# Properties

 Label 1155.1 Modulus $1155$ Conductor $1$ Order $1$ Real yes Primitive no Minimal yes Parity even

# Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

M = H._module

chi = DirichletCharacter(H, M([0,0,0,0]))

pari: [g,chi] = znchar(Mod(1,1155))

## Basic properties

 Modulus: $$1155$$ Conductor: $$1$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$1$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: yes Primitive: no, induced from $$\chi_{1}(1,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1155.a

sage: chi.galois_orbit()

order = charorder(g,chi)

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

## Related number fields

 Field of values: $$\Q$$ Fixed field: $$\Q$$

## Values on generators

$$(386,232,661,211)$$ → $$(1,1,1,1)$$

## Values

 $$a$$ $$-1$$ $$1$$ $$2$$ $$4$$ $$8$$ $$13$$ $$16$$ $$17$$ $$19$$ $$23$$ $$26$$ $$29$$ $$\chi_{ 1155 }(1, a)$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
sage: chi.jacobi_sum(n)

$$\chi_{ 1155 }(1,a) \;$$ at $$\;a =$$ e.g. 2