# Properties

 Label 1400.993 Modulus $1400$ Conductor $35$ Order $4$ 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(1400, base_ring=CyclotomicField(4))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,0,3,2]))

pari: [g,chi] = znchar(Mod(993,1400))

## Basic properties

 Modulus: $$1400$$ Conductor: $$35$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$4$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{35}(13,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1400.x

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: $$\Q(\sqrt{-1})$$ Fixed field: 4.4.6125.1

## Values on generators

$$(351,701,1177,801)$$ → $$(1,1,-i,-1)$$

## Values

 $$-1$$ $$1$$ $$3$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$27$$ $$29$$ $$31$$ $$1$$ $$1$$ $$-i$$ $$-1$$ $$1$$ $$-i$$ $$i$$ $$1$$ $$i$$ $$i$$ $$-1$$ $$-1$$
 value at e.g. 2