Think about the magnitude of the physics quantity is very important when we study physics.

Did you notice that the radius is very small: $10^{-4}$ m
And the period of one resolution is very small,too. $T=3.57\times 10^{-10}$ s.
So the electron will make almost $3\times 10^9$ turns in one second.
There is no way you can observed such trajectory with your eye or ordinary device.
And the velocity is very large. $v=1.88\times 10^6$ m/s.
If only 1% of velocity component is along the field line, the electron will move along the field line with speed $u\approx 10^4$m/s $\approx 10$ km/s.

So on average, the electron will move along the field line.  That is also how electrons move between sourth pole and north pole-- following the field line of earth's magnetic field.

When the magnetic field is very strong, it will force electron moving back -- that need more physics analysis.
(or check out [url=http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=182.0]Helmholtz coil / particle trapped in magnetic mirror field[/url])