# Properties

 Modulus $546$ Structure $$C_{12}\times C_{6}\times C_{2}$$ Order $144$

# Learn more

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(546)

pari: g = idealstar(,546,2)

## Character group

 sage: G.order()  pari: g.no Order = 144 sage: H.invariants()  pari: g.cyc Structure = $$C_{12}\times C_{6}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{546}(365,\cdot)$, $\chi_{546}(157,\cdot)$, $\chi_{546}(379,\cdot)$

## First 32 of 144 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 $$-1$$ $$1$$ $$5$$ $$11$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{546}(1,\cdot)$$ 546.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{546}(5,\cdot)$$ 546.cb 12 no $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-i$$
$$\chi_{546}(11,\cdot)$$ 546.bw 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$i$$ $$e\left(\frac{1}{3}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{546}(17,\cdot)$$ 546.bi 6 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{546}(19,\cdot)$$ 546.by 12 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{546}(23,\cdot)$$ 546.w 6 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{546}(25,\cdot)$$ 546.bk 6 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$
$$\chi_{546}(29,\cdot)$$ 546.t 6 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{546}(31,\cdot)$$ 546.bz 12 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$
$$\chi_{546}(37,\cdot)$$ 546.bs 12 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-i$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{546}(41,\cdot)$$ 546.ca 12 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{546}(43,\cdot)$$ 546.s 6 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{546}(47,\cdot)$$ 546.cb 12 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$i$$
$$\chi_{546}(53,\cdot)$$ 546.bl 6 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$
$$\chi_{546}(55,\cdot)$$ 546.r 6 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{546}(59,\cdot)$$ 546.bt 12 no $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-1$$ $$e\left(\frac{5}{12}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-i$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{546}(61,\cdot)$$ 546.bo 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{546}(67,\cdot)$$ 546.ce 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{546}(71,\cdot)$$ 546.bu 12 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{546}(73,\cdot)$$ 546.bz 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$
$$\chi_{546}(79,\cdot)$$ 546.i 3 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$
$$\chi_{546}(83,\cdot)$$ 546.n 4 no $$-1$$ $$1$$ $$-i$$ $$-i$$ $$-1$$ $$i$$ $$1$$ $$-1$$ $$-1$$ $$i$$ $$i$$ $$-i$$
$$\chi_{546}(85,\cdot)$$ 546.cd 12 no $$-1$$ $$1$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{546}(89,\cdot)$$ 546.bt 12 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$ $$e\left(\frac{1}{12}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{546}(95,\cdot)$$ 546.w 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{546}(97,\cdot)$$ 546.bx 12 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{546}(101,\cdot)$$ 546.bn 6 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{546}(103,\cdot)$$ 546.ba 6 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$
$$\chi_{546}(107,\cdot)$$ 546.bj 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{546}(109,\cdot)$$ 546.cf 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-i$$
$$\chi_{546}(113,\cdot)$$ 546.t 6 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{546}(115,\cdot)$$ 546.by 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$