Properties

 Label 1148.bt Modulus $1148$ Conductor $287$ Order $30$ Real no Primitive no Minimal yes Parity odd

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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([0,5,9]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(45,1148))

pari: order = charorder(g,chi)

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

Basic properties

 Modulus: $$1148$$ Conductor: $$287$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$30$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 287.x sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: odd sage: chi.is_odd()  pari: zncharisodd(g,chi)

Related number fields

 Field of values: $$\Q(\zeta_{15})$$ Fixed field: 30.0.47056013503315267757707869738647378732273238450224554604301383567.1

Characters in Galois orbit

Character $$-1$$ $$1$$ $$3$$ $$5$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$23$$ $$25$$
$$\chi_{1148}(45,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{1148}(269,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{1148}(353,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{1148}(537,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$
$$\chi_{1148}(605,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{1148}(761,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{1148}(845,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{1148}(1097,\cdot)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$