Invertible 3 × 3 symmetric matrices with no entries greater than one in absolute value

These are all such matrices up to multiplication by -1, in which case, the eigenvalues are also negated.

1, -1, -1, $\left(\begin{array}{rrr} 0 & 0 & 1 \\ 0 & -1 & 0 \\ 1 & 0 & 0 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} 0 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} -1 \\ 0 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{r} 0 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{rrr} -\frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right) \right\}$

-1, 1, 1, $\left(\begin{array}{rrr} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} 0 \\ 1 \\ 0 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{rrr} 0 \\ 1 \\ 0 \end{array}\right) \right\}$

1, -2, -1, $\left(\begin{array}{rrr} 0 & 1 & -1 \\ 1 & -1 & 0 \\ -1 & 0 & -1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -2 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} 0 \\ 1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{2}{\sqrt{6}} \\ -\frac{1}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{rrr} 0 \\ \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{array}\right) \right\}$

2, -1, -1, $\left(\begin{array}{rrr} 0 & 1 & -1 \\ 1 & 0 & -1 \\ -1 & -1 & 0 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 1 \\ 0 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{rrr} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right) \right\}$

1, 1, -2, $\left(\begin{array}{rrr} 0 & 1 & -1 \\ 1 & 0 & 1 \\ -1 & 1 & 0 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} 1 \\ -1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$

1, -1, 2, $\left(\begin{array}{rrr} 0 & 1 & -1 \\ 1 & 1 & 0 \\ -1 & 0 & 1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 0 \\ 1 \\ 1 \end{array}\right), \left(\begin{array}{r} 2 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ -1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} 0 \\ \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{r} \frac{2}{\sqrt{6}} \\ -\frac{1}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right), \left(\begin{array}{rrr} -\frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$

-1, -1, 1, $\left(\begin{array}{rrr} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & -1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 0 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 0 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} 0 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right) \right\}$

-1, 1, 1, $\left(\begin{array}{rrr} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} 0 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 0 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right), \left(\begin{array}{r} 0 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right) \right\}$

-2, 1, -1, $\left(\begin{array}{rrr} 0 & 1 & 1 \\ 1 & -1 & 0 \\ 1 & 0 & -1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ 1 \\ 1 \end{array}\right), \left(\begin{array}{r} 2 \\ 1 \\ 1 \end{array}\right), \left(\begin{array}{r} 0 \\ -1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{r} \frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right), \left(\begin{array}{rrr} 0 \\ -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{array}\right) \right\}$

1, 1, -2, $\left(\begin{array}{rrr} 0 & 1 & 1 \\ 1 & 0 & -1 \\ 1 & -1 & 0 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} -1 \\ 1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right), \left(\begin{array}{rrr} -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$

2, -1, -1, $\left(\begin{array}{rrr} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ 1 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 1 \\ 0 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{r} -\frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{rrr} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right) \right\}$

2, -1, 1, $\left(\begin{array}{rrr} 0 & 1 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & 1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ 1 \\ 1 \end{array}\right), \left(\begin{array}{r} -2 \\ 1 \\ 1 \end{array}\right), \left(\begin{array}{r} 0 \\ -1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{r} -\frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right), \left(\begin{array}{rrr} 0 \\ -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{array}\right) \right\}$

-2, 2, 1, $\left(\begin{array}{rrr} 1 & -1 & -1 \\ -1 & -1 & -1 \\ -1 & -1 & 1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ 2 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ -1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{6}} \\ \frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right), \left(\begin{array}{r} -\frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$

-2, 2, -1, $\left(\begin{array}{rrr} 1 & -1 & -1 \\ -1 & -1 & 1 \\ -1 & 1 & -1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 0 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} -2 \\ 1 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} 0 \\ -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{r} -\frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$

-2, 1, 2, $\left(\begin{array}{rrr} 1 & -1 & -1 \\ -1 & 1 & -1 \\ -1 & -1 & -1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ 1 \\ 2 \end{array}\right), \left(\begin{array}{r} -1 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 1 \\ 0 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \\ \frac{2}{\sqrt{6}} \end{array}\right), \left(\begin{array}{r} -\frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{rrr} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right) \right\}$

-1, 2, 2, $\left(\begin{array}{rrr} 1 & -1 & -1 \\ -1 & 1 & -1 \\ -1 & -1 & 1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ 1 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 1 \\ 0 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{r} -\frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{rrr} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right) \right\}$

-1, 1, 2, $\left(\begin{array}{rrr} 1 & -1 & 0 \\ -1 & 0 & -1 \\ 0 & -1 & 1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ 2 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ -1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{6}} \\ \frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right), \left(\begin{array}{r} -\frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$

2, 1, -1, $\left(\begin{array}{rrr} 1 & -1 & 0 \\ -1 & 0 & 1 \\ 0 & 1 & 1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ 1 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ -2 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{rrr} -\frac{1}{\sqrt{6}} \\ -\frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right) \right\}$

-1, 2, -2, $\left(\begin{array}{rrr} 1 & -1 & 1 \\ -1 & -1 & -1 \\ 1 & -1 & -1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} 2 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} 0 \\ 1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{r} \frac{2}{\sqrt{6}} \\ -\frac{1}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right), \left(\begin{array}{rrr} 0 \\ \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{array}\right) \right\}$

1, 2, -2, $\left(\begin{array}{rrr} 1 & -1 & 1 \\ -1 & -1 & 1 \\ 1 & 1 & 1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ 1 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ -2 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{rrr} -\frac{1}{\sqrt{6}} \\ -\frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right) \right\}$

-2, 2, 1, $\left(\begin{array}{rrr} 1 & -1 & 1 \\ -1 & 1 & 1 \\ 1 & 1 & -1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ -1 \\ 2 \end{array}\right), \left(\begin{array}{r} -1 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{6}} \\ -\frac{1}{\sqrt{6}} \\ \frac{2}{\sqrt{6}} \end{array}\right), \left(\begin{array}{r} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$

2, 2, -1, $\left(\begin{array}{rrr} 1 & -1 & 1 \\ -1 & 1 & 1 \\ 1 & 1 & 1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} -1 \\ -1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{r} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right), \left(\begin{array}{rrr} -\frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$

-1, 2, 1, $\left(\begin{array}{rrr} 1 & 0 & -1 \\ 0 & 1 & -1 \\ -1 & -1 & 0 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ 1 \\ 2 \end{array}\right), \left(\begin{array}{r} -1 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 1 \\ 0 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \\ \frac{2}{\sqrt{6}} \end{array}\right), \left(\begin{array}{r} -\frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{rrr} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right) \right\}$

2, -1, 1, $\left(\begin{array}{rrr} 1 & 0 & -1 \\ 0 & 1 & 1 \\ -1 & 1 & 0 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ 1 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ -1 \\ 2 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 0 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{6}} \\ -\frac{1}{\sqrt{6}} \\ \frac{2}{\sqrt{6}} \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right) \right\}$

-1, 1, 1, $\left(\begin{array}{rrr} 1 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & -1 & 0 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 0 \\ 1 \\ 1 \end{array}\right), \left(\begin{array}{r} 0 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 0 \\ 0 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} 0 \\ \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{r} 0 \\ -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{rrr} 1 \\ 0 \\ 0 \end{array}\right) \right\}$

-1, 1, 1, $\left(\begin{array}{rrr} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 0 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} 0 \\ 1 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 0 \\ 0 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} 0 \\ -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{r} 0 \\ \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{rrr} 1 \\ 0 \\ 0 \end{array}\right) \right\}$

2, 1, -1, $\left(\begin{array}{rrr} 1 & 0 & 1 \\ 0 & 1 & -1 \\ 1 & -1 & 0 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} -1 \\ 1 \\ 2 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right), \left(\begin{array}{rrr} -\frac{1}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \\ \frac{2}{\sqrt{6}} \end{array}\right) \right\}$

1, -1, 2, $\left(\begin{array}{rrr} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 0 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} -1 \\ -1 \\ 2 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right), \left(\begin{array}{r} -\frac{1}{\sqrt{6}} \\ -\frac{1}{\sqrt{6}} \\ \frac{2}{\sqrt{6}} \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$

-2, 2, -1, $\left(\begin{array}{rrr} 1 & 1 & -1 \\ 1 & -1 & -1 \\ -1 & -1 & -1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 0 \\ 1 \\ 1 \end{array}\right), \left(\begin{array}{r} -2 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ -1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} 0 \\ \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{r} -\frac{2}{\sqrt{6}} \\ -\frac{1}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$

-2, 2, 1, $\left(\begin{array}{rrr} 1 & 1 & -1 \\ 1 & -1 & 1 \\ -1 & 1 & 1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ -2 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{6}} \\ -\frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right), \left(\begin{array}{r} -\frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$

-2, 2, 1, $\left(\begin{array}{rrr} 1 & 1 & -1 \\ 1 & 1 & 1 \\ -1 & 1 & -1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ -1 \\ 2 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} -1 \\ 1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{6}} \\ -\frac{1}{\sqrt{6}} \\ \frac{2}{\sqrt{6}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right), \left(\begin{array}{rrr} -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$

2, 2, -1, $\left(\begin{array}{rrr} 1 & 1 & -1 \\ 1 & 1 & 1 \\ -1 & 1 & 1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} 1 \\ -1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$

2, -1, 1, $\left(\begin{array}{rrr} 1 & 1 & 0 \\ 1 & 0 & -1 \\ 0 & -1 & 1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 2 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 0 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{r} -\frac{1}{\sqrt{6}} \\ \frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right) \right\}$

2, 1, -1, $\left(\begin{array}{rrr} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ 1 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ -2 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{r} -\frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{6}} \\ -\frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right) \right\}$

-2, 1, 2, $\left(\begin{array}{rrr} 1 & 1 & 1 \\ 1 & -1 & -1 \\ 1 & -1 & 1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ 2 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 0 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{6}} \\ \frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right), \left(\begin{array}{r} -\frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right) \right\}$

-1, 2, -2, $\left(\begin{array}{rrr} 1 & 1 & 1 \\ 1 & -1 & 1 \\ 1 & 1 & -1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ 1 \\ 1 \end{array}\right), \left(\begin{array}{r} 2 \\ 1 \\ 1 \end{array}\right), \left(\begin{array}{r} 0 \\ -1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{r} \frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right), \left(\begin{array}{rrr} 0 \\ -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{array}\right) \right\}$

2, -2, 1, $\left(\begin{array}{rrr} 1 & 1 & 1 \\ 1 & 1 & -1 \\ 1 & -1 & -1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} -1 \\ 1 \\ 2 \end{array}\right), \left(\begin{array}{r} 1 \\ -1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right), \left(\begin{array}{r} -\frac{1}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \\ \frac{2}{\sqrt{6}} \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$

2, 2, -1, $\left(\begin{array}{rrr} 1 & 1 & 1 \\ 1 & 1 & -1 \\ 1 & -1 & 1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} -1 \\ 1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right), \left(\begin{array}{rrr} -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$