^^
Nissan's factory fill is the Nissan Ester 5w30 which is a conventional oil base with Ester.
Ester's are typically found in some of the more expensive Group V synthetics but when combined with the conventional oil base, some people call them "blends" which isn't a bad interpretation. It is however, different from the synthetic blends found on the market which don't have Esters.
To touch on the original post, the 370Z can definitely run a synthetic but there is always debate as to when to make the switch. Most people recommend somewhere between 3 - 10K. I'll probably make the switch myself at 7,500 miles. I may be able to do it earlier with no harm to break-in but its not really worth the risk in my opinion. Running the car for the first couple thousand miles on the Nissan Ester "blend" won't hurt it.
Also, many cite that a lot of cars (for ex. the GTR, Corvette, MB cars) come with a synthetic factory fill and therefore come to the conclusion that synthetics are preferred for brand new engines. Keep in mind, that the oil manufacturers negotiated these factory fill contracts with the auto companies. While synthetic in a new engine probably isn't as bad as some claim, this doesn't mean its the best or ideal oil for the first 3-10K. Remember that most drivers don't want to go through all the research and trouble that we do here on oils and break-in so if the manufacturer recommends a synthetic for the long-term use of the car and wants to keep the instructions simple, I can't argue with them for putting it in there from day one.
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