The field at the centre of a long circular coil carrying current will be parallel straight lines.
When a current is passed in a circular coil, it behaves as a magnet.One of the face of coil behaves as North pole and other one as South pole.
Now, if you will draw its field lines like a bar magnet, you'll find that all the lines will form a loop around the wire. They will exit from one face of coil (North pole) and enter at the other face(South pole). Hence, they will appear parallel and straight at the center.