# Properties

 Label 1470.73 Modulus $1470$ Conductor $245$ Order $84$ 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([0,63,74]))

pari: [g,chi] = znchar(Mod(73,1470))

## Basic properties

 Modulus: $$1470$$ Conductor: $$245$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$84$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{245}(73,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1470.bu

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

$$(491,1177,1081)$$ → $$(1,-i,e\left(\frac{37}{42}\right))$$

## Values

 $$-1$$ $$1$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$1$$ $$1$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{79}{84}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{15}{28}\right)$$
 value at e.g. 2

## Related number fields

 Field of values: $\Q(\zeta_{84})$ Fixed field: Number field defined by a degree 84 polynomial