Extending the works arXiv:1504.05991 and arXiv:1510.02142, we study threedimensional Euclidean higher spin gravity with negative cosmological constant.This theory can be formulated in terms of SL(N,C) Chern-Simons theory. Byintroducing auxiliary fields, we rewrite it in a supersymmetric way and computeits partition function exactly by using the localization method. We obtain agood expression for the partition function in terms of characters for thevacuum and primaries in 2D unitary CFT with W_N symmetry. We also check thatthe coefficients of the character expansion are positive integers and exhibitCardy formula in the large central charge limit.
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