# Properties

 Modulus 4725 Conductor 4725 Order 90 Real no Primitive yes Minimal yes Parity even Orbit label 4725.gm

# Related objects

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter

sage: H = DirichletGroup(4725)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([5,54,45]))

pari: [g,chi] = znchar(Mod(3296,4725))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 4725 Conductor = 4725 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 90 Real = no sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = yes Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = even Orbit label = 4725.gm Orbit index = 169

## Galois orbit

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

$$(4376,1702,2026)$$ → $$(e\left(\frac{1}{18}\right),e\left(\frac{3}{5}\right),-1)$$

## Values

 -1 1 2 4 8 11 13 16 17 19 22 23 $$1$$ $$1$$ $$e\left(\frac{59}{90}\right)$$ $$e\left(\frac{14}{45}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{29}{90}\right)$$ $$e\left(\frac{31}{90}\right)$$ $$e\left(\frac{28}{45}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{44}{45}\right)$$ $$e\left(\frac{19}{90}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{45})$$