# Properties

 Label 3267.40 Modulus $3267$ Conductor $297$ Order $90$ Real no Primitive no Minimal no Parity odd

# Related objects

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

H = DirichletGroup(3267, base_ring=CyclotomicField(90))

M = H._module

chi = DirichletCharacter(H, M([40,63]))

pari: [g,chi] = znchar(Mod(40,3267))

## Basic properties

 Modulus: $$3267$$ Conductor: $$297$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$90$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{297}(40,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 3267.bf

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: $\Q(\zeta_{45})$ Fixed field: Number field defined by a degree 90 polynomial

## Values on generators

$$(3026,244)$$ → $$(e\left(\frac{4}{9}\right),e\left(\frac{7}{10}\right))$$

## First values

 $$a$$ $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$7$$ $$8$$ $$10$$ $$13$$ $$14$$ $$16$$ $$17$$ $$\chi_{ 3267 }(40, a)$$ $$-1$$ $$1$$ $$e\left(\frac{13}{90}\right)$$ $$e\left(\frac{13}{45}\right)$$ $$e\left(\frac{1}{45}\right)$$ $$e\left(\frac{1}{90}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{23}{90}\right)$$ $$e\left(\frac{7}{45}\right)$$ $$e\left(\frac{26}{45}\right)$$ $$e\left(\frac{29}{30}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 3267 }(40,a) \;$$ at $$\;a =$$ e.g. 2