Properties

Label 5520.2321
Modulus $5520$
Conductor $69$
Order $22$
Real no
Primitive no
Minimal no
Parity even

Related objects

Learn more

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([0,0,11,0,13]))
 
pari: [g,chi] = znchar(Mod(2321,5520))
 

Basic properties

Modulus: \(5520\)
Conductor: \(69\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(22\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{69}(44,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 5520.dt

\(\chi_{5520}(401,\cdot)\) \(\chi_{5520}(641,\cdot)\) \(\chi_{5520}(881,\cdot)\) \(\chi_{5520}(1121,\cdot)\) \(\chi_{5520}(1601,\cdot)\) \(\chi_{5520}(2081,\cdot)\) \(\chi_{5520}(2321,\cdot)\) \(\chi_{5520}(3041,\cdot)\) \(\chi_{5520}(3281,\cdot)\) \(\chi_{5520}(4481,\cdot)\)

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: \(\Q(\zeta_{69})^+\)

Values on generators

\((4831,1381,1841,4417,1201)\) → \((1,1,-1,1,e\left(\frac{13}{22}\right))\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{5}{22}\right)\)\(e\left(\frac{9}{11}\right)\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{7}{11}\right)\)\(e\left(\frac{19}{22}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{9}{22}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{21}{22}\right)\)
value at e.g. 2