Cannot config GoogleLegitimate translator to work

[s5706820]

Let say i am stupid.
I Try free trial of google cloud
get the project up, enable translate API, Set service account for Translated API Agent , Get Json file for API key
try to copy "private_key" to the GoogleAPIKey box in the config file.

Translator output show that "Failed to retrieved translation"
So, i think i config something wrong

But what is it? 😢😢😢

in API analyzed show zero traffic, so i guess it the Translator client that i got it wrong
My Json file is in the format like this.

is the private_key an API key in the first place? 😢😢

{ "type": "service_account", "project_id": *** "private_key_id": *** "private_key": "-----BEGIN PRIVATE KEY-----\n*** "client_email": *** "client_id": *** "auth_uri": *** "token_uri": "https://oauth2.googleapis.com/token", "auth_provider_x509_cert_url": "https://www.googleapis.com/oauth2/v1/certs", "client_x509_cert_url": *** "universe_domain": "googleapis.com" }
please forgive me if this is stupid but i try to read as much doc as i can, but still have no idea.