# Properties

 Modulus $900$ Structure $$C_{60}\times C_{2}\times C_{2}$$ Order $240$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(900)

pari: g = idealstar(,900,2)

## 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 = $\chi_{900}(451,\cdot)$, $\chi_{900}(101,\cdot)$, $\chi_{900}(577,\cdot)$

## 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 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{900}(1,\cdot)$$ 900.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{900}(7,\cdot)$$ 900.bf 12 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$i$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{900}(11,\cdot)$$ 900.br 30 yes $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{900}(13,\cdot)$$ 900.bv 60 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{900}(17,\cdot)$$ 900.bk 20 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{900}(19,\cdot)$$ 900.bb 10 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{900}(23,\cdot)$$ 900.bu 60 yes $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{900}(29,\cdot)$$ 900.bo 30 no $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{900}(31,\cdot)$$ 900.bp 30 yes $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{900}(37,\cdot)$$ 900.bi 20 no $$-1$$ $$1$$ $$i$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{900}(41,\cdot)$$ 900.bm 30 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{900}(43,\cdot)$$ 900.bf 12 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-i$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{900}(47,\cdot)$$ 900.bu 60 yes $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{900}(49,\cdot)$$ 900.s 6 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{900}(53,\cdot)$$ 900.bk 20 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{900}(59,\cdot)$$ 900.bn 30 yes $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{900}(61,\cdot)$$ 900.bg 15 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$
$$\chi_{900}(67,\cdot)$$ 900.bs 60 yes $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{900}(71,\cdot)$$ 900.v 10 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{900}(73,\cdot)$$ 900.bi 20 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{900}(77,\cdot)$$ 900.bt 60 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{900}(79,\cdot)$$ 900.bl 30 yes $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{900}(83,\cdot)$$ 900.bu 60 yes $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{13}{30}\right)$$
$$\chi_{900}(89,\cdot)$$ 900.y 10 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{900}(91,\cdot)$$ 900.x 10 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{900}(97,\cdot)$$ 900.bv 60 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{900}(101,\cdot)$$ 900.p 6 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{900}(103,\cdot)$$ 900.bs 60 yes $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{900}(107,\cdot)$$ 900.m 4 no $$-1$$ $$1$$ $$-i$$ $$1$$ $$-i$$ $$-i$$ $$1$$ $$-i$$ $$1$$ $$-1$$ $$i$$ $$-1$$
$$\chi_{900}(109,\cdot)$$ 900.w 10 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{900}(113,\cdot)$$ 900.bt 60 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{900}(119,\cdot)$$ 900.bn 30 yes $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{30}\right)$$