LMFDB - Dirichlet character orbit 8112.dv

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from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8112, base_ring=CyclotomicField(52))

M = H._module

chi = DirichletCharacter(H, M([0,39,26,51]))

chi.galois_orbit()

[g,chi] = znchar(Mod(317,8112))

order = charorder(g,chi)

[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8112$
Conductor:	$8112$	sage: chi.conductor() pari: znconreyconductor(g,chi)
Order:	$52$	sage: chi.multiplicative_order() pari: charorder(g,chi)
Real:	no
Primitive:	yes	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	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{8112}(317,\cdot)$	$1$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{9}{13}\right)$	$1$	$-1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{27}{52}\right)$
$\chi_{8112}(941,\cdot)$	$1$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{3}{13}\right)$	$1$	$-1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{35}{52}\right)$
$\chi_{8112}(1061,\cdot)$	$1$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{6}{13}\right)$	$1$	$-1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{5}{52}\right)$
$\chi_{8112}(1565,\cdot)$	$1$	$1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{10}{13}\right)$	$1$	$-1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{43}{52}\right)$
$\chi_{8112}(1685,\cdot)$	$1$	$1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{12}{13}\right)$	$1$	$-1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{49}{52}\right)$
$\chi_{8112}(2189,\cdot)$	$1$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{4}{13}\right)$	$1$	$-1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{51}{52}\right)$
$\chi_{8112}(2309,\cdot)$	$1$	$1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{5}{13}\right)$	$1$	$-1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{41}{52}\right)$
$\chi_{8112}(2813,\cdot)$	$1$	$1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{11}{13}\right)$	$1$	$-1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{7}{52}\right)$
$\chi_{8112}(2933,\cdot)$	$1$	$1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{11}{13}\right)$	$1$	$-1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{33}{52}\right)$
$\chi_{8112}(3437,\cdot)$	$1$	$1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{5}{13}\right)$	$1$	$-1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{15}{52}\right)$
$\chi_{8112}(3557,\cdot)$	$1$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{4}{13}\right)$	$1$	$-1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{25}{52}\right)$
$\chi_{8112}(4061,\cdot)$	$1$	$1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{12}{13}\right)$	$1$	$-1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{23}{52}\right)$
$\chi_{8112}(4181,\cdot)$	$1$	$1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{10}{13}\right)$	$1$	$-1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{17}{52}\right)$
$\chi_{8112}(4685,\cdot)$	$1$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{6}{13}\right)$	$1$	$-1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{31}{52}\right)$
$\chi_{8112}(4805,\cdot)$	$1$	$1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{3}{13}\right)$	$1$	$-1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{9}{52}\right)$
$\chi_{8112}(5429,\cdot)$	$1$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{9}{13}\right)$	$1$	$-1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{1}{52}\right)$
$\chi_{8112}(5933,\cdot)$	$1$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{7}{13}\right)$	$1$	$-1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{47}{52}\right)$
$\chi_{8112}(6053,\cdot)$	$1$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{2}{13}\right)$	$1$	$-1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{45}{52}\right)$
$\chi_{8112}(6557,\cdot)$	$1$	$1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{1}{13}\right)$	$1$	$-1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{3}{52}\right)$
$\chi_{8112}(6677,\cdot)$	$1$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{8}{13}\right)$	$1$	$-1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{37}{52}\right)$
$\chi_{8112}(7181,\cdot)$	$1$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{8}{13}\right)$	$1$	$-1$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{11}{52}\right)$
$\chi_{8112}(7301,\cdot)$	$1$	$1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{1}{13}\right)$	$1$	$-1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{29}{52}\right)$
$\chi_{8112}(7805,\cdot)$	$1$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{2}{13}\right)$	$1$	$-1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{19}{52}\right)$
$\chi_{8112}(7925,\cdot)$	$1$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{7}{13}\right)$	$1$	$-1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{21}{52}\right)$

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 $\F_{q}$

Character	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{8112}(317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)
\(\chi_{8112}(941,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)
\(\chi_{8112}(1061,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)
\(\chi_{8112}(1565,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)
\(\chi_{8112}(1685,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)
\(\chi_{8112}(2189,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)
\(\chi_{8112}(2309,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)
\(\chi_{8112}(2813,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)
\(\chi_{8112}(2933,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)
\(\chi_{8112}(3437,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)
\(\chi_{8112}(3557,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)
\(\chi_{8112}(4061,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)
\(\chi_{8112}(4181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)
\(\chi_{8112}(4685,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)
\(\chi_{8112}(4805,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)
\(\chi_{8112}(5429,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)
\(\chi_{8112}(5933,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)
\(\chi_{8112}(6053,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)
\(\chi_{8112}(6557,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)
\(\chi_{8112}(6677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)
\(\chi_{8112}(7181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)
\(\chi_{8112}(7301,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)
\(\chi_{8112}(7805,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)
\(\chi_{8112}(7925,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)

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

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