Singular Values & the SVD · Superchallenge problem

Index rows and columns by $0, 1, \ldots, 6$ and let $A$ be the $7\times 7$ matrix with $a_{ij} = 1$ if $j - i \equiv 0$, $1$ or $3 \pmod 7$, and $a_{ij} = 0$ otherwise. Find the nuclear norm $\|A\|_* = \sum\sigma_k$. Give your answer in simplest radical form.