@karlnapf sorry I didn't get it. LLT works for this matrix. I tested with another symmetric matrix whose diagonal had real coeffs but non-diagonal elements had imaginary coeffs. LLT failed in that (and LDLT too). (and they did not raise any NumericalIssue in that case, just plain failed!).
I fixed the solver type as complex cause template may cause unnecessary overhead in compile time, because we only need this for complex, so.. :-/ I'm confused!