# Properties

 Label 1470.209 Modulus $1470$ Conductor $735$ Order $14$ Real no Primitive no Minimal yes Parity even

# Related objects

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

sage: H = DirichletGroup(1470)

sage: M = H._module

sage: chi = DirichletCharacter(H, M([7,7,11]))

pari: [g,chi] = znchar(Mod(209,1470))

## Basic properties

 Modulus: $$1470$$ Conductor: $$735$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$14$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{735}(209,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1470.bc

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

$$(491,1177,1081)$$ → $$(-1,-1,e\left(\frac{11}{14}\right))$$

## Values

 $$-1$$ $$1$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$1$$ $$1$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$-1$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$-1$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$
 value at e.g. 2

## Related number fields

 Field of values: $$\Q(\zeta_{7})$$ Fixed field: 14.14.229134146187897752973821015625.1