2] |
| -6, -2, 1, 2, 4 | [ 1 -4 2 -3 0; -4 -2 -4 -4 4; 0 -4 -2 4 0; 0 0 0 -2 0; -3 -4 2 -3 4] |
| -3, -2, 2, 3, 4 | [ 2 -4 1 3 -4; 1 4 -1 1 -1; 2 -4 1 4 -1; 0 3 0 -1 0; -1 0 1 2 -2] |
| -6, -1, 2, 3, 4 | [ 4 3 -3 -3 1; -1 2 -2 -2 -2; -1 -4 -4 -2 2; 1 1 -2 -1 1; -2 -3 0 3 1] |
| -2, -1, 1, 2, 4 | [-1 -4 -2 1 2; 1 4 1 -1 -3; -1 -2 2 -1 4; 1 -2 -4 1 -2; 4 3 -1 -1 -2] |
| -5, -2, -1, 1, 6 | [ 1 0 -4 1 0; 2 2 -3 -4 -1; -4 -2 -1 1 -1; -4 -2 1 0 -2; -4 -2 1 1 -3] |
| -3, 1, 3, 6, 8 | [ 2 -4 0 0 4; -3 2 -3 4 2; 4 -1 4 0 2; -2 4 3 4 0; 2 1 -3 4 3] |
| -3, -2, -1, 1, 3 | [-1 0 -2 -4 1; 2 3 -2 2 1; 1 0 1 1 1; -2 -4 2 -3 -1; 1 2 1 4 -2] |
| -5, 1, 1, 2, 5 | [ 1 2 -2 2 -3; 0 3 2 4 -2; 0 4 4 1 -2; 0 0 -2 -1 4; 0 -4 0 -1 -3] |
| -8, -5, -2, -2, 5 | [ 1 -3 0 1 -3; 0 -4 3 2 -1; -3 2 -4 -3 3; 3 2 -1 -3 -4; -3 1 2 -2 -2] |
| -5, 2, 3, 5, 6 | [-2 -2 4 -3 2; 2 4 2 2 3; 3 -2 4 0 4; -3 2 -1 3 -4; -3 2 -1 -3 2] |
| -6, -4, -1, 2, 5 | [ 3 -4 0 -3 0; -4 -3 0 1 -1; 0 -3 -4 -2 -3; -1 -2 0 -1 -2; -2 -4 0 -1 1] |
| -5, -3, 1, 3, 7 | [ 3 4 -1 -4 4; 4 3 0 4 -3; -4 -4 -1 0 2; -1 1 -3 -3 3; -2 -2 3 0 1] |
| -5, -3, -1, 3, 6 | [ 3 -4 2 0 -4; -3 -1 4 -4 1; 0 -4 -2 2 1; 4 -4 2 -1 -4; 0 -4 4 -4 1] |
| -2, -1, 1, 2, 5 | [ 0 -1 -3 -2 -1; 4 4 -2 2 -2; -1 -1 2 -1 -2; -2 2 2 0 1; 2 -2 2 2 -1] |
| -7, -3, -1, 1, 7 | [ 2 -1 -3 3 -1; -2 3 -4 -4 2; 3 -3 -3 0 1; 3 -3 -2 -1 1; -3 3 -3 3 -4] |
| -3, -3, -1, -1, 4 | [ 3 -3 3 0 -4; -1 0 -1 0 -2; 1 2 -3 0 0; -2 3 0 -3 2; 0 0 0 0 -1] |
Invertible 5 × 5 non-symmetric matrices with no entries greater than five in absolute value
| Eigenvalues | Matrix |
|---|---|
| -5, -5, -2, 1, 6 | [-5 0 0 0 0; -4 -4 -4 -4 0; -3 0 3 4 -1; -3 -5 -1 4 3; -5 0 -1 -3 -3] |
| -5, -4, -2, 3, 4 | [ 3 -1 -1 1 0; 2 3 2 0 0; -4 -1 -2 1 0; 3 2 -5 -4 2; 5 0 5 5 -4] |
| -7, -5, -3, 5, 8 | [-5 -2 0 -4 2; -1 -3 0 5 -1; -1 -1 0 -2 4; -4 3 0 5 1; 4 3 5 -2 1] |
| -6, -1, 2, 4, 6 | [ 1 -5 0 1 -4; 3 0 -4 3 -3; 0 -2 4 2 -1; -2 3 5 2 -3; -5 0 5 -3 -2] |
| -4, -1, 1, 3, 8 | [ 5 -4 0 -3 3; -5 -4 4 -5 4; -5 0 0 -5 -1; -4 4 2 4 -5; -5 0 -3 -5 2] |
| -4, -3, 1, 2, 6 | [ 4 0 2 -1 -4; -5 -1 -4 -5 1; -2 -3 -1 5 2; 2 0 3 1 1; -2 -3 -4 5 -1] |
| -5, -1, 3, 4, 7 | [-2 4 3 -1 -1; 5 5 0 1 -2; 0 -1 4 -4 2; 1 0 0 4 -4; 0 5 3 0 -3] |
| -3, -1, 3, 4, 5 | [ 4 -4 5 -1 -3; -4 4 1 1 0; 1 3 -1 -2 1; 5 -4 5 -2 -3; 5 -3 5 -4 3] |
| -5, -4, 2, 4, 7 | [ 3 1 -5 -2 1; -1 3 5 0 -4; -4 -4 -4 3 -4; -2 -2 2 -2 -2; -1 -3 -1 -2 4] |
| -5, 1, 2, 4, 4 | [-1 3 0 3 -2; 5 2 -4 1 -1; -1 -2 2 2 -4; -5 0 2 5 -3; 3 -3 -3 3 -2] |
| -7, -3, -2, 2, 8 | [-5 -5 1 2 -2; -2 -1 0 -3 1; 0 -2 -1 0 -2; 0 -4 2 0 -4; -2 -1 -5 -1 5] |
| -3, -2, -1, 1, 3 | [ 0 -3 -3 3 0; 5 2 0 3 3; -3 -3 -2 -1 -2; 3 -1 -4 -3 0; -3 1 2 2 1] |
| -3, -2, -1, 1, 3 | [-2 0 0 -3 -3; -2 4 4 -1 2; 3 -1 -2 -3 -5; 3 1 3 0 1; -3 -1 -3 -1 -2] |
| -4, -3, 1, 3, 4 | [2 2 1 2 -1; 4 -1 -3 -1 1; 4 -4 2 2 1; -3 3 -2 -5 4; -1 0 0 -2 3] |
| -5, -4, -3, -1, 4 | [-3 -1 2 -3 -4; 1 -3 3 -1 -4; 1 -2 -5 -1 3; -4 3 -4 1 4; 1 3 1 4 1] |
| -6, -4, -3, 1, 2 | [-4 -4 1 3 3; 2 -4 4 -5 -2; 2 0 2 3 4; -2 0 -3 1 1; 2 0 5 -3 -5] |
| -4, -2, 2, 3, 7 | [5 4 -4 -1 -3; -1 4 -2 2 -4; -2 2 -3 3 -2; 2 4 -4 2 5; -2 -4 2 0 -2] |
| -5, -3, -2, 1, 6 | [3 -2 -1 -4 4; 4 -3 -3 -4 2; 2 -2 2 -1 5; -5 -1 4 -4 4; -5 -1 4 1 -1] |
| -7, -3, 1, 3, 8 | [2 -5 2 -3 -5; 2 -1 3 -1 1; 4 2 4 3 -3; -4 1 0 0 4; -3 2 -5 1 -3] |
| -3, -2, -1, 2, 5 | [3 2 -4 0 1; -5 -3 0 0 5; -3 1 2 0 3; 4 2 -4 -2 -4; 2 2 -2 0 1] |
| -3, -1, 1, 5, 5 | [4 0 -4 -1 -3; 5 1 2 5 4; 0 0 5 0 0; -5 0 3 0 -4; 0 0 -2 0 -3] |
| -6, -5, -2, -1, 2 | [-2 -1 5 -1 1; -5 -2 0 0 1; 3 1 -3 2 0; 4 1 4 -4 0; -4 -2 1 1 -1] |
| 1, 2, 2, 4, 11 | [5 -2 -5 -5 1; 3 3 -2 0 2; -5 -2 5 -3 -4; -3 0 3 5 -1; 0 0 0 0 2] |
| -2, -1, 2, 3, 5 | [-2 5 -5 0 5; 0 -1 5 3 0; 0 -2 4 3 -2; -4 3 -3 5 3; 1 2 -3 -1 1] |
| 1, 4, 4, 5, 6 | [4 -1 -5 4 -5; 0 5 -2 -3 0; 0 3 1 -2 0; 0 -5 4 5 0; 0 2 -4 3 5] |
| -4, -4, -3, 4, 4 | [-2 3 0 0 0; 4 2 0 0 0; -5 -3 -3 0 0; 4 -5 2 4 -1; 2 3 0 0 -4] |
| -4, -3, -2, -1, 1 | [-5 4 3 2 -5; -3 2 3 0 -3; 3 -3 -1 0 2; 5 -5 3 -5 5; 1 -1 1 -2 0] |
| -6, 1, 2, 3, 8 | [1 2 0 5 0; -2 4 -2 -2 2; 0 -3 5 0 0; 5 0 2 -1 -5; 2 4 0 0 -1] |
| -6, 1, 2, 4, 9 | [5 3 -1 -1 -2; 4 -2 -4 -2 -5; 3 -5 1 -3 -3; 4 4 -4 1 5; -3 -3 3 0 5] |
| -6, -4, 1, 2, 3 | [0 -4 3 -5 -2; 4 1 4 2 5; -2 2 -3 2 -4; -4 2 -1 -3 -4; -1 1 -3 1 1] |
| -7, -4, 1, 2, 9 | [3 -4 -3 4 5; -3 -3 -2 -2 -5; 1 0 1 2 5; 3 0 0 -5 3; 1 -1 -1 5 5] |
| -5, -3, -2, -1, 3 | [-3 -5 -2 3 3; 1 3 2 -3 -2; 3 0 -3 1 4; 1 -5 0 -1 3; -3 0 4 -4 -4] |
| -1, -1, 3, 4, 4 | [-1 0 0 0 -5; -5 4 -4 -3 -3; 4 0 4 -4 3; -4 0 0 3 4; 0 0 0 0 -1] |
| -4, -2, -1, 2, 5 | [0 -4 4 2 -2; -1 1 -3 0 1; -4 -5 2 4 -3; 2 -2 3 -1 -1; 1 0 -1 0 -2] |
| -5, -2, -1, 3, 7 | [-4 0 -2 2 5; 2 -1 0 1 3; 2 0 0 -2 -5; -1 0 4 5 5; -1 0 -5 3 2] |
| -5, -1, 1, 3, 4 | [0 0 -4 -1 -1; 2 -1 2 -1 5; -1 2 -3 0 0; 1 2 5 3 -5; 3 1 0 -1 3] |
Douglas Wilhelm Harder
Department of Electrical and Computer Engineering
University of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
Department of Electrical and Computer Engineering
University of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
Website maintained by Douglas Wilhelm Harder