Supplementary materials to

# Improving empirical interatomic potentials for predicting thermophysical
properties by using an irreducible derivatives approach: The case of thorium
dioxide

Shuxiang Zhou1, Chao Jiang1, Enda Xiao2, Michael W.D. Cooper3, Miaomiao Jin4,
Chris A. Marianetti5, David H Hurley1, Marat Khafizov6 1Idaho National
Laboratory, Idaho Falls, ID 83415, USA
2Department of Chemistry, Columbia University, New York, NY 10027, USA
3Los Alamos National Laboratory, Los Alamos, NM 87545, USA
4Department of Nuclear Engineering, The Pennsylvania State University,
University Park, PA 16802, USA
5Department of Applied Physics and Applied Mathematics, Columbia University,
New York, NY 10027, USA
6Department of Mechanical and Aerospace Engineering, The Ohio State
University, Columbus, OH 43210, USA

##  I Irreducible derivatives of
$\mathbf{\hat{S}}_{\mathrm{BZ}}=2\mathbf{\hat{S}}_{C}$

In this supplementary material, we discuss irreducible derivatives (IDs) based
on the $Fm\bar{3}m$ space group symmetry of ThO2, while complete definitions
and proofs are presented in Fu _et al._ [1]. Details on the second- and third-
order displacement IDs of
$\mathbf{\hat{S}}_{\mathrm{BZ}}=2\mathbf{\hat{S}}_{C}$ are given in this
section. For $\mathbf{\hat{S}}_{\mathrm{BZ}}=2\mathbf{\hat{S}}_{C}$, the
irreducible set of $\tilde{q}_{\mathrm{BZ}}$ is given by:

$\tilde{q}_{\mathrm{IBZ}}=\\{\Gamma,X\\},$ (1)

where $\Gamma=(0,0,0),X=(0.5,0.5,0)$ in the reciprocal lattice basis. The
irreducible representation of the displacements are:

$\displaystyle\mathcal{U}_{\Gamma}=\\{T_{2g},T_{1u}\\},$ (2)
$\displaystyle\mathcal{U}_{X}=\\{A_{1g},B_{1u},E_{g},{}^{1}E_{u},A_{2u},E_{u}\\},$

Restricted by $(\sum_{\mathbf{q}\in\mathcal{Q}}\mathbf{q})\in\mathbb{Z}$, for
$\mathcal{N}=2$, the irreducible set of $\tilde{\mathcal{Q}}_{\mathrm{BZ}}$ is
given by:

$\tilde{\mathcal{Q}}_{\mathrm{IBZ}}=\\{(\Gamma,\Gamma),(X,X)\\};$ (3)

while for $\mathcal{N}=3$, it is:

$\tilde{\mathcal{Q}}_{\mathrm{IBZ}}=\\{(\Gamma,\Gamma,\Gamma),(\Gamma,X,X),(X,X,X)\\}.$
(4)

The nine second-order and 37 third-order displacement IDs of
$\mathbf{\hat{S}}_{\mathrm{BZ}}=2\mathbf{\hat{S}}_{C}$ are given in Table S1.

Table S1:  Second- and third-order displacement IDs of $\mathbf{\hat{S}}_{\mathrm{BZ}}=2\mathbf{\hat{S}}_{\mathrm{I}}$ $\mathcal{Q}$ | Count | Derivatives
---|---|---
Irreducible derivatives for $\mathcal{N}=2$,
$\mathbf{\hat{S}}_{\mathrm{BZ}}=2\mathbf{\hat{S}}_{\mathrm{I}}$
$(\Gamma,\Gamma)$ | 2 |  $d\indices*{*_{\Gamma}^{T_{2g}}{}_{\Gamma}^{T_{2g}}}$, $d\indices*{*_{\Gamma}^{T_{1u}}{}_{\Gamma}^{T_{1u}}}$
$(X,X)$ | 7 |  $d\indices*{*_{X}^{A_{1g}}{}_{X}^{A_{1g}}}$, $d\indices*{*_{X}^{E_{g}}{}_{X}^{E_{g}}}$, $d\indices*{*_{X}^{A_{2u}}{}_{X}^{A_{2u}}}$, $d\indices*{*_{X}^{B_{1u}}{}_{X}^{B_{1u}}}$, $d\indices*{*_{X}^{E_{u}}{}_{X}^{E_{u}}}$, $d\indices*{*_{X}^{\tensor{*}[^{1}]{E}{}_{u}}{}_{X}^{\tensor{*}[^{1}]{E}{}_{u}}}$, $d\indices*{*_{X}^{E_{u}}{}_{X}^{\tensor{*}[^{1}]{E}{}_{u}}}$
Irreducible derivatives for $\mathcal{N}=3$,
$\mathbf{\hat{S}}_{\mathrm{BZ}}=2\mathbf{\hat{S}}_{\mathrm{I}}$
$(\Gamma,\Gamma,\Gamma)$ | 2 |  $d\indices*{*_{\Gamma}^{T_{2g}}{}_{\Gamma}^{T_{2g}}{}_{\Gamma}^{T_{2g}}}$, $d\indices*{*_{\Gamma}^{T_{1u}}{}_{\Gamma}^{T_{1u}}{}_{\Gamma}^{T_{2g}}}$
$(\Gamma,X,X)$ | 17 |  $d\indices*{*_{\Gamma}^{T_{2g}}{}_{X}^{A_{1g}}{}_{X}^{E_{g}}}$, $d\indices*{*_{\Gamma}^{T_{2g}}{}_{X}^{A_{2u}}{}_{X}^{E_{u}}}$, $d\indices*{*_{\Gamma}^{T_{2g}}{}_{X}^{A_{2u}}{}_{X}^{\tensor{*}[^{1}]{E}{}_{u}}}$, $d\indices*{*_{\Gamma}^{T_{2g}}{}_{X}^{B_{1u}}{}_{X}^{E_{u}}}$, $d\indices*{*_{\Gamma}^{T_{2g}}{}_{X}^{B_{1u}}{}_{X}^{\tensor{*}[^{1}]{E}{}_{u}}}$, $d\indices*{*_{\Gamma}^{T_{2g}}{}_{X}^{E_{g}}{}_{X}^{E_{g}}}$, $d\indices*{*_{\Gamma}^{T_{2g}}{}_{X}^{B_{1u}}{}_{X}^{A_{2u}}}$, $d\indices*{*_{\Gamma}^{T_{2g}}{}_{X}^{E_{u}}{}_{X}^{E_{u}}}$, $d\indices*{*_{\Gamma}^{T_{2g}}{}_{X}^{E_{u}}{}_{X}^{\tensor{*}[^{1}]{E}{}_{u}}}$, $d\indices*{*_{\Gamma}^{T_{2g}}{}_{X}^{\tensor{*}[^{1}]{E}{}_{u}}{}_{X}^{\tensor{*}[^{1}]{E}{}_{u}}}$, $d\indices*{*_{\Gamma}^{T_{1u}}{}_{X}^{A_{1g}}{}_{X}^{E_{u}}}$, $d\indices*{*_{\Gamma}^{T_{1u}}{}_{X}^{A_{1g}}{}_{X}^{\tensor{*}[^{1}]{E}{}_{u}}}$, $d\indices*{*_{\Gamma}^{T_{1u}}{}_{X}^{B_{1u}}{}_{X}^{E_{g}}}$, $d\indices*{*_{\Gamma}^{T_{1u}}{}_{X}^{E_{g}}{}_{X}^{A_{2u}}}$, $d\indices*{*_{\Gamma}^{T_{1u}}{}_{X}^{A_{1g}}{}_{X}^{A_{2u}}}$, $d\indices*{*_{\Gamma}^{T_{1u}}{}_{X}^{E_{g}}{}_{X}^{E_{u}}}$, $d\indices*{*_{\Gamma}^{T_{1u}}{}_{X}^{E_{g}}{}_{X}^{\tensor{*}[^{1}]{E}{}_{u}}}$,
$(X,X,X)$ | 18 |  $d\indices*{*_{X_{1}}^{A_{1g}}{}_{X_{2}}^{A_{1g}}{}_{X}^{A_{1g}}}$, $d\indices*{*_{X_{1}}^{A_{1g}}{}_{X_{2}}^{E_{g}}{}_{X}^{E_{g}}}$, $d\indices*{*_{X_{1}}^{A_{1g}}{}_{X_{2}}^{A_{2u}}{}_{X}^{E_{u}}}$, $d\indices*{*_{X_{1}}^{A_{1g}}{}_{X_{2}}^{A_{2u}}{}_{X}^{\tensor{*}[^{1}]{E}{}_{u}}}$, $d\indices*{*_{X_{1}}^{A_{1g}}{}_{X_{2}}^{B_{1u}}{}_{X}^{B_{1u}}}$, $d\indices*{*_{X_{1}}^{A_{1g}}{}_{X_{2}}^{E_{u}}{}_{X}^{E_{u}}}$, $d\indices*{*_{X_{1}}^{A_{1g}}{}_{X_{2}}^{E_{u}}{}_{X}^{\tensor{*}[^{1}]{E}{}_{u}}}$, $d\indices*{*_{X_{1}}^{A_{1g}}{}_{X_{2}}^{\tensor{*}[^{1}]{E}{}_{u}}{}_{X}^{\tensor{*}[^{1}]{E}{}_{u}}}$, $d\indices*{*_{X_{1}}^{E_{g}}{}_{X_{2}}^{E_{g}}{}_{X}^{E_{g}}}$, $d\indices*{*_{X_{1}}^{B_{1u}}{}_{X_{2}}^{A_{2u}}{}_{X}^{E_{g}}}$, $d\indices*{*_{X_{1}}^{B_{1u}}{}_{X_{2}}^{E_{g}}{}_{X}^{E_{u}}}$, $d\indices*{*_{X_{1}}^{B_{1u}}{}_{X_{2}}^{E_{g}}{}_{X}^{\tensor{*}[^{1}]{E}{}_{u}}}$, $d\indices*{*_{X_{1}}^{E_{g}}{}_{X_{2}}^{E_{u}}{}_{X}^{A_{2u}}}$, $d\indices*{*_{X_{1}}^{E_{g}}{}_{X_{2}}^{E_{u}}{}_{X}^{E_{u}}}$, $\tensor{*}[^{0}]{d}{}\indices*{*_{X_{1}}^{E_{g}}{}_{X_{2}}^{E_{u}}{}_{X}^{\tensor{*}[^{1}]{E}{}_{u}}}$, $d\indices*{*_{X_{1}}^{E_{g}}{}_{X_{2}}^{\tensor{*}[^{1}]{E}{}_{u}}{}_{X}^{A_{2u}}}$, $\tensor{*}[^{1}]{d}{}\indices*{*_{X_{1}}^{E_{g}}{}_{X_{2}}^{E_{u}}{}_{X}^{\tensor{*}[^{1}]{E}{}_{u}}}$, $d\indices*{*_{X_{1}}^{E_{g}}{}_{X_{2}}^{\tensor{*}[^{1}]{E}{}_{u}}{}_{X}^{\tensor{*}[^{1}]{E}{}_{u}}}$

##  II IFCs of $\mathbf{\hat{S}}_{\mathrm{BZ}}=2\mathbf{\hat{S}}_{C}$

The second- and third-order interatomic force constants (IFCs) are defined as:

$\Phi_{ij}^{\alpha\beta}=\frac{\partial^{2}\mathcal{V}}{\partial
r_{i}^{\alpha}\partial r_{j}^{\beta}},$ (5)
$\Phi_{ijk}^{\alpha\beta\gamma}=\frac{\partial^{3}\mathcal{V}}{\partial
r_{i}^{\alpha}\partial r_{j}^{\beta}\partial r_{k}^{\gamma}},$ (6)

where $\mathcal{V}$ is the Born-Oppenheimer potential energy, $i$ and $j$ are
the indices of atoms in a supercell, and $\alpha$ and $\beta$ are the
Cartesian indices. Therefore, in a 3-D real space, for a $N$-atom supercell
multiplied by a $n$-atom primitive cell with multiplicity $m$ ($m=N/n$), the
full matrix of the second-order (third-order) IFC $\Phi_{ij}^{\alpha\beta}$
($\Phi_{ijk}^{\alpha\beta\gamma}$) contains $(3N)^{2}$ ($(3N)^{3}$)
components.

These matrix components are non-independent and are correlated by crystal
symmetry. The independent number of the second-order (third-order) IFCs are
the number of second-order (third-order) displacement IDs. Here, we discuss
the number of IFCs, based on general symmetries. For $\mathcal{N}=2$, these
symmetries include (1) $\Phi_{ij}^{\alpha\beta}=\Phi_{ji}^{\beta\alpha}$ and
(2) translation invariance. For
$\Phi_{ij}^{\alpha\beta}=\Phi_{ji}^{\beta\alpha}$, the independent number of
$\Phi_{ij}^{\alpha\beta}$ equals the number of $\Phi_{ij}^{\alpha\beta}$ when
$i\leq j$. For translation invariance, every atom pair $(i,j)$ can be
translated to an atom pair in which the first atom is in the first unitcell
($i\leq n$). Therefore, in combining the two symmetries, the restrictions of
$(i,j)$ are $i\leq j$ and $i\leq n$, and the number of independent $(i,j)$ is
$\sum_{i=1,2,...,n}{N-i+1}=\frac{n(2N-n+1)}{2}$. Similarly, for
$\mathcal{N}=3$, the restrictions of $(i,j,k)$ are $i\leq j\leq k$ and $i\leq
n$, and the number of independent $(i,j,k)$ is
$\sum_{i=1,2,...,n}{\sum_{j=i,i+1,...,N}{N-j+1}}=\sum_{i=1,2,...,n}{\frac{1}{2}\left[(N+2)(N+1)-i(2N+3)+i^{2}\right]}=\frac{n(N+2)(N-n)}{2}+\frac{n(n+1)(n+2)}{6}$.

Next, we consider the independent combination of $(\alpha,\beta)$ and
$(\alpha,\beta,\gamma)$ for anisotropic and isotropic crystals. For an
anisotropic crystal at order $\mathcal{N}$, all combinations are different,
thus yielding $3^{\mathcal{N}}$ combinations. Therefore, the number of second-
and third-order IFCs for an anisotropic crystal is $\frac{9n(2N-n+1)}{2}$ and
$\frac{9n(N+2)(N-n)}{2}+\frac{3n(n+1)(n+2)}{2}$, respectively. For an
isotropic crystal, the $x$, $y$, and $z$ directions are equivalent. For order
$\mathcal{N}$, an isotropic crystal yields $\frac{3^{\mathcal{N}-1}+1}{2}$
combinations; the number of second- and third-order IFCs for an isotropic
crystal is $n(2N-n+1)$ and $\frac{5n(N+2)(N-n)}{2}+\frac{5n(n+1)(n+2)}{6}$,
respectively.

ThO2 is isotropic and features a primitive cell of $n=3$. For
$\mathbf{\hat{S}}_{\mathrm{BZ}}=2\mathbf{\hat{S}}_{C}$, $m=4$, $N=12$. the
number of second- and third-order IFCs is 66 and 995, respectively.

In our training data, two third-order displacement IDs from
$\mathbf{\hat{S}}_{\mathrm{BZ}}=\mathbf{\hat{S}}_{\mathrm{I}}$ are used, and
are equivalent to 50 third-order IFCs. For both the second and the third order
as the training data, the 116 IFCs can be reduced to 11 displacement IDs by
applying our EIP training approach.

##  III Validation of second-order displacement irreducible derivatives

Figure S1: Comparison of second-order displacement IDs of (a) CRG vs. LDA, and
(b) PW vs. LDA. All symbols represent the 91 second-order displacement IDs of
$4\mathbf{\hat{S}}_{\mathrm{I}}$, and the filled square symbols represent the
nine second-order displacement IDs of $\mathbf{\hat{S}}_{\mathrm{C}}$.

In this work, phonon spectra were calculated using
$\mathbf{\hat{S}}_{\mathrm{BZ}}=4\mathbf{\hat{S}}_{\mathrm{I}}$. The
irreducible set of $\tilde{q}_{\mathrm{BZ}}$ is given by:

$\tilde{q}_{\mathrm{IBZ}}=\\{\Gamma,X,L,A,W,\Delta,\Lambda,B\\},$ (7)

where
$\Gamma=(0,0,0),X=(0.5,0.5,0),L=(0.5,0,0),A=(0.25,0.75,0),W=(0.25,0.75,0.5),\Delta=(0.25,0.25,0),\Lambda=(0.25,0,0),$
and $B=(0.25,0.5,0)$ in the reciprocal lattice basis. The irreducible
representations of the displacements are:

$\displaystyle\mathcal{U}_{\Gamma}=\\{T_{2g},T_{1u}\\},$ (8)
$\displaystyle\mathcal{U}_{X}=\\{A_{1g},B_{1u},E_{g},{}^{1}E_{u},A_{2u},E_{u}\\},$
$\displaystyle\mathcal{U}_{L}=\\{A_{1g},E_{g},{}^{1}A_{2u},{}^{1}E_{u},A_{2u},E_{u}\\},$
$\displaystyle\mathcal{U}_{A}=\\{A_{1},{}^{1}A_{1},{}^{2}A_{1},A_{2},B_{1},{}^{1}B_{1},{}^{2}B_{1},B_{2},{}^{1}B_{2}\\},$
$\displaystyle\mathcal{U}_{W}=\\{A_{1},A_{2},B_{1},{}^{1}B_{1},B_{2},E,{}^{1}E\\},$
$\displaystyle\mathcal{U}_{\Delta}=\\{A_{1},{}^{1}A_{1},B_{2},E,{}^{1}E,{}^{2}E\\},$
$\displaystyle\mathcal{U}_{\Lambda}=\\{A_{1},{}^{1}A_{1},{}^{2}A_{1},E,{}^{1}E,{}^{2}E\\},$
$\displaystyle\mathcal{U}_{B}=\\{A,{}^{1}A,{}^{2}A,{}^{3}A,{}^{4}A,{}^{5}A,B,{}^{1}B,{}^{2}B\\}.$

And the irreducible set of $\tilde{\mathcal{Q}}_{\mathrm{BZ}}$ is given by:

$\tilde{\mathcal{Q}}_{\mathrm{IBZ}}=\\{(\Gamma,\Gamma),(X,X),(L,L),(\bar{A},A),(\bar{W},W),(\bar{\Delta},\Delta),(\bar{\Lambda},\Lambda),(\bar{B},B)\\}.$
(9)

These yield 91 second-order displacement IDs of
$4\mathbf{\hat{S}}_{\mathrm{I}}$, including nine second-order displacement IDs
of $\mathbf{\hat{S}}_{\mathrm{C}}$. The second-order displacement IDs of
$4\mathbf{\hat{S}}_{\mathrm{I}}$—as calculated by LDA, the CRG, and the
present work (PW)—are compared in Figure S1. We denote the nine second-order
displacement IDs of $\mathbf{\hat{S}}_{\mathrm{C}}$ as the fitting set (as
they were in the training data), and the other 82 second-order displacement
IDs of $4\mathbf{\hat{S}}_{\mathrm{I}}$ as the validation set. The values of
the second-order displacement IDs of the fitting set are presented in Table
III of the main text. The residual mean square error (RMSE) of the fitting set
is $5.85$eV/Å2 for the CRG, and is $3.09$eV/Å2 for the PW; the RMSE of the
validation set is $2.70$eV/Å2 for the CRG, and $1.64$eV/Å2 for the PW. Our
training process successfully reduced the RMSE of the fitting set, while
showing a smaller RMSE for the validation set.

##  IV Validation of third-order displacement irreducible derivatives

Figure S2: Comparison of third-order displacement IDs of (a) CRG vs. LDA, and
(b) PW vs. LDA. All symbols represent the 644 third-order displacement IDs of
$\mathbf{\hat{S}}_{\mathrm{O}}$, and the filled square symbols represent the
two third-order displacement IDs of $\mathbf{\hat{S}}_{\mathrm{I}}$.

The phonon thermal conductivity calculation in this work uses third-order
displacement IDs of
$\mathbf{\hat{S}}_{\mathrm{BZ}}=\mathbf{\hat{S}}_{\mathrm{O}}$. The
irreducible set of $\tilde{q}_{\mathrm{BZ}}$ is given by:

$\tilde{q}_{\mathrm{IBZ}}=\\{\Gamma,X,A\\},$ (10)

where $\Gamma=(0,0,0),X=(0.5,0.5,0),$ and $A=(0.25,0.75,0)$ in the reciprocal
lattice basis. The irreducible representations of the displacements are:

$\displaystyle\mathcal{U}_{\Gamma}=\\{T_{2g},T_{1u}\\},$ (11)
$\displaystyle\mathcal{U}_{X}=\\{A_{1g},B_{1u},E_{g},{}^{1}E_{u},A_{2u},E_{u}\\},$
$\displaystyle\mathcal{U}_{A}=\\{A_{1},{}^{1}A_{1},{}^{2}A_{1},A_{2},B_{1},{}^{1}B_{1},{}^{2}B_{1},B_{2},{}^{1}B_{2}\\}.$

And the irreducible set of $\tilde{\mathcal{Q}}_{\mathrm{BZ}}$ is given by:

$\tilde{\mathcal{Q}}_{\mathrm{IBZ}}=\\{(\Gamma,\Gamma,\Gamma),(\Gamma,X,X),(\Gamma,A,\bar{A}),(X,\bar{A},\bar{A}),(X_{1},X_{2},X),(A_{3},X_{2},\bar{A_{1}}),(A_{5},\bar{A_{4}},\bar{A_{1}}),(\bar{A_{1}},\bar{A_{2}},\bar{A_{5}})\\}.$
(12)

These yield 644 third-order displacement IDs within
$\mathbf{\hat{S}}_{\mathrm{BZ}}=\mathbf{\hat{S}}_{\mathrm{O}}$, which includes
two displacement IDs within
$\mathbf{\hat{S}}_{\mathrm{BZ}}=\mathbf{\hat{S}}_{\mathrm{I}}$, as shown in
the main manuscript. The third-order displacement IDs within
$\mathbf{\hat{S}}_{\mathrm{BZ}}=\mathbf{\hat{S}}_{\mathrm{O}}$—as calculated
by LDA, the CRG, and the present work (PW)—are compared in Figure S2. We
denote the two displacement IDs within
$\mathbf{\hat{S}}_{\mathrm{BZ}}=\mathbf{\hat{S}}_{\mathrm{I}}$ (
$d\indices*{*_{\Gamma}^{T_{2g}}{}_{\Gamma}^{T_{2g}}{}_{\Gamma}^{T_{2g}}}$ and
$d\indices*{*_{\Gamma}^{T_{1u}}{}_{\Gamma}^{T_{1u}}{}_{\Gamma}^{T_{2g}}}$ ) as
the fitting set (as they were in the training data), and the other 642
displacement IDs within $\mathbf{\hat{S}}_{\mathrm{O}}$ as the validation set.
The values of the third-order displacement IDs from the fitting set are
presented in Table III of the main text. The residual mean square error (RMSE)
of the fitting set is $32.41$eV/Å2 for the CRG, and $2.42$eV/Å2 for the PW;
the RMSE of the validation set is $3.06$eV/Å2 for the CRG, and $2.35$eV/Å2 for
the PW. As with the second-order displacement IDs, our training process
successfully reduced the RMSE of the third-order displacement IDs’ fitting
set, while showing a smaller RMSE for the validation set.

##  V EIP trained by using LDA data

To present that our EIP training approach is robust and irrelevant with the
used DFT functional, we trained an EIP (denoted PW_LDA, whereas the PW in the
main text is denoted PW_SCAN in this section) by using DFT data calculated by
the LDA functional. The DFT calculation setups are identical for both the SCAN
and LDA calculations, while the EIP training setups are also identical for
both PW_SCAN and PW_LDA. The parameters of PW_LDA are given in Tables S2 and
S3. The lattice constants for LDA and PW_LDA are both $5.529$Å, smaller than
the lattice constants measured in the experiments or from SCAN. The elastic
constants (see Table S4), phonon spectra (see Figure S3) and lattice thermal
conductivity (see Figure S4) are also calculated for LDA and PW_LDA, and
compared with SCAN and PW_SCAN. Using LDA data as the training data, a similar
level of agreement in terms of elastic constants, phonon dispersion, and
lattice thermal conductivity were obtained by PW_LDA, as compared to PW_SCAN.

Table S2: Parameters of PW_LDA for the short-range pairwise potentials.  Interaction | $\phi_{B}(r_{ij})$ | $\phi_{M}(r_{ij})$
---|---|---
$\alpha$-$\beta$ | $A_{\alpha\beta}(eV)$ | $\rho_{\alpha\beta}(\AA)$ | $C_{\alpha\beta}(eV\AA^{6})$ | $D_{\alpha\beta}(eV)$ | $\gamma_{\alpha\beta}(\AA^{-1})$ | $r_{0}(\AA)$
Th-Th | 19193 | 0.3362 | 0.0 | - | - | -
Th-O | 369.587 | 0.3952 | 0.0 | 0.6038 | 1.823 | 2.451
O-O | 829.025 | 0.3332 | 5.9335 | - | - | -
Table S3: Parameters of PW_LDA for the Coulomb potential and many-body interactions.  Species | $G_{\alpha}(eV\AA^{1.5})$ | $n_{\beta}(\AA^{5})$ | $q_{\alpha}(|e|)$
---|---|---|---
Th | 0.988 | 968.456 | 2.4294
O | 0.846 | 322.553 | -1.2147
Table S4: Elastic constants calculated using SCAN, LDA, CRG, PW_SCAN, PW_LDA, and PW_SDID, as compared to the experimental data.  |  $C_{11}$ (GPa) |  $C_{12}$ (GPa) |  $C_{44}$ (GPa)
---|---|---|---
Clausen et al. [2] | 377 | 146 | 89
Macedo et al. [3] | 367 | 106 | 79
Khanolkar et al. [4] | 361 | 115 | 78
LDA | 380 | 130 | 96
SCAN | 376 | 117 | 90
CRG | 352 | 113 | 72
PW_LDA | 381 | 131 | 95
PW_SCAN | 376 | 120 | 89
PW_2ID | 324 | 131 | 95

Figure S3: Calculated phonon spectra and density of states using (a) SCAN and
LDA, and (b) PW_SCAN and PW_LDA, compared with experimental data from Bryan
_et al._ [5]. The phonon spectra are interpolated by the measured data points,
which are presented as open circles. Figure S4: Calculated lattice thermal
conductivity of SCAN, LDA, CRG, PW_SCAN, and PW_LDA at 50 – 600 K, compared
with experimental data from Xiao _et al._ [6], Muta _et al._ [7], and Bakker
_et al._ [8].

##  VI EIP trained solely by using the second-order displacement IDs

To justify the effect of third-order displacement IDs and strain IDs in the
EIP training, we trained an EIP (denoted PW_2ID) by only using lattice
constant and second-order displacement IDs from SCAN calculations. The
parameters of PW_2ID are given in Tables S5 and S6. The lattice constants for
SCAN and PW_2ID are both $5.592$Å. The elastic constants (see Table S4) and
phonon spectra (see Figure S5) are also calculated for PW_2ID. The absence of
strain IDs in the training data results in a high degree of error for
$C_{11}$. When only fitting to second-order displacement IDs, a portion of
errors in PW_SCAN are fixed, such as the large phonon frequency of LO2 and TO2
branches at the $X$ point. Notably, however, certain errors remain, including
that the phonon frequency of TO1 and TO2 branches is dependent on $\zeta$ at
the $(\zeta,0,0)$ direction (which is approximately independent of $\zeta$ in
the experiment), and that the phonon branches of TO2 and LO2 cross near
$(0.5,0.5,0)$ and at the $L$ point (which does not exist in the experiment).
As PW_2ID is trained without using third-order displacement IDs and strain
IDs, these remaining errors are not produced by fitting to those types of IDs,
but are caused by the form of the potential.

Table S5: Parameters of PW_2ID for the short-range pairwise potentials.  Interaction | $\phi_{B}(r_{ij})$ | $\phi_{M}(r_{ij})$
---|---|---
$\alpha$-$\beta$ | $A_{\alpha\beta}(eV)$ | $\rho_{\alpha\beta}(\AA)$ | $C_{\alpha\beta}(eV\AA^{6})$ | $D_{\alpha\beta}(eV)$ | $\gamma_{\alpha\beta}(\AA^{-1})$ | $r_{0}(\AA)$
Th-Th | 20999 | 0.3383 | 0.0 | - | - | -
Th-O | 424.188 | 0.3919 | 0.0 | 0.5000 | 1.946 | 2.456
O-O | 618.638 | 0.3307 | 8.2222 | - | - | -
Table S6: Parameters of PW_2ID for the Coulomb potential and many-body interactions.  Species | $G_{\alpha}(eV\AA^{1.5})$ | $n_{\beta}(\AA^{5})$ | $q_{\alpha}(|e|)$
---|---|---|---
Th | 0.926 | 853.615 | 2.3559
O | 0.969 | 386.312 | -1.1779
Figure S5: Calculated phonon spectra and density of states when using PW_2ID,
compared with experimental data from Bryan _et al._ [5]. The phonon spectra
are interpolated by the measured data points, which are presented as open
circles.

##  VII Defect formation energy

The defect formation energy of isolated charge-neutral defect complexes, O
Frenkel pairs (FPs), Th FPs, and Schottky defects are determined via DFT and
EIP calculations (see Table S7). In the DFT calculation, both formally charged
point defects and neutral point defects are measured using SCAN and GGA, with
the GGA calculations carried out for direct comparison with previous GGA
studies [9, 10, 11]. Our GGA results are in excellent agreement with
Kuganathan _et al._[9] and Murphy _et al._[10], as the error for every
measurement is $<1$ eV. The formation energies calculated via SCAN are higher
than GGA and are close to the LDA results determined by Jiang _et al._[12].
Compared to SCAN, the PW decreases the errors of O FPs and Schottky defects,
but increases the error of Th FPs.

Table S7: Formation energies (eV) of isolated charge-neutral defect complexes in ThO2, as calculated using DFT (GGA and SCAN functionals) and EIPs (CRG and PW), compared with previous DFT results.  |  | GGA | GGA | GGA | LDA | GGA | SCAN | CRG | PW
---|---|---|---|---|---|---|---|---|---
|  | Kuganathan [9] | Murphy [10] | Lu [11] | Jiang [12] |  |  |  |
O FP | $V_{O}^{2+}+O_{i}^{2-}$ | 4.6 | 5.0 | 6.8 | 5.1 | 4.8 | 5.2 | 6.0 | 5.7
| $V_{O}^{0}+O_{i}^{0}$ | 9.1 | 9.3 | 9.3 |  | 9.4 | 10.5 |  |
Th FP | $V_{Th}^{4-}+Th_{i}^{4+}$ | 13.6 | 13.7 | 16.7 | 15.6 | 14.1 | 15.5 | 18.2 | 23.3
| $V_{Th}^{0}+Th_{i}^{0}$ | 24.6 | 25.4 | 24.4 |  | 24.7 | 27.5 |  |
Schottky | $V_{Th}^{4-}+2V_{O}^{2+}$ | 8.9 | 8.0 | 8.2 | 10.0 | 8.0 | 9.6 | 13.1 | 11.0
| $V_{Th}^{0}+2V_{O}^{0}$ | 20.0 | 20.0 | 19.5 |  | 19.6 | 22.2 |  |

##  VIII Primary $\mathbf{q}$ points and correlated atomic displacement basis

The primary $\mathbf{q}$ points for ThO2 are listed in Eq. (13), and the
correlated atomic displacement basis of the primary $\mathbf{q}$ points are
tabulated in Table LABEL:tab:SMqbasis.

$\displaystyle{\Gamma}={\left(000\right)}$ (13)
$\displaystyle{L}={\left(\frac{1}{2}00\right)}$
$\displaystyle{L_{1}}={\left(\frac{1}{2}\frac{1}{2}\frac{1}{2}\right)}$
$\displaystyle{L_{2}}={\left(0\frac{1}{2}0\right)}$
$\displaystyle{L_{3}}={\left(00\frac{1}{2}\right)}$
$\displaystyle{X}={\left(\frac{1}{2}\frac{1}{2}0\right)}$
$\displaystyle{X_{1}}={\left(0\frac{1}{2}\frac{1}{2}\right)}$
$\displaystyle{X_{2}}={\left(\frac{1}{2}0\frac{1}{2}\right)}$
$\displaystyle{\Delta}={\left(\frac{1}{4}\frac{1}{4}0\right)}$
$\displaystyle{\bar{\Delta}}={\left(\frac{3}{4}\frac{3}{4}0\right)}$
$\displaystyle{\Delta_{1}}={\left(0\frac{1}{4}\frac{1}{4}\right)}$
$\displaystyle{\bar{\Delta}_{1}}={\left(0\frac{3}{4}\frac{3}{4}\right)}$
$\displaystyle{\Delta_{2}}={\left(\frac{3}{4}0\frac{3}{4}\right)}$
$\displaystyle{\bar{\Delta}_{2}}={\left(\frac{1}{4}0\frac{1}{4}\right)}$
$\displaystyle{W}={\left(\frac{1}{4}\frac{3}{4}\frac{1}{2}\right)}$
$\displaystyle{\bar{W}}={\left(\frac{3}{4}\frac{1}{4}\frac{1}{2}\right)}$
$\displaystyle{W_{1}}={\left(\frac{1}{2}\frac{1}{4}\frac{3}{4}\right)}$
$\displaystyle{\bar{W}_{1}}={\left(\frac{1}{2}\frac{3}{4}\frac{1}{4}\right)}$
$\displaystyle{W_{2}}={\left(\frac{1}{4}\frac{1}{2}\frac{3}{4}\right)}$
$\displaystyle{\bar{W}_{2}}={\left(\frac{3}{4}\frac{1}{2}\frac{1}{4}\right)}$
$\displaystyle{A}={\left(\frac{1}{4}\frac{3}{4}0\right)}$
$\displaystyle{\bar{A}}={\left(\frac{3}{4}\frac{1}{4}0\right)}$
$\displaystyle{A_{1}}={\left(\frac{1}{2}\frac{3}{4}\frac{3}{4}\right)}$
$\displaystyle{\bar{A}_{1}}={\left(\frac{1}{2}\frac{1}{4}\frac{1}{4}\right)}$
$\displaystyle{A_{2}}={\left(\frac{1}{4}0\frac{3}{4}\right)}$
$\displaystyle{\bar{A}_{2}}={\left(\frac{3}{4}0\frac{1}{4}\right)}$
$\displaystyle{A_{3}}={\left(0\frac{3}{4}\frac{1}{4}\right)}$
$\displaystyle{\bar{A}_{3}}={\left(0\frac{1}{4}\frac{3}{4}\right)}$
$\displaystyle{A_{4}}={\left(\frac{3}{4}\frac{1}{2}\frac{3}{4}\right)}$
$\displaystyle{\bar{A}_{4}}={\left(\frac{1}{4}\frac{1}{2}\frac{1}{4}\right)}$
$\displaystyle{A_{5}}={\left(\frac{1}{4}\frac{1}{4}\frac{1}{2}\right)}$
$\displaystyle{\bar{A}_{5}}={\left(\frac{3}{4}\frac{3}{4}\frac{1}{2}\right)}$
$\displaystyle{\Lambda}={\left(\frac{1}{4}00\right)}$
$\displaystyle{\bar{\Lambda}}={\left(\frac{3}{4}00\right)}$
$\displaystyle{\Lambda_{1}}={\left(0\frac{3}{4}0\right)}$
$\displaystyle{\bar{\Lambda}_{1}}={\left(0\frac{1}{4}0\right)}$
$\displaystyle{\Lambda_{2}}={\left(00\frac{3}{4}\right)}$
$\displaystyle{\bar{\Lambda}_{2}}={\left(00\frac{1}{4}\right)}$
$\displaystyle{\Lambda_{3}}={\left(\frac{1}{4}\frac{1}{4}\frac{1}{4}\right)}$
$\displaystyle{\bar{\Lambda}_{3}}={\left(\frac{3}{4}\frac{3}{4}\frac{3}{4}\right)}$
$\displaystyle{B}={\left(\frac{1}{4}\frac{1}{2}0\right)}$
$\displaystyle{\bar{B}}={\left(\frac{3}{4}\frac{1}{2}0\right)}$
$\displaystyle{B_{1}}={\left(\frac{1}{2}\frac{3}{4}\frac{1}{2}\right)}$
$\displaystyle{\bar{B}_{1}}={\left(\frac{1}{2}\frac{1}{4}\frac{1}{2}\right)}$
$\displaystyle{B_{2}}={\left(\frac{3}{4}\frac{3}{4}\frac{1}{4}\right)}$
$\displaystyle{\bar{B}_{2}}={\left(\frac{1}{4}\frac{1}{4}\frac{3}{4}\right)}$
$\displaystyle{B_{3}}={\left(\frac{1}{4}\frac{3}{4}\frac{3}{4}\right)}$
$\displaystyle{\bar{B}_{3}}={\left(\frac{3}{4}\frac{1}{4}\frac{1}{4}\right)}$
$\displaystyle{B_{4}}={\left(\frac{1}{2}\frac{1}{2}\frac{1}{4}\right)}$
$\displaystyle{\bar{B}_{4}}={\left(\frac{1}{2}\frac{1}{2}\frac{3}{4}\right)}$
$\displaystyle{B_{5}}={\left(\frac{3}{4}\frac{1}{4}\frac{3}{4}\right)}$
$\displaystyle{\bar{B}_{5}}={\left(\frac{1}{4}\frac{3}{4}\frac{1}{4}\right)}$
$\displaystyle{B_{6}}={\left(\frac{1}{4}\frac{1}{2}\frac{1}{2}\right)}$
$\displaystyle{\bar{B}_{6}}={\left(\frac{3}{4}\frac{1}{2}\frac{1}{2}\right)}$
$\displaystyle{B_{7}}={\left(\frac{1}{2}\frac{3}{4}0\right)}$
$\displaystyle{\bar{B}_{7}}={\left(\frac{1}{2}\frac{1}{4}0\right)}$
$\displaystyle{B_{8}}={\left(\frac{1}{4}0\frac{1}{2}\right)}$
$\displaystyle{\bar{B}_{8}}={\left(\frac{3}{4}0\frac{1}{2}\right)}$
$\displaystyle{B_{9}}={\left(\frac{1}{2}0\frac{1}{4}\right)}$
$\displaystyle{\bar{B}_{9}}={\left(\frac{1}{2}0\frac{3}{4}\right)}$
$\displaystyle{B_{10}}={\left(0\frac{1}{4}\frac{1}{2}\right)}$
$\displaystyle{\bar{B}_{10}}={\left(0\frac{3}{4}\frac{1}{2}\right)}$
$\displaystyle{B_{11}}={\left(0\frac{1}{2}\frac{1}{4}\right)}$
$\displaystyle{\bar{B}_{11}}={\left(0\frac{1}{2}\frac{3}{4}\right)}$

Table S8:  Atomic displacement basis for the primary $\mathbf{q}$ points.  | Thx | Thy | Thz | O${}^{1}_{x}$ | O${}^{1}_{y}$ | O${}^{1}_{z}$ | O${}^{2}_{x}$ | O${}^{2}_{y}$ | O${}^{2}_{z}$
---|---|---|---|---|---|---|---|---|---
${u_{\Gamma}^{T_{2g}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$
$0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$
$0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$
${u_{\Gamma}^{T_{1u}}}$ | $\frac{\sqrt{6}}{3}$ | $0$ | $0$ | $-\frac{\sqrt{6}}{6}$ | $0$ | $0$ | $-\frac{\sqrt{6}}{6}$ | $0$ | $0$
$0$ | $\frac{\sqrt{6}}{3}$ | $0$ | $0$ | $-\frac{\sqrt{6}}{6}$ | $0$ | $0$ | $-\frac{\sqrt{6}}{6}$ | $0$
$0$ | $0$ | $\frac{\sqrt{6}}{3}$ | $0$ | $0$ | $-\frac{\sqrt{6}}{6}$ | $0$ | $0$ | $-\frac{\sqrt{6}}{6}$
${u_{L}^{A_{1g}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$
${u_{L}^{E_{g}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $\frac{1}{2}$ | $0$ | $\frac{1}{2}$ | $\frac{1}{2}$ | $0$
$0$ | $0$ | $0$ | $-\frac{\sqrt{3}}{6}$ | $\frac{\sqrt{3}}{6}$ | $-\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{6}$ | $\frac{\sqrt{3}}{6}$ | $-\frac{\sqrt{3}}{3}$
${u_{L}^{A_{2u}}}$ | $\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{L}^{E_{u}}}$ | $\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{L}^{\tensor{*}[^{1}]{A}{}_{2u}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$
${u_{L}^{\tensor{*}[^{1}]{E}{}_{u}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{3}}{6}$ | $-\frac{\sqrt{3}}{6}$ | $\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{6}$ | $\frac{\sqrt{3}}{6}$ | $-\frac{\sqrt{3}}{3}$
$0$ | $0$ | $0$ | $\frac{1}{2}$ | $\frac{1}{2}$ | $0$ | $-\frac{1}{2}$ | $-\frac{1}{2}$ | $0$
${u_{L_{1}}^{A_{1g}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$
${u_{L_{1}}^{E_{g}}}$ | $0$ | $0$ | $0$ | $-\frac{1}{2}$ | $\frac{1}{2}$ | $0$ | $-\frac{1}{2}$ | $\frac{1}{2}$ | $0$
$0$ | $0$ | $0$ | $\frac{\sqrt{3}}{6}$ | $\frac{\sqrt{3}}{6}$ | $-\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{6}$ | $\frac{\sqrt{3}}{6}$ | $-\frac{\sqrt{3}}{3}$
${u_{L_{1}}^{A_{2u}}}$ | $\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{L_{1}}^{E_{u}}}$ | $\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{L_{1}}^{\tensor{*}[^{1}]{A}{}_{2u}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$
${u_{L_{1}}^{\tensor{*}[^{1}]{E}{}_{u}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{3}}{6}$ | $-\frac{\sqrt{3}}{6}$ | $\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{6}$ | $\frac{\sqrt{3}}{6}$ | $-\frac{\sqrt{3}}{3}$
$0$ | $0$ | $0$ | $-\frac{1}{2}$ | $\frac{1}{2}$ | $0$ | $\frac{1}{2}$ | $-\frac{1}{2}$ | $0$
${u_{L_{2}}^{A_{1g}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$
${u_{L_{2}}^{E_{g}}}$ | $0$ | $0$ | $0$ | $-\frac{1}{2}$ | $-\frac{1}{2}$ | $0$ | $-\frac{1}{2}$ | $-\frac{1}{2}$ | $0$
$0$ | $0$ | $0$ | $\frac{\sqrt{3}}{6}$ | $-\frac{\sqrt{3}}{6}$ | $-\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{6}$ | $-\frac{\sqrt{3}}{6}$ | $-\frac{\sqrt{3}}{3}$
${u_{L_{2}}^{A_{2u}}}$ | $-\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{L_{2}}^{E_{u}}}$ | $-\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{L_{2}}^{\tensor{*}[^{1}]{A}{}_{2u}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$
${u_{L_{2}}^{\tensor{*}[^{1}]{E}{}_{u}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{3}}{6}$ | $\frac{\sqrt{3}}{6}$ | $\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{6}$ | $-\frac{\sqrt{3}}{6}$ | $-\frac{\sqrt{3}}{3}$
$0$ | $0$ | $0$ | $-\frac{1}{2}$ | $-\frac{1}{2}$ | $0$ | $\frac{1}{2}$ | $\frac{1}{2}$ | $0$
${u_{L_{3}}^{A_{1g}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$
${u_{L_{3}}^{E_{g}}}$ | $0$ | $0$ | $0$ | $-\frac{1}{2}$ | $\frac{1}{2}$ | $0$ | $-\frac{1}{2}$ | $\frac{1}{2}$ | $0$
$0$ | $0$ | $0$ | $\frac{\sqrt{3}}{6}$ | $\frac{\sqrt{3}}{6}$ | $\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{6}$ | $\frac{\sqrt{3}}{6}$ | $\frac{\sqrt{3}}{3}$
${u_{L_{3}}^{A_{2u}}}$ | $-\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{L_{3}}^{E_{u}}}$ | $-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{L_{3}}^{\tensor{*}[^{1}]{A}{}_{2u}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$
${u_{L_{3}}^{\tensor{*}[^{1}]{E}{}_{u}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{3}}{6}$ | $-\frac{\sqrt{3}}{6}$ | $-\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{6}$ | $\frac{\sqrt{3}}{6}$ | $\frac{\sqrt{3}}{3}$
$0$ | $0$ | $0$ | $-\frac{1}{2}$ | $\frac{1}{2}$ | $0$ | $\frac{1}{2}$ | $-\frac{1}{2}$ | $0$
${u_{X}^{A_{1g}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$
${u_{X}^{E_{g}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$
$0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$
${u_{X}^{A_{2u}}}$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{X}^{B_{1u}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$
${u_{X}^{E_{u}}}$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{X}^{\tensor{*}[^{1}]{E}{}_{u}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$
$0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$
${u_{X_{1}}^{A_{1g}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$
${u_{X_{1}}^{E_{g}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$
$0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$
${u_{X_{1}}^{A_{2u}}}$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{X_{1}}^{B_{1u}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$
${u_{X_{1}}^{E_{u}}}$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$0$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{X_{1}}^{\tensor{*}[^{1}]{E}{}_{u}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$
$0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$
${u_{X_{2}}^{A_{1g}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$
${u_{X_{2}}^{E_{g}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$
$0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$
${u_{X_{2}}^{A_{2u}}}$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{X_{2}}^{B_{1u}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$
${u_{X_{2}}^{E_{u}}}$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$0$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{X_{2}}^{\tensor{*}[^{1}]{E}{}_{u}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$
$0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$
${u_{\Delta}^{A_{1}}}$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\Delta}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$
${u_{\Delta}^{B_{2}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$
${u_{\Delta}^{E}}$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\Delta}^{\tensor{*}[^{1}]{E}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$
$0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$
${u_{\Delta}^{\tensor{*}[^{2}]{E}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$
$0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$
${u_{\bar{\Delta}}^{A_{1}}}$ | $0$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{\Delta}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$
${u_{\bar{\Delta}}^{B_{2}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$
${u_{\bar{\Delta}}^{E}}$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{\Delta}}^{\tensor{*}[^{1}]{E}}}$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$
$0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$
${u_{\bar{\Delta}}^{\tensor{*}[^{2}]{E}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$
$0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$
${u_{\Delta_{1}}^{A_{1}}}$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\Delta_{1}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$
${u_{\Delta_{1}}^{B_{2}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$
${u_{\Delta_{1}}^{E}}$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\Delta_{1}}^{\tensor{*}[^{1}]{E}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$
$0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$
${u_{\Delta_{1}}^{\tensor{*}[^{2}]{E}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$
$0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$
${u_{\bar{\Delta}_{1}}^{A_{1}}}$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{\Delta}_{1}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$
${u_{\bar{\Delta}_{1}}^{B_{2}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$
${u_{\bar{\Delta}_{1}}^{E}}$ | $0$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{\Delta}_{1}}^{\tensor{*}[^{1}]{E}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$
$0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$
${u_{\bar{\Delta}_{1}}^{\tensor{*}[^{2}]{E}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$
$0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$
${u_{\Delta_{2}}^{A_{1}}}$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\Delta_{2}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$
${u_{\Delta_{2}}^{B_{2}}}$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$
${u_{\Delta_{2}}^{E}}$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\Delta_{2}}^{\tensor{*}[^{1}]{E}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$
$0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$
${u_{\Delta_{2}}^{\tensor{*}[^{2}]{E}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$
$0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$
${u_{\bar{\Delta}_{2}}^{A_{1}}}$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{\Delta}_{2}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$
${u_{\bar{\Delta}_{2}}^{B_{2}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$
${u_{\bar{\Delta}_{2}}^{E}}$ | $0$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{\Delta}_{2}}^{\tensor{*}[^{1}]{E}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$
$0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$
${u_{\bar{\Delta}_{2}}^{\tensor{*}[^{2}]{E}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$
$0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$
${u_{W}^{A_{1}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}$ | $0$
${u_{W}^{B_{1}}}$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{W}^{\tensor{*}[^{1}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $-\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}$ | $0$
${u_{W}^{A_{2}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $\frac{1}{2}i$ | $0$ | $-\frac{1}{2}i$ | $-\frac{1}{2}$ | $0$
${u_{W}^{B_{2}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $-\frac{1}{2}i$ | $0$ | $-\frac{1}{2}i$ | $\frac{1}{2}$ | $0$
${u_{W}^{E}}$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{W}^{\tensor{*}[^{1}]{E}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$
$0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$
${u_{\bar{W}}^{A_{1}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}$ | $0$ | $\frac{1}{2}$ | $\frac{1}{2}i$ | $0$
${u_{\bar{W}}^{B_{1}}}$ | $0$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{W}}^{\tensor{*}[^{1}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}$ | $0$ | $\frac{1}{2}$ | $-\frac{1}{2}i$ | $0$
${u_{\bar{W}}^{A_{2}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}$ | $0$ | $-\frac{1}{2}$ | $-\frac{1}{2}i$ | $0$
${u_{\bar{W}}^{B_{2}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}$ | $0$ | $-\frac{1}{2}$ | $\frac{1}{2}i$ | $0$
${u_{\bar{W}}^{E}}$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{W}}^{\tensor{*}[^{1}]{E}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$
$0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$
${u_{W_{1}}^{A_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}$
${u_{W_{1}}^{B_{1}}}$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{W_{1}}^{\tensor{*}[^{1}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $-\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}$
${u_{W_{1}}^{A_{2}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $\frac{1}{2}i$ | $0$ | $-\frac{1}{2}i$ | $-\frac{1}{2}$
${u_{W_{1}}^{B_{2}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $-\frac{1}{2}i$ | $0$ | $-\frac{1}{2}i$ | $\frac{1}{2}$
${u_{W_{1}}^{E}}$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{W_{1}}^{\tensor{*}[^{1}]{E}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$
$0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$
${u_{\bar{W}_{1}}^{A_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}$ | $0$ | $\frac{1}{2}$ | $\frac{1}{2}i$
${u_{\bar{W}_{1}}^{B_{1}}}$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{W}_{1}}^{\tensor{*}[^{1}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}$ | $0$ | $\frac{1}{2}$ | $-\frac{1}{2}i$
${u_{\bar{W}_{1}}^{A_{2}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}$ | $0$ | $-\frac{1}{2}$ | $-\frac{1}{2}i$
${u_{\bar{W}_{1}}^{B_{2}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}$ | $0$ | $-\frac{1}{2}$ | $\frac{1}{2}i$
${u_{\bar{W}_{1}}^{E}}$ | $0$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{W}_{1}}^{\tensor{*}[^{1}]{E}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$
$0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$
${u_{W_{2}}^{A_{1}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}i$ | $0$ | $\frac{1}{2}$
${u_{W_{2}}^{B_{1}}}$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{W_{2}}^{\tensor{*}[^{1}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $-\frac{1}{2}$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}i$ | $0$ | $\frac{1}{2}$
${u_{W_{2}}^{A_{2}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}i$ | $0$ | $-\frac{1}{2}$
${u_{W_{2}}^{B_{2}}}$ | $0$ | $0$ | $0$ | $-\frac{1}{2}$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}i$ | $0$ | $-\frac{1}{2}$
${u_{W_{2}}^{E}}$ | $0$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{W_{2}}^{\tensor{*}[^{1}]{E}}}$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$
$0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$
${u_{\bar{W}_{2}}^{A_{1}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $0$ | $\frac{1}{2}$ | $\frac{1}{2}$ | $0$ | $\frac{1}{2}i$
${u_{\bar{W}_{2}}^{B_{1}}}$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{W}_{2}}^{\tensor{*}[^{1}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $-\frac{1}{2}i$ | $0$ | $\frac{1}{2}$ | $-\frac{1}{2}$ | $0$ | $\frac{1}{2}i$
${u_{\bar{W}_{2}}^{A_{2}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $0$ | $\frac{1}{2}$ | $-\frac{1}{2}$ | $0$ | $-\frac{1}{2}i$
${u_{\bar{W}_{2}}^{B_{2}}}$ | $0$ | $0$ | $0$ | $-\frac{1}{2}i$ | $0$ | $\frac{1}{2}$ | $\frac{1}{2}$ | $0$ | $-\frac{1}{2}i$
${u_{\bar{W}_{2}}^{E}}$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{W}_{2}}^{\tensor{*}[^{1}]{E}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$
$0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$
${u_{A}^{A_{1}}}$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{A}^{B_{2}}}$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{A}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $-\frac{1}{2}$ | $0$ | $\frac{1}{2}$ | $-\frac{1}{2}$ | $0$
${u_{A}^{\tensor{*}[^{1}]{B}{}_{2}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $\frac{1}{2}$ | $0$ | $\frac{1}{2}$ | $\frac{1}{2}$ | $0$
${u_{A}^{\tensor{*}[^{2}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$
${u_{A}^{\tensor{*}[^{1}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $-\frac{1}{2}$ | $0$ | $-\frac{1}{2}$ | $\frac{1}{2}$ | $0$
${u_{A}^{A_{2}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $\frac{1}{2}$ | $0$ | $-\frac{1}{2}$ | $-\frac{1}{2}$ | $0$
${u_{A}^{B_{1}}}$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{A}^{\tensor{*}[^{2}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$
${u_{\bar{A}}^{A_{1}}}$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{A}}^{B_{2}}}$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{A}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $-\frac{1}{2}$ | $\frac{1}{2}$ | $0$ | $-\frac{1}{2}$ | $\frac{1}{2}$ | $0$
${u_{\bar{A}}^{\tensor{*}[^{1}]{B}{}_{2}}}$ | $0$ | $0$ | $0$ | $-\frac{1}{2}$ | $-\frac{1}{2}$ | $0$ | $-\frac{1}{2}$ | $-\frac{1}{2}$ | $0$
${u_{\bar{A}}^{\tensor{*}[^{2}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$
${u_{\bar{A}}^{\tensor{*}[^{1}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $-\frac{1}{2}$ | $\frac{1}{2}$ | $0$ | $\frac{1}{2}$ | $-\frac{1}{2}$ | $0$
${u_{\bar{A}}^{A_{2}}}$ | $0$ | $0$ | $0$ | $-\frac{1}{2}$ | $-\frac{1}{2}$ | $0$ | $\frac{1}{2}$ | $\frac{1}{2}$ | $0$
${u_{\bar{A}}^{B_{1}}}$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{A}}^{\tensor{*}[^{2}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$
${u_{A_{1}}^{A_{1}}}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{A_{1}}^{B_{2}}}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{A_{1}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}i$ | $0$ | $-\frac{1}{2}i$ | $-\frac{1}{2}i$
${u_{A_{1}}^{\tensor{*}[^{1}]{B}{}_{2}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}i$ | $0$ | $-\frac{1}{2}i$ | $\frac{1}{2}i$
${u_{A_{1}}^{\tensor{*}[^{2}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$
${u_{A_{1}}^{\tensor{*}[^{1}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}i$
${u_{A_{1}}^{A_{2}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}i$
${u_{A_{1}}^{B_{1}}}$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{A_{1}}^{\tensor{*}[^{2}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$
${u_{\bar{A}_{1}}^{A_{1}}}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{A}_{1}}^{B_{2}}}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{A}_{1}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}i$ | $0$ | $-\frac{1}{2}i$ | $-\frac{1}{2}i$
${u_{\bar{A}_{1}}^{\tensor{*}[^{1}]{B}{}_{2}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}i$ | $0$ | $-\frac{1}{2}i$ | $\frac{1}{2}i$
${u_{\bar{A}_{1}}^{\tensor{*}[^{2}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$
${u_{\bar{A}_{1}}^{\tensor{*}[^{1}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}i$
${u_{\bar{A}_{1}}^{A_{2}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}i$
${u_{\bar{A}_{1}}^{B_{1}}}$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{A}_{1}}^{\tensor{*}[^{2}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$
${u_{A_{2}}^{A_{1}}}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{A_{2}}^{B_{2}}}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{A_{2}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $0$ | $-\frac{1}{2}$ | $\frac{1}{2}$ | $0$ | $-\frac{1}{2}$
${u_{A_{2}}^{\tensor{*}[^{1}]{B}{}_{2}}}$ | $0$ | $0$ | $0$ | $-\frac{1}{2}$ | $0$ | $-\frac{1}{2}$ | $-\frac{1}{2}$ | $0$ | $-\frac{1}{2}$
${u_{A_{2}}^{\tensor{*}[^{2}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$
${u_{A_{2}}^{\tensor{*}[^{1}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $0$ | $-\frac{1}{2}$ | $-\frac{1}{2}$ | $0$ | $\frac{1}{2}$
${u_{A_{2}}^{A_{2}}}$ | $0$ | $0$ | $0$ | $-\frac{1}{2}$ | $0$ | $-\frac{1}{2}$ | $\frac{1}{2}$ | $0$ | $\frac{1}{2}$
${u_{A_{2}}^{B_{1}}}$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{A_{2}}^{\tensor{*}[^{2}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$
${u_{\bar{A}_{2}}^{A_{1}}}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{A}_{2}}^{B_{2}}}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{A}_{2}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $-\frac{1}{2}$ | $0$ | $\frac{1}{2}$ | $-\frac{1}{2}$ | $0$ | $\frac{1}{2}$
${u_{\bar{A}_{2}}^{\tensor{*}[^{1}]{B}{}_{2}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $0$ | $\frac{1}{2}$ | $\frac{1}{2}$ | $0$ | $\frac{1}{2}$
${u_{\bar{A}_{2}}^{\tensor{*}[^{2}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$
${u_{\bar{A}_{2}}^{\tensor{*}[^{1}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $-\frac{1}{2}$ | $0$ | $\frac{1}{2}$ | $\frac{1}{2}$ | $0$ | $-\frac{1}{2}$
${u_{\bar{A}_{2}}^{A_{2}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $0$ | $\frac{1}{2}$ | $-\frac{1}{2}$ | $0$ | $-\frac{1}{2}$
${u_{\bar{A}_{2}}^{B_{1}}}$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{A}_{2}}^{\tensor{*}[^{2}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$
${u_{A_{3}}^{A_{1}}}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{A_{3}}^{B_{2}}}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{A_{3}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $-\frac{1}{2}$ | $\frac{1}{2}$ | $0$ | $-\frac{1}{2}$ | $\frac{1}{2}$
${u_{A_{3}}^{\tensor{*}[^{1}]{B}{}_{2}}}$ | $0$ | $0$ | $0$ | $0$ | $-\frac{1}{2}$ | $-\frac{1}{2}$ | $0$ | $-\frac{1}{2}$ | $-\frac{1}{2}$
${u_{A_{3}}^{\tensor{*}[^{2}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$
${u_{A_{3}}^{\tensor{*}[^{1}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $-\frac{1}{2}$ | $\frac{1}{2}$ | $0$ | $\frac{1}{2}$ | $-\frac{1}{2}$
${u_{A_{3}}^{A_{2}}}$ | $0$ | $0$ | $0$ | $0$ | $-\frac{1}{2}$ | $-\frac{1}{2}$ | $0$ | $\frac{1}{2}$ | $\frac{1}{2}$
${u_{A_{3}}^{B_{1}}}$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{A_{3}}^{\tensor{*}[^{2}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$
${u_{\bar{A}_{3}}^{A_{1}}}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{A}_{3}}^{B_{2}}}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{A}_{3}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $-\frac{1}{2}$ | $0$ | $\frac{1}{2}$ | $-\frac{1}{2}$
${u_{\bar{A}_{3}}^{\tensor{*}[^{1}]{B}{}_{2}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $\frac{1}{2}$ | $0$ | $\frac{1}{2}$ | $\frac{1}{2}$
${u_{\bar{A}_{3}}^{\tensor{*}[^{2}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$
${u_{\bar{A}_{3}}^{\tensor{*}[^{1}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $-\frac{1}{2}$ | $0$ | $-\frac{1}{2}$ | $\frac{1}{2}$
${u_{\bar{A}_{3}}^{A_{2}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{1}{2}$ | $\frac{1}{2}$ | $0$ | $-\frac{1}{2}$ | $-\frac{1}{2}$
${u_{\bar{A}_{3}}^{B_{1}}}$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{A}_{3}}^{\tensor{*}[^{2}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$
${u_{A_{4}}^{A_{1}}}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{A_{4}}^{B_{2}}}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{A_{4}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}i$ | $0$ | $-\frac{1}{2}i$
${u_{A_{4}}^{\tensor{*}[^{1}]{B}{}_{2}}}$ | $0$ | $0$ | $0$ | $-\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}i$ | $0$ | $-\frac{1}{2}i$
${u_{A_{4}}^{\tensor{*}[^{2}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$
${u_{A_{4}}^{\tensor{*}[^{1}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$
${u_{A_{4}}^{A_{2}}}$ | $0$ | $0$ | $0$ | $-\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$
${u_{A_{4}}^{B_{1}}}$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{A_{4}}^{\tensor{*}[^{2}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$
${u_{\bar{A}_{4}}^{A_{1}}}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{A}_{4}}^{B_{2}}}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{A}_{4}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}i$ | $0$ | $-\frac{1}{2}i$
${u_{\bar{A}_{4}}^{\tensor{*}[^{1}]{B}{}_{2}}}$ | $0$ | $0$ | $0$ | $-\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}i$ | $0$ | $-\frac{1}{2}i$
${u_{\bar{A}_{4}}^{\tensor{*}[^{2}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$
${u_{\bar{A}_{4}}^{\tensor{*}[^{1}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$
${u_{\bar{A}_{4}}^{A_{2}}}$ | $0$ | $0$ | $0$ | $-\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$
${u_{\bar{A}_{4}}^{B_{1}}}$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{A}_{4}}^{\tensor{*}[^{2}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$
${u_{A_{5}}^{A_{1}}}$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{A_{5}}^{B_{2}}}$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{A_{5}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}i$ | $0$ | $-\frac{1}{2}i$ | $-\frac{1}{2}i$ | $0$
${u_{A_{5}}^{\tensor{*}[^{1}]{B}{}_{2}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}i$ | $0$ | $-\frac{1}{2}i$ | $\frac{1}{2}i$ | $0$
${u_{A_{5}}^{\tensor{*}[^{2}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$
${u_{A_{5}}^{\tensor{*}[^{1}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}i$ | $0$
${u_{A_{5}}^{A_{2}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}i$ | $0$
${u_{A_{5}}^{B_{1}}}$ | $0$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{A_{5}}^{\tensor{*}[^{2}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$
${u_{\bar{A}_{5}}^{A_{1}}}$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{A}_{5}}^{B_{2}}}$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{A}_{5}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}i$ | $0$ | $-\frac{1}{2}i$ | $-\frac{1}{2}i$ | $0$
${u_{\bar{A}_{5}}^{\tensor{*}[^{1}]{B}{}_{2}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}i$ | $0$ | $-\frac{1}{2}i$ | $\frac{1}{2}i$ | $0$
${u_{\bar{A}_{5}}^{\tensor{*}[^{2}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$
${u_{\bar{A}_{5}}^{\tensor{*}[^{1}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$ | $\frac{1}{2}i$ | $0$
${u_{\bar{A}_{5}}^{A_{2}}}$ | $0$ | $0$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}i$ | $0$ | $\frac{1}{2}i$ | $-\frac{1}{2}i$ | $0$
${u_{\bar{A}_{5}}^{B_{1}}}$ | $0$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{A}_{5}}^{\tensor{*}[^{2}]{B}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$
${u_{\Lambda}^{A_{1}}}$ | $\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\Lambda}^{E}}$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$-\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\Lambda}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{3}$ | $0$ | $0$ | $0$
${u_{\Lambda}^{\tensor{*}[^{1}]{E}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$
$0$ | $0$ | $0$ | $-\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{3}$ | $0$ | $0$ | $0$
${u_{\Lambda}^{\tensor{*}[^{2}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{3}$
${u_{\Lambda}^{\tensor{*}[^{2}]{E}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$
$0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{3}$
${u_{\bar{\Lambda}}^{A_{1}}}$ | $-\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{\Lambda}}^{E}}$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{\Lambda}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{3}}{3}i$ | $\frac{\sqrt{3}}{3}i$ | $\frac{\sqrt{3}}{3}i$
${u_{\bar{\Lambda}}^{\tensor{*}[^{1}]{E}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $-\frac{\sqrt{2}}{2}i$ | $0$
$0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{6}}{6}i$ | $-\frac{\sqrt{6}}{6}i$ | $\frac{\sqrt{6}}{3}i$
${u_{\bar{\Lambda}}^{\tensor{*}[^{2}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{3}}{3}i$ | $\frac{\sqrt{3}}{3}i$ | $\frac{\sqrt{3}}{3}i$ | $0$ | $0$ | $0$
${u_{\bar{\Lambda}}^{\tensor{*}[^{2}]{E}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$ | $0$
$0$ | $0$ | $0$ | $\frac{\sqrt{6}}{6}i$ | $-\frac{\sqrt{6}}{6}i$ | $\frac{\sqrt{6}}{3}i$ | $0$ | $0$ | $0$
${u_{\Lambda_{1}}^{A_{1}}}$ | $\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\Lambda_{1}}^{E}}$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$-\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\Lambda_{1}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{3}}{3}i$ | $-\frac{\sqrt{3}}{3}i$ | $\frac{\sqrt{3}}{3}i$
${u_{\Lambda_{1}}^{\tensor{*}[^{1}]{E}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $\frac{\sqrt{2}}{2}i$ | $0$
$0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{6}}{6}i$ | $\frac{\sqrt{6}}{6}i$ | $\frac{\sqrt{6}}{3}i$
${u_{\Lambda_{1}}^{\tensor{*}[^{2}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{3}}{3}i$ | $-\frac{\sqrt{3}}{3}i$ | $\frac{\sqrt{3}}{3}i$ | $0$ | $0$ | $0$
${u_{\Lambda_{1}}^{\tensor{*}[^{2}]{E}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$ | $0$
$0$ | $0$ | $0$ | $-\frac{\sqrt{6}}{6}i$ | $\frac{\sqrt{6}}{6}i$ | $\frac{\sqrt{6}}{3}i$ | $0$ | $0$ | $0$
${u_{\bar{\Lambda}_{1}}^{A_{1}}}$ | $-\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{\Lambda}_{1}}^{E}}$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{\Lambda}_{1}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{3}$ | $0$ | $0$ | $0$
${u_{\bar{\Lambda}_{1}}^{\tensor{*}[^{1}]{E}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$
$0$ | $0$ | $0$ | $\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{3}$ | $0$ | $0$ | $0$
${u_{\bar{\Lambda}_{1}}^{\tensor{*}[^{2}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{3}$
${u_{\bar{\Lambda}_{1}}^{\tensor{*}[^{2}]{E}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$
$0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{3}$
${u_{\Lambda_{2}}^{A_{1}}}$ | $\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\Lambda_{2}}^{E}}$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\Lambda_{2}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{3}}{3}i$ | $\frac{\sqrt{3}}{3}i$ | $-\frac{\sqrt{3}}{3}i$
${u_{\Lambda_{2}}^{\tensor{*}[^{1}]{E}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $-\frac{\sqrt{2}}{2}i$ | $0$
$0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{6}}{6}i$ | $-\frac{\sqrt{6}}{6}i$ | $-\frac{\sqrt{6}}{3}i$
${u_{\Lambda_{2}}^{\tensor{*}[^{2}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{3}}{3}i$ | $\frac{\sqrt{3}}{3}i$ | $-\frac{\sqrt{3}}{3}i$ | $0$ | $0$ | $0$
${u_{\Lambda_{2}}^{\tensor{*}[^{2}]{E}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$ | $0$
$0$ | $0$ | $0$ | $-\frac{\sqrt{6}}{6}i$ | $-\frac{\sqrt{6}}{6}i$ | $-\frac{\sqrt{6}}{3}i$ | $0$ | $0$ | $0$
${u_{\bar{\Lambda}_{2}}^{A_{1}}}$ | $-\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{\Lambda}_{2}}^{E}}$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{\Lambda}_{2}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{3}$ | $0$ | $0$ | $0$
${u_{\bar{\Lambda}_{2}}^{\tensor{*}[^{1}]{E}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$
$0$ | $0$ | $0$ | $\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{3}$ | $0$ | $0$ | $0$
${u_{\bar{\Lambda}_{2}}^{\tensor{*}[^{2}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{3}$
${u_{\bar{\Lambda}_{2}}^{\tensor{*}[^{2}]{E}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$
$0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{3}$
${u_{\Lambda_{3}}^{A_{1}}}$ | $-\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\Lambda_{3}}^{E}}$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\Lambda_{3}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{3}$
${u_{\Lambda_{3}}^{\tensor{*}[^{1}]{E}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$
$0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{3}$
${u_{\Lambda_{3}}^{\tensor{*}[^{2}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{3}$ | $-\frac{\sqrt{3}}{3}$ | $0$ | $0$ | $0$
${u_{\Lambda_{3}}^{\tensor{*}[^{2}]{E}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$
$0$ | $0$ | $0$ | $\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{3}$ | $0$ | $0$ | $0$
${u_{\bar{\Lambda}_{3}}^{A_{1}}}$ | $\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{3}$ | $\frac{\sqrt{3}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{\Lambda}_{3}}^{E}}$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
$-\frac{\sqrt{6}}{6}$ | $-\frac{\sqrt{6}}{6}$ | $\frac{\sqrt{6}}{3}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{\Lambda}_{3}}^{\tensor{*}[^{1}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{3}}{3}i$ | $\frac{\sqrt{3}}{3}i$ | $\frac{\sqrt{3}}{3}i$ | $0$ | $0$ | $0$
${u_{\bar{\Lambda}_{3}}^{\tensor{*}[^{1}]{E}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$ | $0$
$0$ | $0$ | $0$ | $-\frac{\sqrt{6}}{6}i$ | $-\frac{\sqrt{6}}{6}i$ | $\frac{\sqrt{6}}{3}i$ | $0$ | $0$ | $0$
${u_{\bar{\Lambda}_{3}}^{\tensor{*}[^{2}]{A}{}_{1}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{3}}{3}i$ | $-\frac{\sqrt{3}}{3}i$ | $-\frac{\sqrt{3}}{3}i$
${u_{\bar{\Lambda}_{3}}^{\tensor{*}[^{2}]{E}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $\frac{\sqrt{2}}{2}i$ | $0$
$0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{6}}{6}i$ | $\frac{\sqrt{6}}{6}i$ | $-\frac{\sqrt{6}}{3}i$
${u_{B}^{A}}$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B}^{B}}$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B}^{\tensor{*}[^{1}]{A}}}$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$
${u_{B}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$
${u_{B}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$
${u_{B}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$
${u_{B}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$
${u_{B}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1$
${u_{\bar{B}}^{A}}$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}}^{B}}$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}}^{\tensor{*}[^{1}]{A}}}$ | $0$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $-\frac{\sqrt{2}}{2}i$ | $0$
${u_{\bar{B}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $\frac{\sqrt{2}}{2}i$ | $0$
${u_{\bar{B}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1i$
${u_{\bar{B}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1i$ | $0$ | $0$ | $0$
${u_{B_{1}}^{A}}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{1}}^{B}}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{1}}^{\tensor{*}[^{1}]{A}}}$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{1}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$
${u_{B_{1}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$
${u_{B_{1}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$
${u_{B_{1}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $\frac{\sqrt{2}}{2}$
${u_{B_{1}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $\frac{\sqrt{2}}{2}$
${u_{B_{1}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1$ | $0$
${u_{\bar{B}_{1}}^{A}}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{1}}^{B}}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{1}}^{\tensor{*}[^{1}]{A}}}$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{1}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $\frac{\sqrt{2}}{2}i$
${u_{\bar{B}_{1}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $\frac{\sqrt{2}}{2}i$
${u_{\bar{B}_{1}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1i$ | $0$
${u_{\bar{B}_{1}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$
${u_{\bar{B}_{1}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$
${u_{\bar{B}_{1}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $1i$ | $0$ | $0$ | $0$ | $0$
${u_{B_{2}}^{A}}$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{2}}^{B}}$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{2}}^{\tensor{*}[^{1}]{A}}}$ | $0$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{2}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$ | $0$
${u_{B_{2}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$ | $0$
${u_{B_{2}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-1i$ | $0$ | $0$ | $0$
${u_{B_{2}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $-\frac{\sqrt{2}}{2}i$ | $0$
${u_{B_{2}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $\frac{\sqrt{2}}{2}i$ | $0$
${u_{B_{2}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1i$
${u_{\bar{B}_{2}}^{A}}$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{2}}^{B}}$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{2}}^{\tensor{*}[^{1}]{A}}}$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{2}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$
${u_{\bar{B}_{2}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$
${u_{\bar{B}_{2}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1$
${u_{\bar{B}_{2}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{2}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{2}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-1$ | $0$ | $0$ | $0$
${u_{B_{3}}^{A}}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{3}}^{B}}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{3}}^{\tensor{*}[^{1}]{A}}}$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{3}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$
${u_{B_{3}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$
${u_{B_{3}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $-1i$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{3}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $-\frac{\sqrt{2}}{2}i$
${u_{B_{3}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $\frac{\sqrt{2}}{2}i$
${u_{B_{3}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1i$ | $0$ | $0$
${u_{\bar{B}_{3}}^{A}}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{3}}^{B}}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{3}}^{\tensor{*}[^{1}]{A}}}$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{3}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$
${u_{\bar{B}_{3}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$
${u_{\bar{B}_{3}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1$ | $0$ | $0$
${u_{\bar{B}_{3}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$
${u_{\bar{B}_{3}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$
${u_{\bar{B}_{3}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{4}}^{A}}$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{4}}^{B}}$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{4}}^{\tensor{*}[^{1}]{A}}}$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{4}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $\frac{\sqrt{2}}{2}i$ | $0$
${u_{B_{4}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $-\frac{\sqrt{2}}{2}i$ | $0$
${u_{B_{4}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1i$
${u_{B_{4}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$ | $0$
${u_{B_{4}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$ | $0$
${u_{B_{4}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1i$ | $0$ | $0$ | $0$
${u_{\bar{B}_{4}}^{A}}$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{4}}^{B}}$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{4}}^{\tensor{*}[^{1}]{A}}}$ | $0$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{4}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{4}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{4}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$
${u_{\bar{B}_{4}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$
${u_{\bar{B}_{4}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$
${u_{\bar{B}_{4}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1$
${u_{B_{5}}^{A}}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{5}}^{B}}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{5}}^{\tensor{*}[^{1}]{A}}}$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{5}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$
${u_{B_{5}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$
${u_{B_{5}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $-1i$ | $0$ | $0$ | $0$ | $0$
${u_{B_{5}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $-\frac{\sqrt{2}}{2}i$
${u_{B_{5}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $-\frac{\sqrt{2}}{2}i$
${u_{B_{5}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1i$ | $0$
${u_{\bar{B}_{5}}^{A}}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{5}}^{B}}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{5}}^{\tensor{*}[^{1}]{A}}}$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{5}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $-\frac{\sqrt{2}}{2}$
${u_{\bar{B}_{5}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $-\frac{\sqrt{2}}{2}$
${u_{\bar{B}_{5}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1$ | $0$
${u_{\bar{B}_{5}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$
${u_{\bar{B}_{5}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$
${u_{\bar{B}_{5}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$
${u_{B_{6}}^{A}}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{6}}^{B}}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{6}}^{\tensor{*}[^{1}]{A}}}$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{6}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $\frac{\sqrt{2}}{2}i$
${u_{B_{6}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $-\frac{\sqrt{2}}{2}i$
${u_{B_{6}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1i$ | $0$ | $0$
${u_{B_{6}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$
${u_{B_{6}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$
${u_{B_{6}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $1i$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{6}}^{A}}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{6}}^{B}}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{6}}^{\tensor{*}[^{1}]{A}}}$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{6}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$
${u_{\bar{B}_{6}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$
${u_{\bar{B}_{6}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{6}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$
${u_{\bar{B}_{6}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$
${u_{\bar{B}_{6}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1$ | $0$ | $0$
${u_{B_{7}}^{A}}$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{7}}^{B}}$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{7}}^{\tensor{*}[^{1}]{A}}}$ | $0$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{7}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $\frac{\sqrt{2}}{2}i$ | $0$
${u_{B_{7}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $-\frac{\sqrt{2}}{2}i$ | $0$
${u_{B_{7}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1i$
${u_{B_{7}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$ | $0$
${u_{B_{7}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$ | $0$
${u_{B_{7}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1i$ | $0$ | $0$ | $0$
${u_{\bar{B}_{7}}^{A}}$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{7}}^{B}}$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{7}}^{\tensor{*}[^{1}]{A}}}$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{7}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{7}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{7}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$
${u_{\bar{B}_{7}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$
${u_{\bar{B}_{7}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$
${u_{\bar{B}_{7}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1$
${u_{B_{8}}^{A}}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{8}}^{B}}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{8}}^{\tensor{*}[^{1}]{A}}}$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{8}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$
${u_{B_{8}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$
${u_{B_{8}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$
${u_{B_{8}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $-\frac{\sqrt{2}}{2}$
${u_{B_{8}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $-\frac{\sqrt{2}}{2}$
${u_{B_{8}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1$ | $0$
${u_{\bar{B}_{8}}^{A}}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{8}}^{B}}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{8}}^{\tensor{*}[^{1}]{A}}}$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{8}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $-\frac{\sqrt{2}}{2}i$
${u_{\bar{B}_{8}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $-\frac{\sqrt{2}}{2}i$
${u_{\bar{B}_{8}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1i$ | $0$
${u_{\bar{B}_{8}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$
${u_{\bar{B}_{8}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$
${u_{\bar{B}_{8}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $1i$ | $0$ | $0$ | $0$ | $0$
${u_{B_{9}}^{A}}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{9}}^{B}}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{9}}^{\tensor{*}[^{1}]{A}}}$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{9}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$
${u_{B_{9}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$
${u_{B_{9}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$
${u_{B_{9}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $\frac{\sqrt{2}}{2}$
${u_{B_{9}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $0$ | $\frac{\sqrt{2}}{2}$
${u_{B_{9}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1$ | $0$
${u_{\bar{B}_{9}}^{A}}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{9}}^{B}}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{9}}^{\tensor{*}[^{1}]{A}}}$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{9}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $\frac{\sqrt{2}}{2}i$
${u_{\bar{B}_{9}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $\frac{\sqrt{2}}{2}i$
${u_{\bar{B}_{9}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1i$ | $0$
${u_{\bar{B}_{9}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$
${u_{\bar{B}_{9}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$
${u_{\bar{B}_{9}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $1i$ | $0$ | $0$ | $0$ | $0$
${u_{B_{10}}^{A}}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{10}}^{B}}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{10}}^{\tensor{*}[^{1}]{A}}}$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{10}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$
${u_{B_{10}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$
${u_{B_{10}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{10}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$
${u_{B_{10}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$
${u_{B_{10}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1$ | $0$ | $0$
${u_{\bar{B}_{10}}^{A}}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{10}}^{B}}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{10}}^{\tensor{*}[^{1}]{A}}}$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{10}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $-\frac{\sqrt{2}}{2}i$
${u_{\bar{B}_{10}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $\frac{\sqrt{2}}{2}i$
${u_{\bar{B}_{10}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1i$ | $0$ | $0$
${u_{\bar{B}_{10}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$
${u_{\bar{B}_{10}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $\frac{\sqrt{2}}{2}i$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$
${u_{\bar{B}_{10}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $1i$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{11}}^{A}}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{11}}^{B}}$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{11}}^{\tensor{*}[^{1}]{A}}}$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{11}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$
${u_{B_{11}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$
${u_{B_{11}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{B_{11}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$
${u_{B_{11}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$
${u_{B_{11}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1$ | $0$ | $0$
${u_{\bar{B}_{11}}^{A}}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $-\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{11}}^{B}}$ | $0$ | $\frac{\sqrt{2}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{11}}^{\tensor{*}[^{1}]{A}}}$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$
${u_{\bar{B}_{11}}^{\tensor{*}[^{2}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $\frac{\sqrt{2}}{2}i$
${u_{\bar{B}_{11}}^{\tensor{*}[^{1}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $-\frac{\sqrt{2}}{2}i$
${u_{\bar{B}_{11}}^{\tensor{*}[^{3}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1i$ | $0$ | $0$
${u_{\bar{B}_{11}}^{\tensor{*}[^{4}]{A}}}$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$
${u_{\bar{B}_{11}}^{\tensor{*}[^{2}]{B}}}$ | $0$ | $0$ | $0$ | $0$ | $-\frac{\sqrt{2}}{2}i$ | $-\frac{\sqrt{2}}{2}i$ | $0$ | $0$ | $0$
${u_{\bar{B}_{11}}^{\tensor{*}[^{5}]{A}}}$ | $0$ | $0$ | $0$ | $1i$ | $0$ | $0$ | $0$ | $0$ | $0$

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