Properties

Label 3549.ck
Modulus $3549$
Conductor $3549$
Order $26$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3549, base_ring=CyclotomicField(26))
 
M = H._module
 
chi = DirichletCharacter(H, M([13,13,25]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(272,3549))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(3549\)
Conductor: \(3549\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(26\)
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: \(\Q(\zeta_{13})\)
Fixed field: Number field defined by a degree 26 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(5\) \(8\) \(10\) \(11\) \(16\) \(17\) \(19\) \(20\)
\(\chi_{3549}(272,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(1\) \(e\left(\frac{15}{26}\right)\)
\(\chi_{3549}(545,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(1\) \(e\left(\frac{17}{26}\right)\)
\(\chi_{3549}(818,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(1\) \(e\left(\frac{19}{26}\right)\)
\(\chi_{3549}(1091,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(1\) \(e\left(\frac{21}{26}\right)\)
\(\chi_{3549}(1364,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(1\) \(e\left(\frac{23}{26}\right)\)
\(\chi_{3549}(1637,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(1\) \(e\left(\frac{25}{26}\right)\)
\(\chi_{3549}(1910,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(1\) \(e\left(\frac{1}{26}\right)\)
\(\chi_{3549}(2183,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(1\) \(e\left(\frac{3}{26}\right)\)
\(\chi_{3549}(2456,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(1\) \(e\left(\frac{5}{26}\right)\)
\(\chi_{3549}(2729,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(1\) \(e\left(\frac{7}{26}\right)\)
\(\chi_{3549}(3002,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(1\) \(e\left(\frac{9}{26}\right)\)
\(\chi_{3549}(3275,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(1\) \(e\left(\frac{11}{26}\right)\)