The actual internal value on the weapon is an attack time of 625ms - the 1.6 base attacks per second is calculated from this.
Average damage per hit is (143+268)/2 = 205.5
Attack time is 625 / 1.23 = 508ms (rounded down to integer value)
Attacks per second from that is 1000/508= 1.968..., rounded for display on item tooltip to 1.97
The displayed PDPS (which is not actually something the weapon has and isn't as meaningful a value as the importance some players put in it, but that's neither here nor there) appears to be calculated by 205.5 x 1.968... (neither value rounded) giving 404.52755..., which is rounded for display (and this value is only ever for display because it has no relevance to actual damage calculation), resulting in 404.53
I can't guaruntee that's the exact method used for this because I'm only familiar with the code for actually calculating damage dealt, which this isn't a part of, but it gets the correct value and I worked it out entirely ...
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