No way, a Roman coin with a cheap detector? That's wild. What kind of field was it, like a plowed farm field or just some random pasture? I always wonder if the good spots are just someone's boring old cow field.
Plowed fields are your best bet, hands down. The plow brings stuff up from deeper layers every year, especially after a good rain when the ground is soft. Pasture can hold Roman stuff too if it's old enough, but you're fighting roots and a thick mat of grass that makes the detector scream. The trick with a cheap detector is to run the sensitivity a notch lower than max in plowed fields, otherwise you'll chase every nail within 50 feet. And don't skip the trashy spots - Roman coins and bronze bits often get dumped in the same areas as old horseshoes and scrap. Focus on fields that have been farmed for centuries, not just recent corn rotations, and you'll save yourself a lot of ankle pain.