We know that the coefficients of the $ n$ th cyclotomic polynomial can be large.
However if $ n=2^kp^rq^m$ where $ p,q$ are odd primes then the coefficients are in $ \{0,1,1\}$ .
Given cyclotomic polynomial $ \Phi_{2^kp^rq^m}(x)$ denote $ \Phi_{abs,2^kp^rq^m}(x)$ to be polynomial with coefficients being absolute value of coefficients of $ \Phi_{2^kp^rq^m}(x)$ .
Consider map $ \pi_{c}:f(x))\rightarrow\Bbb Z^{deg(f(x))+1}$ where $ x^t$ coefficient of $ f(x)$ are mapped to $ deg(f(x))+1$ length vector with integer coefficients at location $ (t+c)\bmod deg(f(x))+1$ (the locations are $ 0$ through $ deg(f(x))$ ).
Are there infinitely many $ k,p,q,r,m$ at which
 at every $ 0\leq c<c’\leq deg(\Phi_{2^kp^rq^m}(x))$ we have $ $ \pi_c(\Phi_{2^kp^rq^m}(x))\neq \pi_{c’}(\Phi_{2^kp^rq^m}(x))?$ $
From MTyson’s comment it looks like $ k=0$ , $ rm=0$ and $ r+m=1$ is needed for this (that is $ 2^kp^rq^m$ is either $ p$ or $ q$ ). Nevertheless we have infinitely many $ k,p,q,r,m$ at which $ 1$ . holds.

at every $ 0\leq c<c’\leq deg(\Phi_{2^kp^rq^m}(x))$ we have $ 0\leq c<c’\leq deg(\Phi_{abs,2^kp^rq^m}(x))$ do we have $ $ \pi_c(\Phi_{abs,2^kp^rq^m}(x))\neq \pi_{c’}(\Phi_{abs,2^kp^rq^m}(x))?$ $

$ \Phi_{abs,2^kp^rq^m}(x))$ does not have more than $ \frac{deg(\Phi_{abs,2^kp^rq^m}(x))}{(\log(deg(\Phi_{abs,2^kp^rq^m}(x))))!}$ contiguous repeating coefficient ($ 0,1$ varies sufficiently enough)?

What are the distributions of $ $ \langle\pi_c(\Phi_{2^kp^rq^m}(x)), \pi_{c’}(\Phi_{2^kp^rq^m}(x))\rangle$ $ $ $ \langle\pi_{c}(\Phi_{abs,2^kp^rq^m}(x)), \pi_{c’}(\Phi_{abs,2^kp^rq^m}(x))\rangle?$ $