Chebyshev pole calculation
As I've mentioned in a comment, the poles are not "ordered" in any way. You can come up with different versions of the formula for the pole locations, which will give you the same poles in different orders.

But anyway, looking at the formulae in your question, the first thing to notice is that there should be a negative sign in the formula for the real parts $\sigma_k$. Second, the values that you got must be the imaginary parts $\omega_k$ (and not $\sigma_k$ as written in your question). If I evaluate the formula for $\omega_k$ given in your question for $k=1,2,3$ I get the following values (for $n=3$ and $1$ dB pass band ripple):
$$\begin{align}\omega_1&amp;=0.966i\\
\omega_2&amp;=0\\
\omega_3&amp;=-0.966i\end{align}$$

So I get a positive sign for $k=1$ and a negative sign for $k=3$.