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 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 15 | 15 | 15 | 15 |
| order | 1 | 2 | 4 | 4 | 3 | 5 | 5 | 6 | 10 | 10 | 12 | 12 | 15 | 15 | 15 | 15 | 20 | 20 | 20 | 20 | 30 | 30 | 30 | 30 | 60 | 60 | 60 | 60 | 60 | 60 | 60 | 60 | 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 | 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 | 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 | ||||
| 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 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | ||||
| χ5 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | ζ7+ζ23+ζ31+ζ47+ζ71+ζ79+ζ103+ζ119 | −ζ7−ζ23−ζ31−ζ47−ζ71−ζ79−ζ103−ζ119 | −ζ13−ζ29−ζ37−ζ53−ζ61−ζ77−ζ101−ζ109 | ζ13+ζ29+ζ37+ζ53+ζ61+ζ77+ζ101+ζ109 | ||||||||||||||||
| χ6 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | −ζ7−ζ23−ζ31−ζ47−ζ71−ζ79−ζ103−ζ119 | ζ7+ζ23+ζ31+ζ47+ζ71+ζ79+ζ103+ζ119 | ζ13+ζ29+ζ37+ζ53+ζ61+ζ77+ζ101+ζ109 | −ζ13−ζ29−ζ37−ζ53−ζ61−ζ77−ζ101−ζ109 | ||||||||||||||||
| χ7 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | −ζ13−ζ29−ζ37−ζ53−ζ61−ζ77−ζ101−ζ109 | ζ13+ζ29+ζ37+ζ53+ζ61+ζ77+ζ101+ζ109 | ζ7+ζ23+ζ31+ζ47+ζ71+ζ79+ζ103+ζ119 | −ζ7−ζ23−ζ31−ζ47−ζ71−ζ79−ζ103−ζ119 | ||||||||||||||||
| χ8 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | ζ13+ζ29+ζ37+ζ53+ζ61+ζ77+ζ101+ζ109 | −ζ13−ζ29−ζ37−ζ53−ζ61−ζ77−ζ101−ζ109 | −ζ7−ζ23−ζ31−ζ47−ζ71−ζ79−ζ103−ζ119 | ζ7+ζ23+ζ31+ζ47+ζ71+ζ79+ζ103+ζ119 | ||||||||||||||||
| χ9 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | ||||||||||||||||||||||||
| χ10 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | ||||||||||||||||||||||||
| χ11 | 2 | 2 | 2 | 2 | -1 | 2 | 2 | -1 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | 2 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 0 | 0 | 0 | 0 |
| χ12 | 2 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | −ζ52−ζ68 | −ζ28−ζ92 | −ζ44−ζ76 | −ζ4−ζ116 | −ζ52−ζ68 | −ζ28−ζ92 | −ζ44−ζ76 | −ζ4−ζ116 | −ζ52−ζ68 | −ζ28−ζ92 | −ζ44−ζ76 | −ζ4−ζ116 | −ζ52−ζ68 | −ζ28−ζ92 | −ζ44−ζ76 | −ζ4−ζ116 | 0 | 0 | 0 | 0 | ||||||||
| χ13 | 2 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | −ζ28−ζ92 | −ζ52−ζ68 | −ζ4−ζ116 | −ζ44−ζ76 | −ζ28−ζ92 | −ζ52−ζ68 | −ζ4−ζ116 | −ζ44−ζ76 | −ζ28−ζ92 | −ζ52−ζ68 | −ζ4−ζ116 | −ζ44−ζ76 | −ζ28−ζ92 | −ζ52−ζ68 | −ζ4−ζ116 | −ζ44−ζ76 | 0 | 0 | 0 | 0 | ||||||||
| χ14 | 2 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | −ζ44−ζ76 | −ζ4−ζ116 | −ζ28−ζ92 | −ζ52−ζ68 | −ζ44−ζ76 | −ζ4−ζ116 | −ζ28−ζ92 | −ζ52−ζ68 | −ζ44−ζ76 | −ζ4−ζ116 | −ζ28−ζ92 | −ζ52−ζ68 | −ζ44−ζ76 | −ζ4−ζ116 | −ζ28−ζ92 | −ζ52−ζ68 | 0 | 0 | 0 | 0 | ||||||||
| χ15 | 2 | 2 | 2 | 2 | -1 | -1 | -1 | -1 | −ζ4−ζ116 | −ζ44−ζ76 | −ζ52−ζ68 | −ζ28−ζ92 | −ζ4−ζ116 | −ζ44−ζ76 | −ζ52−ζ68 | −ζ28−ζ92 | −ζ4−ζ116 | −ζ44−ζ76 | −ζ52−ζ68 | −ζ28−ζ92 | −ζ4−ζ116 | −ζ44−ζ76 | −ζ52−ζ68 | −ζ28−ζ92 | 0 | 0 | 0 | 0 | ||||||||
| χ16 | 2 | 2 | -2 | -2 | 2 | 2 | -2 | -2 | 0 | 0 | 0 | 0 | ||||||||||||||||||||||||
| χ17 | 2 | 2 | -2 | -2 | 2 | 2 | -2 | -2 | 0 | 0 | 0 | 0 | ||||||||||||||||||||||||
| χ18 | 2 | 2 | -2 | -2 | -1 | 2 | 2 | -1 | 2 | 2 | 1 | 1 | -1 | -1 | -1 | -1 | -2 | -2 | -2 | -2 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
| χ19 | 2 | 2 | -2 | -2 | -1 | -1 | 1 | 1 | −ζ52−ζ68 | −ζ28−ζ92 | −ζ44−ζ76 | −ζ4−ζ116 | −ζ52−ζ68 | −ζ28−ζ92 | −ζ44−ζ76 | −ζ4−ζ116 | ζ52+ζ68 | ζ28+ζ92 | ζ44+ζ76 | ζ4+ζ116 | ζ52+ζ68 | ζ28+ζ92 | ζ44+ζ76 | ζ4+ζ116 | 0 | 0 | 0 | 0 | ||||||||
| χ20 | 2 | 2 | -2 | -2 | -1 | -1 | 1 | 1 | −ζ28−ζ92 | −ζ52−ζ68 | −ζ4−ζ116 | −ζ44−ζ76 | −ζ28−ζ92 | −ζ52−ζ68 | −ζ4−ζ116 | −ζ44−ζ76 | ζ28+ζ92 | ζ52+ζ68 | ζ4+ζ116 | ζ44+ζ76 | ζ28+ζ92 | ζ52+ζ68 | ζ4+ζ116 | ζ44+ζ76 | 0 | 0 | 0 | 0 | ||||||||
| χ21 | 2 | 2 | -2 | -2 | -1 | -1 | 1 | 1 | −ζ44−ζ76 | −ζ4−ζ116 | −ζ28−ζ92 | −ζ52−ζ68 | −ζ44−ζ76 | −ζ4−ζ116 | −ζ28−ζ92 | −ζ52−ζ68 | ζ44+ζ76 | ζ4+ζ116 | ζ28+ζ92 | ζ52+ζ68 | ζ44+ζ76 | ζ4+ζ116 | ζ28+ζ92 | ζ52+ζ68 | 0 | 0 | 0 | 0 | ||||||||
| χ22 | 2 | 2 | -2 | -2 | -1 | -1 | 1 | 1 | −ζ4−ζ116 | −ζ44−ζ76 | −ζ52−ζ68 | −ζ28−ζ92 | −ζ4−ζ116 | −ζ44−ζ76 | −ζ52−ζ68 | −ζ28−ζ92 | ζ4+ζ116 | ζ44+ζ76 | ζ52+ζ68 | ζ28+ζ92 | ζ4+ζ116 | ζ44+ζ76 | ζ52+ζ68 | ζ28+ζ92 | 0 | 0 | 0 | 0 | ||||||||
| χ23 | 2 | -2 | 2 | -2 | −ζ22−ζ38−ζ62−ζ118 | −ζ14−ζ46−ζ86−ζ94 | ζ22+ζ38+ζ62+ζ118 | ζ14+ζ46+ζ86+ζ94 | −ζ22−ζ38−ζ62−ζ118 | −ζ22−ζ38−ζ62−ζ118 | −ζ14−ζ46−ζ86−ζ94 | −ζ14−ζ46−ζ86−ζ94 | ζ22+ζ38+ζ62+ζ118 | ζ22+ζ38+ζ62+ζ118 | ζ14+ζ46+ζ86+ζ94 | ζ14+ζ46+ζ86+ζ94 | 0 | 0 | 0 | 0 | ||||||||||||||||
| χ24 | 2 | -2 | 2 | -2 | −ζ14−ζ46−ζ86−ζ94 | −ζ22−ζ38−ζ62−ζ118 | ζ14+ζ46+ζ86+ζ94 | ζ22+ζ38+ζ62+ζ118 | −ζ14−ζ46−ζ86−ζ94 | −ζ14−ζ46−ζ86−ζ94 | −ζ22−ζ38−ζ62−ζ118 | −ζ22−ζ38−ζ62−ζ118 | ζ14+ζ46+ζ86+ζ94 | ζ14+ζ46+ζ86+ζ94 | ζ22+ζ38+ζ62+ζ118 | ζ22+ζ38+ζ62+ζ118 | 0 | 0 | 0 | 0 | ||||||||||||||||
| χ25 | 2 | -2 | -1 | 2 | 2 | 1 | -2 | -2 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | ||||||||||||||||
| χ26 | 2 | -2 | -1 | 1 | −ζ52−ζ68 | −ζ28−ζ92 | −ζ44−ζ76 | −ζ4−ζ116 | −ζ22−ζ38−ζ62−ζ118 | −ζ14−ζ46−ζ86−ζ94 | ζ22+ζ38+ζ62+ζ118 | ζ14+ζ46+ζ86+ζ94 | ζ52+ζ68 | ζ28+ζ92 | ζ44+ζ76 | ζ4+ζ116 | ζ22+ζ38 | ζ62+ζ118 | ζ14+ζ46 | ζ86+ζ94 | −ζ22−ζ38 | −ζ62−ζ118 | −ζ14−ζ46 | −ζ86−ζ94 | 0 | 0 | 0 | 0 | ||||||||
| χ27 | 2 | -2 | -1 | 1 | −ζ28−ζ92 | −ζ52−ζ68 | −ζ4−ζ116 | −ζ44−ζ76 | −ζ22−ζ38−ζ62−ζ118 | −ζ14−ζ46−ζ86−ζ94 | ζ22+ζ38+ζ62+ζ118 | ζ14+ζ46+ζ86+ζ94 | ζ28+ζ92 | ζ52+ζ68 | ζ4+ζ116 | ζ44+ζ76 | ζ62+ζ118 | ζ22+ζ38 | ζ86+ζ94 | ζ14+ζ46 | −ζ62−ζ118 | −ζ22−ζ38 | −ζ86−ζ94 | −ζ14−ζ46 | 0 | 0 | 0 | 0 | ||||||||
| χ28 | 2 | -2 | -1 | 1 | −ζ44−ζ76 | −ζ4−ζ116 | −ζ28−ζ92 | −ζ52−ζ68 | −ζ14−ζ46−ζ86−ζ94 | −ζ22−ζ38−ζ62−ζ118 | ζ14+ζ46+ζ86+ζ94 | ζ22+ζ38+ζ62+ζ118 | ζ44+ζ76 | ζ4+ζ116 | ζ28+ζ92 | ζ52+ζ68 | ζ14+ζ46 | ζ86+ζ94 | ζ62+ζ118 | ζ22+ζ38 | −ζ14−ζ46 | −ζ86−ζ94 | −ζ62−ζ118 | −ζ22−ζ38 | 0 | 0 | 0 | 0 | ||||||||
| χ29 | 2 | -2 | -1 | 1 | −ζ4−ζ116 | −ζ44−ζ76 | −ζ52−ζ68 | −ζ28−ζ92 | −ζ14−ζ46−ζ86−ζ94 | −ζ22−ζ38−ζ62−ζ118 | ζ14+ζ46+ζ86+ζ94 | ζ22+ζ38+ζ62+ζ118 | ζ4+ζ116 | ζ44+ζ76 | ζ52+ζ68 | ζ28+ζ92 | ζ86+ζ94 | ζ14+ζ46 | ζ22+ζ38 | ζ62+ζ118 | −ζ86−ζ94 | −ζ14−ζ46 | −ζ22−ζ38 | −ζ62−ζ118 | 0 | 0 | 0 | 0 | ||||||||
| χ30 | 2 | -2 | 2 | -2 | ζ22+ζ38+ζ62+ζ118 | ζ14+ζ46+ζ86+ζ94 | −ζ22−ζ38−ζ62−ζ118 | −ζ14−ζ46−ζ86−ζ94 | ζ22+ζ38+ζ62+ζ118 | ζ22+ζ38+ζ62+ζ118 | ζ14+ζ46+ζ86+ζ94 | ζ14+ζ46+ζ86+ζ94 | −ζ22−ζ38−ζ62−ζ118 | −ζ22−ζ38−ζ62−ζ118 | −ζ14−ζ46−ζ86−ζ94 | −ζ14−ζ46−ζ86−ζ94 | 0 | 0 | 0 | 0 | ||||||||||||||||
| χ31 | 2 | -2 | 2 | -2 | ζ14+ζ46+ζ86+ζ94 | ζ22+ζ38+ζ62+ζ118 | −ζ14−ζ46−ζ86−ζ94 | −ζ22−ζ38−ζ62−ζ118 | ζ14+ζ46+ζ86+ζ94 | ζ14+ζ46+ζ86+ζ94 | ζ22+ζ38+ζ62+ζ118 | ζ22+ζ38+ζ62+ζ118 | −ζ14−ζ46−ζ86−ζ94 | −ζ14−ζ46−ζ86−ζ94 | −ζ22−ζ38−ζ62−ζ118 | −ζ22−ζ38−ζ62−ζ118 | 0 | 0 | 0 | 0 | ||||||||||||||||
| χ32 | 2 | -2 | -1 | 2 | 2 | 1 | -2 | -2 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | ||||||||||||||||
| χ33 | 2 | -2 | -1 | 1 | −ζ52−ζ68 | −ζ28−ζ92 | −ζ44−ζ76 | −ζ4−ζ116 | ζ22+ζ38+ζ62+ζ118 | ζ14+ζ46+ζ86+ζ94 | −ζ22−ζ38−ζ62−ζ118 | −ζ14−ζ46−ζ86−ζ94 | ζ52+ζ68 | ζ28+ζ92 | ζ44+ζ76 | ζ4+ζ116 | −ζ22−ζ38 | −ζ62−ζ118 | −ζ14−ζ46 | −ζ86−ζ94 | ζ22+ζ38 | ζ62+ζ118 | ζ14+ζ46 | ζ86+ζ94 | 0 | 0 | 0 | 0 | ||||||||
| χ34 | 2 | -2 | -1 | 1 | −ζ28−ζ92 | −ζ52−ζ68 | −ζ4−ζ116 | −ζ44−ζ76 | ζ22+ζ38+ζ62+ζ118 | ζ14+ζ46+ζ86+ζ94 | −ζ22−ζ38−ζ62−ζ118 | −ζ14−ζ46−ζ86−ζ94 | ζ28+ζ92 | ζ52+ζ68 | ζ4+ζ116 | ζ44+ζ76 | −ζ62−ζ118 | −ζ22−ζ38 | −ζ86−ζ94 | −ζ14−ζ46 | ζ62+ζ118 | ζ22+ζ38 | ζ86+ζ94 | ζ14+ζ46 | 0 | 0 | 0 | 0 | ||||||||
| χ35 | 2 | -2 | -1 | 1 | −ζ44−ζ76 | −ζ4−ζ116 | −ζ28−ζ92 | −ζ52−ζ68 | ζ14+ζ46+ζ86+ζ94 | ζ22+ζ38+ζ62+ζ118 | −ζ14−ζ46−ζ86−ζ94 | −ζ22−ζ38−ζ62−ζ118 | ζ44+ζ76 | ζ4+ζ116 | ζ28+ζ92 | ζ52+ζ68 | −ζ14−ζ46 | −ζ86−ζ94 | −ζ62−ζ118 | −ζ22−ζ38 | ζ14+ζ46 | ζ86+ζ94 | ζ62+ζ118 | ζ22+ζ38 | 0 | 0 | 0 | 0 | ||||||||
| χ36 | 2 | -2 | -1 | 1 | −ζ4−ζ116 | −ζ44−ζ76 | −ζ52−ζ68 | −ζ28−ζ92 | ζ14+ζ46+ζ86+ζ94 | ζ22+ζ38+ζ62+ζ118 | −ζ14−ζ46−ζ86−ζ94 | −ζ22−ζ38−ζ62−ζ118 | ζ4+ζ116 | ζ44+ζ76 | ζ52+ζ68 | ζ28+ζ92 | −ζ86−ζ94 | −ζ14−ζ46 | −ζ22−ζ38 | −ζ62−ζ118 | ζ86+ζ94 | ζ14+ζ46 | ζ22+ζ38 | ζ62+ζ118 | 0 | 0 | 0 | 0 |
Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.