Any person intending to contest the election or the eligibility of any one returned by the board of canvass as a member of either branch of the General Assembly from any of the counties of this State shall at least 20 days before the meeting of the General Assembly give written notice of such intention to the person whose seat that person intends to contest, and within 10 days after the notice shall deliver to the person a written specification of the several grounds upon which that person intends to contest the election or the eligibility of such person. If 1 of such grounds shall be that illegal votes were given at such election for the person so returned, then such specification shall particularly set forth the name of each alleged illegal voter, with the several objections to the legality of that voter's vote.