2002 Saturn SL2 P0404 and P0405 Codes - How to Complete Drive Cycle for Smog Check

I'm currently going through the vehicle registration process in California, but during the mandatory smog check, my 2002 Saturn SL2 triggered two diagnostic trouble codes: P0404 and P0405. The check engine light has been on steadily, indicating an issue with the exhaust system. Rather than continue driving a potentially non-compliant vehicle, I returned it to the point of purchase where they replaced the fuel pump valve. After the repair, the check engine light turned off, and the vehicle appears to be functioning normally. However, I'm still unsure about whether a specific drive cycle is required for these codes to clear completely. I need clarification on which drive cycle is necessary for my 2002 Saturn SL2—whether it's a simple or full cycle—and if simply turning the car off and on will complete the cycle. Any guidance would be greatly appreciated, as I'm concerned about the vehicle being impounded before I can finalize the smog check process. Thank you in advance for your help.