# Properties

 Label 5520.3073 Modulus $5520$ Conductor $115$ Order $44$ Real no Primitive no Minimal no Parity even

# Related objects

Show commands: 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([0,0,0,33,42]))

pari: [g,chi] = znchar(Mod(3073,5520))

## 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 $$\chi_{115}(83,\cdot)$$ 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

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

$$(4831,1381,1841,4417,1201)$$ → $$(1,1,1,-i,e\left(\frac{21}{22}\right))$$

## Values

 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$1$$ $$1$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{1}{44}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 5520 }(3073,a) \;$$ at $$\;a =$$ e.g. 2