# Properties

 Label 6001.766 Modulus $6001$ Conductor $353$ Order $16$ 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(6001)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,13]))

pari: [g,chi] = znchar(Mod(766,6001))

## Basic properties

 Modulus: $$6001$$ Conductor: $$353$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$16$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{353}(60,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 6001.bc

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

$$(2825,3180)$$ → $$(1,e\left(\frac{13}{16}\right))$$

## Values

 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$11$$ $$1$$ $$1$$ $$i$$ $$e\left(\frac{13}{16}\right)$$ $$-1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$-i$$
 value at e.g. 2

## Related number fields

 Field of values: $$\Q(\zeta_{16})$$ Fixed field: 16.16.164672311157017194379126294334593898657.1