Frank Zinn resigned in 1959 upon his appointment as a judge of the New Mexico District Court. The Governor appointed Hilton Dickson to fill the vacancy and Dickson served the remainder of the term.
The source for the canvass is New Mexico Election Returns 1911-1969, compiled by the New Mexico Secretary of State in 1970 and available at the state library in Santa Fe.
Source for Popular Vote data: New Mexico Secretary of State, "For Attorney General," Canvass of Returns of General Election Held November 4, 1958 (Santa Fe, 1958)