Does 'Incognito Browsing' or 'Private Browsing' leaves any traces of visited sites in the router's log?

i share my connection with my landlord who is monitoring my internet activity.
i wonder if i use 'private' or 'incognito' browsing (chrome/safari) - will it leave any traces of visited sites in his FRITZ!Box 7170 router. such as router logs etc.

thank you
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