Properties

 Label 2960.gm Modulus $2960$ Conductor $740$ Order $36$ Real no Primitive no Minimal yes Parity even

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

sage: H = DirichletGroup(2960, base_ring=CyclotomicField(36))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([18,0,18,23]))

sage: chi.galois_orbit()

pari: [g,chi] = znchar(Mod(79,2960))

pari: order = charorder(g,chi)

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

Basic properties

 Modulus: $$2960$$ Conductor: $$740$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$36$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from 740.ca sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

Characters in Galois orbit

Character $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$21$$ $$23$$ $$27$$
$$\chi_{2960}(79,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{2960}(239,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2960}(479,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2960}(799,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2960}(1199,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2960}(1519,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2960}(1759,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2960}(1919,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{2960}(2159,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{2960}(2239,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{2960}(2719,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{2960}(2799,\cdot)$$ $$1$$ $$1$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$