One of earliest goals of knot theory was the development of a knot tables. A knot table consist of a list of prime knots (knots that are not connected sums of non-trivial knots) that are sorted by their crossing number. Classically such tables were constructed combinatorially using knot invariants to distinguish inequivalent pairs (such as the Alexander and Jones polynomial). Moving apart from the classical knot theory in S^3, knots have been so far classified only in the projective space up to 6 crossings. We will present the computational methods used to construct knot tables of non-affine prime knots in the solid torus and the infinite family of lens spaces L(p,q). In addition, we will establish which of these knots are amphichiral. We will take a brief look at why classical knot invariants are very weak at distinguishing between these knots and will provide stronger invariants, namely the Kauffman bracket skein module and the HOMLFY skein module.