LMFDB - Dirichlet character orbit 169.k

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(169, base_ring=CyclotomicField(78)) M = H._module chi = DirichletCharacter(H, M([1])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(4,169)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$169$
Conductor:	$169$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$78$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{39})$
Fixed field:	Number field defined by a degree 78 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{169}(4,\cdot)$	$1$	$1$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{25}{78}\right)$
$\chi_{169}(10,\cdot)$	$1$	$1$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{47}{78}\right)$
$\chi_{169}(17,\cdot)$	$1$	$1$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{31}{78}\right)$
$\chi_{169}(30,\cdot)$	$1$	$1$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{37}{78}\right)$
$\chi_{169}(36,\cdot)$	$1$	$1$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{5}{78}\right)$
$\chi_{169}(43,\cdot)$	$1$	$1$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{43}{78}\right)$
$\chi_{169}(49,\cdot)$	$1$	$1$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{23}{78}\right)$
$\chi_{169}(56,\cdot)$	$1$	$1$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{49}{78}\right)$
$\chi_{169}(62,\cdot)$	$1$	$1$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{41}{78}\right)$
$\chi_{169}(69,\cdot)$	$1$	$1$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{55}{78}\right)$
$\chi_{169}(75,\cdot)$	$1$	$1$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{59}{78}\right)$
$\chi_{169}(82,\cdot)$	$1$	$1$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{61}{78}\right)$
$\chi_{169}(88,\cdot)$	$1$	$1$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{77}{78}\right)$
$\chi_{169}(95,\cdot)$	$1$	$1$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{67}{78}\right)$
$\chi_{169}(101,\cdot)$	$1$	$1$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{17}{78}\right)$
$\chi_{169}(108,\cdot)$	$1$	$1$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{73}{78}\right)$
$\chi_{169}(114,\cdot)$	$1$	$1$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{35}{78}\right)$
$\chi_{169}(121,\cdot)$	$1$	$1$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{1}{78}\right)$
$\chi_{169}(127,\cdot)$	$1$	$1$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{53}{78}\right)$
$\chi_{169}(134,\cdot)$	$1$	$1$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{7}{78}\right)$
$\chi_{169}(140,\cdot)$	$1$	$1$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{71}{78}\right)$
$\chi_{169}(153,\cdot)$	$1$	$1$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{11}{78}\right)$
$\chi_{169}(160,\cdot)$	$1$	$1$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{19}{78}\right)$
$\chi_{169}(166,\cdot)$	$1$	$1$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{29}{78}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{169}(4,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{25}{78}\right)\)
\(\chi_{169}(10,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{47}{78}\right)\)
\(\chi_{169}(17,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{31}{78}\right)\)
\(\chi_{169}(30,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{37}{78}\right)\)
\(\chi_{169}(36,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{5}{78}\right)\)
\(\chi_{169}(43,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{43}{78}\right)\)
\(\chi_{169}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{23}{78}\right)\)
\(\chi_{169}(56,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{49}{78}\right)\)
\(\chi_{169}(62,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{41}{78}\right)\)
\(\chi_{169}(69,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)
\(\chi_{169}(75,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{59}{78}\right)\)
\(\chi_{169}(82,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{61}{78}\right)\)
\(\chi_{169}(88,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{77}{78}\right)\)
\(\chi_{169}(95,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{67}{78}\right)\)
\(\chi_{169}(101,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{17}{78}\right)\)
\(\chi_{169}(108,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{73}{78}\right)\)
\(\chi_{169}(114,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{35}{78}\right)\)
\(\chi_{169}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{1}{78}\right)\)
\(\chi_{169}(127,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{53}{78}\right)\)
\(\chi_{169}(134,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{7}{78}\right)\)
\(\chi_{169}(140,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{71}{78}\right)\)
\(\chi_{169}(153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{11}{78}\right)\)
\(\chi_{169}(160,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{19}{78}\right)\)
\(\chi_{169}(166,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{29}{78}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Basic properties

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Characters in Galois orbit

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	169.k
Modulus	$169$
Conductor	$169$
Order	$78$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(169\)
Conductor:	\(169\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(78\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)