LMFDB - Dirichlet character orbit 7742.bh

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7742, base_ring=CyclotomicField(78)) M = H._module chi = DirichletCharacter(H, M([26,32])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(177,7742)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$7742$
Conductor:	$553$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$39$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 553.y	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{39})$
Fixed field:	39.39.12088669642594427834079815641631684897704150233955220736437592661471356964310045748175158745489.2

Characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{7742}(177,\cdot)$	$1$	$1$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{39}\right)$
$\chi_{7742}(361,\cdot)$	$1$	$1$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{16}{39}\right)$
$\chi_{7742}(753,\cdot)$	$1$	$1$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{34}{39}\right)$
$\chi_{7742}(863,\cdot)$	$1$	$1$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{39}\right)$
$\chi_{7742}(1047,\cdot)$	$1$	$1$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{37}{39}\right)$
$\chi_{7742}(1059,\cdot)$	$1$	$1$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{39}\right)$
$\chi_{7742}(1537,\cdot)$	$1$	$1$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{22}{39}\right)$
$\chi_{7742}(1843,\cdot)$	$1$	$1$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{39}\right)$
$\chi_{7742}(2137,\cdot)$	$1$	$1$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{39}\right)$
$\chi_{7742}(2419,\cdot)$	$1$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{39}\right)$
$\chi_{7742}(3399,\cdot)$	$1$	$1$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{39}\right)$
$\chi_{7742}(3803,\cdot)$	$1$	$1$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{39}\right)$
$\chi_{7742}(4587,\cdot)$	$1$	$1$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{35}{39}\right)$
$\chi_{7742}(5175,\cdot)$	$1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{38}{39}\right)$
$\chi_{7742}(5555,\cdot)$	$1$	$1$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{31}{39}\right)$
$\chi_{7742}(5653,\cdot)$	$1$	$1$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{39}\right)$
$\chi_{7742}(6155,\cdot)$	$1$	$1$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{39}\right)$
$\chi_{7742}(6351,\cdot)$	$1$	$1$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{14}{39}\right)$
$\chi_{7742}(6449,\cdot)$	$1$	$1$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{32}{39}\right)$
$\chi_{7742}(6633,\cdot)$	$1$	$1$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{10}{39}\right)$
$\chi_{7742}(6645,\cdot)$	$1$	$1$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{20}{39}\right)$
$\chi_{7742}(6731,\cdot)$	$1$	$1$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{39}\right)$
$\chi_{7742}(7123,\cdot)$	$1$	$1$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{28}{39}\right)$
$\chi_{7742}(7319,\cdot)$	$1$	$1$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{39}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{7742}(177,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{39}\right)\)
\(\chi_{7742}(361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{16}{39}\right)\)
\(\chi_{7742}(753,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{34}{39}\right)\)
\(\chi_{7742}(863,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{39}\right)\)
\(\chi_{7742}(1047,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{37}{39}\right)\)
\(\chi_{7742}(1059,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{39}\right)\)
\(\chi_{7742}(1537,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{22}{39}\right)\)
\(\chi_{7742}(1843,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{39}\right)\)
\(\chi_{7742}(2137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{39}\right)\)
\(\chi_{7742}(2419,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{39}\right)\)
\(\chi_{7742}(3399,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{39}\right)\)
\(\chi_{7742}(3803,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{39}\right)\)
\(\chi_{7742}(4587,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{35}{39}\right)\)
\(\chi_{7742}(5175,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{38}{39}\right)\)
\(\chi_{7742}(5555,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{31}{39}\right)\)
\(\chi_{7742}(5653,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{39}\right)\)
\(\chi_{7742}(6155,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{39}\right)\)
\(\chi_{7742}(6351,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{14}{39}\right)\)
\(\chi_{7742}(6449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{32}{39}\right)\)
\(\chi_{7742}(6633,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{10}{39}\right)\)
\(\chi_{7742}(6645,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{20}{39}\right)\)
\(\chi_{7742}(6731,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{39}\right)\)
\(\chi_{7742}(7123,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{28}{39}\right)\)
\(\chi_{7742}(7319,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{39}\right)\)

Introduction

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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	7742.bh
Modulus	$7742$
Conductor	$553$
Order	$39$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(7742\)
Conductor:	\(553\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(39\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 553.y	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)