Do I need to report any gains or losses in a roth ira for purposes of filing my income taxes

No, you will not enter any gains or losses that occur within your Roth IRA on your income tax return. You will only need to report any distribution/withdrawals/rollovers related to your Roth IRA on your income tax return. (For any reportable Roth IRA transaction, you will receive a 1099-R from your Roth IRA administrator.)

Please refer to IRS - Roth IRAs - Publication 590 for more information about Roth IRAs.

You only report contributions or withdrawals or rollovers.  You will get a 1099R for those.  You have to report any 1099R you get.