| \(D^0\) | EAZ & character of irrep | |
| A | \(\left(0,0,0\right)\) | \(\left( \begin{array}{cccccccccccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{001}\right\} & \left\{4^-{}_{001}\right\} & \left\{2_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{2_{010},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{2_{001}\right\} & \left\{2_{110},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{2_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{\bar{1}\right\} & \left\{\bar{4}_{001}\right\} & \left\{\bar{4}^-{}_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{001}\right\} & \left\{m_{110},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} \\ \text{A}_1 & \text{BDI} & 2 & -\sqrt{2} & \sqrt{2} & 0 & 0 & 0 & 0 & 0 & -2 & \sqrt{2} & -\sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \text{A}_2 & \text{BDI} & 2 & -\sqrt{2} & \sqrt{2} & 0 & 0 & 0 & 0 & 0 & 2 & -\sqrt{2} & \sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \text{A}_3 & \text{BDI} & 2 & \sqrt{2} & -\sqrt{2} & 0 & 0 & 0 & 0 & 0 & -2 & -\sqrt{2} & \sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \text{A}_4 & \text{BDI} & 2 & \sqrt{2} & -\sqrt{2} & 0 & 0 & 0 & 0 & 0 & 2 & \sqrt{2} & -\sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| B | \(\left(0,\frac{1}{2},0\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{2_{010},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{2_{001}\right\} & \left\{\bar{1}\right\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{001}\right\} \\ \text{B}_1 & \text{AIII} & 2 & 0 & 0 & -2\mathrm{i}& 0 & 0 & 0 & 0 \\ \text{B}_2 & \text{AIII} & 2 & 0 & 0 & 2\mathrm{i}& 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| C | \(\left(\frac{1}{2},\frac{1}{2},0\right)\) | \(\left( \begin{array}{cccccccccccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{001}\right\} & \left\{4^-{}_{001}\right\} & \left\{2_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{2_{010},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{2_{001}\right\} & \left\{2_{110},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{2_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{\bar{1}\right\} & \left\{\bar{4}_{001}\right\} & \left\{\bar{4}^-{}_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{001}\right\} & \left\{m_{110},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} \\ \text{C}_1 & \text{AIII} & 2 & -\mathrm{i} \sqrt{2} & -\mathrm{i} \sqrt{2} & 0 & 0 & 0 & 0 & 0 & -2 &\mathrm{i}\sqrt{2} &\mathrm{i}\sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \text{C}_2 & \text{AIII} & 2 & -\mathrm{i} \sqrt{2} & -\mathrm{i} \sqrt{2} & 0 & 0 & 0 & 0 & 0 & 2 & -\mathrm{i} \sqrt{2} & -\mathrm{i} \sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \text{C}_3 & \text{AIII} & 2 &\mathrm{i}\sqrt{2} &\mathrm{i}\sqrt{2} & 0 & 0 & 0 & 0 & 0 & -2 & -\mathrm{i} \sqrt{2} & -\mathrm{i} \sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \text{C}_4 & \text{AIII} & 2 &\mathrm{i}\sqrt{2} &\mathrm{i}\sqrt{2} & 0 & 0 & 0 & 0 & 0 & 2 &\mathrm{i}\sqrt{2} &\mathrm{i}\sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| D | \(\left(0,0,\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccccccccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{001}\right\} & \left\{4^-{}_{001}\right\} & \left\{2_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{2_{010},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{2_{001}\right\} & \left\{2_{110},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{2_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{\bar{1}\right\} & \left\{\bar{4}_{001}\right\} & \left\{\bar{4}^-{}_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{001}\right\} & \left\{m_{110},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} \\ \text{D}_1 & \text{D} & 2 & -\sqrt{2} & \sqrt{2} & 0 & 0 & 0 & 0 & 0 & -2 & \sqrt{2} & -\sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \text{D}_2 & \text{D} & 2 & -\sqrt{2} & \sqrt{2} & 0 & 0 & 0 & 0 & 0 & 2 & -\sqrt{2} & \sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \text{D}_3 & \text{D} & 2 & \sqrt{2} & -\sqrt{2} & 0 & 0 & 0 & 0 & 0 & -2 & -\sqrt{2} & \sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \text{D}_4 & \text{D} & 2 & \sqrt{2} & -\sqrt{2} & 0 & 0 & 0 & 0 & 0 & 2 & \sqrt{2} & -\sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| E | \(\left(0,\frac{1}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{2_{010},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{2_{001}\right\} & \left\{\bar{1}\right\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{001}\right\} \\ \text{E}_1 & \text{AIII} & 2 & 0 & 0 & -2\mathrm{i}& 0 & 0 & 0 & 0 \\ \text{E}_2 & \text{AIII} & 2 & 0 & 0 & 2\mathrm{i}& 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| F | \(\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccccccccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{001}\right\} & \left\{4^-{}_{001}\right\} & \left\{2_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{2_{010},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{2_{001}\right\} & \left\{2_{110},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{2_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{\bar{1}\right\} & \left\{\bar{4}_{001}\right\} & \left\{\bar{4}^-{}_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{001}\right\} & \left\{m_{110},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} \\ \text{F}_1 & \text{A} & 2 & -\mathrm{i} \sqrt{2} & -\mathrm{i} \sqrt{2} & 0 & 0 & 0 & 0 & 0 & -2 &\mathrm{i}\sqrt{2} &\mathrm{i}\sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \text{F}_2 & \text{A} & 2 & -\mathrm{i} \sqrt{2} & -\mathrm{i} \sqrt{2} & 0 & 0 & 0 & 0 & 0 & 2 & -\mathrm{i} \sqrt{2} & -\mathrm{i} \sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \text{F}_3 & \text{A} & 2 &\mathrm{i}\sqrt{2} &\mathrm{i}\sqrt{2} & 0 & 0 & 0 & 0 & 0 & -2 & -\mathrm{i} \sqrt{2} & -\mathrm{i} \sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \text{F}_4 & \text{A} & 2 &\mathrm{i}\sqrt{2} &\mathrm{i}\sqrt{2} & 0 & 0 & 0 & 0 & 0 & 2 &\mathrm{i}\sqrt{2} &\mathrm{i}\sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| \(D^1\) | EAZ & character of irrep | |
| \(a\) | \(\left(0,\frac{t}{2},0\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{010},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{001}\right\} \\ a_1 & \text{BDI} & 2 & 0 & 0 & 0 \\ \end{array} \right)\) |
| \(b\) | \(\left(\frac{1-t}{2},\frac{1}{2},0\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{001}\right\} \\ b_1 & \text{CII} & 2 & 0 & 0 & 0 \\ \end{array} \right)\) |
| \(c\) | \(\left(\frac{t}{2},\frac{t}{2},0\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{110},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{001}\right\} & \left\{m_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} \\ c_1 & \text{BDI} & 2 & 0 & 0 & 0 \\ \end{array} \right)\) |
| \(d\) | \(\left(0,\frac{t}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{010},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{001}\right\} \\ d_1 & \text{DIII} & 2 & 0 & 0 & 0 \\ \end{array} \right)\) |
| \(e\) | \(\left(\frac{1-t}{2},\frac{1}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{001}\right\} \\ e_1 & \text{CII} & 2 & 0 & 0 & 0 \\ \end{array} \right)\) |
| \(f\) | \(\left(\frac{t}{2},\frac{t}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{110},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{001}\right\} & \left\{m_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} \\ f_1 & \text{DIII} & 2 & 0 & 0 & 0 \\ \end{array} \right)\) |
| \(g\) | \(\left(0,0,\frac{t}{2}\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{001}\right\} & \left\{4^-{}_{001}\right\} & \left\{2_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{110},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} \\ g_1 & \text{BDI} & 2 & -\sqrt{2} & \sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ g_2 & \text{BDI} & 2 & \sqrt{2} & -\sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| \(h\) | \(\left(0,\frac{1}{2},\frac{t}{2}\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} \\ h_1 & \text{A} & 1 & -\mathrm{i} & -1 & -\mathrm{i} \\ h_2 & \text{A} & 1 & -\mathrm{i} & 1 &\mathrm{i}\\ h_3 & \text{A} & 1 &\mathrm{i}& -1 &\mathrm{i}\\ h_4 & \text{A} & 1 &\mathrm{i}& 1 & -\mathrm{i} \\ \end{array} \right)\) |
| \(i\) | \(\left(\frac{1}{2},\frac{1}{2},\frac{t}{2}\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{001}\right\} & \left\{4^-{}_{001}\right\} & \left\{2_{001}\right\} & \left\{m_{100},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{010},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{110},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} & \left\{m_{\text{1-10}},\left\{\frac{1}{2},\frac{1}{2},0\right\}\right\} \\ i_1 & \text{AIII} & 2 & -\mathrm{i} \sqrt{2} & -\mathrm{i} \sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ i_2 & \text{AIII} & 2 &\mathrm{i}\sqrt{2} &\mathrm{i}\sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |