Is the $4415 your total net income during the year after adjustments and the standard deduction was applied. if so, you need to allocate that portion of your income as NY sourced income. Aslo you have adjustments against your income of $-9640. You need to determine if these adjustments occurred while living in Colorado or living in NY. You need to indicate what portion of those adjustments are NY based adjustments and report that in your return. if you are not sure on the adjustments you might apply a ratio. So since you lived in NY for 7 months (06/01-12/31) you can take 7/12 X -9640 to determine a pro-rata allocation for NY.
Anyhow, this is the best assessment i can give you without looking at your actual return.
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