# Properties

 Conductor 573 Order 190 Real No Primitive No Parity Odd Orbit Label 4011.ca

# Learn more about

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

sage: H = DirichletGroup_conrey(4011)

sage: chi = H[386]

pari: [g,chi] = znchar(Mod(386,4011))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 573 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 190 Real = No sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = No sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = Odd Orbit label = 4011.ca Orbit index = 53

## 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

$$(2675,2866,2311)$$ → $$(-1,1,e\left(\frac{44}{95}\right))$$

## Values

 -1 1 2 4 5 8 10 11 13 16 17 19 $$-1$$ $$1$$ $$e\left(\frac{167}{190}\right)$$ $$e\left(\frac{72}{95}\right)$$ $$e\left(\frac{25}{38}\right)$$ $$e\left(\frac{121}{190}\right)$$ $$e\left(\frac{51}{95}\right)$$ $$e\left(\frac{33}{38}\right)$$ $$e\left(\frac{83}{95}\right)$$ $$e\left(\frac{49}{95}\right)$$ $$e\left(\frac{169}{190}\right)$$ $$e\left(\frac{44}{95}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{95})$$