Properties

Label 5520.487
Modulus $5520$
Conductor $920$
Order $44$
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(44))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([22,22,0,11,8]))
 
pari: [g,chi] = znchar(Mod(487,5520))
 

Basic properties

Modulus: \(5520\)
Conductor: \(920\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{920}(27,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 5520.ev

\(\chi_{5520}(487,\cdot)\) \(\chi_{5520}(583,\cdot)\) \(\chi_{5520}(823,\cdot)\) \(\chi_{5520}(1543,\cdot)\) \(\chi_{5520}(1687,\cdot)\) \(\chi_{5520}(1783,\cdot)\) \(\chi_{5520}(1927,\cdot)\) \(\chi_{5520}(2263,\cdot)\) \(\chi_{5520}(2647,\cdot)\) \(\chi_{5520}(2743,\cdot)\) \(\chi_{5520}(2887,\cdot)\) \(\chi_{5520}(2983,\cdot)\) \(\chi_{5520}(3223,\cdot)\) \(\chi_{5520}(3367,\cdot)\) \(\chi_{5520}(3463,\cdot)\) \(\chi_{5520}(3847,\cdot)\) \(\chi_{5520}(4087,\cdot)\) \(\chi_{5520}(4327,\cdot)\) \(\chi_{5520}(4567,\cdot)\) \(\chi_{5520}(4903,\cdot)\)

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: \(\Q(\zeta_{44})\)
Fixed field: 44.44.25298996654427333182343480348559113656901710330851609956835131392000000000000000000000000000000000.1

Values on generators

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

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{9}{44}\right)\)\(e\left(\frac{7}{11}\right)\)\(e\left(\frac{35}{44}\right)\)\(e\left(\frac{23}{44}\right)\)\(e\left(\frac{5}{22}\right)\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{25}{44}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{29}{44}\right)\)
value at e.g. 2