# Properties

 Label 3600.2299 Modulus $3600$ Conductor $720$ Order $12$ Real no Primitive no Minimal no Parity odd

# Related objects

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

sage: H = DirichletGroup(3600)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([6,3,4,6]))

pari: [g,chi] = znchar(Mod(2299,3600))

## Basic properties

 Modulus: $$3600$$ Conductor: $$720$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$12$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{720}(139,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 3600.dp

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

$$(3151,901,2801,577)$$ → $$(-1,i,e\left(\frac{1}{3}\right),-1)$$

## Values

 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$
 value at e.g. 2

## Related number fields

 Field of values: $$\Q(\zeta_{12})$$ Fixed field: 12.0.5777633090469888000000.1