Properties

Label 5520.3217
Modulus $5520$
Conductor $115$
Order $44$
Real no
Primitive no
Minimal no
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([0,0,0,11,10]))
 
pari: [g,chi] = znchar(Mod(3217,5520))
 

Basic properties

Modulus: \(5520\)
Conductor: \(115\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{115}(112,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 5520.fq

\(\chi_{5520}(97,\cdot)\) \(\chi_{5520}(337,\cdot)\) \(\chi_{5520}(433,\cdot)\) \(\chi_{5520}(1537,\cdot)\) \(\chi_{5520}(1873,\cdot)\) \(\chi_{5520}(2113,\cdot)\) \(\chi_{5520}(2353,\cdot)\) \(\chi_{5520}(2593,\cdot)\) \(\chi_{5520}(2977,\cdot)\) \(\chi_{5520}(3073,\cdot)\) \(\chi_{5520}(3217,\cdot)\) \(\chi_{5520}(3457,\cdot)\) \(\chi_{5520}(3553,\cdot)\) \(\chi_{5520}(3697,\cdot)\) \(\chi_{5520}(3793,\cdot)\) \(\chi_{5520}(4177,\cdot)\) \(\chi_{5520}(4513,\cdot)\) \(\chi_{5520}(4657,\cdot)\) \(\chi_{5520}(4753,\cdot)\) \(\chi_{5520}(4897,\cdot)\)

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: \(\Q(\zeta_{115})^+\)

Values on generators

\((4831,1381,1841,4417,1201)\) → \((1,1,1,i,e\left(\frac{5}{22}\right))\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\(1\)\(1\)\(e\left(\frac{25}{44}\right)\)\(e\left(\frac{1}{22}\right)\)\(e\left(\frac{41}{44}\right)\)\(e\left(\frac{37}{44}\right)\)\(e\left(\frac{10}{11}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{4}{11}\right)\)\(e\left(\frac{1}{44}\right)\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{39}{44}\right)\)
value at e.g. 2