# Properties

 Label 2200.901 Modulus $2200$ Conductor $88$ Order $2$ Real yes Primitive no Minimal yes Parity odd

# Related objects

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2200, base_ring=CyclotomicField(2))

M = H._module

chi = DirichletCharacter(H, M([0,1,0,1]))

pari: [g,chi] = znchar(Mod(901,2200))

## Basic properties

 Modulus: $$2200$$ Conductor: $$88$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$2$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: yes Primitive: no, induced from $$\chi_{88}(21,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 2200.d

sage: chi.galois_orbit()

order = charorder(g,chi)

[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

## Related number fields

 Field of values: $$\Q$$ Fixed field: $$\Q(\sqrt{-22})$$

## Values on generators

$$(551,1101,177,1201)$$ → $$(1,-1,1,-1)$$

## First values

 $$a$$ $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$13$$ $$17$$ $$19$$ $$21$$ $$23$$ $$27$$ $$29$$ $$\chi_{ 2200 }(901, a)$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$
sage: chi.jacobi_sum(n)

$$\chi_{ 2200 }(901,a) \;$$ at $$\;a =$$ e.g. 2