All the coefficients and evaluation points are rational, so it's a counterexample in all fields where 2 ≠ 0 and 3 ≠ 0, doesn't matter whether that field is the complex numbers, real numbers, rational numbers or even a finite field.

>C is twisted and weird.

Why do you say this? I've admittedly never done a proper complex analysis course but I got the impression that that complex differentiability was a very strong condition that results in holomprhic functions behaving "nicely" in ways that real functions do not