# Properties

 Label 1260.811 Modulus $1260$ Conductor $28$ Order $2$ Real yes Primitive no Minimal yes Parity even

# Related objects

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

H = DirichletGroup(1260, base_ring=CyclotomicField(2))

M = H._module

chi = DirichletCharacter(H, M([1,0,0,1]))

pari: [g,chi] = znchar(Mod(811,1260))

## Basic properties

 Modulus: $$1260$$ Conductor: $$28$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$2$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: yes Primitive: no, induced from $$\chi_{28}(27,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1260.c

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: $$\Q(\sqrt{7})$$

## Values on generators

$$(631,281,757,1081)$$ → $$(-1,1,1,-1)$$

## First values

 $$a$$ $$-1$$ $$1$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$\chi_{ 1260 }(811, a)$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$
sage: chi.jacobi_sum(n)

$$\chi_{ 1260 }(811,a) \;$$ at $$\;a =$$ e.g. 2