Dirichlet character orbit 5733.mf

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

Basic properties

Modulus:	$5733$
Conductor:	$5733$
Order:	$84$
Real:	no
Primitive:	yes
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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$16$	$17$	$19$	$20$
$\chi_{5733}(11,\cdot)$	$1$	$1$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{10}{21}\right)$	$i$	$e\left(\frac{61}{84}\right)$
$\chi_{5733}(149,\cdot)$	$1$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{17}{21}\right)$	$-i$	$e\left(\frac{47}{84}\right)$
$\chi_{5733}(527,\cdot)$	$1$	$1$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{8}{21}\right)$	$i$	$e\left(\frac{53}{84}\right)$
$\chi_{5733}(830,\cdot)$	$1$	$1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{16}{21}\right)$	$i$	$e\left(\frac{1}{84}\right)$
$\chi_{5733}(968,\cdot)$	$1$	$1$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{8}{21}\right)$	$-i$	$e\left(\frac{11}{84}\right)$
$\chi_{5733}(1346,\cdot)$	$1$	$1$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{20}{21}\right)$	$i$	$e\left(\frac{17}{84}\right)$
$\chi_{5733}(1523,\cdot)$	$1$	$1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{21}\right)$	$-i$	$e\left(\frac{31}{84}\right)$
$\chi_{5733}(1649,\cdot)$	$1$	$1$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{21}\right)$	$i$	$e\left(\frac{25}{84}\right)$
$\chi_{5733}(1787,\cdot)$	$1$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{20}{21}\right)$	$-i$	$e\left(\frac{59}{84}\right)$
$\chi_{5733}(2165,\cdot)$	$1$	$1$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{21}\right)$	$i$	$e\left(\frac{65}{84}\right)$
$\chi_{5733}(2342,\cdot)$	$1$	$1$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{19}{21}\right)$	$-i$	$e\left(\frac{55}{84}\right)$
$\chi_{5733}(2606,\cdot)$	$1$	$1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{21}\right)$	$-i$	$e\left(\frac{23}{84}\right)$
$\chi_{5733}(2984,\cdot)$	$1$	$1$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{2}{21}\right)$	$i$	$e\left(\frac{29}{84}\right)$
$\chi_{5733}(3161,\cdot)$	$1$	$1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{4}{21}\right)$	$-i$	$e\left(\frac{79}{84}\right)$
$\chi_{5733}(3287,\cdot)$	$1$	$1$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{21}\right)$	$i$	$e\left(\frac{73}{84}\right)$
$\chi_{5733}(3425,\cdot)$	$1$	$1$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{2}{21}\right)$	$-i$	$e\left(\frac{71}{84}\right)$
$\chi_{5733}(3980,\cdot)$	$1$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{10}{21}\right)$	$-i$	$e\left(\frac{19}{84}\right)$
$\chi_{5733}(4106,\cdot)$	$1$	$1$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{19}{21}\right)$	$i$	$e\left(\frac{13}{84}\right)$
$\chi_{5733}(4622,\cdot)$	$1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{21}\right)$	$i$	$e\left(\frac{41}{84}\right)$
$\chi_{5733}(4799,\cdot)$	$1$	$1$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{16}{21}\right)$	$-i$	$e\left(\frac{43}{84}\right)$
$\chi_{5733}(4925,\cdot)$	$1$	$1$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{4}{21}\right)$	$i$	$e\left(\frac{37}{84}\right)$
$\chi_{5733}(5063,\cdot)$	$1$	$1$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{21}\right)$	$-i$	$e\left(\frac{83}{84}\right)$
$\chi_{5733}(5441,\cdot)$	$1$	$1$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{17}{21}\right)$	$i$	$e\left(\frac{5}{84}\right)$
$\chi_{5733}(5618,\cdot)$	$1$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{21}\right)$	$-i$	$e\left(\frac{67}{84}\right)$