Realizing tangle embeddings

A straightforward way of identifying a tangle embedded in a knot is to construct a knot from a given tangle. Since we are interested in the knots in the table up to $9$ crossings and tangles in the table up to $7$ crossings, we try the following procedures: For a given tangle $T$ from the table, add a rational tangle $R$ to obtain $T+R$, then take closures $N(T+R)$ and $D(T+R)$, and see which knots in the table result. We list all such embeddings we find this way.