The $S^3$ column of Toda's 2003 table
H. Toda, Unstable 3-primary Homotopy Groups of Spheres, Econoinformatics (Himeji Dokkyo University) 29 (2003), 1–77 (NDL BibID 6899969, CiNii crid 1523669554954337536). An OCR'd scan is on D. Ravenel's page: Toda03-ocr.pdf (PDF pages 67–68: §5.6, $k\le55$; 80–81: §6.5, $56\le k\le79$).
How we read it. We took only the column $n=3$, that is, $_3\pi_{3+k}(S^3)={}_3\pi_{3+k}(S^2)$. Each dot is a $\mathbb Z/3$ (by the Cohen–Moore–Neisendorfer theorem the exponent of the 3-torsion of $\pi_*(S^3)$ is 3). A row of the table that starts to the right of $n=3$ is not counted.
“mod A”. The table of §6.5 is given modulo the unstable α-families. By §4.3 such a family contributes to $S^3$ one $\mathbb Z/3$ in each of the stems $rq-2$ and $rq-1$ ($q=4$), that is, for $k\equiv2,3\pmod4$: these are the sandwiches and the Toda elements. We added them back (column “+α”). This is the point of our reading to check first.
Checks of the reading: for $n\le22$ it agrees with Toda's 1962 book; for no $n$ does it exceed $E_2$.
| k | n | printed | +α | total | Toda 1962 | source | |
|---|---|---|---|---|---|---|---|
| 3 | 6 | 1 | 1 | 1 | §5.6, with α-families | ||
| 4 | 7 | 0 | 0 | 0 | §5.6, with α-families | ||
| 5 | 8 | 0 | 0 | 0 | §5.6, with α-families | ||
| 6 | 9 | 1 | 1 | 1 | §5.6, with α-families | ||
| 7 | 10 | 1 | 1 | 1 | §5.6, with α-families | ||
| 8 | 11 | 0 | 0 | 0 | §5.6, with α-families | ||
| 9 | 12 | 0 | 0 | 0 | §5.6, with α-families | ||
| 10 | 13 | 1 | 1 | 1 | §5.6, with α-families | ||
| 11 | 14 | 1 | 1 | 1 | §5.6, with α-families | ||
| 12 | 15 | 0 | 0 | 0 | §5.6, with α-families | ||
| 13 | 16 | 1 | 1 | 1 | §5.6, with α-families | ||
| 14 | 17 | 1 | 1 | 1 | §5.6, with α-families | ||
| 15 | 18 | 1 | 1 | 1 | §5.6, with α-families | ||
| 16 | 19 | 1 | 1 | 1 | §5.6, with α-families | ||
| 17 | 20 | 1 | 1 | 1 | §5.6, with α-families | ||
| 18 | 21 | 1 | 1 | 1 | §5.6, with α-families | ||
| 19 | 22 | 1 | 1 | 1 | §5.6, with α-families | ||
| 20 | 23 | 0 | 0 | §5.6, with α-families | |||
| 21 | 24 | 0 | 0 | §5.6, with α-families | |||
| 22 | 25 | 1 | 1 | §5.6, with α-families | |||
| 23 | 26 | 2 | 2 | §5.6, with α-families | |||
| 24 | 27 | 1 | 1 | §5.6, with α-families | |||
| 25 | 28 | 0 | 0 | §5.6, with α-families | |||
| 26 | 29 | 2 | 2 | §5.6, with α-families | |||
| 27 | 30 | 2 | 2 | §5.6, with α-families | |||
| 28 | 31 | 0 | 0 | §5.6, with α-families | |||
| 29 | 32 | 0 | 0 | §5.6, with α-families | |||
| 30 | 33 | 1 | 1 | §5.6, with α-families | |||
| 31 | 34 | 1 | 1 | §5.6, with α-families | |||
| 32 | 35 | 1 | 1 | §5.6, with α-families | |||
| 33 | 36 | 2 | 2 | §5.6, with α-families | |||
| 34 | 37 | 2 | 2 | §5.6, with α-families | |||
| 35 | 38 | 1 | 1 | §5.6, with α-families | |||
| 36 | 39 | 1 | 1 | §5.6, with α-families | |||
| 37 | 40 | 1 | 1 | §5.6, with α-families | |||
| 38 | 41 | 1 | 1 | §5.6, with α-families | |||
| 39 | 42 | 2 | 2 | §5.6, with α-families | |||
| 40 | 43 | 1 | 1 | §5.6, with α-families | |||
| 41 | 44 | 0 | 0 | §5.6, with α-families | |||
| 42 | 45 | 2 | 2 | §5.6, with α-families | |||
| 43 | 46 | 3 | 3 | §5.6, with α-families | |||
| 44 | 47 | 1 | 1 | §5.6, with α-families | |||
| 45 | 48 | 0 | 0 | §5.6, with α-families | |||
| 46 | 49 | 1 | 1 | §5.6, with α-families | |||
| 47 | 50 | 1 | 1 | §5.6, with α-families | |||
| 48 | 51 | 0 | 0 | §5.6, with α-families | |||
| 49 | 52 | 2 | 2 | §5.6, with α-families | |||
| 50 | 53 | 3 | 3 | §5.6, with α-families | |||
| 51 | 54 | 2 | 2 | §5.6, with α-families | |||
| 52 | 55 | 1 | 1 | §5.6, with α-families | |||
| 53 | 56 | 2 | 2 | §5.6, with α-families | |||
| 54 | 57 | 2 | 2 | §5.6, with α-families | |||
| 55 | 58 | 2 | 2 | §5.6, with α-families | |||
| 56 | 59 | 1 | 1 | §6.5, mod A | |||
| 57 | 60 | 0 | 0 | §6.5, mod A | |||
| 58 | 61 | 1 | +1 | 2 | §6.5, mod A | ||
| 59 | 62 | 2 | +1 | 3 | §6.5, mod A | ||
| 60 | 63 | 2 | 2 | §6.5, mod A | |||
| 61 | 64 | 1 | 1 | §6.5, mod A | |||
| 62 | 65 | 1 | +1 | 2 | §6.5, mod A | ||
| 63 | 66 | 1 | +1 | 2 | §6.5, mod A | ||
| 64 | 67 | 0 | 0 | §6.5, mod A | |||
| 65 | 68 | 1 | 1 | §6.5, mod A | |||
| 66 | 69 | 1 | +1 | 2 | §6.5, mod A | ||
| 67 | 70 | 0 | +1 | 1 | §6.5, mod A | ||
| 68 | 71 | 1 | 1 | §6.5, mod A | |||
| 69 | 72 | 1 | 1 | §6.5, mod A | |||
| 70 | 73 | 0 | +1 | 1 | §6.5, mod A | ||
| 71 | 74 | 0 | +1 | 1 | §6.5, mod A | ||
| 72 | 75 | 0 | 0 | §6.5, mod A | |||
| 73 | 76 | 0 | 0 | §6.5, mod A | |||
| 74 | 77 | 0 | +1 | 1 | §6.5, mod A | ||
| 75 | 78 | 1 | +1 | 2 | §6.5, mod A | ||
| 76 | 79 | 1 | 1 | §6.5, mod A | Toda: not final | ||
| 77 | 80 | 0 | 0 | §6.5, mod A | Toda: not final | ||
| 78 | 81 | 1 | +1 | 2 | §6.5, mod A | ||
| 79 | 82 | 2 | +1 | 3 | §6.5, mod A |