Algebraically overtwisted tight 3-manifolds from + 1 $+1$ surgeries

We execute Avdek's algorithm to find many algebraically overtwisted and tight 3-manifolds by contact $+1$ surgeries. In particular, we show that a contact $1/k$ surgery on the standard contact 3-sphere along any Legendrian positive torus knot with the maximal Thurston–Bennequin invariant yields an algebraically overtwisted and tight 3-manifold, where $k$ is a positive integer.