| \(D^0\) | EAZ & character of irrep | |
| A | \(\left(0,0,0\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{001},\left\{0,\frac{1}{2},\frac{1}{4}\right\}\right\} & \left\{4^-{}_{001},\left\{0,\frac{1}{2},\frac{1}{4}\right\}\right\} & \left\{2_{001}\right\} & \left\{m_{100}\right\} & \left\{m_{010}\right\} & \left\{m_{110},\left\{0,\frac{1}{2},\frac{1}{4}\right\}\right\} & \left\{m_{\text{1-10}},\left\{0,\frac{1}{2},\frac{1}{4}\right\}\right\} \\ \text{A}_1 & \text{BDI} & 2 & -\sqrt{2} & \sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \text{A}_2 & \text{BDI} & 2 & \sqrt{2} & -\sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| B | \(\left(\frac{1}{2},\frac{1}{2},0\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{m_{110},\left\{0,\frac{1}{2},\frac{1}{4}\right\}\right\} & \left\{m_{\text{1-10}},\left\{0,\frac{1}{2},\frac{1}{4}\right\}\right\} \\ \text{B}_1 & \text{AIII} & 1 & -\mathrm{i} &\mathrm{i}& 1 \\ \text{B}_2 & \text{AIII} & 1 & -\mathrm{i} & -\mathrm{i} & -1 \\ \text{B}_3 & \text{AIII} & 1 &\mathrm{i}&\mathrm{i}& -1 \\ \text{B}_4 & \text{AIII} & 1 &\mathrm{i}& -\mathrm{i} & 1 \\ \end{array} \right)\) |
| C | \(\left(0,0,1\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{001},\left\{0,\frac{1}{2},\frac{1}{4}\right\}\right\} & \left\{4^-{}_{001},\left\{0,\frac{1}{2},\frac{1}{4}\right\}\right\} & \left\{2_{001}\right\} & \left\{m_{100}\right\} & \left\{m_{010}\right\} & \left\{m_{110},\left\{0,\frac{1}{2},\frac{1}{4}\right\}\right\} & \left\{m_{\text{1-10}},\left\{0,\frac{1}{2},\frac{1}{4}\right\}\right\} \\ \text{C}_1 & \text{AIII} & 2 &\mathrm{i}\sqrt{2} & -\mathrm{i} \sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \text{C}_2 & \text{AIII} & 2 & -\mathrm{i} \sqrt{2} &\mathrm{i}\sqrt{2} & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| D | \(\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{m_{110},\left\{0,\frac{1}{2},\frac{1}{4}\right\}\right\} & \left\{m_{\text{1-10}},\left\{0,\frac{1}{2},\frac{1}{4}\right\}\right\} \\ \text{D}_1 & \text{BDI} & 1 & -\mathrm{i} & \sqrt[4]{-1} & -(-1)^{3/4} \\ \text{D}_2 & \text{BDI} & 1 & -\mathrm{i} & -\sqrt[4]{-1} & (-1)^{3/4} \\ \text{D}_3 & \text{AIII} & 1 &\mathrm{i}& \sqrt[4]{-1} & (-1)^{3/4} \\ \text{D}_4 & \text{AIII} & 1 &\mathrm{i}& -\sqrt[4]{-1} & -(-1)^{3/4} \\ \end{array} \right)\) |
| E | \(\left(0,\frac{1}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{100}\right\} \\ \text{E}_1 & \text{AIII} & 1 & -\mathrm{i} \\ \text{E}_2 & \text{AIII} & 1 &\mathrm{i}\\ \end{array} \right)\) |
| \(D^1\) | EAZ & character of irrep | |
| \(a\) | \(\left(0,0,t\right)\) | \(\left( \begin{array}{cccccccccc} \text{} & \text{EAZ} & \{1\} & \left\{4_{001},\left\{0,\frac{1}{2},\frac{1}{4}\right\}\right\} & \left\{4^-{}_{001},\left\{0,\frac{1}{2},\frac{1}{4}\right\}\right\} & \left\{2_{001}\right\} & \left\{m_{100}\right\} & \left\{m_{010}\right\} & \left\{m_{110},\left\{0,\frac{1}{2},\frac{1}{4}\right\}\right\} & \left\{m_{\text{1-10}},\left\{0,\frac{1}{2},\frac{1}{4}\right\}\right\} \\ a_1 & \text{AIII} & 2 & -\sqrt{2} e^{-\frac{1}{2}\mathrm{i}\pi t} & \sqrt{2} e^{-\frac{1}{2}\mathrm{i}\pi t} & 0 & 0 & 0 & 0 & 0 \\ a_2 & \text{AIII} & 2 & \sqrt{2} e^{-\frac{1}{2}\mathrm{i}\pi t} & -\sqrt{2} e^{-\frac{1}{2}\mathrm{i}\pi t} & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)\) |
| \(b\) | \(\left(\frac{1}{2},\frac{1}{2},\frac{t}{2}\right)\) | \(\left( \begin{array}{cccccc} \text{} & \text{EAZ} & \{1\} & \left\{2_{001}\right\} & \left\{m_{110},\left\{0,\frac{1}{2},\frac{1}{4}\right\}\right\} & \left\{m_{\text{1-10}},\left\{0,\frac{1}{2},\frac{1}{4}\right\}\right\} \\ b_1 & \text{AIII} & 1 & -\mathrm{i} &\mathrm{i}e^{-\frac{1}{4}\mathrm{i}\pi t} & e^{-\frac{1}{4}\mathrm{i}\pi t} \\ b_2 & \text{AIII} & 1 & -\mathrm{i} & e^{-\frac{1}{4}\mathrm{i}\pi (t+2)} & -e^{-\frac{1}{4}\mathrm{i}\pi t} \\ b_3 & \text{AIII} & 1 &\mathrm{i}&\mathrm{i}e^{-\frac{1}{4}\mathrm{i}\pi t} & -e^{-\frac{1}{4}\mathrm{i}\pi t} \\ b_4 & \text{AIII} & 1 &\mathrm{i}& e^{-\frac{1}{4}\mathrm{i}\pi (t+2)} & e^{-\frac{1}{4}\mathrm{i}\pi t} \\ \end{array} \right)\) |
| \(c\) | \(\left(\frac{t}{2},\frac{t}{2},1-\frac{t}{2}\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{\text{1-10}},\left\{0,\frac{1}{2},\frac{1}{4}\right\}\right\} \\ c_1 & \text{AIII} & 1 & -e^{-\frac{1}{4}\mathrm{i}\pi t} \\ c_2 & \text{AIII} & 1 & e^{-\frac{1}{4}\mathrm{i}\pi t} \\ \end{array} \right)\) |
| \(d\) | \(\left(\frac{t}{2},\frac{t}{2},0\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{\text{1-10}},\left\{0,\frac{1}{2},\frac{1}{4}\right\}\right\} \\ d_1 & \text{BDI} & 1 & -\mathrm{i} e^{-\frac{1}{2}\mathrm{i}\pi t} \\ d_2 & \text{BDI} & 1 &\mathrm{i}e^{-\frac{1}{2}\mathrm{i}\pi t} \\ \end{array} \right)\) |
| \(e\) | \(\left(\frac{t}{2},1-\frac{t}{2},0\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{110},\left\{0,\frac{1}{2},\frac{1}{4}\right\}\right\} \\ e_1 & \text{AIII} & 1 & e^{\frac{i \pi t}{2}} \\ e_2 & \text{AIII} & 1 & -e^{\frac{i \pi t}{2}} \\ \end{array} \right)\) |
| \(f\) | \(\left(\frac{1-t}{2},\frac{1}{2},\frac{1}{2}\right)\) | \(\left( \begin{array}{ccc} \text{} & \text{EAZ} & \{1\} \\ f_1 & \text{BDI} & 1 \\ \end{array} \right)\) |
| \(g\) | \(\left(0,t,0\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{100}\right\} \\ g_1 & \text{BDI} & 1 & -\mathrm{i} \\ g_2 & \text{BDI} & 1 &\mathrm{i}\\ \end{array} \right)\) |
| \(h\) | \(\left(0,\frac{t}{2},1-\frac{t}{2}\right)\) | \(\left( \begin{array}{cccc} \text{} & \text{EAZ} & \{1\} & \left\{m_{100}\right\} \\ h_1 & \text{AIII} & 1 & -\mathrm{i} \\ h_2 & \text{AIII} & 1 &\mathrm{i}\\ \end{array} \right)\) |