Exporting a logo from from ai format to good quality Instagram profile picture

Hello, 

I have been struggling to find the proper settings (mostly thinking about dimensions, resolution and export method) to export the logo found at the end of this post from ai format to png (I have tried JPEG but I'm having trouble finding the right size/quality balance for IG upload so png has been working better). I have tried all sorts of dimensions (from 180 to 1440 pixels by pixels) and resolutions (from 72 to 288 ppi) but it always turns out that it is blurry, in a pretty ugly way, when uploaded as profile picture on Instagram. 

Any help would be greatly appreciated!