Section 126. The regular election under Plan F shall take place on the Tuesday next following the first Monday of November in every odd-numbered year. The mayor, all members of the city council, the school committee, and any board of trustees or other officers whose election by the voters of the city is required by reason of the fact that the city has accepted any gift, devise or bequest shall be elected at each such election. In the case of offices to be filled by all the voters of the city nomination papers shall be signed by a number of voters as follows:?for mayor, three hundred voters; for school committee, councillor-at-large and any other office, two hundred voters. In the case of ward councillor, nomination papers shall be signed by at least one hundred voters of the ward. In order that their names may be certified on said nomination papers signers shall not be enrolled in any other party than that whose nomination the candidate seeks.