LMFDB - Dirichlet character orbit 8216.ip

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8216, base_ring=CyclotomicField(156)) M = H._module chi = DirichletCharacter(H, M([0,78,117,124])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(5,8216)) 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:	$156$	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:	$\Q(\zeta_{156})$
Fixed field:	Number field defined by a degree 156 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{8216}(5,\cdot)$	$-1$	$1$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(421,\cdot)$	$-1$	$1$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(437,\cdot)$	$-1$	$1$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{8216}(525,\cdot)$	$-1$	$1$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{8216}(629,\cdot)$	$-1$	$1$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{8216}(645,\cdot)$	$-1$	$1$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{8216}(941,\cdot)$	$-1$	$1$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(957,\cdot)$	$-1$	$1$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(1269,\cdot)$	$-1$	$1$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(1685,\cdot)$	$-1$	$1$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(1789,\cdot)$	$-1$	$1$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{8216}(1893,\cdot)$	$-1$	$1$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{8216}(2085,\cdot)$	$-1$	$1$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(2205,\cdot)$	$-1$	$1$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{77}{156}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(2293,\cdot)$	$-1$	$1$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{8216}(2917,\cdot)$	$-1$	$1$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(3021,\cdot)$	$-1$	$1$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(3125,\cdot)$	$-1$	$1$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{8216}(3349,\cdot)$	$-1$	$1$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(3437,\cdot)$	$-1$	$1$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(3557,\cdot)$	$-1$	$1$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{8216}(3645,\cdot)$	$-1$	$1$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(3749,\cdot)$	$-1$	$1$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{8216}(4061,\cdot)$	$-1$	$1$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(4181,\cdot)$	$-1$	$1$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(4285,\cdot)$	$-1$	$1$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{77}{156}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(4389,\cdot)$	$-1$	$1$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{8216}(4701,\cdot)$	$-1$	$1$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(4789,\cdot)$	$-1$	$1$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{8216}(4909,\cdot)$	$-1$	$1$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{8216}(4997,\cdot)$	$-1$	$1$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{5}{6}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{8216}(5,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(421,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(437,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{8216}(525,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{8216}(629,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{8216}(645,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{8216}(941,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(957,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(1269,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(1685,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(1789,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{8216}(1893,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{8216}(2085,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(2205,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{77}{156}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(2293,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{8216}(2917,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(3021,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(3125,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{8216}(3349,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(3437,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(3557,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{8216}(3645,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(3749,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{8216}(4061,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(4181,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(4285,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{77}{156}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(4389,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{8216}(4701,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(4789,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{8216}(4909,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{8216}(4997,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{5}{6}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 48 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	8216.ip
Modulus	$8216$
Conductor	$8216$
Order	$156$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(8216\)
Conductor:	\(8216\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(156\)	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)