Dirichlet character orbit 3380.cz

• Label: 3380.cz
• Modulus: $3380$
• Conductor: $3380$
• Order: $156$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$3380$
Conductor:	$3380$
Order:	$156$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Related number fields

Field of values:	$\Q(\zeta_{156})$
Fixed field:	Number field defined by a degree 156 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{3380}(63,\cdot)$	$-1$	$1$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{41}{78}\right)$
$\chi_{3380}(67,\cdot)$	$-1$	$1$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{77}{78}\right)$
$\chi_{3380}(163,\cdot)$	$-1$	$1$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{43}{78}\right)$
$\chi_{3380}(227,\cdot)$	$-1$	$1$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{1}{78}\right)$
$\chi_{3380}(323,\cdot)$	$-1$	$1$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{47}{78}\right)$
$\chi_{3380}(327,\cdot)$	$-1$	$1$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{71}{78}\right)$
$\chi_{3380}(423,\cdot)$	$-1$	$1$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{19}{78}\right)$
$\chi_{3380}(487,\cdot)$	$-1$	$1$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{25}{78}\right)$
$\chi_{3380}(583,\cdot)$	$-1$	$1$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{53}{78}\right)$
$\chi_{3380}(683,\cdot)$	$-1$	$1$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{73}{78}\right)$
$\chi_{3380}(747,\cdot)$	$-1$	$1$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{49}{78}\right)$
$\chi_{3380}(843,\cdot)$	$-1$	$1$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{59}{78}\right)$
$\chi_{3380}(847,\cdot)$	$-1$	$1$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{59}{78}\right)$
$\chi_{3380}(943,\cdot)$	$-1$	$1$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{49}{78}\right)$
$\chi_{3380}(1007,\cdot)$	$-1$	$1$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{73}{78}\right)$
$\chi_{3380}(1107,\cdot)$	$-1$	$1$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{53}{78}\right)$
$\chi_{3380}(1203,\cdot)$	$-1$	$1$	$e\left(\frac{77}{156}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{25}{78}\right)$
$\chi_{3380}(1267,\cdot)$	$-1$	$1$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{19}{78}\right)$
$\chi_{3380}(1363,\cdot)$	$-1$	$1$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{71}{78}\right)$
$\chi_{3380}(1367,\cdot)$	$-1$	$1$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{47}{78}\right)$
$\chi_{3380}(1463,\cdot)$	$-1$	$1$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{1}{78}\right)$
$\chi_{3380}(1527,\cdot)$	$-1$	$1$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{43}{78}\right)$
$\chi_{3380}(1623,\cdot)$	$-1$	$1$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{77}{78}\right)$
$\chi_{3380}(1627,\cdot)$	$-1$	$1$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{77}{156}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{41}{78}\right)$
$\chi_{3380}(1723,\cdot)$	$-1$	$1$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{55}{78}\right)$
$\chi_{3380}(1787,\cdot)$	$-1$	$1$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{67}{78}\right)$
$\chi_{3380}(1883,\cdot)$	$-1$	$1$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{5}{78}\right)$
$\chi_{3380}(1887,\cdot)$	$-1$	$1$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{35}{78}\right)$
$\chi_{3380}(1983,\cdot)$	$-1$	$1$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{31}{78}\right)$
$\chi_{3380}(2143,\cdot)$	$-1$	$1$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{11}{78}\right)$
$\chi_{3380}(2147,\cdot)$	$-1$	$1$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{29}{78}\right)$