Given the value and the pattern, how can I determine a value for this knife?
There are Steam groups dedicated to finding the correct values for items like Blue Gems, Crimson Webs with intricate webbings, low float items, etc. That would probably be the best place you can ask and get a knowledgeable answer.
Otherwise, csgo.steamanalyst.com tracks the current price as well as the price history of every item in the game. It also tells you price trends and amount of items sold. However, these are for market value items only.
CSGO trading reddit may also give you insight on how much your item is worth as people request to trade certain items for theirs and you can get a sense of what item is equivalent to another.