Hatch theme: centering menu below a logo

I’m trying to change the header of my WordPress site (currently only running on my computer), which uses Hatch — I want to have a centred logo image, and a centred main menu below that. Through tinkering with the code I have managed to achieve everything but the centering of the links *in* the menu. It appears that the divs containing the menu have been successfully centred, but I can only align the links themselves to the left or the right.

Can anyone give me some suggestions? I wonder if it might be to do with the formatting of the ul and li elements in the menu.

Thanks in advance.