# Properties

 Label 3920.41 Modulus $3920$ Conductor $392$ Order $14$ Real no Primitive no Minimal no Parity odd

# Related objects

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

sage: H = DirichletGroup(3920, base_ring=CyclotomicField(14))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,7,0,5]))

pari: [g,chi] = znchar(Mod(41,3920))

## Basic properties

 Modulus: $$3920$$ Conductor: $$392$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$14$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{392}(237,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 3920.dh

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: $$\Q(\zeta_{7})$$ Fixed field: 14.0.2812424737865523319657201664.1

## Values on generators

$$(1471,981,3137,3041)$$ → $$(1,-1,1,e\left(\frac{5}{14}\right))$$

## Values

 $$-1$$ $$1$$ $$3$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$27$$ $$29$$ $$31$$ $$-1$$ $$1$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$1$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$-1$$
 value at e.g. 2