$$
\begin{array}{l}
\text { Let } z=-\frac{1}{2}+t \text {, then }\left(t-\frac{1}{2}\right)^{4}+2\left(t-\frac{1}{2}\right)^{3}+2\left(t-\frac{1}{2}\right)^{2}+\left(t-\frac{1}{2}\right)+\frac{1}{5}=0 \\
\Rightarrow\left[t^{4}+C_{4}^{1}\left(-\frac{1}{2}\right) t^{3}+C_{4}^{2}\left(-\frac{1}{2}\right)^{2} t^{2}+C_{4}^{3}\left(-\frac{1}{2}\right)^{3} t+\left(-\frac{1}{2}\right)^{4}\right] \\
\quad+2\left[t^{3}+C_{3}^{1}\left(-\frac{1}{2}\right) t^{2}+C_{3}^{2}\left(-\frac{1}{2}\right)^{2} t+\left(-\frac{1}{2}\right)^{3}\right]+2\left(t^{2}-t+\frac{1}{4}\right)+t-\frac{3}{10}=0 \\
\Rightarrow t^{4}+\frac{1}{2} t^{2}+\frac{1}{80}=0 \Rightarrow t^{2}=\frac{-5 \pm 2 \sqrt{5}}{20} .
\end{array}
$$

Thus, the complex root with the largest modulus of the original equation is $z=-\frac{1}{2} \pm \sqrt{\frac{5+2 \sqrt{5}}{20}} \mathrm{i}$, with the real part being $-\frac{1}{2}$.
8. The equation $5 z^{4}+10 z^{3}+10 z^{2}+5 z+1=0$ has four complex roots, the real part of the complex root with the largest modulus is $\qquad$ _.