# Properties

 Label 1792.37 Modulus $1792$ Conductor $1792$ Order $192$ Real no Primitive yes Minimal yes Parity even

# Related objects

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter

sage: H = DirichletGroup(1792, base_ring=CyclotomicField(192))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,75,64]))

pari: [g,chi] = znchar(Mod(37,1792))

## Basic properties

 Modulus: $$1792$$ Conductor: $$1792$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$192$$ 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 1792.cb

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

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

## Related number fields

 Field of values: $\Q(\zeta_{192})$ Fixed field: Number field defined by a degree 192 polynomial (not computed)

## Values on generators

$$(1023,1541,1025)$$ → $$(1,e\left(\frac{25}{64}\right),e\left(\frac{1}{3}\right))$$

## Values

 $$-1$$ $$1$$ $$3$$ $$5$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$23$$ $$25$$ $$1$$ $$1$$ $$e\left(\frac{1}{192}\right)$$ $$e\left(\frac{11}{192}\right)$$ $$e\left(\frac{1}{96}\right)$$ $$e\left(\frac{103}{192}\right)$$ $$e\left(\frac{23}{64}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{125}{192}\right)$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{11}{96}\right)$$
 value at e.g. 2