# Properties

 Label 7098.3347 Modulus $7098$ Conductor $507$ Order $156$ Real no Primitive no Minimal yes Parity even

# Related objects

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

sage: H = DirichletGroup(7098, base_ring=CyclotomicField(156))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([78,0,149]))

pari: [g,chi] = znchar(Mod(3347,7098))

## Basic properties

 Modulus: $$7098$$ Conductor: $$507$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$156$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{507}(305,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 7098.ek

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: $\Q(\zeta_{156})$ Fixed field: Number field defined by a degree 156 polynomial (not computed)

## Values on generators

$$(4733,5071,6931)$$ → $$(-1,1,e\left(\frac{149}{156}\right))$$

## Values

 $$-1$$ $$1$$ $$5$$ $$11$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$ $$1$$ $$1$$ $$e\left(\frac{5}{52}\right)$$ $$e\left(\frac{137}{156}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{55}{78}\right)$$ $$e\left(\frac{3}{52}\right)$$ $$e\left(\frac{35}{156}\right)$$ $$e\left(\frac{107}{156}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 7098 }(3347,a) \;$$ at $$\;a =$$ e.g. 2