Origa (Olga Vitalevna Yakovleva – or – Ольга Витальевна Яковлева) was a Russian-born singer who made a name for herself in Japan. I first ran across her music when she was tasked with singing the opening song‡ for Ghost in the Shell: Stand Alone Complex. But her voice had a haunting quality. Sadly she passed away in 2015 at the age of 44 from heart failure.
This is “Electra’s Song” from her 2003 album Era Of Queens.
‡ That opening song, “Inner Universe” can be found at this link. It is the 2nd video in the list. (Only about a minute or two were used for the TV show’s theme.)