Dirichlet character orbit 1053.cm

• Label: 1053.cm
• Modulus: $1053$
• Conductor: $1053$
• Order: $108$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1053$
Conductor:	$1053$
Order:	$108$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{108})$
Fixed field:	Number field defined by a degree 108 polynomial (not computed)

First 31 of 36 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$14$	$16$	$17$
$\chi_{1053}(20,\cdot)$	$1$	$1$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{1053}(41,\cdot)$	$1$	$1$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{1053}(50,\cdot)$	$1$	$1$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{1053}(110,\cdot)$	$1$	$1$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{1053}(137,\cdot)$	$1$	$1$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{1053}(158,\cdot)$	$1$	$1$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{1053}(167,\cdot)$	$1$	$1$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{1053}(227,\cdot)$	$1$	$1$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{1053}(254,\cdot)$	$1$	$1$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{1053}(275,\cdot)$	$1$	$1$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{1053}(284,\cdot)$	$1$	$1$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{1053}(344,\cdot)$	$1$	$1$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{1053}(371,\cdot)$	$1$	$1$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{1053}(392,\cdot)$	$1$	$1$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{1053}(401,\cdot)$	$1$	$1$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{1053}(461,\cdot)$	$1$	$1$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{1053}(488,\cdot)$	$1$	$1$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{1053}(509,\cdot)$	$1$	$1$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{1053}(518,\cdot)$	$1$	$1$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{1053}(578,\cdot)$	$1$	$1$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{1053}(605,\cdot)$	$1$	$1$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{1053}(626,\cdot)$	$1$	$1$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{1053}(635,\cdot)$	$1$	$1$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{1053}(695,\cdot)$	$1$	$1$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{1053}(722,\cdot)$	$1$	$1$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{1053}(743,\cdot)$	$1$	$1$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{1053}(752,\cdot)$	$1$	$1$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{1053}(812,\cdot)$	$1$	$1$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{1053}(839,\cdot)$	$1$	$1$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{1053}(860,\cdot)$	$1$	$1$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{1053}(869,\cdot)$	$1$	$1$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{2}{9}\right)$