# Properties

 Label 2880.11 Modulus $2880$ Conductor $576$ Order $48$ Real no Primitive no Minimal yes Parity even

# Related objects

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

sage: H = DirichletGroup(2880, base_ring=CyclotomicField(48))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([24,15,8,0]))

pari: [g,chi] = znchar(Mod(11,2880))

## Basic properties

 Modulus: $$2880$$ 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 $$\chi_{576}(11,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 2880.ff

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

$$(2431,901,641,577)$$ → $$(-1,e\left(\frac{5}{16}\right),e\left(\frac{1}{6}\right),1)$$

## Values

 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$1$$ $$1$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$i$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{5}{24}\right)$$
 value at e.g. 2