# Properties

 Label 2960.2437 Modulus $2960$ Conductor $2960$ Order $36$ Real no Primitive yes Minimal yes Parity even

# Learn more

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

H = DirichletGroup(2960, base_ring=CyclotomicField(36))

M = H._module

chi = DirichletCharacter(H, M([0,9,9,5]))

pari: [g,chi] = znchar(Mod(2437,2960))

## Basic properties

 Modulus: $$2960$$ Conductor: $$2960$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$36$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 2960.gq

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: $$\Q(\zeta_{36})$$ Fixed field: Number field defined by a degree 36 polynomial

## Values on generators

$$(2591,741,1777,2481)$$ → $$(1,i,i,e\left(\frac{5}{36}\right))$$

## First values

 $$a$$ $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$21$$ $$23$$ $$27$$ $$\chi_{ 2960 }(2437, a)$$ $$1$$ $$1$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 2960 }(2437,a) \;$$ at $$\;a =$$ e.g. 2