# Properties

 Label 5520.59 Modulus $5520$ Conductor $5520$ Order $44$ Real no Primitive yes Minimal yes Parity even

# Learn more about

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([22,11,22,22,28]))

pari: [g,chi] = znchar(Mod(59,5520))

## Basic properties

 Modulus: $$5520$$ Conductor: $$5520$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$44$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 5520.fy

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

$$(4831,1381,1841,4417,1201)$$ → $$(-1,i,-1,-1,e\left(\frac{7}{11}\right))$$

## Values

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