  In this paper, we introduce concise expressions for the complex Bessel
integral that enables us to improve the spectral large sieve inequality of Watt
for $\mathrm{PGL}_2 (\mathbb{Z}[i]) \backslash \mathrm{PGL}_2 (\mathbb{C})$.
Our result is optimistic in the case when the average of spectral parameters is
on a square centered at $(0, 0)$.
