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We present formulas for a family of integrated correlators in 4d maximally supersymmetric SU(N) super Yang-Mills theory, labeled by arbitrary rank N and arbitrary SU(4) charge p. This gives rise to exact results at large charge, for any rank N and complexified gauge coupling \tau (including various double-scaling limits). We discuss features of this expansion, and contrast with known results for extremal two-point functions in superconformal QCD. Our computations are greatly facilitated by the use of SL(2,Z) spectral theory.