LMFDB - Dirichlet character orbit 4056.cr

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from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4056, base_ring=CyclotomicField(52))

M = H._module

chi = DirichletCharacter(H, M([0,0,0,17]))

chi.galois_orbit()

[g,chi] = znchar(Mod(73,4056))

order = charorder(g,chi)

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

Basic properties

Modulus:	$4056$
Conductor:	$169$	sage: chi.conductor() pari: znconreyconductor(g,chi)
Order:	$52$	sage: chi.multiplicative_order() pari: charorder(g,chi)
Real:	no
Primitive:	no, induced from 169.j	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:	$\Q(\zeta_{52})$
Fixed field:	Number field defined by a degree 52 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{4056}(73,\cdot)$	$-1$	$1$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{19}{26}\right)$	$i$	$-1$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{4056}(265,\cdot)$	$-1$	$1$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{19}{26}\right)$	$-i$	$-1$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{4056}(385,\cdot)$	$-1$	$1$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{25}{26}\right)$	$i$	$-1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{4056}(697,\cdot)$	$-1$	$1$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{5}{26}\right)$	$i$	$-1$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{4056}(889,\cdot)$	$-1$	$1$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{7}{26}\right)$	$-i$	$-1$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{4056}(1009,\cdot)$	$-1$	$1$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{11}{26}\right)$	$i$	$-1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{4056}(1201,\cdot)$	$-1$	$1$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{1}{26}\right)$	$-i$	$-1$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{4056}(1321,\cdot)$	$-1$	$1$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{17}{26}\right)$	$i$	$-1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{4056}(1513,\cdot)$	$-1$	$1$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{21}{26}\right)$	$-i$	$-1$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{4056}(1633,\cdot)$	$-1$	$1$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{23}{26}\right)$	$i$	$-1$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{4056}(1825,\cdot)$	$-1$	$1$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{15}{26}\right)$	$-i$	$-1$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{4056}(1945,\cdot)$	$-1$	$1$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{3}{26}\right)$	$i$	$-1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{4056}(2137,\cdot)$	$-1$	$1$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{9}{26}\right)$	$-i$	$-1$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{4056}(2257,\cdot)$	$-1$	$1$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{9}{26}\right)$	$i$	$-1$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{4056}(2449,\cdot)$	$-1$	$1$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{3}{26}\right)$	$-i$	$-1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{4056}(2569,\cdot)$	$-1$	$1$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{15}{26}\right)$	$i$	$-1$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{4056}(2761,\cdot)$	$-1$	$1$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{23}{26}\right)$	$-i$	$-1$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{4056}(2881,\cdot)$	$-1$	$1$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{21}{26}\right)$	$i$	$-1$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{4056}(3073,\cdot)$	$-1$	$1$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{17}{26}\right)$	$-i$	$-1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{8}{13}\right)$
$\chi_{4056}(3193,\cdot)$	$-1$	$1$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{1}{26}\right)$	$i$	$-1$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{4056}(3385,\cdot)$	$-1$	$1$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{11}{26}\right)$	$-i$	$-1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{4056}(3505,\cdot)$	$-1$	$1$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{7}{26}\right)$	$i$	$-1$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{4056}(3697,\cdot)$	$-1$	$1$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{5}{26}\right)$	$-i$	$-1$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{4056}(4009,\cdot)$	$-1$	$1$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{25}{26}\right)$	$-i$	$-1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{11}{13}\right)$

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Classical	Maass
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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Character	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{4056}(73,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{4056}(265,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{4056}(385,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{4056}(697,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{4056}(889,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{4056}(1009,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{4056}(1201,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{4056}(1321,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{4056}(1513,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{4056}(1633,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{4056}(1825,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{4056}(1945,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{4056}(2137,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{4056}(2257,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{4056}(2449,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{4056}(2569,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{4056}(2761,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{4056}(2881,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{4056}(3073,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)
\(\chi_{4056}(3193,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{4056}(3385,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{4056}(3505,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{4056}(3697,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{4056}(4009,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)

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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	4056.cr
Modulus	$4056$
Conductor	$169$
Order	$52$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(4056\)
Conductor:	\(169\)	sage: chi.conductor() pari: znconreyconductor(g,chi)
Order:	\(52\)	sage: chi.multiplicative_order() pari: charorder(g,chi)
Real:	no
Primitive:	no, induced from 169.j	sage: chi.is_primitive() pari: #znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage: chi.is_odd() pari: zncharisodd(g,chi)