Properties

Label 3024.2747
Modulus $3024$
Conductor $3024$
Order $36$
Real no
Primitive yes
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(36))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([18,9,14,6]))
 
pari: [g,chi] = znchar(Mod(2747,3024))
 

Basic properties

Modulus: \(3024\)
Conductor: \(3024\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(36\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3024.hg

\(\chi_{3024}(131,\cdot)\) \(\chi_{3024}(227,\cdot)\) \(\chi_{3024}(635,\cdot)\) \(\chi_{3024}(731,\cdot)\) \(\chi_{3024}(1139,\cdot)\) \(\chi_{3024}(1235,\cdot)\) \(\chi_{3024}(1643,\cdot)\) \(\chi_{3024}(1739,\cdot)\) \(\chi_{3024}(2147,\cdot)\) \(\chi_{3024}(2243,\cdot)\) \(\chi_{3024}(2651,\cdot)\) \(\chi_{3024}(2747,\cdot)\)

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

Related number fields

Field of values: \(\Q(\zeta_{36})\)
Fixed field: 36.0.124687723528889177570420723064261381086672513377851660184757530334936556972919209118584893066969088.2

Values on generators

\((1135,757,785,2593)\) → \((-1,i,e\left(\frac{7}{18}\right),e\left(\frac{1}{6}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)
\(-1\)\(1\)\(e\left(\frac{1}{36}\right)\)\(e\left(\frac{17}{36}\right)\)\(e\left(\frac{13}{36}\right)\)\(1\)\(-i\)\(e\left(\frac{11}{18}\right)\)\(e\left(\frac{1}{18}\right)\)\(e\left(\frac{5}{36}\right)\)\(e\left(\frac{4}{9}\right)\)\(e\left(\frac{11}{12}\right)\)
value at e.g. 2