I have a dataset of $N$ points each with some different value $y$ I try to fit the data to the form $a\cos(2\pi t)+b\sin(2\pi t)+c\cos(4\pi t)+d\sin(4\pi t)+e$. When I'm looking at the standard errors in the fitted parameters for $a,b,c,d,e$, they are really, really small. For $a=-11$, the standard error in $a$ is only around $0.03$. This well-determinedness is kind of unsettling and I doubt its correctness.
Should note that my $N$ is fairly large, around 400, and I'm using Mathematica to find standard errors in the fitted parameters (i.e. [ParameterTable]).
How can one compute the errors in the fitted parameters? Are the standard errors for the parameters it? They seem too small to be true.