Melbourne ‘parakeet’

I wonder if anyone can assist with an identification as my reference books are not accessible.
This morning a green 'parakeet' flew over and landed in a nearby tree. It was green overall. The bill was pinkish red, the head green, no collar was evident, chest and belly green suffused brown (not as clear green as the head), the wing coverts were much paler green than the head, the flight feathers looked dark blue-green. The tail was much longer than the wings.
It was not a Rose-ringed Parakeet, which is a bird I know well from a significant feral population in Durban, South Africa. 

Regards
Richard

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