# Properties

 Label 1225.247 Modulus $1225$ Conductor $1225$ Order $420$ Real no Primitive yes Minimal yes Parity odd

# Related objects

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

sage: H = DirichletGroup(1225, base_ring=CyclotomicField(420))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([357,260]))

pari: [g,chi] = znchar(Mod(247,1225))

## Basic properties

 Modulus: $$1225$$ Conductor: $$1225$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$420$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1225.bv

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: $\Q(\zeta_{420})$ Fixed field: Number field defined by a degree 420 polynomial (not computed)

## Values on generators

$$(1177,101)$$ → $$(e\left(\frac{17}{20}\right),e\left(\frac{13}{21}\right))$$

## Values

 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$8$$ $$9$$ $$11$$ $$12$$ $$13$$ $$16$$ $$-1$$ $$1$$ $$e\left(\frac{397}{420}\right)$$ $$e\left(\frac{239}{420}\right)$$ $$e\left(\frac{187}{210}\right)$$ $$e\left(\frac{18}{35}\right)$$ $$e\left(\frac{117}{140}\right)$$ $$e\left(\frac{29}{210}\right)$$ $$e\left(\frac{38}{105}\right)$$ $$e\left(\frac{193}{420}\right)$$ $$e\left(\frac{81}{140}\right)$$ $$e\left(\frac{82}{105}\right)$$
 value at e.g. 2