  Utilizing inverse Mellin transform of the symmetric square $L$-function
attached to Ramanujan tau function, Hafner and Stopple proved a conjecture of
Zagier, which states that the constant term of the automorphic function
$y^{12}|\Delta(z)|^2$ i.e., the Lambert series $y^{12}\sum_{n=1}^\infty
\tau(n)^2 e^{-4 \pi n y}$ can be expressed in terms of the non-trivial zeros of
the Riemann zeta function. This study examines certain Lambert series
associated to Siegel cusp forms of degree $n$ twisted by a character $\chi$ and
observes a similar phenomenon.
