LMFDB - Dirichlet character orbit 8112.dx

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8112, base_ring=CyclotomicField(52)) M = H._module chi = DirichletCharacter(H, M([0,13,0,42])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(181,8112)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8112$
Conductor:	$2704$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$52$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2704.cb	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:	$\Q(\zeta_{52})$
Fixed field:	Number field defined by a degree 52 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{8112}(181,\cdot)$	$1$	$1$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{12}{13}\right)$	$i$	$-1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{23}{52}\right)$
$\chi_{8112}(493,\cdot)$	$1$	$1$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{1}{13}\right)$	$-i$	$-1$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{29}{52}\right)$
$\chi_{8112}(805,\cdot)$	$1$	$1$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{3}{13}\right)$	$i$	$-1$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{35}{52}\right)$
$\chi_{8112}(1117,\cdot)$	$1$	$1$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{5}{13}\right)$	$-i$	$-1$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{41}{52}\right)$
$\chi_{8112}(1429,\cdot)$	$1$	$1$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{7}{13}\right)$	$i$	$-1$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{47}{52}\right)$
$\chi_{8112}(1741,\cdot)$	$1$	$1$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{9}{13}\right)$	$-i$	$-1$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{1}{52}\right)$
$\chi_{8112}(2053,\cdot)$	$1$	$1$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{11}{13}\right)$	$i$	$-1$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{7}{52}\right)$
$\chi_{8112}(2677,\cdot)$	$1$	$1$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{2}{13}\right)$	$i$	$-1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{19}{52}\right)$
$\chi_{8112}(2989,\cdot)$	$1$	$1$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{4}{13}\right)$	$-i$	$-1$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{25}{52}\right)$
$\chi_{8112}(3301,\cdot)$	$1$	$1$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{6}{13}\right)$	$i$	$-1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{31}{52}\right)$
$\chi_{8112}(3613,\cdot)$	$1$	$1$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{8}{13}\right)$	$-i$	$-1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{37}{52}\right)$
$\chi_{8112}(3925,\cdot)$	$1$	$1$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{10}{13}\right)$	$i$	$-1$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{43}{52}\right)$
$\chi_{8112}(4237,\cdot)$	$1$	$1$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{12}{13}\right)$	$-i$	$-1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{49}{52}\right)$
$\chi_{8112}(4549,\cdot)$	$1$	$1$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{1}{13}\right)$	$i$	$-1$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{3}{52}\right)$
$\chi_{8112}(4861,\cdot)$	$1$	$1$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{3}{13}\right)$	$-i$	$-1$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{9}{52}\right)$
$\chi_{8112}(5173,\cdot)$	$1$	$1$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{5}{13}\right)$	$i$	$-1$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{15}{52}\right)$
$\chi_{8112}(5485,\cdot)$	$1$	$1$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{7}{13}\right)$	$-i$	$-1$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{21}{52}\right)$
$\chi_{8112}(5797,\cdot)$	$1$	$1$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{9}{13}\right)$	$i$	$-1$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{27}{52}\right)$
$\chi_{8112}(6109,\cdot)$	$1$	$1$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{11}{13}\right)$	$-i$	$-1$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{33}{52}\right)$
$\chi_{8112}(6733,\cdot)$	$1$	$1$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{2}{13}\right)$	$-i$	$-1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{45}{52}\right)$
$\chi_{8112}(7045,\cdot)$	$1$	$1$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{4}{13}\right)$	$i$	$-1$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{51}{52}\right)$
$\chi_{8112}(7357,\cdot)$	$1$	$1$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{6}{13}\right)$	$-i$	$-1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{5}{52}\right)$
$\chi_{8112}(7669,\cdot)$	$1$	$1$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{8}{13}\right)$	$i$	$-1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{11}{52}\right)$
$\chi_{8112}(7981,\cdot)$	$1$	$1$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{10}{13}\right)$	$-i$	$-1$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{17}{52}\right)$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{8112}(181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{23}{52}\right)\)
\(\chi_{8112}(493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{29}{52}\right)\)
\(\chi_{8112}(805,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{35}{52}\right)\)
\(\chi_{8112}(1117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{41}{52}\right)\)
\(\chi_{8112}(1429,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{47}{52}\right)\)
\(\chi_{8112}(1741,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{1}{52}\right)\)
\(\chi_{8112}(2053,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{7}{52}\right)\)
\(\chi_{8112}(2677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{19}{52}\right)\)
\(\chi_{8112}(2989,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{25}{52}\right)\)
\(\chi_{8112}(3301,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{31}{52}\right)\)
\(\chi_{8112}(3613,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{37}{52}\right)\)
\(\chi_{8112}(3925,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{43}{52}\right)\)
\(\chi_{8112}(4237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{49}{52}\right)\)
\(\chi_{8112}(4549,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{3}{52}\right)\)
\(\chi_{8112}(4861,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{9}{52}\right)\)
\(\chi_{8112}(5173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{15}{52}\right)\)
\(\chi_{8112}(5485,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{21}{52}\right)\)
\(\chi_{8112}(5797,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{27}{52}\right)\)
\(\chi_{8112}(6109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{33}{52}\right)\)
\(\chi_{8112}(6733,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{45}{52}\right)\)
\(\chi_{8112}(7045,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{51}{52}\right)\)
\(\chi_{8112}(7357,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{5}{52}\right)\)
\(\chi_{8112}(7669,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{11}{52}\right)\)
\(\chi_{8112}(7981,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{17}{52}\right)\)

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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	8112.dx
Modulus	$8112$
Conductor	$2704$
Order	$52$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8112\)
Conductor:	\(2704\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(52\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2704.cb	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)