# Properties

 Label 7098.239 Modulus $7098$ Conductor $39$ Order $4$ Real no Primitive no Minimal yes Parity even

# Learn more

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

sage: H = DirichletGroup(7098, base_ring=CyclotomicField(4))

sage: M = H._module

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

pari: [g,chi] = znchar(Mod(239,7098))

## Basic properties

 Modulus: $$7098$$ Conductor: $$39$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$4$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{39}(5,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 7098.p

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: 4.4.19773.1

## Values on generators

$$(4733,5071,6931)$$ → $$(-1,1,-i)$$

## Values

 $$-1$$ $$1$$ $$5$$ $$11$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$ $$1$$ $$1$$ $$i$$ $$-i$$ $$1$$ $$-i$$ $$1$$ $$-1$$ $$-1$$ $$-i$$ $$i$$ $$i$$
 value at e.g. 2