Dirichlet character orbit 216000.vj

• Label: 216000.vj
• Modulus: $216000$
• Conductor: $36000$
• Order: $600$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$216000$
Conductor:	$36000$
Order:	$600$
Real:	no
Primitive:	no, induced from 36000.mt
Minimal:	no
Parity:	odd

Related number fields

Field of values:	$\Q(\zeta_{600})$
Fixed field:	Number field defined by a degree 600 polynomial (not computed)

First 31 of 160 characters in Galois orbit

Character	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{216000}(89,\cdot)$	$-1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{571}{600}\right)$	$e\left(\frac{569}{600}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{151}{200}\right)$	$e\left(\frac{13}{300}\right)$	$e\left(\frac{277}{600}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{53}{200}\right)$	$e\left(\frac{187}{300}\right)$
$\chi_{216000}(1529,\cdot)$	$-1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{47}{600}\right)$	$e\left(\frac{133}{600}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{107}{200}\right)$	$e\left(\frac{41}{300}\right)$	$e\left(\frac{89}{600}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{121}{200}\right)$	$e\left(\frac{59}{300}\right)$
$\chi_{216000}(3689,\cdot)$	$-1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{461}{600}\right)$	$e\left(\frac{79}{600}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{41}{200}\right)$	$e\left(\frac{83}{300}\right)$	$e\left(\frac{107}{600}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{123}{200}\right)$	$e\left(\frac{17}{300}\right)$
$\chi_{216000}(4409,\cdot)$	$-1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{319}{600}\right)$	$e\left(\frac{341}{600}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{139}{200}\right)$	$e\left(\frac{157}{300}\right)$	$e\left(\frac{553}{600}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{17}{200}\right)$	$e\left(\frac{43}{300}\right)$
$\chi_{216000}(6569,\cdot)$	$-1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{253}{600}\right)$	$e\left(\frac{167}{600}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{193}{200}\right)$	$e\left(\frac{259}{300}\right)$	$e\left(\frac{211}{600}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{179}{200}\right)$	$e\left(\frac{241}{300}\right)$
$\chi_{216000}(8009,\cdot)$	$-1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{209}{600}\right)$	$e\left(\frac{451}{600}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{29}{200}\right)$	$e\left(\frac{227}{300}\right)$	$e\left(\frac{383}{600}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{87}{200}\right)$	$e\left(\frac{173}{300}\right)$
$\chi_{216000}(8729,\cdot)$	$-1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{427}{600}\right)$	$e\left(\frac{353}{600}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{87}{200}\right)$	$e\left(\frac{181}{300}\right)$	$e\left(\frac{349}{600}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{61}{200}\right)$	$e\left(\frac{19}{300}\right)$
$\chi_{216000}(10169,\cdot)$	$-1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{143}{600}\right)$	$e\left(\frac{277}{600}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{83}{200}\right)$	$e\left(\frac{29}{300}\right)$	$e\left(\frac{41}{600}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{49}{200}\right)$	$e\left(\frac{71}{300}\right)$
$\chi_{216000}(10889,\cdot)$	$-1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{241}{600}\right)$	$e\left(\frac{299}{600}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{21}{200}\right)$	$e\left(\frac{223}{300}\right)$	$e\left(\frac{367}{600}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{63}{200}\right)$	$e\left(\frac{277}{300}\right)$
$\chi_{216000}(12329,\cdot)$	$-1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{317}{600}\right)$	$e\left(\frac{463}{600}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{177}{200}\right)$	$e\left(\frac{251}{300}\right)$	$e\left(\frac{179}{600}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{131}{200}\right)$	$e\left(\frac{149}{300}\right)$
$\chi_{216000}(14489,\cdot)$	$-1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{131}{600}\right)$	$e\left(\frac{409}{600}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{111}{200}\right)$	$e\left(\frac{293}{300}\right)$	$e\left(\frac{197}{600}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{133}{200}\right)$	$e\left(\frac{107}{300}\right)$
$\chi_{216000}(15209,\cdot)$	$-1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{589}{600}\right)$	$e\left(\frac{71}{600}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{9}{200}\right)$	$e\left(\frac{67}{300}\right)$	$e\left(\frac{43}{600}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{27}{200}\right)$	$e\left(\frac{133}{300}\right)$
$\chi_{216000}(17369,\cdot)$	$-1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{523}{600}\right)$	$e\left(\frac{497}{600}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{63}{200}\right)$	$e\left(\frac{169}{300}\right)$	$e\left(\frac{301}{600}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{189}{200}\right)$	$e\left(\frac{31}{300}\right)$
$\chi_{216000}(18809,\cdot)$	$-1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{479}{600}\right)$	$e\left(\frac{181}{600}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{99}{200}\right)$	$e\left(\frac{137}{300}\right)$	$e\left(\frac{473}{600}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{97}{200}\right)$	$e\left(\frac{263}{300}\right)$
$\chi_{216000}(19529,\cdot)$	$-1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{97}{600}\right)$	$e\left(\frac{83}{600}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{157}{200}\right)$	$e\left(\frac{91}{300}\right)$	$e\left(\frac{439}{600}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{71}{200}\right)$	$e\left(\frac{109}{300}\right)$
$\chi_{216000}(20969,\cdot)$	$-1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{413}{600}\right)$	$e\left(\frac{7}{600}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{153}{200}\right)$	$e\left(\frac{239}{300}\right)$	$e\left(\frac{131}{600}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{59}{200}\right)$	$e\left(\frac{161}{300}\right)$
$\chi_{216000}(21689,\cdot)$	$-1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{511}{600}\right)$	$e\left(\frac{29}{600}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{91}{200}\right)$	$e\left(\frac{133}{300}\right)$	$e\left(\frac{457}{600}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{73}{200}\right)$	$e\left(\frac{67}{300}\right)$
$\chi_{216000}(23129,\cdot)$	$-1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{587}{600}\right)$	$e\left(\frac{193}{600}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{47}{200}\right)$	$e\left(\frac{161}{300}\right)$	$e\left(\frac{269}{600}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{141}{200}\right)$	$e\left(\frac{239}{300}\right)$
$\chi_{216000}(25289,\cdot)$	$-1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{401}{600}\right)$	$e\left(\frac{139}{600}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{181}{200}\right)$	$e\left(\frac{203}{300}\right)$	$e\left(\frac{287}{600}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{143}{200}\right)$	$e\left(\frac{197}{300}\right)$
$\chi_{216000}(26009,\cdot)$	$-1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{259}{600}\right)$	$e\left(\frac{401}{600}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{79}{200}\right)$	$e\left(\frac{277}{300}\right)$	$e\left(\frac{133}{600}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{37}{200}\right)$	$e\left(\frac{223}{300}\right)$
$\chi_{216000}(28169,\cdot)$	$-1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{193}{600}\right)$	$e\left(\frac{227}{600}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{133}{200}\right)$	$e\left(\frac{79}{300}\right)$	$e\left(\frac{391}{600}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{199}{200}\right)$	$e\left(\frac{121}{300}\right)$
$\chi_{216000}(29609,\cdot)$	$-1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{149}{600}\right)$	$e\left(\frac{511}{600}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{169}{200}\right)$	$e\left(\frac{47}{300}\right)$	$e\left(\frac{563}{600}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{107}{200}\right)$	$e\left(\frac{53}{300}\right)$
$\chi_{216000}(30329,\cdot)$	$-1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{367}{600}\right)$	$e\left(\frac{413}{600}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{27}{200}\right)$	$e\left(\frac{1}{300}\right)$	$e\left(\frac{529}{600}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{81}{200}\right)$	$e\left(\frac{199}{300}\right)$
$\chi_{216000}(31769,\cdot)$	$-1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{83}{600}\right)$	$e\left(\frac{337}{600}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{23}{200}\right)$	$e\left(\frac{149}{300}\right)$	$e\left(\frac{221}{600}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{69}{200}\right)$	$e\left(\frac{251}{300}\right)$
$\chi_{216000}(32489,\cdot)$	$-1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{181}{600}\right)$	$e\left(\frac{359}{600}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{161}{200}\right)$	$e\left(\frac{43}{300}\right)$	$e\left(\frac{547}{600}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{83}{200}\right)$	$e\left(\frac{157}{300}\right)$
$\chi_{216000}(33929,\cdot)$	$-1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{257}{600}\right)$	$e\left(\frac{523}{600}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{117}{200}\right)$	$e\left(\frac{71}{300}\right)$	$e\left(\frac{359}{600}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{151}{200}\right)$	$e\left(\frac{29}{300}\right)$
$\chi_{216000}(36089,\cdot)$	$-1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{71}{600}\right)$	$e\left(\frac{469}{600}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{51}{200}\right)$	$e\left(\frac{113}{300}\right)$	$e\left(\frac{377}{600}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{153}{200}\right)$	$e\left(\frac{287}{300}\right)$
$\chi_{216000}(36809,\cdot)$	$-1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{529}{600}\right)$	$e\left(\frac{131}{600}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{149}{200}\right)$	$e\left(\frac{187}{300}\right)$	$e\left(\frac{223}{600}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{47}{200}\right)$	$e\left(\frac{13}{300}\right)$
$\chi_{216000}(38969,\cdot)$	$-1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{463}{600}\right)$	$e\left(\frac{557}{600}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{3}{200}\right)$	$e\left(\frac{289}{300}\right)$	$e\left(\frac{481}{600}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{9}{200}\right)$	$e\left(\frac{211}{300}\right)$
$\chi_{216000}(40409,\cdot)$	$-1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{419}{600}\right)$	$e\left(\frac{241}{600}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{39}{200}\right)$	$e\left(\frac{257}{300}\right)$	$e\left(\frac{53}{600}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{117}{200}\right)$	$e\left(\frac{143}{300}\right)$
$\chi_{216000}(41129,\cdot)$	$-1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{37}{600}\right)$	$e\left(\frac{143}{600}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{97}{200}\right)$	$e\left(\frac{211}{300}\right)$	$e\left(\frac{19}{600}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{91}{200}\right)$	$e\left(\frac{289}{300}\right)$