# Properties

 Label 1900.607 Modulus $1900$ Conductor $380$ Order $4$ Real no Primitive no Minimal yes Parity odd

# Related objects

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

sage: H = DirichletGroup(1900, base_ring=CyclotomicField(4))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([2,1,2]))

pari: [g,chi] = znchar(Mod(607,1900))

## Basic properties

 Modulus: $$1900$$ Conductor: $$380$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$4$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{380}(227,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1900.j

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

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

## Related number fields

 Field of values: $$\Q(\sqrt{-1})$$ Fixed field: 4.0.722000.3

## Values on generators

$$(951,77,401)$$ → $$(-1,i,-1)$$

## Values

 $$a$$ $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$21$$ $$23$$ $$27$$ $$29$$ $$\chi_{ 1900 }(607, a)$$ $$-1$$ $$1$$ $$-i$$ $$-i$$ $$-1$$ $$-1$$ $$i$$ $$i$$ $$-1$$ $$i$$ $$i$$ $$1$$
sage: chi.jacobi_sum(n)

$$\chi_{ 1900 }(607,a) \;$$ at $$\;a =$$ e.g. 2