Let $F/\mathbb{Q}$ be a number field. I'm interested in knowing if there are formulas for the values of the derivatives $\zeta_{F}^{(n)}(0)$ of the Dedekind zeta function of $F$ at zero.

Maybe if in the general case for an arbitrary number field there are no results, are there any results for particular types of number fields, like quadratic number fields or cyclotomic fields?

I would also appreciate any references you can provide.

Thank you for any help.

PS: I would also be interested if anything is known only for the first values, say for $n = 1, 2, 3$ or so.