Properties

Label 6384.295
Modulus $6384$
Conductor $152$
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(6384, base_ring=CyclotomicField(18))
 
M = H._module
 
chi = DirichletCharacter(H, M([9,9,0,0,17]))
 
pari: [g,chi] = znchar(Mod(295,6384))
 

Basic properties

Modulus: \(6384\)
Conductor: \(152\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(18\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{152}(67,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6384.km

\(\chi_{6384}(295,\cdot)\) \(\chi_{6384}(3319,\cdot)\) \(\chi_{6384}(4327,\cdot)\) \(\chi_{6384}(4999,\cdot)\) \(\chi_{6384}(5335,\cdot)\) \(\chi_{6384}(6007,\cdot)\)

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

Related number fields

Field of values: \(\Q(\zeta_{9})\)
Fixed field: 18.18.735565072612935262326166126592.1

Values on generators

\((799,4789,2129,913,1009)\) → \((-1,-1,1,1,e\left(\frac{17}{18}\right))\)

First values

\(a\) \(-1\)\(1\)\(5\)\(11\)\(13\)\(17\)\(23\)\(25\)\(29\)\(31\)\(37\)\(41\)
\( \chi_{ 6384 }(295, a) \) \(1\)\(1\)\(e\left(\frac{11}{18}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{2}{9}\right)\)\(e\left(\frac{4}{9}\right)\)\(e\left(\frac{7}{18}\right)\)\(e\left(\frac{2}{9}\right)\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{2}{3}\right)\)\(1\)\(e\left(\frac{5}{18}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6384 }(295,a) \;\) at \(\;a = \) e.g. 2