How to set specific colors and values for a Jet colorbar?

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The attached file contains a contour plor code which gets the following colorbar:
I would like to obtain the same contour plot but following these color bar colors and limits:
colorbarlimits=[6.5696e+000
9.4236e+000
1.3517e+001
1.9390e+001
2.7813e+001
3.9896e+001
5.7228e+001
8.2089e+001
1.1775e+002
1.6890e+002
2.4228e+002
3.4753e+002
4.9851e+002
7.1508e+002
1.0257e+003
1.4713e+003];

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