**Appendix A**

(1) The unknown functions *g*0 *i* (*Z*) and *f* 0 *i* (*Z*) (*i* = 1, 2, 3): From Equations (27) and (33), we can obtain the unknown functions *g*0 *i*(*Z*) and *f* 0 *i*(*Z*) (*i* = 1, 2, 3),

$$\begin{cases} \begin{aligned} \mathcal{g}\_1^0(Z) &= B\_1^0 Z + B\_2^0 \\ \mathcal{g}\_2^0(Z) &= B\_3^0 Z + B\_4^0 \\ \mathcal{g}\_3^0(Z) &= -\frac{1}{3\overline{\lambda}\_{33}} B\_1^0 Z^3 - \frac{1}{\overline{\lambda}\_{33}} B\_2^0 Z^2 + B\_5^0 Z + B\_6^0 \end{aligned} \end{cases} \tag{A1}$$

and

$$\begin{cases} \begin{aligned} f\_1^0(Z) &= \frac{1}{6} \mathcal{C}\_1^0 Z^3 + \frac{1}{2} \mathcal{C}\_2^0 Z^2 + \mathcal{C}\_3^0 Z + \mathcal{C}\_4^0 \\\ f\_2^0(Z) &= \frac{1}{6} \mathcal{C}\_5^0 Z^3 + \frac{1}{2} \mathcal{C}\_6^0 Z^2 + \mathcal{C}\_7^0 Z + \mathcal{C}\_8^0 \\\ f\_3^0(Z) &= -\frac{1}{120} (2\mathcal{S}\_{13} + \mathcal{S}\_{44}) \mathcal{C}\_1^0 Z^5 - \frac{1}{24} (2\mathcal{S}\_{13} + \mathcal{S}\_{44}) \mathcal{C}\_2^0 Z^4 \\\ + \frac{1}{6} \mathcal{C}\_9^0 Z^3 + \frac{1}{2} \mathcal{C}\_{10}^0 Z^2 + \mathcal{C}\_{11}^0 Z + \mathcal{C}\_{12}^0 \end{aligned} \tag{A2}$$

where *B*<sup>0</sup> *i* (*i* = 1, 2, 3, ... , 6) and *C*<sup>0</sup> *i* (*i* = 1, 2, 3, ... , 12) are undetermined constants which can be determined by Equations (28)–(32),

$$\begin{aligned} \mathbf{C}\_1^0 &= -12\overline{\boldsymbol{\eta}}, \mathbf{C}\_2^0 = \mathbf{0}, \mathbf{C}\_3^0 = \frac{3}{2}\overline{\boldsymbol{\eta}}, \mathbf{C}\_4^0 = -\frac{\overline{\boldsymbol{\eta}}}{2}, \mathbf{C}\_5^0 = -\frac{12\overline{\boldsymbol{\eta}}}{\overline{\boldsymbol{b}}}, \mathbf{C}\_6^0 = \mathbf{0},\\ \mathbf{C}\_7^0 &= \frac{3}{2}\frac{\overline{\boldsymbol{\eta}}}{\overline{\boldsymbol{b}}}, \mathbf{C}\_9^0 = \frac{12\overline{\boldsymbol{\eta}}}{\overline{\boldsymbol{b}}} - \frac{3}{10}(2\mathbf{S}\_{13} + \mathbf{S}\_{44})\overline{\boldsymbol{\eta}}, \mathbf{C}\_{10}^0 = \mathbf{0} \end{aligned} \tag{A3}$$

$$B\_1^0 = 0, B\_2^0 = 0, B\_3^0 = 0, B\_5^0 = 0. \tag{A4}$$

(2) The unknown functions *g*I *i*(Z) and *f* I *i*(Z) (i = 1,2,3,. . . ,9):

 From Equations (34)–(36) and (42), we can obtain the unknown functions *g*I *i* (*Z*) and *f* I *i* (*Z*) (*i* = 1, 2, 3, ... , 9),

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩*g*I 1(*Z*) = 1 4λ33 *C*<sup>0</sup> 1*Z*<sup>2</sup> + *B*I 1*Z* + *B*I 2 *g*I 2(*Z*) = 1 2λ33 *C*<sup>0</sup> 5*Z*<sup>2</sup> + *B*I 3*Z* + *B*I 4 *g*I 3(*Z*) = − 1 <sup>24</sup>(<sup>λ</sup>33) 2 *C*<sup>0</sup> 1*Z*<sup>4</sup> − 1 3λ33 *B*I 1*Z*<sup>3</sup> − 1 λ33 *B*I 2*Z*<sup>2</sup> − (2*S*13+*S*44) 24λ33 *C*<sup>0</sup> 1*Z*<sup>4</sup> −(2*S*13+*S*44) 6λ33 *C*<sup>0</sup> 2*Z*<sup>3</sup> + 1 2λ33 *C*<sup>0</sup> 9*Z*<sup>2</sup> + *B*I 5*Z* + *B*I 6 *g*I 6(*Z*) = − 1 3λ33 *B*I 7*Z*<sup>3</sup> − 1 λ33 *B*I 8*Z*<sup>2</sup> + *C*<sup>0</sup> 1 24λ33 *Z*<sup>4</sup> + *C*<sup>0</sup> 2 6λ33 *Z*<sup>3</sup> + *C*<sup>0</sup> 3 2λ33 *Z*<sup>2</sup> + *B*I11 *Z* + *B*I12 *g*I 9(*Z*) = − 1 3λ33 *B*I13 *Z*<sup>3</sup> − 1 λ33 *B*I14 *Z*<sup>2</sup> − *C*<sup>0</sup> 1 24λ33 *Z*<sup>4</sup> − *C*<sup>0</sup> 2 6λ33 *Z*<sup>3</sup> − *C*<sup>0</sup> 3 2λ33 *Z*<sup>2</sup> + *B*I17 *Z* + *B*I18 , (A5) *g*I *i* (*Z*) = *B*I <sup>2</sup>*i*−1*<sup>Z</sup>* + *B*I 2*i* (*i* = 4, 5, 7, <sup>8</sup>), (A6) 1 1

$$f\_i^1(Z) = \frac{1}{6} \mathcal{C}\_{4i-3}^1 Z^3 + \frac{1}{2} \mathcal{C}\_{4i-2}^1 Z^2 + \mathcal{C}\_{4i-1}^1 Z + \mathcal{C}\_{4i}^1 (i = 1, 2, 4, 5, 7, 8), \tag{A7}$$

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

$$\begin{cases} \begin{array}{l} f\_{3}^{1}(Z) = -\frac{(2S\_{13}+S\_{44})}{120} \mathbf{C}\_{1}^{1} Z^{5} - \frac{(2S\_{13}+S\_{44})}{24} \mathbf{C}\_{2}^{1} Z^{4} - \frac{1}{12\bar{\lambda}\_{33}} B\_{1}^{0} Z^{4} \\ \quad + \frac{1}{6} \mathbf{C}\_{9}^{1} Z^{3} + \frac{1}{2} \mathbf{C}\_{10}^{1} Z^{2} + \mathbf{C}\_{11}^{1} Z + \mathbf{C}\_{12}^{1} \\ \quad f\_{6}^{1}(Z) = -\frac{(2S\_{13}+S\_{44})}{120} \mathbf{C}\_{13}^{1} Z^{5} - \frac{(2S\_{13}+S\_{44})}{24} \mathbf{C}\_{14}^{1} Z^{4} + \frac{1}{12} B\_{1}^{0} Z^{4} \\ \quad + \frac{1}{6} \mathbf{C}\_{12}^{1} Z^{3} + \frac{1}{2} \mathbf{C}\_{22}^{1} Z^{2} + \mathbf{C}\_{23}^{1} Z + \mathbf{C}\_{24}^{1} \\ \quad f\_{9}^{1}(Z) = -\frac{(2S\_{13}+S\_{44})}{120} \mathbf{C}\_{25}^{1} Z^{5} - \frac{(2S\_{13}+S\_{44})}{24} \mathbf{C}\_{26}^{1} Z^{4} - \frac{B\_{1}^{0}}{12} Z^{4} \\ \quad + \frac{1}{6} \mathbf{C}\_{33}^{1} Z^{3} + \frac{1}{2} \mathbf{C}\_{34}^{1} Z^{2} + \mathbf{C}\_{35}^{1} Z + \mathbf{C}\_{36}^{1} \end{array} \tag{A8}$$

where *B*I *i* (*i* = 1, 2, 3, ... , 18) and *C*I *i* (*i* = 1, 2, 3, ... , 36) are undetermined constants which can be determined by Equations (37)–(41),

$$\mathbf{C}\_1^\mathrm{l} = 0, \mathbf{C}\_2^\mathrm{l} = 0, \mathbf{C}\_3^\mathrm{l} = 0, \mathbf{C}\_4^\mathrm{l} = 0, \mathbf{C}\_5^\mathrm{l} = 0, \mathbf{C}\_6^\mathrm{l} = 0, \mathbf{C}\_7^\mathrm{l} = 0, \mathbf{C}\_9^\mathrm{l} = 0, \mathbf{C}\_{10}^\mathrm{l} = \frac{1}{12\overline{\lambda}\_{33}} \mathbf{B}\_{1'}^\mathrm{l} \tag{A9}$$

$$B\_1^\mathrm{I} = \frac{\mathcal{C}\_2^0}{2\overline{\lambda}\_{33}}, B\_2^\mathrm{I} = -\frac{\mathcal{C}\_1^0}{48\overline{\lambda}\_{33}}, B\_3^\mathrm{I} = \frac{\mathcal{C}\_6^0}{\overline{\lambda}\_{33}}, B\_4^\mathrm{I} = -\frac{\mathcal{C}\_5^0}{24\overline{\lambda}\_{33}}, B\_5^\mathrm{I} = \frac{\mathcal{C}\_{10}^0}{\overline{\lambda}\_{33}} + \frac{\mathcal{C}\_2^0}{8(\overline{\lambda}\_{33})^2},\tag{A10}$$

$$\mathbf{C}\_{13}^{\mathbf{I}} = 0, \mathbf{C}\_{14}^{\mathbf{I}} = 0, \mathbf{C}\_{15}^{\mathbf{I}} = 0, \mathbf{C}\_{16}^{\mathbf{I}} = 0, \mathbf{C}\_{17}^{\mathbf{I}} = 0, \mathbf{C}\_{18}^{\mathbf{I}} = 0, \mathbf{C}\_{19}^{\mathbf{I}} = 0, \mathbf{C}\_{21}^{\mathbf{I}} = 0, \mathbf{C}\_{22}^{\mathbf{I}} = -\frac{1}{12} B\_{1\prime}^{0} \tag{A11}$$

$$B\_7^\mathrm{I} = 0, B\_8^\mathrm{I} = 0, B\_9^\mathrm{I} = 0, B\_{10}^\mathrm{I} = 0, B\_{11}^\mathrm{I} = \frac{C\_4^0}{\overline{\lambda}\_{33}},\tag{A12}$$

$$\mathbf{C}\_{25}^{\mathrm{I}} = 0, \mathbf{C}\_{26}^{\mathrm{I}} = 0, \mathbf{C}\_{27}^{\mathrm{I}} = 0, \mathbf{C}\_{28}^{\mathrm{I}} = 0, \mathbf{C}\_{29}^{\mathrm{I}} = 0, \mathbf{C}\_{30}^{\mathrm{I}} = 0, \mathbf{C}\_{31}^{\mathrm{I}} = 0, \mathbf{C}\_{33}^{\mathrm{I}} = 0, \mathbf{C}\_{34}^{\mathrm{I}} = \frac{B\_{1}^{0}}{12},\tag{A13}$$

$$B^{\rm I}\_{13} = 0,\\ B^{\rm I}\_{14} = -\frac{1}{48} \mathcal{C}^{0}\_{1} - \frac{1}{2} \mathcal{C}^{0}\_{3'}\\ B^{\rm I}\_{15} = 0,\\ B^{\rm I}\_{16} = -\frac{1}{24} \mathcal{C}^{0}\_{5} - \mathcal{C}^{0}\_{7'}\\ B^{\rm I}\_{17} = \frac{\mathcal{C}^{0}\_{2}}{8\overline{\lambda}\_{33}}.\tag{A14}$$

(3) The unknown functions *g*II *i* (Z) and *f* II *i*(Z) ( i = 1,2,3,. . . ,18):

From Equations (43)–(48) and (54), we may obtain the unknown functions of *g*II *i* (*Z*) and *f* II *i* (*Z*) (*i* = 1, 2, 3, ... , 18), 

$$\begin{cases} \mathbf{g}\_i^{\text{II}}(Z) = \mathbf{K}\_i Z^2 + B\_{2i-1}^{\text{II}} Z + B\_{2i}^{\text{II}} (i = 1, 2, 10, 11, 13, 14) \\\ \mathbf{g}\_i^{\text{II}}(Z) = B\_{2i-1}^{\text{II}} Z + B\_{2i}^{\text{II}} (i = 4, 5, 7, 8, 16, 17) \end{cases} \tag{A15}$$

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩*g*II 3 (*Z*) = − *C*I 1 <sup>24</sup>(<sup>λ</sup>33) 2 *Z*<sup>4</sup> − 1 3λ33 *B*II 1 *Z*<sup>3</sup> − 1 λ33 *B*II 2 *Z*<sup>2</sup> − (2*S*13+*S*44) 24λ33 *C*I 1*Z*<sup>4</sup> −(2*S*13+*S*44) 6λ33 *C*I 2*Z*<sup>3</sup> − 1 <sup>3</sup>(<sup>λ</sup>33) 2 *B*<sup>0</sup> 1*Z*<sup>3</sup> + 1 2λ33 *C*I 9*Z*<sup>2</sup> + *B*II 5 *Z* + *B*II 6 *g*II 6 (*Z*) = − 1 3λ33 *B*II 7 *Z*<sup>3</sup> − 1 λ33 *B*II 8 *Z*<sup>2</sup> + 1 24λ33 *C*I13 *Z*<sup>4</sup> + 1 6λ33 *C*I14 *Z*<sup>3</sup> + 1 2λ33 *C*I15 *Z*<sup>2</sup> + *B*II11 *Z* + *B*II12 *g*II 9 (*Z*) = − 1 3λ33 *B*II13 *Z*<sup>3</sup> − 1 λ33 *B*II14 *Z*<sup>2</sup> − 1 24λ33 *C*I25 *Z*<sup>4</sup> − *C*I26 6λ33 *Z*<sup>3</sup> − *C*I27 2λ33 *Z*<sup>2</sup> + *B*II17 *Z* + *B*II18 *g*II12(*Z*) = − *C*I13 <sup>24</sup>(<sup>λ</sup>33) 2 *Z*<sup>4</sup> − 1 3λ33 *B*II19 *Z*<sup>3</sup> − 1 λ33 *B*II20 *Z*<sup>2</sup> + 1 24λ33 *C*I 1*Z*<sup>4</sup> + 1 6λ33 *C*I 2*Z*<sup>3</sup> + 1 2λ33 *C*I 3*Z*<sup>2</sup> −(2*S*13+*S*44) 24λ33 *C*I13 *Z*<sup>4</sup> − (2*S*13+*S*44) 6λ33 *C*I14 *Z*<sup>3</sup> + 1 3λ33 *B*<sup>0</sup> 1*Z*<sup>3</sup> + 1 2λ33 *C*I21 *Z*<sup>2</sup> + *B*II23 *Z* + *B*II24 *g*II15(*Z*) = − *C*I25 <sup>24</sup>(<sup>λ</sup>33) 2 *Z*<sup>4</sup> − 1 3λ33 *B*II25 *Z*<sup>3</sup> − 1 λ33 *B*II26 *Z*<sup>2</sup> − (2*S*13+*S*44) 24λ33 *C*I25 *Z*<sup>4</sup> − (2*S*13+*S*44) 6λ33 *C*I26 *Z*<sup>3</sup> − 1 3λ33 *B*<sup>0</sup> 1*Z*<sup>3</sup> + *C*I33 2λ33 *Z*<sup>2</sup> − 1 24λ33 *C*I 1*Z*<sup>4</sup> − *C*I 2 6λ33 *Z*<sup>3</sup> − *C*I 3 2λ33 *Z*<sup>2</sup> + *B*II29 *Z* + *B*II30 *g*II18(*Z*) = − 1 3λ33 *B*II31 *Z*<sup>3</sup> − 1 λ33 *B*II32 *Z*<sup>2</sup> + *C*I25 24λ33 *Z*<sup>4</sup> + *C*I26 6λ33 *Z*<sup>3</sup> + *C*I27 2λ33 *Z*<sup>2</sup> − *C*I13 24λ33 *Z*<sup>4</sup> − *C*I14 6λ33 *Z*<sup>3</sup> − *C*I15 2λ33 *Z*<sup>2</sup> + *B*II35 *Z* + *B*II36 , (A16)

$$\begin{array}{l} f\_i^{\Pi}(Z) = \frac{1}{6} \mathcal{C}\_{4i-3}^{\Pi} Z^3 + \frac{1}{2} \mathcal{C}\_{4i-2}^{\Pi} Z^2 + \mathcal{C}\_{4i-1}^{\Pi} Z \\ + \mathcal{C}\_{4i}^{\Pi}(i = 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17) \end{array} \tag{A17}$$

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩*f* II 3 (*Z*) = −(2*S*13+*S*44) 120 *C*II1 *Z*<sup>5</sup> − (2*S*13+*S*44) 24 *C*II2 *Z*<sup>4</sup> − *C*01 <sup>120</sup>(<sup>λ</sup>33)<sup>2</sup> *Z*<sup>5</sup> − 1 12λ33 *B*I1*Z*<sup>4</sup> −(2*S*13+*S*44) 120λ33 *C*01*Z*<sup>5</sup> − (2*S*13+*S*44) 24λ33 *C*02*Z*<sup>4</sup> + 16*C*II9 *Z*<sup>3</sup> + 12*C*II10*Z*<sup>2</sup> + *C*II11*Z* + *C*II12 *f* II 6 (*Z*) = −(2*S*13+*S*44) 120 *C*II13*Z*<sup>5</sup> − (2*S*13+*S*44) 24 *C*II14*Z*<sup>4</sup> + 112*B*I7*Z*<sup>4</sup> +16*C*II21*Z*<sup>3</sup> + 12*C*II22*Z*<sup>2</sup> + *C*II23*Z* + *C*II24 *f* II 9 (*Z*) = −(2*S*13+*S*44) 120 *C*II25*Z*<sup>5</sup> − (2*S*13+*S*44) 24 *C*II26*Z*<sup>4</sup> − 112*B*I13*Z*<sup>4</sup> +16*C*II33*Z*<sup>3</sup> + 12*C*II34*Z*<sup>2</sup> + *C*II35*Z* + *C*II36 *f* II 12(*Z*) = −(2*S*13+*S*44) 120 *C*II37*Z*<sup>5</sup> − (2*S*13+*S*44) 24 *C*II38*Z*<sup>4</sup> − 1 12λ33 *B*I7*Z*<sup>4</sup> + *C*01 60λ33 *Z*<sup>5</sup> + *C*02 24λ33 *Z*<sup>4</sup> + 112*B*I1*Z*<sup>4</sup> + 16*C*II45*Z*<sup>3</sup> + 12*C*II46*Z*<sup>2</sup> + *C*II47*Z* + *C*II48 *f* II 15(*Z*) = −(2*S*13+*S*44) 120 *C*II49*Z*<sup>5</sup> − (2*S*13+*S*44) 24 *C*II50*Z*<sup>4</sup> − 1 12λ33 *B*I13*Z*<sup>4</sup> − *C*01 60λ33 *Z*<sup>5</sup> − *C*02 24λ33 *Z*<sup>4</sup> − 112*B*I1*Z*<sup>4</sup> + 16*C*II57*Z*<sup>3</sup> + 12*C*II58*Z*<sup>2</sup> + *C*II59*Z* + *C*II60 *f* II 18(*Z*) = −(2*S*13+*S*44) 120 *C*II61*Z*<sup>5</sup> − (2*S*13+*S*44) 24 *C*II62*Z*<sup>4</sup> + 112*B*I13*Z*<sup>4</sup> − 112*B*I7*Z*<sup>4</sup> + 16*C*II69*Z*<sup>3</sup> + 12*C*II70*Z*<sup>2</sup> + *C*II71*Z* + *C*II72 , (A18)

20λ33

12λ33

$$K\_1 = \frac{\mathcal{C}\_1^1}{4\overline{\lambda}\_{33}}, K\_2 = \frac{\mathcal{C}\_5^1}{2\overline{\lambda}\_{33}}, K\_{10} = \frac{\mathcal{C}\_{13}^1}{4\overline{\lambda}\_{33}}, K\_{11} = \frac{\mathcal{C}\_{17}^1}{2\overline{\lambda}\_{33}}, K\_{13} = \frac{\mathcal{C}\_{25}^1}{4\overline{\lambda}\_{33}}, K\_{14} = \frac{\mathcal{C}\_{29}^1}{2\overline{\lambda}\_{33}}\tag{A19}$$

where *B*II*i* (*i* = 1, 2, 3, ... , 36) and *C*II*i* (*i* = 1, 2, 3, ... , 72) are undetermined constants which can be determined by Equations (49)–(53),

$$\begin{aligned} \mathbf{C}\_{1}^{\Pi} &= 0, \mathbf{C}\_{2}^{\Pi} = 0, \mathbf{C}\_{3}^{\Pi} = 0, \mathbf{C}\_{4}^{\Pi} = 0, \mathbf{C}\_{5}^{\Pi} = 0, \mathbf{C}\_{6}^{\Pi} = 0, \mathbf{C}\_{7}^{\Pi} = 0, \\ \mathbf{C}\_{9}^{\Pi} &= \frac{1}{40(\overline{\lambda}\_{33})} \mathbf{C}\_{1}^{0} + \frac{(2S\_{13} + S\_{44})}{40\overline{\lambda}\_{33}} \mathbf{C}\_{1}^{0}, \mathbf{C}\_{10}^{\Pi} = \frac{1}{12\overline{\lambda}\_{33}} B\_{1}^{1} + \frac{(2S\_{13} + S\_{44})}{24\overline{\lambda}\_{33}} \mathbf{C}\_{2}^{0} \end{aligned} \tag{A20}$$

$$B\_1^{\Pi} = \frac{\mathcal{C}\_2^{\mathcal{I}}}{2\overline{\lambda}\_{33}}, B\_2^{\Pi} = -\frac{\mathcal{C}\_1^{\mathcal{I}}}{48\overline{\lambda}\_{33}}, B\_3^{\Pi} = \frac{\mathcal{C}\_6^{\mathcal{I}}}{\overline{\lambda}\_{33}}, B\_4^{\Pi} = -\frac{\mathcal{C}\_5^{\mathcal{I}}}{24\overline{\lambda}\_{33}}, B\_5^{\Pi} = \frac{\mathcal{C}\_{10}^{\mathcal{I}}}{\overline{\lambda}\_{33}} + \frac{\mathcal{C}\_2^{\mathcal{I}}}{8(\overline{\lambda}\_{33})^2} \tag{A21}$$

$$\mathbf{C}\_{13}^{\mathrm{II}} = 0, \mathbf{C}\_{14}^{\mathrm{II}} = 0, \mathbf{C}\_{15}^{\mathrm{II}} = 0, \mathbf{C}\_{16}^{\mathrm{II}} = 0, \mathbf{C}\_{17}^{\mathrm{II}} = 0, \mathbf{C}\_{18}^{\mathrm{II}} = 0, \mathbf{C}\_{19}^{\mathrm{II}} = 0, \mathbf{C}\_{21}^{\mathrm{II}} = 0, \mathbf{C}\_{22}^{\mathrm{II}} = -\frac{1}{12} B\_{7'}^{\mathrm{I}} \tag{A.22}$$

$$B\_7^{\text{II}} = 0, B\_8^{\text{II}} = 0, B\_9^{\text{II}} = 0, B\_{10}^{\text{II}} = 0, B\_{11}^{\text{II}} = \frac{C\_{16}^{\text{I}}}{\overline{\lambda}\_{33}},\tag{A23}$$

$$\mathbf{C\_{25}^{\mathrm{II}}} = 0, \mathbf{C\_{26}^{\mathrm{II}}} = 0, \mathbf{C\_{27}^{\mathrm{II}}} = 0, \mathbf{C\_{28}^{\mathrm{II}}} = 0, \mathbf{C\_{29}^{\mathrm{II}}} = 0, \mathbf{C\_{30}^{\mathrm{II}}} = 0, \mathbf{C\_{31}^{\mathrm{II}}} = 0, \mathbf{C\_{33}^{\mathrm{II}}} = 0, \mathbf{C\_{34}^{\mathrm{II}}} = \frac{1}{12} \mathbf{B\_{13}^{\mathrm{I}}} \tag{A24}$$

$$\mathbf{B}\_{13}^{\mathrm{II}} = 0, \mathbf{B}\_{14}^{\mathrm{II}} = -\frac{1}{48} \mathbf{C}\_{25}^{\mathrm{I}} - \frac{1}{2} \mathbf{C}\_{27}^{\mathrm{I}}, \mathbf{B}\_{15}^{\mathrm{II}} = 0, \mathbf{B}\_{16}^{\mathrm{II}} = -\frac{1}{24} \mathbf{C}\_{29}^{\mathrm{I}} - \mathbf{C}\_{31}^{\mathrm{I}}, \mathbf{B}\_{17}^{\mathrm{II}} = \frac{\mathbf{C}\_{26}^{\mathrm{I}}}{8\overline{\lambda}\_{33}}, \tag{A25}$$

$$\begin{aligned} \mathbf{C}\_{37}^{\mathrm{II}} &= 0, \mathbf{C}\_{38}^{\mathrm{II}} = 0, \mathbf{C}\_{39}^{\mathrm{II}} = 0, \mathbf{C}\_{40}^{\mathrm{II}} = 0, \mathbf{C}\_{41}^{\mathrm{II}} = 0, \mathbf{C}\_{42}^{\mathrm{II}} = 0, \mathbf{C}\_{43}^{\mathrm{II}} = 0, \\ \mathbf{C}\_{45}^{\mathrm{II}} &= -\frac{\mathbf{C}\_{1}^{\mathrm{0}}}{20\overline{\lambda}\omega}, \mathbf{C}\_{46}^{\mathrm{II}} = \frac{1}{12\overline{\lambda}\omega} \mathbf{B}\_{7}^{\mathrm{I}} - \frac{\mathbf{C}\_{2}^{\mathrm{0}}}{24\overline{\lambda}\omega} - \frac{1}{12} \mathbf{B}\_{1}^{\mathrm{I}} \end{aligned} \tag{A26}$$

$$B\_{19}^{\text{II}} = \frac{\mathbf{C}\_{14}^{\text{I}}}{2\overline{\lambda}\_{33}}, B\_{20}^{\text{II}} = -\frac{\mathbf{C}\_{13}^{\text{I}}}{48\overline{\lambda}\_{33}}, B\_{21}^{\text{II}} = \frac{\mathbf{C}\_{18}^{\text{I}}}{\overline{\lambda}\_{33}}, B\_{22}^{\text{II}} = -\frac{\mathbf{C}\_{17}^{\text{I}}}{24\overline{\lambda}\_{33}}, B\_{23}^{\text{II}} = \frac{\mathbf{C}\_{22}^{\text{I}}}{\overline{\lambda}\_{33}} + \frac{\mathbf{C}\_{4}^{\text{I}}}{\overline{\lambda}\_{33}} + \frac{\mathbf{C}\_{14}^{\text{I}}}{8\left(\overline{\lambda}\_{33}\right)^{2}},\tag{A27}$$

24λ33

$$\begin{array}{l} \mathbf{C}\_{49}^{\mathrm{II}} = 0, \mathbf{C}\_{50}^{\mathrm{II}} = 0, \mathbf{C}\_{51}^{\mathrm{II}} = 0, \mathbf{C}\_{52}^{\mathrm{II}} = 0, \mathbf{C}\_{53}^{\mathrm{II}} = 0, \mathbf{C}\_{54}^{\mathrm{II}} = 0, \mathbf{C}\_{55}^{\mathrm{II}} = 0, \\\mathbf{C}\_{57}^{\mathrm{II}} = \frac{\mathbf{C}\_{1}^{\mathrm{0}}}{20\overline{\lambda}\_{33}}, \mathbf{C}\_{58}^{\mathrm{II}} = \frac{1}{12\overline{\lambda}\_{33}} B\_{13}^{\mathrm{I}} + \frac{\mathbf{C}\_{2}^{\mathrm{0}}}{24\overline{\lambda}\_{33}} + \frac{1}{12} B\_{1}^{\mathrm{I}} \end{array} \tag{A28}$$

$$\begin{aligned} B\_{25}^{\text{II}} &= \frac{\mathbf{C}\_{26}^{\text{I}}}{2\overline{\lambda}\_{33}}, B\_{26}^{\text{II}} = -\frac{\mathbf{C}\_{1}^{\text{I}}}{48} - \frac{\mathbf{C}\_{3}^{\text{I}}}{2} - \frac{\mathbf{C}\_{25}^{\text{I}}}{48\overline{\lambda}\_{33}}, B\_{27}^{\text{II}} = \frac{\mathbf{C}\_{31}^{\text{I}}}{\overline{\lambda}\_{33}} \\ B\_{28}^{\text{II}} &= -\frac{1}{24}\mathbf{C}\_{5}^{\text{I}} - \mathbf{C}\_{7}^{\text{I}} - \frac{\mathbf{C}\_{29}^{\text{I}}}{24\overline{\lambda}\_{33}}, B\_{29}^{\text{II}} = \frac{\mathbf{C}\_{34}^{\text{I}}}{\overline{\lambda}\_{33}} + \frac{\mathbf{C}\_{26}^{\text{I}}}{8\left(\overline{\lambda}\_{33}\right)^{2}} + \frac{\mathbf{C}\_{2}^{\text{I}}}{8\overline{\lambda}\_{33}} \end{aligned} \tag{A29}$$

$$\begin{aligned} \mathbf{C}\_{61}^{\mathrm{II}} &= 0, \mathbf{C}\_{62}^{\mathrm{II}} = 0, \mathbf{C}\_{63}^{\mathrm{II}} = 0, \mathbf{C}\_{64}^{\mathrm{II}} = 0, \mathbf{C}\_{65}^{\mathrm{II}} = 0, \mathbf{C}\_{66}^{\mathrm{II}} = 0, \mathbf{C}\_{67}^{\mathrm{II}} = 0, \\ \mathbf{C}\_{69}^{\mathrm{II}} &= 0, \mathbf{C}\_{70}^{\mathrm{II}} = -\frac{1}{12} B\_{13}^{\mathrm{I}} + \frac{1}{12} B\_{7}^{\mathrm{I}} \end{aligned} \tag{A30}$$

$$\begin{aligned} B\_{31}^{\text{II}} &= 0, B\_{32}^{\text{II}} = -\frac{1}{48} \mathcal{C}\_{13}^{\text{I}} - \frac{1}{2} \mathcal{C}\_{15}^{\text{I}}, B\_{33}^{\text{II}} = 0, \\ B\_{34}^{\text{II}} &= -\frac{1}{24} \mathcal{C}\_{17}^{\text{I}} - \mathcal{C}\_{19}^{\text{I}}, B\_{35}^{\text{II}} = \frac{\mathcal{C}\_{28}^{\text{I}}}{\bar{\lambda}\_{33}} + \frac{\mathcal{C}\_{14}^{\text{I}}}{8 \overline{\lambda}\_{33}} \end{aligned} \tag{A31}$$
