You must be viewing the data in table view. There's an upper limit measured in pixels, not number of fields that limits the number of columns you can view at one time. You can see the rest of the columns be removing othere columns from the view. You can also use list view instead of table view. You can also set up several layouts, each with a different table view of a different set of the fields and switch between them to view the data.
For what it's worth, 350 columns is a lot of fields for a single table. It may be that you need to consider a different structure for your data that breaks up this data into several related tables instead of one table with so many fields.