Properties

Label 3724.979
Modulus $3724$
Conductor $532$
Order $18$
Real no
Primitive no
Minimal yes
Parity odd

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(3724, base_ring=CyclotomicField(18))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([9,9,17]))
 
pari: [g,chi] = znchar(Mod(979,3724))
 

Basic properties

Modulus: \(3724\)
Conductor: \(532\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(18\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{532}(447,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3724.cp

\(\chi_{3724}(979,\cdot)\) \(\chi_{3724}(1371,\cdot)\) \(\chi_{3724}(1763,\cdot)\) \(\chi_{3724}(1959,\cdot)\) \(\chi_{3724}(2351,\cdot)\) \(\chi_{3724}(2939,\cdot)\)

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: \(\Q(\zeta_{9})\)
Fixed field: 18.0.57974030982712602914750026736730112.1

Values on generators

\((1863,3041,3137)\) → \((-1,-1,e\left(\frac{17}{18}\right))\)

Values

\(-1\)\(1\)\(3\)\(5\)\(9\)\(11\)\(13\)\(15\)\(17\)\(23\)\(25\)\(27\)
\(-1\)\(1\)\(e\left(\frac{5}{18}\right)\)\(e\left(\frac{11}{18}\right)\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{2}{9}\right)\)\(e\left(\frac{8}{9}\right)\)\(e\left(\frac{17}{18}\right)\)\(e\left(\frac{7}{18}\right)\)\(e\left(\frac{2}{9}\right)\)\(e\left(\frac{5}{6}\right)\)
value at e.g. 2