Adobe Illustrator Color Palette Not Matching Actual Colors of the Image

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Hi folks,

I am currently using Adobe Illustrator for my paintings by numbers. Right now, I have the following issue: 

The colors from my color pallette do not match the colors on the actual picture/image. I have attached an image to this thread so you can see the difference I am talking about.  Can you please tell what the issue is here? And what should I do to fix it?

Any leads would be much appreciated.

Best,
Branimir

[Monika Gause]

Can we please see the original image?

And how is Image Trace set up?

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[Monika Gause]

With your options you are reducing the number of colors. So Illustrator combines several different original colors into one.

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Hi Monika, 

I currently use my own color pallette of 400 individual colors, which I physically have in small bottles. I usually always use 24 colors for the tracing, because if the colors are less than that the image will be no good. The problem is the following:
After I try to replace the original colors of the picture/image with the ones from my pallete, they eventually appear pale and are obviously different from the pallete's colors. This makes it really hard for me to work. Can you please tell me where the problem is?