Corinne Malvern a character supposed to be three years old), a 1907 New York Evening Telegram article and ships' passenger records, make it clear she was born in 1901. Malvern performed in the Henry W. Savage New English Grand Opera Company in the American premiere of Puccini's opera Madama Butterfly in the role of the child "Dolore" ("Sorrow," or "Trouble" in English), Butterfly's son, in front of an audience that included the Viscount Aoki, Japanese Ambassador to the United States, and John Luther Long, author of the novella on which the opera was based, on October 15, 1907, and subsequently toured with
Dirichlet character 1, Euler's theorem says that "a" ≡ 1 (mod "k") (where φ("k") is the totient function). Therefore, by 5) and 4), χ("a") = χ(1) = 1, and by 3), χ("a") =χ("a"). So The unique character of period 1 is called the trivial character. Note that any character vanishes at 0 except the trivial one, which is 1 on all integers. A character is called principal if it assumes the value 1 for arguments coprime to its modulus and otherwise is 0. A character is called real if it assumes real values only. A character which is not real is called