Chapter 5 of Ravenel's green book starts with the sentence “[The chromatic spectral sequence] is a mechanism for organizing the Adams-Novikov $E_2$ term and ultimately $\pi_*(S^0)$ itself." My reference question is: where (and how) is the data of this organization clearly recorded for known homotopy groups? I am trying to understand what this filtration is explicitly in relatively low degrees at the prime 2. It is standard to break off the first chromatic piece, like in Figure 1 of https://arxiv.org/abs/2001.04247, but I am looking for tables, figures (color would be great!) or interpretation of labeling schemes (e.g for Figure A.3.2 of Ravenel’s book) to understand in which part of the chromatic filtration each element of homotopy lies, ideally say through the 30-stem.
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