MSG 83.45
\[\begin{align*}
&E_{2}^{1,-1}=\mathbb{Z}^2\\
&E_{1}^{0,-1}=0\\
&E_{1}^{1,-1}=\mathbb{Z}[\boldsymbol{b}^{(1)}_{e_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{g_1}]\\
&E_{1}^{2,-1}=0
\end{align*}\]
\[\begin{align*}
&[X^{(1)}]^{-1}=\left(
\begin{array}{cc}
e_1 & g_1 \\
1 & 0 \\
0 & 1 \\
\end{array}
\right)
\end{align*}
\]