A short answer is no, the M6E Nano does not work with those frequencies. The Nano will only work with Gen2 UHF tags like these. The UHF frequency bands are 902-928MHz and 865-868MHz depending on your region.
We do not have any RFID readers that would work at 250Hz but we do have this MIFARE RFID Module that works with 13.56MHz tags. We have an Arduino shield for this reader here and have some example code to get you started with that shield here.
I hope this helps you find the right parts for your project. If you have any other questions about the M6E Nano or our MIFARE RFID readers and compatible tags and shields, let us know and we would be happy to help as much as we can.