The 120 ml bottles have no nicotine. The only thing I can find about the nicotine I want to buy is:
It is 99.9% pure nicotine
100mg/ml and comes in 100% VG or PG base.
An important bit of terminology: 100 mg/ml nicotine base is actually about 10% nicotine. 99% pure nicotine almost certainly refers to the nicotine used to make the 10% solution. Pure nicotine is extremely toxic and should only be handled by trained professional chemists in a laboratory. And note that 10% (100 mg/ml) nicotine is strong enough that safety precautions should be used. Do read the stickies at the top of this DIY subforum before proceeding.
All that said, Sgt.Rock's math is correct; if you are using 100 mg/ml base, you would need to add 23 ml total to the 360 ml of liquid you have, making the final volume 383 ml, and you can scale that if using different base strength, e.g. 46 ml of 50 mg/ml base. It is highly recommended that, along with reading the stickies, you download one of the e-liquid calculators and learn how to use it.