Properties

Label 3024.61
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([0,27,32,30]))
 
pari: [g,chi] = znchar(Mod(61,3024))
 

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.hf

\(\chi_{3024}(61,\cdot)\) \(\chi_{3024}(157,\cdot)\) \(\chi_{3024}(565,\cdot)\) \(\chi_{3024}(661,\cdot)\) \(\chi_{3024}(1069,\cdot)\) \(\chi_{3024}(1165,\cdot)\) \(\chi_{3024}(1573,\cdot)\) \(\chi_{3024}(1669,\cdot)\) \(\chi_{3024}(2077,\cdot)\) \(\chi_{3024}(2173,\cdot)\) \(\chi_{3024}(2581,\cdot)\) \(\chi_{3024}(2677,\cdot)\)

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

\((1135,757,785,2593)\) → \((1,-i,e\left(\frac{8}{9}\right),e\left(\frac{5}{6}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)
\(-1\)\(1\)\(e\left(\frac{13}{36}\right)\)\(e\left(\frac{23}{36}\right)\)\(e\left(\frac{31}{36}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{17}{18}\right)\)\(e\left(\frac{13}{18}\right)\)\(e\left(\frac{5}{36}\right)\)\(e\left(\frac{11}{18}\right)\)\(-i\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{36})\)
Fixed field: 36.0.13854191503209908618935635896029042342963612597539073353861947814992950774768801013176099229663232.2