  In 2018, Sz\"{o}ll\H{o}si and \"{O}sterg\r{a}rd enumerated some sets of
equiangular lines with common angle $\arccos(1/3)$ with a computer.
Furthermore, they verified that the numbers $\omega(n)$ of sets of $n$
equiangular lines with common angle $\arccos(1/3)$ in dimension $7$ are almost
symmetric around $n=14$. In this paper, we construct the other sets of
equiangular lines with common angle $\arccos(1/3)$ from root lattices of type
$A$ or $D$ with the aid of switching roots. In addition, we prove that the
numbers $\omega(n)$ are almost symmetric without a computer.
