# Properties

 Label 5520.451 Modulus $5520$ Conductor $368$ Order $44$ Real no Primitive no Minimal yes Parity even

# Related objects

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([22,33,0,0,42]))

pari: [g,chi] = znchar(Mod(451,5520))

## Basic properties

 Modulus: $$5520$$ Conductor: $$368$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$44$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{368}(83,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 5520.gc

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

## Values on generators

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

## Values

 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$1$$ $$1$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{44}\right)$$
 value at e.g. 2