Came across silver ring but its dirty. How can i clean it?

[JustTrynaGrow]

Basically the title. I don't have silver polish and don't plan on buying any. the ring was turned dark grey and washing it with washing up liquid got it to a mostly silver colour but it still has a rose gold- bronze tint that I'm fairly sure isn't actually ment to be part of the ring.

any at home supplies I can use to properly clean this thing and make it shine? I tried leaving it in coke already to no avail

 

[Petsmart]

It’s probably tarnished, i don’t know if you can untarnish something