# Properties

 Label 1336.901 Modulus $1336$ Conductor $1336$ Order $166$ Real no Primitive yes Minimal yes Parity even

# Related objects

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter

sage: H = DirichletGroup(1336)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,83,162]))

pari: [g,chi] = znchar(Mod(901,1336))

## Basic properties

 Modulus: $$1336$$ Conductor: $$1336$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$166$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1336.o

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

$$(335,669,673)$$ → $$(1,-1,e\left(\frac{81}{83}\right))$$

## Values

 $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$21$$ $$1$$ $$1$$ $$e\left(\frac{39}{166}\right)$$ $$e\left(\frac{79}{166}\right)$$ $$e\left(\frac{13}{83}\right)$$ $$e\left(\frac{39}{83}\right)$$ $$e\left(\frac{137}{166}\right)$$ $$e\left(\frac{3}{166}\right)$$ $$e\left(\frac{59}{83}\right)$$ $$e\left(\frac{60}{83}\right)$$ $$e\left(\frac{17}{166}\right)$$ $$e\left(\frac{65}{166}\right)$$
 value at e.g. 2

## Related number fields

 Field of values: $\Q(\zeta_{83})$ Fixed field: Number field defined by a degree 166 polynomial