# Properties

 Label 3040.949 Modulus $3040$ Conductor $3040$ Order $8$ Real no Primitive yes Minimal yes Parity odd

# Related objects

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

H = DirichletGroup(3040, base_ring=CyclotomicField(8))

M = H._module

chi = DirichletCharacter(H, M([0,5,4,4]))

pari: [g,chi] = znchar(Mod(949,3040))

## Basic properties

 Modulus: $$3040$$ Conductor: $$3040$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$8$$ 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 3040.cn

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: $$\Q(\zeta_{8})$$ Fixed field: 8.0.174913885306880000.1

## Values on generators

$$(191,2661,1217,1921)$$ → $$(1,e\left(\frac{5}{8}\right),-1,-1)$$

## First values

 $$a$$ $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$21$$ $$23$$ $$27$$ $$29$$ $$\chi_{ 3040 }(949, a)$$ $$-1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 3040 }(949,a) \;$$ at $$\;a =$$ e.g. 2