LMFDB - Dirichlet character orbit 8112.ev

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8112, base_ring=CyclotomicField(78)) M = H._module chi = DirichletCharacter(H, M([39,0,39,37])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(95,8112)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8112$
Conductor:	$2028$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$78$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2028.bn	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:	$\Q(\zeta_{39})$
Fixed field:	Number field defined by a degree 78 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{8112}(95,\cdot)$	$1$	$1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{1}{39}\right)$
$\chi_{8112}(335,\cdot)$	$1$	$1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{8}{39}\right)$
$\chi_{8112}(719,\cdot)$	$1$	$1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{28}{39}\right)$
$\chi_{8112}(959,\cdot)$	$1$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{11}{39}\right)$
$\chi_{8112}(1343,\cdot)$	$1$	$1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{16}{39}\right)$
$\chi_{8112}(1583,\cdot)$	$1$	$1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{14}{39}\right)$
$\chi_{8112}(1967,\cdot)$	$1$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{4}{39}\right)$
$\chi_{8112}(2207,\cdot)$	$1$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{17}{39}\right)$
$\chi_{8112}(2591,\cdot)$	$1$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{31}{39}\right)$
$\chi_{8112}(2831,\cdot)$	$1$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{20}{39}\right)$
$\chi_{8112}(3215,\cdot)$	$1$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{19}{39}\right)$
$\chi_{8112}(3455,\cdot)$	$1$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{23}{39}\right)$
$\chi_{8112}(3839,\cdot)$	$1$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{7}{39}\right)$
$\chi_{8112}(4463,\cdot)$	$1$	$1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{34}{39}\right)$
$\chi_{8112}(4703,\cdot)$	$1$	$1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{29}{39}\right)$
$\chi_{8112}(5087,\cdot)$	$1$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{22}{39}\right)$
$\chi_{8112}(5327,\cdot)$	$1$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{32}{39}\right)$
$\chi_{8112}(5711,\cdot)$	$1$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{10}{39}\right)$
$\chi_{8112}(5951,\cdot)$	$1$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{35}{39}\right)$
$\chi_{8112}(6335,\cdot)$	$1$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{37}{39}\right)$
$\chi_{8112}(6575,\cdot)$	$1$	$1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{38}{39}\right)$
$\chi_{8112}(6959,\cdot)$	$1$	$1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{25}{39}\right)$
$\chi_{8112}(7199,\cdot)$	$1$	$1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{2}{39}\right)$
$\chi_{8112}(7823,\cdot)$	$1$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{5}{39}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{8112}(95,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)
\(\chi_{8112}(335,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)
\(\chi_{8112}(719,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)
\(\chi_{8112}(959,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)
\(\chi_{8112}(1343,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)
\(\chi_{8112}(1583,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)
\(\chi_{8112}(1967,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)
\(\chi_{8112}(2207,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)
\(\chi_{8112}(2591,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)
\(\chi_{8112}(2831,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)
\(\chi_{8112}(3215,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)
\(\chi_{8112}(3455,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)
\(\chi_{8112}(3839,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{7}{39}\right)\)
\(\chi_{8112}(4463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)
\(\chi_{8112}(4703,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{29}{39}\right)\)
\(\chi_{8112}(5087,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)
\(\chi_{8112}(5327,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)
\(\chi_{8112}(5711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)
\(\chi_{8112}(5951,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)
\(\chi_{8112}(6335,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{37}{39}\right)\)
\(\chi_{8112}(6575,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{38}{39}\right)\)
\(\chi_{8112}(6959,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{25}{39}\right)\)
\(\chi_{8112}(7199,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{2}{39}\right)\)
\(\chi_{8112}(7823,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{5}{39}\right)\)

Introduction

L-functions

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Varieties

Fields

Representations

Groups

Database

Properties

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Basic properties

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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.ev
Modulus	$8112$
Conductor	$2028$
Order	$78$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8112\)
Conductor:	\(2028\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(78\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2028.bn	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)