Maji–Sarkar conjecture on zeros of higher-power Ramanujan polynomials

Let $k$ and $\ell$ be fixed natural numbers, and define

$$R_{2k+1}^{(\ell)}(Z):=\sum_{j=0}^{k+1}(-1)^{(\ell+1)j}\frac{B_{2j}^{\ell}}{((2j)!)^{\ell}}\frac{B_{2k+2-2j}^{\ell}}{((2k+2-2j)!)^{\ell}}Z^j.$$

Here $B_m$ denotes the $m$th Bernoulli number; the variable $Z$ replaces $z^{2\ell}$ in the one-variable generalization of the Ramanujan polynomial. Conjecture on the zeros of $R_{2k+1}^{(\ell)}$. All non-real roots of $R_{2k+1}^{(\ell)}(Z)$ are simple and lie on the unit circle $|Z|=1$. For $\ell=1$, this polynomial coincides with the classical Ramanujan polynomial. The conjecture is motivated by numerical evidence and proposes a unit-circle property for the non-real zeros, but the supplied text gives no resolution.