# Properties

 Modulus $9360$ Structure $$C_{2}\times C_{2}\times C_{4}\times C_{12}\times C_{12}$$ Order $2304$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(9360)

pari: g = idealstar(,9360,2)

## Character group

 sage: G.order()  pari: g.no Order = 2304 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{4}\times C_{12}\times C_{12}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{9360}(8191,\cdot)$, $\chi_{9360}(2341,\cdot)$, $\chi_{9360}(2081,\cdot)$, $\chi_{9360}(5617,\cdot)$, $\chi_{9360}(5761,\cdot)$

## First 32 of 2304 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character Orbit Order Primitive $$-1$$ $$1$$ $$7$$ $$11$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$
$$\chi_{9360}(1,\cdot)$$ 9360.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{9360}(7,\cdot)$$ 9360.kx 12 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$i$$
$$\chi_{9360}(11,\cdot)$$ 9360.xm 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{9360}(17,\cdot)$$ 9360.pk 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{9360}(19,\cdot)$$ 9360.vx 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{9360}(23,\cdot)$$ 9360.pp 12 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$1$$ $$i$$
$$\chi_{9360}(29,\cdot)$$ 9360.mf 12 yes $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{9360}(31,\cdot)$$ 9360.qr 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{9360}(37,\cdot)$$ 9360.yj 12 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{9360}(41,\cdot)$$ 9360.rt 12 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$i$$ $$1$$
$$\chi_{9360}(43,\cdot)$$ 9360.sw 12 yes $$1$$ $$1$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$1$$
$$\chi_{9360}(47,\cdot)$$ 9360.zi 12 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$i$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{9360}(49,\cdot)$$ 9360.kk 6 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$-1$$
$$\chi_{9360}(53,\cdot)$$ 9360.du 4 no $$1$$ $$1$$ $$i$$ $$-i$$ $$i$$ $$i$$ $$i$$ $$-i$$ $$1$$ $$1$$ $$1$$ $$-1$$
$$\chi_{9360}(59,\cdot)$$ 9360.xz 12 yes $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{9360}(61,\cdot)$$ 9360.kq 12 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-1$$ $$-i$$
$$\chi_{9360}(67,\cdot)$$ 9360.lg 12 yes $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$-1$$
$$\chi_{9360}(71,\cdot)$$ 9360.rn 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{9360}(73,\cdot)$$ 9360.by 4 no $$1$$ $$1$$ $$-1$$ $$i$$ $$i$$ $$i$$ $$-i$$ $$1$$ $$i$$ $$1$$ $$i$$ $$i$$
$$\chi_{9360}(77,\cdot)$$ 9360.te 12 yes $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{9360}(79,\cdot)$$ 9360.he 6 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{9360}(83,\cdot)$$ 9360.lu 12 yes $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-i$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{9360}(89,\cdot)$$ 9360.uw 12 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{9360}(97,\cdot)$$ 9360.lb 12 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$i$$
$$\chi_{9360}(101,\cdot)$$ 9360.ni 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{9360}(103,\cdot)$$ 9360.wv 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{9360}(107,\cdot)$$ 9360.sb 12 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{9360}(109,\cdot)$$ 9360.es 4 no $$-1$$ $$1$$ $$i$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$i$$ $$-i$$ $$-1$$ $$i$$ $$-i$$
$$\chi_{9360}(113,\cdot)$$ 9360.op 12 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{9360}(119,\cdot)$$ 9360.us 12 no $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{9360}(121,\cdot)$$ 9360.jp 6 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{9360}(127,\cdot)$$ 9360.pz 12 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$