LMFDB - Dirichlet character orbit 8216.hg

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8216, base_ring=CyclotomicField(78)) M = H._module chi = DirichletCharacter(H, M([0,39,26,11])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(29,8216)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8216$
Conductor:	$8216$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$78$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{39})$
Fixed field:	Number field defined by a degree 78 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{8216}(29,\cdot)$	$-1$	$1$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{3}{26}\right)$	$1$
$\chi_{8216}(477,\cdot)$	$-1$	$1$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{5}{26}\right)$	$1$
$\chi_{8216}(549,\cdot)$	$-1$	$1$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{1}{26}\right)$	$1$
$\chi_{8216}(581,\cdot)$	$-1$	$1$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{19}{26}\right)$	$1$
$\chi_{8216}(1725,\cdot)$	$-1$	$1$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{1}{26}\right)$	$1$
$\chi_{8216}(1933,\cdot)$	$-1$	$1$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{17}{26}\right)$	$1$
$\chi_{8216}(2661,\cdot)$	$-1$	$1$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{9}{26}\right)$	$1$
$\chi_{8216}(2733,\cdot)$	$-1$	$1$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{9}{26}\right)$	$1$
$\chi_{8216}(3149,\cdot)$	$-1$	$1$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{15}{26}\right)$	$1$
$\chi_{8216}(3357,\cdot)$	$-1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{19}{26}\right)$	$1$
$\chi_{8216}(3773,\cdot)$	$-1$	$1$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{17}{26}\right)$	$1$
$\chi_{8216}(3877,\cdot)$	$-1$	$1$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{25}{26}\right)$	$1$
$\chi_{8216}(4013,\cdot)$	$-1$	$1$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{15}{26}\right)$	$1$
$\chi_{8216}(4221,\cdot)$	$-1$	$1$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{21}{26}\right)$	$1$
$\chi_{8216}(4325,\cdot)$	$-1$	$1$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{25}{26}\right)$	$1$
$\chi_{8216}(4533,\cdot)$	$-1$	$1$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{23}{26}\right)$	$1$
$\chi_{8216}(4709,\cdot)$	$-1$	$1$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{7}{26}\right)$	$1$
$\chi_{8216}(5573,\cdot)$	$-1$	$1$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{11}{26}\right)$	$1$
$\chi_{8216}(5853,\cdot)$	$-1$	$1$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{5}{26}\right)$	$1$
$\chi_{8216}(6197,\cdot)$	$-1$	$1$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{3}{26}\right)$	$1$
$\chi_{8216}(6373,\cdot)$	$-1$	$1$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{21}{26}\right)$	$1$
$\chi_{8216}(6789,\cdot)$	$-1$	$1$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{11}{26}\right)$	$1$
$\chi_{8216}(7029,\cdot)$	$-1$	$1$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{7}{26}\right)$	$1$
$\chi_{8216}(7101,\cdot)$	$-1$	$1$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{23}{26}\right)$	$1$

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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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{8216}(29,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(1\)
\(\chi_{8216}(477,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(1\)
\(\chi_{8216}(549,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(1\)
\(\chi_{8216}(581,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(1\)
\(\chi_{8216}(1725,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(1\)
\(\chi_{8216}(1933,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(1\)
\(\chi_{8216}(2661,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(1\)
\(\chi_{8216}(2733,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(1\)
\(\chi_{8216}(3149,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(1\)
\(\chi_{8216}(3357,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(1\)
\(\chi_{8216}(3773,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(1\)
\(\chi_{8216}(3877,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(1\)
\(\chi_{8216}(4013,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(1\)
\(\chi_{8216}(4221,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(1\)
\(\chi_{8216}(4325,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(1\)
\(\chi_{8216}(4533,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(1\)
\(\chi_{8216}(4709,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(1\)
\(\chi_{8216}(5573,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(1\)
\(\chi_{8216}(5853,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(1\)
\(\chi_{8216}(6197,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(1\)
\(\chi_{8216}(6373,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(1\)
\(\chi_{8216}(6789,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(1\)
\(\chi_{8216}(7029,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(1\)
\(\chi_{8216}(7101,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(1\)

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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	8216.hg
Modulus	$8216$
Conductor	$8216$
Order	$78$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(8216\)
Conductor:	\(8216\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(78\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)