Properties

Label 5520.257
Modulus $5520$
Conductor $345$
Order $44$
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(44))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,0,22,11,8]))
 
pari: [g,chi] = znchar(Mod(257,5520))
 

Basic properties

Modulus: \(5520\)
Conductor: \(345\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{345}(257,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 5520.fs

\(\chi_{5520}(257,\cdot)\) \(\chi_{5520}(353,\cdot)\) \(\chi_{5520}(593,\cdot)\) \(\chi_{5520}(1313,\cdot)\) \(\chi_{5520}(1457,\cdot)\) \(\chi_{5520}(1553,\cdot)\) \(\chi_{5520}(1697,\cdot)\) \(\chi_{5520}(2033,\cdot)\) \(\chi_{5520}(2417,\cdot)\) \(\chi_{5520}(2513,\cdot)\) \(\chi_{5520}(2657,\cdot)\) \(\chi_{5520}(2753,\cdot)\) \(\chi_{5520}(2993,\cdot)\) \(\chi_{5520}(3137,\cdot)\) \(\chi_{5520}(3233,\cdot)\) \(\chi_{5520}(3617,\cdot)\) \(\chi_{5520}(3857,\cdot)\) \(\chi_{5520}(4097,\cdot)\) \(\chi_{5520}(4337,\cdot)\) \(\chi_{5520}(4673,\cdot)\)

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: 44.44.10759477646680772288556262812807675479811013525016604751482416550745256245136260986328125.1

Values on generators

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

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{31}{44}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{13}{44}\right)\)\(e\left(\frac{1}{44}\right)\)\(e\left(\frac{5}{22}\right)\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{3}{44}\right)\)\(e\left(\frac{15}{22}\right)\)\(e\left(\frac{29}{44}\right)\)
value at e.g. 2