Your sample code was missing some variable definitions, so there may be other issues, but here is what I see:
Assuming that you are passing your lim_plot > 0 test, your next line is calls nthroot on the vector [1] and asks for the lim_plot^th real root of [1].
help nthroot
If I change that line to:
plot(nthroot(c1,lim_plot), '*');
I get the output you are looking for (assuming that my dummy lim_plot and c1 variables are similar to yours).
Hopefully that helps.
Cheers