linear algebra - How to find the eigen values of the following matrix:

Is there any way to find the eigen values of the following matrix:

$A_{2n\times 2n}=$
$$\begin{bmatrix}\textbf{0} & E_{n\times n}\\E^T&\textbf{0}\end{bmatrix}$$

where $E=$
$$\begin{bmatrix}1&1&1&\ldots1\\2&2&2&\ldots 2\\2&2&2&\ldots 2\\\ldots&\ldots&\ldots&\ldots\\\ldots&\ldots&\ldots&\ldots\\\ldots&\ldots&\ldots&\ldots \\2&2&2&\ldots 2\\\end{bmatrix}$$

My try:

I find that rows of $E$ are linearly dependent.
Also every row of $E$ is just a scalar multiple of the first row.

So I was guessing may be $0$ may occur as its eigen value many number of times.

What are some methods to calculate the characteristic polynomial?

Can someone kindly help?