We consider the Dirichlet Laplacian in a thin curvedthree-dimensional rod. The rod is finite. Its cross-section isconstant and small, and rotates along the reference curve in anarbitrary way. We find a two-parametric set of the eigenvalues ofsuch operator and construct their complete asymptotic expansions. Weshow that this two-parametric set contains any prescribed number ofthe first eigenvalues of the considered operator. We obtain thecomplete asymptotic expansions for the eigenfunctions associatedwith these first eigenvalues.
