# Properties

 Modulus 861 Structure $$C_{120}\times C_{2}\times C_{2}$$ Order 480

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(861)

pari: g = idealstar(,861,2)

## Character group

 sage: G.order()  pari: g.no Order = 480 sage: H.invariants()  pari: g.cyc Structure = $$C_{120}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{861}(334,\cdot)$, $\chi_{861}(286,\cdot)$, $\chi_{861}(575,\cdot)$

## First 32 of 480 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.

orbit label order primitive -1 1 2 4 5 8 10 11 13 16 17 19
$$\chi_{861}(1,\cdot)$$ 861.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{861}(2,\cdot)$$ 861.ch 60 yes $$-1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{31}{60}\right)$$
$$\chi_{861}(4,\cdot)$$ 861.bz 30 no $$1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{861}(5,\cdot)$$ 861.cg 60 yes $$1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$
$$\chi_{861}(8,\cdot)$$ 861.bl 20 no $$-1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{861}(10,\cdot)$$ 861.by 30 no $$-1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$
$$\chi_{861}(11,\cdot)$$ 861.cl 120 yes $$1$$ $$1$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{47}{120}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{77}{120}\right)$$ $$e\left(\frac{1}{120}\right)$$
$$\chi_{861}(13,\cdot)$$ 861.cd 40 no $$1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{19}{40}\right)$$
$$\chi_{861}(16,\cdot)$$ 861.bk 15 no $$1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{861}(17,\cdot)$$ 861.cj 120 yes $$-1$$ $$1$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{77}{120}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{107}{120}\right)$$ $$e\left(\frac{31}{120}\right)$$
$$\chi_{861}(19,\cdot)$$ 861.ci 120 no $$1$$ $$1$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{120}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{31}{120}\right)$$ $$e\left(\frac{23}{120}\right)$$
$$\chi_{861}(20,\cdot)$$ 861.bm 20 yes $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$
$$\chi_{861}(22,\cdot)$$ 861.cb 40 no $$-1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$
$$\chi_{861}(23,\cdot)$$ 861.bu 30 yes $$-1$$ $$1$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$
$$\chi_{861}(25,\cdot)$$ 861.bz 30 no $$1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{861}(26,\cdot)$$ 861.cj 120 yes $$-1$$ $$1$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{13}{120}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{43}{120}\right)$$ $$e\left(\frac{119}{120}\right)$$
$$\chi_{861}(29,\cdot)$$ 861.ca 40 no $$1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$
$$\chi_{861}(31,\cdot)$$ 861.bx 30 no $$-1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$
$$\chi_{861}(32,\cdot)$$ 861.bg 12 yes $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{861}(34,\cdot)$$ 861.cd 40 no $$1$$ $$1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{31}{40}\right)$$
$$\chi_{861}(37,\cdot)$$ 861.bk 15 no $$1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{861}(38,\cdot)$$ 861.br 24 yes $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{17}{24}\right)$$
$$\chi_{861}(40,\cdot)$$ 861.q 6 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{861}(43,\cdot)$$ 861.bo 20 no $$1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$
$$\chi_{861}(44,\cdot)$$ 861.bp 24 yes $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{1}{24}\right)$$
$$\chi_{861}(46,\cdot)$$ 861.ce 60 no $$1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{17}{60}\right)$$
$$\chi_{861}(47,\cdot)$$ 861.cj 120 yes $$-1$$ $$1$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{109}{120}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{19}{120}\right)$$ $$e\left(\frac{47}{120}\right)$$
$$\chi_{861}(50,\cdot)$$ 861.m 4 no $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-i$$ $$i$$ $$1$$ $$i$$ $$-i$$
$$\chi_{861}(52,\cdot)$$ 861.ci 120 no $$1$$ $$1$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{107}{120}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{77}{120}\right)$$ $$e\left(\frac{61}{120}\right)$$
$$\chi_{861}(53,\cdot)$$ 861.cl 120 yes $$1$$ $$1$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{23}{120}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{53}{120}\right)$$ $$e\left(\frac{49}{120}\right)$$
$$\chi_{861}(55,\cdot)$$ 861.v 8 no $$1$$ $$1$$ $$i$$ $$-1$$ $$i$$ $$-i$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{861}(58,\cdot)$$ 861.ck 120 no $$-1$$ $$1$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{97}{120}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{67}{120}\right)$$ $$e\left(\frac{11}{120}\right)$$