Improper sampling of wave
You are doing 2000 samples really close together in rapid succession with no concept of time between them, then you are spending a considerable amount of time sending that data through serial. 

That's not how you sample signals. 

Instead, you need to set up some kind of time-based periodic sampling system, either through a timer interrupt or some other facility provided by the ADC (read the datasheet to see what interrupts the ADC can generate and what sample trigger sources there are) which runs completely asynchronously.  Then when (and only when) a sample set has been captured do you send that data through serial.

If your sampling takes longer than your sending through serial (unlikely) and you have the memory for it you can set up two buffers and "ping-pong" between them so you are sampling at the same time as sending.  Otherwise, all you will be able to do is capture a short window of data and then send it afterwards, so you get short bursts of samples.