Properties

Label 4256.gn
Modulus $4256$
Conductor $133$
Order $18$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4256, base_ring=CyclotomicField(18))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0,15,7]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(33,4256))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(4256\)
Conductor: \(133\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(18\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 133.bf
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: \(\Q(\zeta_{9})\)
Fixed field: 18.18.26018473705616588670034125883291477.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(9\) \(11\) \(13\) \(15\) \(17\) \(23\) \(25\) \(27\)
\(\chi_{4256}(33,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{4256}(129,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{4256}(705,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{4256}(1473,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{4256}(2369,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{4256}(3841,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{3}\right)\)