The Qomar were a species of mathematicians, and believe everything had a complex equation behind its existence. A common cultural point was that people were regarded higher for the number of decimal places to which they can calculate pi in their head. The Doctor was asked how many digits he could calculate in a fan letter from a Qomar.
Physiologically, they were humanoid in appearance, bearing a ridged protrusion that passed from the top of their nose to the top of their forehead. Their height was also shorter than that of the average humanoid. Their vocal cords were capable of speech, like many species, however, they were incapable of allowing a Qomar to sing. As such, their species had never heard anything like music (also attributable to their xenophobic nature).
In 2376, while a Qomar transport was returning to their system, the USS Voyager's primitive scanning beam damaged their propulsion systems, and they were brought aboard for medical treatment. While in sickbay, The Doctor, the ship's holographic Chief Medical Officer, hummed a Human tune. This fascinated the Qomar, and they relayed the information to Prelate Koru, who permitted Voyager to enter orbit of their homeworld.
After an initial concert aboard Voyager and another on the planet, The Doctor became a pop icon. Seven of Nine believed the huge amount of fan mail that The Doctor received was actually an attempt by the Qomar to overload Voyager's communications array. (VOY: "Virtuoso")
Technologically, the Qomar regard themselves as a relatively advanced species. Their ships were so powerful they typically disregarded inferior races they come across. Failing to consider other ships' technology led to the starship Voyager's scanning beam to damage one of their vessels.
Their holographic technology was far more advanced than that of the Federation as of 2376; they considered the Emergency Medical Hologram extremely simplistic. The Qomar on board Voyager at first talked very slowly to him and worried that his medical knowledge was insufficient to treat their injuries. (VOY: "Virtuoso")