text:
\section{Introduction}\label{intro}

\ssec{General remarks} The problem \lq\lq find the inverses of Cartan matrices" might look as a topic of a somewhat boring course work for a first year student taking linear algebra.

However, the explicit answer is needed in a number of situations, so the problem formulated above was solved --- for finite-dimensional simple Lie algebras over $\Cee$ --- long ago, see Dynkin's paper \cite[Ch.1]{D1}. Here are examples where these inverses are used.

$\bullet$ The inverse of the Cartan matrix $A$ (or rather of its transposed, $A^T$)  of a given simple finite-dimensional Lie algebra over $\Cee$ is a tool to obtain the set of \textbf{fundamental weights} from the set of simple roots, see, e.g., \cite[Ch.6, \S 1, Subsect. 10, eq.~(14)]{Bbk}, where \textbf{the result} of using the inverse of $A^T$ is given, \textbf{but not the inverse of $A^T$ itself} (being considered, perhaps, well-known  by that time not only to experts for more than a decade). The inverses of matrices $A^T$ are contained, among other very useful tables, in the book  by Dynkin's former Ph.D. students, see \cite[Table 2]{OV}. Any sufficiently comprehensive textbook on representations of Lie algebras, see, e.g., \cite{Hm}, reproduces the  statement of Bourbaki because the fundamental weights are important:

(1) they form a basis in the weight lattice,

(2) any finite-dimensional irreducible representation of a simple finite-dimensional Lie algebra over $\Cee$ is a direct summand in the tensor product of tensor powers of fundamental representations.

$\bullet$  We found out that we need the results of this paper over fields of positive characteristic in our study of the notions related with the Duflo--Serganova functor, a newly discovered powerful tool in representation theory of Lie superalgebras, see \cite{DS,EAS,KLLS, BGKL}.

$\bullet$  Another natural motivation to invert the Cartan matrices that springs to mind is the fact that the Cartan matrix of $\fsl(n+1)$ is the matrix of the difference operator corresponding to $-(\frac{d}{dx})^2$. Under the name \textit{Toeplitz matrix} $K_n$ it is known to experts in the method of finite differences. Together with the Cartan matrix $T_n$ of the Lie superalgebra $\fosp(1|2n)$, which is the Cartan matrix of $\fsp(2n)$ with the last row divided by 2, these are the invertible two of the \lq\lq four special matrices" (actually, series of matrices) spoken about in \cite[Section~1.1]{Str}. (The two non-invertible of the \lq\lq four special matrices" correspond to an affine Lie algebra and an affine Lie superalgebra, respectively; for the classification of affine Lie (super)algebras, see~\cite{CCLL}.)

$\bullet$  For inverses of \textbf{partial} Cartan matrices, and some examples of their usage, see \cite[Tables A.11--A.13]{Stk}; the inverses of Cartan matrices are also recalled there (Tables A.14--A.15).

$\bullet$  For several  more instances where the  inverses of Cartan matrices of Lie algebras are considered, see the bibliography in \cite{WZ}, and \cite{MOV}. In particular, there is a reference to a paper by Lusztig and Tits which, though interesting, is rather unclear at places, so we give an elucidation.

\ssec{A result due to Lusztig and Tits}
The title of the paper \cite{LT} is misleading  since the paper contains a much stronger result than an already   known one.  Lusztig and Tits  established certain common properties of the inverses of matrices \textit{much more general} than the Cartan matrices of simple finite-dimensional Lie algebras over $\Cee$, see Proposition \ref{LTT} (not explicitly formulated in \cite{LT}, but  follows from a more general statement formulated in \cite{LT}).

Recall that a \textit{forest} is a disjoint union of \textit{trees}, the latter being undirected graphs in which any two vertices are connected by exactly one path. A \textit{graph loop} is an edge going in and out of the same vertex.  A \textit{simple graph} is an unweighted, undirected graph containing no graph loops or multiple edges. For a finite simple graph, the  \textit{adjacency matrix} $A$  is an $n\times n$ matrix, where $n$ is the quantity of vertices,  with 0s on its diagonal and $A_{ij}=A_{ji}=1$ if the $i$th and $j$th vertices are connected. Recall, see \cite{V}, that $B$ is a \textit{main submatrix} of a given matrix $C$ if $B$ is obtained by deleting from $C$ any number of pairs (a row, a column) each pair intersecting on the main diagonal.

Given the \textit{adjacency} (not \textit{incidence}, it is a misprint in \cite{LT}) matrix $A$ of a forest, the matrices $C$ of the same size as $A$ are constructed in \cite{LT}  by replacing any of the diagonal elements and non-zero off-diagonal elements of $A$ with elements in $\Ree$ --- conditions a) and b) in \eqref{LTcon} --- provided two more conditions (c) and d) are met:
\be\label{LTcon}
\begin{minipage}[l]{14cm}
\begin{description}
\item[a)] $C_{ij} = 0 \Longleftrightarrow C_{ji}=0$;
\item[b)] if $i\neq j$, then $A_{ij}=1\Longleftrightarrow C_{ij} \neq 0$;
\item[c)] $C_{ij}\leq 0$ if $i\neq j$;
\item[d)] $\det C>0$ and $\det B>0$ for all main submatrices $B$ of $C$; in parti\-cular, this means that $C_{ii}>0$ for all $i$.\end{description}
\end{minipage}
\ee
More exactly, conditions a) and b) are stronger than the conditions imposed on $C$ in \cite{LT}. Conditions c) and d) (or something equivalent to them)  are implicit in \cite{LT}, but used in the proof of  the following statement (in the form formulated by A.~Lebedev).

\sssbegin{Proposition}[A Corollary of \cite{LT}]\label{LTT}  For any tree, let $A$ be the adjacency matrix; let $C$ be a matrix satisfying conditions \eqref{LTcon}.
Then all elements of  $C^{-1}$ are positive.
\end{Proposition}

\ssec{Two interpretations of $\det C$} For the Cartan matrix $C$ of the simple  finite-dimensional Lie algebra over $\Cee$, we have, see \cite{OV}:
\be\label{LTdet}
\begin{minipage}[l]{14cm}
\begin{description}
\item[a)] $\det C$ is equal to the order of the center of the simply connected compact group corresponding to $C$.
\item[b)] $\det C=|P/Q|$, where $P$ and $Q$ denote the weight lattice and root lattice, respectively.
\end{description}
\end{minipage}
\ee

\ssec{Cartan matrices of hyperbolic Lie algebras and almost affine Lie superalgebras} The Cartan matrix of any hyperbolic Lie algebra is \textit{hyperbolic} if,  its $i$th row and its $i$th column being deleted for any $i$, it becomes the Cartan matrix of the direct sum of finite-dimensional or affine Kac--Moody algebras. For the definition of Lie (super)algebras $\fg(A)$ with Cartan matrix $A$, see \S2; for superization of hyperbolic Lie algebras, called \textit{almost affine} Lie superalgebras, and classification of both types,  see \cite{CCLL}. Recall that a given Lie  \textbf{super}algebra $\fg(A)$ with Cartan matrix $A$ is \textit{almost affine} if it is not finite-dimensional or affine Kac--Moody, but any its main submatrix corresponds to a direct sum of finite-dimensional or affine Kac--Moody superalgebras, \textbf{and all  Cartan matrices of $\fg(A)$ are almost affine}.

For Cartan matrices $C$ of hyperbolic Lie algebras Zhang Hechun \cite{ZH}  established that
\be\label{ZH}
\text{\lq\lq the entries of $C^{-1}$ are \textbf{non-positive} rational numbers".}
\ee

The almost affine Lie superalgebras, except for $NS3_{82}-NS3_{86}$, also have property \eqref{ZH}; this follows from their classification and the explicit form of their Cartan matrices.

Explicit results given in Section ~\ref{AA}, allow us to sharpen the description \eqref{ZH}. We discovered two new phenomena:
\begin{eqnarray}
\text{\textbf{all} elements of the matrices $C^{-1}$ marked $\fbox{!!!}$ in Section ~\ref{AA} are  \textbf{negative};}\label{a}\\
\text{in each of the remaining matrices $C^{-1}$, the 0s occur only on the main diagonal.}\label{b}
\end{eqnarray}

\ssec{Natural generalizations and sharpenings of the problems posed in \cite{WZ}}\label{NP}{}~{}

A) \textbf{For any isotropic reflection $r$ acting on Cartan matrix $A\longmapsto r(A)$, see Subsect.~\ref{refl}, describe an algorithm for the passage $A^{-1}\longmapsto (r(A))^{-1}$.} In other words, find inverses of  not one --- selected by a random criteria (for a description of numerous possibilities in the infinite-dimensional case, see \cite{Eg}) --- Cartan matrix of a given Lie superalgebra $\fg(A)$, but of all its Cartan matrices (for $\dim \fg(A)<\infty$).

B) For the exceptional simple Lie (super)algebras, give the complete explicit answer --- list inverse of all inequivalent Cartan matrices --- in the following two cases:

Ba) for finite-dimensional ones (in any characteristic);

Bb) for hyperbolic Lie algebras and almost affine Lie superalgebras.

C) Investigate what can be said about inverses of Cartan matrices, if exist, for \textbf{various} other types of Lie (super)algebras corresponding to the cases of Vinberg's theorem, see \cite{V, ZH}. \textbf{This problem remains open}.

\subsubsection{Disclamer}\label{Discl} The \lq\lq fundamental weights"
are not as important in the representation theories of modular Lie algebras and of Lie superalgebras (in any characteristic) due to the lack of complete reducibility of their representations, and due to existence of deforms of vacuum (highest or lowest) weight modules, and of modules without vacuum weight vector.

\textbf{However}, even for $p>0$, these fundamental weights are as good as their namesakes over $\Cee$ if we confine ourselves to the \textbf{restricted} representations, the very first (if not the only) ones to be studied from a point of view of the geometer (P.~Deligne, see his Appendix to \cite{LL}).

\ssec{Our results} In Section ~\ref{S3} and formula \eqref{Cinv} we solved Problem A, see Subsection~\ref{NP}: we described an algorithm for the passage $A^{-1}\longmapsto (r(A))^{-1}$, where $r$ is any isotropic reflection.

In Sections~\ref{S4}--\ref{AA} we solved Problem B, see Subsection~\ref{NP}:
we computed the inverses of indecomposable Cartan matrices  for finite-dimensional Lie algebras and Lie superalgebras over fields of positive characteristic as well as for almost affine (hyperbolic) infinite-dimensional complex Lie (super)algebras. (For the classifications of Lie (super)algebras with indecomposable Cartan matrices over $\Cee$ in the almost affine (hyperbolic) case, and finite-dimensional over algebraically closed fields of characteristic $p>0$, see \cite{CCLL} (with prerequisites in  \cite{Se, HS}) and \cite{BGL}, respectively.)

We have discovered phenomena \eqref{a} and \eqref{b}.
We have discovered that the determinants of inequivalent Cartan matrices of the  simple  Lie (super)algebra may differ (in any characteristic).

For the serial Lie superalgebras, the inverses of Cartan matrices are explicitly given for certain \lq\lq basic" Cartan matrices from which all the other Cartan  matrices of the given Lie superalgebra are obtained by means of isotropic (odd) reflections as explained in Subsection~\ref{refInv}.

We also corrected and widened the list of references (and the range of applications) of inverses of Cartan matrices as compared with those given in \cite{WZ}, e.g., the explicit form of inverse Cartan matrices of finite-dimensional simple  Lie algebras is reproduced in  \cite{WZ} as if new, though well-known, see \cite{D1,OV, Stk}. These omissions and the desire to solve the problem considered, but not solved, in  \cite{WZ}, except for occasional coincidences of Cartan matrices with Gram matrices of non-degenerate invariant symmetric bilinear forms (NISes) on the (super)algebras considered, is what prompted our work.

\subsubsection{Open questions} 1) How to explain newly found phenomena \eqref{a} and \eqref{b}?

2) In characteristic $p>0$, the determinants of Cartan matrices of exceptional simple Lie superalgebras are mostly equal to 1, but not always; over $\Cee$, we see that these determinants are \textbf{different} for inequivalent Cartan matrices of the same Lie superalgebra. What is the meaning of these determinants?

3) How to interpret the determinants of the matrices described in Proposition \ref{LTT}; the determinants of the Cartan matrices of hyperbolic Lie algebras, and almost affine Lie superalgebras, cf. with properties~\eqref{LTdet}?

\subsubsection{Remark} V.~Kac was the first to realize that certain finite-dimensional Lie superalgebras have analogs of Cartan matrices and defined them imitating the definition for Lie algebras, compare \cite{K} with \cite{Kapp}, where the exceptional simple Lie superalgebras first appeared. In these cases, V.~Kac listed the indecomposable Cartan matrices (with a gap, corrected in \cite{Se, vdL}, where infinite-dimensional generalizations with symmetrizable Cartan matrices were also considered). For further improvements of the definitions, see  \cite{HS, CCLL, BGL}.

In \cite{WZ}, the Gram matrices of the non-degenerate symmetric bilinear form on the space of roots, that never explicitly appeared before, but can be recovered from the data in \cite{Se1}, or by symmetrizing Cartan matrices, were misattributed to works of V.~Kac and called \textit{Cartan matrices}. Kac never used such matrices (and would hardly apply the term \textit{Cartan matrix} to a matrix with both 2 and $-2$  appearing simultaneously on the main diagonal). Analogs of Cartan matrices $A$ with $A_{ii}\leq 0$ were introduced by Borcherds, see \cite{B, R} and references in \cite{CCLL}.

\section{Chevalley generators, Cartan matrices, reflections (from \cite{CCLL, BGL})}\label{S2}

\ssec{Chevalley generators and Cartan matrices} Let us start with the construction of Lie
(super)algebras with Cartan matrix. Let $A=(A_{ij})$ be an $n\times n$-matrix
whose entries lie in the ground field $\Kee$. Let $\rk
A=n-l$. It means that there exists an $l\times n$-matrix
$T=(T_{ij})$ such that
\begin{equation}\label{rankCM}
\begin{tabular}{l}
a) the rows of $T$ are linearly independent;\\
b) $TA=0$ (or, more precisely, ``zero $l\times n$-matrix'').
\end{tabular}
\end{equation}
Indeed, if $\rk A^T=\rk A=n-l$, then there exist $l$ linearly
independent vectors $v_i$ such that $A^Tv_i=0$; set
\[
T_{ij}=(v_i)_j.
\]

Let the elements $e_i^\pm$ and $h_i$, where $i=1,\dots,n$, generate
a Lie superalgebra denoted $\fG(A, I)$, where $I=(p_1, \dots
p_n)\in(\Zee/2)^n$ is a collection of parities ($p(e_i^\pm)=p_i$),
free except for the relations
\begin{equation}\label{gArel_0}
{}[e_{i}^+, e_{j}^-] = \delta_{ij}h_i; \quad [h_j, e_{j}^\pm]=\pm
A_{ij}e_{j}^\pm\text{~~and~~}[h_i, h_j]=0 \text{~~for any $i, j$}.
\end{equation}
Let Lie (super)algebras with Cartan matrix $ \fg(A,
I)$ be the quotient of $\fG(A, I)$ modulo
the ideal explicitly described in \cite{GL, BGL3, BGLL}.

By abuse of notation we denote by $e_j^\pm$ and $h_j$ ---
the elements of $\fG(A,I)$
--- also their images in $\fg(A,I)$ and $\fg^{(i)}(A,I)$ and call these images, and their pre-images, the \textit{Chevalley generators} of $\fG(A,I)$, $\fg(A,I)$, and $\fg^{(i)}(A,I)$, cf. Subsection~\ref{SsChev}.

\subsubsection{In small font} The additional to \eqref{gArel_0} relations that turn $\fG(A,
I)$ into $\fg(A, I)$ are of the form $R_i=0$ whose left sides are
implicitly described, for the general Cartan matrix with entries in
$\Kee$, as
\begin{equation}\label{myst}
\text{\begin{minipage}[c]{14cm} the $R_i$ that generate the ideal
$\fr$ maximal among the ideals of $\fG (A, I)$ whose
intersection with the span of the above $h_i$ and the $d_j$
described in eq. \eqref{central3} is zero.\end{minipage}}
\end{equation}

Set
\begin{equation}\label{central}
c_i=\mathop{\sum}\limits_{1\leq j\leq n} T_{ij}h_j, \text{~~where~~}
i=1,\dots,l.
\end{equation}
Then, from the properties of the matrix $T$, we deduce that
\begin{equation}\label{central1}
\begin{tabular}{l}
a) the elements $c_i$ are linearly independent;\\
b) the elements $c_i$ are central, because\\
$[c_i,e_j^\pm]=\pm\left(\sum\limits_{1\leq k\leq n} T_{ik}A_{kj}\right)
e_j^\pm=\pm (TA)_{ij} e_j^\pm $.
\end{tabular}
\end{equation}
The existence of central elements means that the linear span of all
the roots is of dimension $n-l$ only. (This can be explained even
without central elements: The weights can be considered as
column-vectors whose $i$-th coordinates are the corresponding
eigenvalues of $\ad_{h_i}$. The weight of $e_i$ is, therefore, the
$i$-th column of $A$. Since $\rk A=n-l$, the linear span of all
columns of $A$ is $(n-l)$-dimensional just by definition of the
rank. Since any root is an (integer) linear combination of the
weights of the $e_i$, the linear span of all roots is
$(n-l)$-dimensional.)

This means that some elements which we would like to see having
different (even opposite if $p=2$) weights, actually,  have identical
weights. To remedy this, we do the following: let $B$ be an arbitrary
$l\times n$-matrix such that
\begin{equation}\label{matrixB}
\text{the~~}(n+l)\times
n\text{-matrix~~}\begin{lmatrix}A\\B\end{lmatrix}\text{~~has
rank~}n.
\end{equation}
Let us add to the algebra $\fg=\fG(A, I)$ (and hence $\fg(A,
I)$) the grading elements $d_i$, where $i=1,\dots,l$, subject to the
following relations:
\begin{equation}\label{central3}
{}[d_i,e_j^\pm]=\pm B_{ij}e_j;\quad [d_i,d_j]=0;\quad [d_i,h_j]=0
\end{equation}
(the last two relations mean that the $d_i$ lie in the Cartan
subalgebra, and even in the maximal torus which will be denoted by
$\fh$).

Note that these $d_i$ are \textit{outer} derivations of $\fg(A,
I)^{(1)}$, i.e., they can not be obtained as linear combinations of
brackets of the elements of $\fg(A, I)$ (i.e., the $d_i$ do not lie
in $\fg(A, I)^{(1)}$).

\ssec{Roots and weights}\label{roots} In this subsection, $\fg$
denotes one of the algebras $\fg(A,I)$ or $\fG(A,I)$.

Let $\fh$ be the span of the $h_i$ and the $d_j$. The elements of
$\fh^*$ are called \textit{weights}.\index{weight} For a given
weight $\alpha$, the \textit{weight subspace} of a given
$\fg$-module $V$ is defined as
\[
V_\alpha=\{x\in V\mid \text{an integer $N>0$ exists such that
$(\alpha(h)-\ad_h)^N x=0$ for any $h\in\fh$}\}.
\]

Any non-zero element $x\in V$ is said to be \textit{of weight
$\alpha$}. For the roots, which are particular cases of weights if
$p=0$, the above definition is inconvenient because it does not lead
to the modular analog of the following useful statement.

\sssbegin{Statement}[\cite{K}]\label{rootdec} Over $\Cee$, the space
of any Lie algebra $\fg$ can be represented as a direct sum of
subspaces
\begin{equation}\label{rootdeceq}
\fg=\mathop{\bigoplus}\limits_{\alpha\in \fh^*} \fg_\alpha.
\end{equation}
\end{Statement}
Note that if $p=2$, it might happen that $\fh\subsetneq\fg_0$. (For
example, all weights of the form $2\alpha$ over $\Cee$ become 0 over
$\Kee$.)

To salvage the formulation of Statement in the modular case with
minimal changes, \textit{at least for the Lie (super)algebras $\fg$ with
Cartan matrix} --- and only this case we will have in mind speaking
of roots, we decree that the elements $e_i^\pm$ with the same
superscript (either $+$ or $-$) correspond to linearly independent
\textit{roots} $\alpha_i$, and any root $\alpha$ such that
$\fg_\alpha\neq 0$ lies in the $\Zee$-span of
$\{\alpha_1,\dots,\alpha_n\}$, i.e.,
\begin{equation}\label{rootdeceqnew}
\fg=\mathop{\bigoplus}\limits_{\alpha\in
\Zee\{\alpha_1,\dots,\alpha_n\}} \fg_\alpha.
\end{equation}

Thus, $\fg$ has a $\Ree^n$-grading such that $e_i^\pm$ has grade
$(0,\dots,0,\pm 1,0,\dots,0)$, where $\pm 1$ stands in the $i$-th
slot (this can also be considered as $\Zee^n$-grading, but we use
$\Ree^n$ for simplicity of formulations). If $p=0$, this grading is
equivalent to the weight grading of $\fg$. If $p>0$, these gradings
may be inequivalent; in particular, if $p=2$, then the elements
$e_i^+$ and $e_i^-$ have the same weight. (That is why in what
follows we consider roots as elements of $\Ree^n$, not as weights.)

Any non-zero element $\alpha\in\Ree^n$ is called \textit{a
root}\index{root} if the corresponding eigenspace of grade $\alpha$
(which we denote $\fg_\alpha$ by abuse of notation) is non-zero. The
set $R$ of all roots is called \textit{the root system}\index{root
system} of $\fg$.

Clearly, the subspaces $\fg_\alpha$ are purely even or purely odd,
and the corresponding roots are said to be \textit{even} or
\textit{odd}.

\ssec{Systems of simple and positive roots} In this subsection,
$\fg=\fg(A,I)$, and $R$ is the root system of $\fg$.

For any subset $B=\{\sigma_{1}, \dots, \sigma_{m}\} \subset R$, we
set (we denote by $\Zee_{+}$ the set of non-negative integers):
\[
R_{B}^{\pm} =\{ \alpha \in R \mid \alpha = \pm \sum n_{i}
\sigma_{i},\;\text{where }\;n_{i} \in \Zee_{+} \}.
\]
The set $B$ is called a \textit{system of simple roots~}\index{Root!
simple system of}\; of $R$ (or $\fg$) if $ \sigma_{1}, \dots ,
\sigma_{m}$ are linearly independent and $R=R_B^+\cup R_B^-$. Note
that $R$ contains basis coordinate vectors, and therefore spans
$\Ree^n$; thus, any system of simple roots contains exactly $n$
elements.

A subset $R^+\subset R$ is called a \textit{system of positive
roots~}\index{Root! positive system of}\; of $R$ (or $\fg$) if there
exists $x\in\Ree^n$ such that
\begin{equation}\label{x}
\begin{split}
 &(\alpha,x)\in\Ree\backslash \{0\}\text{ for all $\alpha\in R$},\\
 &R^+=\{\alpha\in R\mid (\alpha,x)>0\}.
\end{split}
\end{equation} (Here $(\cdot,\cdot)$ is the standard Euclidean inner
product in $\Ree^n$.) Since $R$ is a finite (or, at least, countable
if $\dim \fg(A)=\infty$) set, so the set
\[\{y\in\Ree^n\mid\text{there exists $\alpha\in R$ such that }
(\alpha,y)=0\} \] is a finite/countable union of $(n-1)$-dimensional
subspaces in $\Ree^n$, so it has zero measure. So for almost every
$x$, condition (\ref{x}) holds.

By construction, any system $B$ of simple roots is contained in
exactly one system of positive roots, which is precisely $R_B^+$.

\sssbegin{Statement} Any finite system $R^+$ of positive roots of
$\fg$ contains exactly one system of simple roots. This system
consists of all the positive roots \textup{(i.e., elements of $R^+$)} that
can not be represented as a sum of two positive
roots.\end{Statement}

We can not give an \textit{a priori} proof of the fact that each set
of all positive roots each of which is not a sum of two other
positive roots consists of linearly independent elements. This is,
however, true for finite dimensional Lie algebras and Lie
superalgebras of the form $\fg(A)$ if $p\neq 2$.

\ssec{Normalization convention}\label{normA} Clearly,
\begin{equation}
\label{rescale} \text{the rescaling
$e_i^\pm\mapsto\sqrt{\lambda_i}e_i^\pm$, sends $A$ to $A':=
\diag(\lambda_1, \dots , \lambda_n)\cdot A$.}
\end{equation}

Two pairs $(A, I)$ and $(A', I')$ are said to be \textit{equivalent}
if $(A', I')$ is obtained from $(A, I)$ by a composition of a
permutation of parities and a rescaling $A' = \diag (\lambda_{1},
\dots, \lambda_{n})\cdot A$, where $\lambda_{1}\dots \lambda_{n}\neq
0$. Clearly, equivalent pairs determine isomorphic Lie
superalgebras.

The rescaling affects only the matrix $A_B$, not the set of parities
$I_B$. The Cartan matrix $A$ is said to be
\textit{normalized}\index{Cartan matrix, normalized} if
\begin{equation}
\label{norm} A_{jj}=0\text{~~ or 1, or 2.}
\end{equation}
We let $A_{jj}=2$ only if $i_j=\ev$; in order to eliminate possible confusion, we write $A_{jj}=\ev$ or
$\od$ if $i_j=\ev$, whereas if $i_j=\od$, we write $A_{jj}=0$ or
$1$.

Normalization conditions correspond to the \lq\lq natural" Chevalley generators of the most usual \lq\lq building blocks" of finite-dimensional Lie (super)algebras with Cartan matrix: $\fsl(2)$ if $A_{jj}=2$, $\fsl(1|1)$ if $A_{jj}=0$, and $\fosp(1|2)$ if $A_{jj}=1$, respectively. (In this paper we do not need $A_{jj}=\ev$ or
$\od$, see \cite{BGL,CCLL}.)

\textbf{We will only consider
normalized Cartan matrices; for them, we do not have to indicate the set of parities
$I$.}

\subsubsection{Warning}\label{War} Unlike the case of simple finite-dimensional Lie algebras over $\Cee$, where the normalized Cartan matrix $A$ is uniquely defined, generally this is not so: each row with a 0 or $\ev$ on the main diagonal can be multiplied by
any nonzero factor; usually (not only in this paper) we multiply the
rows so as to make $A_{B}$ symmetric, if possible. Which version of the Cartan matrix should be considered as its \lq\lq normal form"? The defining relations give the answer:

The normalized Cartan matrix is used, for example, to describe presentation of the given Lie superalgebra (relations between, or rather \textit{among}\footnote{Because analogs of the Serre relations in the super setting involve \textit{several} generators, see \cite{GL, BGL, BGLL}.} the Chevalley generators).

\ssec{Equivalent systems of simple roots} \label{EqSSR} Let
$B=\{\alpha_1,\dots,\alpha_n\}$ be a system of simple roots. Choose
non-zero elements $e_i^\pm$ in the 1-dimensional (by definition)
superspaces $\fg_{\pm\alpha_i}$; set $h_{i}=[e_{i}^{+}, e_{i}^-]$,
let $A_{B} =(A_{ij})$, where the entries $A_{ij}$ are recovered from
relations \eqref{gArel_0}, and let $I_{B}=\{p(e_{1}), \cdots,
p(e_{n})\}$. Lemma \ref{serg} claims that all the pairs $(A_B,I_B)$
are equivalent to each other.

Two systems of simple roots $B_{1}$ and $B_{2}$ are said to be
\textit{equivalent} if the pairs $(A_{B_{1}}, I_{B_{1}})$ and
$(A_{B_{2}}, I_{B_{2}})$ are equivalent.

It would be nice to find a convenient way to fix some distinguished
pair $(A_B,I_B)$ in the equivalence class. For the role of the
``best'' (first among equals) order of indices we propose the one
that minimizes the value
\begin{equation}\label{minCM}
\max\limits_{i,j\in\{1,\dots,n\}\text{~such that~}(A_B)_{ij}\neq
0}|i-j|
\end{equation}
(i.e., gather the non-zero entries of $A$ as close to the main
diagonal as possible). Observe that this numbering differs from the
one that Bourbaki use for the $\fe$ type Lie algebras.

\subsubsection{Chevalley generators and Chevalley bases}\label{SsChev} We
often denote the set of generators of $\fg(A,I)$ and $\fg^{(i)}(A,I)$ corresponding to a normalized
Cartan matrix by $X_{1}^{\pm},\dots , X_{n}^{\pm}$ instead of
$e_{1}^{\pm},\dots , e_{n}^{\pm}$; and call these generators, together with the
elements $H_i:=[X_{i}^{+}, X_{i}^{-}]$, and the derivations $d_j$,
see~\eqref{central3}, the \textit{Chevalley
generators}.\index{Chevalley generator}

For $p=0$ and normalized Cartan matrices of simple finite
dimensional Lie algebras, there exists only one (up to signs) basis
containing $X_i^\pm$ and $H_i$ in which $A_{ii}=2$ for all $i$ and
all structure constants are integer, cf. \cite{St}. Such a basis is
called the \textit{Chevalley}\index{Basis! Chevalley}  basis.

Observe that, having normalized the Cartan matrix of $\fsp(2n)$ so
that $A_{ii}=2$ for all $i\neq n$, but $A_{nn}=1$, we get
\textbf{another} basis with integer structure constants. We think
that this basis also qualifies to be called \textit{Chevalley
basis}; for Lie superalgebras, and if $p=2$, such normalization is a
must.

\begin{Conjecture} If $p>2$, then for finite dimensional Lie
(super)algebras with indecomposable Cartan matrices normalized as in
$(\ref{norm})$, there also exists only one (up to signs) analog of
the Chevalley basis. \end{Conjecture}

From \cite{BGL}: \lq\lq We had no idea how to describe analogs of Chevalley bases for $p=2$
until recently; it seems, the methods of the recent paper \cite{CR}
should solve the problem." (Now, more than a decade ago, \textbf{this problem is still open}.)

\ssec{Reflections}\label{refl} Let $R^+$ be a system of positive roots of Lie
superalgebra $\fg$ over a field $\Kee$ of characteristic $p>0$, and let $B=\{\sigma_1,\dots,\sigma_n\}$ be the
corresponding system of simple roots with some corresponding pair
$(A=A_B,I=I_B)$. Then for any $k\in \{1, \dots, n\}$, the set
$(R^+\backslash\{\sigma_k\})\coprod\{-\sigma_k\}$ is a system of
positive roots. This operation is called \textit{the reflection in
$\sigma_k$}; it changes the system of simple roots by the formulas
\begin{equation}
\label{oddrefl}
r_{\sigma_k}(\sigma_{j})= \begin{cases}{-\sigma_j}&\text{if~}k=j,\\
\sigma_j+B_{kj}\sigma_k&\text{if~}k\neq j,\end{cases}\end{equation}
where
\begin{equation}
\label{Boddrefl} B_{kj}=\begin{cases}
-\displaystyle\frac{2A_{kj}}{A_{kk}}& \text{~if~}A_{kk}\neq
0,\ev\text{~and~}
-\displaystyle\frac{2A_{kj}}{A_{kk}}\in \Zee/p\Zee,\\
p-1&\text{~if~}A_{kk}\neq 0, \ev\text{~and~}
 -\displaystyle\frac{2A_{kj}}{A_{kk}}\not\in \Zee/p\Zee,\\
&\text{~or~} A_{kk}=\ev\text{~(and hence~}i_k=\ev), \; A_{kj}\neq 0,\\
1&\text{~if~}i_k=\od, A_{kk}=0,A_{kj}\neq 0,\\
0&\text{~if~} A_{kk}=A_{kj}=0,
\end{cases}
\end{equation}
where we consider $\Zee/p\Zee$ as a subfield of $\Kee$.

The name ``reflection'' is used because in the case of simple
finite-dimensional complex Lie algebras this action, extended on the whole
$R$ by linearity, is a map from $R$ to $R$, and it does not depend on
$R^+$, only on $\sigma_k$. This map is usually denoted by
$r_{\sigma_k}$ or just $r_{k}$. The map $r_{\sigma_k}$ extended to
the $\Ree$-span of $R$ is reflection in the hyperplane orthogonal to
$\sigma_k$ relative the bilinear form dual to the Killing form.

The reflections in the even (odd) roots are referred to as
\textit{even} (\textit{odd}) \textit{reflections}.\index{Reflection!
odd}\index{Reflection! even! non-isotropic} \index{Reflection! even!
isotropic} A simple root is called \textit{isotropic}, if the
corresponding row of the Cartan matrix has zero on the diagonal, and
\textit{non-isotropic} otherwise. The reflections that correspond to
isotropic or non-isotropic roots will be referred to accordingly.

If there are isotropic simple roots, the reflections $r_\alpha$ do
not, as a rule, generate a version of the \textit{Weyl group}
because the product of two reflections in nodes not connected by one
(perhaps, multiple) edge is not defined. These reflections just
connect a pair of ``neighboring'' systems of simple roots and there is
no reason to expect that we can multiply such two distinct
reflections. In  the case of modular Lie algebras or
of Lie superalgebras for any $p$,
the action of a given isotropic reflection (\ref{oddrefl}) can not,
generally, be extended to a linear map $R\tto R$. For Lie
superalgebras over $\Cee$, one can extend the action of reflections
by linearity to the root lattice, but this extension preserves the
root system only for $\fsl(m|n)$ and $\fosp(2m+1|2n)$, cf.
\cite{Se1}.

We would like to draw attention of the reader to an under-appreciated paper \cite{SkB}, where the analog of Weyl group for $\fbr(3)$ was considered.

\ssec{How reflections act on Chevalley generators}
If $\sigma_i$ is an isotropic root, then the corresponding
reflection $r_i$ sends one set of Chevalley generators into a new one:
\begin{equation}
\label{oddrefx} \tilde X_{i}^{\pm}=X_{i}^{\mp};\;\;
\tilde X_{j}^{\pm}=\begin{cases}[X_{i}^{\pm},
X_{j}^{\pm}]&\text{if $A_{ij}\neq 0, \ev$},\\
X_{j}^{\pm}&\text{otherwise}.\end{cases}
\end{equation}

The Cartan matrix $r_i(A)$ corresponding to the Chevalley generators  \eqref{oddrefx} should be obtained as described above: set
\[
\tilde H_i:=[\tilde X_{i}^+, \tilde X_{i}^-]
\]
and compute
\[
[\tilde H_i, \tilde X_{j}^+]=\tilde B_{ij}\tilde X_{j}^+.
\]
Normalize the matrix $\tilde B$ as we agreed, see Subsection~\ref{normA}; let $B$ be the normalized matrix.
Then $r_i(A):=B=(B_{kl})$.

\subsubsection{Lebedev's lemma} Serganova \cite{Se}
proved (for $p=0$) that there is always a chain of
reflections connecting $B_1$ with some system of simple roots $B'_2$
equivalent to $B_2$ in the sense of definition in Subsection~\ref{refl}. Here is
the modular version of this statement due to Serganova.

\begin{Lemma}[Lebedev, unpublished]\label{serg} For any two systems of simple roots
$B_1$ and $B_2$ of any finite dimensional Lie superalgebra with
indecomposable Cartan matrix, there is always a chain of reflections
connecting $B_1$ with $B_2$.\end{Lemma}

\subsubsection{Important convention}\label{sssIC}
The values $-\frac{2A_{kj}}{A_{kk}}$ in \eqref{Boddrefl} are
elements of $\Kee$, while the roots are elements of a vector space
over $\Ree$. Therefore these expressions in the first case in
\eqref{Boddrefl} \textbf{should be understood} as ``\textbf{the smallest
non-negative integer congruent to} $-\nfrac{2A_{kj}}{A_{kk}}$''.

This convention is important in describing Serre relations and their analogs for $p>0$, see \cite{BGLL}. \textbf{We do not know yet what is an equally \lq\lq natural" (or correct) way of presenting the elements of the inverse Cartan matrices.}

There is known just one case where the convention should be modified: if $p=2$ and $A_{kk}=A_{jk}$,
then the expression $-\frac{2A_{jk}}{A_{kk}}$ \textbf{should be understood}
as $2$, not 0. (If $\dim\fg<\infty$, the expressions
$-\frac{2A_{jk}}{A_{kk}}$ are always congruent to integers.)

\subsubsection{How reflections act on Cartan matrices ([CCLL])}\label{refInv} Let $A$ be a Cartan matrix of size $n$ and $I = (p_1,\ldots , p_n)$ the vector of parities. If $p_k = \od$ and $A_{kk} = 0$, then the reflection  in the $k$th simple odd root sends $A$ to $r_k( A)$, where
\be\label{oddR}
(r_k(A))_{i j} = A_{i j} + b_i A_{k j} + c_j A_{i k},
\ee
and where (for $p\neq 2$)
\[
b_i = \begin{cases}-2&\text{if $i = k$},\\
0&\text{if $i\neq k$ and $A_{ik} = 0$,}\\
\frac{A_{ik}}{A_{ki}}&\text{if $i\neq k$ and $A_{ik} \neq 0$;}\\
\end{cases}\quad
\text{~~
 and ~~}\quad c_j = \begin{cases}-2&\text{if $j = k$},\\
 0&\text{if $j\neq k$ and $A_{jk} = 0$,}\\
1&\text{if $j\neq k$ and $A_{jk} \neq 0$.}\\
\end{cases}
\]
This can be expressed in terms of matrices as
\[
r_k(A) =(E+B)A(E+C),
\]
where all columns of the matrix $B$, except the $k$th one, are zero, whereas the $i$th coordinate of the $k$th column-vector is $b_i$, the $i$th coordinate of the $k$th row-vector of $C$ is $c_i$, the other rows of $C$ being zero; $E$ is the unit matrix. Therefore, $B^2=C^2=0$, and
\be\label{Cinv}
(r_k(A) )^{-1} =(E-C)A^{-1}(E-B).
\ee

The reflected matrix $r_k( A)$ might have to be normalized; the new parities are
\[
\widetilde p_j \equiv p_j + c_j \pmod 2.
\]

\section{The matrices considered in \cite{WZ}  are not Cartan matrices}\label{sNotCM}

For any simple finite-dimensional Lie algebra over $\Cee$, we know  two ways to introduce its Cartan matrix $A=(A_{ij})$.

\textbf{First approach}:
take $3n$ Chevalley generators and compute $[h_i, e_j^{\pm}]=\pm A_{ij}e_j^{\pm}$, see~\eqref{gArel_0}.

\textbf{Second approach}:  take an auxiliary space --- the space spanned by the roots or, sometimes, a bit larger space, see tables in \cite{Bbk, OV}; for $\fsl(V)$, this auxiliary space is the space $V$ or its dual. Let it be spanned by column-vectors $\eps_i:=(0,\dots, 0,1,0\dots, 0)^T$ with a 1 on the $i$th place.

Assume that there is a~ Euclidean inner product on $V$ given by
\be\label{inProdRoot}
(\eps_i, \eps_j)=\delta_{ij}.
\ee
The Gram matrix of this inner product in the basis of simple roots is precisely the Cartan matrix of $\fsl(V)$.
This inner product in the  space spanned by roots is induced by the restriction of the Killing form from $\fsl(V)$ on the maximal torus, i.e., the space of coroots. For the Lie algebras of series $\fsl$, $\fo$ and $\fsp$, this inner product can be also defined by means of the form proportional to the Killing form, but much easier to compute:
\[
(X, Y)=\tr(XY)\text{~~for any $X,Y\in \fsl(V)$}.
\]
The above description yields the Gram matrix of a nondegenerate invariant symmetric bilinear form
on the Lie algebras whose roots are of equal length. For the simple Lie algebras whose roots are of different lengths, the matrix thus obtained is a symmetrization of the Gram matrix, see \cite{BKLS}.

Passing to the Lie superalgebras, we can also follow either of these two procedures. The \textbf{first approach} does indeed lead to Cartan matrices, as described in the beginning of this section.

The \textbf{second approach} uses  a basis of the superspace $V$, such that the vectors $\eps_i$ span $V_\ev$, while the vectors $\delta_j$ span $V_\od$, with the pseudo-Eucledian inner product
\be\label{inProdSRoot}
(\eps_i, \eps_j)=\delta_{ij};\ \  (\eps_i, \delta_j)=0\text{~~for any $i,j$};\ \
(\delta_i, \delta_j)=-\delta_{ij}.
\ee
For the Lie superalgebras $\fgl(V)$ and $\fpsl(V)$, this inner product is induced by the supertrace
\[
(X, Y)=\str(XY)\text{~~for any $X,Y\in \fsl(V)$};
\]
it is non-degenerate for any $V$, whereas the Killing form is degenerate if $\dim V_\ev=\dim V_\od$.

Serganova ( \cite{Se1}) showed that a natural generalization of the axioms of root systems to the case of pseudo-Euclidean inner product leads precisely to the root systems of Lie superalgebras with indecomposable Cartan matrices and their simple relatives over $\Cee$, see \cite{CCLL}.

It seems that the Gram matrix of this inner product in the basis of simple roots  first appeared in \cite{WZ}: Serganova never wrote it explicitly for any Lie superalgebra. For Lie superalgebras, no Gram matrix of the above inner product in the root space of $\fg$ is equivalent (in any conventional way) to any Cartan matrix of $\fg$, except for $\fosp(1|2n)$. However,
\be\label{SergInv}
\begin{minipage}[l]{13.5cm}
\textit{For the root space of $\fg=\fsl(m+1|n+1)$, the Gram matrix of the above inner product calculated in the standard supermatrix format of $\fg$ turns into the Cartan matrix \eqref{slmn} if its bottom $n+1$ rows are multiplied by $-1$}.
\end{minipage}
\ee

\subsection{Remark} To describe defining relations of $\fg(A)$ in terms of Chevalley generators, we need the Cartan matrix $A$ corresponding to the selected supermatrix format of elements of $\fg(A)$, see \cite{GL}, not the Gram matrix of the inner product in the space spanned by roots.

When we learn what the inverse of any of these Gram matrices is needed for, we will probably have to compute it in just one basis: the NIS on a simple finite-dimensional Lie superalgebra of characteristic $\neq 2$ is unique, up to a proportionality; for a recipe for constructing NIS from the Cartan matrix, see \cite{BKLS}; the Gram matrix of its restriction onto the space spanned by the $h_i$ is the dual of the Gram matrix of the inner product on the space spanned by roots.

\section{Finite-dimensional serial Lie (super)algebras over $\Cee$}\label{S3}

\ssbegin{Remark}\label{Rem} Remember that the Cartan matrix with a 0 on the main
diagonal is not uniquely defined: the line with this 0 can be multiplied by any non-zero number, e.g., by a $-1$, see Subsection~\ref{War}. For any invertible matrix, its inverse is uniquely defined, of course.
\end{Remark}

For the series $\fsl$ and $\fosp$, there are 9 types of pairs of \lq\lq basic" Cartan matrices connected by odd reflections, see \cite[Subsection 4.1, Table 1]{CCLL}. From one such Cartan matrix all the other Cartan  matrices of the given Lie superalgebra of the given type are obtained by means of odd reflections, see~\eqref{oddR}.   It is a matter of taste which one in the pair of \lq\lq basic"  matrices  is most simple; we selected (any) one  with the smallest number of 0s on the main diagonal.

In \cite{WZ}, Gram matrices are inverted;  this sometimes gives the answer for the Cartan matrices as well, thanks to the fact \eqref{SergInv}. However, inverting Cartan matrices of the $\fsl$ cases, we have to consider 2 more types of cases as compared with \cite{WZ}; for the $\fosp$ series, we have to consider 7 types of cases, not 3 as in \cite{WZ}.

Let $A_m$ denote the normalized Cartan matrix of $\fsl(m+1)$.  Below, in formulas \eqref{sl}--\eqref{osp6}, instead of $A_m$ there can be  any Cartan matrix of $\fsl(a|b)$ with $a+b=m+1$. To derive the explicit expression of the inverse matrix $C^{-1}$ in this general case, apply an odd reflection ~\eqref{Cinv}.

\ssec{The case of $\fsl$} For $\fsl(m+1|1)$, the \lq\lq basic"  Cartan matrix and its inverse \eqref{sl} is a particular cases of the expression ~\eqref{slmn}, up to an occasional minus sign, see Remark~\ref{Rem}.

\be\label{sl}\tiny{
\mleft(
\begin{array}{c|c}
 A_m & \begin{array}{c}\vdots \\
  0\\
  -1\end{array}\\
  \hline
\dots 0 1 &0
\end{array}
\mright)
^{-1}=-\nfrac{1}{m}
L_1, } \text{~~\normalfont{see \eqref{L123} for $n=0$.}}
\ee

For $\fsl(m+1|n+1)$, where $mn\neq 0$, there are 2 \lq\lq basic"  types of Cartan matrices, see \eqref{slmn} and \eqref{slmn2}:
\be\label{slmn}\tin
 A_{m,0,n}^{-1} :=\mleft(
\begin{array}{c|c|c}
 A_m & \begin{array}{c}
  \vdots \\
  0\\
  -1\end{array}&0\\
  \hline
 \dots 0 -1 &0&1 0 \dots\\
 \hline
0& \begin{array}{c}
  -1 \\
  0\\
 \vdots\end{array}&A_n\\
\end{array}
\mright)^{-1}=\nfrac{1}{n-m}\smat{
L_1&L_2\\
L_2^T&L_4\\
},
\ee
where, as shown in \cite{WZ}, $L_1$ and $L_4$ are  $(m+1)\times (m+1)$ and $n\times n$ matrices, respectively, defined, together with $L_2$, by the following formulas
\be\label{L123}
\begin{array}{l}
(L_1)_{ij} = ij+(n-m)\min\{i,j\},\\
(L_2)_{ij} = i(n+1-j),\\
(L_4)_{ij} =(n-m)\min\{i,j\}-(m+1)(n+1-i-j)+ij.\\
\end{array}
\ee

To invert the Cartan matrix of the other type, namely \eqref{slmn2}, we set
\be\label{KW}
\text{$\tau_{n}:=A_{n}-\alpha$,  where $\alpha :=
\begin{pmatrix}
1 & 0 \\
0 & 0_{n-1}
\end{pmatrix}$}.\ee

Let us transform $M\mapsto N$, where
\be\label{slmn2}\tin
M:=A_{m,00,n} :=\mleft(
\begin{array}{c|c|c}
A_{m-1} & \begin{array}{cc}
  \vdots &\vdots\\
  0&0\\
  -1& 0\end{array}&0\\
  \hline
 \begin{array}{ccc}
 \dots& 0 &-1 \\
  \dots &0 &0\\
 \end{array}
 &  \begin{array}{cc}
0&1\\
-1 &0\\
\end{array}&
\begin{array}{ccc}
0 &0&\dots \\
 1&0&\dots\\
 \end{array}\\
 \hline
0& \begin{array}{cc}
  -1& 0\\
  0&0\\
\vdots& \vdots\end{array}&A_n\\
\end{array}
\mright)
\ee
and
\begin{equation*}\label{slmn21}\tiny
N:=\left(
\begin{array}{c|c|c}
A_{m-1} &
\begin{array}{cc}
\vdots  & \vdots  \\
0 & 0 \\
-1 & 0%
\end{array}
& 0 \\ \hline
\begin{array}{ccc}
\dots  & 0 & 0 \\
\dots  & 0 & 0%
\end{array}
&
\begin{array}{cc}
1 & 0 \\
0 & 1%
\end{array}
&
\begin{array}{ccc}
-1 & 0 & \dots  \\
0 & 0 & \dots
\end{array}
\\ \hline
0 &
\begin{array}{cc}
0 & 0 \\
0 & 0 \\
\vdots  & \vdots
\end{array}
& \tau_{n}%
\end{array}%
\right) =\left(
\begin{array}{c|c|c}
A_{m-1} & U & 0 \\ \hline
0 & 1_2 & V \\ \hline
0 & 0 & \tau_n%
\end{array}%
\right).
\end{equation*}
We are seeking the matrix $N^{-1}$ in the form
$
\left(
\begin{array}{c|c|c}
X & K & L \\ \hline
0 & 1_2 & R \\ \hline
0 & 0 & Z%
\end{array}%
\right)$.

Denote  the $i^{th}$
row (resp. column) by $r(i)$ (resp. $c(i)$).
Consider the following transformations:
\begin{equation}\label{trans}
\begin{minipage}[c]{14cm}
a) $\id+\{c(m-1)\mapsto c(m-1)+c(m+1)\}$; \\
b) $\id+\{r(m+2)\mapsto r(m+2)-r(m+1)\}$; \\
c) $\{r(m+1)\mapsto -r(m+1)\}$; \\d) $\{r(m)\leftrightarrow r(m+1)\}$.
\end{minipage}
\end{equation}

Observe that $\tau_{n}$ is obtained from $T_n$, see \eqref{osp0},  by transposing with respect to the side diagonal. Applying transformations a)--d) in lexicographic order we obtain $N$ from $M$.

From the equation $\left(
\begin{array}{c|c|c}
A_{m-1} & U & 0 \\ \hline
0 & 1_2 & V \\ \hline
0 & 0 & \tau_{n}%
\end{array}%
\right) \cdot \left(
\begin{array}{c|c|c}
X & K & L \\ \hline
0 & 1_2  & R \\ \hline
0 & 0 & Z%
\end{array}%
\right) =1_{m+n+1}$ we get
\be\label{KW1}
\begin{array}{l}
Z=(\tau_n)^{-1}=W_{n}=\left(
\begin{array}{cc}
n &
\begin{array}{ccc}
n-1 & \cdots & 1%
\end{array}
\\
\begin{array}{c}
n-1 \\
\vdots \\
1%
\end{array}
& W_{n-1}%
\end{array}%
\right) ,
\ \ \ \ R=-VZ=-VW_{n}, \\
X=A_{m-1}^{-1}, \ \ \ \ K=-A_{m-1}^{-1}U,  \ \ \ \ %
L=-A_{m-1}^{-1}UR=A_{m-1}^{-1}UVW_{n}.
\end{array}
\ee

\ssec{The case of $\fosp$} For $\fosp(a|2b)$, there are 6 pairs of series and one single series of \lq\lq basic"  types of Cartan matrices  which, together with their inverses, are \eqref{osp0} --- \eqref{osp6}:
\be\label{osp0}
\begin{array}{l}
\text{the matrix $T_n$, see \cite[Section~1.1]{Str},  is inverted, e.g., in \cite{WZ}, where it is denoted $S_n$};\\
(T_n^{-1})_{ij} =\min(i,j), \text{~~where $1\leq i,j\leq n$}.
\end{array}
\ee
\be\label{osp1}\tin
B_{1,0,n}^{-1} :=\mleft(
\begin{array}{c|c}
\begin{array}{cc}
1&-1\\
-1&0\\
\end{array}&
\begin{array}{ccc}
  0 & 0 & \cdots\\
1 & 0 & \cdots
\end{array}\\
\hline
\begin{array}{cc}
0 & -1 \\
0 & 0 \\
\vdots & \vdots
\end{array}&
A_n\\
\end{array}
\mright)^{-1}=\text{see \eqref{41}, \eqref{main}}.
\ee

\ssec{Remark} Clearly, $\det X_0=-2$, see eq.~\eqref{osp1}. Applying the recipe of Remark~\ref{Rem}, we get the expression of $\det X_0$  without any minus sign. The same applies to matrices~\eqref{osp2} --- \eqref{osp6}.
\be\label{osp2}\tin
B_{1,00,n}^{-1} :=\mleft(
\begin{array}{c|c}
\begin{array}{ccc}
2&-2&0\\
-1&0&1\\
0&-1&0\\
\end{array}&
\begin{array}{ccc}
0 & 0 & \cdots \\
0 & 0 & \cdots\\
1 & 0 & \cdots
\end{array}\\
\hline
\begin{array}{ccc}
0 & 0 & -1 \\
0 & 0 & 0 \\
\vdots & \vdots & \vdots
\end{array}&
A_n\\
\end{array}
\mright)^{-1}=\text{see \eqref{41}, \eqref{main}}.
\ee

\be\label{osp3}\tin
C_{1,0,n}^{-1} :=\mleft(
\begin{array}{c|c}
\begin{array}{cc}
2&-1\\
-2&0\\
\end{array}&
\begin{array}{ccc}
0 & 0 & \cdots\\
1 & 0 & \cdots
\end{array}\\
\hline
\begin{array}{cc}
0 & -1 \\
 0 & 0 \\
 \vdots & \vdots
\end{array}&
A_n\\
\end{array}
\mright)^{-1}=\text{see \eqref{41}, \eqref{main}}.
\ee
\be\label{osp4}\tin
B_{2,0,n}^{-1} :=\mleft(
\begin{array}{c|c}
\begin{array}{cc}
2&-2\\
-1&0\\
\end{array}&
\begin{array}{ccc}
0 & 0 & \cdots\\
1 & 0 & \cdots
\end{array}\\
\hline
\begin{array}{cc}
0 & -1 \\
0 & 0 \\
 \vdots & \vdots
\end{array}&
A_n\\
\end{array}
\mright)^{-1}=\text{see \eqref{41}, \eqref{main}}.
\ee
\be\label{osp5}\tin
D_{2,0,n}^{-1} :=\mleft(
\begin{array}{c|c}
\begin{array}{ccc}
2&0&-1\\
0&2&-1\\
-1&-1&0\\
\end{array}&
\begin{array}{ccc}
0 & 0 & \cdots \\
0 & 0 & \cdots\\
1 & 0 & \cdots
\end{array}\\
\hline
\begin{array}{ccc}
0 & 0 & -1 \\
0 & 0 & 0 \\
 \vdots & \vdots & \vdots
\end{array}&
A_n\\
\end{array}
\mright)^{-1}=\text{see \eqref{41}, \eqref{main}}.
\ee

\be\label{osp6}\tin
D_{2,00,n}^{-1} :=\mleft(
\begin{array}{c|c}
\begin{array}{cccc}
2&0&-1&0\\
0&2&-1&0\\
-1&-1&0&1\\
0&0&-1&0\\
\end{array}&
\begin{array}{ccc}
0 & 0 & \cdots \\
0 & 0 & \cdots \\
0 & 0 & \cdots\\
1 & 0 & \cdots
\end{array}\\
\hline
\begin{array}{cccc}
0 & 0 & 0 & -1 \\
0 & 0 & 0 & 0 \\
\vdots & \vdots & \vdots & \vdots
\end{array}&
A_n\\
\end{array}
\mright)^{-1}=\text{see \eqref{41}, \eqref{main}}.
\ee

\section{Proof of formulas \eqref{osp1}--\eqref{osp6}. Answers: eqs. \eqref{41}, \eqref{main}}\label{Sinv}

There are several formulas for the inverse of various (invertible) block $2\times 2$ matrices.
In our particular cases, we can use the following ad hoc transformations and the known expressions of $A_n^{-1}$
and $W_{n}=\tau_n^{-1}$,  see \eqref{KW1}.

 \textbf{1)} Let $m=2$, or 3, or 4, and $U$ is the $m\times n$-matrix with only non-zero element, 1, in the bottom left corner.
Invert the matrix of the form
\[
M=
\begin{pmatrix}
1_{m} & U \\
V & A_{n}%
\end{pmatrix},
\text{~~where ~~$V=U^{T}$}.
\]

Note that $VU=\alpha $, see \eqref{KW}.
It is easy to verify that
\[
M^{-1}=\left(
\begin{array}{cc}
1_{m} & U \\
V & A_{n}%
\end{array}%
\right) ^{-1}=
\begin{pmatrix}
1_{m}+UW_{n}V & -UW_{n} \\
-W_{n}V & W_{n}%
\end{pmatrix}.
\]

\bigskip

\textbf{2) \ \ } In the above notation, consider the matrix of the form
\[
N=
\begin{pmatrix}
Q & U \\
-V & A_{n}%
\end{pmatrix}%
\]
and find matrices $L=
\begin{pmatrix}
l & 0 \\
0 & 1_{n}
\end{pmatrix}
$ and $R=
\begin{pmatrix}
r & 0 \\
0 & 1_{n}%
\end{pmatrix}$ such  that $\ LNR=M$,
i.e.,
\[
lQr=1_{m},\ \ lU=U,\ \ \ \ Vr=-V.
\]

Set $P:=Q^{-1}$. In what follows, for the cases \eqref{osp1}--\eqref{osp6}, we prove the existence of matrices $L$ and $R$  and give the matrices $P$.

Since $rl=Q^{-1}=P$, we have the following uniform answer for eqs. \eqref{osp1}--\eqref{osp6}:
\be\label{41}
\begin{array}{ll}
N^{-1}&=RM^{-1}L=
\begin{pmatrix}
r & 0 \\
0 & 1_{n}
\end{pmatrix}%
\begin{pmatrix}
1_{m}+UW_{n}V & -UW_{n} \\
-W_{n}V & W_{n}%
\end{pmatrix}%
\begin{pmatrix}
l & 0 \\
0 & 1_{n}
\end{pmatrix}%
\\
&=
\begin{pmatrix}
r & 0 \\
0 & 1_{n}
\end{pmatrix}%
\begin{pmatrix}
1_{m}-lUW_{n}Vr & -lUW_{n} \\
W_{n}Vr & W_{n}%
\end{pmatrix}%
\begin{pmatrix}
l & 0 \\
0 & 1_{n}
\end{pmatrix}\\
&=
\begin{pmatrix}
rl-rlUW_{n}Vrl & -rlUW_{n} \\
W_{n}Vrl & W_{n}%
\end{pmatrix}
=
\begin{pmatrix}
P-PUW_{n}VP & -PUW_{n} \\
W_{n}VP & W_{n}%
\end{pmatrix}=\begin{pmatrix}
F & G \\
H & W_{n}%
\end{pmatrix}.\\
\end{array}
\ee

\textbf{Eq. \eqref{osp1}}. We perform the following transformations (recall eq.~\eqref{trans}):

a) $c(2)\mapsto c(2)+c(1)$; $r(2)\mapsto r(2)+r(1)$; \ $%
c(2)\mapsto -c(2)$;

b) $r(3)\mapsto r(3)-r(2)$:
\begin{eqnarray*}
B_{1,0,n}:=\left(
\begin{array}{c|c}
\begin{array}{cc}
1 & -1 \\
-1 & 0%
\end{array}
&
\begin{array}{ccc}
0 & 0 & \cdots  \\
1 & 0 & \cdots
\end{array}
\\ \hline
\begin{array}{cc}
0 & -1 \\
0 & 0 \\
\vdots  & \vdots
\end{array}
& A_{n}%
\end{array}%
\right) \stackrel{\text{a)}}{\mapsto }\left(
\begin{array}{c|c}
\begin{array}{cc}
1 & 0 \\
0 & 1%
\end{array}
&
\begin{array}{ccc}
0 & 0 & \cdots  \\
1 & 0 & \cdots
\end{array}
\\ \hline
\begin{array}{cc}
0 & 1 \\
0 & 0 \\
\vdots  & \vdots
\end{array}
& A_{n}%
\end{array}%
\right) \stackrel{\text{b)}}{\mapsto }\\
\tiny\left(
\begin{array}{c|c}
\begin{array}{cc}
1 & 0 \\
0 & 1%
\end{array}
&
\begin{array}{ccc}
0 & 0 & \cdots  \\
1 & 0 & \cdots
\end{array}
\\ \hline
\begin{array}{cc}
0 & 0 \\
0 & 0 \\
\vdots  & \vdots
\end{array}
& A_{n}-\alpha
\end{array}%
\right) =C:=
\begin{pmatrix}
1 & U \\
0 & A_{n}-\alpha
\end{pmatrix}%
 \Longrightarrow C^{-1}=
\begin{pmatrix}
1 & -UW_{n} \\
0 & W_{n}%
\end{pmatrix}%
;\ \
P=-\begin{pmatrix}
0 & 1 \\
1 & 1%
\end{pmatrix}.
\end{eqnarray*}

\textbf{Eq. \eqref{osp2}}. We perform the following transformations:

a) \bigskip $r(2)\mapsto r(2)+\frac{1}{2}r(1);$ $c(2)\mapsto
c(2)+c(1)$; \ $c(3)\mapsto c(3)+c(2);$ \ \ $r(3)\mapsto r(3)-r(2)$;

b) $c(1)\mapsto \frac{1}{2}c(1);$ \ \ \ $c(2)\mapsto -c(2);$ \ \ \ $%
c(3)\mapsto -c(3)$;

c) $r(4)\mapsto r(4)=r(3)$:
\begin{eqnarray*}
B_{1,00,n}:=\tiny\left(
\begin{array}{c|c}
\begin{array}{ccc}
2 & -2 & 0 \\
-1 & 0 & 1 \\
0 & -1 & 0%
\end{array}
&
\begin{array}{ccc}
0 & 0 & \cdots  \\
0 & 0 & \cdots  \\
1 & 0 & \cdots
\end{array}
\\ \hline
\begin{array}{ccc}
0 & 0 & -1 \\
0 & 0 & 0 \\
\vdots  & \vdots  & \vdots
\end{array}
& A_{n}%
\end{array}%
\right) \stackrel{\text{a)}}{\mapsto }\left(
\begin{array}{c|c}
\begin{array}{ccc}
2 & 0 & 0 \\
0 & -1 & 0 \\
0 & 0 & -1%
\end{array}
&
\begin{array}{ccc}
0 & 0 & \cdots  \\
0 & 0 & \cdots  \\
1 & 0 & \cdots
\end{array}
\\ \hline
\begin{array}{ccc}
0 & 0 & -1 \\
0 & 0 & 0 \\
\vdots  & \vdots  & \vdots
\end{array}
& A_{n}%
\end{array}%
\right) \stackrel{\text{b)}}{\mapsto }\\
\tiny\left(
\begin{array}{c|c}
\begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1%
\end{array}
&
\begin{array}{ccc}
0 & 0 & \cdots  \\
0 & 0 & \cdots  \\
1 & 0 & \cdots
\end{array}
\\ \hline
\begin{array}{ccc}
0 & 0 & 1 \\
0 & 0 & 0 \\
\vdots  & \vdots  & \vdots
\end{array}
& A_{n}%
\end{array}%
\right) \stackrel{\text{c)}}{\mapsto } \left(
\begin{array}{c|c}
\begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1%
\end{array}
&
\begin{array}{ccc}
0 & 0 & \cdots  \\
0 & 0 & \cdots  \\
1 & 0 & \cdots
\end{array}
\\ \hline
\begin{array}{ccc}
0 & 0 & 0 \\
0 & 0 & 0 \\
\vdots  & \vdots  & \vdots
\end{array}
& A_{n}-\alpha
\end{array}%
\right) =C:=\left(
\begin{array}{cc}
1 & U \\
0 & A_{n}-\alpha
\end{array}%
\right) \\
\Longrightarrow C^{-1}=
\begin{pmatrix}
1 & -UW_{n} \\
0 & W_{n}%
\end{pmatrix};\ \
P=\frac12\begin{pmatrix}
1 & 0&-2 \\
0&0 & -2\\
1&2&-2\\
\end{pmatrix} .
\end{eqnarray*}

\textbf{Eq. \eqref{osp3}}. We perform the following transformations:

a) \ $r(2)\mapsto r(2)+r(1);\ \ c(2)\mapsto \frac{1}{2}\
c(2);\ \ \ c(2)\mapsto c(2)+c(1);\ \ c(2)\mapsto -c(2)$;

b) \ $r(3)\mapsto r((3)-r(2)$:
\begin{eqnarray*}
C_{1,0,n}:=\tiny\left(
\begin{array}{c|c}
\begin{array}{cc}
2 & -1 \\
-2 & 0%
\end{array}
&
\begin{array}{ccc}
0 & 0 & \cdots  \\
1 & 0 & \cdots
\end{array}
\\ \hline
\begin{array}{cc}
0 & -1 \\
0 & 0 \\
\vdots  & \vdots
\end{array}
& A_{n}%
\end{array}%
\right) \stackrel{\text{a)}}{\mapsto }\left(
\begin{array}{c|c}
\begin{array}{cc}
1 & 0 \\
0 & 1%
\end{array}
&
\begin{array}{ccc}
0 & 0 & \cdots  \\
1 & 0 & \cdots
\end{array}
\\ \hline
\begin{array}{cc}
0 & 1 \\
0 & 0 \\
\vdots  & \vdots
\end{array}
& A_{n}%
\end{array}%
\right) \stackrel{\text{b)}}{\mapsto }\\
\tiny\left(
\begin{array}{c|c}
\begin{array}{cc}
1 & 0 \\
0 & 1%
\end{array}
&
\begin{array}{ccc}
0 & 0 & \cdots  \\
1 & 0 & \cdots
\end{array}
\\ \hline
\begin{array}{cc}
0 & 0 \\
0 & 0 \\
\vdots  & \vdots
\end{array}
& A_{n}-\alpha
\end{array}%
\right) =C=
\begin{pmatrix}
1 & U \\
0 & A_{n}-\alpha
\end{pmatrix}%
\Longrightarrow C^{-1}=
\begin{pmatrix}
1 & -UW_{n} \\
0 & W_{n}\\
\end{pmatrix};\ \
P=-\frac12\begin{pmatrix}
0&1 \\
2 & 2\\
\end{pmatrix} .
\end{eqnarray*}

\textbf{Eq. \eqref{osp4}}. We perform the following transformations:

a) \ $c(2)\mapsto c(2)+c(1);\ \ r(1)\mapsto \frac{1}{2}\
r(1);\ \ \ r(2)\mapsto r(2)+r(1);\ \ c(2)\mapsto -c(2)$;

b) \ $r(3)\mapsto r((3)-r(2)$:
\begin{eqnarray*}
B_{2,0,n}:=\tiny\left(
\begin{array}{c|c}
\begin{array}{cc}
2 & -2 \\
-1 & 0%
\end{array}
&
\begin{array}{ccc}
0 & 0 & \cdots  \\
1 & 0 & \cdots
\end{array}
\\ \hline
\begin{array}{cc}
0 & -1 \\
0 & 0 \\
\vdots  & \vdots
\end{array}
& A_{n}%
\end{array}%
\right) \stackrel{\text{a)}}{\mapsto }\left(
\begin{array}{c|c}
\begin{array}{cc}
1 & 0 \\
0 & 1%
\end{array}
&
\begin{array}{ccc}
0 & 0 & \cdots  \\
1 & 0 & \cdots
\end{array}
\\ \hline
\begin{array}{cc}
0 & 1 \\
0 & 0 \\
\vdots  & \vdots
\end{array}
& A_{n}%
\end{array}%
\right) \stackrel{\text{b)}}{\mapsto }\\
\tiny\left(
\begin{array}{c|c}
\begin{array}{cc}
1 & 0 \\
0 & 1%
\end{array}
&
\begin{array}{ccc}
0 & 0 & \cdots  \\
1 & 0 & \cdots
\end{array}
\\ \hline
\begin{array}{cc}
0 & 0 \\
0 & 0 \\
\vdots  & \vdots
\end{array}
& A_{n}-\alpha
\end{array}%
\right) =C:=\left(
\begin{array}{cc}
1 & U \\
0 & A_{n}-\alpha
\end{array}%
\right) \Longrightarrow C^{-1}=
\begin{pmatrix}
1 & -UW_{n} \\
0 & W_{n}%
\end{pmatrix};\ \
P=-\frac12\begin{pmatrix}
0&2 \\
1 & 2\\
\end{pmatrix}
\end{eqnarray*}

\textbf{Eq. \eqref{osp5}} We perform the following transformations:

a) $r(3)\mapsto r(3)+\frac{1}{2}(r(1)+r(2))$;\ \ \
$c(1)\mapsto \frac{1}{2}c(1)$;\ \ $c(2)\mapsto \frac{1}{2}c(2)$;\ \
$c(3)\mapsto c(3)+c(1)+c(2)$;\\  $c(3)\mapsto -c(3)$;

b) \ $r(4)\mapsto r(4)-r(3)$:
\begin{eqnarray*}
D_{2,0,n}:=\tiny\left(
\begin{array}{c|c}
\begin{array}{ccc}
2 & 0 & -1 \\
0 & 2 & -1 \\
-1 & -1 & 0%
\end{array}
&
\begin{array}{ccc}
0 & 0 & \cdots  \\
0 & 0 & \cdots  \\
1 & 0 & \cdots
\end{array}
\\ \hline
\begin{array}{ccc}
0 & 0 & -1 \\
0 & 0 & 0 \\
\vdots  & \vdots  & \vdots
\end{array}
& A_{n}%
\end{array}%
\right) \stackrel{\text{a)}}{\mapsto }\left(
\begin{array}{c|c}
\begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1%
\end{array}
&
\begin{array}{ccc}
0 & 0 & \cdots  \\
0 & 0 & \cdots  \\
1 & 0 & \cdots
\end{array}
\\ \hline
\begin{array}{ccc}
0 & 0 & 1 \\
0 & 0 & 0 \\
\vdots  & \vdots  & \vdots
\end{array}
& A_{n}%
\end{array}%
\right) \stackrel{\text{b)}}{\mapsto }\\
\small C:=
\begin{pmatrix}
1 & U \\
0 & A_{n}-\alpha
\end{pmatrix}%
 \Longrightarrow C^{-1}=
\begin{pmatrix}
1 & -UW_{n} \\
0 & W_{n}%
\end{pmatrix};\ \
P=-\frac14\begin{pmatrix}
1 & -1&-2 \\
-1&1 & -2\\
-2&-2&-4
\end{pmatrix} .
\end{eqnarray*}

\textbf{Eq. \eqref{osp6}} We perform the following transformations:

a) \ $r(3)\mapsto r(3)+\frac{1}{2}(r(1)+r(2));$  \ $%
c(1)\mapsto \frac{1}{2}c(1)$;   \ $c(2)\mapsto \frac{1}{2}c(2);$ \
$c(3)\mapsto c(3)+c(1)+c(2)$;

b) $\ c(4)\mapsto c(4)+c(3);\ \ r(4)\mapsto r(4)-r(3);\ \ \ $\ $\
c(3)\mapsto -c(3);$ \ \ \ \ $\ c(4)\mapsto -c(4)$;

c) \ $r(5)\mapsto r(5)-r(4)$:
\begin{eqnarray*}
D_{2,00,n}:=\tiny\left(
\begin{array}{c|c}
\begin{array}{cccc}
2 & 0 & -1 & 0 \\
0 & 2 & -1 & 0 \\
-1 & -1 & 0 & 1 \\
0 & 0 & -1 & 0%
\end{array}
&
\begin{array}{ccc}
0 & 0 & \cdots  \\
0 & 0 & \cdots  \\
0 & 0 & \cdots  \\
1 & 0 & \cdots
\end{array}
\\ \hline
\begin{array}{cccc}
0 & 0 & 0 & -1 \\
0 & 0 & 0 & 0 \\
\vdots  & \vdots  & \vdots  & \vdots
\end{array}
& A_{n}%
\end{array}%
\right) \stackrel{\text{a)}}{\mapsto }\left(
\begin{array}{c|c}
\begin{array}{cccc}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & -1 & 1 \\
0 & 0 & -1 & 0%
\end{array}
&
\begin{array}{ccc}
0 & 0 & \cdots  \\
0 & 0 & \cdots  \\
0 & 0 & \cdots  \\
1 & 0 & \cdots
\end{array}
\\ \hline
\begin{array}{cccc}
0 & 0 & 0 & -1 \\
0 & 0 & 0 & 0 \\
\vdots  & \vdots  & \vdots  & \vdots
\end{array}
& A_{n}%
\end{array}%
\right) \stackrel{\text{b)}}{\mapsto }\\
\tiny\left(
\begin{array}{c|c}
\begin{array}{cccc}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1%
\end{array}
&
\begin{array}{ccc}
0 & 0 & \cdots  \\
0 & 0 & \cdots  \\
0 & 0 & \cdots  \\
1 & 0 & \cdots
\end{array}
\\ \hline
\begin{array}{cccc}
0 & 0 & 0 & 1 \\
0 & 0 & 0 & 0 \\
\vdots  & \vdots  & \vdots  & \vdots
\end{array}
& A_{n}%
\end{array}%
\right) \stackrel{\text{c)}}{\mapsto }C:=
\begin{pmatrix}
1 & U \\
0 & A_{n}-\alpha
\end{pmatrix} \Longrightarrow C^{-1}=
\begin{pmatrix}
1 & -UW_{n} \\
0 & W_{n}%
\end{pmatrix};\ \
P=\frac12\begin{pmatrix}
1 & 0&0&-1 \\
0&1&0 & -1\\
0&0&0&-2\\
1 & 1&2&-2 \\
\end{pmatrix} .
\end{eqnarray*}

Therefore (recall that $m$ is the size of the upper left block of $N$), in eq. \eqref{41} we have
\be\label{main}
\begin{array}{l}
F_{ij}=P_{ij}-nP_{im}P_{mj}, \text{~~so}\\
F=\begin{cases}P-n\begin{pmatrix}
1\times1&1\times1\\
1\times1&1\times1\\
\end{pmatrix}=-\begin{pmatrix}
n&n+1\\
n+1&n+1\\
\end{pmatrix}&\text{in case Eq. \eqref{osp1}},\\
??&\text{in case Eq. \eqref{osp2}},\\
??&\text{in case Eq. \eqref{osp3}},\\
P-\frac{n}4\begin{pmatrix}
2\times1&2\times2\\
1\times2&2\times2\\
\end{pmatrix}=-\frac14\begin{pmatrix}
2&4(n+1)\\
n+2&4(n+1)\\
\end{pmatrix}&\text{in case Eq. \eqref{osp4}},\\
??&\text{in case Eq. \eqref{osp5}},\\
??&\text{in case Eq. \eqref{osp6}},\\
\end{cases}
\\
G_{ib }=-(n-b +1)P_{ib},\\
H_{a j}=(n-a +1)P_{aj}.\\
\end{array}
\ee

\section{Finite-dimensional exceptional Lie (super)algebras over $\Cee$}\label{S4}

In this section, the determinant of the Cartan matrix is equal to the minus denominator of the fraction serving as a factor of the \lq\lq matrix part" of the inverse matrix;  if the factor is equal to 1, then the determinant is equal to 1.

\ssec{$\fosp(4|2; \alpha)$} Since $\fosp(4|2; 1)\simeq \fosp(4|2)$, it is convenient to set
$\alpha=1-\eps$ to express the deformed bracket in terms of $\eps$.
The inequivalent Cartan matrices of $\fosp(4|2; \alpha)$, where
$\alpha\neq 0, -1$, i.e., $\eps\neq 1, 2$, and their inverses, are
\begin{equation}\label{CM1}\tiny\arraycolsep=1.5pt
\begin{array}{l}
1)\;\smat{ 2 & -1 & 0 \\ -1 & 0 & -\alpha \\ 0 & -1 & 2
}^{-1}=\smat{ 2 & -1 & 0 \\ -1 & 0 & -1+\eps \\
0 & -1 & 2
}^{-1}=
-\frac{1}{2(2-\eps)}\smat{
\eps -1 & 2 & 1-\eps \\
2& 4&\ 2(1-\eps) \\
1 &2 & -1 \\
},\\
\\
2)\;\smat{
0 & 1 & -1 - \alpha \\
-1 & 0 & -\alpha \\
 -1 - \alpha & \alpha & 0
}^{-1}=\smat{
0 & 1 & -2+\eps \\
-1 & 0 & -1+\eps \\
 -2+\eps & 1-\eps & 0
}^{-1}=-\frac{1}{2(\eps-1)(2-\eps)}\smat{
(\eps -1)^2 & -(\eps-1)(\eps-2) & \eps -1\\
(\eps-1)(\eps-2) & -(\eps-2)^2 & -(\eps -2)\\
\eps -1 &\eps -2 & 1 \\
}.\\
\end{array}
\end{equation}

\ssec{$\fag(2)$} The inequivalent Cartan matrices  and their inverses are
\begin{equation}\label{ag2cm}\tiny\arraycolsep=1.5pt
\begin{array}{l}
1)\; \smat{ 0 & -1 & 0 \\ -1 & 2 & -3 \\ 0 & -1 & 2
}^{-1}=-\frac{1}{2}
  \smat{
   1 & 2 & 3 \\
   2 & 0 & 0 \\
   1 & 0 & -1 \\
  },
\quad 2)\; \smat{
0 & -1 & 0 \\ -1 & 0 & 3 \\ 0 & -1 & 2
}^{-1}=-\frac{1}{2}
  \smat{
   3 & 2 & -3 \\
   2 & 0 & 0 \\
   1 & 0 & -1 \\
  },\\
3)\; \smat{
0 & -3 & 1 \\ -3 & 0 & 2 \\ -1 & -2 & 2
}^{-1}=-\frac{1}{6}
  \smat{
   4 & 4 & -6 \\
   4 & 1 & -3 \\
   6 & 3 & -9 \\
  },
\quad 4)\;
\smat{
2 & -1 & 0 \\ -3 & 0 & 2 \\ 0 & -1 & 1\\
}^{-1}=
\smat{
2 & 1 & -2 \\
3 & 2 & -4 \\
3 & 2 & -3 \\
}
\end{array}\end{equation}

\ssec{$\fab(3)$} The inequivalent Cartan matrices  and their inverses are
\begin{equation}\label{ab3cm}\tiny\arraycolsep=1.5pt
\begin{matrix}
1)\; \smat{
2 & -1 & 0 & 0 \\ -3 & 0 & 1 & 0 \\ 0 & -1 & 2 & -2 \\
 0 & 0 & -1 & 2\\
}^{-1}=-\frac{1}{2}
  \smat{
   2 & 2 & -2 & -2 \\
   6 & 4 & -4 & -4 \\
   6 & 4 & -6 & -6 \\
   3 & 2 & -3 & -4 \\
  },
\quad 2)\;
\smat{
0 & -3 & 1 & 0 \\ -3 & 0 & 2 & 0 \\ 1 & 2 & 0 & -2 \\
0 & 0 & -1 & 2
}^{-1}=-\frac{1}{6}
  \smat{
   -8 & -2 & -12 & -12 \\
   -2 & -2 & -6 & -6 \\
   -12 & -6 & -18 & -18 \\
   -6 & -3 & -9 & -12 \\
  },\\
3)\;
\smat{
2 & -1 & 0 & 0 \\ -1 & 2 & -1 & 0 \\ 0 & -2 & 0 & 3 \\
0 & 0 & -1 & 2
}^{-1}=\smat{
2 & 3 & 2 & -3 \\
3 & 6 & 4 & -6 \\
4 & 8 & 6 & -9 \\
2 & 4 & 3 & -4 \\
},
\quad 4)\; \smat{
2 & -1 & 0 & 0 \\ -2 & 0 & 2 & -1 \\ 0 & 2 & 0 & -1 \\
0 & -1 & -1 & 2
}^{-1}=-\frac{1}{6}
\smat{
 -4 & -1 & -3 & -2 \\
 -2 & -2 & -6 & -4 \\
 -6 & -6 & -6 & -6 \\
 -4 & -4 & -6 & -8 \\
},\\
5)\;
\smat{
0 & -1 & 0 & 0 \\
-1 & 0 & 2 & 0 \\
0 & -1 & 2 & -1 \\
0 & 0 & -1 & 2
}^{-1}=\frac{1}{3}
  \smat{
   -4 & 3 & -4 & -2 \\
   -3 & 0 & 0 & 0 \\
   -2 & 0 & -2 & -1 \\
   -1 & 0 & -1 & -2 \\
  },
\quad 6)\;
\smat{
2 & -1 & 0 & 0 \\ -1 & 2 & -1 & 0 \\ 0 & -2 & 2 & -1 \\ 0 & 0 & -1 &
0
}^{-1}=-\frac{1}{3}
  \smat{
   -2 & -1 & 0 & 1 \\
   -1 & -2 & 0 & 2 \\
   0 & 0 & 0 & 3 \\
   2 & 4 & 3 & 2 \\
  }
\end{matrix}
\end{equation}

\section{Finite-dimensional exceptional simple modular Lie (super)algebras}\label{S5}

For each  Lie (super)algebra, we list its inequivalent Cartan matrices  and their inverses.

\ssec{$p=2$; Lie (super)algebras} In this Subsection, $\ast$ on the main diagonal stands for either $\ev$ or 0; both can be viewed as $0$ for our purposes.

\subsubsection{$\fwk(4;a)$ and $\fbgl(4;a)$, where $a\neq 0, 1$}
\[\tiny\arraycolsep=1.5pt
\begin{matrix}
1)\; \smat{ \ev &a &0&0\\
a &\ast&1&0\\
0&1&\ast&1\\
0&0&1&\ast }^{-1}=
\smat{
0 & a^{-1} & 0 & a^{-1} \\
a^{-1}& 0 & 0 & 0 \\
0 & 0 & 0 & 1 \\
a^{-1}& 0 & 1& 0 \\
}
,\ \

2)\; \smat{ \ev &1 &1+a&0\\
1 &\ast& a & 0\\
a+1& a &\ast&a\\
0&0&a&\ast }^{-1}=
\smat{
0 & 1 & 0 & 1 \\
1 & 0 & 0 & 1+a^{-1} \\
0 & 0 & 0 & a^{-1} \\
1 & 1+a^{-1} & a^{-1} & 0 \\
}\\
3)\;\smat{ \ev &a & 0 &0\\
a &\ast& a+1 & 0\\
0& a+1 &\ast&1\\
0&0&1&\ast }^{-1}=
\smat{
0 & a^{-1} & 0 & 1+a^{-1} \\
a^{-1} & 0 & 0 & 0 \\
0 & 0 & 0 & 1 \\
1+a^{-1} & 0 & 1 & 0 \\
}
\end{matrix}
\]

\subsubsection{$\Delta_n=\textbf{F}(\fo\fo_{I\Pi}^{(1)}(n_\ev|n_\od))$, where $\textbf{F}$ is the desuperization functor, and $\fo\fo_{I\Pi}^{(1)}(n_\ev|n_\od)$, see \cite{BGL}} In the simplest case, $\Delta_n=\textbf{F}(\fosp(1|2n))$; cf. \cite{WK}.
\begin{equation}\label{oowith1}
\smat{ \ddots&\ddots&\ddots&\vdots\\
\ddots&\ast&1&0\\
\ddots&1&\ast&1\\
\cdots&0&1&1}^{-1}=
\smat{
1 & 1 & 1 & 1 & 1 & 1 &\cdots \\
1 & 0 & 0 & 0 & 0 & 0 &\cdots\\
1 & 0 & 1 & 1 & 1 & 1 &\cdots\\
1 & 0 & 1 & 0 & 0 & 0 &\cdots\\
1 & 0 & 1 & 0 & 1 & 1 &\cdots\\
1 & 0 & 1 & 0 & 1 & 0 &\cdots\\
\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \ddots \\
}
\end{equation}

\subsubsection{$\fe(6)$, $\fe(6,1)$ and $\fe(6,6)$}
\[\arraycolsep=1.5pt
\smat{\ast&1&0&0&0&0\\
1&\ast&1&0&0&0\\
0&1&\ast&1&0&1\\
0&0&1&\ast&1&0\\
0&0&0&1&\ast&0\\
0&0&1&0&0&\ast
}^{-1}=
\smat{
 0& 1& 0 & 0 & 0& 1\\
 1& 0& 0 & 0 & 0 & 0\\
 0 & 0 & 0 & 0 & 0 & 1\\
 0 & 0 & 0 & 0 & 1& 0 \\
 0 & 0 & 0 & 1& 0& 1\\
 1& 0 & 1& 0& 1& 0\\
}
\]

\subsubsection{
$\fe(8)$, $\fe(8,1)$ and $\fe(8,8)$}
\[\arraycolsep=1.5pt
\smat{
 \ast & 1 &  0 &  0 &  0 &  0 &  0 & 0 \\
1 &  \ast & 1&  0 &  0 &  0 &  0 & 0 \\
 0 & 1 &  \ast & 1 &  0 &  0 &  0 & 0 \\
 0 &  0 & 1 &  \ast & 1 &  0 &  0 & 0 \\
 0 &  0 &  0 & 1 &  \ast & 1 &  0 & 1 \\
 0 &  0 &  0 &  0 & 1 &  \ast & 1 & 0 \\
 0 &  0 &  0 &  0 &  0 & 1 &  \ast & 0 \\
 0 &  0 & 0 &  0 &  1 &  0 &  0 & \ast
}^{-1}=
\smat{
 0& 1& 0& 1& 0 & 0 & 0& 1\\
 1& 0& 0 & 0& 0 & 0 & 0 & 0 \\
 0& 0 & 0& 1& 0& 0 & 0& 1\\
 1& 0& 1& 0& 0 & 0& 0 & 0\\
 0& 0 & 0 & 0 & 0 & 0 & 0& 1\\
 0 & 0& 0 & 0 & 0 & 0& 1& 0\\
 0 & 0 & 0& 0 & 0 & 1& 0& 1\\
 1& 0 & 1& 0 & 1& 0 & 1& 0 \\
}
\]

\subsubsection{$\fsl(2n+1)$ and $\fsl(a|b)$ for $a+b=2n+1$}
\begin{equation}\label{oowith1}
\smat{ \ddots&\ddots&\ddots&\vdots\\
\ddots&\ast&1&0\\
\ddots&1&\ast&1\\
\cdots&0&1&\ast}^{-1}=
\smat{
0 & 1 & 0 & 1 & 0 & 1 & \dots\\
1 & 0 & 0 & 0 & 0 & 0 & \dots \\
0 & 0 & 0 & 1 & 0 & 1 & \dots \\
1 & 0 & 1 & 0 & 0 & 0 & \dots \\
0 & 0 & 0 & 0 & 0 & 1 & \dots \\
1 & 0 & 1 & 0 & 1 & 0 & \dots \\
0 & 0 & 0 & 0 & 0 & 0 & \dots \\
\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \ddots  \\
}\\
\end{equation}

\ssec{$p=3$; Lie algebras}{}~{}

\subsubsection{$\fbr(2;\eps)$ for $\eps\neq 0$} $\tiny \smat{2&-1\\-2&1-\eps\\
}^{-1}=\eps^{-1}\smat{1-\eps&1\\2&2\\
}$

\subsubsection{$\fbr(3)$}\label{br3a}
$
1)
\smat{
2&-1&0\\
-1&2&-1\\
0&-1&\ev}^{-1}=
\smat{
 2 & 0 & 1 \\
 0 & 0 & 2 \\
 1 & 2 & 0 \\
},
\qquad 2)
\smat{
2&-1&0\\
-2&2&-1\\
0&-1&\ev}^{-1}=
\smat{
 2 & 0 & 1 \\
 0 & 0 & 2 \\
 2 & 2 & 2 \\
}
$

\ssec{$p=3$; Lie superalgebras}{}~{}

\subsubsection{$\fbrj(2;3)$}
$\tiny
1)\ \smat{0&-1\\
-2&1}^{-1}=\smat{1&1\\
2&0}, \quad 2)\ \smat{0&-1\\
-1&\ev}^{-1}=\smat{0&1\\
1&\ev}, \quad 3)\ \smat{1&-1\\
-1&\ev}^{-1}=\smat{0&1\\
1&1}.
$

\subsubsection{$\fg(1,6)$}
$\tiny \arraycolsep=1.5pt
1) \smat{
 2&-1&0 \\
 -1&1&-1 \\
 0&-1&0
 }^{-1}=
 \smat{
 2 & 0 & 1 \\
 0 & 0 & 2 \\
 1 & 2 & 1 \\
},\quad
2) \smat{
 2&-1&0 \\
 -1&2&-2 \\
 0&-2&0
 }^{-1}=
 \smat{
 2 & 0 & 2 \\
 0 & 0 & 1 \\
 2 & 1 & 0 \\
}.
$

\subsubsection{$\fg(3,6)$}
\[\tiny \arraycolsep=1.5pt
\begin{matrix}
1) \smat{
 0&-1&0&0 \\
 -1&2&-1&0 \\
 0&-1&1&-1 \\
 0&0&-1&0
 }^{-1}=
 \smat{
 1 & 2 & 0 & 1 \\
 2 & 0 & 0 & 0 \\
 0 & 0 & 0 & 2 \\
 1 & 0 & 2 & 2 \\
} \quad
2) \smat{
 0&-1&0&0 \\
 -1&0&-1&0 \\
 0&-1&1&-1 \\
 0&0&-1&0
 }^{-1}=
 \smat{
 0 & 2 & 0 & 1 \\
 2 & 0 & 0 & 0 \\
 0 & 0 & 0 & 2 \\
 1 & 0 & 2 & 2 \\
}
\\
3) \smat{
 0&-1&0&0 \\
 -1&2&-1&0 \\
 0&-1&2&-2 \\
 0&0&-1&0
 }^{-1}=
 \smat{
 1 & 2 & 0 & 1 \\
 2 & 0 & 0 & 0 \\
 0 & 0 & 0 & 2 \\
 2 & 0 & 1 & 2 \\
}\quad

4)
\smat{
 2&-1&0&0 \\
 -1&0&-2&0 \\
 0&-2&2&-1 \\
 0&0&-1&0
 }^{-1}=
 \smat{
 0 & 2 & 0 & 2 \\
 2 & 1 & 0 & 1 \\
 0 & 0 & 0 & 2 \\
 2 & 1 & 2 & 2 \\
}\\
5) \smat{
 0&-1&0&0 \\
 -2&0&-1&0 \\
 0&-1&2&-2 \\
 0&0&-1&0
 }^{-1}=
 \smat{
 0 & 1 & 0 & 2 \\
 2 & 0 & 0 & 0 \\
 0 & 0 & 0 & 2 \\
 2 & 0 & 1 & 2 \\
}
\ \
6) \smat{
 2&-1&0&0 \\
 -1&0&-2&0 \\
 0&-2&0&-2 \\
 0&0&-1&0
 }^{-1}=
 \smat{
 0 & 2 & 0 & 2 \\
 2 & 1 & 0 & 1 \\
 0 & 0 & 0 & 2 \\
 1 & 2 & 1 & 2 \\
}\\
7) \smat{
 2&-1&0&0 \\
 -1&2&-1&-1 \\
 0&-1&0&-1 \\
 0&-1&-1&2
 }^{-1}=
 \smat{
 0 & 2 & 0 & 1 \\
 2 & 1 & 0 & 2 \\
 0 & 0 & 1 & 2 \\
 1 & 2 & 2 & 1 \\
}\\
\end{matrix}
\]

\subsubsection{$\fg(4,3)$}
\[
 \tiny \arraycolsep=1.5pt
 \begin{matrix} 1) \smat{
 2&-1&0&0 \\
 -1&2&-2&-1 \\
 0&-1&2&0 \\
 0&-1&0&0
 }^{-1}=
 \smat{
 2 & 0 & 0 & 1 \\
 0 & 0 & 0 & 2 \\
 0 & 0 & 2 & 1 \\
 1 & 2 & 2 & 1 \\
}\ \
2) \smat{
 2&-1&0&0 \\
 -1&0&-2&-2 \\
 0&-1&2&0 \\
 0&-1&0&0
 }^{-1}=
 \smat{
 2 & 0 & 0 & 1 \\
 0 & 0 & 0 & 2 \\
 0 & 0 & 2 & 1 \\
 2 & 1 & 1 & 0 \\
}\\
3) \smat{
 0&-1&0&0 \\
 -2&0&-1&-1 \\
 0&-1&0&-1 \\
 0&-1&-1&2
 }^{-1}=
 \smat{
 1 & 1 & 0 & 2 \\
 2 & 0 & 0 & 0 \\
 0 & 0 & 1 & 2 \\
 1 & 0 & 2 & 0 \\
}\ \
4) \smat{
 0&-1&0&0 \\
 -1&2&-1&-1 \\
 0&-1&0&-1 \\
 0&-1&-1&2
 }^{-1}=
 \smat{
 0 & 2 & 0 & 1 \\
 2 & 0 & 0 & 0 \\
 0 & 0 & 1 & 2 \\
 1 & 0 & 2 & 0 \\
}
\\
5) \smat{
 0&-1&0&0 \\
 -1&2&-1&0 \\
 0&-1&0&-1 \\
 0&0&-1&0
 }^{-1}=
\smat{
 1 & 2 & 0 & 1 \\
 2 & 0 & 0 & 0 \\
 0 & 0 & 0 & 2 \\
 1 & 0 & 2 & 0 \\
}\quad
6) \smat{
 0&-1&0&0 \\
 -1&0&-2&0 \\
 0&-1&0&-1 \\
 0&0&-1&0
 }^{-1}=
 \smat{
 0 & 2 & 0 & 2 \\
 2 & 0 & 0 & 0 \\
 0 & 0 & 0 & 2 \\
 1 & 0 & 2 & 0 \\
}\quad\\
7) \smat{
 0&-1&0&0 \\
 -1&2&-1&0 \\
 0&-2&2&-1 \\
 0&0&-1&0
 }^{-1}=
 \smat{
 1 & 2 & 0 & 1 \\
 2 & 0 & 0 & 0 \\
 0 & 0 & 0 & 2 \\
 2 & 0 & 2 & 1 \\
}
8) \smat{
 2&-1&0&0 \\
 -2&0&-1&0 \\
 0&-1&2&-2 \\
 0&0&-1&0
 }^{-1}=
 \smat{
 0 & 1 & 0 & 2 \\
 2 & 2 & 0 & 1 \\
 0 & 0 & 0 & 2 \\
 2 & 2 & 1 & 0 \\
}\quad\\
9) \smat{
 0&-1&0&0 \\
 -1&0&-2&0 \\
 0&-2&2&-1 \\
 0&0&-1&0
 }^{-1}=
 \smat{
 0 & 2 & 0 & 2 \\
 2 & 0 & 0 & 0 \\
 0 & 0 & 0 & 2 \\
 2 & 0 & 2 & 1 \\
}\quad
10) \smat{
 2&-1&0&0 \\
 -2&0&-1&0 \\
 0&-1&1&-1 \\
 0&0&-1&0
 }^{-1}=
 \smat{
 0 & 1 & 0 & 2 \\
 2 & 2 & 0 & 1 \\
 0 & 0 & 0 & 2 \\
 1 & 1 & 2 & 1 \\
}\\
\end{matrix}
\]

\subsubsection{$\fg(8,3)$}

\[\tiny
\arraycolsep=1.5pt
\begin{matrix}
1)
\smat{
 2&-1&0&0&0 \\
 -1&2&-1&0&0 \\
 0&-2&2&-1&0 \\
 0&0&-1&2&-1 \\
 0&0&0&1&0
 }^{-1}=
\smat{
 1 & 1 & 2 & 0 & 2 \\
 1 & 2 & 1 & 0 & 1 \\
 1 & 2 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 1 \\
 2 & 1 & 0 & 2 & 2 \\
}\ \
2) \smat{
 2&-1&0&0&0 \\
 -1&2&-1&0&0 \\
 0&-2&2&-1&0 \\
 0&0&-2&0&-1 \\
 0&0&0&-1&0
 }^{-1}=
\smat{
 1 & 1 & 2 & 0 & 1 \\
 1 & 2 & 1 & 0 & 2 \\
 1 & 2 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 2 \\
 1 & 2 & 0 & 2 & 0 \\
}\\
3) \smat{
 2&-1&0&0&0 \\
 -1&2&-1&0&0 \\
 0&-1&0&-1&0 \\
 0&0&-1&0&-2 \\
 0&0&0&-1&2
 }^{-1}=
\smat{
 1 & 1 & 1 & 2 & 2 \\
 1 & 2 & 2 & 1 & 1 \\
 1 & 2 & 0 & 0 & 0 \\
 2 & 1 & 0 & 2 & 2 \\
 1 & 2 & 0 & 1 & 0 \\
}\ \
4) \smat{
 2&-1&0&0&0 \\
 -1&0&-2&-2&0 \\
 0&-1&0&-1&0 \\
 0&-1&-1&2&-1 \\
 0&0&0&-1&2
 }^{-1}=
\smat{
 1 & 1 & 1 & 1 & 2 \\
 1 & 2 & 2 & 2 & 1 \\
 2 & 1 & 1 & 0 & 0 \\
 2 & 1 & 0 & 1 & 2 \\
 1 & 2 & 0 & 2 & 0 \\
}\\
5) \smat{
 0&-1&0&0&0 \\
 -2&0&-1&-1&0 \\
 0&-1&2&0&0 \\
 0&-1&0&0&-2 \\
 0&0&0&-1&2
 }^{-1}=
\smat{
 2 & 1 & 2 & 2 & 2 \\
 2 & 0 & 0 & 0 & 0 \\
 1 & 0 & 2 & 0 & 0 \\
 1 & 0 & 0 & 2 & 2 \\
 2 & 0 & 0 & 1 & 0 \\
}\ \
6) \smat{
 0&-1&0&0&0 \\
 -1&2&-1&-1&0 \\
 0&-1&2&0&0 \\
 0&-1&0&0&-2 \\
 0&0&0&-1&2
 }^{-1}=
\smat{
 2 & 2 & 1 & 1 & 1 \\
 2 & 0 & 0 & 0 & 0 \\
 1 & 0 & 2 & 0 & 0 \\
 1 & 0 & 0 & 2 & 2 \\
 2 & 0 & 0 & 1 & 0 \\
}\\
7) \smat{
 0&-1&0&0&0 \\
 -1&2&-2&-1&0 \\
 0&-1&2&0&0 \\
 0&-2&0&0&-1 \\
 0&0&0&-1&0
 }^{-1}=
\smat{
 2 & 2 & 2 & 0 & 1 \\
 2 & 0 & 0 & 0 & 0 \\
 1 & 0 & 2 & 0 & 0 \\
 0 & 0 & 0 & 0 & 2 \\
 2 & 0 & 0 & 2 & 0 \\
}\ \
8) \smat{
 0&-1&0&0&0 \\
 -1&0&-1&-2&0 \\
 0&-1&2&0&0 \\
 0&-2&0&0&-1 \\
 0&0&0&-1&0
 }^{-1}=
\smat{
 2 & 2 & 1 & 0 & 2 \\
 2 & 0 & 0 & 0 & 0 \\
 1 & 0 & 2 & 0 & 0 \\
 0 & 0 & 0 & 0 & 2 \\
 2 & 0 & 0 & 2 & 0 \\
}\\

9) \smat{
 0&-1&0&0&0 \\
 -1&2&-2&-1&0 \\
 0&-1&2&0&0 \\
 0&-1&0&2&-1 \\
 0&0&0&-1&0
 }^{-1}=
\smat{
 2 & 2 & 2 & 0 & 1 \\
 2 & 0 & 0 & 0 & 0 \\
 1 & 0 & 2 & 0 & 0 \\
 0 & 0 & 0 & 0 & 2 \\
 1 & 0 & 0 & 2 & 1 \\
}\ \
10) \arraycolsep=2.8pt
 \smat{
 2&-1&-1&0&0 \\
 1&0&1&2&0 \\
 1&1&0&0&0 \\
 0&-1&0&2&-1 \\
 0&0&0&-1&0
 }^{-1}=
\smat{
 1 & 1 & 1 & 0 & 2 \\
 2 & 2 & 0 & 0 & 1 \\
 2 & 0 & 2 & 0 & 0 \\
 0 & 0 & 0 & 0 & 2 \\
 1 & 1 & 0 & 2 & 0 \\
}\\

11) \smat{
 0&-1&0&0&0 \\
 -1&0&-1&-2&0 \\
 0&-1&2&0&0 \\
 0&-1&0&2&-1 \\
 0&0&0&-1&0
 }^{-1}=
\smat{
 2 & 2 & 1 & 0 & 2 \\
 2 & 0 & 0 & 0 & 0 \\
 1 & 0 & 2 & 0 & 0 \\
 0 & 0 & 0 & 0 & 2 \\
 1 & 0 & 0 & 2 & 1 \\
}\ \
12) \smat{
 0&0&-1&0&0 \\
 0&2&-1&-1&0 \\
 -1&-1&0&0&0 \\
 0&-1&0&2&-1 \\
 0&0&0&-1&0
 }^{-1}=
\smat{
 2 & 1 & 2 & 0 & 2 \\
 1 & 2 & 0 & 0 & 1 \\
 2 & 0 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 2 \\
 2 & 1 & 0 & 2 & 0 \\
}\\
13)
 \smat{
 2&-1&-1&0&0 \\
 -1&0&-1&-2&0 \\
 -1&-1&0&0&0 \\
 0&-2&0&0&-1 \\
 0&0&0&-1&0
 }^{-1}=
\smat{
 1 & 2 & 2 & 0 & 2 \\
 2 & 1 & 0 & 0 & 1 \\
 2 & 0 & 1 & 0 & 0 \\
 0 & 0 & 0 & 0 & 2 \\
 2 & 1 & 0 & 2 & 1 \\
}\ \
14) \smat{
 0&0&-1&0&0 \\
 0&2&-1&-1&0 \\
 -1&-2&2&0&0 \\
 0&-1&0&2&-1 \\
 0&0&0&-1&0
 }^{-1}=
\smat{
 2 & 2 & 2 & 0 & 1 \\
 1 & 2 & 0 & 0 & 1 \\
 2 & 0 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 2 \\
 2 & 1 & 0 & 2 & 0 \\
}\\
15) \smat{
 0&0&-1&0&0 \\
 0&2&-1&-1&0 \\
 -1&-1&0&0&0 \\
 0&-2&0&0&-1 \\
 0&0&0&-1&0
 }^{-1}=
\smat{
 2 & 1 & 2 & 0 & 2 \\
 1 & 2 & 0 & 0 & 1 \\
 2 & 0 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 2 \\
 1 & 2 & 0 & 2 & 1 \\
}\quad
16)
 \smat{
 2&-1&-1&0&0 \\
 -1&2&-1&-1&0 \\
 -1&-1&0&0&0 \\
 0&-1&0&0&-2 \\
 0&0&0&-1&2
 }^{-1}=
\smat{
 1 & 2 & 2 & 1 & 1 \\
 2 & 1 & 0 & 2 & 2 \\
 2 & 0 & 1 & 0 & 0 \\
 1 & 2 & 0 & 0 & 0 \\
 2 & 1 & 0 & 0 & 2 \\
}\\
17) \smat{
 0&0&-1&0&0 \\
 0&2&-1&-1&0 \\
 -1&-2&2&0&0 \\
 0&-2&0&0&-1 \\
 0&0&0&-1&0
 }^{-1}=
\smat{
 2 & 2 & 2 & 0 & 1 \\
 1 & 2 & 0 & 0 & 1 \\
 2 & 0 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 2 \\
 1 & 2 & 0 & 2 & 1 \\
}\quad
18) \smat{
 0&0&-1&0&0 \\
 0&0&-2&-1&0 \\
 -1&-1&0&0&0 \\
 0&-1&0&0&-2 \\
 0&0&0&-1&2
 }^{-1}=
\smat{
 2 & 2 & 2 & 1 & 1 \\
 1 & 1 & 0 & 2 & 2 \\
 2 & 0 & 0 & 0 & 0 \\
 2 & 2 & 0 & 0 & 0 \\
 1 & 1 & 0 & 0 & 2 \\
}\\ \quad
19)
 \smat{
 0&0&-1&0&0 \\
 0&0&-2&-1&0 \\
 -1&-2&2&0&0 \\
 0&-1&0&0&-2 \\
 0&0&0&-1&2
 }^{-1}=
\smat{
 2 & 1 & 2 & 2 & 2 \\
 1 & 1 & 0 & 2 & 2 \\
 2 & 0 & 0 & 0 & 0 \\
 2 & 2 & 0 & 0 & 0 \\
 1 & 1 & 0 & 0 & 2 \\
}\ \
20) \smat{
 0&0&-1&0&0 \\
 0&0&-1&-2&0 \\
 -2&-1&2&0&0 \\
 0&-1&0&2&-1 \\
 0&0&0&-1&2
 }^{-1}=
 \smat{
 2 & 0 & 1 & 2 & 1 \\
 0 & 0 & 0 & 2 & 1 \\
 2 & 0 & 0 & 0 & 0 \\
 2 & 1 & 0 & 0 & 0 \\
 1 & 2 & 0 & 0 & 2 \\
}\\
21) \smat{
 0&0&-1&0&0 \\
 0&0&-1&-2&0 \\
 -1&-1&1&0&0 \\
 0&-1&0&2&-1 \\
 0&0&0&-1&2
 }^{-1}=
\smat{
 2 & 0 & 2 & 1 & 2 \\
 0 & 0 & 0 & 2 & 1 \\
 2 & 0 & 0 & 0 & 0 \\
 2 & 1 & 0 & 0 & 0 \\
 1 & 2 & 0 & 0 & 2 \\
}\\
\end{matrix}
\]
\subsubsection{$\fel(5;3)$}
\[ \tiny\arraycolsep=1.5pt
\begin{matrix}
1) \;
\smat{
 0 & -1 & 0 & 0 & 0 \\
 -1 & 0 & 0 & -1 & 0 \\
 0 & 0 & 2 & -1 & -1 \\
 0 & -1 & -1 & 2 & 0 \\
 0 & 0 & -1 & 0 & 2
}^{-1}=
\smat{
 0 & 2 & 1 & 0 & 2 \\
 2 & 0 & 0 & 0 & 0 \\
 1 & 0 & 1 & 2 & 2 \\
 0 & 0 & 2 & 0 & 1 \\
 2 & 0 & 2 & 1 & 0 \\
},
2) \;
\smat{
 0 &-2 & 0 & 0 & 0 \\
 -1 & 2 & 0 & -2 & 0 \\
 0 & 0 & 2 & -1 & -1 \\
 0 & -1 & -1 & 2 & 0 \\
 0 & 0 & -1 & 0 & 2
}^{-1}=
\smat{
 2 & 2 & 2 & 0 & 1 \\
 1 & 0 & 0 & 0 & 0 \\
 2 & 0 & 1 & 2 & 2 \\
 0 & 0 & 2 & 0 & 1 \\
 1 & 0 & 2 & 1 & 0 \\
},
\\
 3) \;
\smat{
 2 & -1 & 0 & -1 & 0 \\
-2 & 0 & 0 &-2 & 0 \\
 0 & 0 & 2 & -1 & -1 \\
-2 &-2 & -1 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2
}^{-1}=
\smat{
 0 & 1 & 1 & 0 & 2 \\
 2 & 2 & 0 & 0 & 0 \\
 2 & 0 & 1 & 2 & 2 \\
 0 & 0 & 2 & 0 & 1 \\
 1 & 0 & 2 & 1 & 0 \\
},
\quad 4) \;
\smat{
 0 & 0 & 0 & -1 & 0 \\
 0 & 2 & 0 & -1 & 0 \\
 0 & 0 & 0 &-2 & -1 \\
 -1 & -1 &-2 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2
}^{-1}=
\smat{
 0 & 1 & 1 & 2 & 2 \\
 1 & 2 & 0 & 0 & 0 \\
 1 & 0 & 1 & 0 & 2 \\
 2 & 0 & 0 & 0 & 0 \\
 2 & 0 & 2 & 0 & 0 \\
},
\\
 5) \;
\smat{
 0 & 0 & 0 &-2 & 0 \\
 0 & 2 & 0 & -1 & 0 \\
 0 & 0 & 0 &-2 & -1 \\
 -1 & -2 & -1 & 2 & 0 \\
 0 & 0 & -1 & 0 & 2
}^{-1}=
\smat{
 2 & 2 & 2 & 2 & 1 \\
 2 & 2 & 0 & 0 & 0 \\
 2 & 0 & 1 & 0 & 2 \\
 1 & 0 & 0 & 0 & 0 \\
 1 & 0 & 2 & 0 & 0 \\
},
\quad 6) \;
\smat{
 0 & 0 & 0 & -1 & 0 \\
 0 & 2 & 0 & -1 & 0 \\
 0 & 0 & 0 & -1 &-2 \\
 -1 & -1 & -1 & 2 & 0 \\
 0 & 0 &-2 & 0 & 0
}^{-1}=
\smat{
 0 & 1 & 0 & 2 & 2 \\
 1 & 2 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 1 \\
 2 & 0 & 0 & 0 & 0 \\
 2 & 0 & 1 & 0 & 0 \\
},
\\
7) \;
\smat{
 0 & 0 & 0 &-2 & 0 \\
 0 & 2 & 0 & -1 & 0 \\
 0 & 0 & 0 & -1 &-2 \\
-2 & -1 & -1 & 0 & 0 \\
 0 & 0 &-2 & 0 & 0
}^{-1}=
\smat{
 2 & 2 & 0 & 1 & 1 \\
 2 & 2 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 1 \\
 1 & 0 & 0 & 0 & 0 \\
 1 & 0 & 1 & 0 & 0 \\
},
\quad 8) \;
\smat{
 0 & 0 & 0 & -1 & 0 \\
 0 & 2 & 0 & -1 & 0 \\
 0 & 0 & 2 & -1 & -1 \\
 -1 & -1 & -1 & 2 & 0 \\
 0 & 0 & -1 & 0 & 0
}^{-1}=
\smat{
 0 & 1 & 0 & 2 & 1 \\
 1 & 2 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 2 \\
 2 & 0 & 0 & 0 & 0 \\
 1 & 0 & 2 & 0 & 1 \\
}, \\
9) \;
\smat{
 2 & 0 & 0 & -1 & 0 \\
 0 & 0 &-2 &-2 & 0 \\
 0 & -1 & 2 & -1 & -1 \\
 -1 &-2 &-2 & 0 & 0 \\
 0 & 0 &-2 & 0 & 0
}^{-1}=
\smat{
 2 & 2 & 0 & 0 & 1 \\
 2 & 2 & 0 & 1 & 0 \\
 0 & 0 & 0 & 0 & 1 \\
 0 & 1 & 0 & 0 & 2 \\
 1 & 0 & 2 & 2 & 0 \\
},\quad
 10)\;
\smat{
 0 & 0 & 0 &-2 & 0 \\
 0 & 2 & 0 & -1 & 0 \\
 0 & 0 & 2 & -1 & -1 \\
-2 & -1 & -1 & 0 & 0 \\
 0 & 0 & -1 & 0 & 0
}^{-1}=
\smat{
 2 & 2 & 0 & 1 & 2 \\
 2 & 2 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 2 \\
 1 & 0 & 0 & 0 & 0 \\
 2 & 0 & 2 & 0 & 1 \\
},\\
11)\;
\smat{
 2 & 0 & 0 & -1 & 0 \\
 0 & 0 & -1 & -1 & 0 \\
 0 & -1 & 0 & 0 &-2 \\
 -1 & -1 & 0 & 2 & 0 \\
 0 & 0 &-2 & 0 & 0
}^{-1}=
\smat{
 2 & 1 & 0 & 0 & 1 \\
 1 & 0 & 0 & 2 & 0 \\
 0 & 0 & 0 & 0 & 1 \\
 0 & 2 & 0 & 0 & 2 \\
 1 & 0 & 1 & 2 & 0 \\
},
\quad 12)\;
\smat{
 2 & 0 & 0 & -1 & 0 \\
 0 & 0 &-2 &-2 & 0 \\
 0 &-2 & 0 &-2 & -1 \\
 -1 &-2 &-2 & 0 & 0 \\
 0 & 0 & -1 & 0 & 0
}^{-1}=
\smat{
 2 & 2 & 0 & 0 & 2 \\
 2 & 2 & 0 & 1 & 0 \\
 0 & 0 & 0 & 0 & 2 \\
 0 & 1 & 0 & 0 & 1 \\
 2 & 0 & 2 & 1 & 1 \\
},
\\ 13)\;
\smat{
 2 & 0 & 0 & -1 & 0 \\
 0 & 2 & -1 & -2 & 0 \\
 0 &-2 & 0 & 0 & -1 \\
 -1 & -1 & 0 & 2 & 0 \\
 0 & 0 & -1 & 0 & 2
}^{-1}=
\smat{
 2 & 2 & 2 & 0 & 1 \\
 1 & 0 & 0 & 2 & 0 \\
 2 & 0 & 1 & 1 & 2 \\
 0 & 1 & 1 & 0 & 2 \\
 1 & 0 & 2 & 2 & 0 \\
},
\quad 14)\;
\smat{
 2 & 0 & 0 & -1 & 0 \\
 0 & 0 & -1 & -1 & 0 \\
 0 & -1 & 2 & 0 & -1 \\
 -1 & -1 & 0 & 2 & 0 \\
 0 & 0 & -1 & 0 & 0
}^{-1}=
\smat{
 2 & 1 & 0 & 0 & 2 \\
 1 & 0 & 0 & 2 & 0 \\
 0 & 0 & 0 & 0 & 2 \\
 0 & 2 & 0 & 0 & 1 \\
 2 & 0 & 2 & 1 & 1 \\
},
\\ \quad 15)\;
\smat{
 2 & 0 & 0 & -1 & 0 \\
 0 & 2 & -1 & 0 & 0 \\
 0 & -1 & 0 & -1 &-2 \\
 -1 & 0 & -1 & 2 & 0 \\
 0 & 0 & -1 & 0 & 2
}^{-1}=
\smat{
 2 & 2 & 1 & 0 & 1 \\
 2 & 2 & 0 & 1 & 0 \\
 1 & 0 & 0 & 2 & 0 \\
 0 & 1 & 2 & 0 & 2 \\
 2 & 0 & 0 & 1 & 2 \\
}
\end{matrix}
\]

\subsubsection{$\fg(4,6)$}
\[
\tiny
\arraycolsep=1.5pt
\begin{matrix}
1) \smat{
 2&-1&0&0&0&0 \\
 -1&2&-1&0&0&0 \\
 0&-1&2&-1&0&0 \\
 0&0&-2&0&-2&-1 \\
 0&0&0&-1&2&0 \\
 0&0&0&-1&0&0
 }^{-1}=
\smat{
 0 & 2 & 1 & 0 & 0 & 2 \\
 2 & 1 & 2 & 0 & 0 & 1 \\
 1 & 2 & 0 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & 2 \\
 0 & 0 & 0 & 0 & 2 & 1 \\
 1 & 2 & 0 & 2 & 2 & 1 \\
}\ \
2) \smat{
 2&-1&0&0&0&0 \\
 -1&2&-1&0&0&0 \\
 0&-2&0&-1&-1&0 \\
 0&0&-1&0&-1&-2 \\
 0&0&-1&-1&0&0 \\
 0&0&0&-1&0&2
 }^{-1}=
\smat{
 0 & 2 & 2 & 1 & 0 & 1 \\
 2 & 1 & 1 & 2 & 0 & 2 \\
 1 & 2 & 0 & 0 & 0 & 0 \\
 2 & 1 & 0 & 0 & 2 & 0 \\
 0 & 0 & 0 & 2 & 1 & 2 \\
 1 & 2 & 0 & 0 & 1 & 2 \\
}
\\
3) \smat{
 2&-1&0&0&0&0 \\
 -1&2&-1&0&0&0 \\
 0&-1&2&-1&0&0 \\
 0&0&-1&2&-1&-1 \\
 0&0&0&-1&2&0 \\
 0&0&0&-1&0&0
 }^{-1}=
\smat{
 0 & 2 & 1 & 0 & 0 & 2 \\
 2 & 1 & 2 & 0 & 0 & 1 \\
 1 & 2 & 0 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & 2 \\
 0 & 0 & 0 & 0 & 2 & 1 \\
 2 & 1 & 0 & 2 & 1 & 0 \\
}\ \
\ \ 4)
 \smat{
 2&-1&0&0&0&0 \\
 -2&0&-1&0&0&0 \\
 0&-1&0&-2&-2&0 \\
 0&0&-1&2&0&-1 \\
 0&0&-1&0&2&0 \\
 0&0&0&-1&0&2
 }^{-1}=
 \smat{
 0 & 1 & 0 & 2 & 0 & 1 \\
 2 & 2 & 0 & 1 & 0 & 2 \\
 0 & 0 & 0 & 2 & 0 & 1 \\
 2 & 2 & 1 & 0 & 1 & 0 \\
 0 & 0 & 0 & 1 & 2 & 2 \\
 1 & 1 & 2 & 0 & 2 & 2 \\
}
\\
5) \smat{
 2&-1&0&0&0&0 \\
 -1&2&-1&0&0&0 \\
 0&-1&2&0&-1&0 \\
 0&0&0&2&-1&-1 \\
 0&0&-1&-1&0&0 \\
 0&0&0&-1&0&2
 }^{-1}=
\smat{
 0 & 2 & 1 & 2 & 0 & 1 \\
 2 & 1 & 2 & 1 & 0 & 2 \\
 1 & 2 & 0 & 0 & 0 & 0 \\
 2 & 1 & 0 & 0 & 2 & 0 \\
 0 & 0 & 0 & 2 & 0 & 1 \\
 1 & 2 & 0 & 0 & 1 & 2 \\
}\ \
6)
 \smat{
 0&-1&0&0&0&0 \\
 -1&0&-2&0&0&0 \\
 0&-1&2&-1&-1&0 \\
 0&0&-1&2&0&-1 \\
 0&0&-1&0&2&0 \\
 0&0&0&-1&0&2
 }^{-1}=
 \smat{
 0 & 2 & 0 & 2 & 0 & 1 \\
 2 & 0 & 0 & 0 & 0 & 0 \\
 0 & 0 & 0 & 2 & 0 & 1 \\
 1 & 0 & 2 & 0 & 1 & 0 \\
 0 & 0 & 0 & 1 & 2 & 2 \\
 2 & 0 & 1 & 0 & 2 & 2 \\
}\\
7) \smat{
 0&-1&0&0&0&0 \\
 -1&2&-1&0&0&0 \\
 0&-1&2&-1&-1&0 \\
 0&0&-1&2&0&-1 \\
 0&0&-1&0&2&0 \\
 0&0&0&-1&0&2
 }^{-1}=
 \smat{
 1 & 2 & 0 & 1 & 0 & 2 \\
 2 & 0 & 0 & 0 & 0 & 0 \\
 0 & 0 & 0 & 2 & 0 & 1 \\
 1 & 0 & 2 & 0 & 1 & 0 \\
 0 & 0 & 0 & 1 & 2 & 2 \\
 2 & 0 & 1 & 0 & 2 & 2 \\
}\\
\end{matrix}
\]
\subsubsection{$\fg(6,6)$}
\[
\tiny \arraycolsep=1.5pt
 \begin{matrix}
1)
\smat{
 0&-1&0&0&0&0 \\
 -1&0&-2&0&0&0 \\
 0&-1&2&-1&0&0 \\
 0&0&-2&0&-2&-1 \\
 0&0&0&-1&2&0 \\
 0&0&0&-1&0&0
 }^{-1}=
 \smat{
 1 & 2 & 2 & 0 & 0 & 1 \\
 2 & 0 & 0 & 0 & 0 & 0 \\
 1 & 0 & 2 & 0 & 0 & 1 \\
 0 & 0 & 0 & 0 & 0 & 2 \\
 0 & 0 & 0 & 0 & 2 & 1 \\
 1 & 0 & 2 & 2 & 2 & 2 \\
}\ \
2) \smat{
 0&-2&0&0&0&0 \\
 -1&2&-1&0&0&0 \\
 0&-1&2&-1&0&0 \\
 0&0&-2&0&-2&-1 \\
 0&0&0&-1&2&0 \\
 0&0&0&-1&0&0
 }^{-1}=
 \smat{
 0 & 2 & 1 & 0 & 0 & 2 \\
 1 & 0 & 0 & 0 & 0 & 0 \\
 2 & 0 & 2 & 0 & 0 & 1 \\
 0 & 0 & 0 & 0 & 0 & 2 \\
 0 & 0 & 0 & 0 & 2 & 1 \\
 2 & 0 & 2 & 2 & 2 & 2 \\
}\\

3) \smat{
 2&-1&0&0&0&0 \\
 -2&0&-1&0&0&0 \\
 0&-1&0&-2&0&0 \\
 0&0&-2&0&-2&-1 \\
 0&0&0&-1&2&0 \\
 0&0&0&-1&0&0
 }^{-1}=
 \smat{
 2 & 0 & 1 & 0 & 0 & 1 \\
 0 & 0 & 2 & 0 & 0 & 2 \\
 2 & 2 & 1 & 0 & 0 & 1 \\
 0 & 0 & 0 & 0 & 0 & 2 \\
 0 & 0 & 0 & 0 & 2 & 1 \\
 2 & 2 & 1 & 2 & 2 & 2 \\
}
\ \
4)
\smat{
 0&-1&0&0&0&0 \\
 -1&0&-2&0&0&0 \\
 0&-2&0&-1&-1&0 \\
 0&0&-1&0&-1&-2 \\
 0&0&-1&-1&0&0 \\
 0&0&0&-1&0&2
 }^{-1}=
 \smat{
 1 & 2 & 1 & 2 & 0 & 2 \\
 2 & 0 & 0 & 0 & 0 & 0 \\
 1 & 0 & 1 & 2 & 0 & 2 \\
 2 & 0 & 2 & 1 & 2 & 1 \\
 0 & 0 & 0 & 2 & 1 & 2 \\
 1 & 0 & 1 & 2 & 1 & 1 \\
}\\

5) \smat{
 0&-1&0&0&0&0 \\
 -1&0&-2&0&0&0 \\
 0&-1&2&-1&0&0 \\
 0&0&-1&2&-1&-1 \\
 0&0&0&-1&2&0 \\
 0&0&0&-1&0&0
 }^{-1}=
 \smat{
 1 & 2 & 2 & 0 & 0 & 1 \\
 2 & 0 & 0 & 0 & 0 & 0 \\
 1 & 0 & 2 & 0 & 0 & 1 \\
 0 & 0 & 0 & 0 & 0 & 2 \\
 0 & 0 & 0 & 0 & 2 & 1 \\
 2 & 0 & 1 & 2 & 1 & 2 \\
}
\ \
6) \smat{
 0&-1&0&0&0&0 \\
 -1&2&-1&0&0&0 \\
 0&-2&0&-1&-1&0 \\
 0&0&-1&0&-1&-2 \\
 0&0&-1&-1&0&0 \\
 0&0&0&-1&0&2
 }^{-1}=
 \smat{
 0 & 2 & 2 & 1 & 0 & 1 \\
 2 & 0 & 0 & 0 & 0 & 0 \\
 1 & 0 & 1 & 2 & 0 & 2 \\
 2 & 0 & 2 & 1 & 2 & 1 \\
 0 & 0 & 0 & 2 & 1 & 2 \\
 1 & 0 & 1 & 2 & 1 & 1 \\
}\\
7)
 \smat{
 0&-1&0&0&0&0 \\
 -1&2&-1&0&0&0 \\
 0&-1&2&-1&0&0 \\
 0&0&-1&2&-1&-1 \\
 0&0&0&-1&2&0 \\
 0&0&0&-1&0&0
 }^{-1}=
 \smat{
 0 & 2 & 1 & 0 & 0 & 2 \\
 2 & 0 & 0 & 0 & 0 & 0 \\
 1 & 0 & 2 & 0 & 0 & 1 \\
 0 & 0 & 0 & 0 & 0 & 2 \\
 0 & 0 & 0 & 0 & 2 & 1 \\
 2 & 0 & 1 & 2 & 1 & 2 \\
}\ \
8) \smat{
 2&-1&0&0&0&0 \\
 -1&2&-1&0&0&0 \\
 0&-2&0&-1&0&0 \\
 0&0&-1&2&-2&-1 \\
 0&0&0&-1&2&0 \\
 0&0&0&-1&0&0
 }^{-1}=
 \smat{
 2 & 0 & 2 & 0 & 0 & 1 \\
 0 & 0 & 1 & 0 & 0 & 2 \\
 1 & 2 & 0 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & 2 \\
 0 & 0 & 0 & 0 & 2 & 1 \\
 2 & 1 & 0 & 2 & 2 & 2 \\
}\\
9)
\smat{
 2&-1&0&0&0&0 \\
 -2&0&-1&0&0&0 \\
 0&-1&2&-1&-1&0 \\
 0&0&-1&0&-1&-2 \\
 0&0&-1&-1&0&0 \\
 0&0&0&-1&0&2
 }^{-1}=
 \smat{
 2 & 0 & 1 & 2 & 0 & 2 \\
 0 & 0 & 2 & 1 & 0 & 1 \\
 2 & 2 & 1 & 2 & 0 & 2 \\
 1 & 1 & 2 & 1 & 2 & 1 \\
 0 & 0 & 0 & 2 & 1 & 2 \\
 2 & 2 & 1 & 2 & 1 & 1 \\
}\ \
10)
 \smat{
 2&-1&0&0&0&0 \\
 -2&0&-1&0&0&0 \\
 0&-1&0&-2&0&0 \\
 0&0&-1&2&-1&-1 \\
 0&0&0&-1&2&0 \\
 0&0&0&-1&0&0
 }^{-1}=
 \smat{
 2 & 0 & 1 & 0 & 0 & 1 \\
 0 & 0 & 2 & 0 & 0 & 2 \\
 2 & 2 & 1 & 0 & 0 & 1 \\
 0 & 0 & 0 & 0 & 0 & 2 \\
 0 & 0 & 0 & 0 & 2 & 1 \\
 1 & 1 & 2 & 2 & 1 & 2 \\
}\\
11) \smat{
 0&-1&0&0&0&0 \\
 -1&2&-1&0&0&0 \\
 0&-1&0&-2&-2&0 \\
 0&0&-1&2&0&-1 \\
 0&0&-1&0&2&0 \\
 0&0&0&-1&0&2
 }^{-1}=
 \smat{
 1 & 2 & 0 & 1 & 0 & 2 \\
 2 & 0 & 0 & 0 & 0 & 0 \\
 0 & 0 & 0 & 2 & 0 & 1 \\
 2 & 0 & 1 & 2 & 1 & 1 \\
 0 & 0 & 0 & 1 & 2 & 2 \\
 1 & 0 & 2 & 1 & 2 & 1 \\
}\ \
12)
 \smat{
 0&-1&0&0&0&0 \\
 -1&0&-2&0&0&0 \\
 0&-1&2&0&-1&0 \\
 0&0&0&2&-1&-1 \\
 0&0&-1&-1&0&0 \\
 0&0&0&-1&0&2
 }^{-1}=
 \smat{
 1 & 2 & 2 & 1 & 0 & 2 \\
 2 & 0 & 0 & 0 & 0 & 0 \\
 1 & 0 & 2 & 1 & 0 & 2 \\
 2 & 0 & 1 & 2 & 2 & 1 \\
 0 & 0 & 0 & 2 & 0 & 1 \\
 1 & 0 & 2 & 1 & 1 & 1 \\
}\\
13)
 \smat{
 0&-1&0&0&0&0 \\
 -2&0&-1&0&0&0 \\
 0&-1&0&-2&-2&0 \\
 0&0&-1&2&0&-1 \\
 0&0&-1&0&2&0 \\
 0&0&0&-1&0&2
 }^{-1}=
 \smat{
 0 & 1 & 0 & 2 & 0 & 1 \\
 2 & 0 & 0 & 0 & 0 & 0 \\
 0 & 0 & 0 & 2 & 0 & 1 \\
 2 & 0 & 1 & 2 & 1 & 1 \\
 0 & 0 & 0 & 1 & 2 & 2 \\
 1 & 0 & 2 & 1 & 2 & 1 \\
}\ \
14) \smat{
 0&-1&0&0&0&0 \\
 -1&2&-1&0&0&0 \\
 0&-1&2&0&-1&0 \\
 0&0&0&2&-1&-1 \\
 0&0&-1&-1&0&0 \\
 0&0&0&-1&0&2
 }^{-1}=
 \smat{
 0 & 2 & 1 & 2 & 0 & 1 \\
 2 & 0 & 0 & 0 & 0 & 0 \\
 1 & 0 & 2 & 1 & 0 & 2 \\
 2 & 0 & 1 & 2 & 2 & 1 \\
 0 & 0 & 0 & 2 & 0 & 1 \\
 1 & 0 & 2 & 1 & 1 & 1 \\
}\\
15) \smat{
 2&-1&0&0&0&0 \\
 -1&2&-1&0&0&0 \\
 0&-2&0&-1&0&0 \\
 0&0&-1&0&-2&-2 \\
 0&0&0&-1&2&0 \\
 0&0&0&-1&0&0
 }^{-1}=
 \smat{
 2 & 0 & 2 & 0 & 0 & 1 \\
 0 & 0 & 1 & 0 & 0 & 2 \\
 1 & 2 & 0 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & 2 \\
 0 & 0 & 0 & 0 & 2 & 1 \\
 1 & 2 & 0 & 1 & 1 & 2 \\
}\ \
16)
 \smat{
 2&-1&0&0&0&0 \\
 -2&0&-1&0&0&0 \\
 0&-1&0&0&-2&0 \\
 0&0&0&2&-1&-1 \\
 0&0&-1&-1&0&0 \\
 0&0&0&-1&0&2
 }^{-1}=
 \smat{
 2 & 0 & 1 & 1 & 0 & 2 \\
 0 & 0 & 2 & 2 & 0 & 1 \\
 2 & 2 & 1 & 1 & 0 & 2 \\
 1 & 1 & 2 & 2 & 2 & 1 \\
 0 & 0 & 0 & 2 & 0 & 1 \\
 2 & 2 & 1 & 1 & 1 & 1 \\
}\\
17) \smat{
 2&-1&0&0&0&0 \\
 -1&0&-2&0&0&0 \\
 0&-1&2&-1&-1&0 \\
 0&0&-1&2&0&-1 \\
 0&0&-1&0&2&0 \\
 0&0&0&-1&0&2
 }^{-1}=
 \smat{
 0 & 2 & 0 & 2 & 0 & 1 \\
 2 & 1 & 0 & 1 & 0 & 2 \\
 0 & 0 & 0 & 2 & 0 & 1 \\
 1 & 2 & 2 & 2 & 1 & 1 \\
 0 & 0 & 0 & 1 & 2 & 2 \\
 2 & 1 & 1 & 1 & 2 & 1 \\
}
\ \
18) \smat{
 2&-1&0&0&0&0 \\
 -1&2&-1&0&0&0 \\
 0&-1&2&-1&0&0 \\
 0&0&-2&0&-1&-1 \\
 0&0&0&-1&0&-1 \\
 0&0&0&-1&-1&2
 }^{-1}=
 \smat{
 2 & 0 & 1 & 1 & 0 & 2 \\
 0 & 0 & 2 & 2 & 0 & 1 \\
 1 & 2 & 0 & 0 & 0 & 0 \\
 2 & 1 & 0 & 1 & 0 & 2 \\
 0 & 0 & 0 & 0 & 1 & 2 \\
 1 & 2 & 0 & 2 & 2 & 1 \\
}\\
19)
 \smat{
 2&-1&0&0&0&0 \\
 -1&2&-1&0&0&0 \\
 0&-2&0&0&-1&0 \\
 0&0&0&2&-1&-1 \\
 0&0&-1&-2&2&0 \\
 0&0&0&-1&0&2
 }^{-1}=
 \smat{
 2 & 0 & 2 & 1 & 0 & 2 \\
 0 & 0 & 1 & 2 & 0 & 1 \\
 1 & 2 & 0 & 0 & 0 & 0 \\
 1 & 2 & 0 & 2 & 1 & 1 \\
 0 & 0 & 0 & 2 & 0 & 1 \\
 2 & 1 & 0 & 1 & 2 & 1 \\
}\ \
20) \smat{
 2&-1&0&0&0&0 \\
 -1&2&-1&0&0&0 \\
 0&-1&2&-1&0&0 \\
 0&0&-1&2&-1&0 \\
 0&0&0&-1&0&-1 \\
 0&0&0&0&-1&0
 }^{-1}=
 \smat{
 2 & 0 & 1 & 2 & 0 & 1 \\
 0 & 0 & 2 & 1 & 0 & 2 \\
 1 & 2 & 0 & 0 & 0 & 0 \\
 2 & 1 & 0 & 2 & 0 & 1 \\
 0 & 0 & 0 & 0 & 0 & 2 \\
 1 & 2 & 0 & 1 & 2 & 2 \\
}\\
21) \smat{
 2&-1&0&0&0&0 \\
 -1&2&-1&0&0&0 \\
 0&-1&2&-1&0&0 \\
 0&0&-1&2&-1&0 \\
 0&0&0&-2&2&-1 \\
 0&0&0&0&-1&0
 }^{-1}=
 \smat{
 2 & 0 & 1 & 2 & 0 & 1 \\
 0 & 0 & 2 & 1 & 0 & 2 \\
 1 & 2 & 0 & 0 & 0 & 0 \\
 2 & 1 & 0 & 2 & 0 & 1 \\
 0 & 0 & 0 & 0 & 0 & 2 \\
 2 & 1 & 0 & 2 & 2 & 2 \\
}\\
\end{matrix}
\]

\subsubsection{$\fg{}(8,6)$}
\[\tiny \arraycolsep=1.5pt
\begin{matrix} 1)
\smat{
 2&0&-1&0&0&0&0 \\
 0&2&0&-1&0&0&0 \\
 -1&0&2&-1&0&0&0 \\
 0&-1&-1&2&-1&0&0 \\
 0&0&0&-1&2&-1&0 \\
 0&0&0&0&-2&0&-1 \\
 0&0&0&0&0&-1&0
 }^{-1}=
 \smat{
 1 & 2 & 1 & 1 & 2 & 0 & 1 \\
 2 & 2 & 1 & 0 & 0 & 0 & 0 \\
 1 & 1 & 2 & 2 & 1 & 0 & 2 \\
 1 & 0 & 2 & 0 & 0 & 0 & 0 \\
 2 & 0 & 1 & 0 & 2 & 0 & 1 \\
 0 & 0 & 0 & 0 & 0 & 0 & 2 \\
 2 & 0 & 1 & 0 & 2 & 2 & 1 \\
}\ \
2) \smat{
 2&0&-1&0&0&0&0 \\
 0&2&0&-1&0&0&0 \\
 -1&0&2&-1&0&0&0 \\
 0&-1&-1&2&-1&0&0 \\
 0&0&0&-2&0&-1&0 \\
 0&0&0&0&-1&0&-2 \\
 0&0&0&0&0&-1&2
 }^{-1}=
 \smat{
 1 & 2 & 1 & 1 & 1 & 2 & 2 \\
 2 & 2 & 1 & 0 & 0 & 0 & 0 \\
 1 & 1 & 2 & 2 & 2 & 1 & 1 \\
 1 & 0 & 2 & 0 & 0 & 0 & 0 \\
 2 & 0 & 1 & 0 & 1 & 2 & 2 \\
 1 & 0 & 2 & 0 & 2 & 0 & 0 \\
 2 & 0 & 1 & 0 & 1 & 0 & 2 \\
}\\
3)
 \smat{
 2&0&-1&0&0&0&0 \\
 0&2&0&-1&0&0&0 \\
 -1&0&2&-1&0&0&0 \\
 0&-1&-1&2&-1&0&0 \\
 0&0&0&-1&2&-1&0 \\
 0&0&0&0&-1&2&-1 \\
 0&0&0&0&0&-1&0
 }^{-1}=
 \smat{
 1 & 2 & 1 & 1 & 2 & 0 & 1 \\
 2 & 2 & 1 & 0 & 0 & 0 & 0 \\
 1 & 1 & 2 & 2 & 1 & 0 & 2 \\
 1 & 0 & 2 & 0 & 0 & 0 & 0 \\
 2 & 0 & 1 & 0 & 2 & 0 & 1 \\
 0 & 0 & 0 & 0 & 0 & 0 & 2 \\
 1 & 0 & 2 & 0 & 1 & 2 & 0 \\
}
\ \
4) \smat{
 2&0&-1&0&0&0&0 \\
 0&2&0&-1&0&0&0 \\
 -1&0&2&-1&0&0&0 \\
 0&-2&-2&0&-1&0&0 \\
 0&0&0&-1&0&-2&0 \\
 0&0&0&0&-1&2&-1 \\
 0&0&0&0&0&-1&2
 }^{-1}=
 \smat{
 1 & 2 & 1 & 2 & 0 & 1 & 2 \\
 2 & 2 & 1 & 0 & 0 & 0 & 0 \\
 1 & 1 & 2 & 1 & 0 & 2 & 1 \\
 1 & 0 & 2 & 0 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & 2 & 1 \\
 1 & 0 & 2 & 0 & 1 & 0 & 0 \\
 2 & 0 & 1 & 0 & 2 & 0 & 2 \\
}\\
5)
 \smat{
 2&0&-1&0&0&0&0 \\
 0&0&-1&-1&0&0&0 \\
 -2&-1&0&-1&0&0&0 \\
 0&-1&-1&0&-2&0&0 \\
 0&0&0&-1&2&-1&0 \\
 0&0&0&0&-1&2&-1 \\
 0&0&0&0&0&-1&2
 }^{-1}=
 \smat{
 1 & 1 & 2 & 1 & 0 & 1 & 2 \\
 2 & 1 & 2 & 0 & 0 & 0 & 0 \\
 1 & 2 & 1 & 2 & 0 & 2 & 1 \\
 2 & 0 & 2 & 1 & 0 & 1 & 2 \\
 0 & 0 & 0 & 0 & 0 & 2 & 1 \\
 1 & 0 & 1 & 2 & 2 & 0 & 0 \\
 2 & 0 & 2 & 1 & 1 & 0 & 2 \\
}\ \
6) \smat{
 2&0&-1&0&0&0&0 \\
 0&0&-2&-2&0&0&0 \\
 -1&-1&2&0&0&0&0 \\
 0&-1&0&2&-1&0&0 \\
 0&0&0&-1&2&-1&0 \\
 0&0&0&0&-1&2&-1 \\
 0&0&0&0&0&-1&2
 }^{-1}=
 \smat{
 1 & 2 & 1 & 2 & 0 & 1 & 2 \\
 1 & 0 & 2 & 0 & 0 & 0 & 0 \\
 1 & 1 & 2 & 1 & 0 & 2 & 1 \\
 2 & 0 & 1 & 2 & 0 & 1 & 2 \\
 0 & 0 & 0 & 0 & 0 & 2 & 1 \\
 1 & 0 & 2 & 1 & 2 & 0 & 0 \\
 2 & 0 & 1 & 2 & 1 & 0 & 2 \\
}\\
7)
 \smat{
 0&0&-1&0&0&0&0 \\
 0&2&-1&0&0&0&0 \\
 -1&-2&0&-2&0&0&0 \\
 0&0&-1&2&-1&0&0 \\
 0&0&0&-1&2&-1&0 \\
 0&0&0&0&-1&2&-1 \\
 0&0&0&0&0&-1&2
 }^{-1}=
 \smat{
 2 & 2 & 2 & 2 & 0 & 1 & 2 \\
 1 & 2 & 0 & 0 & 0 & 0 & 0 \\
 2 & 0 & 0 & 0 & 0 & 0 & 0 \\
 1 & 0 & 0 & 2 & 0 & 1 & 2 \\
 0 & 0 & 0 & 0 & 0 & 2 & 1 \\
 2 & 0 & 0 & 1 & 2 & 0 & 0 \\
 1 & 0 & 0 & 2 & 1 & 0 & 2 \\
}\ \
8)\smat{
 0&0&-1&0&0&0&0 \\
 0&2&-1&0&0&0&0 \\
 -1&-1&2&-1&0&0&0 \\
 0&0&-1&2&-1&0&0 \\
 0&0&0&-1&2&-1&0 \\
 0&0&0&0&-1&2&-1 \\
 0&0&0&0&0&-1&2
 }^{-1}=
 \smat{
 2 & 1 & 2 & 1 & 0 & 2 & 1 \\
 1 & 2 & 0 & 0 & 0 & 0 & 0 \\
 2 & 0 & 0 & 0 & 0 & 0 & 0 \\
 1 & 0 & 0 & 2 & 0 & 1 & 2 \\
 0 & 0 & 0 & 0 & 0 & 2 & 1 \\
 2 & 0 & 0 & 1 & 2 & 0 & 0 \\
 1 & 0 & 0 & 2 & 1 & 0 & 2 \\
}\\
\end{matrix}
\]

\subsubsection{$\fel(5;3)$}
\[\tiny \arraycolsep=1.5pt
 \begin{matrix}
1) \;
\smat{
 0 & -1 & 0 & 0 & 0 \\
 -1 & 0 & 0 & -1 & 0 \\
 0 & 0 & 2 & -1 & -1 \\
 0 & -1 & -1 & 2 & 0 \\
 0 & 0 & -1 & 0 & 2\\
}^{-1}=
\smat{
 0 & 2 & 1 & 0 & 2 \\
 2 & 0 & 0 & 0 & 0 \\
 1 & 0 & 1 & 2 & 2 \\
 0 & 0 & 2 & 0 & 1 \\
 2 & 0 & 2 & 1 & 0 \\
}\ \
2) \;
\smat{
 0 &-2 & 0 & 0 & 0 \\
 -1 & 2 & 0 & -2 & 0 \\
 0 & 0 & 2 & -1 & -1 \\
 0 & -1 & -1 & 2 & 0 \\
 0 & 0 & -1 & 0 & 2\\
}^{-1}=
\smat{
 2 & 2 & 2 & 0 & 1 \\
 1 & 0 & 0 & 0 & 0 \\
 2 & 0 & 1 & 2 & 2 \\
 0 & 0 & 2 & 0 & 1 \\
 1 & 0 & 2 & 1 & 0 \\
 }
\\
 3) \;
\smat{
 2 & -1 & 0 & -1 & 0 \\
-2 & 0 & 0 &-2 & 0 \\
 0 & 0 & 2 & -1 & -1 \\
-2 &-2 & -1 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2\\
}^{-1}=
\smat{
 0 & 1 & 1 & 0 & 2 \\
 2 & 2 & 0 & 0 & 0 \\
 2 & 0 & 1 & 2 & 2 \\
 0 & 0 & 2 & 0 & 1 \\
 1 & 0 & 2 & 1 & 0 \\
 }
\ \ 4) \;
\smat{
 0 & 0 & 0 & -1 & 0 \\
 0 & 2 & 0 & -1 & 0 \\
 0 & 0 & 0 &-2 & -1 \\
 -1 & -1 &-2 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2\\
}^{-1}=
\smat{
 0 & 1 & 1 & 2 & 2 \\
 1 & 2 & 0 & 0 & 0 \\
 1 & 0 & 1 & 0 & 2 \\
 2 & 0 & 0 & 0 & 0 \\
 2 & 0 & 2 & 0 & 0 \\
 }
\\
 5) \;
\smat{
 0 & 0 & 0 &-2 & 0 \\
 0 & 2 & 0 & -1 & 0 \\
 0 & 0 & 0 &-2 & -1 \\
 -1 & -2 & -1 & 2 & 0 \\
 0 & 0 & -1 & 0 & 2\\
}^{-1}=
\smat{
 2 & 2 & 2 & 2 & 1 \\
 2 & 2 & 0 & 0 & 0 \\
 2 & 0 & 1 & 0 & 2 \\
 1 & 0 & 0 & 0 & 0 \\
 1 & 0 & 2 & 0 & 0 \\
 }
\ \ 6) \;
\smat{
 0 & 0 & 0 & -1 & 0 \\
 0 & 2 & 0 & -1 & 0 \\
 0 & 0 & 0 & -1 &-2 \\
 -1 & -1 & -1 & 2 & 0 \\
 0 & 0 &-2 & 0 & 0\\
}^{-1}=
\smat{
 0 & 1 & 0 & 2 & 2 \\
 1 & 2 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 1 \\
 2 & 0 & 0 & 0 & 0 \\
 2 & 0 & 1 & 0 & 0 \\
 }
\\
7) \;
\smat{
 0 & 0 & 0 &-2 & 0 \\
 0 & 2 & 0 & -1 & 0 \\
 0 & 0 & 0 & -1 &-2 \\
-2 & -1 & -1 & 0 & 0 \\
 0 & 0 &-2 & 0 & 0\\
}^{-1}=
\smat{
 2 & 2 & 0 & 1 & 1 \\
 2 & 2 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 1 \\
 1 & 0 & 0 & 0 & 0 \\
 1 & 0 & 1 & 0 & 0 \\
 }
\ \ 8) \;
\smat{
 0 & 0 & 0 & -1 & 0 \\
 0 & 2 & 0 & -1 & 0 \\
 0 & 0 & 2 & -1 & -1 \\
 -1 & -1 & -1 & 2 & 0 \\
 0 & 0 & -1 & 0 & 0\\
}^{-1}=
\smat{
 0 & 1 & 0 & 2 & 1 \\
 1 & 2 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 2 \\
 2 & 0 & 0 & 0 & 0 \\
 1 & 0 & 2 & 0 & 1 \\
 }
\\ 9) \;
\smat{
 2 & 0 & 0 & -1 & 0 \\
 0 & 0 &-2 &-2 & 0 \\
 0 & -1 & 2 & -1 & -1 \\
 -1 &-2 &-2 & 0 & 0 \\
 0 & 0 &-2 & 0 & 0\\
}^{-1}=
\smat{
 2 & 2 & 0 & 0 & 1 \\
 2 & 2 & 0 & 1 & 0 \\
 0 & 0 & 0 & 0 & 1 \\
 0 & 1 & 0 & 0 & 2 \\
 1 & 0 & 2 & 2 & 0 \\
 }
\ \ 10)\;
\smat{
 0 & 0 & 0 &-2 & 0 \\
 0 & 2 & 0 & -1 & 0 \\
 0 & 0 & 2 & -1 & -1 \\
-2 & -1 & -1 & 0 & 0 \\
 0 & 0 & -1 & 0 & 0\\
}^{-1}=
\smat{
 2 & 2 & 0 & 1 & 2 \\
 2 & 2 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 2 \\
 1 & 0 & 0 & 0 & 0 \\
 2 & 0 & 2 & 0 & 1 \\
 }
\\ 11)\;
\smat{
 2 & 0 & 0 & -1 & 0 \\
 0 & 0 & -1 & -1 & 0 \\
 0 & -1 & 0 & 0 &-2 \\
 -1 & -1 & 0 & 2 & 0 \\
 0 & 0 &-2 & 0 & 0\\
}^{-1}=
\smat{
 2 & 1 & 0 & 0 & 1 \\
 1 & 0 & 0 & 2 & 0 \\
 0 & 0 & 0 & 0 & 1 \\
 0 & 2 & 0 & 0 & 2 \\
 1 & 0 & 1 & 2 & 0 \\
 }
\ \ 12)\;
\smat{
 2 & 0 & 0 & -1 & 0 \\
 0 & 0 &-2 &-2 & 0 \\
 0 &-2 & 0 &-2 & -1 \\
 -1 &-2 &-2 & 0 & 0 \\
 0 & 0 & -1 & 0 & 0\\
}^{-1}=
\smat{
 2 & 2 & 0 & 0 & 2 \\
 2 & 2 & 0 & 1 & 0 \\
 0 & 0 & 0 & 0 & 2 \\
 0 & 1 & 0 & 0 & 1 \\
 2 & 0 & 2 & 1 & 1 \\
 }
\\ 13)\;
\smat{
 2 & 0 & 0 & -1 & 0 \\
 0 & 2 & -1 & -2 & 0 \\
 0 &-2 & 0 & 0 & -1 \\
 -1 & -1 & 0 & 2 & 0 \\
 0 & 0 & -1 & 0 & 2\\
}^{-1}=
\smat{
 2 & 2 & 2 & 0 & 1 \\
 1 & 0 & 0 & 2 & 0 \\
 2 & 0 & 1 & 1 & 2 \\
 0 & 1 & 1 & 0 & 2 \\
 1 & 0 & 2 & 2 & 0 \\
 }
\ \ 14)\;
\smat{
 2 & 0 & 0 & -1 & 0 \\
 0 & 0 & -1 & -1 & 0 \\
 0 & -1 & 2 & 0 & -1 \\
 -1 & -1 & 0 & 2 & 0 \\
 0 & 0 & -1 & 0 & 0\\
}^{-1}=
\smat{
 2 & 1 & 0 & 0 & 2 \\
 1 & 0 & 0 & 2 & 0 \\
 0 & 0 & 0 & 0 & 2 \\
 0 & 2 & 0 & 0 & 1 \\
 2 & 0 & 2 & 1 & 1 \\
 }
\\ 15)\;
\smat{
 2 & 0 & 0 & -1 & 0 \\
 0 & 2 & -1 & 0 & 0 \\
 0 & -1 & 0 & -1 &-2 \\
 -1 & 0 & -1 & 2 & 0 \\
 0 & 0 & -1 & 0 & 2\\
}^{-1}=
\smat{
 2 & 2 & 1 & 0 & 1 \\
 2 & 2 & 0 & 1 & 0 \\
 1 & 0 & 0 & 2 & 0 \\
 0 & 1 & 2 & 0 & 2 \\
 2 & 0 & 0 & 1 & 2 \\
 }
\end{matrix}
\]

\ssec{$p=5$}{}~{}

\subsubsection{$\fbrj(2;5)$} $ 1)\; \smat{0&-1\\
-2&1\\}^{-1}=\frac13\smat{1&1\\
2&0\\}, \quad 2)\; \smat{0&-1\\
-3&2\\}^{-1}=\frac12\smat{2&1\\
3&0\\
}.
$

\subsubsection{$\fel(5;5)$}
\[\tiny\arraycolsep=1.5pt
\begin{matrix}
1) \smat{
2&0&-1&0&0 \\
 0&2&0&0&-1 \\
 -1&0&0&-4&-4 \\
 0&0&-4&0&-2 \\
 0&-1&-4&-2&0\\
}^{-1}=
\smat{
 2 & 2 & 3 & 3 & 4 \\
 2 & 4 & 4 & 0 & 2 \\
 3 & 4 & 1 & 1 & 3 \\
 3 & 0 & 1 & 3 & 0 \\
 4 & 2 & 3 & 0 & 4 \\
}\ \
2) \smat{
 0&0&-4&0&0 \\
 0&2&0&0&-1 \\
 -4&0&0&-1&-1 \\
 0&0&-1&2&0 \\
 0&-1&-1&0&2\\
}^{-1}=
\smat{
 2 & 2 & 1 & 3 & 4 \\
 2 & 4 & 0 & 0 & 2 \\
 1 & 0 & 0 & 0 & 0 \\
 3 & 0 & 0 & 3 & 0 \\
 4 & 2 & 0 & 0 & 4 \\
}\\
3) \smat{
 2&0&-1&0&0 \\
 0&2&0&0&-1 \\
 -1&0&2&-1&0 \\
 0&0&-1&0&2 \\
 0&-2&0&-1&2\\
}^{-1}=
\smat{
 2 & 2 & 3 & 4 & 2 \\
 2 & 4 & 4 & 1 & 1 \\
 3 & 4 & 1 & 3 & 4 \\
 4 & 1 & 3 & 2 & 1 \\
 4 & 2 & 3 & 2 & 2 \\
}\ \
4) \smat{
 2&0&-1&0&0 \\
 0&0&0&2&-4 \\
 -1&0&2&0&-1 \\
 0&-1&0&2&-1 \\
 0&-4&-1&2&0\\
}^{-1}=
 \smat{
 2 & 2 & 3 & 4 & 4 \\
 2 & 4 & 4 & 0 & 1 \\
 3 & 4 & 1 & 3 & 3 \\
 3 & 0 & 1 & 4 & 4 \\
 4 & 1 & 3 & 2 & 2 \\
}\\

5) \smat{
 0&0&-1&0&0 \\
 0&2&0&0&-1 \\
 -1&0&2&-1&-1 \\
 0&0&-1&2&0 \\
 0&-1&-1&0&2\\
}^{-1}=
\smat{
 0 & 3 & 4 & 2 & 1 \\
 3 & 4 & 0 & 0 & 2 \\
 4 & 0 & 0 & 0 & 0 \\
 2 & 0 & 0 & 3 & 0 \\
 1 & 2 & 0 & 0 & 4 \\
}\ \
6) \smat{
 2&0&-1&0&0 \\
 0&0&0&-2&-1 \\
 -1&0&2&0&-1 \\
 0&-2&0&0&0 \\
 0&-1&-1&0&2\\
}^{-1}=
\smat{
 2 & 0 & 3 & 3 & 4 \\
 0 & 0 & 0 & 2 & 0 \\
 3 & 0 & 1 & 1 & 3 \\
 3 & 2 & 1 & 3 & 4 \\
 4 & 0 & 3 & 4 & 2 \\
}
\\
7)\smat{
 2&0&-1&0&0 \\
 0&2&0&-1&-2 \\
 -1&0&2&0&-1 \\
 0&2&0&0&0 \\
 0&-1&-1&0&2\\
}^{-1}=
\smat{
 2 & 0 & 3 & 2 & 4 \\
 0 & 0 & 0 & 3 & 0 \\
 3 & 0 & 1 & 4 & 3 \\
 2 & 4 & 4 & 4 & 1 \\
 4 & 0 & 3 & 1 & 2 \\
}\\
\end{matrix}
\]

\section[Almost affine Lie (super)algebras]{Simple hyperbolic Lie algebras and almost affine Lie superalgebras over $\Cee$}\label{AA}

The numbering of Cartan matrices follows that in the arXiv version of \cite{CCLL}, which contains Cartan matrices of all hyperbolic Lie algebras (classified by Li Wang Lai; for history, and rediscovery of Li Wang Lai's result in relation with cosmological billiards, see \cite{CCLL}). The published version of \cite{CCLL} has only new results: the Cartan matrices of almost affine Lie \textbf{super}algebras, whereas the arXiv version reproduces Li Wang Lai's result.

Below, the symbol $\fbox{!!!}$ marks the cases where the inverse of the Cartan matrix has no zero elements, cf. \cite{ZH}.

\subsection{Cartan matrices $A$, their inverses, and $\det A$ for almost affine Lie superalgebras}\label{ss8.1}{}~{}

\stab{
\noindent\fbox{!!!}$NS3_2$&
$\smat{
 2 & -1 & -1 \\
 -1 & 1 & -1 \\
 -3 & -1 & 2 \\
}$
 & $\frac{1}{7}$
$\smat{
 -1 & -3 & -2 \\
 -5 & -1 & -3 \\
 -4 & -5 & -1 \\
}$
 & -7 } \\
 \stab{$NS3_3$&
$\smat{
 2 & -1 & -1 \\
 -1 & 1 & -1 \\
 -4 & -1 & 2 \\
}$
 & $\frac{1}{9}$
$\smat{
 -1 & -3 & -2 \\
 -6 & 0 & -3 \\
 -5 & -6 & -1 \\
}$
 & -9 } \\
 \stab{$S3_4$&
$\smat{
 2 & -1 & -2 \\
 -1 & 1 & -1 \\
 -2 & -1 & 2 \\
}$
 & $\frac{1}{8}$
$\smat{
 -1 & -4 & -3 \\
 -4 & 0 & -4 \\
 -3 & -4 & -1 \\
}$
 & -8 } \\
 \stab{\fbox{!!!}$S3_5$&
$\smat{
 2 & -1 & -1 \\
 -1 & 1 & -1 \\
 -1 & -1 & 2 \\
}$
 & $\frac{1}{3}$
$\smat{
 -1 & -3 & -2 \\
 -3 & -3 & -3 \\
 -2 & -3 & -1 \\
}$
 & -3 } \\
 \stab{$S3_6$&
$\smat{
 2 & -1 & -1 \\
 -2 & 1 & -1 \\
 -2 & -1 & 2 \\
}$
 & $\frac{1}{8}$
$\smat{
 -1 & -3 & -2 \\
 -6 & -2 & -4 \\
 -4 & -4 & 0 \\
}$
 & -8 } \\
 \stab{$NS3_7$&
$\smat{
 2 & -1 & -1 \\
 -2 & 1 & -1 \\
 -3 & -1 & 2 \\
}$
 & $\frac{1}{10}$
$\smat{
 -1 & -3 & -2 \\
 -7 & -1 & -4 \\
 -5 & -5 & 0 \\
}$
 & -10 } \\
 \stab{$NS3_8$&
$\smat{
 2 & -1 & -1 \\
 -2 & 1 & -1 \\
 -4 & -1 & 2 \\
}$
 & $\frac{1}{12}$
$\smat{
 -1 & -3 & -2 \\
 -8 & 0 & -4 \\
 -6 & -6 & 0 \\
}$
 & -12 } \\
 \stab{$NS3_9$&
$\smat{
 2 & -1 & -2 \\
 -2 & 1 & -1 \\
 -2 & -1 & 2 \\
}$
 & $\frac{1}{12}$
$\smat{
 -1 & -4 & -3 \\
 -6 & 0 & -6 \\
 -4 & -4 & 0 \\
}$
 & -12 } \\
 \stab{$NS3_{10}$&
$\smat{
 2 & -1 & -1 \\
 -2 & 1 & -1 \\
 -1 & -1 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 -1 & -3 & -2 \\
 -5 & -3 & -4 \\
 -3 & -3 & 0 \\
}$
 & -6 } \\
 \stab{$NS3_{11}$&
$\smat{
 2 & -1 & -2 \\
 -2 & 1 & -1 \\
 -1 & -1 & 2 \\
}$
 & $\frac{1}{9}$
$\smat{
 -1 & -4 & -3 \\
 -5 & -2 & -6 \\
 -3 & -3 & 0 \\
}$
 & -9 } \\
 \stab{$NS3_{12}$&
$\smat{
 2 & -1 & -3 \\
 -2 & 1 & -1 \\
 -1 & -1 & 2 \\
}$
 & $\frac{1}{12}$
$\smat{
 -1 & -5 & -4 \\
 -5 & -1 & -8 \\
 -3 & -3 & 0 \\
}$
 & -12 } \\
 \stab{$NS3_{13}$&
$\smat{
 2 & -1 & -4 \\
 -2 & 1 & -1 \\
 -1 & -1 & 2 \\
}$
 & $\frac{1}{15}$
$\smat{
 -1 & -6 & -5 \\
 -5 & 0 & -10 \\
 -3 & -3 & 0 \\
}$
 & -15 } \\
 \stab{$NS3_{14}$&
$\smat{
 2 & -2 & -1 \\
 -1 & 1 & -1 \\
 -2 & -1 & 2 \\
}$
 & $\frac{1}{9}$
$\smat{
 -1 & -5 & -3 \\
 -4 & -2 & -3 \\
 -3 & -6 & 0 \\
}$
 & -9 } \\
 \stab{$NS3_{15}$&
$\smat{
 2 & -2 & -1 \\
 -1 & 1 & -1 \\
 -3 & -1 & 2 \\
}$
 & $\frac{1}{12}$
$\smat{
 -1 & -5 & -3 \\
 -5 & -1 & -3 \\
 -4 & -8 & 0 \\
}$
 & -12 } \\
 \stab{$NS3_{16}$&
$\smat{
 2 & -2 & -1 \\
 -1 & 1 & -1 \\
 -4 & -1 & 2 \\
}$
 & $\frac{1}{15}$
$\smat{
 -1 & -5 & -3 \\
 -6 & 0 & -3 \\
 -5 & -10 & 0 \\
}$
 & -15 } \\
 \stab{$NS3_{17}$&
$\smat{
 2 & -2 & -2 \\
 -1 & 1 & -1 \\
 -2 & -1 & 2 \\
}$
 & $\frac{1}{12}$
$\smat{
 -1 & -6 & -4 \\
 -4 & 0 & -4 \\
 -3 & -6 & 0 \\
}$
 & -12 } \\
 \stab{$NS3_{18}$&
$\smat{
 2 & -2 & -1 \\
 -1 & 1 & -1 \\
 -1 & -1 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 -1 & -5 & -3 \\
 -3 & -3 & -3 \\
 -2 & -4 & 0 \\
}$
 & -6 } \\
 \stab{$S3_{19}$&
$\smat{
 2 & -2 & -2 \\
 -1 & 1 & -1 \\
 -1 & -1 & 2 \\
}$
 & $\frac{1}{8}$
$\smat{
 -1 & -6 & -4 \\
 -3 & -2 & -4 \\
 -2 & -4 & 0 \\
}$
 & -8 } \\
 \stab{$NS3_{20}$&
$\smat{
 2 & -2 & -3 \\
 -1 & 1 & -1 \\
 -1 & -1 & 2 \\
}$
 & $\frac{1}{10}$
$\smat{
 -1 & -7 & -5 \\
 -3 & -1 & -5 \\
 -2 & -4 & 0 \\
}$
 & -10 } \\
 \stab{$NS3_{21}$&
$\smat{
 2 & -2 & -4 \\
 -1 & 1 & -1 \\
 -1 & -1 & 2 \\
}$
 & $\frac{1}{12}$
$\smat{
 -1 & -8 & -6 \\
 -3 & 0 & -6 \\
 -2 & -4 & 0 \\
}$
 & -12 } \\
 \stab{$NS3_{22}$&
$\smat{
 2 & -1 & -1 \\
 -2 & 1 & -2 \\
 -2 & -1 & 2 \\
}$
 & $\frac{1}{12}$
$\smat{
 0 & -3 & -3 \\
 -8 & -2 & -6 \\
 -4 & -4 & 0 \\
}$
 & -12 } \\
 \stab{$NS3_{23}$&
$\smat{
 2 & -1 & -1 \\
 -2 & 1 & -2 \\
 -3 & -1 & 2 \\
}$
 & $\frac{1}{15}$
$\smat{
 0 & -3 & -3 \\
 -10 & -1 & -6 \\
 -5 & -5 & 0 \\
}$
 & -15 } \\
 \stab{$NS3_{24}$&
$\smat{
 2 & -1 & -1 \\
 -2 & 1 & -2 \\
 -4 & -1 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 0 & -1 & -1 \\
 -4 & 0 & -2 \\
 -2 & -2 & 0 \\
}$
 & -18 } \\
 \stab{$S3_{25}$&
$\smat{
 2 & -1 & -2 \\
 -2 & 1 & -2 \\
 -2 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -1 & -1 \\
 -2 & 0 & -2 \\
 -1 & -1 & 0 \\
}$
 & -16 } \\
 \stab{$S3_{26}$&
$\smat{
 2 & -1 & -1 \\
 -2 & 1 & -2 \\
 -1 & -1 & 2 \\
}$
 & $\frac{1}{3}$
$\smat{
 0 & -1 & -1 \\
 -2 & -1 & -2 \\
 -1 & -1 & 0 \\
}$
 & -9 } \\
 \stab{$NS3_{27}$&
$\smat{
 2 & -2 & -1 \\
 -1 & 1 & -2 \\
 -2 & -1 & 2 \\
}$
 & $\frac{1}{15}$
$\smat{
 0 & -5 & -5 \\
 -6 & -2 & -5 \\
 -3 & -6 & 0 \\
}$
 & -15 } \\
 \stab{$NS3_{28}$&
$\smat{
 2 & -2 & -1 \\
 -1 & 1 & -2 \\
 -3 & -1 & 2 \\
}$
 & $\frac{1}{20}$
$\smat{
 0 & -5 & -5 \\
 -8 & -1 & -5 \\
 -4 & -8 & 0 \\
}$
 & -20 } \\
 \stab{$NS3_{29}$&
$\smat{
 2 & -2 & -1 \\
 -1 & 1 & -2 \\
 -4 & -1 & 2 \\
}$
 & $\frac{1}{5}$
$\smat{
 0 & -1 & -1 \\
 -2 & 0 & -1 \\
 -1 & -2 & 0 \\
}$
 & -25 } \\
 \stab{$NS3_{30}$&
$\smat{
 2 & -2 & -2 \\
 -1 & 1 & -2 \\
 -2 & -1 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 0 & -2 & -2 \\
 -2 & 0 & -2 \\
 -1 & -2 & 0 \\
}$
 & -18 } \\
 \stab{$NS3_{31}$&
$\smat{
 2 & -2 & -1 \\
 -1 & 1 & -2 \\
 -1 & -1 & 2 \\
}$
 & $\frac{1}{10}$
$\smat{
 0 & -5 & -5 \\
 -4 & -3 & -5 \\
 -2 & -4 & 0 \\
}$
 & -10 } \\
 \stab{$NS3_{32}$&
$\smat{
 2 & -2 & -2 \\
 -1 & 1 & -2 \\
 -1 & -1 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 0 & -3 & -3 \\
 -2 & -1 & -3 \\
 -1 & -2 & 0 \\
}$
 & -12 } \\
 \stab{$NS3_{33}$&
$\smat{
 2 & -2 & -3 \\
 -1 & 1 & -2 \\
 -1 & -1 & 2 \\
}$
 & $\frac{1}{14}$
$\smat{
 0 & -7 & -7 \\
 -4 & -1 & -7 \\
 -2 & -4 & 0 \\
}$
 & -14 } \\
 \stab{$S3_{34}$&
$\smat{
 2 & -2 & -4 \\
 -1 & 1 & -2 \\
 -1 & -1 & 2 \\
}$
 & $\frac{1}{8}$
$\smat{
 0 & -4 & -4 \\
 -2 & 0 & -4 \\
 -1 & -2 & 0 \\
}$
 & -16 } \\
 \stab{$S3_{35}$&
$\smat{
 2 & -2 & -1 \\
 -1 & 1 & -1 \\
 -2 & -2 & 2 \\
}$
 & $\frac{1}{12}$
$\smat{
 0 & -6 & -3 \\
 -4 & -2 & -3 \\
 -4 & -8 & 0 \\
}$
 & -12 } \\
 \stab{$NS3_{36}$&
$\smat{
 2 & -2 & -1 \\
 -1 & 1 & -1 \\
 -3 & -2 & 2 \\
}$
 & $\frac{1}{15}$
$\smat{
 0 & -6 & -3 \\
 -5 & -1 & -3 \\
 -5 & -10 & 0 \\
}$
 & -15 } \\
 \stab{$NS3_{37}$&
$\smat{
 2 & -2 & -1 \\
 -1 & 1 & -1 \\
 -4 & -2 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 0 & -2 & -1 \\
 -2 & 0 & -1 \\
 -2 & -4 & 0 \\
}$
 & -18 } \\
 \stab{$S3_{38}$&
$\smat{
 2 & -2 & -2 \\
 -1 & 1 & -1 \\
 -2 & -2 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -2 & -1 \\
 -1 & 0 & -1 \\
 -1 & -2 & 0 \\
}$
 & -16 } \\
 \stab{$S3_{39}$&
$\smat{
 2 & -2 & -1 \\
 -1 & 1 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{3}$
$\smat{
 0 & -2 & -1 \\
 -1 & -1 & -1 \\
 -1 & -2 & 0 \\
}$
 & -9 } \\
 \stab{$S3_{40}$&
$\smat{
 2 & -1 & -1 \\
 -1 & 1 & -1 \\
 -1 & -1 & 1 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -2 & -2 \\
 -2 & -1 & -3 \\
 -2 & -3 & -1 \\
}$
 & -4 } \\
 \stab{$NS3_{41}$&
$\smat{
 2 & -1 & -1 \\
 -2 & 1 & -1 \\
 -1 & -1 & 1 \\
}$
 & $\frac{1}{6}$
$\smat{
 0 & -2 & -2 \\
 -3 & -1 & -4 \\
 -3 & -3 & 0 \\
}$
 & -6 } \\
 \stab{$NS3_{42}$&
$\smat{
 2 & -2 & -1 \\
 -1 & 1 & -1 \\
 -1 & -1 & 1 \\
}$
 & $\frac{1}{6}$
$\smat{
 0 & -3 & -3 \\
 -2 & -1 & -3 \\
 -2 & -4 & 0 \\
}$
 & -6 } \\
 \stab{$S3_{43}$&
$\smat{
 2 & -1 & -1 \\
 -2 & 1 & -1 \\
 -2 & -1 & 1 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -1 & -1 \\
 -2 & 0 & -2 \\
 -2 & -2 & 0 \\
}$
 & -8 } \\
 \stab{$NS3_{44}$&
$\smat{
 2 & -2 & -1 \\
 -1 & 1 & -1 \\
 -2 & -1 & 1 \\
}$
 & $\frac{1}{3}$
$\smat{
 0 & -1 & -1 \\
 -1 & 0 & -1 \\
 -1 & -2 & 0 \\
}$
 & -9 } \\
 \stab{$S3_{45}$&
$\smat{
 2 & -2 & -2 \\
 -1 & 1 & -1 \\
 -1 & -1 & 1 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -2 & -2 \\
 -1 & 0 & -2 \\
 -1 & -2 & 0 \\
}$
 & -8 } \\
 \stab{$S3_{46}$&
$\smat{
 1 & -1 & -1 \\
 -1 & 1 & -1 \\
 -1 & -1 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -1 & -1 \\
 -1 & 0 & -1 \\
 -1 & -1 & 0 \\
}$
 & -4 } \\
 \stab{$S3_{47}$&
$\smat{
 2 & -1 & 0 \\
 -2 & 1 & -1 \\
 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -1 & -2 & -1 \\
 -4 & -4 & -2 \\
 -2 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$S3_{48}$&
$\smat{
 2 & -2 & 0 \\
 -1 & 1 & -1 \\
 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -1 & -4 & -2 \\
 -2 & -4 & -2 \\
 -1 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$S3_{49}$&
$\smat{
 2 & -1 & 0 \\
 -2 & 1 & -2 \\
 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -1 & -1 \\
 -2 & -2 & -2 \\
 -1 & -1 & 0 \\
}$
 & -4 } \\
 \stab{$S3_{50}$&
$\smat{
 2 & -2 & 0 \\
 -1 & 1 & -2 \\
 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -4 & -4 \\
 -2 & -4 & -4 \\
 -1 & -2 & 0 \\
}$
 & -4 } \\
 \stab{$S3_{51}$&
$\smat{
 2 & -2 & 0 \\
 -1 & 1 & -1 \\
 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -1 \\
 -1 & -2 & -1 \\
 -1 & -2 & 0 \\
}$
 & -4 } \\
 \stab{\fbox{!!!}$S3_{52}$&
$\smat{
 2 & -1 & 0 \\
 -3 & 2 & -1 \\
 0 & -1 & 1 \\
}$
 &
$\smat{
 -1 & -1 & -1 \\
 -3 & -2 & -2 \\
 -3 & -2 & -1 \\
}$
 & -1 } \\
 \stab{$S3_{53}$&
$\smat{
 2 & -1 & 0 \\
 -4 & 2 & -1 \\
 0 & -1 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 -1 & -1 & -1 \\
 -4 & -2 & -2 \\
 -4 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$S3_{54}$&
$\smat{
 2 & -2 & 0 \\
 -2 & 2 & -1 \\
 0 & -1 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 -1 & -2 & -2 \\
 -2 & -2 & -2 \\
 -2 & -2 & 0 \\
}$
 & -2 } \\
 \stab{\fbox{!!!}$S3_{55}$&
$\smat{
 2 & -3 & 0 \\
 -1 & 2 & -1 \\
 0 & -1 & 1 \\
}$
 &
$\smat{
 -1 & -3 & -3 \\
 -1 & -2 & -2 \\
 -1 & -2 & -1 \\
}$
 & -1 } \\
 \stab{$S3_{56}$&
$\smat{
 2 & -4 & 0 \\
 -1 & 2 & -1 \\
 0 & -1 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 -1 & -4 & -4 \\
 -1 & -2 & -2 \\
 -1 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$S3_{57}$&
$\smat{
 2 & -1 & 0 \\
 -2 & 2 & -1 \\
 0 & -2 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -1 & -1 \\
 -2 & -2 & -2 \\
 -4 & -4 & -2 \\
}$
 & -2 } \\
 \stab{$S3_{58}$&
$\smat{
 2 & -1 & 0 \\
 -3 & 2 & -1 \\
 0 & -2 & 1 \\
}$
 & $\frac{1}{3}$
$\smat{
 0 & -1 & -1 \\
 -3 & -2 & -2 \\
 -6 & -4 & -1 \\
}$
 & -3 } \\
 \stab{$S3_{59}$&
$\smat{
 2 & -1 & 0 \\
 -4 & 2 & -1 \\
 0 & -2 & 1 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -1 & -1 \\
 -4 & -2 & -2 \\
 -8 & -4 & 0 \\
}$
 & -4 } \\
 \stab{$S3_{60}$&
$\smat{
 2 & -2 & 0 \\
 -2 & 2 & -1 \\
 0 & -2 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -1 & -1 \\
 -1 & -1 & -1 \\
 -2 & -2 & 0 \\
}$
 & -4 } \\
 \stab{$S3_{61}$&
$\smat{
 2 & -1 & 0 \\
 -1 & 2 & -1 \\
 0 & -2 & 1 \\
}$
 &
$\smat{
 0 & -1 & -1 \\
 -1 & -2 & -2 \\
 -2 & -4 & -3 \\
}$
 & -1 } \\
 \stab{$S3_{62}$&
$\smat{
 2 & -2 & 0 \\
 -1 & 2 & -1 \\
 0 & -2 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -2 \\
 -1 & -2 & -2 \\
 -2 & -4 & -2 \\
}$
 & -2 } \\
 \stab{$S3_{63}$&
$\smat{
 2 & -3 & 0 \\
 -1 & 2 & -1 \\
 0 & -2 & 1 \\
}$
 & $\frac{1}{3}$
$\smat{
 0 & -3 & -3 \\
 -1 & -2 & -2 \\
 -2 & -4 & -1 \\
}$
 & -3 } \\
 \stab{$S3_{64}$&
$\smat{
 2 & -4 & 0 \\
 -1 & 2 & -1 \\
 0 & -2 & 1 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -4 & -4 \\
 -1 & -2 & -2 \\
 -2 & -4 & 0 \\
}$
 & -4 } \\
 \stab{$S3_{65}$&
$\smat{
 2 & -1 & 0 \\
 -2 & 2 & -2 \\
 0 & -1 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -1 & -2 \\
 -2 & -2 & -4 \\
 -2 & -2 & -2 \\
}$
 & -2 } \\
 \stab{$S3_{66}$&
$\smat{
 2 & -1 & 0 \\
 -3 & 2 & -2 \\
 0 & -1 & 1 \\
}$
 & $\frac{1}{3}$
$\smat{
 0 & -1 & -2 \\
 -3 & -2 & -4 \\
 -3 & -2 & -1 \\
}$
 & -3 } \\
 \stab{$S3_{67}$&
$\smat{
 2 & -1 & 0 \\
 -4 & 2 & -2 \\
 0 & -1 & 1 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -1 & -2 \\
 -4 & -2 & -4 \\
 -4 & -2 & 0 \\
}$
 & -4 } \\
 \stab{$S3_{68}$&
$\smat{
 2 & -2 & 0 \\
 -2 & 2 & -2 \\
 0 & -1 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -1 & -2 \\
 -1 & -1 & -2 \\
 -1 & -1 & 0 \\
}$
 & -4 } \\
 \stab{$S3_{69}$&
$\smat{
 2 & -1 & 0 \\
 -1 & 2 & -2 \\
 0 & -1 & 1 \\
}$
 &
$\smat{
 0 & -1 & -2 \\
 -1 & -2 & -4 \\
 -1 & -2 & -3 \\
}$
 & -1 } \\
 \stab{$S3_{70}$&
$\smat{
 2 & -2 & 0 \\
 -1 & 2 & -2 \\
 0 & -1 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -4 \\
 -1 & -2 & -4 \\
 -1 & -2 & -2 \\
}$
 & -2 } \\
 \stab{$S3_{71}$&
$\smat{
 2 & -3 & 0 \\
 -1 & 2 & -2 \\
 0 & -1 & 1 \\
}$
 & $\frac{1}{3}$
$\smat{
 0 & -3 & -6 \\
 -1 & -2 & -4 \\
 -1 & -2 & -1 \\
}$
 & -3 } \\
 \stab{$S3_{72}$&
$\smat{
 2 & -4 & 0 \\
 -1 & 2 & -2 \\
 0 & -1 & 1 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -4 & -8 \\
 -1 & -2 & -4 \\
 -1 & -2 & 0 \\
}$
 & -4 } \\
 \stab{$S3_{73}$&
$\smat{
 1 & -2 & 0 \\
 -1 & 2 & -1 \\
 0 & -1 & 1 \\
}$
 &
$\smat{
 -1 & -2 & -2 \\
 -1 & -1 & -1 \\
 -1 & -1 & 0 \\
}$
 & -1 } \\
 \stab{$S3_{74}$&
$\smat{
 1 & -1 & 0 \\
 -2 & 2 & -1 \\
 0 & -1 & 1 \\
}$
 &
$\smat{
 -1 & -1 & -1 \\
 -2 & -1 & -1 \\
 -2 & -1 & 0 \\
}$
 & -1 } \\
 \stab{$S3_{75}$&
$\smat{
 1 & -2 & 0 \\
 -1 & 2 & -1 \\
 0 & -2 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -2 \\
 -1 & -1 & -1 \\
 -2 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$S3_{76}$&
$\smat{
 1 & -1 & 0 \\
 -2 & 2 & -1 \\
 0 & -2 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -1 & -1 \\
 -2 & -1 & -1 \\
 -4 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$S3_{77}$&
$\smat{
 1 & -1 & 0 \\
 -2 & 2 & -2 \\
 0 & -1 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -1 & -2 \\
 -2 & -1 & -2 \\
 -2 & -1 & 0 \\
}$
 & -2 } \\
 \stab{$S3_{78}$&
$\smat{
 2 & -1 & 0 \\
 -1 & 1 & -1 \\
 0 & -1 & 1 \\
}$
 &
$\smat{
 0 & -1 & -1 \\
 -1 & -2 & -2 \\
 -1 & -2 & -1 \\
}$
 & -1 } \\
 \stab{$S3_{79}$&
$\smat{
 2 & -1 & 0 \\
 -2 & 1 & -1 \\
 0 & -1 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -1 & -1 \\
 -2 & -2 & -2 \\
 -2 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$S3_{80}$&
$\smat{
 2 & -2 & 0 \\
 -1 & 1 & -1 \\
 0 & -1 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -2 \\
 -1 & -2 & -2 \\
 -1 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$S3_{81}$&
$\smat{
 1 & -1 & 0 \\
 -1 & 1 & -1 \\
 0 & -1 & 1 \\
}$
 &
$\smat{
 0 & -1 & -1 \\
 -1 & -1 & -1 \\
 -1 & -1 & 0 \\
}$
 & -1 } \\
 \stab{$S4_{1}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -1 & 1 & -1 & 0 \\
 0 & -1 & 2 & -1 \\
 0 & 0 & -1 & 2 \\
}$
 &
$\smat{
 -1 & -3 & -2 & -1 \\
 -3 & -6 & -4 & -2 \\
 -2 & -4 & -2 & -1 \\
 -1 & -2 & -1 & 0 \\
}$
 & -1 } \\
 \stab{$S4_{2}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -1 & 1 & -1 & 0 \\
 0 & -1 & 2 & -2 \\
 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -2 & -2 \\
 -2 & -4 & -4 & -4 \\
 -2 & -4 & -2 & -2 \\
 -1 & -2 & -1 & 0 \\
}$
 & -2 } \\
 \stab{$S4_{3}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -1 & 1 & -1 & 0 \\
 0 & -1 & 2 & -1 \\
 0 & 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -2 & -1 \\
 -2 & -4 & -4 & -2 \\
 -2 & -4 & -2 & -1 \\
 -2 & -4 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$S4_{4}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -3 & 2 & -1 & 0 \\
 0 & -1 & 2 & -1 \\
 0 & 0 & -1 & 1 \\
}$
 &
$\smat{
 -1 & -1 & -1 & -1 \\
 -3 & -2 & -2 & -2 \\
 -3 & -2 & -1 & -1 \\
 -3 & -2 & -1 & 0 \\
}$
 & -1 } \\
 \stab{$S4_{5}$&
$\smat{
 2 & -3 & 0 & 0 \\
 -1 & 2 & -1 & 0 \\
 0 & -1 & 2 & -1 \\
 0 & 0 & -1 & 1 \\
}$
 &
$\smat{
 -1 & -3 & -3 & -3 \\
 -1 & -2 & -2 & -2 \\
 -1 & -2 & -1 & -1 \\
 -1 & -2 & -1 & 0 \\
}$
 & -1 } \\
 \stab{$S4_{6}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -2 & 2 & -1 & 0 \\
 0 & -2 & 2 & -1 \\
 0 & 0 & -1 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -1 & -1 & -1 \\
 -2 & -2 & -2 & -2 \\
 -4 & -4 & -2 & -2 \\
 -4 & -4 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$S4_{7}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -1 & 2 & -1 & 0 \\
 0 & -2 & 2 & -1 \\
 0 & 0 & -1 & 1 \\
}$
 &
$\smat{
 0 & -1 & -1 & -1 \\
 -1 & -2 & -2 & -2 \\
 -2 & -4 & -3 & -3 \\
 -2 & -4 & -3 & -2 \\
}$
 & -1 } \\
 \stab{$S4_{8}$&
$\smat{
 2 & -2 & 0 & 0 \\
 -1 & 2 & -1 & 0 \\
 0 & -2 & 2 & -1 \\
 0 & 0 & -1 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -2 & -2 \\
 -1 & -2 & -2 & -2 \\
 -2 & -4 & -2 & -2 \\
 -2 & -4 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$S4_{9}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -2 & 2 & -2 & 0 \\
 0 & -1 & 2 & -1 \\
 0 & 0 & -1 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -1 & -2 & -2 \\
 -2 & -2 & -4 & -4 \\
 -2 & -2 & -2 & -2 \\
 -2 & -2 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$S4_{10}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -1 & 2 & -2 & 0 \\
 0 & -1 & 2 & -1 \\
 0 & 0 & -1 & 1 \\
}$
 &
$\smat{
 0 & -1 & -2 & -2 \\
 -1 & -2 & -4 & -4 \\
 -1 & -2 & -3 & -3 \\
 -1 & -2 & -3 & -2 \\
}$
 & -1 } \\
 \stab{$S4_{11}$&
$\smat{
 2 & -2 & 0 & 0 \\
 -1 & 2 & -2 & 0 \\
 0 & -1 & 2 & -1 \\
 0 & 0 & -1 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -4 & -4 \\
 -1 & -2 & -4 & -4 \\
 -1 & -2 & -2 & -2 \\
 -1 & -2 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$S4_{12}$&
$\smat{
 1 & -1 & 0 & 0 \\
 -1 & 2 & -1 & 0 \\
 0 & -2 & 2 & -1 \\
 0 & 0 & -1 & 1 \\
}$
 &
$\smat{
 0 & -1 & -1 & -1 \\
 -1 & -1 & -1 & -1 \\
 -2 & -2 & -1 & -1 \\
 -2 & -2 & -1 & 0 \\
}$
 & -1 } \\
 \stab{$S4_{13}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -1 & 1 & -1 & 0 \\
 0 & -1 & 2 & -1 \\
 0 & 0 & -1 & 1 \\
}$
 &
$\smat{
 0 & -1 & -1 & -1 \\
 -1 & -2 & -2 & -2 \\
 -1 & -2 & -1 & -1 \\
 -1 & -2 & -1 & 0 \\
}$
 & -1 } \\
 \stab{$S4_{14}$&
$\smat{
 2 & -1 & 0 & -1 \\
 -1 & 1 & -1 & 0 \\
 0 & -1 & 2 & -1 \\
 -1 & 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 -1 & -4 & -3 & -2 \\
 -4 & -4 & -4 & -4 \\
 -3 & -4 & -1 & -2 \\
 -2 & -4 & -2 & 0 \\
}$
 & -4 } \\
 \stab{$NS4_{15}$&
$\smat{
 2 & -1 & 0 & -2 \\
 -1 & 1 & -1 & 0 \\
 0 & -1 & 2 & -1 \\
 -1 & 0 & -1 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 -1 & -5 & -4 & -3 \\
 -4 & -2 & -4 & -6 \\
 -3 & -3 & 0 & -3 \\
 -2 & -4 & -2 & 0 \\
}$
 & -6 } \\
 \stab{$NS4_{16}$&
$\smat{
 2 & -1 & 0 & -1 \\
 -1 & 1 & -1 & 0 \\
 0 & -1 & 2 & -1 \\
 -2 & 0 & -1 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 -1 & -4 & -3 & -2 \\
 -5 & -2 & -3 & -4 \\
 -4 & -4 & 0 & -2 \\
 -3 & -6 & -3 & 0 \\
}$
 & -6 } \\
 \stab{$S4_{17}$&
$\smat{
 2 & -1 & 0 & -2 \\
 -1 & 1 & -1 & 0 \\
 0 & -1 & 2 & -2 \\
 -1 & 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -2 & -2 & -2 \\
 -2 & 0 & -2 & -4 \\
 -2 & -2 & 0 & -2 \\
 -1 & -2 & -1 & 0 \\
}$
 & -8 } \\
 \stab{$NS4_{18}$&
$\smat{
 2 & -1 & 0 & -1 \\
 -1 & 1 & -1 & 0 \\
 0 & -1 & 2 & -2 \\
 -2 & 0 & -1 & 2 \\
}$
 & $\frac{1}{3}$
$\smat{
 0 & -1 & -1 & -1 \\
 -2 & 0 & -1 & -2 \\
 -2 & -2 & 0 & -1 \\
 -1 & -2 & -1 & 0 \\
}$
 & -9 } \\
 \stab{$S4_{19}$&
$\smat{
 2 & -1 & 0 & -1 \\
 -1 & 1 & -1 & 0 \\
 0 & -1 & 2 & -1 \\
 -2 & 0 & -2 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -2 & -2 & -1 \\
 -2 & 0 & -2 & -2 \\
 -2 & -2 & 0 & -1 \\
 -2 & -4 & -2 & 0 \\
}$
 & -8 } \\
 \stab{$S4_{20}$&
$\smat{
 2 & -1 & 0 & -1 \\
 -1 & 1 & -1 & 0 \\
 0 & -1 & 2 & -1 \\
 -1 & 0 & -1 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -1 & -1 & -1 \\
 -1 & 0 & -1 & -2 \\
 -1 & -1 & 0 & -1 \\
 -1 & -2 & -1 & 0 \\
}$
 & -4 } \\
 \stab{$S4_{21}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -1 & 1 & -1 & -1 \\
 0 & -1 & 2 & 0 \\
 0 & -1 & 0 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -1 & -1 \\
 -2 & -4 & -2 & -2 \\
 -1 & -2 & 0 & -1 \\
 -1 & -2 & -1 & 0 \\
}$
 & -4 } \\
 \stab{$S4_{22}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -2 & 2 & -1 & -1 \\
 0 & -1 & 1 & 0 \\
 0 & -1 & 0 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -1 & -2 & -2 & -1 \\
 -4 & -4 & -4 & -2 \\
 -4 & -4 & -2 & -2 \\
 -2 & -2 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$S4_{23}$&
$\smat{
 2 & -2 & 0 & 0 \\
 -1 & 2 & -1 & -1 \\
 0 & -1 & 1 & 0 \\
 0 & -1 & 0 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -1 & -4 & -4 & -2 \\
 -2 & -4 & -4 & -2 \\
 -2 & -4 & -2 & -2 \\
 -1 & -2 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$S4_{24}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -2 & 2 & -1 & -2 \\
 0 & -1 & 1 & 0 \\
 0 & -1 & 0 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -1 & -1 & -1 \\
 -2 & -2 & -2 & -2 \\
 -2 & -2 & 0 & -2 \\
 -1 & -1 & -1 & 0 \\
}$
 & -4 } \\
 \stab{$S4_{25}$&
$\smat{
 2 & -2 & 0 & 0 \\
 -1 & 2 & -1 & -2 \\
 0 & -1 & 1 & 0 \\
 0 & -1 & 0 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -4 & -4 & -4 \\
 -2 & -4 & -4 & -4 \\
 -2 & -4 & 0 & -4 \\
 -1 & -2 & -2 & 0 \\
}$
 & -4 } \\
 \stab{$S4_{26}$&
$\smat{
 2 & -2 & 0 & 0 \\
 -1 & 2 & -1 & -1 \\
 0 & -1 & 1 & 0 \\
 0 & -2 & 0 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -2 & -1 \\
 -1 & -2 & -2 & -1 \\
 -1 & -2 & 0 & -1 \\
 -1 & -2 & -2 & 0 \\
}$
 & -4 } \\
 \stab{$S4_{27}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -1 & 2 & -1 & -1 \\
 0 & -1 & 1 & 0 \\
 0 & -1 & 0 & 1 \\
}$
 &
$\smat{
 0 & -1 & -1 & -1 \\
 -1 & -2 & -2 & -2 \\
 -1 & -2 & -1 & -2 \\
 -1 & -2 & -2 & -1 \\
}$
 & -1 } \\
 \stab{$S4_{28}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -2 & 2 & -1 & -1 \\
 0 & -1 & 1 & 0 \\
 0 & -1 & 0 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -1 & -1 & -1 \\
 -2 & -2 & -2 & -2 \\
 -2 & -2 & 0 & -2 \\
 -2 & -2 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$S4_{29}$&
$\smat{
 2 & -2 & 0 & 0 \\
 -1 & 2 & -1 & -1 \\
 0 & -1 & 1 & 0 \\
 0 & -1 & 0 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -2 & -2 \\
 -1 & -2 & -2 & -2 \\
 -1 & -2 & 0 & -2 \\
 -1 & -2 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$S4_{30}$&
$\smat{
 1 & -1 & 0 & 0 \\
 -1 & 2 & -1 & -1 \\
 0 & -1 & 1 & 0 \\
 0 & -1 & 0 & 1 \\
}$
 &
$\smat{
 0 & -1 & -1 & -1 \\
 -1 & -1 & -1 & -1 \\
 -1 & -1 & 0 & -1 \\
 -1 & -1 & -1 & 0 \\
}$
 & -1 } \\
 \stab{$S4_{31}$&
$\smat{
 1 & -1 & 0 & 0 \\
 -1 & 2 & -1 & -1 \\
 0 & -1 & 2 & -1 \\
 0 & -1 & -1 & 2 \\
}$
 & $\frac{1}{3}$
$\smat{
 0 & -3 & -3 & -3 \\
 -3 & -3 & -3 & -3 \\
 -3 & -3 & -1 & -2 \\
 -3 & -3 & -2 & -1 \\
}$
 & -3 } \\
 \stab{$S5_{1}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 \\
 0 & -2 & 2 & -1 & 0 \\
 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & -1 & 1 \\
}$
 &
$\smat{
 0 & -1 & -1 & -1 & -1 \\
 -1 & -2 & -2 & -2 & -2 \\
 -2 & -4 & -3 & -3 & -3 \\
 -2 & -4 & -3 & -2 & -2 \\
 -2 & -4 & -3 & -2 & -1 \\
}$
 & -1 } \\
 \stab{$S5_{2}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -1 & 2 & -2 & 0 & 0 \\
 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & -1 & 1 \\
}$
 &
$\smat{
 0 & -1 & -2 & -2 & -2 \\
 -1 & -2 & -4 & -4 & -4 \\
 -1 & -2 & -3 & -3 & -3 \\
 -1 & -2 & -3 & -2 & -2 \\
 -1 & -2 & -3 & -2 & -1 \\
}$
 & -1 } \\
 \stab{$S5_{3}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -1 & 2 & -1 & -1 & -1 \\
 0 & -1 & 1 & 0 & 0 \\
 0 & -1 & 0 & 2 & 0 \\
 0 & -1 & 0 & 0 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -2 & -1 & -1 \\
 -2 & -4 & -4 & -2 & -2 \\
 -2 & -4 & -2 & -2 & -2 \\
 -1 & -2 & -2 & 0 & -1 \\
 -1 & -2 & -2 & -1 & 0 \\
}$
 & -4 } \\
 \stab{$S5_{4}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -2 & 2 & -1 & -1 & 0 \\
 0 & -1 & 2 & 0 & 0 \\
 0 & -1 & 0 & 2 & -1 \\
 0 & 0 & 0 & -1 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 -1 & -2 & -1 & -2 & -2 \\
 -4 & -4 & -2 & -4 & -4 \\
 -2 & -2 & 0 & -2 & -2 \\
 -4 & -4 & -2 & -2 & -2 \\
 -4 & -4 & -2 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$S5_{5}$&
$\smat{
 2 & -2 & 0 & 0 & 0 \\
 -1 & 2 & -1 & -1 & 0 \\
 0 & -1 & 2 & 0 & 0 \\
 0 & -1 & 0 & 2 & -1 \\
 0 & 0 & 0 & -1 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 -1 & -4 & -2 & -4 & -4 \\
 -2 & -4 & -2 & -4 & -4 \\
 -1 & -2 & 0 & -2 & -2 \\
 -2 & -4 & -2 & -2 & -2 \\
 -2 & -4 & -2 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$S5_{6}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -1 & 2 & -1 & -1 & 0 \\
 0 & -1 & 1 & 0 & 0 \\
 0 & -1 & 0 & 2 & -1 \\
 0 & 0 & 0 & -1 & 2 \\
}$
 &
$\smat{
 -1 & -3 & -3 & -2 & -1 \\
 -3 & -6 & -6 & -4 & -2 \\
 -3 & -6 & -5 & -4 & -2 \\
 -2 & -4 & -4 & -2 & -1 \\
 -1 & -2 & -2 & -1 & 0 \\
}$
 & -1 } \\
 \stab{$S5_{7}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -1 & 2 & -1 & -1 & 0 \\
 0 & -1 & 1 & 0 & 0 \\
 0 & -1 & 0 & 2 & -2 \\
 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -2 & -2 & -2 \\
 -2 & -4 & -4 & -4 & -4 \\
 -2 & -4 & -2 & -4 & -4 \\
 -2 & -4 & -4 & -2 & -2 \\
 -1 & -2 & -2 & -1 & 0 \\
}$
 & -2 } \\
 \stab{$S5_{8}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -1 & 2 & -1 & -1 & 0 \\
 0 & -1 & 1 & 0 & 0 \\
 0 & -1 & 0 & 2 & -1 \\
 0 & 0 & 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -2 & -2 & -1 \\
 -2 & -4 & -4 & -4 & -2 \\
 -2 & -4 & -2 & -4 & -2 \\
 -2 & -4 & -4 & -2 & -1 \\
 -2 & -4 & -4 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$S5_{9}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -1 & 2 & -1 & -1 & 0 \\
 0 & -1 & 1 & 0 & 0 \\
 0 & -1 & 0 & 2 & -1 \\
 0 & 0 & 0 & -1 & 1 \\
}$
 &
$\smat{
 0 & -1 & -1 & -1 & -1 \\
 -1 & -2 & -2 & -2 & -2 \\
 -1 & -2 & -1 & -2 & -2 \\
 -1 & -2 & -2 & -1 & -1 \\
 -1 & -2 & -2 & -1 & 0 \\
}$
 & -1 } \\
 \stab{$S5_{10}$&
$\smat{
 1 & -1 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & -1 \\
 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & -1 & 2 & -1 \\
 0 & -1 & 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -4 & -4 & -4 & -4 \\
 -4 & -4 & -4 & -4 & -4 \\
 -4 & -4 & -1 & -2 & -3 \\
 -4 & -4 & -2 & 0 & -2 \\
 -4 & -4 & -3 & -2 & -1 \\
}$
 & -4 } \\
 \stab{$S6_{1}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & -1 & -1 & 0 \\
 0 & -1 & 2 & 0 & 0 & 0 \\
 0 & -1 & 0 & 2 & 0 & 0 \\
 0 & -1 & 0 & 0 & 2 & -1 \\
 0 & 0 & 0 & 0 & -1 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -1 & -1 & -2 & -2 \\
 -2 & -4 & -2 & -2 & -4 & -4 \\
 -1 & -2 & 0 & -1 & -2 & -2 \\
 -1 & -2 & -1 & 0 & -2 & -2 \\
 -2 & -4 & -2 & -2 & -2 & -2 \\
 -2 & -4 & -2 & -2 & -2 & 0 \\
}$
 & -4 } \\
 \stab{$S6_{2}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 \\
 0 & 0 & 0 & 0 & -1 & 1 \\
}$
 &
$\smat{
 0 & -1 & -2 & -1 & -2 & -2 \\
 -1 & -2 & -4 & -2 & -4 & -4 \\
 -2 & -4 & -6 & -3 & -6 & -6 \\
 -1 & -2 & -3 & -1 & -3 & -3 \\
 -2 & -4 & -6 & -3 & -5 & -5 \\
 -2 & -4 & -6 & -3 & -5 & -4 \\
}$
 & -1 } \\
 \stab{$S6_{3}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 \\
 -2 & 2 & -1 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 \\
 0 & 0 & 0 & 0 & -1 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -1 & -2 & -1 & -2 & -2 \\
 -2 & -2 & -4 & -2 & -4 & -4 \\
 -4 & -4 & -4 & -2 & -4 & -4 \\
 -2 & -2 & -2 & 0 & -2 & -2 \\
 -4 & -4 & -4 & -2 & -2 & -2 \\
 -4 & -4 & -4 & -2 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$S6_{4}$&
$\smat{
 2 & -2 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 \\
 0 & 0 & 0 & 0 & -1 & 1 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -4 & -2 & -4 & -4 \\
 -1 & -2 & -4 & -2 & -4 & -4 \\
 -2 & -4 & -4 & -2 & -4 & -4 \\
 -1 & -2 & -2 & 0 & -2 & -2 \\
 -2 & -4 & -4 & -2 & -2 & -2 \\
 -2 & -4 & -4 & -2 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$S6_{5}$&
$\smat{
 1 & -1 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 \\
 0 & 0 & 0 & 0 & -1 & 1 \\
}$
 &
$\smat{
 0 & -1 & -2 & -1 & -2 & -2 \\
 -1 & -1 & -2 & -1 & -2 & -2 \\
 -2 & -2 & -2 & -1 & -2 & -2 \\
 -1 & -1 & -1 & 0 & -1 & -1 \\
 -2 & -2 & -2 & -1 & -1 & -1 \\
 -2 & -2 & -2 & -1 & -1 & 0 \\
}$
 & -1 } \\
 \stab{$S6_{6}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 \\
 0 & -2 & 2 & -1 & 0 & 0 \\
 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & 0 & -1 & 1 \\
}$
 &
$\smat{
 0 & -1 & -1 & -1 & -1 & -1 \\
 -1 & -2 & -2 & -2 & -2 & -2 \\
 -2 & -4 & -3 & -3 & -3 & -3 \\
 -2 & -4 & -3 & -2 & -2 & -2 \\
 -2 & -4 & -3 & -2 & -1 & -1 \\
 -2 & -4 & -3 & -2 & -1 & 0 \\
}$
 & -1 } \\
 \stab{$S6_{7}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -2 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & 0 & 0 \\
 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & 0 & -1 & 1 \\
}$
 &
$\smat{
 0 & -1 & -2 & -2 & -2 & -2 \\
 -1 & -2 & -4 & -4 & -4 & -4 \\
 -1 & -2 & -3 & -3 & -3 & -3 \\
 -1 & -2 & -3 & -2 & -2 & -2 \\
 -1 & -2 & -3 & -2 & -1 & -1 \\
 -1 & -2 & -3 & -2 & -1 & 0 \\
}$
 & -1 } \\
 \stab{$S7_1$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 & 0 \\
 0 & 0 & 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & 0 & 0 & -1 & 1 \\
}$
 &
$\smat{
 0 & -1 & -2 & -1 & -2 & -2 & -2 \\
 -1 & -2 & -4 & -2 & -4 & -4 & -4 \\
 -2 & -4 & -6 & -3 & -6 & -6 & -6 \\
 -1 & -2 & -3 & -1 & -3 & -3 & -3 \\
 -2 & -4 & -6 & -3 & -5 & -5 & -5 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -4 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -3 \\
}$
 & -1 } \\
 \stab{$S8_1$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 & 0 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 & 0 & 0 \\
 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1 \\
}$
 &
$\smat{
 0 & -1 & -2 & -1 & -2 & -2 & -2 & -2 \\
 -1 & -2 & -4 & -2 & -4 & -4 & -4 & -4 \\
 -2 & -4 & -6 & -3 & -6 & -6 & -6 & -6 \\
 -1 & -2 & -3 & -1 & -3 & -3 & -3 & -3 \\
 -2 & -4 & -6 & -3 & -5 & -5 & -5 & -5 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -4 & -4 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -3 & -3 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -3 & -2 \\
}$
 & -1 } \\
 \stab{$S9_1$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1 \\
}$
 &
$\smat{
 0 & -1 & -2 & -1 & -2 & -2 & -2 & -2 & -2 \\
 -1 & -2 & -4 & -2 & -4 & -4 & -4 & -4 & -4 \\
 -2 & -4 & -6 & -3 & -6 & -6 & -6 & -6 & -6 \\
 -1 & -2 & -3 & -1 & -3 & -3 & -3 & -3 & -3 \\
 -2 & -4 & -6 & -3 & -5 & -5 & -5 & -5 & -5 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -4 & -4 & -4 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -3 & -3 & -3 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -3 & -2 & -2 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -3 & -2 & -1 \\
}$
 & -1 } \\
 \stab{$S10_1$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 & 0 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 1 \\
}$
 &
$\smat{
 0 & -1 & -2 & -1 & -2 & -2 & -2 & -2 & -2 & -2 \\
 -1 & -2 & -4 & -2 & -4 & -4 & -4 & -4 & -4 & -4 \\
 -2 & -4 & -6 & -3 & -6 & -6 & -6 & -6 & -6 & -6 \\
 -1 & -2 & -3 & -1 & -3 & -3 & -3 & -3 & -3 & -3 \\
 -2 & -4 & -6 & -3 & -5 & -5 & -5 & -5 & -5 & -5 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -4 & -4 & -4 & -4 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -3 & -3 & -3 & -3 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -3 & -2 & -2 & -2 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -3 & -2 & -1 & -1 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -3 & -2 & -1 & 0 \\
}$
 & -1 } \\[2mm]
 \normalsize

\subsection{ matrices $A$, their inverses, and $\det A$ for hyperbolic Lie algebras}\label{ss8.2}
 \stab{\fbox{!!!}$NH3_1$&
$\smat{
 2 & -1 & -1 \\
 -2 & 2 & -1 \\
 -2 & -2 & 2 \\
}$
 & $\frac{1}{10}$
$\smat{
 -2 & -4 & -3 \\
 -6 & -2 & -4 \\
 -8 & -6 & -2 \\
}$
 & -10 } \\
 \stab{\fbox{!!!}$NH3_2$&
$\smat{
 2 & -1 & -1 \\
 -3 & 2 & -1 \\
 -2 & -2 & 2 \\
}$
 & $\frac{1}{14}$
$\smat{
 -2 & -4 & -3 \\
 -8 & -2 & -5 \\
 -10 & -6 & -1 \\
}$
 & -14 } \\
 \stab{$NH3_3$&
$\smat{
 2 & -1 & -1 \\
 -4 & 2 & -1 \\
 -2 & -2 & 2 \\
}$
 & $\frac{1}{18}$
$\smat{
 -2 & -4 & -3 \\
 -10 & -2 & -6 \\
 -12 & -6 & 0 \\
}$
 & -18 } \\
 \stab{$H3_4$&
$\smat{
 2 & -2 & -1 \\
 -2 & 2 & -1 \\
 -2 & -2 & 2 \\
}$
 & $\frac{1}{8}$
$\smat{
 -1 & -3 & -2 \\
 -3 & -1 & -2 \\
 -4 & -4 & 0 \\
}$
 & -16 } \\
 \stab{\fbox{!!!}$H3_5$&
$\smat{
 2 & -1 & -1 \\
 -1 & 2 & -1 \\
 -2 & -2 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 -2 & -4 & -3 \\
 -4 & -2 & -3 \\
 -6 & -6 & -3 \\
}$
 & -6 } \\
 \stab{\fbox{!!!}$NH3_6$&
$\smat{
 2 & -1 & -1 \\
 -2 & 2 & -1 \\
 -3 & -2 & 2 \\
}$
 & $\frac{1}{13}$
$\smat{
 -2 & -4 & -3 \\
 -7 & -1 & -4 \\
 -10 & -7 & -2 \\
}$
 & -13 } \\
 \stab{\fbox{!!!}$NH3_7$&
$\smat{
 2 & -1 & -1 \\
 -3 & 2 & -1 \\
 -3 & -2 & 2 \\
}$
 & $\frac{1}{17}$
$\smat{
 -2 & -4 & -3 \\
 -9 & -1 & -5 \\
 -12 & -7 & -1 \\
}$
 & -17 } \\
 \stab{$NH3_8$&
$\smat{
 2 & -1 & -1 \\
 -4 & 2 & -1 \\
 -3 & -2 & 2 \\
}$
 & $\frac{1}{21}$
$\smat{
 -2 & -4 & -3 \\
 -11 & -1 & -6 \\
 -14 & -7 & 0 \\
}$
 & -21 } \\
 \stab{$NH3_9$&
$\smat{
 2 & -2 & -1 \\
 -2 & 2 & -1 \\
 -3 & -2 & 2 \\
}$
 & $\frac{1}{20}$
$\smat{
 -2 & -6 & -4 \\
 -7 & -1 & -4 \\
 -10 & -10 & 0 \\
}$
 & -20 } \\
 \stab{\fbox{!!!}$NH3_{10}$&
$\smat{
 2 & -1 & -1 \\
 -1 & 2 & -1 \\
 -3 & -2 & 2 \\
}$
 & $\frac{1}{9}$
$\smat{
 -2 & -4 & -3 \\
 -5 & -1 & -3 \\
 -8 & -7 & -3 \\
}$
 & -9 } \\
 \stab{\fbox{!!!}$NH3_{11}$&
$\smat{
 2 & -2 & -1 \\
 -1 & 2 & -1 \\
 -3 & -2 & 2 \\
}$
 & $\frac{1}{14}$
$\smat{
 -2 & -6 & -4 \\
 -5 & -1 & -3 \\
 -8 & -10 & -2 \\
}$
 & -14 } \\
 \stab{\fbox{!!!}$NH3_{12}$&
$\smat{
 2 & -3 & -1 \\
 -1 & 2 & -1 \\
 -3 & -2 & 2 \\
}$
 & $\frac{1}{19}$
$\smat{
 -2 & -8 & -5 \\
 -5 & -1 & -3 \\
 -8 & -13 & -1 \\
}$
 & -19 } \\
 \stab{$NH3_{13}$&
$\smat{
 2 & -4 & -1 \\
 -1 & 2 & -1 \\
 -3 & -2 & 2 \\
}$
 & $\frac{1}{24}$
$\smat{
 -2 & -10 & -6 \\
 -5 & -1 & -3 \\
 -8 & -16 & 0 \\
}$
 & -24 } \\
 \stab{$H3_{14}$&
$\smat{
 2 & -1 & -1 \\
 -2 & 2 & -1 \\
 -4 & -2 & 2 \\
}$
 & $\frac{1}{16}$
$\smat{
 -2 & -4 & -3 \\
 -8 & 0 & -4 \\
 -12 & -8 & -2 \\
}$
 & -16 } \\
 \stab{$NH3_{15}$&
$\smat{
 2 & -1 & -1 \\
 -3 & 2 & -1 \\
 -4 & -2 & 2 \\
}$
 & $\frac{1}{20}$
$\smat{
 -2 & -4 & -3 \\
 -10 & 0 & -5 \\
 -14 & -8 & -1 \\
}$
 & -20 } \\
 \stab{$NH3_{16}$&
$\smat{
 2 & -1 & -1 \\
 -4 & 2 & -1 \\
 -4 & -2 & 2 \\
}$
 & $\frac{1}{24}$
$\smat{
 -2 & -4 & -3 \\
 -12 & 0 & -6 \\
 -16 & -8 & 0 \\
}$
 & -24 } \\
 \stab{$NH3_{17}$&
$\smat{
 2 & -2 & -1 \\
 -2 & 2 & -1 \\
 -4 & -2 & 2 \\
}$
 & $\frac{1}{12}$
$\smat{
 -1 & -3 & -2 \\
 -4 & 0 & -2 \\
 -6 & -6 & 0 \\
}$
 & -24 } \\
 \stab{$NH3_{18}$&
$\smat{
 2 & -1 & -1 \\
 -1 & 2 & -1 \\
 -4 & -2 & 2 \\
}$
 & $\frac{1}{12}$
$\smat{
 -2 & -4 & -3 \\
 -6 & 0 & -3 \\
 -10 & -8 & -3 \\
}$
 & -12 } \\
 \stab{$NH3_{19}$&
$\smat{
 2 & -2 & -1 \\
 -1 & 2 & -1 \\
 -4 & -2 & 2 \\
}$
 & $\frac{1}{18}$
$\smat{
 -2 & -6 & -4 \\
 -6 & 0 & -3 \\
 -10 & -12 & -2 \\
}$
 & -18 } \\
 \stab{$NH3_{20}$&
$\smat{
 2 & -3 & -1 \\
 -1 & 2 & -1 \\
 -4 & -2 & 2 \\
}$
 & $\frac{1}{24}$
$\smat{
 -2 & -8 & -5 \\
 -6 & 0 & -3 \\
 -10 & -16 & -1 \\
}$
 & -24 } \\
 \stab{$NH3_{21}$&
$\smat{
 2 & -4 & -1 \\
 -1 & 2 & -1 \\
 -4 & -2 & 2 \\
}$
 & $\frac{1}{30}$
$\smat{
 -2 & -10 & -6 \\
 -6 & 0 & -3 \\
 -10 & -20 & 0 \\
}$
 & -30 } \\
 \stab{$NH3_{22}$&
$\smat{
 2 & -1 & -2 \\
 -2 & 2 & -1 \\
 -2 & -2 & 2 \\
}$
 & $\frac{1}{18}$
$\smat{
 -2 & -6 & -5 \\
 -6 & 0 & -6 \\
 -8 & -6 & -2 \\
}$
 & -18 } \\
 \stab{$NH3_{23}$&
$\smat{
 2 & -1 & -2 \\
 -3 & 2 & -1 \\
 -2 & -2 & 2 \\
}$
 & $\frac{1}{24}$
$\smat{
 -2 & -6 & -5 \\
 -8 & 0 & -8 \\
 -10 & -6 & -1 \\
}$
 & -24 } \\
 \stab{$NH3_{24}$&
$\smat{
 2 & -1 & -2 \\
 -4 & 2 & -1 \\
 -2 & -2 & 2 \\
}$
 & $\frac{1}{30}$
$\smat{
 -2 & -6 & -5 \\
 -10 & 0 & -10 \\
 -12 & -6 & 0 \\
}$
 & -30 } \\
 \stab{$NH3_{25}$&
$\smat{
 2 & -2 & -2 \\
 -2 & 2 & -1 \\
 -2 & -2 & 2 \\
}$
 & $\frac{1}{12}$
$\smat{
 -1 & -4 & -3 \\
 -3 & 0 & -3 \\
 -4 & -4 & 0 \\
}$
 & -24 } \\
 \stab{$NH3_{26}$&
$\smat{
 2 & -1 & -2 \\
 -1 & 2 & -1 \\
 -2 & -2 & 2 \\
}$
 & $\frac{1}{12}$
$\smat{
 -2 & -6 & -5 \\
 -4 & 0 & -4 \\
 -6 & -6 & -3 \\
}$
 & -12 } \\
 \stab{$H3_{27}$&
$\smat{
 2 & -2 & -2 \\
 -1 & 2 & -1 \\
 -2 & -2 & 2 \\
}$
 & $\frac{1}{8}$
$\smat{
 -1 & -4 & -3 \\
 -2 & 0 & -2 \\
 -3 & -4 & -1 \\
}$
 & -16 } \\
 \stab{$NH3_{28}$&
$\smat{
 2 & -3 & -2 \\
 -1 & 2 & -1 \\
 -2 & -2 & 2 \\
}$
 & $\frac{1}{20}$
$\smat{
 -2 & -10 & -7 \\
 -4 & 0 & -4 \\
 -6 & -10 & -1 \\
}$
 & -20 } \\
 \stab{$NH3_{29}$&
$\smat{
 2 & -4 & -2 \\
 -1 & 2 & -1 \\
 -2 & -2 & 2 \\
}$
 & $\frac{1}{12}$
$\smat{
 -1 & -6 & -4 \\
 -2 & 0 & -2 \\
 -3 & -6 & 0 \\
}$
 & -24 } \\
 \stab{\fbox{!!!}$NH3_{30}$&
$\smat{
 2 & -1 & -1 \\
 -2 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{7}$
$\smat{
 -2 & -4 & -3 \\
 -5 & -3 & -4 \\
 -6 & -5 & -2 \\
}$
 & -7 } \\
 \stab{\fbox{!!!}$NH3_{31}$&
$\smat{
 2 & -1 & -1 \\
 -3 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{11}$
$\smat{
 -2 & -4 & -3 \\
 -7 & -3 & -5 \\
 -8 & -5 & -1 \\
}$
 & -11 } \\
 \stab{$NH3_{32}$&
$\smat{
 2 & -1 & -1 \\
 -4 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{15}$
$\smat{
 -2 & -4 & -3 \\
 -9 & -3 & -6 \\
 -10 & -5 & 0 \\
}$
 & -15 } \\
 \stab{$NH3_{33}$&
$\smat{
 2 & -2 & -1 \\
 -2 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{12}$
$\smat{
 -2 & -6 & -4 \\
 -5 & -3 & -4 \\
 -6 & -6 & 0 \\
}$
 & -12 } \\
 \stab{\fbox{!!!}$NH3_{34}$&
$\smat{
 2 & -1 & -1 \\
 -1 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{3}$
$\smat{
 -2 & -4 & -3 \\
 -3 & -3 & -3 \\
 -4 & -5 & -3 \\
}$
 & -3 } \\
 \stab{\fbox{!!!}$H3_{35}$&
$\smat{
 2 & -2 & -1 \\
 -1 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 -2 & -6 & -4 \\
 -3 & -3 & -3 \\
 -4 & -6 & -2 \\
}$
 & -6 } \\
 \stab{\fbox{!!!}$NH3_{36}$&
$\smat{
 2 & -3 & -1 \\
 -1 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{9}$
$\smat{
 -2 & -8 & -5 \\
 -3 & -3 & -3 \\
 -4 & -7 & -1 \\
}$
 & -9 } \\
 \stab{$NH3_{37}$&
$\smat{
 2 & -4 & -1 \\
 -1 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{12}$
$\smat{
 -2 & -10 & -6 \\
 -3 & -3 & -3 \\
 -4 & -8 & 0 \\
}$
 & -12 } \\
 \stab{\fbox{!!!}$NH3_{38}$&
$\smat{
 2 & -1 & -2 \\
 -2 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{13}$
$\smat{
 -2 & -6 & -5 \\
 -5 & -2 & -6 \\
 -6 & -5 & -2 \\
}$
 & -13 } \\
 \stab{\fbox{!!!}$NH3_{39}$&
$\smat{
 2 & -1 & -2 \\
 -3 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{19}$
$\smat{
 -2 & -6 & -5 \\
 -7 & -2 & -8 \\
 -8 & -5 & -1 \\
}$
 & -19 } \\
 \stab{$NH3_{40}$&
$\smat{
 2 & -1 & -2 \\
 -4 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{25}$
$\smat{
 -2 & -6 & -5 \\
 -9 & -2 & -10 \\
 -10 & -5 & 0 \\
}$
 & -25 } \\
 \stab{\fbox{!!!}$NH3_{41}$&
$\smat{
 2 & -1 & -3 \\
 -3 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{27}$
$\smat{
 -2 & -8 & -7 \\
 -7 & -1 & -11 \\
 -8 & -5 & -1 \\
}$
 & -27 } \\
 \stab{$NH3_{42}$&
$\smat{
 2 & -1 & -3 \\
 -4 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{35}$
$\smat{
 -2 & -8 & -7 \\
 -9 & -1 & -14 \\
 -10 & -5 & 0 \\
}$
 & -35 } \\
 \stab{$NH3_{43}$&
$\smat{
 2 & -2 & -3 \\
 -2 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{24}$
$\smat{
 -2 & -10 & -8 \\
 -5 & -1 & -8 \\
 -6 & -6 & 0 \\
}$
 & -24 } \\
 \stab{\fbox{!!!}$NH3_{44}$&
$\smat{
 2 & -1 & -3 \\
 -1 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{11}$
$\smat{
 -2 & -8 & -7 \\
 -3 & -1 & -5 \\
 -4 & -5 & -3 \\
}$
 & -11 } \\
 \stab{\fbox{!!!}$NH3_{45}$&
$\smat{
 2 & -3 & -3 \\
 -1 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{17}$
$\smat{
 -2 & -12 & -9 \\
 -3 & -1 & -5 \\
 -4 & -7 & -1 \\
}$
 & -17 } \\
 \stab{$NH3_{46}$&
$\smat{
 2 & -4 & -3 \\
 -1 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{20}$
$\smat{
 -2 & -14 & -10 \\
 -3 & -1 & -5 \\
 -4 & -8 & 0 \\
}$
 & -20 } \\
 \stab{$NH3_{47}$&
$\smat{
 2 & -1 & -4 \\
 -3 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{35}$
$\smat{
 -2 & -10 & -9 \\
 -7 & 0 & -14 \\
 -8 & -5 & -1 \\
}$
 & -35 } \\
 \stab{$NH3_{48}$&
$\smat{
 2 & -1 & -4 \\
 -4 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{45}$
$\smat{
 -2 & -10 & -9 \\
 -9 & 0 & -18 \\
 -10 & -5 & 0 \\
}$
 & -45 } \\
 \stab{$NH3_{49}$&
$\smat{
 2 & -2 & -4 \\
 -2 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{30}$
$\smat{
 -2 & -12 & -10 \\
 -5 & 0 & -10 \\
 -6 & -6 & 0 \\
}$
 & -30 } \\
 \stab{$NH3_{50}$&
$\smat{
 2 & -1 & -4 \\
 -1 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{15}$
$\smat{
 -2 & -10 & -9 \\
 -3 & 0 & -6 \\
 -4 & -5 & -3 \\
}$
 & -15 } \\
 \stab{$NH3_{51}$&
$\smat{
 2 & -3 & -4 \\
 -1 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{21}$
$\smat{
 -2 & -14 & -11 \\
 -3 & 0 & -6 \\
 -4 & -7 & -1 \\
}$
 & -21 } \\
 \stab{$NH3_{52}$&
$\smat{
 2 & -4 & -4 \\
 -1 & 2 & -1 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{24}$
$\smat{
 -2 & -16 & -12 \\
 -3 & 0 & -6 \\
 -4 & -8 & 0 \\
}$
 & -24 } \\
 \stab{\fbox{!!!}$NH3_{53}$&
$\smat{
 2 & -1 & -1 \\
 -3 & 2 & -1 \\
 -3 & -3 & 2 \\
}$
 & $\frac{1}{22}$
$\smat{
 -1 & -5 & -3 \\
 -9 & -1 & -5 \\
 -15 & -9 & -1 \\
}$
 & -22 } \\
 \stab{$NH3_{54}$&
$\smat{
 2 & -1 & -1 \\
 -4 & 2 & -1 \\
 -3 & -3 & 2 \\
}$
 & $\frac{1}{27}$
$\smat{
 -1 & -5 & -3 \\
 -11 & -1 & -6 \\
 -18 & -9 & 0 \\
}$
 & -27 } \\
 \stab{$H3_{55}$&
$\smat{
 2 & -2 & -1 \\
 -2 & 2 & -1 \\
 -3 & -3 & 2 \\
}$
 & $\frac{1}{24}$
$\smat{
 -1 & -7 & -4 \\
 -7 & -1 & -4 \\
 -12 & -12 & 0 \\
}$
 & -24 } \\
 \stab{\fbox{!!!}$H3_{56}$&
$\smat{
 2 & -1 & -1 \\
 -1 & 2 & -1 \\
 -3 & -3 & 2 \\
}$
 & $\frac{1}{12}$
$\smat{
 -1 & -5 & -3 \\
 -5 & -1 & -3 \\
 -9 & -9 & -3 \\
}$
 & -12 } \\
 \stab{$NH3_{57}$&
$\smat{
 2 & -1 & -1 \\
 -3 & 2 & -1 \\
 -4 & -3 & 2 \\
}$
 & $\frac{1}{25}$
$\smat{
 -1 & -5 & -3 \\
 -10 & 0 & -5 \\
 -17 & -10 & -1 \\
}$
 & -25 } \\
 \stab{$NH3_{58}$&
$\smat{
 2 & -1 & -1 \\
 -4 & 2 & -1 \\
 -4 & -3 & 2 \\
}$
 & $\frac{1}{30}$
$\smat{
 -1 & -5 & -3 \\
 -12 & 0 & -6 \\
 -20 & -10 & 0 \\
}$
 & -30 } \\
 \stab{$NH3_{59}$&
$\smat{
 2 & -2 & -1 \\
 -2 & 2 & -1 \\
 -4 & -3 & 2 \\
}$
 & $\frac{1}{28}$
$\smat{
 -1 & -7 & -4 \\
 -8 & 0 & -4 \\
 -14 & -14 & 0 \\
}$
 & -28 } \\
 \stab{$NH3_{60}$&
$\smat{
 2 & -1 & -1 \\
 -1 & 2 & -1 \\
 -4 & -3 & 2 \\
}$
 & $\frac{1}{15}$
$\smat{
 -1 & -5 & -3 \\
 -6 & 0 & -3 \\
 -11 & -10 & -3 \\
}$
 & -15 } \\
 \stab{$NH3_{61}$&
$\smat{
 2 & -3 & -1 \\
 -1 & 2 & -1 \\
 -4 & -3 & 2 \\
}$
 & $\frac{1}{27}$
$\smat{
 -1 & -9 & -5 \\
 -6 & 0 & -3 \\
 -11 & -18 & -1 \\
}$
 & -27 } \\
 \stab{$NH3_{62}$&
$\smat{
 2 & -4 & -1 \\
 -1 & 2 & -1 \\
 -4 & -3 & 2 \\
}$
 & $\frac{1}{33}$
$\smat{
 -1 & -11 & -6 \\
 -6 & 0 & -3 \\
 -11 & -22 & 0 \\
}$
 & -33 } \\
 \stab{$NH3_{63}$&
$\smat{
 2 & -1 & -2 \\
 -3 & 2 & -1 \\
 -2 & -3 & 2 \\
}$
 & $\frac{1}{32}$
$\smat{
 -1 & -8 & -5 \\
 -8 & 0 & -8 \\
 -13 & -8 & -1 \\
}$
 & -32 } \\
 \stab{$NH3_{64}$&
$\smat{
 2 & -1 & -2 \\
 -4 & 2 & -1 \\
 -2 & -3 & 2 \\
}$
 & $\frac{1}{40}$
$\smat{
 -1 & -8 & -5 \\
 -10 & 0 & -10 \\
 -16 & -8 & 0 \\
}$
 & -40 } \\
 \stab{$NH3_{65}$&
$\smat{
 2 & -2 & -2 \\
 -2 & 2 & -1 \\
 -2 & -3 & 2 \\
}$
 & $\frac{1}{30}$
$\smat{
 -1 & -10 & -6 \\
 -6 & 0 & -6 \\
 -10 & -10 & 0 \\
}$
 & -30 } \\
 \stab{$NH3_{66}$&
$\smat{
 2 & -1 & -2 \\
 -1 & 2 & -1 \\
 -2 & -3 & 2 \\
}$
 & $\frac{1}{16}$
$\smat{
 -1 & -8 & -5 \\
 -4 & 0 & -4 \\
 -7 & -8 & -3 \\
}$
 & -16 } \\
 \stab{$H3_{67}$&
$\smat{
 2 & -3 & -2 \\
 -1 & 2 & -1 \\
 -2 & -3 & 2 \\
}$
 & $\frac{1}{24}$
$\smat{
 -1 & -12 & -7 \\
 -4 & 0 & -4 \\
 -7 & -12 & -1 \\
}$
 & -24 } \\
 \stab{$NH3_{68}$&
$\smat{
 2 & -4 & -2 \\
 -1 & 2 & -1 \\
 -2 & -3 & 2 \\
}$
 & $\frac{1}{28}$
$\smat{
 -1 & -14 & -8 \\
 -4 & 0 & -4 \\
 -7 & -14 & 0 \\
}$
 & -28 } \\
 \stab{\fbox{!!!}$NH3_{69}$&
$\smat{
 2 & -1 & -1 \\
 -3 & 2 & -1 \\
 -1 & -3 & 2 \\
}$
 & $\frac{1}{16}$
$\smat{
 -1 & -5 & -3 \\
 -7 & -3 & -5 \\
 -11 & -7 & -1 \\
}$
 & -16 } \\
 \stab{$NH3_{70}$&
$\smat{
 2 & -1 & -1 \\
 -4 & 2 & -1 \\
 -1 & -3 & 2 \\
}$
 & $\frac{1}{21}$
$\smat{
 -1 & -5 & -3 \\
 -9 & -3 & -6 \\
 -14 & -7 & 0 \\
}$
 & -21 } \\
 \stab{$NH3_{71}$&
$\smat{
 2 & -2 & -1 \\
 -2 & 2 & -1 \\
 -1 & -3 & 2 \\
}$
 & $\frac{1}{16}$
$\smat{
 -1 & -7 & -4 \\
 -5 & -3 & -4 \\
 -8 & -8 & 0 \\
}$
 & -16 } \\
 \stab{\fbox{!!!}$NH3_{72}$&
$\smat{
 2 & -1 & -1 \\
 -1 & 2 & -1 \\
 -1 & -3 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 -1 & -5 & -3 \\
 -3 & -3 & -3 \\
 -5 & -7 & -3 \\
}$
 & -6 } \\
 \stab{\fbox{!!!}$H3_{73}$&
$\smat{
 2 & -3 & -1 \\
 -1 & 2 & -1 \\
 -1 & -3 & 2 \\
}$
 & $\frac{1}{12}$
$\smat{
 -1 & -9 & -5 \\
 -3 & -3 & -3 \\
 -5 & -9 & -1 \\
}$
 & -12 } \\
 \stab{$NH3_{74}$&
$\smat{
 2 & -4 & -1 \\
 -1 & 2 & -1 \\
 -1 & -3 & 2 \\
}$
 & $\frac{1}{15}$
$\smat{
 -1 & -11 & -6 \\
 -3 & -3 & -3 \\
 -5 & -10 & 0 \\
}$
 & -15 } \\
 \stab{\fbox{!!!}$NH3_{75}$&
$\smat{
 2 & -1 & -3 \\
 -3 & 2 & -1 \\
 -1 & -3 & 2 \\
}$
 & $\frac{1}{38}$
$\smat{
 -1 & -11 & -7 \\
 -7 & -1 & -11 \\
 -11 & -7 & -1 \\
}$
 & -38 } \\
 \stab{$NH3_{76}$&
$\smat{
 2 & -1 & -3 \\
 -4 & 2 & -1 \\
 -1 & -3 & 2 \\
}$
 & $\frac{1}{49}$
$\smat{
 -1 & -11 & -7 \\
 -9 & -1 & -14 \\
 -14 & -7 & 0 \\
}$
 & -49 } \\
 \stab{$NH3_{77}$&
$\smat{
 2 & -1 & -4 \\
 -4 & 2 & -1 \\
 -1 & -3 & 2 \\
}$
 & $\frac{1}{63}$
$\smat{
 -1 & -14 & -9 \\
 -9 & 0 & -18 \\
 -14 & -7 & 0 \\
}$
 & -63 } \\
 \stab{$NH3_{78}$&
$\smat{
 2 & -2 & -4 \\
 -2 & 2 & -1 \\
 -1 & -3 & 2 \\
}$
 & $\frac{1}{40}$
$\smat{
 -1 & -16 & -10 \\
 -5 & 0 & -10 \\
 -8 & -8 & 0 \\
}$
 & -40 } \\
 \stab{$NH3_{79}$&
$\smat{
 2 & -1 & -4 \\
 -1 & 2 & -1 \\
 -1 & -3 & 2 \\
}$
 & $\frac{1}{21}$
$\smat{
 -1 & -14 & -9 \\
 -3 & 0 & -6 \\
 -5 & -7 & -3 \\
}$
 & -21 } \\
 \stab{$NH3_{80}$&
$\smat{
 2 & -4 & -4 \\
 -1 & 2 & -1 \\
 -1 & -3 & 2 \\
}$
 & $\frac{1}{30}$
$\smat{
 -1 & -20 & -12 \\
 -3 & 0 & -6 \\
 -5 & -10 & 0 \\
}$
 & -30 } \\
 \stab{$NH3_{81}$&
$\smat{
 2 & -1 & -1 \\
 -4 & 2 & -1 \\
 -4 & -4 & 2 \\
}$
 & $\frac{1}{12}$
$\smat{
 0 & -2 & -1 \\
 -4 & 0 & -2 \\
 -8 & -4 & 0 \\
}$
 & -36 } \\
 \stab{$H3_{82}$&
$\smat{
 2 & -2 & -1 \\
 -2 & 2 & -1 \\
 -4 & -4 & 2 \\
}$
 & $\frac{1}{8}$
$\smat{
 0 & -2 & -1 \\
 -2 & 0 & -1 \\
 -4 & -4 & 0 \\
}$
 & -32 } \\
 \stab{$H3_{83}$&
$\smat{
 2 & -1 & -1 \\
 -1 & 2 & -1 \\
 -4 & -4 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 0 & -2 & -1 \\
 -2 & 0 & -1 \\
 -4 & -4 & -1 \\
}$
 & -18 } \\
 \stab{$NH3_{84}$&
$\smat{
 2 & -1 & -2 \\
 -4 & 2 & -1 \\
 -2 & -4 & 2 \\
}$
 & $\frac{1}{10}$
$\smat{
 0 & -2 & -1 \\
 -2 & 0 & -2 \\
 -4 & -2 & 0 \\
}$
 & -50 } \\
 \stab{$NH3_{85}$&
$\smat{
 2 & -2 & -2 \\
 -2 & 2 & -1 \\
 -2 & -4 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 0 & -2 & -1 \\
 -1 & 0 & -1 \\
 -2 & -2 & 0 \\
}$
 & -36 } \\
 \stab{$NH3_{86}$&
$\smat{
 2 & -1 & -2 \\
 -1 & 2 & -1 \\
 -2 & -4 & 2 \\
}$
 & $\frac{1}{20}$
$\smat{
 0 & -10 & -5 \\
 -4 & 0 & -4 \\
 -8 & -10 & -3 \\
}$
 & -20 } \\
 \stab{$H3_{87}$&
$\smat{
 2 & -4 & -2 \\
 -1 & 2 & -1 \\
 -2 & -4 & 2 \\
}$
 & $\frac{1}{8}$
$\smat{
 0 & -4 & -2 \\
 -1 & 0 & -1 \\
 -2 & -4 & 0 \\
}$
 & -32 } \\
 \stab{$NH3_{88}$&
$\smat{
 2 & -1 & -1 \\
 -4 & 2 & -1 \\
 -1 & -4 & 2 \\
}$
 & $\frac{1}{9}$
$\smat{
 0 & -2 & -1 \\
 -3 & -1 & -2 \\
 -6 & -3 & 0 \\
}$
 & -27 } \\
 \stab{$NH3_{89}$&
$\smat{
 2 & -2 & -1 \\
 -2 & 2 & -1 \\
 -1 & -4 & 2 \\
}$
 & $\frac{1}{20}$
$\smat{
 0 & -8 & -4 \\
 -5 & -3 & -4 \\
 -10 & -10 & 0 \\
}$
 & -20 } \\
 \stab{$NH3_{90}$&
$\smat{
 2 & -1 & -1 \\
 -1 & 2 & -1 \\
 -1 & -4 & 2 \\
}$
 & $\frac{1}{3}$
$\smat{
 0 & -2 & -1 \\
 -1 & -1 & -1 \\
 -2 & -3 & -1 \\
}$
 & -9 } \\
 \stab{$H3_{91}$&
$\smat{
 2 & -4 & -1 \\
 -1 & 2 & -1 \\
 -1 & -4 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 0 & -4 & -2 \\
 -1 & -1 & -1 \\
 -2 & -4 & 0 \\
}$
 & -18 } \\
 \stab{$NH3_{92}$&
$\smat{
 2 & -1 & -4 \\
 -4 & 2 & -1 \\
 -1 & -4 & 2 \\
}$
 & $\frac{1}{9}$
$\smat{
 0 & -2 & -1 \\
 -1 & 0 & -2 \\
 -2 & -1 & 0 \\
}$
 & -81 } \\
 \stab{$H3_{93}$&
$\smat{
 2 & -2 & -2 \\
 -2 & 2 & -2 \\
 -2 & -2 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -1 & -1 \\
 -1 & 0 & -1 \\
 -1 & -1 & 0 \\
}$
 & -32 } \\
 \stab{$H3_{94}$&
$\smat{
 2 & -1 & -2 \\
 -1 & 2 & -2 \\
 -2 & -2 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 0 & -2 & -2 \\
 -2 & 0 & -2 \\
 -2 & -2 & -1 \\
}$
 & -18 } \\
 \stab{$H3_{95}$&
$\smat{
 2 & -1 & -1 \\
 -1 & 2 & -2 \\
 -1 & -2 & 2 \\
}$
 & $\frac{1}{8}$
$\smat{
 0 & -4 & -4 \\
 -4 & -3 & -5 \\
 -4 & -5 & -3 \\
}$
 & -8 } \\
 \stab{\fbox{!!!}$H3_{96}$&
$\smat{
 2 & -1 & 0 \\
 -3 & 2 & -2 \\
 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -2 & -2 & -2 \\
 -6 & -4 & -4 \\
 -3 & -2 & -1 \\
}$
 & -2 } \\
 \stab{$H3_{97}$&
$\smat{
 2 & -1 & 0 \\
 -4 & 2 & -2 \\
 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -1 & -1 & -1 \\
 -4 & -2 & -2 \\
 -2 & -1 & 0 \\
}$
 & -4 } \\
 \stab{$H3_{98}$&
$\smat{
 2 & -2 & 0 \\
 -2 & 2 & -2 \\
 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -1 & -2 & -2 \\
 -2 & -2 & -2 \\
 -1 & -1 & 0 \\
}$
 & -4 } \\
 \stab{\fbox{!!!}$H3_{99}$&
$\smat{
 2 & -3 & 0 \\
 -1 & 2 & -2 \\
 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -2 & -6 & -6 \\
 -2 & -4 & -4 \\
 -1 & -2 & -1 \\
}$
 & -2 } \\
 \stab{$H3_{100}$&
$\smat{
 2 & -4 & 0 \\
 -1 & 2 & -2 \\
 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 -2 & -8 & -8 \\
 -2 & -4 & -4 \\
 -1 & -2 & 0 \\
}$
 & -4 } \\
 \stab{\fbox{!!!}$H3_{101}$&
$\smat{
 2 & -1 & 0 \\
 -3 & 2 & -3 \\
 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 -1 & -2 & -3 \\
 -6 & -4 & -6 \\
 -3 & -2 & -1 \\
}$
 & -4 } \\
 \stab{$H3_{102}$&
$\smat{
 2 & -1 & 0 \\
 -4 & 2 & -3 \\
 0 & -1 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 -1 & -2 & -3 \\
 -8 & -4 & -6 \\
 -4 & -2 & 0 \\
}$
 & -6 } \\
 \stab{$H3_{103}$&
$\smat{
 2 & -2 & 0 \\
 -2 & 2 & -3 \\
 0 & -1 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 -1 & -4 & -6 \\
 -4 & -4 & -6 \\
 -2 & -2 & 0 \\
}$
 & -6 } \\
 \stab{\fbox{!!!}$H3_{104}$&
$\smat{
 2 & -2 & 0 \\
 -1 & 2 & -3 \\
 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -1 & -4 & -6 \\
 -2 & -4 & -6 \\
 -1 & -2 & -2 \\
}$
 & -2 } \\
 \stab{\fbox{!!!}$H3_{105}$&
$\smat{
 2 & -3 & 0 \\
 -1 & 2 & -3 \\
 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 -1 & -6 & -9 \\
 -2 & -4 & -6 \\
 -1 & -2 & -1 \\
}$
 & -4 } \\
 \stab{$H3_{106}$&
$\smat{
 2 & -4 & 0 \\
 -1 & 2 & -3 \\
 0 & -1 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 -1 & -8 & -12 \\
 -2 & -4 & -6 \\
 -1 & -2 & 0 \\
}$
 & -6 } \\
 \stab{$H3_{107}$&
$\smat{
 2 & -1 & 0 \\
 -4 & 2 & -4 \\
 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -1 & -2 \\
 -4 & -2 & -4 \\
 -2 & -1 & 0 \\
}$
 & -8 } \\
 \stab{$H3_{108}$&
$\smat{
 2 & -2 & 0 \\
 -2 & 2 & -4 \\
 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -2 & -4 \\
 -2 & -2 & -4 \\
 -1 & -1 & 0 \\
}$
 & -8 } \\
 \stab{$H3_{109}$&
$\smat{
 2 & -1 & 0 \\
 -1 & 2 & -4 \\
 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -4 \\
 -2 & -4 & -8 \\
 -1 & -2 & -3 \\
}$
 & -2 } \\
 \stab{$H3_{110}$&
$\smat{
 2 & -2 & 0 \\
 -1 & 2 & -4 \\
 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -4 & -8 \\
 -2 & -4 & -8 \\
 -1 & -2 & -2 \\
}$
 & -4 } \\
 \stab{$H3_{111}$&
$\smat{
 2 & -3 & 0 \\
 -1 & 2 & -4 \\
 0 & -1 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 0 & -6 & -12 \\
 -2 & -4 & -8 \\
 -1 & -2 & -1 \\
}$
 & -6 } \\
 \stab{$H3_{112}$&
$\smat{
 2 & -4 & 0 \\
 -1 & 2 & -4 \\
 0 & -1 & 2 \\
}$
 & $\frac{1}{8}$
$\smat{
 0 & -8 & -16 \\
 -2 & -4 & -8 \\
 -1 & -2 & 0 \\
}$
 & -8 } \\
 \stab{$H3_{113}$&
$\smat{
 2 & -2 & 0 \\
 -2 & 2 & -2 \\
 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -1 & -1 \\
 -1 & -1 & -1 \\
 -1 & -1 & 0 \\
}$
 & -8 } \\
 \stab{$H3_{114}$&
$\smat{
 2 & -1 & 0 \\
 -1 & 2 & -2 \\
 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -2 \\
 -2 & -4 & -4 \\
 -2 & -4 & -3 \\
}$
 & -2 } \\
 \stab{$H3_{115}$&
$\smat{
 2 & -2 & 0 \\
 -1 & 2 & -2 \\
 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -2 \\
 -1 & -2 & -2 \\
 -1 & -2 & -1 \\
}$
 & -4 } \\
 \stab{$H3_{116}$&
$\smat{
 2 & -3 & 0 \\
 -1 & 2 & -2 \\
 0 & -2 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 0 & -6 & -6 \\
 -2 & -4 & -4 \\
 -2 & -4 & -1 \\
}$
 & -6 } \\
 \stab{$H3_{117}$&
$\smat{
 2 & -4 & 0 \\
 -1 & 2 & -2 \\
 0 & -2 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -4 & -4 \\
 -1 & -2 & -2 \\
 -1 & -2 & 0 \\
}$
 & -8 } \\
 \stab{$H3_{118}$&
$\smat{
 2 & -4 & 0 \\
 -1 & 2 & -1 \\
 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -3 & -8 & -4 \\
 -2 & -4 & -2 \\
 -1 & -2 & 0 \\
}$
 & -2 } \\
 \stab{\fbox{!!!}$H3_{119}$&
$\smat{
 2 & -3 & 0 \\
 -1 & 2 & -1 \\
 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -2 & -6 & -3 \\
 -2 & -4 & -2 \\
 -2 & -4 & -1 \\
}$
 & -2 } \\
 \stab{$H3_{120}$&
$\smat{
 2 & -4 & 0 \\
 -1 & 2 & -1 \\
 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -1 & -4 & -2 \\
 -1 & -2 & -1 \\
 -1 & -2 & 0 \\
}$
 & -4 } \\
 \stab{\fbox{!!!}$H3_{121}$&
$\smat{
 2 & -3 & 0 \\
 -1 & 2 & -1 \\
 0 & -3 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 -1 & -6 & -3 \\
 -2 & -4 & -2 \\
 -3 & -6 & -1 \\
}$
 & -4 } \\
 \stab{$H3_{122}$&
$\smat{
 2 & -4 & 0 \\
 -1 & 2 & -1 \\
 0 & -3 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 -1 & -8 & -4 \\
 -2 & -4 & -2 \\
 -3 & -6 & 0 \\
}$
 & -6 } \\
 \stab{$H3_{123}$&
$\smat{
 2 & -4 & 0 \\
 -1 & 2 & -1 \\
 0 & -4 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -4 & -2 \\
 -1 & -2 & -1 \\
 -2 & -4 & 0 \\
}$
 & -8 } \\
 \stab{$H4_{1}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -2 & 2 & -1 & 0 \\
 0 & -2 & 2 & -2 \\
 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -1 & -1 & -1 \\
 -2 & -2 & -2 & -2 \\
 -4 & -4 & -2 & -2 \\
 -2 & -2 & -1 & 0 \\
}$
 & -4 } \\
 \stab{$H4_{2}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -3 & 2 & -1 & 0 \\
 0 & -1 & 2 & -2 \\
 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -2 & -2 & -2 & -2 \\
 -6 & -4 & -4 & -4 \\
 -6 & -4 & -2 & -2 \\
 -3 & -2 & -1 & 0 \\
}$
 & -2 } \\
 \stab{$H4_{3}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -1 & 2 & -1 & 0 \\
 0 & -2 & 2 & -2 \\
 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -2 & -2 \\
 -2 & -4 & -4 & -4 \\
 -4 & -8 & -6 & -6 \\
 -2 & -4 & -3 & -2 \\
}$
 & -2 } \\
 \stab{$H4_{4}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -1 & 2 & -2 & 0 \\
 0 & -1 & 2 & -2 \\
 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -4 & -4 \\
 -2 & -4 & -8 & -8 \\
 -2 & -4 & -6 & -6 \\
 -1 & -2 & -3 & -2 \\
}$
 & -2 } \\
 \stab{$H4_{5}$&
$\smat{
 2 & -2 & 0 & 0 \\
 -1 & 2 & -1 & 0 \\
 0 & -2 & 2 & -2 \\
 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -2 & -2 \\
 -1 & -2 & -2 & -2 \\
 -2 & -4 & -2 & -2 \\
 -1 & -2 & -1 & 0 \\
}$
 & -4 } \\
 \stab{$H4_{6}$&
$\smat{
 2 & -2 & 0 & 0 \\
 -1 & 2 & -2 & 0 \\
 0 & -1 & 2 & -2 \\
 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -4 & -8 & -8 \\
 -2 & -4 & -8 & -8 \\
 -2 & -4 & -4 & -4 \\
 -1 & -2 & -2 & 0 \\
}$
 & -4 } \\
 \stab{$H4_{7}$&
$\smat{
 2 & -3 & 0 & 0 \\
 -1 & 2 & -1 & 0 \\
 0 & -1 & 2 & -2 \\
 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -2 & -6 & -6 & -6 \\
 -2 & -4 & -4 & -4 \\
 -2 & -4 & -2 & -2 \\
 -1 & -2 & -1 & 0 \\
}$
 & -2 } \\
 \stab{$H4_{8}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -3 & 2 & -1 & 0 \\
 0 & -1 & 2 & -3 \\
 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{3}$
$\smat{
 0 & -1 & -2 & -3 \\
 -3 & -2 & -4 & -6 \\
 -6 & -4 & -2 & -3 \\
 -3 & -2 & -1 & 0 \\
}$
 & -3 } \\
 \stab{$H4_{9}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -1 & 2 & -1 & 0 \\
 0 & -1 & 2 & -3 \\
 0 & 0 & -1 & 2 \\
}$
 &
$\smat{
 0 & -1 & -2 & -3 \\
 -1 & -2 & -4 & -6 \\
 -2 & -4 & -6 & -9 \\
 -1 & -2 & -3 & -4 \\
}$
 & -1 } \\
 \stab{$H4_{10}$&
$\smat{
 2 & -2 & 0 & 0 \\
 -1 & 2 & -1 & 0 \\
 0 & -1 & 2 & -3 \\
 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -4 & -6 \\
 -1 & -2 & -4 & -6 \\
 -2 & -4 & -4 & -6 \\
 -1 & -2 & -2 & -2 \\
}$
 & -2 } \\
 \stab{$H4_{11}$&
$\smat{
 2 & -3 & 0 & 0 \\
 -1 & 2 & -1 & 0 \\
 0 & -1 & 2 & -3 \\
 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{3}$
$\smat{
 0 & -3 & -6 & -9 \\
 -1 & -2 & -4 & -6 \\
 -2 & -4 & -2 & -3 \\
 -1 & -2 & -1 & 0 \\
}$
 & -3 } \\
 \stab{$H4_{12}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -1 & 2 & -3 & 0 \\
 0 & -1 & 2 & -1 \\
 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{3}$
$\smat{
 0 & -3 & -6 & -3 \\
 -3 & -6 & -12 & -6 \\
 -2 & -4 & -6 & -3 \\
 -1 & -2 & -3 & 0 \\
}$
 & -3 } \\
 \stab{$H4_{13}$&
$\smat{
 2 & -2 & 0 & 0 \\
 -1 & 2 & -2 & 0 \\
 0 & -1 & 2 & -1 \\
 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -2 & -6 & -8 & -4 \\
 -3 & -6 & -8 & -4 \\
 -2 & -4 & -4 & -2 \\
 -1 & -2 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$H4_{14}$&
$\smat{
 2 & -2 & 0 & 0 \\
 -1 & 2 & -1 & 0 \\
 0 & -2 & 2 & -1 \\
 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -2 & -6 & -4 & -2 \\
 -3 & -6 & -4 & -2 \\
 -4 & -8 & -4 & -2 \\
 -2 & -4 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$H4_{15}$&
$\smat{
 2 & -3 & 0 & 0 \\
 -1 & 2 & -1 & 0 \\
 0 & -1 & 2 & -1 \\
 0 & 0 & -1 & 2 \\
}$
 &
$\smat{
 -4 & -9 & -6 & -3 \\
 -3 & -6 & -4 & -2 \\
 -2 & -4 & -2 & -1 \\
 -1 & -2 & -1 & 0 \\
}$
 & -1 } \\
 \stab{$H4_{16}$&
$\smat{
 2 & -2 & 0 & 0 \\
 -1 & 2 & -2 & 0 \\
 0 & -1 & 2 & -1 \\
 0 & 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -4 & -2 \\
 -1 & -2 & -4 & -2 \\
 -1 & -2 & -2 & -1 \\
 -1 & -2 & -2 & 0 \\
}$
 & -4 } \\
 \stab{$H4_{17}$&
$\smat{
 2 & -3 & 0 & 0 \\
 -1 & 2 & -1 & 0 \\
 0 & -1 & 2 & -1 \\
 0 & 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -2 & -6 & -6 & -3 \\
 -2 & -4 & -4 & -2 \\
 -2 & -4 & -2 & -1 \\
 -2 & -4 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$H4_{18}$&
$\smat{
 2 & -3 & 0 & 0 \\
 -1 & 2 & -1 & 0 \\
 0 & -1 & 2 & -1 \\
 0 & 0 & -3 & 2 \\
}$
 & $\frac{1}{3}$
$\smat{
 0 & -3 & -6 & -3 \\
 -1 & -2 & -4 & -2 \\
 -2 & -4 & -2 & -1 \\
 -3 & -6 & -3 & 0 \\
}$
 & -3 } \\
 \stab{$H4_{19}$&
$\smat{
 2 & -1 & 0 & -1 \\
 -1 & 2 & -1 & 0 \\
 0 & -2 & 2 & -2 \\
 -1 & 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -2 & -2 & -2 \\
 -2 & -1 & -2 & -3 \\
 -4 & -4 & -2 & -4 \\
 -2 & -3 & -2 & -1 \\
}$
 & -8 } \\
 \stab{$NH4_{20}$&
$\smat{
 2 & -1 & 0 & -1 \\
 -2 & 2 & -1 & 0 \\
 0 & -2 & 2 & -2 \\
 -1 & 0 & -1 & 2 \\
}$
 & $\frac{1}{12}$
$\smat{
 0 & -4 & -4 & -4 \\
 -6 & -2 & -5 & -8 \\
 -12 & -8 & -2 & -8 \\
 -6 & -6 & -3 & 0 \\
}$
 & -12 } \\
 \stab{$NH4_{21}$&
$\smat{
 2 & -2 & 0 & -1 \\
 -1 & 2 & -1 & 0 \\
 0 & -2 & 2 & -2 \\
 -1 & 0 & -1 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 0 & -3 & -3 & -3 \\
 -2 & -1 & -2 & -3 \\
 -4 & -5 & -1 & -3 \\
 -2 & -4 & -2 & 0 \\
}$
 & -12 } \\
 \stab{$H4_{22}$&
$\smat{
 2 & -1 & 0 & -1 \\
 -2 & 2 & -1 & 0 \\
 0 & -2 & 2 & -2 \\
 -2 & 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -1 & -1 & -1 \\
 -2 & 0 & -1 & -2 \\
 -4 & -2 & 0 & -2 \\
 -2 & -2 & -1 & 0 \\
}$
 & -16 } \\
 \stab{$NH4_{23}$&
$\smat{
 2 & -2 & 0 & -1 \\
 -1 & 2 & -1 & 0 \\
 0 & -2 & 2 & -2 \\
 -2 & 0 & -1 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 0 & -2 & -2 & -2 \\
 -2 & 0 & -1 & -2 \\
 -4 & -4 & 0 & -2 \\
 -2 & -4 & -2 & 0 \\
}$
 & -18 } \\
 \stab{$H4_{24}$&
$\smat{
 2 & -2 & 0 & -2 \\
 -1 & 2 & -1 & 0 \\
 0 & -2 & 2 & -2 \\
 -1 & 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -2 & -2 & -2 \\
 -1 & 0 & -1 & -2 \\
 -2 & -2 & 0 & -2 \\
 -1 & -2 & -1 & 0 \\
}$
 & -16 } \\
 \stab{$H4_{25}$&
$\smat{
 2 & -1 & 0 & -1 \\
 -1 & 2 & -1 & 0 \\
 0 & -3 & 2 & -1 \\
 -3 & 0 & -1 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 0 & -3 & -2 & -1 \\
 -3 & 0 & -1 & -2 \\
 -6 & -3 & 0 & -3 \\
 -3 & -6 & -3 & 0 \\
}$
 & -12 } \\
 \stab{$NH4_{26}$&
$\smat{
 2 & -1 & 0 & -1 \\
 -1 & 2 & -1 & 0 \\
 0 & -3 & 2 & -1 \\
 -1 & 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -3 & -2 & -1 \\
 -2 & -2 & -2 & -2 \\
 -4 & -5 & -2 & -3 \\
 -2 & -4 & -2 & 0 \\
}$
 & -8 } \\
 \stab{$NH4_{27}$&
$\smat{
 2 & -1 & 0 & -3 \\
 -1 & 2 & -1 & 0 \\
 0 & -3 & 2 & -1 \\
 -1 & 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -3 & -2 & -1 \\
 -1 & 0 & -1 & -2 \\
 -2 & -1 & 0 & -3 \\
 -1 & -2 & -1 & 0 \\
}$
 & -16 } \\
 \stab{$NH4_{28}$&
$\smat{
 2 & -1 & 0 & -2 \\
 -1 & 2 & -1 & 0 \\
 0 & -3 & 2 & -1 \\
 -1 & 0 & -1 & 2 \\
}$
 & $\frac{1}{12}$
$\smat{
 0 & -9 & -6 & -3 \\
 -4 & -2 & -4 & -6 \\
 -8 & -7 & -2 & -9 \\
 -4 & -8 & -4 & 0 \\
}$
 & -12 } \\
 \stab{$NH4_{29}$&
$\smat{
 2 & -1 & 0 & -1 \\
 -1 & 2 & -1 & 0 \\
 0 & -3 & 2 & -1 \\
 -2 & 0 & -1 & 2 \\
}$
 & $\frac{1}{10}$
$\smat{
 0 & -6 & -4 & -2 \\
 -5 & -2 & -3 & -4 \\
 -10 & -8 & -2 & -6 \\
 -5 & -10 & -5 & 0 \\
}$
 & -10 } \\
 \stab{\fbox{!!!}$NH4_{30}$&
$\smat{
 2 & -2 & 0 & -1 \\
 -1 & 2 & -1 & 0 \\
 0 & -1 & 2 & -1 \\
 -1 & 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 -4 & -7 & -6 & -5 \\
 -4 & -4 & -4 & -4 \\
 -4 & -5 & -2 & -3 \\
 -4 & -6 & -4 & -2 \\
}$
 & -4 } \\
 \stab{$NH4_{31}$&
$\smat{
 2 & -1 & 0 & -2 \\
 -2 & 2 & -1 & 0 \\
 0 & -1 & 2 & -1 \\
 -1 & 0 & -1 & 2 \\
}$
 & $\frac{1}{9}$
$\smat{
 -4 & -5 & -6 & -7 \\
 -7 & -2 & -6 & -10 \\
 -6 & -3 & 0 & -6 \\
 -5 & -4 & -3 & -2 \\
}$
 & -9 } \\
 \stab{$H4_{32}$&
$\smat{
 2 & -1 & 0 & -1 \\
 -2 & 2 & -1 & 0 \\
 0 & -1 & 2 & -1 \\
 -2 & 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 -2 & -2 & -2 & -2 \\
 -4 & -1 & -2 & -3 \\
 -4 & -2 & 0 & -2 \\
 -4 & -3 & -2 & -1 \\
}$
 & -8 } \\
 \stab{\fbox{!!!}$H4_{33}$&
$\smat{
 2 & -2 & 0 & -1 \\
 -1 & 2 & -1 & 0 \\
 0 & -1 & 2 & -1 \\
 -1 & 0 & -2 & 2 \\
}$
 & $\frac{1}{7}$
$\smat{
 -2 & -6 & -8 & -5 \\
 -3 & -2 & -5 & -4 \\
 -4 & -5 & -2 & -3 \\
 -5 & -8 & -6 & -2 \\
}$
 & -7 } \\
 \stab{\fbox{!!!}$NH4_{34}$&
$\smat{
 2 & -1 & 0 & -1 \\
 -2 & 2 & -1 & 0 \\
 0 & -1 & 2 & -1 \\
 -1 & 0 & -2 & 2 \\
}$
 & $\frac{1}{8}$
$\smat{
 -2 & -4 & -6 & -4 \\
 -5 & -2 & -7 & -6 \\
 -6 & -4 & -2 & -4 \\
 -7 & -6 & -5 & -2 \\
}$
 & -8 } \\
 \stab{$NH4_{35}$&
$\smat{
 2 & -1 & 0 & -2 \\
 -2 & 2 & -1 & 0 \\
 0 & -1 & 2 & -1 \\
 -1 & 0 & -2 & 2 \\
}$
 & $\frac{1}{15}$
$\smat{
 -2 & -6 & -10 & -7 \\
 -5 & 0 & -10 & -10 \\
 -6 & -3 & 0 & -6 \\
 -7 & -6 & -5 & -2 \\
}$
 & -15 } \\
 \stab{$NH4_{36}$&
$\smat{
 2 & -1 & 0 & -1 \\
 -2 & 2 & -1 & 0 \\
 0 & -1 & 2 & -2 \\
 -2 & 0 & -1 & 2 \\
}$
 & $\frac{1}{12}$
$\smat{
 -2 & -3 & -4 & -5 \\
 -8 & 0 & -4 & -8 \\
 -12 & -6 & 0 & -6 \\
 -8 & -6 & -4 & -2 \\
}$
 & -12 } \\
 \stab{$NH4_{37}$&
$\smat{
 2 & -1 & 0 & -2 \\
 -2 & 2 & -1 & 0 \\
 0 & -2 & 2 & -1 \\
 -1 & 0 & -2 & 2 \\
}$
 & $\frac{1}{5}$
$\smat{
 0 & -2 & -2 & -1 \\
 -1 & 0 & -2 & -2 \\
 -2 & -1 & 0 & -2 \\
 -2 & -2 & -1 & 0 \\
}$
 & -25 } \\
 \stab{$H4_{38}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -2 & 2 & -2 & -2 \\
 0 & -1 & 2 & 0 \\
 0 & -1 & 0 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -1 & -1 & -1 \\
 -2 & -2 & -2 & -2 \\
 -1 & -1 & 0 & -1 \\
 -1 & -1 & -1 & 0 \\
}$
 & -8 } \\
 \stab{$H4_{39}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -1 & 2 & -2 & -2 \\
 0 & -1 & 2 & 0 \\
 0 & -1 & 0 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -2 & -2 \\
 -2 & -4 & -4 & -4 \\
 -1 & -2 & -1 & -2 \\
 -1 & -2 & -2 & -1 \\
}$
 & -4 } \\
 \stab{$H4_{40}$&
$\smat{
 2 & -2 & 0 & 0 \\
 -1 & 2 & -2 & -2 \\
 0 & -1 & 2 & 0 \\
 0 & -1 & 0 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -4 & -4 & -4 \\
 -2 & -4 & -4 & -4 \\
 -1 & -2 & 0 & -2 \\
 -1 & -2 & -2 & 0 \\
}$
 & -8 } \\
 \stab{$H4_{41}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -1 & 2 & -3 & -1 \\
 0 & -1 & 2 & 0 \\
 0 & -1 & 0 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -3 & -1 \\
 -2 & -4 & -6 & -2 \\
 -1 & -2 & -2 & -1 \\
 -1 & -2 & -3 & 0 \\
}$
 & -4 } \\
 \stab{$H4_{42}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -1 & 2 & -1 & -1 \\
 0 & -1 & 2 & 0 \\
 0 & -3 & 0 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -1 & -1 \\
 -2 & -4 & -2 & -2 \\
 -1 & -2 & 0 & -1 \\
 -3 & -6 & -3 & -2 \\
}$
 & -4 } \\
 \stab{$H4_{43}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -2 & 2 & -1 & -1 \\
 0 & -1 & 2 & 0 \\
 0 & -2 & 0 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -1 & -2 & -1 & -1 \\
 -4 & -4 & -2 & -2 \\
 -2 & -2 & 0 & -1 \\
 -4 & -4 & -2 & -1 \\
}$
 & -4 } \\
 \stab{$H4_{44}$&
$\smat{
 2 & -2 & 0 & 0 \\
 -1 & 2 & -1 & -1 \\
 0 & -1 & 2 & 0 \\
 0 & -2 & 0 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -1 & -4 & -2 & -2 \\
 -2 & -4 & -2 & -2 \\
 -1 & -2 & 0 & -1 \\
 -2 & -4 & -2 & -1 \\
}$
 & -4 } \\
 \stab{$H4_{45}$&
$\smat{
 2 & -2 & 0 & 0 \\
 -1 & 2 & -2 & -1 \\
 0 & -1 & 2 & 0 \\
 0 & -2 & 0 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -4 & -4 & -2 \\
 -2 & -4 & -4 & -2 \\
 -1 & -2 & 0 & -1 \\
 -2 & -4 & -4 & 0 \\
}$
 & -8 } \\
 \stab{$H4_{46}$&
$\smat{
 2 & -2 & 0 & 0 \\
 -1 & 2 & -1 & -1 \\
 0 & -2 & 2 & 0 \\
 0 & -2 & 0 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -1 & -1 \\
 -1 & -2 & -1 & -1 \\
 -1 & -2 & 0 & -1 \\
 -1 & -2 & -1 & 0 \\
}$
 & -8 } \\
 \stab{$H4_{47}$&
$\smat{
 2 & -1 & -1 & -1 \\
 -1 & 2 & -1 & -1 \\
 -1 & -1 & 2 & -1 \\
 -1 & -1 & -1 & 2 \\
}$
 & $\frac{1}{3}$
$\smat{
 0 & -1 & -1 & -1 \\
 -1 & 0 & -1 & -1 \\
 -1 & -1 & 0 & -1 \\
 -1 & -1 & -1 & 0 \\
}$
 & -27 } \\
 \stab{$H4_{48}$&
$\smat{
 2 & -1 & 0 & -1 \\
 -1 & 2 & -1 & -1 \\
 0 & -1 & 2 & -1 \\
 -1 & -1 & -1 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 0 & -3 & -3 & -3 \\
 -3 & -2 & -3 & -4 \\
 -3 & -3 & 0 & -3 \\
 -3 & -4 & -3 & -2 \\
}$
 & -12 } \\
 \stab{$H4_{49}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -3 & 2 & -1 & -1 \\
 0 & -1 & 2 & -1 \\
 0 & -1 & -1 & 2 \\
}$
 & $\frac{1}{3}$
$\smat{
 0 & -1 & -1 & -1 \\
 -3 & -2 & -2 & -2 \\
 -3 & -2 & 0 & -1 \\
 -3 & -2 & -1 & 0 \\
}$
 & -9 } \\
 \stab{$H4_{50}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -1 & 2 & -1 & -1 \\
 0 & -1 & 2 & -1 \\
 0 & -1 & -1 & 2 \\
}$
 & $\frac{1}{3}$
$\smat{
 0 & -3 & -3 & -3 \\
 -3 & -6 & -6 & -6 \\
 -3 & -6 & -4 & -5 \\
 -3 & -6 & -5 & -4 \\
}$
 & -3 } \\
 \stab{$H4_{51}$&
$\smat{
 2 & -3 & 0 & 0 \\
 -1 & 2 & -1 & -1 \\
 0 & -1 & 2 & -1 \\
 0 & -1 & -1 & 2 \\
}$
 & $\frac{1}{3}$
$\smat{
 0 & -3 & -3 & -3 \\
 -1 & -2 & -2 & -2 \\
 -1 & -2 & 0 & -1 \\
 -1 & -2 & -1 & 0 \\
}$
 & -9 } \\
 \stab{$H4_{52}$&
$\smat{
 2 & -2 & 0 & 0 \\
 -1 & 2 & -1 & -1 \\
 0 & -1 & 2 & -1 \\
 0 & -1 & -1 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 0 & -6 & -6 & -6 \\
 -3 & -6 & -6 & -6 \\
 -3 & -6 & -2 & -4 \\
 -3 & -6 & -4 & -2 \\
}$
 & -6 } \\
 \stab{$H4_{53}$&
$\smat{
 2 & -1 & 0 & 0 \\
 -2 & 2 & -1 & -1 \\
 0 & -1 & 2 & -1 \\
 0 & -1 & -1 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 0 & -3 & -3 & -3 \\
 -6 & -6 & -6 & -6 \\
 -6 & -6 & -2 & -4 \\
 -6 & -6 & -4 & -2 \\
}$
 & -6 } \\
 \stab{$H5_{1}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -2 & 2 & -1 & 0 & 0 \\
 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & -2 & 2 & -1 \\
 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -1 & -2 & -3 & -2 & -1 \\
 -4 & -4 & -6 & -4 & -2 \\
 -6 & -6 & -6 & -4 & -2 \\
 -8 & -8 & -8 & -4 & -2 \\
 -4 & -4 & -4 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$H5_{2}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -2 & 2 & -1 & 0 & 0 \\
 0 & -1 & 2 & -2 & 0 \\
 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -1 & -2 & -3 & -4 & -2 \\
 -4 & -4 & -6 & -8 & -4 \\
 -6 & -6 & -6 & -8 & -4 \\
 -4 & -4 & -4 & -4 & -2 \\
 -2 & -2 & -2 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$H5_{3}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -1 & 2 & -2 & 0 & 0 \\
 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -4 & -4 & -2 \\
 -2 & -4 & -8 & -8 & -4 \\
 -2 & -4 & -6 & -6 & -3 \\
 -2 & -4 & -6 & -4 & -2 \\
 -2 & -4 & -6 & -4 & -1 \\
}$
 & -2 } \\
 \stab{$H5_{4}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 \\
 0 & -2 & 2 & -1 & 0 \\
 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -2 & -2 & -1 \\
 -2 & -4 & -4 & -4 & -2 \\
 -4 & -8 & -6 & -6 & -3 \\
 -4 & -8 & -6 & -4 & -2 \\
 -4 & -8 & -6 & -4 & -1 \\
}$
 & -2 } \\
 \stab{\fbox{!!!}$NH5_{5}$&
$\smat{
 2 & -1 & 0 & 0 & -1 \\
 -1 & 2 & -1 & 0 & 0 \\
 0 & -1 & 2 & -2 & 0 \\
 0 & 0 & -1 & 2 & -1 \\
 -1 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{5}$
$\smat{
 -1 & -3 & -5 & -7 & -4 \\
 -4 & -2 & -5 & -8 & -6 \\
 -7 & -6 & -5 & -9 & -8 \\
 -5 & -5 & -5 & -5 & -5 \\
 -3 & -4 & -5 & -6 & -2 \\
}$
 & -5 } \\
 \stab{$H5_{6}$&
$\smat{
 2 & -1 & 0 & 0 & -1 \\
 -2 & 2 & -1 & 0 & 0 \\
 0 & -1 & 2 & -2 & 0 \\
 0 & 0 & -1 & 2 & -1 \\
 -1 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{8}$
$\smat{
 -1 & -3 & -5 & -7 & -4 \\
 -6 & -2 & -6 & -10 & -8 \\
 -10 & -6 & -2 & -6 & -8 \\
 -7 & -5 & -3 & -1 & -4 \\
 -4 & -4 & -4 & -4 & 0 \\
}$
 & -8 } \\
 \stab{$NH5_{7}$&
$\smat{
 2 & -2 & 0 & 0 & -1 \\
 -1 & 2 & -1 & 0 & 0 \\
 0 & -1 & 2 & -2 & 0 \\
 0 & 0 & -1 & 2 & -1 \\
 -1 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{9}$
$\smat{
 -1 & -5 & -8 & -11 & -6 \\
 -4 & -2 & -5 & -8 & -6 \\
 -7 & -8 & -2 & -5 & -6 \\
 -5 & -7 & -4 & -1 & -3 \\
 -3 & -6 & -6 & -6 & 0 \\
}$
 & -9 } \\
 \stab{$H5_{8}$&
$\smat{
 2 & -1 & 0 & 0 & -2 \\
 -1 & 2 & -1 & 0 & 0 \\
 0 & -1 & 2 & -2 & 0 \\
 0 & 0 & -1 & 2 & -1 \\
 -1 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{8}$
$\smat{
 -1 & -4 & -7 & -10 & -6 \\
 -4 & 0 & -4 & -8 & -8 \\
 -7 & -4 & -1 & -6 & -10 \\
 -5 & -4 & -3 & -2 & -6 \\
 -3 & -4 & -5 & -6 & -2 \\
}$
 & -8 } \\
 \stab{$H5_{9}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -1 & 2 & -1 & -1 & -2 \\
 0 & -1 & 2 & 0 & 0 \\
 0 & -1 & 0 & 2 & 0 \\
 0 & -1 & 0 & 0 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -1 & -1 & -2 \\
 -2 & -4 & -2 & -2 & -4 \\
 -1 & -2 & 0 & -1 & -2 \\
 -1 & -2 & -1 & 0 & -2 \\
 -1 & -2 & -1 & -1 & -1 \\
}$
 & -8 } \\
 \stab{$H5_{10}$&
$\smat{
 2 & -2 & 0 & 0 & 0 \\
 -1 & 2 & -1 & -1 & -1 \\
 0 & -1 & 2 & 0 & 0 \\
 0 & -1 & 0 & 2 & 0 \\
 0 & -1 & 0 & 0 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -1 & -4 & -2 & -2 & -2 \\
 -2 & -4 & -2 & -2 & -2 \\
 -1 & -2 & 0 & -1 & -1 \\
 -1 & -2 & -1 & 0 & -1 \\
 -1 & -2 & -1 & -1 & 0 \\
}$
 & -8 } \\
 \stab{$H5_{11}$&
$\smat{
 2 & -1 & 0 & -1 & 0 \\
 -1 & 2 & -1 & 0 & -1 \\
 0 & -1 & 2 & -1 & 0 \\
 -1 & 0 & -1 & 2 & -1 \\
 0 & -1 & 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -2 & -2 & -2 & -2 \\
 -2 & -1 & -2 & -3 & -2 \\
 -2 & -2 & 0 & -2 & -2 \\
 -2 & -3 & -2 & -1 & -2 \\
 -2 & -2 & -2 & -2 & 0 \\
}$
 & -16 } \\
 \stab{$H5_{12}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & -1 \\
 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & -1 & 2 & -1 \\
 0 & -1 & 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -4 & -4 & -4 & -4 \\
 -4 & -8 & -8 & -8 & -8 \\
 -4 & -8 & -5 & -6 & -7 \\
 -4 & -8 & -6 & -4 & -6 \\
 -4 & -8 & -7 & -6 & -5 \\
}$
 & -4 } \\
 \stab{$H5_{13}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -2 & 2 & -1 & 0 & -1 \\
 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & -1 & 2 & -1 \\
 0 & -1 & 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -2 & -2 & -2 & -2 \\
 -4 & -4 & -4 & -4 & -4 \\
 -4 & -4 & -1 & -2 & -3 \\
 -4 & -4 & -2 & 0 & -2 \\
 -4 & -4 & -3 & -2 & -1 \\
}$
 & -8 } \\
 \stab{$H5_{14}$&
$\smat{
 2 & -2 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & -1 \\
 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & -1 & 2 & -1 \\
 0 & -1 & 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -4 & -4 & -4 & -4 \\
 -2 & -4 & -4 & -4 & -4 \\
 -2 & -4 & -1 & -2 & -3 \\
 -2 & -4 & -2 & 0 & -2 \\
 -2 & -4 & -3 & -2 & -1 \\
}$
 & -8 } \\
 \stab{$H5_{15}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -1 & 2 & -1 & -2 & 0 \\
 0 & -1 & 2 & 0 & 0 \\
 0 & -1 & 0 & 2 & -1 \\
 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 -1 & -6 & -3 & -8 & -4 \\
 -6 & -12 & -6 & -16 & -8 \\
 -3 & -6 & -1 & -8 & -4 \\
 -4 & -8 & -4 & -8 & -4 \\
 -2 & -4 & -2 & -4 & 0 \\
}$
 & -4 } \\
 \stab{$H5_{16}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -1 & 2 & -1 & -1 & 0 \\
 0 & -1 & 2 & 0 & 0 \\
 0 & -2 & 0 & 2 & -1 \\
 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 -1 & -6 & -3 & -4 & -2 \\
 -6 & -12 & -6 & -8 & -4 \\
 -3 & -6 & -1 & -4 & -2 \\
 -8 & -16 & -8 & -8 & -4 \\
 -4 & -8 & -4 & -4 & 0 \\
}$
 & -4 } \\
 \stab{$H5_{17}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -1 & 2 & -2 & -1 & 0 \\
 0 & -1 & 2 & 0 & 0 \\
 0 & -1 & 0 & 2 & -2 \\
 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -2 & -2 & -2 \\
 -2 & -4 & -4 & -4 & -4 \\
 -1 & -2 & -1 & -2 & -2 \\
 -2 & -4 & -4 & -2 & -2 \\
 -1 & -2 & -2 & -1 & 0 \\
}$
 & -4 } \\
 \stab{$H5_{18}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -1 & 2 & -2 & -1 & 0 \\
 0 & -1 & 2 & 0 & 0 \\
 0 & -1 & 0 & 2 & -1 \\
 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -2 & -6 & -6 & -4 & -2 \\
 -6 & -12 & -12 & -8 & -4 \\
 -3 & -6 & -5 & -4 & -2 \\
 -4 & -8 & -8 & -4 & -2 \\
 -2 & -4 & -4 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$H5_{19}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -1 & 2 & -2 & -1 & 0 \\
 0 & -1 & 2 & 0 & 0 \\
 0 & -1 & 0 & 2 & -1 \\
 0 & 0 & 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -2 & -2 & -1 \\
 -2 & -4 & -4 & -4 & -2 \\
 -1 & -2 & -1 & -2 & -1 \\
 -2 & -4 & -4 & -2 & -1 \\
 -2 & -4 & -4 & -2 & 0 \\
}$
 & -4 } \\
 \stab{$H5_{20}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -1 & 2 & -1 & -1 & 0 \\
 0 & -2 & 2 & 0 & 0 \\
 0 & -1 & 0 & 2 & -2 \\
 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -1 & -2 & -2 \\
 -2 & -4 & -2 & -4 & -4 \\
 -2 & -4 & -1 & -4 & -4 \\
 -2 & -4 & -2 & -2 & -2 \\
 -1 & -2 & -1 & -1 & 0 \\
}$
 & -4 } \\
 \stab{$H5_{21}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -1 & 2 & -1 & -1 & 0 \\
 0 & -2 & 2 & 0 & 0 \\
 0 & -1 & 0 & 2 & -1 \\
 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -2 & -6 & -3 & -4 & -2 \\
 -6 & -12 & -6 & -8 & -4 \\
 -6 & -12 & -5 & -8 & -4 \\
 -4 & -8 & -4 & -4 & -2 \\
 -2 & -4 & -2 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$H5_{22}$&
$\smat{
 2 & -1 & 0 & 0 & 0 \\
 -1 & 2 & -1 & -1 & 0 \\
 0 & -2 & 2 & 0 & 0 \\
 0 & -1 & 0 & 2 & -1 \\
 0 & 0 & 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -1 & -2 & -1 \\
 -2 & -4 & -2 & -4 & -2 \\
 -2 & -4 & -1 & -4 & -2 \\
 -2 & -4 & -2 & -2 & -1 \\
 -2 & -4 & -2 & -2 & 0 \\
}$
 & -4 } \\
 \stab{$H6_{1}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & -1 & 0 & 0 \\
 0 & -1 & 2 & 0 & 0 & 0 \\
 0 & -1 & 0 & 2 & -1 & 0 \\
 0 & 0 & 0 & -2 & 2 & -1 \\
 0 & 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -1 & -3 & -2 & -1 \\
 -2 & -4 & -2 & -6 & -4 & -2 \\
 -1 & -2 & 0 & -3 & -2 & -1 \\
 -3 & -6 & -3 & -6 & -4 & -2 \\
 -4 & -8 & -4 & -8 & -4 & -2 \\
 -2 & -4 & -2 & -4 & -2 & 0 \\
}$
 & -4 } \\
 \stab{$H6_{2}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & -1 & 0 & 0 \\
 0 & -1 & 2 & 0 & 0 & 0 \\
 0 & -1 & 0 & 2 & -2 & 0 \\
 0 & 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -1 & -3 & -4 & -2 \\
 -2 & -4 & -2 & -6 & -8 & -4 \\
 -1 & -2 & 0 & -3 & -4 & -2 \\
 -3 & -6 & -3 & -6 & -8 & -4 \\
 -2 & -4 & -2 & -4 & -4 & -2 \\
 -1 & -2 & -1 & -2 & -2 & 0 \\
}$
 & -4 } \\
 \stab{$NH6_{3}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & -1 \\
 -1 & 2 & -1 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & 0 & 0 \\
 0 & 0 & -1 & 2 & -2 & 0 \\
 0 & 0 & 0 & -1 & 2 & -1 \\
 -1 & 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 0 & -2 & -4 & -6 & -8 & -4 \\
 -3 & 0 & -3 & -6 & -9 & -6 \\
 -6 & -4 & -2 & -6 & -10 & -8 \\
 -9 & -8 & -7 & -6 & -11 & -10 \\
 -6 & -6 & -6 & -6 & -6 & -6 \\
 -3 & -4 & -5 & -6 & -7 & -2 \\
}$
 & -6 } \\
 \stab{$H6_{4}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & -1 \\
 -2 & 2 & -1 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & 0 & 0 \\
 0 & 0 & -1 & 2 & -2 & 0 \\
 0 & 0 & 0 & -1 & 2 & -1 \\
 -1 & 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -1 & -2 & -3 & -4 & -2 \\
 -2 & 0 & -2 & -4 & -6 & -4 \\
 -4 & -2 & 0 & -2 & -4 & -4 \\
 -6 & -4 & -2 & 0 & -2 & -4 \\
 -4 & -3 & -2 & -1 & 0 & -2 \\
 -2 & -2 & -2 & -2 & -2 & 0 \\
}$
 & -8 } \\
 \stab{$NH6_{5}$&
$\smat{
 2 & -2 & 0 & 0 & 0 & -1 \\
 -1 & 2 & -1 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & 0 & 0 \\
 0 & 0 & -1 & 2 & -2 & 0 \\
 0 & 0 & 0 & -1 & 2 & -1 \\
 -1 & 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{3}$
$\smat{
 0 & -1 & -2 & -3 & -4 & -2 \\
 -1 & 0 & -1 & -2 & -3 & -2 \\
 -2 & -2 & 0 & -1 & -2 & -2 \\
 -3 & -4 & -2 & 0 & -1 & -2 \\
 -2 & -3 & -2 & -1 & 0 & -1 \\
 -1 & -2 & -2 & -2 & -2 & 0 \\
}$
 & -9 } \\
 \stab{$H6_{6}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & -1 & -1 & -1 \\
 0 & -1 & 2 & 0 & 0 & 0 \\
 0 & -1 & 0 & 2 & 0 & 0 \\
 0 & -1 & 0 & 0 & 2 & 0 \\
 0 & -1 & 0 & 0 & 0 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -1 & -1 & -1 & -1 \\
 -2 & -4 & -2 & -2 & -2 & -2 \\
 -1 & -2 & 0 & -1 & -1 & -1 \\
 -1 & -2 & -1 & 0 & -1 & -1 \\
 -1 & -2 & -1 & -1 & 0 & -1 \\
 -1 & -2 & -1 & -1 & -1 & 0 \\
}$
 & -16 } \\
 \stab{$H6_{7}$&
$\smat{
 2 & -2 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 \\
 0 & 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -4 & -10 & -12 & -6 & -8 & -4 \\
 -5 & -10 & -12 & -6 & -8 & -4 \\
 -6 & -12 & -12 & -6 & -8 & -4 \\
 -3 & -6 & -6 & -2 & -4 & -2 \\
 -4 & -8 & -8 & -4 & -4 & -2 \\
 -2 & -4 & -4 & -2 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$H6_{8}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 \\
 -2 & 2 & -1 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 \\
 0 & 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -4 & -5 & -6 & -3 & -4 & -2 \\
 -10 & -10 & -12 & -6 & -8 & -4 \\
 -12 & -12 & -12 & -6 & -8 & -4 \\
 -6 & -6 & -6 & -2 & -4 & -2 \\
 -8 & -8 & -8 & -4 & -4 & -2 \\
 -4 & -4 & -4 & -2 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$H6_{9}$&
$\smat{
 2 & -2 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 \\
 0 & 0 & 0 & 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -4 & -2 & -4 & -2 \\
 -1 & -2 & -4 & -2 & -4 & -2 \\
 -2 & -4 & -4 & -2 & -4 & -2 \\
 -1 & -2 & -2 & 0 & -2 & -1 \\
 -2 & -4 & -4 & -2 & -2 & -1 \\
 -2 & -4 & -4 & -2 & -2 & 0 \\
}$
 & -4 } \\
 \stab{$H6_{10}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 \\
 -2 & 2 & -1 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 \\
 0 & 0 & 0 & 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -1 & -2 & -1 & -2 & -1 \\
 -2 & -2 & -4 & -2 & -4 & -2 \\
 -4 & -4 & -4 & -2 & -4 & -2 \\
 -2 & -2 & -2 & 0 & -2 & -1 \\
 -4 & -4 & -4 & -2 & -2 & -1 \\
 -4 & -4 & -4 & -2 & -2 & 0 \\
}$
 & -4 } \\
 \stab{$H6_{11}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 \\
 -2 & 2 & -1 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -2 \\
 0 & 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -1 & -2 & -1 & -2 & -2 \\
 -2 & -2 & -4 & -2 & -4 & -4 \\
 -4 & -4 & -4 & -2 & -4 & -4 \\
 -2 & -2 & -2 & 0 & -2 & -2 \\
 -4 & -4 & -4 & -2 & -2 & -2 \\
 -2 & -2 & -2 & -1 & -1 & 0 \\
}$
 & -4 } \\
 \stab{$H6_{12}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 \\
 -2 & 2 & -1 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & 0 & 0 \\
 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & -2 & 2 & -1 \\
 0 & 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -1 & -2 & -3 & -2 & -1 \\
 -2 & -2 & -4 & -6 & -4 & -2 \\
 -4 & -4 & -4 & -6 & -4 & -2 \\
 -6 & -6 & -6 & -6 & -4 & -2 \\
 -8 & -8 & -8 & -8 & -4 & -2 \\
 -4 & -4 & -4 & -4 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$H6_{13}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 \\
 -2 & 2 & -1 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & 0 & 0 \\
 0 & 0 & -1 & 2 & -2 & 0 \\
 0 & 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -1 & -2 & -3 & -4 & -2 \\
 -2 & -2 & -4 & -6 & -8 & -4 \\
 -4 & -4 & -4 & -6 & -8 & -4 \\
 -6 & -6 & -6 & -6 & -8 & -4 \\
 -4 & -4 & -4 & -4 & -4 & -2 \\
 -2 & -2 & -2 & -2 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$H6_{14}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & 0 & 0 \\
 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & -2 & 2 & -1 \\
 0 & 0 & 0 & 0 & -1 & 2 \\
}$
 &
$\smat{
 0 & -1 & -2 & -3 & -2 & -1 \\
 -1 & -2 & -4 & -6 & -4 & -2 \\
 -2 & -4 & -6 & -9 & -6 & -3 \\
 -3 & -6 & -9 & -12 & -8 & -4 \\
 -4 & -8 & -12 & -16 & -10 & -5 \\
 -2 & -4 & -6 & -8 & -5 & -2 \\
}$
 & -1 } \\
 \stab{$H6_{15}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 \\
 0 & -2 & 2 & -1 & 0 & 0 \\
 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & 0 & -1 & 2 \\
}$
 &
$\smat{
 -2 & -5 & -4 & -3 & -2 & -1 \\
 -5 & -10 & -8 & -6 & -4 & -2 \\
 -8 & -16 & -12 & -9 & -6 & -3 \\
 -6 & -12 & -9 & -6 & -4 & -2 \\
 -4 & -8 & -6 & -4 & -2 & -1 \\
 -2 & -4 & -3 & -2 & -1 & 0 \\
}$
 & -1 } \\
 \stab{$H6_{16}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 \\
 0 & -1 & 2 & -2 & 0 & 0 \\
 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -4 & -6 & -4 & -2 \\
 -2 & -4 & -8 & -12 & -8 & -4 \\
 -4 & -8 & -12 & -18 & -12 & -6 \\
 -3 & -6 & -9 & -12 & -8 & -4 \\
 -2 & -4 & -6 & -8 & -4 & -2 \\
 -1 & -2 & -3 & -4 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$H6_{17}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -2 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & 0 & 0 \\
 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -4 & -4 & -4 & -2 \\
 -2 & -4 & -8 & -8 & -8 & -4 \\
 -2 & -4 & -6 & -6 & -6 & -3 \\
 -2 & -4 & -6 & -4 & -4 & -2 \\
 -2 & -4 & -6 & -4 & -2 & -1 \\
 -2 & -4 & -6 & -4 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$H6_{18}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 \\
 0 & -2 & 2 & -1 & 0 & 0 \\
 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -2 & -2 & -2 & -1 \\
 -2 & -4 & -4 & -4 & -4 & -2 \\
 -4 & -8 & -6 & -6 & -6 & -3 \\
 -4 & -8 & -6 & -4 & -4 & -2 \\
 -4 & -8 & -6 & -4 & -2 & -1 \\
 -4 & -8 & -6 & -4 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$H6_{19}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & -1 \\
 0 & -1 & 2 & -1 & 0 & 0 \\
 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & -1 & 2 & -1 \\
 0 & -1 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{5}$
$\smat{
 0 & -5 & -5 & -5 & -5 & -5 \\
 -5 & -10 & -10 & -10 & -10 & -10 \\
 -5 & -10 & -6 & -7 & -8 & -9 \\
 -5 & -10 & -7 & -4 & -6 & -8 \\
 -5 & -10 & -8 & -6 & -4 & -7 \\
 -5 & -10 & -9 & -8 & -7 & -6 \\
}$
 & -5 } \\
 \stab{$H6_{20}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & -1 & -1 & 0 \\
 0 & -1 & 2 & 0 & 0 & 0 \\
 0 & -1 & 0 & 2 & 0 & 0 \\
 0 & -1 & 0 & 0 & 2 & -1 \\
 0 & 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -2 & -6 & -3 & -3 & -4 & -2 \\
 -6 & -12 & -6 & -6 & -8 & -4 \\
 -3 & -6 & -2 & -3 & -4 & -2 \\
 -3 & -6 & -3 & -2 & -4 & -2 \\
 -4 & -8 & -4 & -4 & -4 & -2 \\
 -2 & -4 & -2 & -2 & -2 & 0 \\
}$
 & -4 } \\
 \stab{$H6_{21}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & -1 & -1 & 0 \\
 0 & -1 & 2 & 0 & 0 & 0 \\
 0 & -1 & 0 & 2 & 0 & 0 \\
 0 & -1 & 0 & 0 & 2 & -1 \\
 0 & 0 & 0 & 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -1 & -1 & -2 & -1 \\
 -2 & -4 & -2 & -2 & -4 & -2 \\
 -1 & -2 & 0 & -1 & -2 & -1 \\
 -1 & -2 & -1 & 0 & -2 & -1 \\
 -2 & -4 & -2 & -2 & -2 & -1 \\
 -2 & -4 & -2 & -2 & -2 & 0 \\
}$
 & -8 } \\
 \stab{$H6_{22}$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & -1 & -1 & 0 \\
 0 & -1 & 2 & 0 & 0 & 0 \\
 0 & -1 & 0 & 2 & 0 & 0 \\
 0 & -1 & 0 & 0 & 2 & -2 \\
 0 & 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -1 & -1 & -2 & -2 \\
 -2 & -4 & -2 & -2 & -4 & -4 \\
 -1 & -2 & 0 & -1 & -2 & -2 \\
 -1 & -2 & -1 & 0 & -2 & -2 \\
 -2 & -4 & -2 & -2 & -2 & -2 \\
 -1 & -2 & -1 & -1 & -1 & 0 \\
}$
 & -8 } \\
 \stab{$H7_1$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 & 0 \\
 0 & 0 & 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & 0 & 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -4 & -2 & -4 & -4 & -2 \\
 -2 & -4 & -8 & -4 & -8 & -8 & -4 \\
 -4 & -8 & -12 & -6 & -12 & -12 & -6 \\
 -2 & -4 & -6 & -2 & -6 & -6 & -3 \\
 -4 & -8 & -12 & -6 & -10 & -10 & -5 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -4 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -3 \\
}$
 & -2 } \\
 \stab{$H7_2$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 & 0 \\
 0 & 0 & 0 & 0 & -1 & 2 & -2 \\
 0 & 0 & 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -4 & -2 & -4 & -4 & -4 \\
 -2 & -4 & -8 & -4 & -8 & -8 & -8 \\
 -4 & -8 & -12 & -6 & -12 & -12 & -12 \\
 -2 & -4 & -6 & -2 & -6 & -6 & -6 \\
 -4 & -8 & -12 & -6 & -10 & -10 & -10 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -8 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -3 \\
}$
 & -2 } \\
 \stab{$H7_3$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 & -1 \\
 0 & -1 & 2 & -1 & 0 & 0 & 0 \\
 0 & 0 & -1 & 2 & -1 & 0 & 0 \\
 0 & 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & 0 & -1 & 2 & -1 \\
 0 & -1 & 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{6}$
$\smat{
 0 & -6 & -6 & -6 & -6 & -6 & -6 \\
 -6 & -12 & -12 & -12 & -12 & -12 & -12 \\
 -6 & -12 & -7 & -8 & -9 & -10 & -11 \\
 -6 & -12 & -8 & -4 & -6 & -8 & -10 \\
 -6 & -12 & -9 & -6 & -3 & -6 & -9 \\
 -6 & -12 & -10 & -8 & -6 & -4 & -8 \\
 -6 & -12 & -11 & -10 & -9 & -8 & -7 \\
}$
 & -6 } \\
 \stab{$H7_4$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & -1 & 0 & 0 \\
 0 & -1 & 2 & -1 & 0 & 0 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 & 0 \\
 0 & -1 & 0 & 0 & 2 & -1 & -1 \\
 0 & 0 & 0 & 0 & -1 & 2 & 0 \\
 0 & 0 & 0 & 0 & -1 & 0 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 -4 & -12 & -8 & -4 & -12 & -6 & -6 \\
 -12 & -24 & -16 & -8 & -24 & -12 & -12 \\
 -8 & -16 & -8 & -4 & -16 & -8 & -8 \\
 -4 & -8 & -4 & 0 & -8 & -4 & -4 \\
 -12 & -24 & -16 & -8 & -20 & -10 & -10 \\
 -6 & -12 & -8 & -4 & -10 & -3 & -5 \\
 -6 & -12 & -8 & -4 & -10 & -5 & -3 \\
}$
 & -4 } \\
 \stab{$H8_1$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 & 0 & -1 \\
 0 & -1 & 2 & -1 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 2 & -1 & 0 & 0 & 0 \\
 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 \\
 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 \\
 0 & -1 & 0 & 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{7}$
$\smat{
 0 & -7 & -7 & -7 & -7 & -7 & -7 & -7 \\
 -7 & -14 & -14 & -14 & -14 & -14 & -14 & -14 \\
 -7 & -14 & -8 & -9 & -10 & -11 & -12 & -13 \\
 -7 & -14 & -9 & -4 & -6 & -8 & -10 & -12 \\
 -7 & -14 & -10 & -6 & -2 & -5 & -8 & -11 \\
 -7 & -14 & -11 & -8 & -5 & -2 & -6 & -10 \\
 -7 & -14 & -12 & -10 & -8 & -6 & -4 & -9 \\
 -7 & -14 & -13 & -12 & -11 & -10 & -9 & -8 \\
}$
 & -7 } \\
 \stab{$H8_2$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 & 0 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 & 0 & 0 \\
 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & 0 & 0 & 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -4 & -2 & -4 & -4 & -4 & -2 \\
 -2 & -4 & -8 & -4 & -8 & -8 & -8 & -4 \\
 -4 & -8 & -12 & -6 & -12 & -12 & -12 & -6 \\
 -2 & -4 & -6 & -2 & -6 & -6 & -6 & -3 \\
 -4 & -8 & -12 & -6 & -10 & -10 & -10 & -5 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -8 & -4 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -6 & -3 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -6 & -2 \\
}$
 & -2 } \\
 \stab{$H8_3$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 & 0 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 & 0 & 0 \\
 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & 0 & 0 & -1 & 2 & -2 \\
 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -4 & -2 & -4 & -4 & -4 & -4 \\
 -2 & -4 & -8 & -4 & -8 & -8 & -8 & -8 \\
 -4 & -8 & -12 & -6 & -12 & -12 & -12 & -12 \\
 -2 & -4 & -6 & -2 & -6 & -6 & -6 & -6 \\
 -4 & -8 & -12 & -6 & -10 & -10 & -10 & -10 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -8 & -8 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -6 & -6 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -3 & -2 \\
}$
 & -2 } \\
 \stab{$H8_4$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 & 0 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 & 0 & 0 \\
 0 & 0 & 0 & 0 & -1 & 2 & -1 & -1 \\
 0 & 0 & 0 & 0 & 0 & -1 & 2 & 0 \\
 0 & 0 & 0 & 0 & 0 & -1 & 0 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -4 & -2 & -4 & -4 & -2 & -2 \\
 -2 & -4 & -8 & -4 & -8 & -8 & -4 & -4 \\
 -4 & -8 & -12 & -6 & -12 & -12 & -6 & -6 \\
 -2 & -4 & -6 & -2 & -6 & -6 & -3 & -3 \\
 -4 & -8 & -12 & -6 & -10 & -10 & -5 & -5 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -4 & -4 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -1 & -2 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -2 & -1 \\
}$
 & -4 } \\
 \stab{$H8_5$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & 0 & 0 & -1 & 0 \\
 0 & 0 & -1 & 2 & -1 & 0 & 0 & 0 \\
 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 \\
 0 & 0 & 0 & 0 & -1 & 2 & 0 & 0 \\
 0 & 0 & -1 & 0 & 0 & 0 & 2 & -1 \\
 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{3}$
$\smat{
 -2 & -7 & -12 & -9 & -6 & -3 & -8 & -4 \\
 -7 & -14 & -24 & -18 & -12 & -6 & -16 & -8 \\
 -12 & -24 & -36 & -27 & -18 & -9 & -24 & -12 \\
 -9 & -18 & -27 & -18 & -12 & -6 & -18 & -9 \\
 -6 & -12 & -18 & -12 & -6 & -3 & -12 & -6 \\
 -3 & -6 & -9 & -6 & -3 & 0 & -6 & -3 \\
 -8 & -16 & -24 & -18 & -12 & -6 & -14 & -7 \\
 -4 & -8 & -12 & -9 & -6 & -3 & -7 & -2 \\
}$
 & -3 } \\
 \stab{$H9_1$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 2 & -1 & -1 & 0 & 0 & 0 \\
 0 & 0 & 0 & -1 & 2 & 0 & 0 & 0 & 0 \\
 0 & 0 & 0 & -1 & 0 & 2 & -1 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 -1 & -4 & -7 & -10 & -5 & -8 & -6 & -4 & -2 \\
 -4 & -8 & -14 & -20 & -10 & -16 & -12 & -8 & -4 \\
 -7 & -14 & -21 & -30 & -15 & -24 & -18 & -12 & -6 \\
 -10 & -20 & -30 & -40 & -20 & -32 & -24 & -16 & -8 \\
 -5 & -10 & -15 & -20 & -9 & -16 & -12 & -8 & -4 \\
 -8 & -16 & -24 & -32 & -16 & -24 & -18 & -12 & -6 \\
 -6 & -12 & -18 & -24 & -12 & -18 & -12 & -8 & -4 \\
 -4 & -8 & -12 & -16 & -8 & -12 & -8 & -4 & -2 \\
 -2 & -4 & -6 & -8 & -4 & -6 & -4 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$H9_2$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & 0 & 0 & 0 & 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -4 & -2 & -4 & -4 & -4 & -4 & -2 \\
 -2 & -4 & -8 & -4 & -8 & -8 & -8 & -8 & -4 \\
 -4 & -8 & -12 & -6 & -12 & -12 & -12 & -12 & -6 \\
 -2 & -4 & -6 & -2 & -6 & -6 & -6 & -6 & -3 \\
 -4 & -8 & -12 & -6 & -10 & -10 & -10 & -10 & -5 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -8 & -8 & -4 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -6 & -6 & -3 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -6 & -4 & -2 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -6 & -4 & -1 \\
}$
 & -2 } \\
 \stab{$H9_3$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 & -2 \\
 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -4 & -2 & -4 & -4 & -4 & -4 & -4 \\
 -2 & -4 & -8 & -4 & -8 & -8 & -8 & -8 & -8 \\
 -4 & -8 & -12 & -6 & -12 & -12 & -12 & -12 & -12 \\
 -2 & -4 & -6 & -2 & -6 & -6 & -6 & -6 & -6 \\
 -4 & -8 & -12 & -6 & -10 & -10 & -10 & -10 & -10 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -8 & -8 & -8 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -6 & -6 & -6 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -6 & -4 & -4 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -3 & -2 & -1 \\
}$
 & -2 } \\
 \stab{$H9_4$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 & -1 \\
 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 & 0 \\
 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 2 \\
}$
 & $\frac{1}{4}$
$\smat{
 0 & -4 & -8 & -4 & -8 & -8 & -8 & -4 & -4 \\
 -4 & -8 & -16 & -8 & -16 & -16 & -16 & -8 & -8 \\
 -8 & -16 & -24 & -12 & -24 & -24 & -24 & -12 & -12 \\
 -4 & -8 & -12 & -4 & -12 & -12 & -12 & -6 & -6 \\
 -8 & -16 & -24 & -12 & -20 & -20 & -20 & -10 & -10 \\
 -8 & -16 & -24 & -12 & -20 & -16 & -16 & -8 & -8 \\
 -8 & -16 & -24 & -12 & -20 & -16 & -12 & -6 & -6 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -6 & -1 & -3 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -6 & -3 & -1 \\
}$
 & -4 } \\
 \stab{$H9_5$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 & -1 \\
 0 & -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 2 & -1 & 0 & 0 & 0 & 0 \\
 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 \\
 0 & -1 & 0 & 0 & 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{8}$
$\smat{
 0 & -8 & -8 & -8 & -8 & -8 & -8 & -8 & -8 \\
 -8 & -16 & -16 & -16 & -16 & -16 & -16 & -16 & -16 \\
 -8 & -16 & -9 & -10 & -11 & -12 & -13 & -14 & -15 \\
 -8 & -16 & -10 & -4 & -6 & -8 & -10 & -12 & -14 \\
 -8 & -16 & -11 & -6 & -1 & -4 & -7 & -10 & -13 \\
 -8 & -16 & -12 & -8 & -4 & 0 & -4 & -8 & -12 \\
 -8 & -16 & -13 & -10 & -7 & -4 & -1 & -6 & -11 \\
 -8 & -16 & -14 & -12 & -10 & -8 & -6 & -4 & -10 \\
 -8 & -16 & -15 & -14 & -13 & -12 & -11 & -10 & -9 \\
}$
 & -8 } \\
 \stab{$H10_1$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 & 0 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 \\
}$
 &
$\smat{
 -4 & -9 & -14 & -7 & -12 & -10 & -8 & -6 & -4 & -2 \\
 -9 & -18 & -28 & -14 & -24 & -20 & -16 & -12 & -8 & -4 \\
 -14 & -28 & -42 & -21 & -36 & -30 & -24 & -18 & -12 & -6 \\
 -7 & -14 & -21 & -10 & -18 & -15 & -12 & -9 & -6 & -3 \\
 -12 & -24 & -36 & -18 & -30 & -25 & -20 & -15 & -10 & -5 \\
 -10 & -20 & -30 & -15 & -25 & -20 & -16 & -12 & -8 & -4 \\
 -8 & -16 & -24 & -12 & -20 & -16 & -12 & -9 & -6 & -3 \\
 -6 & -12 & -18 & -9 & -15 & -12 & -9 & -6 & -4 & -2 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -6 & -4 & -2 & -1 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -3 & -2 & -1 & 0 \\
}$
 & -1 } \\
 \stab{$H10_2$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 & 0 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 \\
 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -2 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -4 & -2 & -4 & -4 & -4 & -4 & -4 & -2 \\
 -2 & -4 & -8 & -4 & -8 & -8 & -8 & -8 & -8 & -4 \\
 -4 & -8 & -12 & -6 & -12 & -12 & -12 & -12 & -12 & -6 \\
 -2 & -4 & -6 & -2 & -6 & -6 & -6 & -6 & -6 & -3 \\
 -4 & -8 & -12 & -6 & -10 & -10 & -10 & -10 & -10 & -5 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -8 & -8 & -8 & -4 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -6 & -6 & -6 & -3 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -6 & -4 & -4 & -2 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -6 & -4 & -2 & -1 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -6 & -4 & -2 & 0 \\
}$
 & -2 } \\
 \stab{$H10_3$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 & 0 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 \\
 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 & -2 \\
 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -4 & -2 & -4 & -4 & -4 & -4 & -4 & -4 \\
 -2 & -4 & -8 & -4 & -8 & -8 & -8 & -8 & -8 & -8 \\
 -4 & -8 & -12 & -6 & -12 & -12 & -12 & -12 & -12 & -12 \\
 -2 & -4 & -6 & -2 & -6 & -6 & -6 & -6 & -6 & -6 \\
 -4 & -8 & -12 & -6 & -10 & -10 & -10 & -10 & -10 & -10 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -8 & -8 & -8 & -8 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -6 & -6 & -6 & -6 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -6 & -4 & -4 & -4 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -6 & -4 & -2 & -2 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -3 & -2 & -1 & 0 \\
}$
 & -2 } \\
 \stab{$H10_4$&
$\smat{
 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
 -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
 0 & -1 & 2 & -1 & -1 & 0 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 2 & 0 & 0 & 0 & 0 & 0 & 0 \\
 0 & 0 & -1 & 0 & 2 & -1 & 0 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 & -1 \\
 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 & 0 \\
 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 2 \\
}$
 & $\frac{1}{2}$
$\smat{
 0 & -2 & -4 & -2 & -4 & -4 & -4 & -4 & -2 & -2 \\
 -2 & -4 & -8 & -4 & -8 & -8 & -8 & -8 & -4 & -4 \\
 -4 & -8 & -12 & -6 & -12 & -12 & -12 & -12 & -6 & -6 \\
 -2 & -4 & -6 & -2 & -6 & -6 & -6 & -6 & -3 & -3 \\
 -4 & -8 & -12 & -6 & -10 & -10 & -10 & -10 & -5 & -5 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -8 & -8 & -4 & -4 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -6 & -6 & -3 & -3 \\
 -4 & -8 & -12 & -6 & -10 & -8 & -6 & -4 & -2 & -2 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -3 & -2 & 0 & -1 \\
 -2 & -4 & -6 & -3 & -5 & -4 & -3 & -2 & -1 & 0 \\
}$
 & -4 } \\

\normalsize

\subsection{$NS3_{82}-NS3_{86}$}\label{ss8.3} Here the values of $\alpha$ can only be equal to
\[
\alpha=\begin{cases}\frac{\sqrt{21}-11}{10},
\ \frac{\sqrt{15}-8}{7},
\ \frac{\sqrt{13}-7}{6}&\text{in cases $NS3_{82}-NS3_{84}$},\\
\frac{2\sqrt{6}-7}{5}, \ \frac{\sqrt{5}-3}{2}&\text{in cases $NS3_{85}-NS3_{86}$}.
\end{cases}
\]
Each of these 5 Lie superalgebras $NS3_{82}-NS3_{86}$ has 4 pairwise non-equivalent Cartan matrices. Observe that the determinant $\det A$ of the Cartan matrix $A$ of each almost affine Lie superalgebra from Subsection~\ref{ss8.1}  is negative (and so is $\det B$ of the Cartan matrix $B$ of each hyperbolic Lie algebra), whereas some of the determinants below are positive; we indicate this. None of the determinants are integer. Observe that the determinants of two Cartan matrices of the same Lie superalgebra can have opposite signs.

We also observe that, unlike the inverses of Cartan matrices of hyperbolic Lie algebras, each of the inverse matrices below has both positive and negative elements. As above, the inverse matrix without zero elements is marked by \fbox{!!!}.
\tiny
\[\arraycolsep=1.5pt
\begin{matrix}
\fbox{!!!}NS3_{82}-NS3_{84}-1)\ \smat{
 0 & 1 & \alpha  \\
 -1 & 0 & 2+\alpha \\
 -1 & 2+\frac{1}{\alpha } & 0 \\
}^{-1}=
-\frac{1}{3(\alpha+1)}\smat{
-2 \alpha -5-\frac{2}{\alpha }& 2 \alpha +1& \alpha +2 \\
-\alpha -2& \alpha & -\alpha\\
-2-\frac{1}{\alpha }& -1 & 1\\
}, &\det=-3(\alpha+1);\\
\fbox{!!!}NS3_{82}-NS3_{84}-2)\ \smat{
 0 & 1 & \alpha  \\
 -1 & 2 & -1 \\
 -1 & -1 & 2 \\
}^{-1}=
-\frac{1}{3 (\alpha +1)} \smat{
 -3 & \alpha +2 & 2 \alpha +1 \\
 -3 & -\alpha  & \alpha  \\
 -3 & 1 & -1 \\
}, &\det=3(\alpha+1)>0;\\
\fbox{!!!}NS3_{82}-3)\ \smat{
 2 & -1 & -1 \\
 -1 & 0 & 2+\alpha \\
-2 & -1 & 2 \\
}^{-1}=
\frac{1}{4 \alpha +5}\smat{
 \alpha +2 & 3 & -\alpha -2 \\
 -2 \alpha -2 & 2 & -2 \alpha -3 \\
 1 & 4 & -1 \\
}, &\det=4\alpha+5>0;\\
\fbox{!!!}NS3_{82}, NS3_{84}-4)\ \smat{
 2 & -1 & -1 \\
 -2 & 2 & -1 \\
-1 &2+\frac{1}{\alpha} & 0 \\
}^{-1}=
\frac{1}{5 \alpha +4} \smat{
 2 \alpha +1 & -2 \alpha -1 & 3 \alpha  \\
 \alpha  & -\alpha  & 4 \alpha  \\
 -2 (\alpha +1) & -3 \alpha -2 & 2 \alpha  \\
}
, &\det=5+\frac{4}{\alpha} ;\\
\fbox{!!!}NS3_{83}-3)\ \smat{
 2 & -1 & -1 \\
 -1 & 0 & 2+\alpha \\
-3 & -1 & 2 \\
}^{-1}=
\frac{1}{5 \alpha+7 } \smat{
 \alpha +2 & 3 & -\alpha -2 \\
 -3 \alpha -4 & 1 & -2 \alpha -3 \\
 1 & 5 & -1 \\
}, &\det=5\alpha+7;\\
\fbox{!!!}NS3_{83}-4)\ \smat{
 2 & -1 & -1 \\
 -3 & 2 & -1 \\
 -\alpha &2+\frac{1}{\alpha} & 0 \\
}^{-1}=-\frac{1}{3 \alpha ^2-10 \alpha-5} \smat{
 2 \alpha +1 & -2 \alpha -1 & 3 \alpha  \\
 \alpha ^2 & -\alpha ^2 & 5 \alpha  \\
 2 \alpha ^2-6 \alpha -3 & \alpha ^2-4 \alpha -2 & \alpha  \\
}, &\det=10-3\alpha+\frac{5}{\alpha}>0;\\
NS3_{84}-3)\ \smat{
 2 & -1 & -1 \\
 -1 & 0 & 2+\alpha \\
-4 & -1 & 2 \\
}^{-1}=\frac{1}{3 (2 \alpha +3)} \smat{
 \alpha +2 & 3 & -\alpha -2 \\
 -2 (2 \alpha +3) & 0 & -2 \alpha -3 \\
 1 & 6 & -1 \\
}, &\det=8\alpha+9>0;\\
\fbox{!!!}NS3_{85}-NS3_{86}-1)\  \smat{
 0 & 1 & \alpha  \\
 -1 & 0 & 3+\alpha \\
 -1 & 3+\frac{1}{\alpha } & 0 \\
}^{-1}=-\frac{1}{4(\alpha+1)}
\smat{
 -3 \alpha -10-\frac{3}{\alpha } & 3 \alpha +1& \alpha +3 \\
 -\alpha -3 & \alpha & -\alpha\\
 -3-\frac{1}{\alpha } & -1&1 \\
}, &\det=-4(\alpha+1); \\
NS3_{85}-NS3_{86}-2)\ \smat{
 0 & 1 & \alpha  \\
 -1 & 2 & -2 \\
 -1 & -2 & 2 \\
}^{-1}=-\frac{1}{4 (\alpha +1)} \smat{
 0 & 2 (\alpha +1) & 2 (\alpha +1) \\
 -4 & -\alpha  & \alpha  \\
 -4 & 1 & -1 \\
}, &\det=4(\alpha+1)>0;\\
\fbox{!!!}NS3_{85}-3)\ \smat{
 2 & -1 & -2 \\
 -1 & 0 & 3+\alpha \\
-1 & -1 & 2 \\
}^{-1}=\frac{1}{3 \alpha +5} \smat{
 \alpha +3 & 4 & -\alpha -3 \\
 -\alpha -1 & 2 & -2 \alpha -4 \\
 1 & 3 & -1 \\
}, &\det=3\alpha+5>0;\\
NS3_{86}-3)\ \smat{
 2 & -1 & -2 \\
 -1 & 0 & 3+\alpha \\
-2 & -1 & 2 \\
}^{-1}=\frac{1}{4 (\alpha +2)} \smat{
 \alpha +3 & 4 & -\alpha -3 \\
 -2 (\alpha +2) & 0 & -2 (\alpha +2) \\
 1 & 4 & -1 \\
}, &\det=4(\alpha+2)>0;\\
\fbox{!!!}NS3_{85}-4)\ \smat{
 2 & -2 & -1 \\
 -1 & 2 & -1 \\
-1 &3+\frac{1}{\alpha} & 0 \\
}^{-1}=\frac{1}{5 \alpha +3} \smat{
 3 \alpha +1 & -3 \alpha -1 & 4 \alpha  \\
 \alpha  & -\alpha  & 3 \alpha  \\
 -\alpha -1 & -2 (2 \alpha +1) & 2 \alpha  \\
}, &\det=5+\frac{3}{\alpha };\\
NS3_{86}-4)\ \smat{
 2 & -2 & -1 \\
 -2 & 2 & -1 \\
-1 &3+\frac{1}{\alpha} & 0 \\
}^{-1}=\frac{1}{4 (2 \alpha +1)} \smat{
 3 \alpha +1 & -3 \alpha -1 & 4 \alpha  \\
 \alpha  & -\alpha  & 4 \alpha  \\
 -2 (2 \alpha +1) & -2 (2 \alpha +1) & 0 \\
}, &\det=8+\frac{4}{\alpha}.\\

\end{matrix}
\]
\normalsize

redpajama_set_name: RedPajamaArXiv