# Properties

 Modulus $2015$ Structure $$C_{60}\times C_{12}\times C_{2}$$ Order $1440$

Show commands for: Pari/GP / SageMath

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

sage: H = DirichletGroup_conrey(2015)

pari: g = idealstar(,2015,2)

## Character group

 sage: G.order()  pari: g.no Order = 1440 sage: H.invariants()  pari: g.cyc Structure = $$C_{60}\times C_{12}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2015}(313,\cdot)$, $\chi_{2015}(1861,\cdot)$, $\chi_{2015}(1704,\cdot)$

## First 32 of 1440 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$6$$ $$7$$ $$8$$ $$9$$ $$11$$ $$12$$ $$14$$
$$\chi_{2015}(1,\cdot)$$ 2015.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2015}(2,\cdot)$$ 2015.hk 60 yes $$1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{2015}(3,\cdot)$$ 2015.gn 60 yes $$1$$ $$1$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$-1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{2015}(4,\cdot)$$ 2015.fm 30 yes $$1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{2015}(6,\cdot)$$ 2015.cr 12 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{2015}(7,\cdot)$$ 2015.gc 60 yes $$1$$ $$1$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{2015}(8,\cdot)$$ 2015.ej 20 yes $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$i$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{2015}(9,\cdot)$$ 2015.fb 30 yes $$1$$ $$1$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{2015}(11,\cdot)$$ 2015.hi 60 no $$1$$ $$1$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{2015}(12,\cdot)$$ 2015.gz 60 yes $$1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$
$$\chi_{2015}(14,\cdot)$$ 2015.ft 30 no $$1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$
$$\chi_{2015}(16,\cdot)$$ 2015.eg 15 no $$1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{2015}(17,\cdot)$$ 2015.gr 60 yes $$1$$ $$1$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$
$$\chi_{2015}(18,\cdot)$$ 2015.hr 60 yes $$1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$
$$\chi_{2015}(19,\cdot)$$ 2015.hj 60 yes $$-1$$ $$1$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{2015}(21,\cdot)$$ 2015.gl 60 no $$1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{2015}(22,\cdot)$$ 2015.gn 60 yes $$1$$ $$1$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$-1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{2015}(23,\cdot)$$ 2015.gp 60 yes $$1$$ $$1$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{2015}(24,\cdot)$$ 2015.hc 60 yes $$1$$ $$1$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$-i$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$
$$\chi_{2015}(27,\cdot)$$ 2015.en 20 no $$1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$-1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{2015}(28,\cdot)$$ 2015.fy 60 yes $$1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$-i$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{2015}(29,\cdot)$$ 2015.fg 30 yes $$-1$$ $$1$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{2015}(32,\cdot)$$ 2015.cp 12 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-i$$ $$-1$$
$$\chi_{2015}(33,\cdot)$$ 2015.hk 60 yes $$1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{2015}(34,\cdot)$$ 2015.hh 60 yes $$1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{2015}(36,\cdot)$$ 2015.bx 6 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{2015}(37,\cdot)$$ 2015.ea 12 yes $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-i$$ $$1$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{2015}(38,\cdot)$$ 2015.hb 60 yes $$-1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{2015}(41,\cdot)$$ 2015.gf 60 no $$-1$$ $$1$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{2015}(42,\cdot)$$ 2015.gu 60 yes $$1$$ $$1$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{2015}(43,\cdot)$$ 2015.gr 60 yes $$1$$ $$1$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$
$$\chi_{2015}(44,\cdot)$$ 2015.hh 60 yes $$1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$