LMFDB - Dirichlet character orbit 2352.dr

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2352, base_ring=CyclotomicField(84)) M = H._module chi = DirichletCharacter(H, M([0,21,42,58])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(5,2352)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2352$
Conductor:	$2352$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$84$	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:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{2352}(5,\cdot)$	$1$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{84}\right)$
$\chi_{2352}(101,\cdot)$	$1$	$1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{84}\right)$
$\chi_{2352}(173,\cdot)$	$1$	$1$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{59}{84}\right)$
$\chi_{2352}(269,\cdot)$	$1$	$1$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{79}{84}\right)$
$\chi_{2352}(341,\cdot)$	$1$	$1$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{84}\right)$
$\chi_{2352}(437,\cdot)$	$1$	$1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{73}{84}\right)$
$\chi_{2352}(605,\cdot)$	$1$	$1$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{67}{84}\right)$
$\chi_{2352}(677,\cdot)$	$1$	$1$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{65}{84}\right)$
$\chi_{2352}(773,\cdot)$	$1$	$1$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{61}{84}\right)$
$\chi_{2352}(845,\cdot)$	$1$	$1$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{84}\right)$
$\chi_{2352}(941,\cdot)$	$1$	$1$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{55}{84}\right)$
$\chi_{2352}(1013,\cdot)$	$1$	$1$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{41}{84}\right)$
$\chi_{2352}(1181,\cdot)$	$1$	$1$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{71}{84}\right)$
$\chi_{2352}(1277,\cdot)$	$1$	$1$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{43}{84}\right)$
$\chi_{2352}(1349,\cdot)$	$1$	$1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{84}\right)$
$\chi_{2352}(1445,\cdot)$	$1$	$1$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{37}{84}\right)$
$\chi_{2352}(1517,\cdot)$	$1$	$1$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{47}{84}\right)$
$\chi_{2352}(1613,\cdot)$	$1$	$1$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{2352}(1781,\cdot)$	$1$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{84}\right)$
$\chi_{2352}(1853,\cdot)$	$1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{2352}(1949,\cdot)$	$1$	$1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{84}\right)$
$\chi_{2352}(2021,\cdot)$	$1$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{53}{84}\right)$
$\chi_{2352}(2117,\cdot)$	$1$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{84}\right)$
$\chi_{2352}(2189,\cdot)$	$1$	$1$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{83}{84}\right)$

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	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)
\(\chi_{2352}(5,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{29}{84}\right)\)
\(\chi_{2352}(101,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{84}\right)\)
\(\chi_{2352}(173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{59}{84}\right)\)
\(\chi_{2352}(269,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{79}{84}\right)\)
\(\chi_{2352}(341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{84}\right)\)
\(\chi_{2352}(437,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{73}{84}\right)\)
\(\chi_{2352}(605,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{67}{84}\right)\)
\(\chi_{2352}(677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{65}{84}\right)\)
\(\chi_{2352}(773,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{61}{84}\right)\)
\(\chi_{2352}(845,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{84}\right)\)
\(\chi_{2352}(941,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{55}{84}\right)\)
\(\chi_{2352}(1013,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{41}{84}\right)\)
\(\chi_{2352}(1181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{71}{84}\right)\)
\(\chi_{2352}(1277,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{43}{84}\right)\)
\(\chi_{2352}(1349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{84}\right)\)
\(\chi_{2352}(1445,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{37}{84}\right)\)
\(\chi_{2352}(1517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{47}{84}\right)\)
\(\chi_{2352}(1613,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{31}{84}\right)\)
\(\chi_{2352}(1781,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{84}\right)\)
\(\chi_{2352}(1853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{84}\right)\)
\(\chi_{2352}(1949,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{84}\right)\)
\(\chi_{2352}(2021,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{53}{84}\right)\)
\(\chi_{2352}(2117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{84}\right)\)
\(\chi_{2352}(2189,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{83}{84}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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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	2352.dr
Modulus	$2352$
Conductor	$2352$
Order	$84$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(2352\)
Conductor:	\(2352\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(84\)	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)