MSG 123.341

\[\begin{align*} &E_{2}^{1,-1}=\mathbb{Z}_2^9\\ &E_{1}^{0,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{A}_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{A}_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{A}_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{A}_4}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{A}_5}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{B}_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{B}_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{B}_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{B}_4}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{C}_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{C}_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{C}_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{C}_4}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{C}_5}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{D}_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{D}_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{D}_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{D}_4}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{D}_5}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{E}_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{E}_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{E}_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{E}_4}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{F}_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{F}_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{F}_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{F}_4}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{\text{F}_5}]\\ &E_{1}^{1,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{a_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{a_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{b_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{b_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{c_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{c_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{d_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{d_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{e_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{e_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{f_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{f_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{g_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{g_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{g_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{g_4}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{g_5}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{h_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{h_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{h_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{h_4}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{i_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{i_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{i_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{i_4}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{i_5}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{j_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{j_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{j_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{j_4}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{j_5}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{k_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{k_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{k_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{k_4}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{l_1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{l_2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{l_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{l_4}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(1)}_{l_5}]\\ &E_{1}^{2,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\alpha _1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\beta _1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\beta _2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\gamma _1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\gamma _2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\delta _1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\delta _2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\varepsilon _1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\varepsilon _2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\zeta _1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\zeta _2}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\eta _1}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(2)}_{\eta _2}] \end{align*}\]

\[\begin{align*} &[X^{(1)}]^{-1}=\left( \begin{array}{cccccccccccccccccccccccccccccccccccccccc} a_1 & a_2 & b_1 & b_2 & c_1 & c_2 & d_1 & d_2 & e_1 & e_2 & f_1 & f_2 & g_1 & g_2 & g_3 & g_4 & g_5 & h_1 & h_2 & h_3 & h_4 & i_1 & i_2 & i_3 & i_4 & i_5 & j_1 & j_2 & j_3 & j_4 & j_5 & k_1 & k_2 & k_3 & k_4 & l_1 & l_2 & l_3 & l_4 & l_5 \\ 1 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & -1 & -1 & -1 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 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