Order 416.
| 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 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| size | 1 | 4 | 4 | 4 | 13 | 13 | 13 | 1 | 4 | 4 | 4 | 13 | 13 | 13 | 2 | 8 | 8 | 8 | 26 | 26 | 26 | 2 | 8 | 8 | 8 | 26 | 26 | 26 | 2 | 8 | 8 | 8 | 26 | 26 | 26 |
| order | 1 | 13 | 13 | 13 | 2 | 4 | 4 | 2 | 26 | 26 | 26 | 2 | 4 | 4 | 2 | 26 | 26 | 26 | 2 | 4 | 4 | 2 | 26 | 26 | 26 | 2 | 4 | 4 | 4 | 52 | 52 | 52 | 4 | 4 | 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 |
| 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 |
| χ3 | 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 | ||||||||||
| χ4 | 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 | ||||||||||
| χ5 | 4 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | 0 | 0 | 0 | 4 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | 0 | 0 | 0 | 4 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | 0 | 0 | 0 | 4 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | 0 | 0 | 0 | 4 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | 0 | 0 | 0 |
| χ6 | 4 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | 0 | 0 | 0 | 4 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | 0 | 0 | 0 | 4 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | 0 | 0 | 0 | 4 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | 0 | 0 | 0 | 4 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | 0 | 0 | 0 |
| χ7 | 4 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | 0 | 0 | 0 | 4 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | 0 | 0 | 0 | 4 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | 0 | 0 | 0 | 4 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | 0 | 0 | 0 | 4 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | 0 | 0 | 0 |
| χ8 | 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 |
| χ9 | 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 |
| χ10 | 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 | ||||||||||
| χ11 | 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 | ||||||||||
| χ12 | 4 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | 0 | 0 | 0 | 4 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | 0 | 0 | 0 | 4 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | 0 | 0 | 0 | -4 | ζ6+ζ22+ζ30+ζ46 | ζ14+ζ18+ζ34+ζ38 | ζ2+ζ10+ζ42+ζ50 | 0 | 0 | 0 | -4 | ζ6+ζ22+ζ30+ζ46 | ζ14+ζ18+ζ34+ζ38 | ζ2+ζ10+ζ42+ζ50 | 0 | 0 | 0 |
| χ13 | 4 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | 0 | 0 | 0 | 4 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | 0 | 0 | 0 | 4 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | 0 | 0 | 0 | -4 | ζ14+ζ18+ζ34+ζ38 | ζ2+ζ10+ζ42+ζ50 | ζ6+ζ22+ζ30+ζ46 | 0 | 0 | 0 | -4 | ζ14+ζ18+ζ34+ζ38 | ζ2+ζ10+ζ42+ζ50 | ζ6+ζ22+ζ30+ζ46 | 0 | 0 | 0 |
| χ14 | 4 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | 0 | 0 | 0 | 4 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | 0 | 0 | 0 | 4 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | 0 | 0 | 0 | -4 | ζ2+ζ10+ζ42+ζ50 | ζ6+ζ22+ζ30+ζ46 | ζ14+ζ18+ζ34+ζ38 | 0 | 0 | 0 | -4 | ζ2+ζ10+ζ42+ζ50 | ζ6+ζ22+ζ30+ζ46 | ζ14+ζ18+ζ34+ζ38 | 0 | 0 | 0 |
| χ15 | 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 |
| χ16 | 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 |
| χ17 | 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 | ||||||||||
| χ18 | 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 | ||||||||||
| χ19 | 4 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | 0 | 0 | 0 | 4 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | 0 | 0 | 0 | -4 | ζ6+ζ22+ζ30+ζ46 | ζ14+ζ18+ζ34+ζ38 | ζ2+ζ10+ζ42+ζ50 | 0 | 0 | 0 | 4 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | 0 | 0 | 0 | -4 | ζ6+ζ22+ζ30+ζ46 | ζ14+ζ18+ζ34+ζ38 | ζ2+ζ10+ζ42+ζ50 | 0 | 0 | 0 |
| χ20 | 4 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | 0 | 0 | 0 | 4 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | 0 | 0 | 0 | -4 | ζ14+ζ18+ζ34+ζ38 | ζ2+ζ10+ζ42+ζ50 | ζ6+ζ22+ζ30+ζ46 | 0 | 0 | 0 | 4 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | 0 | 0 | 0 | -4 | ζ14+ζ18+ζ34+ζ38 | ζ2+ζ10+ζ42+ζ50 | ζ6+ζ22+ζ30+ζ46 | 0 | 0 | 0 |
| χ21 | 4 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | 0 | 0 | 0 | 4 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | 0 | 0 | 0 | -4 | ζ2+ζ10+ζ42+ζ50 | ζ6+ζ22+ζ30+ζ46 | ζ14+ζ18+ζ34+ζ38 | 0 | 0 | 0 | 4 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | 0 | 0 | 0 | -4 | ζ2+ζ10+ζ42+ζ50 | ζ6+ζ22+ζ30+ζ46 | ζ14+ζ18+ζ34+ζ38 | 0 | 0 | 0 |
| χ22 | 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 |
| χ23 | 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 |
| χ24 | 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 | ||||||||||
| χ25 | 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 | ||||||||||
| χ26 | 4 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | 0 | 0 | 0 | 4 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | 0 | 0 | 0 | -4 | ζ6+ζ22+ζ30+ζ46 | ζ14+ζ18+ζ34+ζ38 | ζ2+ζ10+ζ42+ζ50 | 0 | 0 | 0 | -4 | ζ6+ζ22+ζ30+ζ46 | ζ14+ζ18+ζ34+ζ38 | ζ2+ζ10+ζ42+ζ50 | 0 | 0 | 0 | 4 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | 0 | 0 | 0 |
| χ27 | 4 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | 0 | 0 | 0 | 4 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | 0 | 0 | 0 | -4 | ζ14+ζ18+ζ34+ζ38 | ζ2+ζ10+ζ42+ζ50 | ζ6+ζ22+ζ30+ζ46 | 0 | 0 | 0 | -4 | ζ14+ζ18+ζ34+ζ38 | ζ2+ζ10+ζ42+ζ50 | ζ6+ζ22+ζ30+ζ46 | 0 | 0 | 0 | 4 | −ζ14−ζ18−ζ34−ζ38 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | 0 | 0 | 0 |
| χ28 | 4 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | 0 | 0 | 0 | 4 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | 0 | 0 | 0 | -4 | ζ2+ζ10+ζ42+ζ50 | ζ6+ζ22+ζ30+ζ46 | ζ14+ζ18+ζ34+ζ38 | 0 | 0 | 0 | -4 | ζ2+ζ10+ζ42+ζ50 | ζ6+ζ22+ζ30+ζ46 | ζ14+ζ18+ζ34+ζ38 | 0 | 0 | 0 | 4 | −ζ2−ζ10−ζ42−ζ50 | −ζ6−ζ22−ζ30−ζ46 | −ζ14−ζ18−ζ34−ζ38 | 0 | 0 | 0 |
| χ29 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | -2 | -2 | -2 | -2 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ30 | 2 | 2 | 2 | 2 | 2 | -2 | -2 | -2 | -2 | -2 | -2 | -2 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ31 | 2 | 2 | 2 | 2 | -2 | -2 | -2 | -2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||
| χ32 | 2 | 2 | 2 | 2 | -2 | -2 | -2 | -2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||
| χ33 | 8 | −2ζ6−2ζ22−2ζ30−2ζ46 | −2ζ14−2ζ18−2ζ34−2ζ38 | −2ζ2−2ζ10−2ζ42−2ζ50 | 0 | 0 | 0 | -8 | 2ζ6+2ζ22+2ζ30+2ζ46 | 2ζ14+2ζ18+2ζ34+2ζ38 | 2ζ2+2ζ10+2ζ42+2ζ50 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ34 | 8 | −2ζ14−2ζ18−2ζ34−2ζ38 | −2ζ2−2ζ10−2ζ42−2ζ50 | −2ζ6−2ζ22−2ζ30−2ζ46 | 0 | 0 | 0 | -8 | 2ζ14+2ζ18+2ζ34+2ζ38 | 2ζ2+2ζ10+2ζ42+2ζ50 | 2ζ6+2ζ22+2ζ30+2ζ46 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| χ35 | 8 | −2ζ2−2ζ10−2ζ42−2ζ50 | −2ζ6−2ζ22−2ζ30−2ζ46 | −2ζ14−2ζ18−2ζ34−2ζ38 | 0 | 0 | 0 | -8 | 2ζ2+2ζ10+2ζ42+2ζ50 | 2ζ6+2ζ22+2ζ30+2ζ46 | 2ζ14+2ζ18+2ζ34+2ζ38 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Here ζ is a primitive root of unity of order 52 (ζ52 = 1); i = ζ13.