Hey everyone,
I am trying to find the roots of a very large polynomial, specifically targeting the leading Fisher's zero (the root with the smallest positive imaginary part). I'm using Maple's RootFinding[Analytic] package with Digits := 10, but the results only show 5-digit accuracy (see the attached file plz)

1. Why does RootFinding[Analytic] fail to achieve full 10-digit precision despite the Digits setting? Are there hidden limitations or optional parameters to improve this?

2. Are there alternative methods in Maple to accurately locate only the leading zero (without computing all roots in a region)?
   Root_Poly.mw

I started to use maple recently and I do not know why fsolve does not work in this case:

Sol-NLSE.mw

I am wondering if the conjugate(x[j]) is the reason.

Thanks in advance