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The integrated graphics in this processor supports Max Resolution (HDMI 1.4) 2560X1600@60Hz and Max Resolution (DP) 3840x2160@60Hz, you can see here:
If you want to get a higher resolution you will need to lower the refresh rate, you can see more information about resolutions at the Datasheet. You could be able to get 4096x2160 at 24 Hz or maybe 30Hz with HDMI straight connection.
Intel does not validate for the Intel® NUC any adapters, converter etc. If you want to get the resolution you wish, you will need to use straight connection.