\begin{eqnarray}
%%%texparser:LHS:testLq3NSN%%%
&& L_{q,3}^{W^+-W^-,\mathrm{NS}}(N) = \nonumber\\
&&
a_s^2 \textcolor{blue}{C_F T_F} \Biggl\{
        L_Q \biggl[
                -\frac{2 P_9}{9 N^2 (N+1)^2}
                +\frac{4 \big(29 N^2+29 N-6\big)}{9 N (N+1)} S_1
                +\frac{8}{3} S_1^2
                -8 S_2
        \biggr]
\nonumber\\ &&
        +L_M \biggl[
                \frac{2 P_4}{9 N^2 (N+1)^2}
                -\frac{80}{9} S_1
                +\frac{16}{3} S_2
        \biggr]
        -\frac{\gamma_{qq}^{(0)} L_M^2}{3}
        -\frac{\gamma_{qq}^{(0)} L_Q^2}{3}
        +\frac{P_{35}}{27 N^3 (N+1)^3}
\nonumber\\ &&
        +\biggl(
                -\frac{2 P_{14}}{27 N^2 (N+1)^2}
                +\frac{8}{3} S_2
        \biggr) S_1
        -\frac{2 \big(29 N^2+29 N-6\big)}{9 N (N+1)} S_1^2
        -\frac{8}{9} S_1^3
\nonumber\\ &&
        +\frac{2 \big(35 N^2+35 N-2\big)}{3 N (N+1)} S_2
        -\frac{112}{9} S_3
        +\frac{16}{3} S_{2,1}
\Biggr\}
+a_s^3 \Biggl\{
        \textcolor{blue}{C_F^2 T_F} \Biggl[
                \frac{1}{6} {\gamma_{qq}^{(0)}}^2 L_Q 
                        \bigl(L_Q^2 
\nonumber\\ && 
                        + L_M^2 \bigr)
                +L_M^2 \biggl[
                        -\frac{2 P_{29}}{3 N^3 (N+1)^3}
                        +\frac{2 P_8}{3 N^2 (N+1)^2} S_1
                        -\frac{4 (N-1) (N+2)}{N (N+1)} S_1^2
\nonumber\\ &&
                        -\frac{16}{3} S_1^3
                        +\frac{10}{3} \gamma_{qq}^{(0)} S_2
                        +\frac{64}{3} S_3
                        +\biggl(
                                -\frac{64}{3 N (N+1)}
                                +\frac{128}{3} S_1
                        \biggr) S_{-2}
                        +\frac{64}{3} S_{-3}
\nonumber\\ &&
                        -\frac{128}{3} S_{-2,1}
                \biggr]
                +L_Q^2 \biggl[
                        -\frac{2 P_{31}}{9 N^3 (N+1)^3}
                        +\frac{2 P_{15}}{9 N^2 (N+1)^2} S_1
                        -\frac{4 \big(107 N^2+107 N-54\big)}{9 N (N+1)} S_1^2
\nonumber\\ &&
                        -16 S_1^3
                        +\frac{22}{3} \gamma_{qq}^{(0)} S_2
                        +\frac{64}{3} S_3
                        +\biggl(
                                -\frac{64}{3 N (N+1)}
                                +\frac{128}{3} S_1
                        \biggr) S_{-2}
                        +\frac{64}{3} S_{-3}
\nonumber\\ &&
                        -\frac{128}{3} S_{-2,1}
                \biggr]
                +\gamma_{qq}^{(0)} L_M L_Q \biggl[
                        \frac{P_2}{9 N^2 (N+1)^2}
                        +\frac{40}{9} S_1
                        -\frac{8}{3} S_2
                \biggr]
                +L_Q \biggl[
                        \frac{80}{9} S_1^4
                        +\frac{448}{3} S_{-4}
\nonumber\\ &&
                        +\frac{4 P_{50}}{27 (N-1) N^4 (N+1)^4 (N+2)} 
                        +\biggl(
                                -\frac{16 \big(9 N^2+9 N-2\big)}{N (N+1)}
                                +64 S_1
                        \biggr) \zeta_3
\nonumber\\ &&
                        +\biggl(
                                -\frac{4 P_{38}}{27 N^3 (N+1)^3}
                                -\frac{32 \big(67 N^2+67 N-21\big)}{9 N (N+1)} S_2
                                +\frac{640}{9} S_3
                                +\frac{64}{3} S_{2,1}
                                +\frac{512}{3} S_{-2,1}
                        \biggr) S_1
\nonumber\\ &&
                        +\biggl(
                                \frac{2 P_{18}}{27 N^2 (N+1)^2}
                                -\frac{224}{3} S_2
                        \biggr) S_1^2
                        +\frac{32 (4 N-1) (4 N+5)}{9 N (N+1)} S_1^3
                        +\frac{2 P_{17}}{9 N^2 (N+1)^2} S_2
\nonumber\\ &&
                        +48 S_2^2
                        -\frac{32 \big(53 N^2+53 N+16\big)}{9 N (N+1)} S_3
                        +\frac{352}{3} S_4
                        +\biggl(
                                -\frac{64 P_{28}}{9 (N-1) N^2 (N+1)^2 (N+2)} 
\nonumber\\ &&
                                -\frac{128 \big(10 N^2+10 N-3\big)}{9 N (N+1)} S_1
                                -\frac{256}{3} S_1^2
                                +\frac{256}{3} S_2
                        \biggr) S_{-2}
                        +64 S_{-2}^2
                        +64 S_{3,1}
\nonumber\\ &&
                        +\biggl(
                                -\frac{64 \big(10 N^2+10 N+9\big)}{9 N (N+1)}
                                +\frac{256}{3} S_1
                        \biggr) S_{-3}
                        +\frac{16 \big(9 N^2+9 N-2\big)}{3 N (N+1)} S_{2,1}
\nonumber\\ &&                   
                        +\frac{128 \big(10 N^2+10 N-3\big) S_{-2,1}}{9 N (N+1)}
                        -\frac{256}{3} S_{-3,1}
                        -64 S_{2,1,1}
                        -\frac{512}{3} S_{-2,1,1}
                \biggr]
\nonumber\\ &&
                +L_M \biggl[
                        \frac{P_{41}}{9 N^4 (N+1)^4}
                        -32 S_2^2
                        +\biggl(
                                \frac{2 P_{32}}{9 N^3 (N+1)^3}
                                +\frac{16 \big(59 N^2+59 N-6\big)}{9 N (N+1)} S_2
                                -\frac{256}{3} S_3
\nonumber\\ &&
                                -\frac{256}{3} S_{-2,1}
                        \biggr) S_1
                        +\biggl(
                                -\frac{4 P_6}{3 N^2 (N+1)^2}
                                +\frac{32}{3} S_2
                        \biggr) S_1^2
                        -\frac{160}{9} S_1^3
                        -\frac{4 P_{11}}{9 N^2 (N+1)^2} S_2
\nonumber\\ &&
                        +\frac{32 \big(29 N^2+29 N+12\big)}{9 N (N+1)} S_3
                        -\frac{256}{3} S_4
                        +\biggl(
                                -\frac{64 \big(16 N^2+10 N-3\big)}{9 N^2 (N+1)^2}
                                +\frac{1280}{9} S_1
\nonumber\\ &&
                                -\frac{128}{3} S_2
                        \biggr) S_{-2}
                        +\biggl(
                                \frac{64 \big(10 N^2+10 N+3\big)}{9 N (N+1)}
                                -\frac{128}{3} S_1
                        \biggr) S_{-3}
                        -\frac{128}{3} S_{-4}
                        +\frac{128}{3} S_{3,1}
\nonumber\\ &&
                        -\frac{128 \big(10 N^2+10 N-3\big)}{9 N (N+1)} S_{-2,1}
                        -\frac{128}{3} S_{-2,2}
                        +\frac{512}{3} S_{-2,1,1}
                        +8 \gamma_{qq}^{(0)} \zeta_3
                \biggr]
\nonumber\\ &&
                +\frac{P_{48}}{162 N^5 (N+1)^5}
                -\frac{128 \big(112 N^3+112 N^2-39 N+18\big)}{81 N^2 (N+1)} S_{-2,1} 
\nonumber\\ &&               
                +\biggl(
                        \frac{2 P_{16}}{9 N^2 (N+1)^2}
                        -\frac{1208}{9} S_1
                        -\frac{64}{3} S_2
                \biggr) \zeta_3
                +\gamma_{qq}^{(0)} \biggl(
                        -\frac{8 \textcolor{black}{B_4}}{3}
                        +12 \zeta_4
                        +\frac{8}{3} S_{2,1,1}
                \biggr)
\nonumber\\ &&
                +\biggl(
                        \frac{P_{47}}{162 N^4 (N+1)^4}
                        +\frac{8 P_{19}}{81 N^2 (N+1)^2} S_2
                        -\frac{64}{9} S_2^2
                        -\frac{8 \big(347 N^2+347 N+54\big) S_3}{27 N (N+1)}
\nonumber\\ &&
                        +\frac{704}{9} S_4
                        +\frac{128}{9 N (N+1)} S_{2,1}
                        -\frac{320}{9} S_{3,1}
                        -\frac{256 \big(10 N^2+10 N-3\big)}{27 N (N+1)} S_{-2,1}
                        -\frac{256}{9} S_{-2,2}
\nonumber\\ &&
                        +\frac{1024}{9} S_{-2,1,1}
                \biggr) S_1
                +\biggl(
                        \frac{P_{26}}{9 N^3 (N+1)^3}
                        +\frac{16 \big(5 N^2+5 N-4\big)}{9 N (N+1)} S_2
                        +16 S_3
                        -\frac{128}{9} S_{2,1}
\nonumber\\ &&
                        -\frac{256}{9} S_{-2,1}
                \biggr) S_1^2
                +\biggl(
                        -\frac{16 P_7}{27 N^2 (N+1)^2}
                        +\frac{128}{27} S_2
                \biggr) S_1^3
                +\biggl(
                        \frac{P_{25}}{81 N^3 (N+1)^3}
                        +\frac{400}{27} S_3
\nonumber\\ &&
                        +\frac{256}{3} S_{-2,1}
                \biggr) S_2
                -\frac{32 \big(23 N^2+23 N-3\big)}{27 N (N+1)} S_2^2
                +\frac{8 P_{20}}{81 N^2 (N+1)^2} S_3
                +\frac{512}{9} S_5
\nonumber\\ &&
                -\frac{176 \big(17 N^2+17 N+6\big)}{27 N (N+1)} S_4
                +\biggl(
                        -\frac{64 P_{12}}{81 N^3 (N+1)^3}
                        +\frac{128 P_{10}}{81 N^2 (N+1)^2} S_1
                        -\frac{1280}{27} S_2
\nonumber\\ &&
                        -\frac{128}{9 N (N+1)} S_1^2
                        +\frac{256}{27} S_1^3
                        +\frac{512}{27} S_3
                        -\frac{512}{9} S_{2,1}
                \biggr) S_{-2}
                +\biggl(
                        -\frac{128 \big(10 N^2+10 N+3\big)}{27 N (N+1)} S_1
\nonumber\\ &&
                        +\frac{64 \big(112 N^3+224 N^2+169 N+39\big)}{81 N (N+1)^2} 
                        +\frac{128}{9} S_1^2
                        +\frac{128}{9} S_2
                \biggr) S_{-3}
                +\biggl(
                        \frac{256}{9} S_1
\nonumber\\ &&
                        -\frac{128 \big(10 N^2+10 N+3\big)}{27 N (N+1)}
                \biggr) S_{-4}
                +\frac{256}{9} S_{-5}
                +\frac{16 P_5 S_{2,1}}{9 N^2 (N+1)^2}
                +\frac{256}{9} S_{2,3}
                -\frac{512}{9} S_{2,-3}
\nonumber\\ &&
                +\frac{16 \big(89 N^2+89 N+30\big)}{27 N (N+1)} S_{3,1}
                -\frac{512}{9} S_{4,1}
                -\frac{128 \big(10 N^2+10 N-3\big)}{27 N (N+1)} S_{-2,2}
\nonumber\\ &&
                +\frac{256}{9} \bigl(2  S_{-2,3}
                + 2 S_{2,1,-2}
                + S_{3,1,1}
                + 2 S_{-2,2,1} \bigr)
                +\frac{512 \big(10 N^2+10 N-3\big)}{27 N (N+1)} S_{-2,1,1}
\nonumber\\ &&
                -\frac{2048}{9} S_{-2,1,1,1}
        \Biggr]
\nonumber\\ &&
        +\textcolor{blue}{C_A C_F T_F} \Biggl[
                \frac{22 \gamma_{qq}^{(0)}}{27} \left(L_M^3 + 2 L_Q^3\right)
                +L_M^2 \biggl[
                        \frac{\gamma_{qq}^{(0)} P_1}{9 N^2 (N+1)^2}
                        -\frac{16 P_3}{3 N^2 (N+1)^2} S_1
                        -\frac{32}{3} S_3
\nonumber\\ &&                       
                        +\biggl(
                                \frac{32}{3 N (N+1)}
                                -\frac{64}{3} S_1
                        \biggr) S_{-2}
                        -\frac{32}{3} S_{-3}
                        +\frac{64}{3} S_{-2,1}
                \biggr]
                +L_Q^2 \biggl[
                        \frac{2 P_{37}}{27 N^3 (N+1)^3}
\nonumber\\ &&
                        -\frac{16 \big(194 N^2+194 N-33\big)}{27 N (N+1)} S_1
                        -\frac{176}{9} S_1^2
                        +\frac{176}{3} S_2
                        -\frac{32}{3} S_3
                        +\biggl(
                                \frac{32}{3 N (N+1)}
\nonumber\\ &&                               
                        -\frac{64}{3} S_1
                        \biggr) S_{-2}
                        -\frac{32}{3} S_{-3}
                        +\frac{64}{3} S_{-2,1}
                \biggr]
                +L_M \biggl[
                        \frac{P_{40}}{81 N^4 (N+1)^4}
                        +\biggl(
                                -\frac{8 P_{30}}{81 N^3 (N+1)^3}
\nonumber\\ &&
                                +32 S_3
                                +\frac{128}{3} S_{-2,1}
                        \biggr) S_1
                        +\frac{1792}{27} S_2
                        -\frac{16 \big(31 N^2+31 N+9\big)}{9 N (N+1)} S_3
                        +\frac{160}{3} S_4
\nonumber\\ &&
                        +\biggl(
                                \frac{32 \big(16 N^2+10 N-3\big)}{9 N^2 (N+1)^2}
                                -\frac{640}{9} S_1
                                +\frac{64}{3} S_2
                        \biggr) S_{-2}
                        +\biggl(
                                -\frac{32 \big(10 N^2+10 N+3\big)}{9 N (N+1)}
\nonumber\\ &&                              
                                +\frac{64}{3} S_1
                        \biggr) S_{-3}
                        +\frac{64}{3} S_{-4}
                        -\frac{128}{3} S_{3,1}
                        +\frac{64 \big(10 N^2+10 N-3\big)}{9 N (N+1)} S_{-2,1}
                        +\frac{64}{3} S_{-2,2}
\nonumber\\ &&
                        -\frac{256}{3} S_{-2,1,1}
                        -8 \gamma_{qq}^{(0)} \zeta_3
                \biggr]
                +L_Q \biggl[
                        -\frac{16 \big(230 N^3+460 N^2+213 N-11\big)}{9 N (N+1)^2} S_2 
\nonumber\\ &&
                        -\frac{4 P_{51}}{81 (N-1) N^4 (N+1)^4 (N+2)} 
                        +\biggl(
                                \frac{4 P_{39}}{81 N^3 (N+1)^3}
                                -\frac{32 \big(11 N^2+11 N+3\big)}{9 N (N+1)} S_2
\nonumber\\ &&                               
                                +32 S_3
                                -\frac{128}{3} S_{2,1}
                                -\frac{256}{3} S_{-2,1}
                        \biggr) S_1
                        +\biggl(
                                \frac{16 \big(194 N^2+194 N-33\big)}{27 N (N+1)}
                                +\frac{32}{3} S_2
                        \biggr) S_1^2
\nonumber\\ &&
                        +\frac{352}{27} S_1^3
                        -\frac{32}{3} S_2^2
                        +\frac{16 \big(368 N^2+368 N-9\big)}{27 N (N+1)} S_3
                        +\biggl(
                                \frac{32 P_{28}}{9 (N-1) N^2 (N+1)^2 (N+2)} 
\nonumber\\ &&
                                +\frac{64 \big(10 N^2+10 N-3\big)}{9 N (N+1)} S_1
                                +\frac{128}{3} S_1^2
                                -\frac{128}{3} S_2
                        \biggr) S_{-2}
                        -\frac{224}{3} S_4
                        -32 S_{-2}^2
\nonumber\\ &&
                        +\biggl(
                                \frac{32 \big(10 N^2+10 N+9\big)}{9 N (N+1)}
                                -\frac{128}{3} S_1
                        \biggr) S_{-3}
                        -\frac{224}{3} S_{-4}
                        -\frac{64 \big(11 N^2+11 N-3\big)}{9 N (N+1)} S_{2,1}
\nonumber\\ &&
                        -\frac{64}{3} S_{3,1}
                        -\frac{64 \big(10 N^2+10 N-3\big)}{9 N (N+1)} S_{-2,1}
                        +\frac{128}{3} S_{-3,1}
                        +64 S_{2,1,1}
                        +\frac{256}{3} S_{-2,1,1}
\nonumber\\ &&
                        +\biggl(
                                96
                                -64 S_1
                        \biggr) \zeta_3
                \biggr]
                +\frac{P_{49}}{729 N^5 (N+1)^5}
                +\frac{S_{-2,1}}{N^2 (N+1)} \frac{64}{81} \big(112 N^3+112 N^2-39 N
\nonumber\\ &&
+18\big)
                +\biggl(
                        \frac{P_{24}}{27 N^2 (N+1)^2}
                        +\frac{4 \big(593 N^2+593 N+108\big)}{27 N (N+1)} S_1
                        -16 S_1^2
                        +16 S_2
                \biggr) \zeta_3
\nonumber\\ &&
                +\gamma_{qq}^{(0)} \biggl(
                        \frac{4 \textcolor{black}{B_4}}{3}
                        -12 \zeta_4
                        -4 S_{2,1,1}
                \biggr)
                +\biggl(
                        -\frac{4 P_{46}}{729 N^4 (N+1)^4}
                        -\frac{16 (N-1)}{9 N^2 (N+1)^2} S_2
\nonumber\\ &&
                                \times \big(2 N^3-N^2-N-2\big)
                        +\frac{112}{9} S_2^2
                        +\frac{80 (2 N+1)^2 S_3}{9 N (N+1)}
                        -\frac{208}{9} S_4
                        +\frac{64}{3} S_{3,1}
                        +\frac{128}{9} S_{-2,2}
\nonumber\\ &&
                        -\frac{8 \big(9 N^2+9 N+16\big)}{9 N (N+1)} S_{2,1}
                        +\frac{128 \big(10 N^2+10 N-3\big)}{27 N (N+1)} S_{-2,1}
                        -\frac{512}{9} S_{-2,1,1}
                \biggr) S_1
\nonumber\\&&
                +\biggl(
                        \frac{4 P_{21}}{9 N^3 (N+1)^3}
                        +\frac{32}{9 N (N+1)} S_2
                        -\frac{80}{9} S_3
                        +\frac{128}{9} S_{2,1}
                        +\frac{128}{9} S_{-2,1}
                \biggr) S_1^2
                +\biggl(\frac{496}{27} S_3
\nonumber\\ &&
                        +\frac{4 P_{36}}{81 N^3 (N+1)^3}
                        -\frac{64}{3} S_{2,1}
                        -\frac{128}{3} S_{-2,1}
                \biggr) S_2
                -\frac{64}{27} S_1^3 S_2
                -\frac{4 \big(15 N^2+15 N+14\big)}{9 N (N+1)} S_2^2
\nonumber\\ &&
                -\frac{8 P_{23}}{81 N^2 (N+1)^2} S_3
                +\frac{4 \big(443 N^2+443 N+78\big)}{27 N (N+1)} S_4
                -\frac{224}{9} S_5
                +\biggl(
                        \frac{32 P_{12}}{81 N^3 (N+1)^3}
\nonumber\\ &&
                        -\frac{64 P_{10}}{81 N^2 (N+1)^2} S_1
                        +\frac{64}{9 N (N+1)} S_1^2
                        -\frac{128}{27} S_1^3
                        +\frac{640}{27} S_2
                        -\frac{256}{27} S_3
                        +\frac{256}{9} S_{2,1}
                \biggr) S_{-2}
\nonumber\\ &&
                +\biggl(
                        -\frac{32 \big(112 N^3+224 N^2+169 N+39\big)}{81 N (N+1)^2} 
                        +\frac{64 \big(10 N^2+10 N+3\big)}{27 N (N+1)} S_1
\nonumber\\ &&    
                        -\frac{64}{9} S_1^2
                        -\frac{64}{9} S_2
                \biggr) S_{-3}
                +\biggl(
                        \frac{64 \big(10 N^2+10 N+3\big)}{27 N (N+1)}
                        -\frac{128}{9} S_1
                \biggr) S_{-4}
                -\frac{128}{9} S_{-5}
\nonumber\\ &&
                -\frac{8 P_{22}}{9 N^2 (N+1)^2} S_{2,1}
                -\frac{128}{3} S_{2,3}
                +\frac{256}{9} S_{2,-3}
                -\frac{8 (13 N+4) (13 N+9)}{27 N (N+1)} S_{3,1}
                +\frac{256}{9} S_{4,1}
\nonumber\\ &&
                +\frac{64 \big(10 N^2+10 N-3\big)}{27 N (N+1)} S_{-2,2}
                -\frac{256}{9} S_{-2,3}
                -\frac{256}{9} S_{2,1,-2}
                +\frac{64}{3} S_{2,2,1}
                -\frac{256}{9} S_{3,1,1}
\nonumber\\ &&
                -\frac{256 \big(10 N^2+10 N-3\big)}{27 N (N+1)} S_{-2,1,1}
                -\frac{256}{9} S_{-2,2,1}
                +\frac{224}{9} S_{2,1,1,1}
                +\frac{1024}{9} S_{-2,1,1,1}
        \Biggr]
\nonumber\\ &&
        +\textcolor{blue}{C_F T_F^2} \Biggl[
                -\frac{8 \gamma_{qq}^{(0)}}{27}\left( 2 L_M^3 + L_Q^3\right)
                +L_Q^2 \biggl[
                        -\frac{8 P_9}{27 N^2 (N+1)^2}
                        +\frac{32}{9} S_1^2
                        -\frac{32}{3} S_2
\nonumber\\ &&
                        +\frac{16 \big(29 N^2+29 N-6\big)}{27 N (N+1)} S_1
                \biggr]
                +L_M^2 \biggl[
                        \frac{8 P_4}{27 N^2 (N+1)^2}
                        -\frac{320}{27} S_1
                        +\frac{64}{9} S_2
                \biggr]
                - L_M \frac{248 \gamma_{qq}^{(0)}}{81}
\nonumber\\ &&
                +L_Q \biggl[
                        \frac{8 P_{34}}{81 N^3 (N+1)^3}
                        +\biggl(
                                -\frac{16 P_{13}}{81 N^2 (N+1)^2}
                                +\frac{64}{9} S_2
                        \biggr) S_1
                        -\frac{16 \big(29 N^2+29 N-6\big)}{27 N (N+1)} S_1^2
\nonumber\\ &&
                        -\frac{64}{27} S_1^3
                        +\frac{16 \big(35 N^2+35 N-2\big)}{9 N (N+1)} S_2
                        -\frac{896}{27} S_3
                        +\frac{128}{9} S_{2,1}
                \biggr]
                -\frac{2 P_{45}}{729 N^4 (N+1)^4}
\nonumber\\ &&
                +\frac{12064}{729} S_1
                +\frac{64}{81} S_2
                +\frac{320}{81} S_3
                -\frac{64}{27} S_4
                -\frac{112 \gamma_{qq}^{(0)} \zeta_3}{27}
        \Biggr]
\nonumber\\ &&
        +\textcolor{blue}{C_F N_F T_F^2} \Biggl[
                -\frac{8 \gamma_{qq}^{(0)}}{27} \left(L_M^3 +2 L_Q^3\right)
                +L_Q^2 \biggl[
                        -\frac{16 P_9}{27 N^2 (N+1)^2}
                        +\frac{64}{9} S_1^2
                        -\frac{64}{3} S_2
\nonumber\\ &&
                        +\frac{32 \big(29 N^2+29 N-6\big)}{27 N (N+1)} S_1
                \biggr]
                +L_M \biggl[
                        \frac{4 P_{33}}{81 N^3 (N+1)^3}
                        -\frac{2176}{81} S_1
                        -\frac{320}{27} S_2
                        +\frac{64}{9} S_3
                \biggr]
\nonumber\\ &&
                +L_Q \biggl[
                        \frac{16 P_{34}}{81 N^3 (N+1)^3}
                        +\biggl(
                                -\frac{32 P_{13}}{81 N^2 (N+1)^2}
                                +\frac{128}{9} S_2
                        \biggr) S_1
                        -\frac{1792}{27} S_3
\nonumber\\ &&
                        -\frac{32 \big(29 N^2+29 N-6\big)}{27 N (N+1)} S_1^2
                        -\frac{128}{27} S_1^3
                        +\frac{32 \big(35 N^2+35 N-2\big)}{9 N (N+1)} S_2
                        +\frac{256}{9} S_{2,1}
                \biggr]
\nonumber\\ &&
                +\frac{4 P_{44}}{729 N^4 (N+1)^4}
                -\frac{24064}{729} S_1
                +\frac{128}{81} S_2
                +\frac{640}{81} S_3
                -\frac{128}{27} S_4
                +\frac{64 \gamma_{qq}^{(0)} \zeta_3}{27}
        \Biggr]
\nonumber\\ &&
        +\textcolor{blue}{\frac{d^{abc} d^{abc}}{N_c}} \frac{1}{2}L_Q \Biggl[
                -\frac{8 P_{42}}{(N-1) N^5 (N+1)^5 (N+2)} 
                +\frac{4 P_{43}}{(N-1) N^4 (N+1)^4 (N+2)} S_1
\nonumber\\ &&
                +\frac{4 \big(N^2+N+2\big)}{N^2 (N+1)^2} S_3
                +\biggl(
                        \frac{16 \big(N^2+N+2\big)^2}{(N-1) N^2 (N+1)^2 (N+2)} S_1
\nonumber\\ &&                    
                        +\frac{8 P_{27}}{(N-1) N^3 (N+1)^3 (N+2)} 
                \biggr) S_{-2}
                -\frac{8 \big(N^2+N+2\big)}{N^2 (N+1)^2} S_{-3}
\nonumber\\ &&
                +\frac{16 \big(N^2+N+2\big)}{N^2 (N+1)^2} S_{-2,1}
        \Biggr]
        +\hat{C}_{q,3}^{\mathrm{NS},(3)}(N_F)
\Biggr\},
\end{eqnarray}
%-----------------------------------------------------------------------------------------------------
where $\hat{C}_{q,3}^{\mathrm{NS},(3)}(N_F)$ denotes the contribution due to the massless Wilson coefficient at 3-loop 
order \cite{Moch:2008fj}, and the polynomials $P_i$ are
%-----------------------------------------------------------------------------------------------------
\begin{eqnarray}
P_1    &=& -17 N^4-34 N^3-29 N^2-12 N-24 \\
P_2    &=& -3 N^4-6 N^3-47 N^2-20 N+12 \\
P_3    &=& N^4+2 N^3-N^2-2 N-4 \\
P_4    &=& 3 N^4+6 N^3+47 N^2+20 N-12 \\
P_5    &=& 7 N^4+14 N^3+3 N^2-4 N-4 \\
P_6    &=& 19 N^4+38 N^3-9 N^2-20 N+4 \\
P_7    &=& 28 N^4+56 N^3+28 N^2+2 N+1 \\
P_8    &=& 33 N^4+54 N^3+9 N^2-52 N-28 \\
P_9    &=& 57 N^4+96 N^3+65 N^2-10 N-24 \\
P_{10} &=& 112 N^4+224 N^3+121 N^2+9 N+9 \\
P_{11} &=& 141 N^4+246 N^3+241 N^2-8 N-84 \\
P_{12} &=& 181 N^4+266 N^3+82 N^2-3 N+18 \\
P_{13} &=& 235 N^4+524 N^3+211 N^2+30 N+72 \\
P_{14} &=& 359 N^4+772 N^3+335 N^2+30 N+72 \\
P_{15} &=& 501 N^4+894 N^3+541 N^2-116 N-204 \\
P_{16} &=& 561 N^4+1122 N^3+767 N^2+302 N+48 \\
P_{17} &=& 1131 N^4+2118 N^3+1307 N^2+32 N-276 \\
P_{18} &=& 1139 N^4+2710 N^3+635 N^2+216 N+828 \\
P_{19} &=& 1199 N^4+2398 N^3+1181 N^2+18 N+90 \\
P_{20} &=& 1220 N^4+2359 N^3+1934 N^2+357 N-138 \\
P_{21} &=& 3 N^5+11 N^4+10 N^3+19 N^2+23 N+16 \\
P_{22} &=& 12 N^5+16 N^4+18 N^3-15 N^2-5 N-8 \\
P_{23} &=& 27 N^5+863 N^4+1573 N^3+1151 N^2+144 N-36 \\
P_{24} &=& 648 N^5-2103 N^4-4278 N^3-3505 N^2-682 N-432 \\
P_{25} &=& -11145 N^6-32355 N^5-37523 N^4-14329 N^3+1240 N^2-1032 N-2088 \\
P_{26} &=& -151 N^6-469 N^5-181 N^4+305 N^3+80 N^2-88 N-56 \\
P_{27} &=& N^6+3 N^5-8 N^4-21 N^3-23 N^2-12 N-4 \\
P_{28} &=& 6 N^6+18 N^5-N^4-20 N^3+46 N^2+29 N-6 \\
P_{29} &=& 15 N^6+36 N^5+30 N^4-24 N^3+3 N^2+16 N+20 \\
P_{30} &=& 155 N^6+465 N^5+465 N^4+155 N^3+108 N^2+108 N+54 \\
P_{31} &=& 216 N^6+567 N^5+687 N^4+285 N^3+37 N^2-44 N+12 \\
P_{32} &=& 309 N^6+807 N^5+693 N^4-463 N^3-638 N^2+68 N+216 \\
P_{33} &=& 525 N^6+1575 N^5+1535 N^4+973 N^3+536 N^2+48 N-72 \\
P_{34} &=& 609 N^6+1485 N^5+1393 N^4+83 N^3-422 N^2+156 N+216 \\
P_{35} &=& 795 N^6+2043 N^5+2075 N^4+517 N^3-298 N^2+156 N+216 \\
P_{36} &=& 868 N^6+2469 N^5+2487 N^4+940 N^3+171 N^2+207 N+144 \\
P_{37} &=& 1407 N^6+3825 N^5+4211 N^4+1783 N^3-250 N^2-240 N+144 \\
P_{38} &=& 1770 N^6+4671 N^5+4765 N^4+1205 N^3-227 N^2+1044 N+756 \\
P_{39} &=& 7531 N^6+23673 N^5+23055 N^4+7375 N^3+1614 N^2+936 N-324 \\
P_{40} &=& -4785 N^8-19140 N^7-18754 N^6+1320 N^5+12723 N^4+6548 N^3+4080 N^2
\nonumber\\ &&
-648 N-1728 \\
P_{41} &=& -45 N^8-162 N^7-858 N^6-936 N^5-1629 N^4-1094 N^3-804 N^2
\nonumber\\ &&
-40 N+192 \\
P_{42} &=& N^8+4 N^7+13 N^6+25 N^5+57 N^4+77 N^3+55 N^2+20 N+4 \\
P_{43} &=& 3 N^8+12 N^7+16 N^6+6 N^5+30 N^4+64 N^3+73 N^2+40 N+12 \\
P_{44} &=& 3549 N^8+14196 N^7+23870 N^6+25380 N^5+15165 N^4+1712 N^3-2016 N^2
\nonumber\\ &&
+144 N+432 \\
P_{45} &=& 5487 N^8+21948 N^7+36370 N^6+28836 N^5+11943 N^4+4312 N^3+2016 N^2
\nonumber\\ &&
-144 N-432 \\
P_{46} &=& 10807 N^8+43228 N^7+63222 N^6+40150 N^5+14587 N^4+9018 N^3+7452 N^2
\nonumber\\ &&
+2376 N+324 \\
P_{47} &=& 42591 N^8+166764 N^7+245664 N^6+129982 N^5-13295 N^4-25978 N^3
\nonumber\\ &&
+3560 N^2-3192 N-4464 \\
P_{48} &=& -18351 N^{10}-89784 N^9-210021 N^8-271638 N^7-219369 N^6-90572 N^5
\nonumber\\ &&
-26491 N^4-7790 N^3-1992 N^2-2760 N-2160 \\
P_{49} &=& 165 N^{10}+825 N^9+109664 N^8+331682 N^7+457641 N^6+346145 N^5
\nonumber\\ &&
+219290 N^4+86724 N^3+13608 N^2+14256 N+10368 \\
P_{50} &=& 828 N^{10}+3492 N^9+4305 N^8-2013 N^7-8540 N^6-3822 N^5-1157 N^4
\nonumber\\ &&
-3057 N^3-4112 N^2-324 N+576 \\
P_{51} &=& 8274 N^{10}+37149 N^9+53630 N^8+7538 N^7-59902 N^6-55159 N^5
\nonumber\\ &&
-6994 N^4+3272 N^3-9048 N^2-1656 N+2160~.
\end{eqnarray}
