\pi^4}-\frac{p^2 G_{1}(0)}{48 m_{\Delta} \pi^4}+\frac{2qp G_{2}(0)}{192 \pi^4}-\frac{2qp G_{1}(0)}{48 m_{\Delta} \pi^4} \right)\cdot  \mathcal{R}_{3}
\nonumber \\
&+\left( \frac{G_{1}(0) }{96 \pi^4}+\frac{m_{P}G_{1}(0) }{96 m_{\Delta} \pi^4} - \frac{2qpG_{1}(0) }{192 m_{\Delta}^2\pi^4}-\frac{2qpG_{2}(0) }{384 m_{\Delta} \pi^4} \right) \cdot  \mathcal{R}_{4}
\nonumber \\
&+\left( \frac{G_{1}(0)}{32 \pi^4}+\frac{m_{\Delta} G_{2}(0)}{64 \pi^4} \right) \cdot  \mathcal{R}_{5}
\nonumber \\
&+\left( -\frac{m_{P}m_{\Delta}G_{1}(0)}{32 \pi^4}-\frac{p^2G_{1}(0)}{32 \pi^4} -\frac{2qpG_{1}(0)}{32 \pi^4}  \right)\cdot  \mathcal{R}_{6}
\nonumber \\
&+\left( -\frac{m_{P}G_{1}(0)}{32 \pi^4}-\frac{m_{P}m_{\Delta}G_{2}(0)}{48 \pi^4}+\frac{p^2 G_{2}(0)}{48 \pi^4}+\frac{2qpG_{2}(0)}{48 \pi^4} \right)\cdot  \mathcal{R}_{7}
\nonumber \\
&+ \left( \frac{G_{2}(0)}{64 \pi^4} \right) \cdot  \mathcal{R}_{8}
\nonumber \\
&+ \left( \frac{m_{P} G_{1}(0)}{32 \pi^4}+\frac{m_{\Delta} G_{1}(0)}{32 \pi^4}\right)  \cdot  \mathcal{R}_{9}
\nonumber \\
&+ \left( -\frac{G_{1}(0)}{32 \pi^4} +\frac{m_{P}G_{2}(0)}{48 \pi^4}-\frac{m_{\Delta}G_{2}(0)}{48 \pi^4} \right)  \cdot  \mathcal{R}_{10}
\nonumber \\
&+ \left(\frac{G_{1}(0) }{16 \pi^4} \right)\cdot \mathcal{R}_{11} 
+\left.  \left( \frac{m_{\Delta} G_{1}(0)}{16 \pi^4} \right)\cdot \mathcal{R}_{12}\;\hspace{0.3mm}\right]\end{aligned}$$

### The $N \gamma \to N^{*}$ contribution

Analogously one finds for the contribution of the $J^P={\frac{1}{2}}^{-}$ states to Eq.: $$\begin{aligned}
\label{EvilTerm}
T^{\mu \nu}_{1/2}(p,q)e^{(\lambda)}_{\nu}=&- \lambda_{N^{*}} \lambda_N  \frac{1}{\left(m_{*}^2-p^2 \right) \left(m_P^2-(p+q)^2 \right)}
 {\nonumber}\\
&\times\bigg[4 m_P F_2^{*}(0)\cdot \mathcal{R}_{1}-4 F_2^{*}(0)\cdot \mathcal{R}_{2}
{\nonumber}\\
 &\phantom{\times\bigg[}+\left( 4 p^2 F_2^{*}(0) - 4 m_P m_{*}F_2^{*}(0) \right)\cdot \mathcal{R}_{3} 
{\nonumber}\\
&\phantom{\times \bigg[}+\left(2m_{*}F_2^{*}(0) - 2m_P F_2^{*}(0) \right) \cdot \mathcal{R}_{4} \bigg] \mbox{ .}\end{aligned}$$ We see that only the Lorentz structures $\mathcal{R}_1$, $\mathcal{R}_2$, $\mathcal{R}_3$ and $\mathcal{R}_4$ receive spin-1/2-contributions. In addition to that, the coefficient of the linear combination $$\mathcal{R}_{1}+m_{P} \mathcal{R}_{2}$$ vanishes for the $N \gamma \to N^{*}$ 