LMFDB - Dirichlet character orbit 2349.bh

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2349, base_ring=CyclotomicField(84)) M = H._module chi = DirichletCharacter(H, M([56,57])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(55,2349)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2349$
Conductor:	$261$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$84$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 261.w	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{2349}(55,\cdot)$	$-1$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{2349}(217,\cdot)$	$-1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{2349}(271,\cdot)$	$-1$	$1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{2349}(298,\cdot)$	$-1$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{2349}(379,\cdot)$	$-1$	$1$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{2349}(433,\cdot)$	$-1$	$1$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{2349}(514,\cdot)$	$-1$	$1$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{2349}(541,\cdot)$	$-1$	$1$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{2349}(595,\cdot)$	$-1$	$1$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{2349}(757,\cdot)$	$-1$	$1$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{2349}(838,\cdot)$	$-1$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{2349}(946,\cdot)$	$-1$	$1$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{2349}(1000,\cdot)$	$-1$	$1$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{2349}(1081,\cdot)$	$-1$	$1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{2349}(1162,\cdot)$	$-1$	$1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{2349}(1324,\cdot)$	$-1$	$1$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{2349}(1432,\cdot)$	$-1$	$1$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{2349}(1729,\cdot)$	$-1$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{2349}(1837,\cdot)$	$-1$	$1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{2349}(1999,\cdot)$	$-1$	$1$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{2349}(2080,\cdot)$	$-1$	$1$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{2349}(2161,\cdot)$	$-1$	$1$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{2349}(2215,\cdot)$	$-1$	$1$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{2349}(2323,\cdot)$	$-1$	$1$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{8}{21}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{2349}(55,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{2349}(217,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{2349}(271,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{2349}(298,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{2349}(379,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{2349}(433,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{2349}(514,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{2349}(541,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{2349}(595,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{2349}(757,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{2349}(838,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{2349}(946,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{2349}(1000,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{2349}(1081,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{2349}(1162,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{2349}(1324,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{2349}(1432,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{2349}(1729,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{2349}(1837,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{2349}(1999,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{2349}(2080,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{2349}(2161,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{2349}(2215,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{2349}(2323,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

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	2349.bh
Modulus	$2349$
Conductor	$261$
Order	$84$
Real	no
Primitive	no
Minimal	no
Parity	odd

Modulus:	\(2349\)
Conductor:	\(261\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(84\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 261.w	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)