John Nimmo, who pleaded guilty to sending "menacing" tweets to a feminist campaigner, also targeted Labour MP Stella Creasy, a court heard.
Prosecutor Alison Morgan said Ms Creasy had suffered a "substantial impact" as a result of "these events."
More top news
Sunshine with blustery showers and longer downpours
The landowner at the site of excavation to find Ben Needham has said he is considering withdrawing permission to continue with the dig.
Downton Abbey actress Joanne Froggatt is to star in a new ITV drama exploring the devastating cost of deceit.