with a complex scalar in the fundamental representation of $U(N)$ there is such a primary for each positive spin, not just the even ones.) These are symmetric, traceless tensors that can be written schematically as[^8] $$\begin{aligned}
  J_{\mu_1 \dots \mu_s} &= \frac{1}{\sqrt{N}}
  \phi^i \partial_{\mu_1} \cdots \partial_{\mu_s} \phi^i + \cdots {\,.}\end{aligned}$$ For example, the first two such operators are $$\begin{aligned}
  J_{\mu\nu} &= \frac{1}{\sqrt{N}} \left\{
  -\frac{1}{3} \phi^i \partial_\mu \partial_\nu \phi^i + \partial_\mu \phi^i \partial_\nu \phi^i - \frac{1}{3} \delta_{\mu\nu} \partial_\rho \phi^i \partial_\rho \phi^i + \frac{1}{9} \delta_{\mu\nu} \phi^i \square \phi^i \right\}
  {\,,}\label{eq:J2free}\\
  J_{\mu\nu\rho\sigma} &= \frac{1}{\sqrt{N}} \left\{
  \frac{3}{2} \phi^i \partial_\mu \partial_\nu \partial_\rho \partial_\sigma
  \phi^i
  -
  42 \partial_{(\mu} \phi^i
  \partial_\nu \partial_\rho \partial_{\sigma)} \phi^i
  +
  \frac{105}{2} \partial_{(\mu} \partial_\nu \phi^i
  \partial_\rho \partial_{\sigma)} \phi^i
  \right. \nonumber\\ &\quad
  +
  18 \delta_{(\mu\nu} \partial_\rho \partial_{\sigma)}
  \partial_\chi \phi^i \partial_\chi \phi^i
  -
  30 \delta_{(\mu\nu|} \partial_\chi \partial_{|\rho|} \phi^i
  \partial_{\chi} \partial_{|\sigma)} \phi^i
  +
  3 \delta_{(\mu\nu} \delta_{\rho\sigma)}
  \partial_\chi \partial_\xi \phi^i
  \partial_\chi \partial_\xi \phi^i
  \nonumber\\ &\quad
  -
  \frac{9}{7} \delta_{(\mu\nu} \phi^i \partial_\rho \partial_{\sigma)}
  \square \phi^i
  +
  18 \delta_{(\mu\nu} \partial_\rho \phi^i \partial_{\sigma)}
  \square \phi^i
  -
  15 \delta_{(\mu\nu} \partial_\rho \partial_{\sigma)} \phi^i
  \square \phi^i
  \nonumber\\ &\quad \left.
  +
  \frac{9}{70} \delta_{(\mu\nu} \delta_{\rho\sigma)}
  \phi^i \square \square \phi^i
  +
  \frac{3}{2} \delta_{(\mu\nu} \delta_{\rho\sigma)}
  \square \phi^i \square \phi^i
  -
  \frac{18}{5} \delta_{(\mu\nu} \delta_{\rho\sigma)}
  \partial_\chi \phi^i \partial_\chi \square \phi^i \right\} 