On the Twisted Spectral Large Sieve Inequality for ${\mathrm{P}\mathrm{G}\mathrm{L}}_2(\mathbb{Z}[i])\mathrm{\backslash }{\mathrm{P}\mathrm{G}\mathrm{L}}_2(\mathbb{C})$

In this paper, we extend the twisted spectral large sieve inequalities of Deshouillers, Iwaniec, Luo, and Young from ${\mathrm{S}\mathrm{L}}_2(\mathbb{Z})$ onto ${\mathrm{P}\mathrm{G}\mathrm{L}}_2(\mathbb{Z}[i])$.