 Such an element is conjugate to a rotation of the Euclidean plane – they can be interpreted as rotations in a possibly non-orthogonal basis – and the corresponding element of PSL(2,R) acts as (conjugate to) a rotation of the hyperbolic plane and of Minkowski space.Elliptic elements of the modular group must have eigenvalues {ω, ω−1}, where "ω" is a primitive 3rd, 4th, or 6th root of unity.These are all the elements of the modular group with finite order, and they act on the torus as periodic diffeomorphisms.