# Properties

 Label 3960.3169 Modulus $3960$ Conductor $5$ Order $2$ Real yes Primitive no Minimal yes Parity even

# Learn more

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

H = DirichletGroup(3960, base_ring=CyclotomicField(2))

M = H._module

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

pari: [g,chi] = znchar(Mod(3169,3960))

## Basic properties

 Modulus: $$3960$$ Conductor: $$5$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$2$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: yes Primitive: no, induced from $$\chi_{5}(4,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 3960.d

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: $$\Q(\sqrt{5})$$

## Values on generators

$$(991,1981,3521,2377,2521)$$ → $$(1,1,1,-1,1)$$

## First values

 $$a$$ $$-1$$ $$1$$ $$7$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$\chi_{ 3960 }(3169, a)$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$
sage: chi.jacobi_sum(n)

$$\chi_{ 3960 }(3169,a) \;$$ at $$\;a =$$ e.g. 2