Dirichlet character orbit 2352.dn

• Label: 2352.dn
• Modulus: $2352$
• Conductor: $784$
• Order: $84$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$2352$
Conductor:	$784$
Order:	$84$
Real:	no
Primitive:	no, induced from 784.bu
Minimal:	yes
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{2352}(115,\cdot)$	$1$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{67}{84}\right)$
$\chi_{2352}(187,\cdot)$	$1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{65}{84}\right)$
$\chi_{2352}(283,\cdot)$	$1$	$1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{61}{84}\right)$
$\chi_{2352}(355,\cdot)$	$1$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{84}\right)$
$\chi_{2352}(451,\cdot)$	$1$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{55}{84}\right)$
$\chi_{2352}(523,\cdot)$	$1$	$1$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{41}{84}\right)$
$\chi_{2352}(691,\cdot)$	$1$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{71}{84}\right)$
$\chi_{2352}(787,\cdot)$	$1$	$1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{43}{84}\right)$
$\chi_{2352}(859,\cdot)$	$1$	$1$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{84}\right)$
$\chi_{2352}(955,\cdot)$	$1$	$1$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{37}{84}\right)$
$\chi_{2352}(1027,\cdot)$	$1$	$1$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{47}{84}\right)$
$\chi_{2352}(1123,\cdot)$	$1$	$1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{2352}(1291,\cdot)$	$1$	$1$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{84}\right)$
$\chi_{2352}(1363,\cdot)$	$1$	$1$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{2352}(1459,\cdot)$	$1$	$1$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{84}\right)$
$\chi_{2352}(1531,\cdot)$	$1$	$1$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{53}{84}\right)$
$\chi_{2352}(1627,\cdot)$	$1$	$1$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{84}\right)$
$\chi_{2352}(1699,\cdot)$	$1$	$1$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{83}{84}\right)$
$\chi_{2352}(1867,\cdot)$	$1$	$1$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{84}\right)$
$\chi_{2352}(1963,\cdot)$	$1$	$1$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{84}\right)$
$\chi_{2352}(2035,\cdot)$	$1$	$1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{59}{84}\right)$
$\chi_{2352}(2131,\cdot)$	$1$	$1$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{79}{84}\right)$
$\chi_{2352}(2203,\cdot)$	$1$	$1$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{84}\right)$
$\chi_{2352}(2299,\cdot)$	$1$	$1$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{73}{84}\right)$