Dirichlet character orbit 5733.mq

• Label: 5733.mq
• Modulus: $5733$
• Conductor: $637$
• Order: $84$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$5733$
Conductor:	$637$
Order:	$84$
Real:	no
Primitive:	no, induced from 637.cd
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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$16$	$17$	$19$	$20$
$\chi_{5733}(136,\cdot)$	$1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{19}{84}\right)$
$\chi_{5733}(145,\cdot)$	$1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{47}{84}\right)$
$\chi_{5733}(271,\cdot)$	$1$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{84}\right)$
$\chi_{5733}(514,\cdot)$	$1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{37}{84}\right)$
$\chi_{5733}(955,\cdot)$	$1$	$1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{79}{84}\right)$
$\chi_{5733}(964,\cdot)$	$1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{83}{84}\right)$
$\chi_{5733}(1090,\cdot)$	$1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{53}{84}\right)$
$\chi_{5733}(1333,\cdot)$	$1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{84}\right)$
$\chi_{5733}(1774,\cdot)$	$1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{55}{84}\right)$
$\chi_{5733}(1909,\cdot)$	$1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{84}\right)$
$\chi_{5733}(2152,\cdot)$	$1$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{73}{84}\right)$
$\chi_{5733}(2593,\cdot)$	$1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{5733}(2602,\cdot)$	$1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{71}{84}\right)$
$\chi_{5733}(2728,\cdot)$	$1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{41}{84}\right)$
$\chi_{5733}(3421,\cdot)$	$1$	$1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{5733}(3790,\cdot)$	$1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{25}{84}\right)$
$\chi_{5733}(4231,\cdot)$	$1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{67}{84}\right)$
$\chi_{5733}(4240,\cdot)$	$1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{59}{84}\right)$
$\chi_{5733}(4366,\cdot)$	$1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{29}{84}\right)$
$\chi_{5733}(4609,\cdot)$	$1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{84}\right)$
$\chi_{5733}(5050,\cdot)$	$1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{43}{84}\right)$
$\chi_{5733}(5059,\cdot)$	$1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{84}\right)$
$\chi_{5733}(5185,\cdot)$	$1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{65}{84}\right)$
$\chi_{5733}(5428,\cdot)$	$1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{61}{84}\right)$