New Hampshire is one of only five states that still has a party column ballot. Of those, it is the only one that rotates the columns so that every column has an equal chance to appear in the most prominent position, the left-hand side of the ballot.
The other party-column states put the two major parties in the most prominent position. Those states are Connecticut, New York, New Jersey, and Delaware.
This year the New Hampshire lottery for ballot position put the “other” column in the most prominent position.
One can easily criticize New Hampshire for not giving each party its own column. Instead, only the two largest parties gets their own column, and all others are placed in the “other” column. This misleads voters into thinking there is some sort of association between the various minor parties in that column. See this November 2024 ballot. To see any ballot, just choose any town at random. They all look alike. Thanks to Tony Roza for the link.