Be sensible... you're NOT going to get a thousand HSEROUT's executed in ONE SECOND! Unless of course you've set a BAUD RATE of a couple of MILLION bps?

Get a calculator, work out how many bits ONE of your HSEROUT commands is going to send... then at your chosen BAUD rate how long that is going to take to transmit. From that, you can work out how many characters you'll be able to transmit in one second.