Traditional (pre-tax) 401(k) contributions and Roth (after-tax) 401(k) contributions do not count toward your annual IRA or Roth IRA contribution limits.
You can contribute to an IRA or Roth IRA and a Traditional or Roth 401(k), as long as you meet the contribution rules for IRAs and Roth IRAs.
However, contributing to a Traditional or Roth 401(k) may reduce the amount you can deduct from your federal income taxes depending on your income levels.
You should check your eligibility to contribute an IRA or Roth IRA, and the impact on deductions, with the IRS or a tax professional.