LMFDB - Dirichlet character orbit 2366.bl

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2366, base_ring=CyclotomicField(78)) M = H._module chi = DirichletCharacter(H, M([26,50])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(107,2366)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2366$
Conductor:	$1183$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$39$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1183.bi	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:	39.39.253721406991290895924770503111827676888647505643788160579278763946491805765758913183386148271215912203961.2

Characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$9$	$11$	$15$	$17$	$19$	$23$	$25$	$27$
$\chi_{2366}(107,\cdot)$	$1$	$1$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{2366}(165,\cdot)$	$1$	$1$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{2366}(289,\cdot)$	$1$	$1$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{2366}(347,\cdot)$	$1$	$1$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{2366}(471,\cdot)$	$1$	$1$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{2366}(711,\cdot)$	$1$	$1$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{2366}(835,\cdot)$	$1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{2366}(893,\cdot)$	$1$	$1$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{2366}(1017,\cdot)$	$1$	$1$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{2366}(1075,\cdot)$	$1$	$1$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{2366}(1199,\cdot)$	$1$	$1$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{2366}(1257,\cdot)$	$1$	$1$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{2366}(1381,\cdot)$	$1$	$1$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{2366}(1439,\cdot)$	$1$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{2366}(1563,\cdot)$	$1$	$1$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{2366}(1621,\cdot)$	$1$	$1$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{2366}(1745,\cdot)$	$1$	$1$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{2366}(1803,\cdot)$	$1$	$1$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{2366}(1927,\cdot)$	$1$	$1$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{2366}(1985,\cdot)$	$1$	$1$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{2366}(2109,\cdot)$	$1$	$1$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{2366}(2167,\cdot)$	$1$	$1$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{2366}(2291,\cdot)$	$1$	$1$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{2366}(2349,\cdot)$	$1$	$1$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{2}{13}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)	\(27\)
\(\chi_{2366}(107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{2366}(165,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{2366}(289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{2366}(347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{2366}(471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{2366}(711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{2366}(835,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{2366}(893,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{2366}(1017,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{2366}(1075,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{2366}(1199,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{2366}(1257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{2366}(1381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{2366}(1439,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{2366}(1563,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{2366}(1621,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{2366}(1745,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{2366}(1803,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{2366}(1927,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{2366}(1985,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{2366}(2109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{2366}(2167,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{2366}(2291,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{2366}(2349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{2}{13}\right)\)

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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	2366.bl
Modulus	$2366$
Conductor	$1183$
Order	$39$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(2366\)
Conductor:	\(1183\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(39\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1183.bi	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)