# Properties

 Label 85600.1889 Modulus $85600$ Conductor $2675$ Order $530$ Real no Primitive no Minimal yes Parity odd

# Related objects

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

H = DirichletGroup(85600, base_ring=CyclotomicField(530))

M = H._module

chi = DirichletCharacter(H, M([0,0,159,455]))

pari: [g,chi] = znchar(Mod(1889,85600))

## Basic properties

 Modulus: $$85600$$ Conductor: $$2675$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$530$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{2675}(1889,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 85600.gp

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: $\Q(\zeta_{265})$ Fixed field: Number field defined by a degree 530 polynomial (not computed)

## Values on generators

$$(26751,32101,82177,16801)$$ → $$(1,1,e\left(\frac{3}{10}\right),e\left(\frac{91}{106}\right))$$

## First values

 $$a$$ $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$21$$ $$23$$ $$27$$ $$\chi_{ 85600 }(1889, a)$$ $$-1$$ $$1$$ $$e\left(\frac{103}{530}\right)$$ $$e\left(\frac{22}{53}\right)$$ $$e\left(\frac{103}{265}\right)$$ $$e\left(\frac{182}{265}\right)$$ $$e\left(\frac{381}{530}\right)$$ $$e\left(\frac{211}{265}\right)$$ $$e\left(\frac{96}{265}\right)$$ $$e\left(\frac{323}{530}\right)$$ $$e\left(\frac{279}{530}\right)$$ $$e\left(\frac{309}{530}\right)$$
sage: chi.jacobi_sum(n)

$$\chi_{ 85600 }(1889,a) \;$$ at $$\;a =$$ e.g. 2