# Properties

 Modulus $4680$ Structure $$C_{2}\times C_{2}\times C_{2}\times C_{12}\times C_{12}$$ Order $1152$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4680)

pari: g = idealstar(,4680,2)

## Character group

 sage: G.order()  pari: g.no Order = 1152 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{2}\times C_{12}\times C_{12}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{4680}(3511,\cdot)$, $\chi_{4680}(2341,\cdot)$, $\chi_{4680}(2081,\cdot)$, $\chi_{4680}(937,\cdot)$, $\chi_{4680}(1081,\cdot)$

## First 32 of 1152 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 $$-1$$ $$1$$ $$7$$ $$11$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$
$$\chi_{4680}(1,\cdot)$$ 4680.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4680}(7,\cdot)$$ 4680.if 12 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$-i$$
$$\chi_{4680}(11,\cdot)$$ 4680.ln 12 no $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4680}(17,\cdot)$$ 4680.js 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{4680}(19,\cdot)$$ 4680.ll 12 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{4680}(23,\cdot)$$ 4680.nl 12 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$1$$ $$-i$$
$$\chi_{4680}(29,\cdot)$$ 4680.hf 6 yes $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{4680}(31,\cdot)$$ 4680.kn 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{4680}(37,\cdot)$$ 4680.ir 12 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{4680}(41,\cdot)$$ 4680.lq 12 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$-1$$
$$\chi_{4680}(43,\cdot)$$ 4680.nc 12 yes $$1$$ $$1$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-1$$ $$i$$
$$\chi_{4680}(47,\cdot)$$ 4680.oo 12 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$i$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{4680}(49,\cdot)$$ 4680.hy 6 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$-1$$
$$\chi_{4680}(53,\cdot)$$ 4680.cu 4 no $$1$$ $$1$$ $$-i$$ $$1$$ $$i$$ $$1$$ $$-i$$ $$-1$$ $$1$$ $$i$$ $$-1$$ $$-i$$
$$\chi_{4680}(59,\cdot)$$ 4680.mc 12 yes $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{4680}(61,\cdot)$$ 4680.hv 6 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$-1$$
$$\chi_{4680}(67,\cdot)$$ 4680.pc 12 yes $$-1$$ $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$i$$
$$\chi_{4680}(71,\cdot)$$ 4680.lk 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{4680}(73,\cdot)$$ 4680.bk 4 no $$1$$ $$1$$ $$-1$$ $$-i$$ $$i$$ $$-i$$ $$-i$$ $$-1$$ $$i$$ $$-1$$ $$i$$ $$-i$$
$$\chi_{4680}(77,\cdot)$$ 4680.na 12 yes $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$-1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{4680}(79,\cdot)$$ 4680.es 6 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{4680}(83,\cdot)$$ 4680.oq 12 yes $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-i$$ $$i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{4680}(89,\cdot)$$ 4680.mj 12 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{4680}(97,\cdot)$$ 4680.ih 12 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$i$$
$$\chi_{4680}(101,\cdot)$$ 4680.fu 6 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4680}(103,\cdot)$$ 4680.jr 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$-1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{4680}(107,\cdot)$$ 4680.np 12 no $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{4680}(109,\cdot)$$ 4680.cn 4 no $$-1$$ $$1$$ $$-i$$ $$-i$$ $$1$$ $$i$$ $$1$$ $$-1$$ $$-i$$ $$i$$ $$-i$$ $$-1$$
$$\chi_{4680}(113,\cdot)$$ 4680.jn 12 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{4680}(119,\cdot)$$ 4680.lx 12 no $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4680}(121,\cdot)$$ 4680.fr 6 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{4680}(127,\cdot)$$ 4680.kh 12 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$