It's my understanding that 2013 Z1K in the USA should not have O2 sensor installed in the Exhaust. You have a full aftermarket exhaust system so removal of the exhaust servo valve system can be fooled with a servo buddy/Exhaust Servo Eliminator (ESE) or reprogrammed in the re-flash. If for instance this bike's original owner just installed a full exhaust and a ESE I would think it would not run well throughout the power band unless it had a PCV and or re flash. I also have an air box mod with block off plates installed and a different air filter. I have mapped my PCV for more mid-range since I am old and don't do much high rpm work or banging the rev limiter for attention in traffic. I guess you will have to take a close look at the bike and see what was done and go from there. Good luck and enjoy the ZZZZZZ. PM me if I can be of any help or provide you with any information. I have a service manual also for numbers and tech shit.
B.
http://www.ivansperformanceproducts.com/2010z1000.htm
https://www.healtech-electronics.com/products/