Plot a list vertically in a graph

For a parametrized matrix $ H(\lambda)$ , how do I plot all the eigenvalues of the matrix vertically corresponding to a particular value of $ \lambda$ ? i.e. we use $ \lambda$ as the horizontal axis and the eigenvalues are along the vertically axis.

ps. We can for sure plot each of these points separately, but I’m wondering whether there is a simpler way. Thanks.