Please look at the reverse side of your device.  You will see a large square and a small rectangle.  

On a Z1, in the small rectangle you will see either s/n which indicates the serial number or you will see a series of numbers beginning with (01) and several numbers following that.  The serial number in this case begins after the (21) with a letter and six numbers.

On more recent Z2s, the serial number will consist of a letter followed by 6 numbers.