# Properties

 Label 1152.7 Modulus $1152$ Conductor $576$ Order $48$ Real no Primitive no Minimal no Parity odd

# Learn more

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

sage: H = DirichletGroup(1152, base_ring=CyclotomicField(48))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([24,15,32]))

pari: [g,chi] = znchar(Mod(7,1152))

## Basic properties

 Modulus: $$1152$$ Conductor: $$576$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$48$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{576}(331,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: no Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 1152.bo

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: $$\Q(\zeta_{48})$$ Fixed field: Number field defined by a degree 48 polynomial

## Values on generators

$$(127,901,641)$$ → $$(-1,e\left(\frac{5}{16}\right),e\left(\frac{2}{3}\right))$$

## Values

 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$-1$$ $$1$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$-i$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{1}{3}\right)$$
 value at e.g. 2