# Properties

 Label 3600.451 Modulus $3600$ Conductor $16$ Order $4$ Real no Primitive no Minimal yes Parity odd

# Related objects

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

H = DirichletGroup(3600, base_ring=CyclotomicField(4))

M = H._module

chi = DirichletCharacter(H, M([2,3,0,0]))

pari: [g,chi] = znchar(Mod(451,3600))

## Basic properties

 Modulus: $$3600$$ Conductor: $$16$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$4$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{16}(3,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 3600.bo

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: $$\mathbb{Q}(i)$$ Fixed field: 4.0.2048.2

## Values on generators

$$(3151,901,2801,577)$$ → $$(-1,-i,1,1)$$

## First values

 $$a$$ $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$\chi_{ 3600 }(451, a)$$ $$-1$$ $$1$$ $$1$$ $$i$$ $$i$$ $$1$$ $$-i$$ $$1$$ $$i$$ $$-1$$ $$-i$$ $$-1$$
sage: chi.jacobi_sum(n)

$$\chi_{ 3600 }(451,a) \;$$ at $$\;a =$$ e.g. 2