Eigenvalues of a 30 by 30 matrix with constant off-diagonal

Let $A$ be the $30\times30$ matrix whose diagonal entries all equal $30$ and whose off-diagonal entries all equal $1$. It has exactly two distinct eigenvalues $\lambda_1,\lambda_2$, with geometric multiplicities $g_1,g_2$. Writing $\lambda=(\lambda_1,\lambda_2)^T$ and $g=(g_1,g_2)^T$, compute $\|\lambda+g\|^2$.

$6964$. Write $A=J+29I$ where $J$ is the all-ones matrix, whose eigenvalues are $30$ (once, eigenvector of ones) and $0$ ($29$ times). So $A$ has eigenvalue $59$ with multiplicity $1$ and $29$ with multiplicity $29$ ($A$ is symmetric, so these are geometric). Then $\lambda+g=(60,58)$ and $60^2+58^2=6964$ (the order does not matter).