# Properties

 Label 1152.5 Modulus $1152$ Conductor $1152$ Order $96$ Real no Primitive yes Minimal yes Parity odd

# Learn more

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

sage: H = DirichletGroup(1152, base_ring=CyclotomicField(96))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,3,80]))

pari: [g,chi] = znchar(Mod(5,1152))

## Basic properties

 Modulus: $$1152$$ Conductor: $$1152$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$96$$ 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 1152.bt

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: $\Q(\zeta_{96})$ Fixed field: Number field defined by a degree 96 polynomial

## Values on generators

$$(127,901,641)$$ → $$(1,e\left(\frac{1}{32}\right),e\left(\frac{5}{6}\right))$$

## Values

 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$-1$$ $$1$$ $$e\left(\frac{19}{96}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{47}{96}\right)$$ $$e\left(\frac{13}{96}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{23}{32}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{65}{96}\right)$$ $$e\left(\frac{11}{12}\right)$$
 value at e.g. 2