Order 120.
| C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | C11 | C12 | C13 | C14 | C15 | C16 | C17 | C18 | C19 | C20 | C21 | C22 | C23 | C24 | C25 | C26 | C27 | C28 | C29 | C30 | C31 | C32 | C33 | C34 | C35 | C36 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| size | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 15 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 15 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 15 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 15 |
| order | 1 | 3 | 5 | 5 | 15 | 15 | 15 | 15 | 2 | 4 | 12 | 20 | 20 | 60 | 60 | 60 | 60 | 4 | 2 | 6 | 10 | 10 | 30 | 30 | 30 | 30 | 2 | 4 | 12 | 20 | 20 | 60 | 60 | 60 | 60 | 4 |
| χ1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 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 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 |
| χ3 | 2 | 2 | 0 | 2 | 2 | 0 | 2 | 2 | 0 | 2 | 2 | 0 | ||||||||||||||||||||||||
| χ4 | 2 | 2 | 0 | 2 | 2 | 0 | 2 | 2 | 0 | 2 | 2 | 0 | ||||||||||||||||||||||||
| χ5 | 2 | -1 | 2 | 2 | -1 | -1 | -1 | -1 | 0 | 2 | -1 | 2 | 2 | -1 | -1 | -1 | -1 | 0 | 2 | -1 | 2 | 2 | -1 | -1 | -1 | -1 | 0 | 2 | -1 | 2 | 2 | -1 | -1 | -1 | -1 | 0 |
| χ6 | 2 | -1 | −ζ22−ζ38 | −ζ2−ζ58 | −ζ14−ζ46 | −ζ26−ζ34 | 0 | 2 | -1 | −ζ22−ζ38 | −ζ2−ζ58 | −ζ14−ζ46 | −ζ26−ζ34 | 0 | 2 | -1 | −ζ22−ζ38 | −ζ2−ζ58 | −ζ14−ζ46 | −ζ26−ζ34 | 0 | 2 | -1 | −ζ22−ζ38 | −ζ2−ζ58 | −ζ14−ζ46 | −ζ26−ζ34 | 0 | ||||||||
| χ7 | 2 | -1 | −ζ2−ζ58 | −ζ22−ζ38 | −ζ26−ζ34 | −ζ14−ζ46 | 0 | 2 | -1 | −ζ2−ζ58 | −ζ22−ζ38 | −ζ26−ζ34 | −ζ14−ζ46 | 0 | 2 | -1 | −ζ2−ζ58 | −ζ22−ζ38 | −ζ26−ζ34 | −ζ14−ζ46 | 0 | 2 | -1 | −ζ2−ζ58 | −ζ22−ζ38 | −ζ26−ζ34 | −ζ14−ζ46 | 0 | ||||||||
| χ8 | 2 | -1 | −ζ14−ζ46 | −ζ26−ζ34 | −ζ2−ζ58 | −ζ22−ζ38 | 0 | 2 | -1 | −ζ14−ζ46 | −ζ26−ζ34 | −ζ2−ζ58 | −ζ22−ζ38 | 0 | 2 | -1 | −ζ14−ζ46 | −ζ26−ζ34 | −ζ2−ζ58 | −ζ22−ζ38 | 0 | 2 | -1 | −ζ14−ζ46 | −ζ26−ζ34 | −ζ2−ζ58 | −ζ22−ζ38 | 0 | ||||||||
| χ9 | 2 | -1 | −ζ26−ζ34 | −ζ14−ζ46 | −ζ22−ζ38 | −ζ2−ζ58 | 0 | 2 | -1 | −ζ26−ζ34 | −ζ14−ζ46 | −ζ22−ζ38 | −ζ2−ζ58 | 0 | 2 | -1 | −ζ26−ζ34 | −ζ14−ζ46 | −ζ22−ζ38 | −ζ2−ζ58 | 0 | 2 | -1 | −ζ26−ζ34 | −ζ14−ζ46 | −ζ22−ζ38 | −ζ2−ζ58 | 0 | ||||||||
| χ10 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | ||||||||||||||||||
| χ11 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | ||||||||||||||||||
| χ12 | 2 | 2 | 0 | −ζ7−ζ23−ζ43−ζ47 | −ζ11−ζ19−ζ31−ζ59 | −ζ7−ζ23−ζ43−ζ47 | −ζ7−ζ23−ζ43−ζ47 | −ζ11−ζ19−ζ31−ζ59 | −ζ11−ζ19−ζ31−ζ59 | 0 | -2 | -2 | 0 | ζ7+ζ23+ζ43+ζ47 | ζ11+ζ19+ζ31+ζ59 | ζ7+ζ23+ζ43+ζ47 | ζ7+ζ23+ζ43+ζ47 | ζ11+ζ19+ζ31+ζ59 | ζ11+ζ19+ζ31+ζ59 | 0 | ||||||||||||||||
| χ13 | 2 | 2 | 0 | −ζ11−ζ19−ζ31−ζ59 | −ζ7−ζ23−ζ43−ζ47 | −ζ11−ζ19−ζ31−ζ59 | −ζ11−ζ19−ζ31−ζ59 | −ζ7−ζ23−ζ43−ζ47 | −ζ7−ζ23−ζ43−ζ47 | 0 | -2 | -2 | 0 | ζ11+ζ19+ζ31+ζ59 | ζ7+ζ23+ζ43+ζ47 | ζ11+ζ19+ζ31+ζ59 | ζ11+ζ19+ζ31+ζ59 | ζ7+ζ23+ζ43+ζ47 | ζ7+ζ23+ζ43+ζ47 | 0 | ||||||||||||||||
| χ14 | 2 | -1 | 2 | 2 | -1 | -1 | -1 | -1 | 0 | 0 | -2 | 1 | -2 | -2 | 1 | 1 | 1 | 1 | 0 | 0 | ||||||||||||||||
| χ15 | 2 | -1 | −ζ22−ζ38 | −ζ2−ζ58 | −ζ14−ζ46 | −ζ26−ζ34 | 0 | −ζ7−ζ23−ζ43−ζ47 | −ζ11−ζ19−ζ31−ζ59 | ζ7+ζ23 | ζ43+ζ47 | ζ31+ζ59 | ζ11+ζ19 | 0 | -2 | 1 | ζ22+ζ38 | ζ2+ζ58 | ζ14+ζ46 | ζ26+ζ34 | 0 | ζ7+ζ23+ζ43+ζ47 | ζ11+ζ19+ζ31+ζ59 | −ζ7−ζ23 | −ζ43−ζ47 | −ζ31−ζ59 | −ζ11−ζ19 | 0 | ||||||||
| χ16 | 2 | -1 | −ζ2−ζ58 | −ζ22−ζ38 | −ζ26−ζ34 | −ζ14−ζ46 | 0 | −ζ7−ζ23−ζ43−ζ47 | −ζ11−ζ19−ζ31−ζ59 | ζ43+ζ47 | ζ7+ζ23 | ζ11+ζ19 | ζ31+ζ59 | 0 | -2 | 1 | ζ2+ζ58 | ζ22+ζ38 | ζ26+ζ34 | ζ14+ζ46 | 0 | ζ7+ζ23+ζ43+ζ47 | ζ11+ζ19+ζ31+ζ59 | −ζ43−ζ47 | −ζ7−ζ23 | −ζ11−ζ19 | −ζ31−ζ59 | 0 | ||||||||
| χ17 | 2 | -1 | −ζ14−ζ46 | −ζ26−ζ34 | −ζ2−ζ58 | −ζ22−ζ38 | 0 | −ζ11−ζ19−ζ31−ζ59 | −ζ7−ζ23−ζ43−ζ47 | ζ31+ζ59 | ζ11+ζ19 | ζ43+ζ47 | ζ7+ζ23 | 0 | -2 | 1 | ζ14+ζ46 | ζ26+ζ34 | ζ2+ζ58 | ζ22+ζ38 | 0 | ζ11+ζ19+ζ31+ζ59 | ζ7+ζ23+ζ43+ζ47 | −ζ31−ζ59 | −ζ11−ζ19 | −ζ43−ζ47 | −ζ7−ζ23 | 0 | ||||||||
| χ18 | 2 | -1 | −ζ26−ζ34 | −ζ14−ζ46 | −ζ22−ζ38 | −ζ2−ζ58 | 0 | −ζ11−ζ19−ζ31−ζ59 | −ζ7−ζ23−ζ43−ζ47 | ζ11+ζ19 | ζ31+ζ59 | ζ7+ζ23 | ζ43+ζ47 | 0 | -2 | 1 | ζ26+ζ34 | ζ14+ζ46 | ζ22+ζ38 | ζ2+ζ58 | 0 | ζ11+ζ19+ζ31+ζ59 | ζ7+ζ23+ζ43+ζ47 | −ζ11−ζ19 | −ζ31−ζ59 | −ζ7−ζ23 | −ζ43−ζ47 | 0 | ||||||||
| χ19 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 |
| χ20 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 |
| χ21 | 2 | 2 | 0 | -2 | -2 | 0 | 2 | 2 | 0 | -2 | -2 | 0 | ||||||||||||||||||||||||
| χ22 | 2 | 2 | 0 | -2 | -2 | 0 | 2 | 2 | 0 | -2 | -2 | 0 | ||||||||||||||||||||||||
| χ23 | 2 | -1 | 2 | 2 | -1 | -1 | -1 | -1 | 0 | -2 | 1 | -2 | -2 | 1 | 1 | 1 | 1 | 0 | 2 | -1 | 2 | 2 | -1 | -1 | -1 | -1 | 0 | -2 | 1 | -2 | -2 | 1 | 1 | 1 | 1 | 0 |
| χ24 | 2 | -1 | −ζ22−ζ38 | −ζ2−ζ58 | −ζ14−ζ46 | −ζ26−ζ34 | 0 | -2 | 1 | ζ22+ζ38 | ζ2+ζ58 | ζ14+ζ46 | ζ26+ζ34 | 0 | 2 | -1 | −ζ22−ζ38 | −ζ2−ζ58 | −ζ14−ζ46 | −ζ26−ζ34 | 0 | -2 | 1 | ζ22+ζ38 | ζ2+ζ58 | ζ14+ζ46 | ζ26+ζ34 | 0 | ||||||||
| χ25 | 2 | -1 | −ζ2−ζ58 | −ζ22−ζ38 | −ζ26−ζ34 | −ζ14−ζ46 | 0 | -2 | 1 | ζ2+ζ58 | ζ22+ζ38 | ζ26+ζ34 | ζ14+ζ46 | 0 | 2 | -1 | −ζ2−ζ58 | −ζ22−ζ38 | −ζ26−ζ34 | −ζ14−ζ46 | 0 | -2 | 1 | ζ2+ζ58 | ζ22+ζ38 | ζ26+ζ34 | ζ14+ζ46 | 0 | ||||||||
| χ26 | 2 | -1 | −ζ14−ζ46 | −ζ26−ζ34 | −ζ2−ζ58 | −ζ22−ζ38 | 0 | -2 | 1 | ζ14+ζ46 | ζ26+ζ34 | ζ2+ζ58 | ζ22+ζ38 | 0 | 2 | -1 | −ζ14−ζ46 | −ζ26−ζ34 | −ζ2−ζ58 | −ζ22−ζ38 | 0 | -2 | 1 | ζ14+ζ46 | ζ26+ζ34 | ζ2+ζ58 | ζ22+ζ38 | 0 | ||||||||
| χ27 | 2 | -1 | −ζ26−ζ34 | −ζ14−ζ46 | −ζ22−ζ38 | −ζ2−ζ58 | 0 | -2 | 1 | ζ26+ζ34 | ζ14+ζ46 | ζ22+ζ38 | ζ2+ζ58 | 0 | 2 | -1 | −ζ26−ζ34 | −ζ14−ζ46 | −ζ22−ζ38 | −ζ2−ζ58 | 0 | -2 | 1 | ζ26+ζ34 | ζ14+ζ46 | ζ22+ζ38 | ζ2+ζ58 | 0 | ||||||||
| χ28 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | ||||||||||||||||||
| χ29 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | ||||||||||||||||||
| χ30 | 2 | 2 | 0 | ζ7+ζ23+ζ43+ζ47 | ζ11+ζ19+ζ31+ζ59 | ζ7+ζ23+ζ43+ζ47 | ζ7+ζ23+ζ43+ζ47 | ζ11+ζ19+ζ31+ζ59 | ζ11+ζ19+ζ31+ζ59 | 0 | -2 | -2 | 0 | −ζ7−ζ23−ζ43−ζ47 | −ζ11−ζ19−ζ31−ζ59 | −ζ7−ζ23−ζ43−ζ47 | −ζ7−ζ23−ζ43−ζ47 | −ζ11−ζ19−ζ31−ζ59 | −ζ11−ζ19−ζ31−ζ59 | 0 | ||||||||||||||||
| χ31 | 2 | 2 | 0 | ζ11+ζ19+ζ31+ζ59 | ζ7+ζ23+ζ43+ζ47 | ζ11+ζ19+ζ31+ζ59 | ζ11+ζ19+ζ31+ζ59 | ζ7+ζ23+ζ43+ζ47 | ζ7+ζ23+ζ43+ζ47 | 0 | -2 | -2 | 0 | −ζ11−ζ19−ζ31−ζ59 | −ζ7−ζ23−ζ43−ζ47 | −ζ11−ζ19−ζ31−ζ59 | −ζ11−ζ19−ζ31−ζ59 | −ζ7−ζ23−ζ43−ζ47 | −ζ7−ζ23−ζ43−ζ47 | 0 | ||||||||||||||||
| χ32 | 2 | -1 | 2 | 2 | -1 | -1 | -1 | -1 | 0 | 0 | -2 | 1 | -2 | -2 | 1 | 1 | 1 | 1 | 0 | 0 | ||||||||||||||||
| χ33 | 2 | -1 | −ζ22−ζ38 | −ζ2−ζ58 | −ζ14−ζ46 | −ζ26−ζ34 | 0 | ζ7+ζ23+ζ43+ζ47 | ζ11+ζ19+ζ31+ζ59 | −ζ7−ζ23 | −ζ43−ζ47 | −ζ31−ζ59 | −ζ11−ζ19 | 0 | -2 | 1 | ζ22+ζ38 | ζ2+ζ58 | ζ14+ζ46 | ζ26+ζ34 | 0 | −ζ7−ζ23−ζ43−ζ47 | −ζ11−ζ19−ζ31−ζ59 | ζ7+ζ23 | ζ43+ζ47 | ζ31+ζ59 | ζ11+ζ19 | 0 | ||||||||
| χ34 | 2 | -1 | −ζ2−ζ58 | −ζ22−ζ38 | −ζ26−ζ34 | −ζ14−ζ46 | 0 | ζ7+ζ23+ζ43+ζ47 | ζ11+ζ19+ζ31+ζ59 | −ζ43−ζ47 | −ζ7−ζ23 | −ζ11−ζ19 | −ζ31−ζ59 | 0 | -2 | 1 | ζ2+ζ58 | ζ22+ζ38 | ζ26+ζ34 | ζ14+ζ46 | 0 | −ζ7−ζ23−ζ43−ζ47 | −ζ11−ζ19−ζ31−ζ59 | ζ43+ζ47 | ζ7+ζ23 | ζ11+ζ19 | ζ31+ζ59 | 0 | ||||||||
| χ35 | 2 | -1 | −ζ14−ζ46 | −ζ26−ζ34 | −ζ2−ζ58 | −ζ22−ζ38 | 0 | ζ11+ζ19+ζ31+ζ59 | ζ7+ζ23+ζ43+ζ47 | −ζ31−ζ59 | −ζ11−ζ19 | −ζ43−ζ47 | −ζ7−ζ23 | 0 | -2 | 1 | ζ14+ζ46 | ζ26+ζ34 | ζ2+ζ58 | ζ22+ζ38 | 0 | −ζ11−ζ19−ζ31−ζ59 | −ζ7−ζ23−ζ43−ζ47 | ζ31+ζ59 | ζ11+ζ19 | ζ43+ζ47 | ζ7+ζ23 | 0 | ||||||||
| χ36 | 2 | -1 | −ζ26−ζ34 | −ζ14−ζ46 | −ζ22−ζ38 | −ζ2−ζ58 | 0 | ζ11+ζ19+ζ31+ζ59 | ζ7+ζ23+ζ43+ζ47 | −ζ11−ζ19 | −ζ31−ζ59 | −ζ7−ζ23 | −ζ43−ζ47 | 0 | -2 | 1 | ζ26+ζ34 | ζ14+ζ46 | ζ22+ζ38 | ζ2+ζ58 | 0 | −ζ11−ζ19−ζ31−ζ59 | −ζ7−ζ23−ζ43−ζ47 | ζ11+ζ19 | ζ31+ζ59 | ζ7+ζ23 | ζ43+ζ47 | 0 |
Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.