LMFDB - Dirichlet character orbit 5408.ct

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5408, base_ring=CyclotomicField(52)) M = H._module chi = DirichletCharacter(H, M([0,39,28])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(105,5408)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$5408$
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.cd	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:	$\Q(\zeta_{52})$
Fixed field:	Number field defined by a degree 52 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{5408}(105,\cdot)$	$1$	$1$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{8}{13}\right)$	$i$	$e\left(\frac{7}{52}\right)$	$-1$
$\chi_{5408}(313,\cdot)$	$1$	$1$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{11}{13}\right)$	$-i$	$e\left(\frac{21}{52}\right)$	$-1$
$\chi_{5408}(521,\cdot)$	$1$	$1$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{1}{13}\right)$	$i$	$e\left(\frac{35}{52}\right)$	$-1$
$\chi_{5408}(729,\cdot)$	$1$	$1$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{4}{13}\right)$	$-i$	$e\left(\frac{49}{52}\right)$	$-1$
$\chi_{5408}(937,\cdot)$	$1$	$1$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{7}{13}\right)$	$i$	$e\left(\frac{11}{52}\right)$	$-1$
$\chi_{5408}(1145,\cdot)$	$1$	$1$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{10}{13}\right)$	$-i$	$e\left(\frac{25}{52}\right)$	$-1$
$\chi_{5408}(1561,\cdot)$	$1$	$1$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{3}{13}\right)$	$-i$	$e\left(\frac{1}{52}\right)$	$-1$
$\chi_{5408}(1769,\cdot)$	$1$	$1$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{6}{13}\right)$	$i$	$e\left(\frac{15}{52}\right)$	$-1$
$\chi_{5408}(1977,\cdot)$	$1$	$1$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{9}{13}\right)$	$-i$	$e\left(\frac{29}{52}\right)$	$-1$
$\chi_{5408}(2185,\cdot)$	$1$	$1$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{12}{13}\right)$	$i$	$e\left(\frac{43}{52}\right)$	$-1$
$\chi_{5408}(2393,\cdot)$	$1$	$1$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{2}{13}\right)$	$-i$	$e\left(\frac{5}{52}\right)$	$-1$
$\chi_{5408}(2601,\cdot)$	$1$	$1$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{5}{13}\right)$	$i$	$e\left(\frac{19}{52}\right)$	$-1$
$\chi_{5408}(2809,\cdot)$	$1$	$1$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{8}{13}\right)$	$-i$	$e\left(\frac{33}{52}\right)$	$-1$
$\chi_{5408}(3017,\cdot)$	$1$	$1$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{11}{13}\right)$	$i$	$e\left(\frac{47}{52}\right)$	$-1$
$\chi_{5408}(3225,\cdot)$	$1$	$1$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{1}{13}\right)$	$-i$	$e\left(\frac{9}{52}\right)$	$-1$
$\chi_{5408}(3433,\cdot)$	$1$	$1$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{4}{13}\right)$	$i$	$e\left(\frac{23}{52}\right)$	$-1$
$\chi_{5408}(3641,\cdot)$	$1$	$1$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{7}{13}\right)$	$-i$	$e\left(\frac{37}{52}\right)$	$-1$
$\chi_{5408}(3849,\cdot)$	$1$	$1$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{10}{13}\right)$	$i$	$e\left(\frac{51}{52}\right)$	$-1$
$\chi_{5408}(4265,\cdot)$	$1$	$1$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{3}{13}\right)$	$i$	$e\left(\frac{27}{52}\right)$	$-1$
$\chi_{5408}(4473,\cdot)$	$1$	$1$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{6}{13}\right)$	$-i$	$e\left(\frac{41}{52}\right)$	$-1$
$\chi_{5408}(4681,\cdot)$	$1$	$1$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{9}{13}\right)$	$i$	$e\left(\frac{3}{52}\right)$	$-1$
$\chi_{5408}(4889,\cdot)$	$1$	$1$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{12}{13}\right)$	$-i$	$e\left(\frac{17}{52}\right)$	$-1$
$\chi_{5408}(5097,\cdot)$	$1$	$1$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{2}{13}\right)$	$i$	$e\left(\frac{31}{52}\right)$	$-1$
$\chi_{5408}(5305,\cdot)$	$1$	$1$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{5}{13}\right)$	$-i$	$e\left(\frac{45}{52}\right)$	$-1$

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Character	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{5408}(105,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(i\)	\(e\left(\frac{7}{52}\right)\)	\(-1\)
\(\chi_{5408}(313,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(-i\)	\(e\left(\frac{21}{52}\right)\)	\(-1\)
\(\chi_{5408}(521,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(i\)	\(e\left(\frac{35}{52}\right)\)	\(-1\)
\(\chi_{5408}(729,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(-i\)	\(e\left(\frac{49}{52}\right)\)	\(-1\)
\(\chi_{5408}(937,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(i\)	\(e\left(\frac{11}{52}\right)\)	\(-1\)
\(\chi_{5408}(1145,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(-i\)	\(e\left(\frac{25}{52}\right)\)	\(-1\)
\(\chi_{5408}(1561,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(-i\)	\(e\left(\frac{1}{52}\right)\)	\(-1\)
\(\chi_{5408}(1769,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(i\)	\(e\left(\frac{15}{52}\right)\)	\(-1\)
\(\chi_{5408}(1977,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(-i\)	\(e\left(\frac{29}{52}\right)\)	\(-1\)
\(\chi_{5408}(2185,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(i\)	\(e\left(\frac{43}{52}\right)\)	\(-1\)
\(\chi_{5408}(2393,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(-i\)	\(e\left(\frac{5}{52}\right)\)	\(-1\)
\(\chi_{5408}(2601,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(i\)	\(e\left(\frac{19}{52}\right)\)	\(-1\)
\(\chi_{5408}(2809,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(-i\)	\(e\left(\frac{33}{52}\right)\)	\(-1\)
\(\chi_{5408}(3017,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(i\)	\(e\left(\frac{47}{52}\right)\)	\(-1\)
\(\chi_{5408}(3225,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(-i\)	\(e\left(\frac{9}{52}\right)\)	\(-1\)
\(\chi_{5408}(3433,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(i\)	\(e\left(\frac{23}{52}\right)\)	\(-1\)
\(\chi_{5408}(3641,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(-i\)	\(e\left(\frac{37}{52}\right)\)	\(-1\)
\(\chi_{5408}(3849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(i\)	\(e\left(\frac{51}{52}\right)\)	\(-1\)
\(\chi_{5408}(4265,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(i\)	\(e\left(\frac{27}{52}\right)\)	\(-1\)
\(\chi_{5408}(4473,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{33}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(-i\)	\(e\left(\frac{41}{52}\right)\)	\(-1\)
\(\chi_{5408}(4681,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(i\)	\(e\left(\frac{3}{52}\right)\)	\(-1\)
\(\chi_{5408}(4889,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(-i\)	\(e\left(\frac{17}{52}\right)\)	\(-1\)
\(\chi_{5408}(5097,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(i\)	\(e\left(\frac{31}{52}\right)\)	\(-1\)
\(\chi_{5408}(5305,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(-i\)	\(e\left(\frac{45}{52}\right)\)	\(-1\)

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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	5408.ct
Modulus	$5408$
Conductor	$2704$
Order	$52$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(5408\)
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.cd	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)