Properties

Label 5520.3109
Modulus $5520$
Conductor $1840$
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([0,11,0,22,8]))
 
pari: [g,chi] = znchar(Mod(3109,5520))
 

Basic properties

Modulus: \(5520\)
Conductor: \(1840\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1840}(1269,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 5520.em

\(\chi_{5520}(349,\cdot)\) \(\chi_{5520}(469,\cdot)\) \(\chi_{5520}(949,\cdot)\) \(\chi_{5520}(1189,\cdot)\) \(\chi_{5520}(1429,\cdot)\) \(\chi_{5520}(1549,\cdot)\) \(\chi_{5520}(1669,\cdot)\) \(\chi_{5520}(1789,\cdot)\) \(\chi_{5520}(2509,\cdot)\) \(\chi_{5520}(2749,\cdot)\) \(\chi_{5520}(3109,\cdot)\) \(\chi_{5520}(3229,\cdot)\) \(\chi_{5520}(3709,\cdot)\) \(\chi_{5520}(3949,\cdot)\) \(\chi_{5520}(4189,\cdot)\) \(\chi_{5520}(4309,\cdot)\) \(\chi_{5520}(4429,\cdot)\) \(\chi_{5520}(4549,\cdot)\) \(\chi_{5520}(5269,\cdot)\) \(\chi_{5520}(5509,\cdot)\)

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

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

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{39}{44}\right)\)\(e\left(\frac{35}{44}\right)\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{21}{44}\right)\)\(e\left(\frac{1}{44}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{25}{44}\right)\)\(e\left(\frac{15}{22}\right)\)\(e\left(\frac{29}{44}\right)\)
value at e.g. 2