Should I send me ex a Christmas gift?

My ex's birthday is coming up, it's around christmas time, and I would like to get her a gift. We live a distance from each other now but we still contact each other once in a while when we miss eachother. We both couldn't find the roles to play in the relationship, I am free and can't be controlled, and she loves to control. I still love her and think about her every day, and she still contacts me because she misses me. What would getting her a gift for the first time in a year communicate on an human/animal psyche level? Thanks

I really hate questions like these.
What do you think you should do?
This situation doesn't require any guidance or advice.

You both are in contact.
You both still have feelings.
Just not together.