Properties

Label 3024.655
Modulus $3024$
Conductor $756$
Order $18$
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(18))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([9,0,16,12]))
 
pari: [g,chi] = znchar(Mod(655,3024))
 

Basic properties

Modulus: \(3024\)
Conductor: \(756\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(18\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{756}(655,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3024.gf

\(\chi_{3024}(655,\cdot)\) \(\chi_{3024}(751,\cdot)\) \(\chi_{3024}(1663,\cdot)\) \(\chi_{3024}(1759,\cdot)\) \(\chi_{3024}(2671,\cdot)\) \(\chi_{3024}(2767,\cdot)\)

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

\((1135,757,785,2593)\) → \((-1,1,e\left(\frac{8}{9}\right),e\left(\frac{2}{3}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)
\(-1\)\(1\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{13}{18}\right)\)\(e\left(\frac{1}{9}\right)\)\(1\)\(-1\)\(e\left(\frac{11}{18}\right)\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{8}{9}\right)\)\(e\left(\frac{17}{18}\right)\)\(e\left(\frac{2}{3}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{9})\)
Fixed field: 18.0.3573152975240885989444318830547697664.1