# Properties

 Label 6012.25 Modulus $6012$ Conductor $1503$ Order $249$ Real no Primitive no Minimal yes Parity even

# Related objects

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

sage: H = DirichletGroup(6012)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,166,3]))

pari: [g,chi] = znchar(Mod(25,6012))

## Basic properties

 Modulus: $$6012$$ Conductor: $$1503$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$249$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{1503}(25,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 6012.y

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

## Values on generators

$$(3007,3341,4681)$$ → $$(1,e\left(\frac{2}{3}\right),e\left(\frac{1}{83}\right))$$

## Values

 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$1$$ $$1$$ $$e\left(\frac{86}{249}\right)$$ $$e\left(\frac{22}{249}\right)$$ $$e\left(\frac{1}{249}\right)$$ $$e\left(\frac{143}{249}\right)$$ $$e\left(\frac{53}{83}\right)$$ $$e\left(\frac{58}{83}\right)$$ $$e\left(\frac{131}{249}\right)$$ $$e\left(\frac{172}{249}\right)$$ $$e\left(\frac{118}{249}\right)$$ $$e\left(\frac{104}{249}\right)$$
 value at e.g. 2

## Related number fields

 Field of values: $\Q(\zeta_{249})$ Fixed field: Number field defined by a degree 249 polynomial