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A novel method for computing torus amplitudes in orbifold compactificationsis suggested. It applies universally for every Abelian $\mathbb{Z}_{N}$orbifold without requiring the unfolding technique. This method follows fromthe possibility of obtaining integrals over fundamental domains of every Heckecongruence subgroup $\Gamma_{0}[N]$ by computing contour integrals overone-dimensional curves uniformly distributed in these domains.

A novel method for computing torus amplitudes for $\mathbb{Z}_{N}$ orbifolds without the unfolding technique