Properties

Label 3024.53
Modulus $3024$
Conductor $336$
Order $12$
Real no
Primitive no
Minimal yes
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(12))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,3,6,8]))
 
pari: [g,chi] = znchar(Mod(53,3024))
 

Basic properties

Modulus: \(3024\)
Conductor: \(336\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(12\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{336}(53,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3024.eg

\(\chi_{3024}(53,\cdot)\) \(\chi_{3024}(485,\cdot)\) \(\chi_{3024}(1565,\cdot)\) \(\chi_{3024}(1997,\cdot)\)

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

\((1135,757,785,2593)\) → \((1,i,-1,e\left(\frac{2}{3}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)
\(-1\)\(1\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{5}{12}\right)\)\(-i\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{1}{6}\right)\)\(i\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{7}{12}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{12})\)
Fixed field: 12.0.36099543110378323968.1