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

1, 4, -2, $\left(\begin{array}{rrr} 0 & 0 & -2 \\ 0 & 2 & 2 \\ -2 & 2 & 1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -2 \\ -2 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 2 \\ 2 \end{array}\right), \left(\begin{array}{r} 2 \\ -1 \\ 2 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -{\frac{2}{3}} \\ -{\frac{2}{3}} \\ {\frac{1}{3}} \end{array}\right), \left(\begin{array}{r} -{\frac{1}{3}} \\ {\frac{2}{3}} \\ {\frac{2}{3}} \end{array}\right), \left(\begin{array}{rrr} {\frac{2}{3}} \\ -{\frac{1}{3}} \\ {\frac{2}{3}} \end{array}\right) \right\}$

-1, 2, -4, $\left(\begin{array}{rrr} -2 & 0 & 2 \\ 0 & 0 & 2 \\ 2 & 2 & -1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 2 \\ -2 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 2 \\ 2 \end{array}\right), \left(\begin{array}{r} -2 \\ -1 \\ 2 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} {\frac{2}{3}} \\ -{\frac{2}{3}} \\ {\frac{1}{3}} \end{array}\right), \left(\begin{array}{r} {\frac{1}{3}} \\ {\frac{2}{3}} \\ {\frac{2}{3}} \end{array}\right), \left(\begin{array}{rrr} -{\frac{2}{3}} \\ -{\frac{1}{3}} \\ {\frac{2}{3}} \end{array}\right) \right\}$

2, -4, -2, $\left(\begin{array}{rrr} -2 & 2 & 0 \\ 2 & 0 & 2 \\ 0 & 2 & -2 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ 2 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 0 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{6}} \\ \frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{rrr} -\frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right) \right\}$

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

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

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

4, -2, -2, $\left(\begin{array}{rrr} 2 & -2 & 2 \\ -2 & -1 & -1 \\ 2 & -1 & -1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 2 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 0 \\ 2 \end{array}\right), \left(\begin{array}{r} 1 \\ 2 \\ 0 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{2}{\sqrt{6}} \\ -\frac{1}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right), \left(\begin{array}{r} -\frac{1}{\sqrt{5}} \\ 0 \\ \frac{2}{\sqrt{5}} \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{5}} \\ \frac{2}{\sqrt{5}} \\ 0 \end{array}\right) \right\}$

-4, -1, 1, $\left(\begin{array}{rrr} -2 & -1 & 1 \\ -1 & -1 & 2 \\ 1 & 2 & -1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} 2 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} 0 \\ 1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{r} \frac{2}{\sqrt{6}} \\ -\frac{1}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right), \left(\begin{array}{rrr} 0 \\ \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{array}\right) \right\}$

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

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

4, 2, -4, $\left(\begin{array}{rrr} -2 & 2 & 2 \\ 2 & 2 & -2 \\ 2 & -2 & 2 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 0 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 1 \end{array}\right), \left(\begin{array}{r} -2 \\ 1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} 0 \\ -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{rrr} -\frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right) \right\}$

-2, -2, 3, $\left(\begin{array}{rrr} -1 & 2 & 0 \\ 2 & 2 & 0 \\ 0 & 0 & -2 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -2 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} 0 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 2 \\ 0 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{2}{\sqrt{5}} \\ \frac{1}{\sqrt{5}} \\ 0 \end{array}\right), \left(\begin{array}{r} 0 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{5}} \\ \frac{2}{\sqrt{5}} \\ 0 \end{array}\right) \right\}$

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

3, 3, -3, $\left(\begin{array}{rrr} 2 & 1 & -2 \\ 1 & 2 & 2 \\ -2 & 2 & -1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -2 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} 1 \\ -1 \\ 2 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{2}{\sqrt{5}} \\ 0 \\ \frac{1}{\sqrt{5}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{6}} \\ -\frac{1}{\sqrt{6}} \\ \frac{2}{\sqrt{6}} \end{array}\right) \right\}$

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

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

4, -4, -2, $\left(\begin{array}{rrr} 2 & -2 & -2 \\ -2 & -2 & 2 \\ -2 & 2 & -2 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -2 \\ 1 \\ 1 \end{array}\right), \left(\begin{array}{r} 0 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right), \left(\begin{array}{r} 0 \\ -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$

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

1, -1, -5, $\left(\begin{array}{rrr} -2 & -2 & -1 \\ -2 & -1 & -2 \\ -1 & -2 & -2 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ -2 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{6}} \\ -\frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right), \left(\begin{array}{r} -\frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$

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

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

2, -2, 3, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & -1 & -2 \\ 0 & -2 & 2 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ 0 \\ 0 \end{array}\right), \left(\begin{array}{r} 0 \\ 2 \\ 1 \end{array}\right), \left(\begin{array}{r} 0 \\ -1 \\ 2 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} 1 \\ 0 \\ 0 \end{array}\right), \left(\begin{array}{r} 0 \\ \frac{2}{\sqrt{5}} \\ \frac{1}{\sqrt{5}} \end{array}\right), \left(\begin{array}{rrr} 0 \\ -\frac{1}{\sqrt{5}} \\ \frac{2}{\sqrt{5}} \end{array}\right) \right\}$

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

4, 2, -2, $\left(\begin{array}{rrr} 2 & 0 & -2 \\ 0 & 2 & 2 \\ -2 & 2 & 0 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ 1 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} 1 \\ -1 \\ 2 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{6}} \\ -\frac{1}{\sqrt{6}} \\ \frac{2}{\sqrt{6}} \end{array}\right) \right\}$

-4, -4, 2, $\left(\begin{array}{rrr} -2 & -2 & 2 \\ -2 & -2 & -2 \\ 2 & -2 & -2 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} 1 \\ -1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$

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

1, -4, -2, $\left(\begin{array}{rrr} -2 & -2 & -1 \\ -2 & -2 & 1 \\ -1 & 1 & -1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ 1 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} 1 \\ -1 \\ 2 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{6}} \\ -\frac{1}{\sqrt{6}} \\ \frac{2}{\sqrt{6}} \end{array}\right) \right\}$

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

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

2, 2, -4, $\left(\begin{array}{rrr} 1 & -2 & -1 \\ -2 & -2 & -2 \\ -1 & -2 & 1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} -2 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} 1 \\ 2 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{r} -\frac{2}{\sqrt{5}} \\ \frac{1}{\sqrt{5}} \\ 0 \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{6}} \\ \frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right) \right\}$

2, -2, -3, $\left(\begin{array}{rrr} -2 & 0 & 0 \\ 0 & -2 & -2 \\ 0 & -2 & 1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 0 \\ -1 \\ 2 \end{array}\right), \left(\begin{array}{r} 1 \\ 0 \\ 0 \end{array}\right), \left(\begin{array}{r} 0 \\ 2 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} 0 \\ -\frac{1}{\sqrt{5}} \\ \frac{2}{\sqrt{5}} \end{array}\right), \left(\begin{array}{r} 1 \\ 0 \\ 0 \end{array}\right), \left(\begin{array}{rrr} 0 \\ \frac{2}{\sqrt{5}} \\ \frac{1}{\sqrt{5}} \end{array}\right) \right\}$

1, -1, 4, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 1 & 2 \\ -1 & 2 & 1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 2 \\ 1 \\ 1 \end{array}\right), \left(\begin{array}{r} 0 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right), \left(\begin{array}{r} 0 \\ -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{rrr} -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$

-1, 5, 1, $\left(\begin{array}{rrr} 2 & -2 & 1 \\ -2 & 1 & -2 \\ 1 & -2 & 2 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ 2 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 0 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{6}} \\ \frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{rrr} -\frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right) \right\}$

-1, -1, 5, $\left(\begin{array}{rrr} 1 & -2 & -2 \\ -2 & 1 & 2 \\ -2 & 2 & 1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} -1 \\ 1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right), \left(\begin{array}{rrr} -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$

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

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

-1, -1, -4, $\left(\begin{array}{rrr} -2 & 1 & -1 \\ 1 & -2 & 1 \\ -1 & 1 & -2 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} 1 \\ -1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$

1, -3, 2, $\left(\begin{array}{rrr} 1 & 0 & 2 \\ 0 & 1 & 0 \\ 2 & 0 & -2 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 0 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} -1 \\ 0 \\ 2 \end{array}\right), \left(\begin{array}{r} 2 \\ 0 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} 0 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} -\frac{1}{\sqrt{5}} \\ 0 \\ \frac{2}{\sqrt{5}} \end{array}\right), \left(\begin{array}{rrr} \frac{2}{\sqrt{5}} \\ 0 \\ \frac{1}{\sqrt{5}} \end{array}\right) \right\}$

2, 2, -3, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 1 & -2 \\ 0 & -2 & -2 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 0 \\ -2 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 0 \\ 0 \end{array}\right), \left(\begin{array}{r} 0 \\ 1 \\ 2 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} 0 \\ -\frac{2}{\sqrt{5}} \\ \frac{1}{\sqrt{5}} \end{array}\right), \left(\begin{array}{r} 1 \\ 0 \\ 0 \end{array}\right), \left(\begin{array}{rrr} 0 \\ \frac{1}{\sqrt{5}} \\ \frac{2}{\sqrt{5}} \end{array}\right) \right\}$

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

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

1, 1, 4, $\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{r} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right), \left(\begin{array}{rrr} \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$

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

-1, 2, 4, $\left(\begin{array}{rrr} 2 & 1 & -2 \\ 1 & 1 & 1 \\ -2 & 1 & 2 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 2 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 0 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{6}} \\ \frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right), \left(\begin{array}{rrr} -\frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right) \right\}$

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

1, 1, -5, $\left(\begin{array}{rrr} -1 & 2 & 2 \\ 2 & -1 & -2 \\ 2 & -2 & -1 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 1 \\ 0 \end{array}\right), \left(\begin{array}{r} -1 \\ 1 \\ 1 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right), \left(\begin{array}{rrr} -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right) \right\}$

-2, 4, 4, $\left(\begin{array}{rrr} 2 & -2 & 2 \\ -2 & 2 & 2 \\ 2 & 2 & 2 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -1 \\ -1 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 0 \\ 1 \end{array}\right), \left(\begin{array}{r} -1 \\ 1 \\ 0 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{1}{\sqrt{3}} \\ -\frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{3}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{2}} \\ 0 \\ \frac{1}{\sqrt{2}} \end{array}\right), \left(\begin{array}{rrr} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \\ 0 \end{array}\right) \right\}$

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

3, 2, -3, $\left(\begin{array}{rrr} -2 & 1 & 2 \\ 1 & 2 & 0 \\ 2 & 0 & 2 \end{array}\right)$, $\left\{ \left(\begin{array}{r} 1 \\ 1 \\ 2 \end{array}\right), \left(\begin{array}{r} 0 \\ -2 \\ 1 \end{array}\right), \left(\begin{array}{r} -5 \\ 1 \\ 2 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} \frac{1}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \\ \frac{2}{\sqrt{6}} \end{array}\right), \left(\begin{array}{r} 0 \\ -\frac{2}{\sqrt{5}} \\ \frac{1}{\sqrt{5}} \end{array}\right), \left(\begin{array}{rrr} -\frac{5}{\sqrt{30}} \\ \frac{1}{\sqrt{30}} \\ \frac{2}{\sqrt{30}} \end{array}\right) \right\}$

3, -3, -2, $\left(\begin{array}{rrr} 2 & -2 & -1 \\ -2 & -2 & 0 \\ -1 & 0 & -2 \end{array}\right)$, $\left\{ \left(\begin{array}{r} -5 \\ 2 \\ 1 \end{array}\right), \left(\begin{array}{r} 1 \\ 2 \\ 1 \end{array}\right), \left(\begin{array}{r} 0 \\ -1 \\ 2 \end{array}\right) \right\}$, $\left\{ \left(\begin{array}{r} -\frac{5}{\sqrt{30}} \\ \frac{2}{\sqrt{30}} \\ \frac{1}{\sqrt{30}} \end{array}\right), \left(\begin{array}{r} \frac{1}{\sqrt{6}} \\ \frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{6}} \end{array}\right), \left(\begin{array}{rrr} 0 \\ -\frac{1}{\sqrt{5}} \\ \frac{2}{\sqrt{5}} \end{array}\right) \right\}$