# Properties

 Label 1815.16 Modulus $1815$ Conductor $121$ Order $55$ 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(1815, base_ring=CyclotomicField(110))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,0,4]))

pari: [g,chi] = znchar(Mod(16,1815))

## Basic properties

 Modulus: $$1815$$ Conductor: $$121$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$55$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{121}(16,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1815.bk

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

$$(1211,727,1696)$$ → $$(1,1,e\left(\frac{2}{55}\right))$$

## Values

 $$-1$$ $$1$$ $$2$$ $$4$$ $$7$$ $$8$$ $$13$$ $$14$$ $$16$$ $$17$$ $$19$$ $$23$$ $$1$$ $$1$$ $$e\left(\frac{2}{55}\right)$$ $$e\left(\frac{4}{55}\right)$$ $$e\left(\frac{14}{55}\right)$$ $$e\left(\frac{6}{55}\right)$$ $$e\left(\frac{37}{55}\right)$$ $$e\left(\frac{16}{55}\right)$$ $$e\left(\frac{8}{55}\right)$$ $$e\left(\frac{43}{55}\right)$$ $$e\left(\frac{1}{55}\right)$$ $$e\left(\frac{6}{11}\right)$$
 value at e.g. 2

## Related number fields

 Field of values: $\Q(\zeta_{55})$ Fixed field: Number field defined by a degree 55 polynomial