LMFDB - Dirichlet character orbit 8112.fs

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8112, base_ring=CyclotomicField(156)) M = H._module chi = DirichletCharacter(H, M([0,0,78,149])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(305,8112)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8112$
Conductor:	$507$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$156$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 507.x	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	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	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{8112}(305,\cdot)$	$1$	$1$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{23}{78}\right)$
$\chi_{8112}(353,\cdot)$	$1$	$1$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{31}{78}\right)$
$\chi_{8112}(401,\cdot)$	$1$	$1$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{77}{156}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{37}{78}\right)$
$\chi_{8112}(449,\cdot)$	$1$	$1$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{77}{78}\right)$
$\chi_{8112}(929,\cdot)$	$1$	$1$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{127}{156}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{59}{78}\right)$
$\chi_{8112}(977,\cdot)$	$1$	$1$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{11}{156}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{61}{78}\right)$
$\chi_{8112}(1025,\cdot)$	$1$	$1$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{7}{78}\right)$
$\chi_{8112}(1073,\cdot)$	$1$	$1$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{41}{78}\right)$
$\chi_{8112}(1553,\cdot)$	$1$	$1$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{17}{78}\right)$
$\chi_{8112}(1649,\cdot)$	$1$	$1$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{55}{78}\right)$
$\chi_{8112}(1697,\cdot)$	$1$	$1$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{5}{78}\right)$
$\chi_{8112}(2177,\cdot)$	$1$	$1$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{53}{78}\right)$
$\chi_{8112}(2225,\cdot)$	$1$	$1$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{43}{78}\right)$
$\chi_{8112}(2273,\cdot)$	$1$	$1$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{25}{78}\right)$
$\chi_{8112}(2321,\cdot)$	$1$	$1$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{107}{156}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{47}{78}\right)$
$\chi_{8112}(2801,\cdot)$	$1$	$1$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{11}{78}\right)$
$\chi_{8112}(2849,\cdot)$	$1$	$1$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{73}{78}\right)$
$\chi_{8112}(2897,\cdot)$	$1$	$1$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{73}{78}\right)$
$\chi_{8112}(2945,\cdot)$	$1$	$1$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{11}{78}\right)$
$\chi_{8112}(3425,\cdot)$	$1$	$1$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{47}{78}\right)$
$\chi_{8112}(3473,\cdot)$	$1$	$1$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{25}{78}\right)$
$\chi_{8112}(3521,\cdot)$	$1$	$1$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{43}{78}\right)$
$\chi_{8112}(3569,\cdot)$	$1$	$1$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{85}{156}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{53}{78}\right)$
$\chi_{8112}(4049,\cdot)$	$1$	$1$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{5}{78}\right)$
$\chi_{8112}(4097,\cdot)$	$1$	$1$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{55}{78}\right)$
$\chi_{8112}(4193,\cdot)$	$1$	$1$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{17}{78}\right)$
$\chi_{8112}(4673,\cdot)$	$1$	$1$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{41}{78}\right)$
$\chi_{8112}(4721,\cdot)$	$1$	$1$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{7}{78}\right)$
$\chi_{8112}(4769,\cdot)$	$1$	$1$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{61}{78}\right)$
$\chi_{8112}(4817,\cdot)$	$1$	$1$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{59}{78}\right)$
$\chi_{8112}(5297,\cdot)$	$1$	$1$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{19}{156}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{77}{78}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{8112}(305,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{23}{78}\right)\)
\(\chi_{8112}(353,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{31}{78}\right)\)
\(\chi_{8112}(401,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{77}{156}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{37}{78}\right)\)
\(\chi_{8112}(449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{77}{78}\right)\)
\(\chi_{8112}(929,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{59}{78}\right)\)
\(\chi_{8112}(977,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{11}{156}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{61}{78}\right)\)
\(\chi_{8112}(1025,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{7}{78}\right)\)
\(\chi_{8112}(1073,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{41}{78}\right)\)
\(\chi_{8112}(1553,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{17}{78}\right)\)
\(\chi_{8112}(1649,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{55}{78}\right)\)
\(\chi_{8112}(1697,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{5}{78}\right)\)
\(\chi_{8112}(2177,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{53}{78}\right)\)
\(\chi_{8112}(2225,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{43}{78}\right)\)
\(\chi_{8112}(2273,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{25}{78}\right)\)
\(\chi_{8112}(2321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{107}{156}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{47}{78}\right)\)
\(\chi_{8112}(2801,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{11}{78}\right)\)
\(\chi_{8112}(2849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{73}{78}\right)\)
\(\chi_{8112}(2897,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{73}{78}\right)\)
\(\chi_{8112}(2945,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{11}{78}\right)\)
\(\chi_{8112}(3425,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{47}{78}\right)\)
\(\chi_{8112}(3473,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{25}{78}\right)\)
\(\chi_{8112}(3521,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{43}{78}\right)\)
\(\chi_{8112}(3569,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{85}{156}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{53}{78}\right)\)
\(\chi_{8112}(4049,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{5}{78}\right)\)
\(\chi_{8112}(4097,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{55}{78}\right)\)
\(\chi_{8112}(4193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{17}{78}\right)\)
\(\chi_{8112}(4673,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{41}{78}\right)\)
\(\chi_{8112}(4721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{7}{78}\right)\)
\(\chi_{8112}(4769,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{61}{78}\right)\)
\(\chi_{8112}(4817,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{59}{78}\right)\)
\(\chi_{8112}(5297,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{19}{156}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{77}{78}\right)\)

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	8112.fs
Modulus	$8112$
Conductor	$507$
Order	$156$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(8112\)
Conductor:	\(507\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(156\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 507.x	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)