# Properties

 Label 7098.211 Modulus $7098$ Conductor $169$ Order $39$ Real no Primitive no Minimal yes Parity even

# Learn more about

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

sage: H = DirichletGroup(7098, base_ring=CyclotomicField(78))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,0,38]))

pari: [g,chi] = znchar(Mod(211,7098))

## Basic properties

 Modulus: $$7098$$ Conductor: $$169$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$39$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{169}(42,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 7098.cq

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: $\Q(\zeta_{39})$ Fixed field: 39.39.27027636582498189040621249864144468324898507852136260989871841246090732111847218889.1

## Values on generators

$$(4733,5071,6931)$$ → $$(1,1,e\left(\frac{19}{39}\right))$$

## Values

 $$-1$$ $$1$$ $$5$$ $$11$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$ $$1$$ $$1$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{5}{39}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{16}{39}\right)$$
 value at e.g. 2