Take a holomorphic cusp newform, say $f \in S_k(N)^\mathrm{new}$. It is an eigenvalue of the Atkin-Lehner operator, and this feature allows to express its root number as $$\varepsilon_f = i^k \mu(N) \sqrt{N} \lambda_f(N)$$

Is there any such expression for the root number, only in terms of its level, conductor and coefficients, in the case of Maass forms?

Take a holomorphic cusp newform, say $f \in S_k(N)^\mathrm{new}$, for a squarefree level $N$. It is an eigenvalue of the Atkin-Lehner operator, and this feature allows to express its root number as $$\varepsilon_f = i^k \mu(N) \sqrt{N} \lambda_f(N)$$

Is there any such expression for the root number, only in terms of its level, conductor and coefficients, in the case of Maass forms?