Dirichlet character orbit 216000.ye

• Label: 216000.ye
• Modulus: $216000$
• Conductor: $108000$
• Order: $1800$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$216000$
Conductor:	$108000$
Order:	$1800$
Real:	no
Primitive:	no, induced from 108000.tg
Minimal:	no
Parity:	odd

Related number fields

Field of values:	$\Q(\zeta_{1800})$
Fixed field:	Number field defined by a degree 1800 polynomial (not computed)

First 31 of 480 characters in Galois orbit

Character	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{216000}(41,\cdot)$	$-1$	$1$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{167}{1800}\right)$	$e\left(\frac{1513}{1800}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{227}{600}\right)$	$e\left(\frac{251}{900}\right)$	$e\left(\frac{1529}{1800}\right)$	$e\left(\frac{2}{225}\right)$	$e\left(\frac{181}{600}\right)$	$e\left(\frac{599}{900}\right)$
$\chi_{216000}(281,\cdot)$	$-1$	$1$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{889}{1800}\right)$	$e\left(\frac{671}{1800}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{109}{600}\right)$	$e\left(\frac{517}{900}\right)$	$e\left(\frac{1543}{1800}\right)$	$e\left(\frac{109}{225}\right)$	$e\left(\frac{227}{600}\right)$	$e\left(\frac{133}{900}\right)$
$\chi_{216000}(761,\cdot)$	$-1$	$1$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{893}{1800}\right)$	$e\left(\frac{427}{1800}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{233}{600}\right)$	$e\left(\frac{329}{900}\right)$	$e\left(\frac{491}{1800}\right)$	$e\left(\frac{8}{225}\right)$	$e\left(\frac{199}{600}\right)$	$e\left(\frac{821}{900}\right)$
$\chi_{216000}(1481,\cdot)$	$-1$	$1$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{899}{1800}\right)$	$e\left(\frac{61}{1800}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{119}{600}\right)$	$e\left(\frac{47}{900}\right)$	$e\left(\frac{1613}{1800}\right)$	$e\left(\frac{194}{225}\right)$	$e\left(\frac{457}{600}\right)$	$e\left(\frac{503}{900}\right)$
$\chi_{216000}(1721,\cdot)$	$-1$	$1$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{541}{1800}\right)$	$e\left(\frac{299}{1800}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{121}{600}\right)$	$e\left(\frac{673}{900}\right)$	$e\left(\frac{1267}{1800}\right)$	$e\left(\frac{121}{225}\right)$	$e\left(\frac{263}{600}\right)$	$e\left(\frac{577}{900}\right)$
$\chi_{216000}(2441,\cdot)$	$-1$	$1$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{187}{1800}\right)$	$e\left(\frac{293}{1800}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{247}{600}\right)$	$e\left(\frac{211}{900}\right)$	$e\left(\frac{1669}{1800}\right)$	$e\left(\frac{172}{225}\right)$	$e\left(\frac{41}{600}\right)$	$e\left(\frac{439}{900}\right)$
$\chi_{216000}(2921,\cdot)$	$-1$	$1$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{551}{1800}\right)$	$e\left(\frac{1489}{1800}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{131}{600}\right)$	$e\left(\frac{203}{900}\right)$	$e\left(\frac{1337}{1800}\right)$	$e\left(\frac{206}{225}\right)$	$e\left(\frac{493}{600}\right)$	$e\left(\frac{47}{900}\right)$
$\chi_{216000}(3161,\cdot)$	$-1$	$1$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{913}{1800}\right)$	$e\left(\frac{1007}{1800}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{253}{600}\right)$	$e\left(\frac{289}{900}\right)$	$e\left(\frac{631}{1800}\right)$	$e\left(\frac{178}{225}\right)$	$e\left(\frac{59}{600}\right)$	$e\left(\frac{661}{900}\right)$
$\chi_{216000}(3641,\cdot)$	$-1$	$1$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{197}{1800}\right)$	$e\left(\frac{1483}{1800}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{257}{600}\right)$	$e\left(\frac{641}{900}\right)$	$e\left(\frac{1739}{1800}\right)$	$e\left(\frac{32}{225}\right)$	$e\left(\frac{271}{600}\right)$	$e\left(\frac{809}{900}\right)$
$\chi_{216000}(3881,\cdot)$	$-1$	$1$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{919}{1800}\right)$	$e\left(\frac{641}{1800}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{139}{600}\right)$	$e\left(\frac{7}{900}\right)$	$e\left(\frac{1753}{1800}\right)$	$e\left(\frac{139}{225}\right)$	$e\left(\frac{317}{600}\right)$	$e\left(\frac{343}{900}\right)$
$\chi_{216000}(4361,\cdot)$	$-1$	$1$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{923}{1800}\right)$	$e\left(\frac{397}{1800}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{263}{600}\right)$	$e\left(\frac{719}{900}\right)$	$e\left(\frac{701}{1800}\right)$	$e\left(\frac{38}{225}\right)$	$e\left(\frac{289}{600}\right)$	$e\left(\frac{131}{900}\right)$
$\chi_{216000}(5081,\cdot)$	$-1$	$1$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{929}{1800}\right)$	$e\left(\frac{31}{1800}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{149}{600}\right)$	$e\left(\frac{437}{900}\right)$	$e\left(\frac{23}{1800}\right)$	$e\left(\frac{224}{225}\right)$	$e\left(\frac{547}{600}\right)$	$e\left(\frac{713}{900}\right)$
$\chi_{216000}(5321,\cdot)$	$-1$	$1$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{571}{1800}\right)$	$e\left(\frac{269}{1800}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{151}{600}\right)$	$e\left(\frac{163}{900}\right)$	$e\left(\frac{1477}{1800}\right)$	$e\left(\frac{151}{225}\right)$	$e\left(\frac{353}{600}\right)$	$e\left(\frac{787}{900}\right)$
$\chi_{216000}(6041,\cdot)$	$-1$	$1$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{217}{1800}\right)$	$e\left(\frac{263}{1800}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{277}{600}\right)$	$e\left(\frac{601}{900}\right)$	$e\left(\frac{79}{1800}\right)$	$e\left(\frac{202}{225}\right)$	$e\left(\frac{131}{600}\right)$	$e\left(\frac{649}{900}\right)$
$\chi_{216000}(6521,\cdot)$	$-1$	$1$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{581}{1800}\right)$	$e\left(\frac{1459}{1800}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{161}{600}\right)$	$e\left(\frac{593}{900}\right)$	$e\left(\frac{1547}{1800}\right)$	$e\left(\frac{11}{225}\right)$	$e\left(\frac{583}{600}\right)$	$e\left(\frac{257}{900}\right)$
$\chi_{216000}(6761,\cdot)$	$-1$	$1$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{943}{1800}\right)$	$e\left(\frac{977}{1800}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{283}{600}\right)$	$e\left(\frac{679}{900}\right)$	$e\left(\frac{841}{1800}\right)$	$e\left(\frac{208}{225}\right)$	$e\left(\frac{149}{600}\right)$	$e\left(\frac{871}{900}\right)$
$\chi_{216000}(7241,\cdot)$	$-1$	$1$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{227}{1800}\right)$	$e\left(\frac{1453}{1800}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{287}{600}\right)$	$e\left(\frac{131}{900}\right)$	$e\left(\frac{149}{1800}\right)$	$e\left(\frac{62}{225}\right)$	$e\left(\frac{361}{600}\right)$	$e\left(\frac{119}{900}\right)$
$\chi_{216000}(7481,\cdot)$	$-1$	$1$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{949}{1800}\right)$	$e\left(\frac{611}{1800}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{169}{600}\right)$	$e\left(\frac{397}{900}\right)$	$e\left(\frac{163}{1800}\right)$	$e\left(\frac{169}{225}\right)$	$e\left(\frac{407}{600}\right)$	$e\left(\frac{553}{900}\right)$
$\chi_{216000}(7961,\cdot)$	$-1$	$1$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{953}{1800}\right)$	$e\left(\frac{367}{1800}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{293}{600}\right)$	$e\left(\frac{209}{900}\right)$	$e\left(\frac{911}{1800}\right)$	$e\left(\frac{68}{225}\right)$	$e\left(\frac{379}{600}\right)$	$e\left(\frac{341}{900}\right)$
$\chi_{216000}(8681,\cdot)$	$-1$	$1$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{959}{1800}\right)$	$e\left(\frac{1}{1800}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{179}{600}\right)$	$e\left(\frac{827}{900}\right)$	$e\left(\frac{233}{1800}\right)$	$e\left(\frac{29}{225}\right)$	$e\left(\frac{37}{600}\right)$	$e\left(\frac{23}{900}\right)$
$\chi_{216000}(8921,\cdot)$	$-1$	$1$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{601}{1800}\right)$	$e\left(\frac{239}{1800}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{181}{600}\right)$	$e\left(\frac{553}{900}\right)$	$e\left(\frac{1687}{1800}\right)$	$e\left(\frac{181}{225}\right)$	$e\left(\frac{443}{600}\right)$	$e\left(\frac{97}{900}\right)$
$\chi_{216000}(9641,\cdot)$	$-1$	$1$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{247}{1800}\right)$	$e\left(\frac{233}{1800}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{307}{600}\right)$	$e\left(\frac{91}{900}\right)$	$e\left(\frac{289}{1800}\right)$	$e\left(\frac{7}{225}\right)$	$e\left(\frac{221}{600}\right)$	$e\left(\frac{859}{900}\right)$
$\chi_{216000}(10121,\cdot)$	$-1$	$1$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{611}{1800}\right)$	$e\left(\frac{1429}{1800}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{191}{600}\right)$	$e\left(\frac{83}{900}\right)$	$e\left(\frac{1757}{1800}\right)$	$e\left(\frac{41}{225}\right)$	$e\left(\frac{73}{600}\right)$	$e\left(\frac{467}{900}\right)$
$\chi_{216000}(10361,\cdot)$	$-1$	$1$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{973}{1800}\right)$	$e\left(\frac{947}{1800}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{313}{600}\right)$	$e\left(\frac{169}{900}\right)$	$e\left(\frac{1051}{1800}\right)$	$e\left(\frac{13}{225}\right)$	$e\left(\frac{239}{600}\right)$	$e\left(\frac{181}{900}\right)$
$\chi_{216000}(10841,\cdot)$	$-1$	$1$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{257}{1800}\right)$	$e\left(\frac{1423}{1800}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{317}{600}\right)$	$e\left(\frac{521}{900}\right)$	$e\left(\frac{359}{1800}\right)$	$e\left(\frac{92}{225}\right)$	$e\left(\frac{451}{600}\right)$	$e\left(\frac{329}{900}\right)$
$\chi_{216000}(11081,\cdot)$	$-1$	$1$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{979}{1800}\right)$	$e\left(\frac{581}{1800}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{199}{600}\right)$	$e\left(\frac{787}{900}\right)$	$e\left(\frac{373}{1800}\right)$	$e\left(\frac{199}{225}\right)$	$e\left(\frac{497}{600}\right)$	$e\left(\frac{763}{900}\right)$
$\chi_{216000}(11561,\cdot)$	$-1$	$1$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{983}{1800}\right)$	$e\left(\frac{337}{1800}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{323}{600}\right)$	$e\left(\frac{599}{900}\right)$	$e\left(\frac{1121}{1800}\right)$	$e\left(\frac{98}{225}\right)$	$e\left(\frac{469}{600}\right)$	$e\left(\frac{551}{900}\right)$
$\chi_{216000}(12281,\cdot)$	$-1$	$1$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{989}{1800}\right)$	$e\left(\frac{1771}{1800}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{209}{600}\right)$	$e\left(\frac{317}{900}\right)$	$e\left(\frac{443}{1800}\right)$	$e\left(\frac{59}{225}\right)$	$e\left(\frac{127}{600}\right)$	$e\left(\frac{233}{900}\right)$
$\chi_{216000}(12521,\cdot)$	$-1$	$1$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{631}{1800}\right)$	$e\left(\frac{209}{1800}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{211}{600}\right)$	$e\left(\frac{43}{900}\right)$	$e\left(\frac{97}{1800}\right)$	$e\left(\frac{211}{225}\right)$	$e\left(\frac{533}{600}\right)$	$e\left(\frac{307}{900}\right)$
$\chi_{216000}(13241,\cdot)$	$-1$	$1$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{277}{1800}\right)$	$e\left(\frac{203}{1800}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{337}{600}\right)$	$e\left(\frac{481}{900}\right)$	$e\left(\frac{499}{1800}\right)$	$e\left(\frac{37}{225}\right)$	$e\left(\frac{311}{600}\right)$	$e\left(\frac{169}{900}\right)$
$\chi_{216000}(13721,\cdot)$	$-1$	$1$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{641}{1800}\right)$	$e\left(\frac{1399}{1800}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{221}{600}\right)$	$e\left(\frac{473}{900}\right)$	$e\left(\frac{167}{1800}\right)$	$e\left(\frac{71}{225}\right)$	$e\left(\frac{163}{600}\right)$	$e\left(\frac{677}{900}\right)$