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For the contacts to show properly, you need to have a menu item where your contacts would show. Create a menu item that will show the category (or all the categories if your contacts are from several categories). You probably don't want this menu item in your menu but it needs to exist in order for the contacts to load in a page fit for them. Add .item-xxx {display:none} to your template stylesheet. This way, the menu item won't show (xxx is the menu item ID for the menu item created).

Hello!
It does not work because your template overrides the standard way menus are created. You will have to give this menu item a CSS class in your template (hopefully the templates allows that) and give that class a display:none. Moreover, do not put that menu item first or last in your menu because the template adds a specific class to the first and last elements for look purposes.

I just realized that you don't have links on your contacts so you don't even need to have a menu item (it is just a workaround when you get an error 500). The 1057 error is a documented issue with Joomla!. But just get rid of that menu item and this will work for you!