How to find the point on the root locus with a certain damping in Octave

[Deesse23]

So, allegedly, for the gain of 0.723288, the damping is equal to 0.689481 (very close to the required damping of 0.7), and the frequency is 0.104 rad/sec. How do I check whether that's true?

As early as my first semesters at university i figured (and was told by my profs) that anyone calculating 6 digit numbers trying to solve a 2 digit number problem has no idea what he is doing.