  Using our population synthesis code, we found that the typical chirp mass of
Pop III BH-BHs is $\sim30~\msun$ with the total mass of $\sim60~\msun$ so that
the inspiral chirp signal as well as quasi normal mode (QNM) of the merging BH
are interesting targets of KAGRA. The detection rate of the coalescing Pop III
BH-BHs is $\sim$180 $\rm events~yr^{-1}$$(\rm SFR_p/(10^{-2.5}~\msun
\rm~yr^{-1}~Mpc^{-3}))\cdot([f_b/(1+f_b)]/0.33)\cdot Err_{sys}$ in our standard
model where $\rm SFR_{p},~f_b$ and $\rm Err_{sys}$ are the peak value of the
Pop III star formation rate, the binary fraction and the systematic error with
$\rm Err_{sys}=1$ for our standard model, respectively. To evaluate the
robustness of chirp mass distribution and the range of $\rm Err_{sys}$, we
examine the dependence of the results on the unknown parameters and the
distribution functions. We found that the chirp mass has a peak at $\sim 30
~\msun$ in most of parameters and distribution functions as well as $\rm
Err_{sys}$ ranges from 0.046 to 4. The minimum rate corresponds to the worst
model which we think unlikely so that unless $ {\rm
~(SFR_p/(10^{-2.5}~\msun~yr^{-1}~Mpc^{-3}))\cdot([f_b/(1+f_b)]/0.33) \ll 0.1}$,
we expect the Pop III BH-BHs merger rate of at least one event per year by
KAGRA. Nakano, Tanaka \& Nakamura (2015) show that if S/N of QNM is larger than
35, we can confirm or refute the General Relativity (GR) more than 5 sigma
level. In our standard model, the detection rate of Pop III BH-BHs whose S/N is
larger than 35 is $3.2~\rm events~yr^{-1}$$(\rm SFR_p/(10^{-2.5}~\msun
\rm~yr^{-1}~Mpc^{-3}))\cdot([f_b/(1+f_b)]/0.33)\cdot Err_{sys}$. Thus, there is
a good chance to check whether GR is correct or not in the strong gravity
region.
