Properties

Label 5520.4211
Modulus $5520$
Conductor $1104$
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([22,33,22,0,4]))
 
pari: [g,chi] = znchar(Mod(4211,5520))
 

Basic properties

Modulus: \(5520\)
Conductor: \(1104\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1104}(899,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 5520.ep

\(\chi_{5520}(131,\cdot)\) \(\chi_{5520}(371,\cdot)\) \(\chi_{5520}(491,\cdot)\) \(\chi_{5520}(611,\cdot)\) \(\chi_{5520}(731,\cdot)\) \(\chi_{5520}(1451,\cdot)\) \(\chi_{5520}(1691,\cdot)\) \(\chi_{5520}(2051,\cdot)\) \(\chi_{5520}(2171,\cdot)\) \(\chi_{5520}(2651,\cdot)\) \(\chi_{5520}(2891,\cdot)\) \(\chi_{5520}(3131,\cdot)\) \(\chi_{5520}(3251,\cdot)\) \(\chi_{5520}(3371,\cdot)\) \(\chi_{5520}(3491,\cdot)\) \(\chi_{5520}(4211,\cdot)\) \(\chi_{5520}(4451,\cdot)\) \(\chi_{5520}(4811,\cdot)\) \(\chi_{5520}(4931,\cdot)\) \(\chi_{5520}(5411,\cdot)\)

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

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

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{25}{44}\right)\)\(e\left(\frac{23}{44}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{5}{44}\right)\)\(e\left(\frac{17}{44}\right)\)\(e\left(\frac{1}{22}\right)\)\(e\left(\frac{29}{44}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{31}{44}\right)\)
value at e.g. 2