4 ${\mathcal{A}}_{2}$ or ${\mathcal{A}}_{2}$ $\begin{array}{l}\left\{\begin{array}{cc}1& \begin{array}{cc}8& \begin{array}{cc}27& \begin{array}{cc}64& \begin{array}{cc}125& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\right\}\\ \oplus \left\{\begin{array}{cccccc}\left(\begin{array}{c}-2\\ 0\end{array}\right)& \left(\begin{array}{c}-3\\ 0\end{array}\right)& \left(\begin{array}{c}-4\\ 0\end{array}\right)& \left(\begin{array}{c}-4\\ 0\end{array}\right)& \left(\begin{array}{c}-4\\ 0\end{array}\right)& \\ & \left(\begin{array}{c}-3\\ 1\end{array}\right)& \left(\begin{array}{c}-4\\ 1\end{array}\right)& \left(\begin{array}{c}-4\\ 1\end{array}\right)& \left(\begin{array}{c}-4\\ 1\end{array}\right)& \\ & & \left(\begin{array}{c}-4\\ 2\end{array}\right)& \left(\begin{array}{c}-4\\ 2\end{array}\right)& \left(\begin{array}{c}-4\\ 2\end{array}\right)& \cdots \\ & & & \left(\begin{array}{c}-4\\ 3\end{array}\right)& \left(\begin{array}{c}-4\\ 3\end{array}\right)& \\ & & & & \left(\begin{array}{c}-4\\ 4\end{array}\right)& \end{array}\right\}=\left\{\begin{array}{cc}1& \begin{array}{cc}5& 1\end{array}\end{array}\right\}\end{array}$ 5 ${\mathcal{A}}_{3}$ or ${\mathcal{A}}_{3}$ $\begin{array}{l}\left\{\begin{array}{cc}1& \begin{array}{cc}8& \begin{array}{cc}27& \begin{array}{cc}64& \begin{array}{cc}125& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\right\}\\ \oplus \left\{\begin{array}{cccccc}\left(\begin{array}{c}-3\\ 0\end{array}\right)& \left(\begin{array}{c}-4\\ 0\end{array}\right)& \left(\begin{array}{c}-4\\ 0\end{array}\right)& \left(\begin{array}{c}-4\\ 0\end{array}\right)& \left(\begin{array}{c}-4\\ 0\end{array}\right)& \\ & \left(\begin{array}{c}-4\\ 1\end{array}\right)& \left(\begin{array}{c}-4\\ 1\end{array}\right)& \left(\begin{array}{c}-4\\ 1\end{array}\right)& \left(\begin{array}{c}-4\\ 1\end{array}\right)& \\ & & \left(\begin{array}{c}-4\\ 2\end{array}\right)& \left(\begin{array}{c}-4\\ 2\end{array}\right)& \left(\begin{array}{c}-4\\ 2\end{array}\right)& \cdots \\ & & & \left(\begin{array}{c}-4\\ 3\end{array}\right)& \left(\begin{array}{c}-4\\ 3\end{array}\right)& \\ & & & \left(\begin{array}{c}-4\\ 4\end{array}\right)& \left(\begin{array}{c}-4\\ 4\end{array}\right)& \end{array}\right\}=\left\{\begin{array}{cc}1& \begin{array}{cc}4& 1\end{array}\end{array}\right\}\end{array}$ 6 $Ker$ $\begin{array}{l}\left\{\begin{array}{cc}1& \begin{array}{cc}8& \begin{array}{cc}27& \begin{array}{cc}64& \begin{array}{cc}125& \begin{array}{cc}216& \begin{array}{cc}343& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\right\}\\ \oplus \left\{\begin{array}{cccccc}\left(-4\right)& \left(\begin{array}{c}-4\\ 0\end{array}\right)& \left(\begin{array}{c}-4\\ 0\end{array}\right)& \left(\begin{array}{c}-4\\ 0\end{array}\right)& \left(\begin{array}{c}-4\\ 0\end{array}\right)& \\ & \left(\begin{array}{c}-4\\ 1\end{array}\right)& \left(\begin{array}{c}-4\\ 1\end{array}\right)& \left(\begin{array}{c}-4\\ 1\end{array}\right)& \left(\begin{array}{c}-4\\ 1\end{array}\right)& \\ & & \left(\begin{array}{c}-4\\ 2\end{array}\right)& \left(\begin{array}{c}-4\\ 2\end{array}\right)& \left(\begin{array}{c}-4\\ 2\end{array}\right)& \cdots \\ & & & \left(\begin{array}{c}-4\\ 3\end{array}\right)& \left(\begin{array}{c}-4\\ 3\end{array}\right)& \\ & & & & \left(\begin{array}{c}-4\\ 4\end{array}\right)& \end{array}\right\}=〈\begin{array}{cc}1& \begin{array}{cc}4& 1\end{array}\end{array}〉\end{array}$ 7 ${\mathcal{A}}_{4}$ or ${\mathcal{A}}_{4}$ $\begin{array}{l}\left\{\begin{array}{cc}1& \begin{array}{cc}8& \begin{array}{cc}27& \begin{array}{cc}64& \begin{array}{cc}125& \begin{array}{cc}216& \begin{array}{cc}343& \cdots \end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\right\}\\ \oplus \left\{\begin{array}{cccccc}\left(-5\right)& \left(\begin{array}{c}-5\\ 0\end{array}\right)& \left(\begin{array}{c}-5\\ 0\end{array}\right)& \left(\begin{array}{c}-5\\ 0\end{array}\right)& \left(\begin{array}{c}-5\\ 0\end{array}\right)& \left(\begin{array}{c}-5\\ 0\end{array}\right)\\ & \left(\begin{array}{c}-5\\ 1\end{array}\right)& \left(\begin{array}{c}-5\\ 1\end{array}\right)& \left(\begin{array}{c}-5\\ 1\end{array}\right)& \left(\begin{array}{c}-5\\ 1\end{array}\right)& \left(\begin{array}{c}-5\\ 1\end{array}\right)\\ & & \left(\begin{array}{c}-4\\ 2\end{array}\right)& \left(\begin{array}{c}-5\\ 2\end{array}\right)& \left(\begin{array}{c}-5\\ 2\end{array}\right)& \left(\begin{array}{c}-5\\ 2\end{array}\right)\\ & & & \left(\begin{array}{c}-5\\ 3\end{array}\right)& \left(\begin{array}{c}-5\\ 3\end{array}\right)& \left(\begin{array}{c}-5\\ 3\end{array}\right)\\ & & & & \left(\begin{array}{c}-5\\ 4\end{array}\right)& \left(\begin{array}{c}-5\\ 4\end{array}\right)\\ & & & & & \left(\begin{array}{c}-5\\ 5\end{array}\right)\end{array}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\cdots \right\}=\left\{\begin{array}{cc}1& \begin{array}{cc}3& \begin{array}{cc}-3& -1\end{array}\end{array}\end{array}\right\}\end{array}$