Power cord supplied with Luxman L-509X Integrated Amp

You can have a qualified technician wire a normal iec cord in the slot to get better sound but i would use it as is until you mesh it with the rest of your system.

Any reason not to use a better Luxman cable such as the JPA-15000
LUXMAN 1.8m JPA-15000 https://www.amazon.com/dp/B002SDS7DO/ref=cm_sw_r_cp_api_glt_fabc_19K970DWPVWTKPRR9969?_encoding=UTF8...

I agree with everyone saying that power cables are hocus pocus, but then I changed my jug cord amp cable to one I made out of 60A wire for shits and giggles... and it sounded better. So now what do I do?
My guess is that dynamics and note transient attack are dependant on responsive current supply and maybe crappy cords are a bottleneck hindrance to that... I don't know. As for those claiming it improves the sound of source components, who knows.

I found the power cord choice for my 509 to be very influential, and critical, to get the most out of it.  

Have you tried a 3 pin IEC cable? It looks like it may fit.