Many speech applications require understanding aspects beyond the words being spoken, such as recognizing emotion, detecting whether the speaker is wearing a mask, or distinguishing real from synthetic speech. In this work, we introduce a new state-of-the-art paralinguistic representation derived from large-scale, fully self-supervised training of a 600M+ parameter Conformer-based architecture. We benchmark on a diverse set of speech tasks and demonstrate that simple linear classifiers trained on top of our time-averaged representation outperform nearly all previous results, in some cases by large margins. Our analyses of context-window size demonstrate that, surprisingly, 2 second context-windows achieve 98% the performance of the Conformers that use the full long-term context. Furthermore, while the best per-task representations are extracted internally in the network, stable performance across several layers allows a single universal representation to reach near optimal performance on all tasks.