# Properties

 Modulus $1872$ Structure $$C_{12}\times C_{12}\times C_{2}\times C_{2}$$ Order $576$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1872)

pari: g = idealstar(,1872,2)

## Character group

 sage: G.order()  pari: g.no Order = 576 sage: H.invariants()  pari: g.cyc Structure = $$C_{12}\times C_{12}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1872}(703,\cdot)$, $\chi_{1872}(469,\cdot)$, $\chi_{1872}(209,\cdot)$, $\chi_{1872}(145,\cdot)$

## First 32 of 576 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 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$35$$
$$\chi_{1872}(1,\cdot)$$ 1872.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1872}(5,\cdot)$$ 1872.hh 12 yes $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$i$$
$$\chi_{1872}(7,\cdot)$$ 1872.gh 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1872}(11,\cdot)$$ 1872.eo 12 yes $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{1872}(17,\cdot)$$ 1872.dx 6 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1872}(19,\cdot)$$ 1872.ed 12 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{1872}(23,\cdot)$$ 1872.dq 6 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1872}(25,\cdot)$$ 1872.cn 6 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$
$$\chi_{1872}(29,\cdot)$$ 1872.gt 12 yes $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{1872}(31,\cdot)$$ 1872.fg 12 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$
$$\chi_{1872}(35,\cdot)$$ 1872.fc 12 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{5}{12}\right)$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{1872}(37,\cdot)$$ 1872.eb 12 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$i$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{1872}(41,\cdot)$$ 1872.fu 12 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1872}(43,\cdot)$$ 1872.er 12 yes $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{1872}(47,\cdot)$$ 1872.gl 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$1$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$1$$
$$\chi_{1872}(49,\cdot)$$ 1872.cx 6 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1872}(53,\cdot)$$ 1872.z 4 no $$-1$$ $$1$$ $$-i$$ $$-1$$ $$-i$$ $$-1$$ $$-i$$ $$1$$ $$-1$$ $$i$$ $$1$$ $$i$$
$$\chi_{1872}(55,\cdot)$$ 1872.bw 6 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1872}(59,\cdot)$$ 1872.eo 12 yes $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{1872}(61,\cdot)$$ 1872.eq 12 yes $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{1872}(67,\cdot)$$ 1872.hk 12 yes $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{1872}(71,\cdot)$$ 1872.fq 12 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1872}(73,\cdot)$$ 1872.bc 4 no $$-1$$ $$1$$ $$-i$$ $$-i$$ $$i$$ $$-1$$ $$-i$$ $$-1$$ $$-1$$ $$-1$$ $$i$$ $$-1$$
$$\chi_{1872}(77,\cdot)$$ 1872.eu 12 yes $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$
$$\chi_{1872}(79,\cdot)$$ 1872.cp 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$
$$\chi_{1872}(83,\cdot)$$ 1872.ej 12 yes $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$
$$\chi_{1872}(85,\cdot)$$ 1872.hn 12 yes $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{1872}(89,\cdot)$$ 1872.fm 12 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1872}(95,\cdot)$$ 1872.cf 6 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1872}(97,\cdot)$$ 1872.fw 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1872}(101,\cdot)$$ 1872.fb 12 yes $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{1872}(103,\cdot)$$ 1872.ci 6 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$