Properties

Label 5520.3583
Modulus $5520$
Conductor $460$
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([22,0,0,33,24]))
 
pari: [g,chi] = znchar(Mod(3583,5520))
 

Basic properties

Modulus: \(5520\)
Conductor: \(460\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{460}(363,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 5520.fr

\(\chi_{5520}(127,\cdot)\) \(\chi_{5520}(223,\cdot)\) \(\chi_{5520}(463,\cdot)\) \(\chi_{5520}(607,\cdot)\) \(\chi_{5520}(703,\cdot)\) \(\chi_{5520}(1087,\cdot)\) \(\chi_{5520}(1327,\cdot)\) \(\chi_{5520}(1567,\cdot)\) \(\chi_{5520}(1807,\cdot)\) \(\chi_{5520}(2143,\cdot)\) \(\chi_{5520}(3247,\cdot)\) \(\chi_{5520}(3343,\cdot)\) \(\chi_{5520}(3583,\cdot)\) \(\chi_{5520}(4303,\cdot)\) \(\chi_{5520}(4447,\cdot)\) \(\chi_{5520}(4543,\cdot)\) \(\chi_{5520}(4687,\cdot)\) \(\chi_{5520}(5023,\cdot)\) \(\chi_{5520}(5407,\cdot)\) \(\chi_{5520}(5503,\cdot)\)

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: 44.44.6031750835043748183809156500949648298478534300530340661248000000000000000000000000000000000.1

Values on generators

\((4831,1381,1841,4417,1201)\) → \((-1,1,1,-i,e\left(\frac{6}{11}\right))\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{27}{44}\right)\)\(e\left(\frac{9}{22}\right)\)\(e\left(\frac{39}{44}\right)\)\(e\left(\frac{25}{44}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{7}{22}\right)\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{9}{44}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{21}{44}\right)\)
value at e.g. 2