The new Democratic president of the Maine Senate wants to smooth relations with the state’s Republican governor over dinner. Senate President Justin Alfond sent Gov. Paul LePage a handwritten note Thursday inviting the governor and his wife to dinner with Alfond and his wife “at a place of your choosing.” Alfond’s office provided the note in response to a public records request from the Portland Press Herald. The invitation followed LePage’s cancellation Tuesday of a meeting with incoming Democratic legislative leaders to discuss issues facing the new Legislature. LePage said he would not meet with Democrats until the party called off a “tracker” hired by the Maine Democratic Party to videotape LePage’s public appearances. There was no immediate word on whether LePage had accepted the dinner invitation.