Properties

Label 5520.4703
Modulus $5520$
Conductor $1380$
Order $44$
Real no
Primitive no
Minimal yes
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([22,0,22,33,18]))
 
pari: [g,chi] = znchar(Mod(4703,5520))
 

Basic properties

Modulus: \(5520\)
Conductor: \(1380\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1380}(563,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 5520.ft

\(\chi_{5520}(143,\cdot)\) \(\chi_{5520}(287,\cdot)\) \(\chi_{5520}(383,\cdot)\) \(\chi_{5520}(527,\cdot)\) \(\chi_{5520}(1247,\cdot)\) \(\chi_{5520}(1487,\cdot)\) \(\chi_{5520}(1583,\cdot)\) \(\chi_{5520}(2687,\cdot)\) \(\chi_{5520}(3023,\cdot)\) \(\chi_{5520}(3263,\cdot)\) \(\chi_{5520}(3503,\cdot)\) \(\chi_{5520}(3743,\cdot)\) \(\chi_{5520}(4127,\cdot)\) \(\chi_{5520}(4223,\cdot)\) \(\chi_{5520}(4367,\cdot)\) \(\chi_{5520}(4607,\cdot)\) \(\chi_{5520}(4703,\cdot)\) \(\chi_{5520}(4847,\cdot)\) \(\chi_{5520}(4943,\cdot)\) \(\chi_{5520}(5327,\cdot)\)

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: Number field defined by a degree 44 polynomial

Values on generators

\((4831,1381,1841,4417,1201)\) → \((-1,1,-1,-i,e\left(\frac{9}{22}\right))\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{1}{44}\right)\)\(e\left(\frac{15}{22}\right)\)\(e\left(\frac{43}{44}\right)\)\(e\left(\frac{5}{44}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{4}{11}\right)\)\(e\left(\frac{21}{22}\right)\)\(e\left(\frac{15}{44}\right)\)\(e\left(\frac{9}{22}\right)\)\(e\left(\frac{35}{44}\right)\)
value at e.g. 2