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Continuing the work arXiv:1504.05991, we discuss various aspects of threedimensional quantum gravity partition function in AdS in the semi-classicallimit. The partition function is holomorphic and is the one which we obtainedby using the localization technique of Chern-Simons theory in arXiv:1504.05991.We obtain a good expression for it in the summation form over Virasorocharacters for the vacuum and primaries. A key ingredient for that is aninterpretation of boundary localized fermion. We also check that thecoefficients in the summation form over Virasoro characters of the partitionfunction are positive integers and satisfy the Cardy formula. These givephysical interpretation that these coefficients represent the number of primaryfields in the dual CFT in the large k limit.

Exact Path Integral for 3D Quantum Gravity II