Properties

Label 405.p
Modulus $405$
Conductor $135$
Order $18$
Real no
Primitive no
Minimal no
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(405, base_ring=CyclotomicField(18))
 
M = H._module
 
chi = DirichletCharacter(H, M([16,9]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(19,405))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(405\)
Conductor: \(135\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(18\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 135.p
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: \(\Q(\zeta_{9})\)
Fixed field: 18.18.1923380668327365689220703125.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(13\) \(14\) \(16\) \(17\) \(19\)
\(\chi_{405}(19,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{405}(64,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{405}(154,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{405}(199,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{405}(289,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{405}(334,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)