bins}} \sum_{i=1}^{N_{\rm bins}}
[\log_{10} \rho_i - \log_{10} \rho_{\rm NFW}(c)]^2\,.$$

Fig. \[fig:concentration\] shows the measured concentration of the halos contained at least $200$ particles for different $\zeta$ values. In each mass bin, the halos are randomly divided into five parts. Then the average concentration of each part is calculated. The error bars plotted in Fig. \[fig:concentration\] is the standard deviation of five average concentrations. In general the errors of the average concentrations of the total halos can be reduced by a factor of $\sqrt{5}$. For $\zeta=1$, we find that the concentrations of halos with $N>1000$ particles ($M_{200}>13.18\msun$) can be approximately fitted by a power law $c\propto
M_{200}^{-0.1}$, which is in good agreement with the results of @Neto2007. For the halos with $N<1000$ particles, we find the power law index is less than $-0.1$, which is in good agreement with the results calculated by the model of @Zhao2009 [^2].

Because the main focus in this paper is to compare the difference of concentration for different $\zeta$ values, in the lower panel of Fig. \[fig:concentration\], the ratio of the measured halo concentrations is plotted. For a $10\%$ deviation from GR ($|\zeta-1|<0.1$), the deviation of halo concentration can differ by $10-20\%$, which means that 