LMFDB - Dirichlet character orbit 28665.bjs

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(28665, base_ring=CyclotomicField(84)) M = H._module chi = DirichletCharacter(H, M([56,42,2,49])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(934,28665)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$28665$
Conductor:	$28665$	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	$-1$	$1$	$2$	$4$	$8$	$11$	$16$	$17$	$19$	$22$	$23$	$29$
$\chi_{28665}(934,\cdot)$	$1$	$1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{42}\right)$	$-i$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{28665}(2749,\cdot)$	$1$	$1$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{25}{42}\right)$	$i$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{28665}(4084,\cdot)$	$1$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{23}{42}\right)$	$i$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{28665}(5584,\cdot)$	$1$	$1$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{13}{42}\right)$	$-i$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{28665}(6844,\cdot)$	$1$	$1$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{31}{42}\right)$	$i$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{28665}(8179,\cdot)$	$1$	$1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{42}\right)$	$i$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{28665}(9124,\cdot)$	$1$	$1$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{17}{42}\right)$	$-i$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{28665}(9679,\cdot)$	$1$	$1$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{19}{42}\right)$	$-i$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{28665}(10939,\cdot)$	$1$	$1$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{37}{42}\right)$	$i$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{28665}(12274,\cdot)$	$1$	$1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{29}{42}\right)$	$i$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{28665}(13219,\cdot)$	$1$	$1$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{41}{42}\right)$	$-i$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{28665}(13774,\cdot)$	$1$	$1$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{25}{42}\right)$	$-i$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{28665}(15034,\cdot)$	$1$	$1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{42}\right)$	$i$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{28665}(16369,\cdot)$	$1$	$1$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{42}\right)$	$i$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{28665}(17314,\cdot)$	$1$	$1$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{23}{42}\right)$	$-i$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{28665}(17869,\cdot)$	$1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{31}{42}\right)$	$-i$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{28665}(21409,\cdot)$	$1$	$1$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{42}\right)$	$-i$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{28665}(21964,\cdot)$	$1$	$1$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{37}{42}\right)$	$-i$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{28665}(23224,\cdot)$	$1$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{13}{42}\right)$	$i$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{28665}(24559,\cdot)$	$1$	$1$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{17}{42}\right)$	$i$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{28665}(25504,\cdot)$	$1$	$1$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{29}{42}\right)$	$-i$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{28665}(26059,\cdot)$	$1$	$1$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{42}\right)$	$-i$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{28665}(27319,\cdot)$	$1$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{19}{42}\right)$	$i$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{28665}(28654,\cdot)$	$1$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{41}{42}\right)$	$i$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(16\)	\(17\)	\(19\)	\(22\)	\(23\)	\(29\)
\(\chi_{28665}(934,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(-i\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{28665}(2749,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(i\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{28665}(4084,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(i\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{28665}(5584,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(-i\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{28665}(6844,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(i\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{28665}(8179,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(i\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{28665}(9124,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(-i\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{28665}(9679,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(-i\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{28665}(10939,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(i\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{28665}(12274,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(i\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{28665}(13219,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(-i\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{28665}(13774,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(-i\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{28665}(15034,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(i\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{28665}(16369,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(i\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{28665}(17314,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(-i\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{28665}(17869,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(-i\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{28665}(21409,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(-i\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{28665}(21964,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(-i\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{28665}(23224,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(i\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{28665}(24559,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(i\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{28665}(25504,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(-i\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{28665}(26059,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(-i\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{28665}(27319,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(i\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{28665}(28654,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(i\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)

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	28665.bjs
Modulus	$28665$
Conductor	$28665$
Order	$84$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(28665\)
Conductor:	\(28665\)	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)