# Properties

 Modulus $572$ Structure $$C_{60}\times C_{2}\times C_{2}$$ Order $240$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(572)

pari: g = idealstar(,572,2)

## Character group

 sage: G.order()  pari: g.no Order = 240 sage: H.invariants()  pari: g.cyc Structure = $$C_{60}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{572}(287,\cdot)$, $\chi_{572}(365,\cdot)$, $\chi_{572}(353,\cdot)$

## First 32 of 240 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$15$$ $$17$$ $$19$$ $$21$$ $$23$$ $$25$$
$$\chi_{572}(1,\cdot)$$ 572.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{572}(3,\cdot)$$ 572.bl 30 yes $$-1$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{572}(5,\cdot)$$ 572.bi 20 no $$-1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$i$$ $$-1$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{572}(7,\cdot)$$ 572.bt 60 yes $$-1$$ $$1$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{572}(9,\cdot)$$ 572.bg 15 no $$1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{572}(15,\cdot)$$ 572.bs 60 yes $$1$$ $$1$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{572}(17,\cdot)$$ 572.br 30 no $$-1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{572}(19,\cdot)$$ 572.bt 60 yes $$-1$$ $$1$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{572}(21,\cdot)$$ 572.m 4 no $$1$$ $$1$$ $$1$$ $$i$$ $$i$$ $$1$$ $$i$$ $$1$$ $$-i$$ $$i$$ $$-1$$ $$-1$$
$$\chi_{572}(23,\cdot)$$ 572.r 6 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$1$$
$$\chi_{572}(25,\cdot)$$ 572.x 10 no $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{572}(27,\cdot)$$ 572.z 10 no $$-1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{572}(29,\cdot)$$ 572.bp 30 no $$-1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{572}(31,\cdot)$$ 572.bk 20 yes $$1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$i$$ $$1$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{572}(35,\cdot)$$ 572.bm 30 yes $$1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{572}(37,\cdot)$$ 572.bu 60 no $$-1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{572}(41,\cdot)$$ 572.bv 60 no $$1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{572}(43,\cdot)$$ 572.s 6 yes $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$1$$
$$\chi_{572}(45,\cdot)$$ 572.bd 12 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$-i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$
$$\chi_{572}(47,\cdot)$$ 572.bk 20 yes $$1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$-i$$ $$1$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{572}(49,\cdot)$$ 572.bq 30 no $$1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{572}(51,\cdot)$$ 572.bb 10 yes $$1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{572}(53,\cdot)$$ 572.n 5 no $$1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{572}(57,\cdot)$$ 572.bh 20 no $$1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$-i$$ $$-1$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{572}(59,\cdot)$$ 572.bs 60 yes $$1$$ $$1$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{572}(61,\cdot)$$ 572.bp 30 no $$-1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{572}(63,\cdot)$$ 572.bt 60 yes $$-1$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{572}(67,\cdot)$$ 572.bf 12 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$
$$\chi_{572}(69,\cdot)$$ 572.bq 30 no $$1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{572}(71,\cdot)$$ 572.bs 60 yes $$1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{572}(73,\cdot)$$ 572.bh 20 no $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$i$$ $$-1$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{572}(75,\cdot)$$ 572.bo 30 yes $$-1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{4}{5}\right)$$