Order 56.
| C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | C11 | C12 | C13 | C14 | C15 | C16 | C17 | C18 | C19 | C20 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 7 | 7 | 7 | 7 |
| order | 1 | 2 | 4 | 4 | 7 | 7 | 7 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 28 | 28 | 8 | 8 | 8 | 8 |
| χ1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| χ2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 |
| χ3 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | ||||
| χ4 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | ||||
| χ5 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | −ζ15−ζ23−ζ31−ζ39−ζ47−ζ55 | ζ15+ζ23+ζ31+ζ39+ζ47+ζ55 | −ζ5−ζ13−ζ29−ζ37−ζ45−ζ53 | ζ5+ζ13+ζ29+ζ37+ζ45+ζ53 | ||||||||
| χ6 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | ζ15+ζ23+ζ31+ζ39+ζ47+ζ55 | −ζ15−ζ23−ζ31−ζ39−ζ47−ζ55 | ζ5+ζ13+ζ29+ζ37+ζ45+ζ53 | −ζ5−ζ13−ζ29−ζ37−ζ45−ζ53 | ||||||||
| χ7 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | −ζ5−ζ13−ζ29−ζ37−ζ45−ζ53 | ζ5+ζ13+ζ29+ζ37+ζ45+ζ53 | −ζ15−ζ23−ζ31−ζ39−ζ47−ζ55 | ζ15+ζ23+ζ31+ζ39+ζ47+ζ55 | ||||||||
| χ8 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | ζ5+ζ13+ζ29+ζ37+ζ45+ζ53 | −ζ5−ζ13−ζ29−ζ37−ζ45−ζ53 | ζ15+ζ23+ζ31+ζ39+ζ47+ζ55 | −ζ15−ζ23−ζ31−ζ39−ζ47−ζ55 | ||||||||
| χ9 | 2 | 2 | 2 | 2 | −ζ20−ζ36 | −ζ12−ζ44 | −ζ4−ζ52 | −ζ20−ζ36 | −ζ12−ζ44 | −ζ4−ζ52 | −ζ20−ζ36 | −ζ12−ζ44 | −ζ4−ζ52 | −ζ20−ζ36 | −ζ12−ζ44 | −ζ4−ζ52 | 0 | 0 | 0 | 0 |
| χ10 | 2 | 2 | 2 | 2 | −ζ12−ζ44 | −ζ4−ζ52 | −ζ20−ζ36 | −ζ12−ζ44 | −ζ4−ζ52 | −ζ20−ζ36 | −ζ12−ζ44 | −ζ4−ζ52 | −ζ20−ζ36 | −ζ12−ζ44 | −ζ4−ζ52 | −ζ20−ζ36 | 0 | 0 | 0 | 0 |
| χ11 | 2 | 2 | 2 | 2 | −ζ4−ζ52 | −ζ20−ζ36 | −ζ12−ζ44 | −ζ4−ζ52 | −ζ20−ζ36 | −ζ12−ζ44 | −ζ4−ζ52 | −ζ20−ζ36 | −ζ12−ζ44 | −ζ4−ζ52 | −ζ20−ζ36 | −ζ12−ζ44 | 0 | 0 | 0 | 0 |
| χ12 | 2 | 2 | -2 | -2 | −ζ20−ζ36 | −ζ12−ζ44 | −ζ4−ζ52 | −ζ20−ζ36 | −ζ12−ζ44 | −ζ4−ζ52 | ζ20+ζ36 | ζ12+ζ44 | ζ4+ζ52 | ζ20+ζ36 | ζ12+ζ44 | ζ4+ζ52 | 0 | 0 | 0 | 0 |
| χ13 | 2 | 2 | -2 | -2 | −ζ12−ζ44 | −ζ4−ζ52 | −ζ20−ζ36 | −ζ12−ζ44 | −ζ4−ζ52 | −ζ20−ζ36 | ζ12+ζ44 | ζ4+ζ52 | ζ20+ζ36 | ζ12+ζ44 | ζ4+ζ52 | ζ20+ζ36 | 0 | 0 | 0 | 0 |
| χ14 | 2 | 2 | -2 | -2 | −ζ4−ζ52 | −ζ20−ζ36 | −ζ12−ζ44 | −ζ4−ζ52 | −ζ20−ζ36 | −ζ12−ζ44 | ζ4+ζ52 | ζ20+ζ36 | ζ12+ζ44 | ζ4+ζ52 | ζ20+ζ36 | ζ12+ζ44 | 0 | 0 | 0 | 0 |
| χ15 | 2 | -2 | −ζ20−ζ36 | −ζ12−ζ44 | −ζ4−ζ52 | ζ20+ζ36 | ζ12+ζ44 | ζ4+ζ52 | ζ6+ζ22 | ζ30+ζ54 | ζ38+ζ46 | −ζ6−ζ22 | −ζ30−ζ54 | −ζ38−ζ46 | 0 | 0 | 0 | 0 | ||
| χ16 | 2 | -2 | −ζ12−ζ44 | −ζ4−ζ52 | −ζ20−ζ36 | ζ12+ζ44 | ζ4+ζ52 | ζ20+ζ36 | ζ30+ζ54 | ζ38+ζ46 | ζ6+ζ22 | −ζ30−ζ54 | −ζ38−ζ46 | −ζ6−ζ22 | 0 | 0 | 0 | 0 | ||
| χ17 | 2 | -2 | −ζ4−ζ52 | −ζ20−ζ36 | −ζ12−ζ44 | ζ4+ζ52 | ζ20+ζ36 | ζ12+ζ44 | ζ38+ζ46 | ζ6+ζ22 | ζ30+ζ54 | −ζ38−ζ46 | −ζ6−ζ22 | −ζ30−ζ54 | 0 | 0 | 0 | 0 | ||
| χ18 | 2 | -2 | −ζ20−ζ36 | −ζ12−ζ44 | −ζ4−ζ52 | ζ20+ζ36 | ζ12+ζ44 | ζ4+ζ52 | −ζ6−ζ22 | −ζ30−ζ54 | −ζ38−ζ46 | ζ6+ζ22 | ζ30+ζ54 | ζ38+ζ46 | 0 | 0 | 0 | 0 | ||
| χ19 | 2 | -2 | −ζ12−ζ44 | −ζ4−ζ52 | −ζ20−ζ36 | ζ12+ζ44 | ζ4+ζ52 | ζ20+ζ36 | −ζ30−ζ54 | −ζ38−ζ46 | −ζ6−ζ22 | ζ30+ζ54 | ζ38+ζ46 | ζ6+ζ22 | 0 | 0 | 0 | 0 | ||
| χ20 | 2 | -2 | −ζ4−ζ52 | −ζ20−ζ36 | −ζ12−ζ44 | ζ4+ζ52 | ζ20+ζ36 | ζ12+ζ44 | −ζ38−ζ46 | −ζ6−ζ22 | −ζ30−ζ54 | ζ38+ζ46 | ζ6+ζ22 | ζ30+ζ54 | 0 | 0 | 0 | 0 |
Here ζ is a primitive root of unity of order 56 (ζ56 = 1); i = ζ14.