# Properties

 Label 1600.209 Modulus $1600$ Conductor $400$ Order $20$ 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(1600, base_ring=CyclotomicField(20))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,15,14]))

pari: [g,chi] = znchar(Mod(209,1600))

## Basic properties

 Modulus: $$1600$$ Conductor: $$400$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$20$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{400}(109,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1600.cb

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: $$\Q(\zeta_{20})$$ Fixed field: 20.20.20971520000000000000000000000000000000000.1

## Values on generators

$$(1151,901,577)$$ → $$(1,-i,e\left(\frac{7}{10}\right))$$

## Values

 $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$21$$ $$23$$ $$27$$ $$1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$
 value at e.g. 2