the calculator on this site is actually wrong, and has the mana and ability power wrong, it messes up with the staffs, that it should be is 3770 mana and 735 ability power.

the whole idea of this sona is that she fires out her spells as much as possible, with as much results as possible. the main spell here is her W, her healing spell. this that much AP you will be healing a lot, and very fast (every 4 seconds i think it is). dont worry about the staffs max mana thing, with the speed you can pop these spells, u will max it out easy.

Pros:
lots of late game AP
massive heals
powerchord and lich blade combos are great for killing turrets and finishing of champions
great late game support
good for harassing
can help your allies push through a stalemate battle

Cons:
the staff takes a long time 2 make early game
slow movement early game
acceptable 2 magic damage
easy to get ganked early game
sometimes killsteals