# Properties

 Label 2415.374 Modulus $2415$ Conductor $2415$ Order $66$ Real no Primitive yes Minimal yes Parity even

# Related objects

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

sage: H = DirichletGroup(2415, base_ring=CyclotomicField(66))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([33,33,11,54]))

pari: [g,chi] = znchar(Mod(374,2415))

## Basic properties

 Modulus: $$2415$$ Conductor: $$2415$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$66$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 2415.de

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: $$\Q(\zeta_{33})$$ Fixed field: Number field defined by a degree 66 polynomial

## Values on generators

$$(806,967,346,1891)$$ → $$(-1,-1,e\left(\frac{1}{6}\right),e\left(\frac{9}{11}\right))$$

## Values

 $$-1$$ $$1$$ $$2$$ $$4$$ $$8$$ $$11$$ $$13$$ $$16$$ $$17$$ $$19$$ $$22$$ $$26$$ $$1$$ $$1$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$-1$$ $$e\left(\frac{14}{33}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 2415 }(374,a) \;$$ at $$\;a =$$ e.g. 2