Interesting, this seems to be a bug in the Modern theme that I hadn't noticed before.
There actually is a login button in the pop-up side menu in Modern, but because your site has a lot of menu items, and the side menu doesn't scroll, then you can't get down to them!
I will look into the side menu problem in the Modern theme and publish a fix in due course.
In the meantime you can get to the admin pages of your site by going to your site's URL and adding 'admin' on the end. The system will then ask you to log in and check you have admin rights before letting you view the page.
You could also try reorganising your site content to have fewer menu items. Or try switching to the new Fresh theme, which has a different arrangement of menu buttons, or the Bootstrap theme which has all sorts of different menu layout options.
I can make a test site available to you (and indeed to any site owner reading this) if you want to try different themes/layouts before putting them on your live site.