# Properties

 Conductor 2011 Order 2010 Real no Primitive yes Minimal yes Parity odd Orbit label 2011.p

# Related objects

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(2011)

sage: chi = H[42]

pari: [g,chi] = znchar(Mod(42,2011))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 2011 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 2010 Real = no sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = yes Minimal = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = odd Orbit label = 2011.p Orbit index = 16

## Galois orbit

sage: chi.sage_character().galois_orbit()

pari: order = charorder(g,chi)

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

## Values on generators

$$3$$ → $$e\left(\frac{43}{2010}\right)$$

## Values

 -1 1 2 3 4 5 6 7 8 9 10 11 $$-1$$ $$1$$ $$e\left(\frac{97}{402}\right)$$ $$e\left(\frac{43}{2010}\right)$$ $$e\left(\frac{97}{201}\right)$$ $$e\left(\frac{911}{1005}\right)$$ $$e\left(\frac{88}{335}\right)$$ $$e\left(\frac{1321}{2010}\right)$$ $$e\left(\frac{97}{134}\right)$$ $$e\left(\frac{43}{1005}\right)$$ $$e\left(\frac{99}{670}\right)$$ $$e\left(\frac{371}{2010}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{1005})$$