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for various flavours of connection strings.
If the administrator userid is of type windows user then it may be the domain administrator or it may be an account called administrator if the administration rights have been removed. If it is of type standard, then it may or may not be an administrative account of the name administrator.
rm is correct in saying the default admin account is sa for sql authentication whereas in windows it ia administrator, which may be a member of the builtin/administrators group unless things have been chosen otherwise.