Nagi is the sole heir to the Sanzenin fortune—and we're talking absurdly wealthy here. She once threw away 20 trillion yen on a failed investment like it was pocket change. That's the level of money we're dealing with.
Her personality is a mess of contradictions. She's short-tempered, spoiled, and hates losing more than anything. She struggles to admit when she's wrong and has a hard time being honest about her feelings, especially regarding Hayate. She acts immature a lot, though underneath it all she's intelligent and genuinely cares about the people close to her—she just won't admit it directly, preferring to hide her concern behind formal language or blunt indifference. She's a tomboy with a tsundere streak, which means she pushes people away while secretly wanting them around.
Despite having actual financial talent and intelligence, she despises school and learning in general. Somehow she's still smart enough to skip three grades at one of Tokyo's top academies. The contradiction pretty much sums her up: brilliant but resistant, talented but reluctant.
Nagi is basically a hikkikomori princess. Going outside is dangerous because of her status, so she rarely leaves her mansion—a "small" one by Sanzenin standards, but enormous by normal measurements. She keeps minimal staff around because she doesn't like company. Instead, she spends her time on pure otaku hobbies: reading and writing manga, watching anime, playing video games, and drawing her own manga. She's submitted entries to amateur manga competitions multiple times, though none have won yet.
Her only family left is her grandfather, whom she doesn't particularly like. She's closer to Maria, her family's maid, whom she regards as a mother or older sister figure. She's made it crystal clear to Hayate that if he ever touches Maria "indecently," she'll never forgive him.
As for Hayate himself—Nagi has a crush on him, though she's convinced herself he has feelings for her. She hates the idea of anyone else liking him.
Likes: manga (reading, drawing, and writing), anime, video games
Dislikes: school, spicy food, dark places, finance, learning, being kidnapped, losing to anyone, being alone, anyone who "likes" Hayate
Content compiled by AnimeList.moe from publicly available sources.