Properties

Label 5520.119
Modulus $5520$
Conductor $2760$
Order $22$
Real no
Primitive no
Minimal no
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(5520, base_ring=CyclotomicField(22))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([11,11,11,11,4]))
 
pari: [g,chi] = znchar(Mod(119,5520))
 

Basic properties

Modulus: \(5520\)
Conductor: \(2760\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(22\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{2760}(1499,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 5520.dk

\(\chi_{5520}(119,\cdot)\) \(\chi_{5520}(1319,\cdot)\) \(\chi_{5520}(1559,\cdot)\) \(\chi_{5520}(2279,\cdot)\) \(\chi_{5520}(2519,\cdot)\) \(\chi_{5520}(2999,\cdot)\) \(\chi_{5520}(3479,\cdot)\) \(\chi_{5520}(3719,\cdot)\) \(\chi_{5520}(3959,\cdot)\) \(\chi_{5520}(4199,\cdot)\)

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: \(\Q(\zeta_{11})\)
Fixed field: Number field defined by a degree 22 polynomial

Values on generators

\((4831,1381,1841,4417,1201)\) → \((-1,-1,-1,-1,e\left(\frac{2}{11}\right))\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{9}{11}\right)\)\(e\left(\frac{15}{22}\right)\)\(e\left(\frac{9}{22}\right)\)
value at e.g. 2