# Properties

 Conductor 1007 Order 26 Real No Primitive No Parity Odd Orbit Label 6042.bl

# 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(6042)

sage: chi = H[37]

pari: [g,chi] = znchar(Mod(37,6042))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 1007 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 26 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 = 6042.bl Orbit index = 38

## 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

$$(2015,4771,2281)$$ → $$(1,-1,e\left(\frac{15}{26}\right))$$

## Values

 -1 1 5 7 11 13 17 23 25 29 31 35 $$-1$$ $$1$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$-1$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{5}{26}\right)$$
value at  e.g. 2

## Related number fields

 Field of values $$\Q(\zeta_{13})$$