In this v8 revision, in addition to some clarifications, I have added section 12. In this section I describe a method for identifying the latest origins; works with any value of (b) other than 0. Given for example the formulation $\zeta(s)=\sum_{n\ge1}\frac{1}{n^s}$ at each increment of $n$ a point on the complex plane is defined, the traces in question are formed of the vectors connecting these points. The traces resulting on the complex plane from the zeta function of Riemann, can be divided into two parts.In the first part of the traces it is essential to focus attention on the start and end points of the vectors; in the second part it is essential to focus attention on the two origins of particular polygonal spirals, which I call "pseudo-clothoid".All traces start from the origin of the complex plane, the first part of the traces tends to move away from the origin; it develops in a convoluted way reaching variable distances.The two parts behave like two arms, of a mechanism which makes them both rotate but independently and clockwise; the hinge from which the rotation of the second arm begins, is located at the junction point with the first.The rotation of the two arms cyclically brings the free end of the second arm, to pass where the origin of the complex plane is located; but only under one condition does it intercept it.The condition is that the two parts of the trace must compensate each other; in this article I highlight how the compensation takes place between the two parts of the trace.Given a complex number (s) I call (a) the real part and (b) the coefficient of the imaginary part; then s=a+b*i.The value of (b) is the engine of the rotations; only if a=1/2, the value of (b) is neutral with respect to the distances between the two origins, of the pseudo-clothoids.