Properties

 Label 7098.995 Modulus $7098$ Conductor $39$ Order $12$ Real no Primitive no Minimal no Parity even

Related objects

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

sage: H = DirichletGroup(7098, base_ring=CyclotomicField(12))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([6,0,11]))

pari: [g,chi] = znchar(Mod(995,7098))

Basic properties

 Modulus: $$7098$$ Conductor: $$39$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$12$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{39}(20,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

Galois orbit 7098.bu

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: $$\Q(\zeta_{12})$$ Fixed field: $$\Q(\zeta_{39})^+$$

Values on generators

$$(4733,5071,6931)$$ → $$(-1,1,e\left(\frac{11}{12}\right))$$

Values

 $$-1$$ $$1$$ $$5$$ $$11$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$ $$1$$ $$1$$ $$-i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$
 value at e.g. 2