Properties

 Label 1148.bw Modulus $1148$ Conductor $1148$ Order $30$ 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(1148, base_ring=CyclotomicField(30))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([15,5,21]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(31,1148))

pari: order = charorder(g,chi)

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

Basic properties

 Modulus: $$1148$$ Conductor: $$1148$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$30$$ 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)

Related number fields

 Field of values: $$\Q(\zeta_{15})$$ Fixed field: Number field defined by a degree 30 polynomial

Characters in Galois orbit

Character $$-1$$ $$1$$ $$3$$ $$5$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$23$$ $$25$$
$$\chi_{1148}(31,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{1148}(187,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{1148}(271,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{1148}(523,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$
$$\chi_{1148}(619,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{1148}(843,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{1148}(927,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{1148}(1111,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$