Dirichlet character orbit 216000.uz

• Label: 216000.uz
• 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.mj
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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{216000}(73,\cdot)$	$-1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{421}{600}\right)$	$e\left(\frac{269}{600}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{1}{200}\right)$	$e\left(\frac{119}{150}\right)$	$e\left(\frac{127}{600}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{153}{200}\right)$	$e\left(\frac{187}{300}\right)$
$\chi_{216000}(2953,\cdot)$	$-1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{557}{600}\right)$	$e\left(\frac{373}{600}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{17}{200}\right)$	$e\left(\frac{73}{150}\right)$	$e\left(\frac{359}{600}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{1}{200}\right)$	$e\left(\frac{179}{300}\right)$
$\chi_{216000}(3097,\cdot)$	$-1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{247}{600}\right)$	$e\left(\frac{383}{600}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{107}{200}\right)$	$e\left(\frac{83}{150}\right)$	$e\left(\frac{589}{600}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{171}{200}\right)$	$e\left(\frac{109}{300}\right)$
$\chi_{216000}(5977,\cdot)$	$-1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{311}{600}\right)$	$e\left(\frac{79}{600}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{91}{200}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{557}{600}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{123}{200}\right)$	$e\left(\frac{17}{300}\right)$
$\chi_{216000}(7273,\cdot)$	$-1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{161}{600}\right)$	$e\left(\frac{529}{600}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{141}{200}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{107}{600}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{173}{200}\right)$	$e\left(\frac{167}{300}\right)$
$\chi_{216000}(7417,\cdot)$	$-1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{283}{600}\right)$	$e\left(\frac{587}{600}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{23}{200}\right)$	$e\left(\frac{137}{150}\right)$	$e\left(\frac{121}{600}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{119}{200}\right)$	$e\left(\frac{1}{300}\right)$
$\chi_{216000}(8713,\cdot)$	$-1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{349}{600}\right)$	$e\left(\frac{461}{600}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{169}{200}\right)$	$e\left(\frac{11}{150}\right)$	$e\left(\frac{463}{600}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{57}{200}\right)$	$e\left(\frac{103}{300}\right)$
$\chi_{216000}(10297,\cdot)$	$-1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{107}{600}\right)$	$e\left(\frac{523}{600}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{167}{200}\right)$	$e\left(\frac{73}{150}\right)$	$e\left(\frac{209}{600}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{151}{200}\right)$	$e\left(\frac{29}{300}\right)$
$\chi_{216000}(11737,\cdot)$	$-1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{559}{600}\right)$	$e\left(\frac{551}{600}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{179}{200}\right)$	$e\left(\frac{101}{150}\right)$	$e\left(\frac{133}{600}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{187}{200}\right)$	$e\left(\frac{73}{300}\right)$
$\chi_{216000}(13033,\cdot)$	$-1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{73}{600}\right)$	$e\left(\frac{497}{600}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{13}{200}\right)$	$e\left(\frac{47}{150}\right)$	$e\left(\frac{451}{600}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{189}{200}\right)$	$e\left(\frac{31}{300}\right)$
$\chi_{216000}(14617,\cdot)$	$-1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{143}{600}\right)$	$e\left(\frac{127}{600}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{83}{200}\right)$	$e\left(\frac{127}{150}\right)$	$e\left(\frac{341}{600}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{99}{200}\right)$	$e\left(\frac{221}{300}\right)$
$\chi_{216000}(15913,\cdot)$	$-1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{89}{600}\right)$	$e\left(\frac{121}{600}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{109}{200}\right)$	$e\left(\frac{121}{150}\right)$	$e\left(\frac{443}{600}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{77}{200}\right)$	$e\left(\frac{83}{300}\right)$
$\chi_{216000}(17353,\cdot)$	$-1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{37}{600}\right)$	$e\left(\frac{293}{600}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{97}{200}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{319}{600}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{41}{200}\right)$	$e\left(\frac{139}{300}\right)$
$\chi_{216000}(18937,\cdot)$	$-1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{419}{600}\right)$	$e\left(\frac{91}{600}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{39}{200}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{353}{600}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{167}{200}\right)$	$e\left(\frac{293}{300}\right)$
$\chi_{216000}(20233,\cdot)$	$-1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{413}{600}\right)$	$e\left(\frac{157}{600}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{153}{200}\right)$	$e\left(\frac{7}{150}\right)$	$e\left(\frac{431}{600}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{9}{200}\right)$	$e\left(\frac{11}{300}\right)$
$\chi_{216000}(20377,\cdot)$	$-1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{31}{600}\right)$	$e\left(\frac{359}{600}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{11}{200}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{397}{600}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{83}{200}\right)$	$e\left(\frac{157}{300}\right)$
$\chi_{216000}(21673,\cdot)$	$-1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{241}{600}\right)$	$e\left(\frac{449}{600}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{21}{200}\right)$	$e\left(\frac{149}{150}\right)$	$e\left(\frac{67}{600}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{13}{200}\right)$	$e\left(\frac{127}{300}\right)$
$\chi_{216000}(24553,\cdot)$	$-1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{377}{600}\right)$	$e\left(\frac{553}{600}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{37}{200}\right)$	$e\left(\frac{103}{150}\right)$	$e\left(\frac{299}{600}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{61}{200}\right)$	$e\left(\frac{119}{300}\right)$
$\chi_{216000}(24697,\cdot)$	$-1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{427}{600}\right)$	$e\left(\frac{203}{600}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{87}{200}\right)$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{49}{600}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{111}{200}\right)$	$e\left(\frac{169}{300}\right)$
$\chi_{216000}(27577,\cdot)$	$-1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{491}{600}\right)$	$e\left(\frac{499}{600}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{71}{200}\right)$	$e\left(\frac{49}{150}\right)$	$e\left(\frac{17}{600}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{63}{200}\right)$	$e\left(\frac{77}{300}\right)$
$\chi_{216000}(28873,\cdot)$	$-1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{581}{600}\right)$	$e\left(\frac{109}{600}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{161}{200}\right)$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{47}{600}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{33}{200}\right)$	$e\left(\frac{107}{300}\right)$
$\chi_{216000}(29017,\cdot)$	$-1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{463}{600}\right)$	$e\left(\frac{407}{600}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{3}{200}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{181}{600}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{59}{200}\right)$	$e\left(\frac{61}{300}\right)$
$\chi_{216000}(30313,\cdot)$	$-1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{169}{600}\right)$	$e\left(\frac{41}{600}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{189}{200}\right)$	$e\left(\frac{41}{150}\right)$	$e\left(\frac{403}{600}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{117}{200}\right)$	$e\left(\frac{43}{300}\right)$
$\chi_{216000}(31897,\cdot)$	$-1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{287}{600}\right)$	$e\left(\frac{343}{600}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{147}{200}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{269}{600}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{91}{200}\right)$	$e\left(\frac{89}{300}\right)$
$\chi_{216000}(33337,\cdot)$	$-1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{139}{600}\right)$	$e\left(\frac{371}{600}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{159}{200}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{193}{600}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{127}{200}\right)$	$e\left(\frac{133}{300}\right)$
$\chi_{216000}(34633,\cdot)$	$-1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{493}{600}\right)$	$e\left(\frac{77}{600}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{33}{200}\right)$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{391}{600}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{49}{200}\right)$	$e\left(\frac{271}{300}\right)$
$\chi_{216000}(36217,\cdot)$	$-1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{323}{600}\right)$	$e\left(\frac{547}{600}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{63}{200}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{401}{600}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{39}{200}\right)$	$e\left(\frac{281}{300}\right)$
$\chi_{216000}(37513,\cdot)$	$-1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{509}{600}\right)$	$e\left(\frac{301}{600}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{129}{200}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{383}{600}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{137}{200}\right)$	$e\left(\frac{23}{300}\right)$
$\chi_{216000}(38953,\cdot)$	$-1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{457}{600}\right)$	$e\left(\frac{473}{600}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{117}{200}\right)$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{259}{600}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{101}{200}\right)$	$e\left(\frac{79}{300}\right)$
$\chi_{216000}(40537,\cdot)$	$-1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{599}{600}\right)$	$e\left(\frac{511}{600}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{19}{200}\right)$	$e\left(\frac{61}{150}\right)$	$e\left(\frac{413}{600}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{107}{200}\right)$	$e\left(\frac{53}{300}\right)$
$\chi_{216000}(41833,\cdot)$	$-1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{233}{600}\right)$	$e\left(\frac{337}{600}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{173}{200}\right)$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{371}{600}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{69}{200}\right)$	$e\left(\frac{251}{300}\right)$