Table 3:

K₆ → K₆

q	q = 0	q = 1	q = 2
${\mathcal{B}}_{q+1}^{6+0}$	$\begin{array}{cc}& \begin{array}{ccccccc}01& 12& 23& 03& 24& 02& 13\end{array}\\ \begin{array}{c}0\\ 1\\ 2\\ 3\\ 4\end{array}& \left[\begin{array}{ccccccc}-1& 0& 0& -1& 0& -1& 0\\ 1& -1& 0& 0& 0& 0& -1\\ 0& 1& -1& 0& -1& 1& 0\\ 0& 0& 1& 1& 0& 0& 1\\ 0& 0& 0& 0& 1& 0& 0\end{array}\right]\end{array}$	$\begin{array}{cc}& \begin{array}{cccc}012& 023& 013& 123\end{array}\\ \begin{array}{c}01\\ 12\\ 23\\ 03\\ 24\\ 02\\ 13\end{array}& \left[\begin{array}{cccc}1& 0& 1& 0\\ 1& 0& 0& 1\\ 0& 1& 0& 1\\ 0& -1& -1& 0\\ 0& 0& 0& 0\\ -1& 1& 0& 0\\ 0& 0& 1& -1\end{array}\right]\end{array}$	${\mathcal{B}}_3^{6+0}$
${\mathcal{B}}_q^6$	$\begin{array}{cc}& \begin{array}{ccccc}0& 1& 2& 3& 4\end{array}\\ /& \left[\begin{array}{ccccc}0& 0& 0& 0& 0\end{array}\right]\end{array}$	$\begin{array}{cc}& \begin{array}{ccccccc}01& 12& 23& 03& 24& 02& 13\end{array}\\ \begin{array}{c}0\\ 1\\ 2\\ 3\\ 4\end{array}& \left[\begin{array}{ccccccc}-1& 0& 0& -1& 0& -1& 0\\ 1& -1& 0& 0& 0& 0& -1\\ 0& 1& -1& 0& -1& 1& 0\\ 0& 0& 1& 1& 0& 0& 1\\ 0& 0& 0& 0& 1& 0& 0\end{array}\right]\end{array}$	${\mathcal{B}}_2^6$
${\mathcal{L}}_q^{6+0}$	$\left[\begin{array}{ccccc}3& -1& -1& -1& 0\\ -1& 2& -1& 0& 0\\ -1& -1& 4& -1& -1\\ -1& 0& -1& 2& 0\\ 0& 0& -1& 0& 1\end{array}\right]$	$\left[\begin{array}{ccccccc}4& 0& 0& 0& 0& 0& 0\\ 0& 4& 0& 0& -1& 0& 0\\ 0& 0& 4& 0& 1& 0& 0\\ 0& 0& 0& 4& 0& 0& 0\\ 0& -1& 1& 0& 2& -1& 0\\ 0& 0& 0& 0& -1& 4& 0\\ 0& 0& 0& 0& 0& 0& 4\end{array}\right]$	${\mathcal{L}}_3^{6+0}$
${\beta }_q^{6+0}$	1	0	0
$\text{dim}\left({\mathcal{L}}_q^{6+0}\right)$	5	7	4
$\text{rank}\left({\mathcal{L}}_q^{6+0}\right)$	4	7	4
$\text{ nullity }\left({\mathcal{L}}_q^{6+0}\right)$	1	0	0
$\text{ Spectra }\left({\mathcal{L}}_q^{6+0}\right)$	{0, 1, 4, 4, 5}	{1, 4, 4, 4, 4, 4, 5}	{4, 4, 4, 4}