Rinka is a financially struggling high school girl living with her single father in Tokyo. One day, while going home from school, she sees a penguin flying in the sky towards the Tokyo Sky Tree. She chases after it only to find fish swimming in the air! One of the fish goes through Rinka and causes her to pass out. She wakes up to find that she has developed the ability to slip through solid objects. (Source: Crunchyroll)

There’s a New Heroine in Town.
 
Rinka Urushiba’s world is turned upside down when she wakes up one day-after falling right through the floor.Encouraged by another ESPer who believes that Rinka’s destiny is to become a hero of justice, she soon learns to use her powers for good. And not a moment too soon, as those with less-than-admirable ambitions descend on Tokyo with their own sets of superpowers. As the mysterious glowing fish flitting through the city skies gift powers seemingly atrandom, foes become friends and alliances are made and broken.And what about that flying penguin? (Source: Kodansha)

Urushiba Rinka was a fairly normal high school girl, though she was a bit poor and her only family was her father. Then one day, she saw a penguin and some glowing fish swimming through the sky. Rinka might have thought it was a hallucination if there hadn't been another witness with her, a boy from her school with a strangely scratched-up face.
Contact with a fish caused her to pass out, and when she awoke, she had developed the power to move through inanimate objects... such as the floor of her apartment! Later, a call from her father showed her that she was not the only one the flying fish bestowed with hard-to-control superpowers! What exactly is going on here? And does Rinka's classmate know more about this situation than he's letting on?
(Source: MangaHelpers)

An elite squadron trained to combat supernatural forces is called in to investigate reports of invisible monsters terrorizing Tokyo, but their mission is complicated by the interference of a rogue exorcist. When the mysterious female slaughters the overmatched attack force, her former comrades are ordered to lock down the crime scene—and forever silence their old friend.
 
(Source: Crunchyroll)
 
 Note: This series is a prequel to the manga series, Ga-Rei.

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