Properties

Label 3024.167
Modulus $3024$
Conductor $1512$
Order $18$
Real no
Primitive no
Minimal no
Parity odd

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(3024, base_ring=CyclotomicField(18))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([9,9,5,9]))
 
pari: [g,chi] = znchar(Mod(167,3024))
 

Basic properties

Modulus: \(3024\)
Conductor: \(1512\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(18\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1512}(923,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3024.fm

\(\chi_{3024}(167,\cdot)\) \(\chi_{3024}(839,\cdot)\) \(\chi_{3024}(1175,\cdot)\) \(\chi_{3024}(1847,\cdot)\) \(\chi_{3024}(2183,\cdot)\) \(\chi_{3024}(2855,\cdot)\)

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

Values on generators

\((1135,757,785,2593)\) → \((-1,-1,e\left(\frac{5}{18}\right),-1)\)

Values

\(-1\)\(1\)\(5\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)
\(-1\)\(1\)\(e\left(\frac{7}{18}\right)\)\(e\left(\frac{11}{18}\right)\)\(e\left(\frac{2}{9}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{1}{6}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{9})\)
Fixed field: 18.0.16001058221486883031447445258662576128.1