...Mechanic Seventh
The seventh degree components, (top pair), are the "twice-outer" roots of a heptic function.
In this flat view of the complex plane, one readily sees the hyperbolesque shape of these roots.

The vertical line at center is the "real" function: (x to the seventh degree, plus four-thirds x).

It appears as though the center pair may, from this angle, form a rectangular hyperbola.

The upper and lower pairs seem to be a matched set of non-rectangular hyperbolas.

Given the relative simplicity of the curves, it is important to note, again,

that this higher-degree function is pure except for one linear element, (four-thirds x).

If other elements were added to the mix, the curves would become that much more complicated.
Next I thought I'd roll the box down, having not done so lately.

More than anything else it's for a pretty picture, but there's information in every view.

One curious thing here, is the parabolesque gap between the two top root curves.

See also the lower root curves, as they pass behind, then through the curtain.
Rolling it down further, with the fog effect applied.
Full upright; note the complementarity between those root curves close to the main function.

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And below find the same view flat, with these curves overlapped.
In the figures above and below, the image turns toward its profile.

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The heptic function, x to the seventh degree plus four-thirds x, cuts the grain of its roots.
Aphrodite's Last Mechanic