# Properties

 Modulus 6039 Structure $$C_{60}\times C_{30}\times C_{2}$$ Order 3600

# Learn more about

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(6039)
pari: g = idealstar(,6039,2)

## Character group

 sage: G.order() pari: g.no Order = 3600 sage: H.invariants() pari: g.cyc Structure = $$C_{60}\times C_{30}\times C_{2}$$ sage: H.gens() pari: g.gen Generators = $\chi_{6039}(5248,\cdot)$, $\chi_{6039}(4820,\cdot)$, $\chi_{6039}(1099,\cdot)$

## First 32 of 3600 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 7 8 10 13 14 16 17
$$\chi_{6039}(1,\cdot)$$ 6039.a 1 No $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{6039}(2,\cdot)$$ 6039.nc 60 Yes $$-1$$ $$1$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{60}\right)$$
$$\chi_{6039}(4,\cdot)$$ 6039.hj 30 Yes $$1$$ $$1$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{6039}(5,\cdot)$$ 6039.hb 30 Yes $$-1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{6039}(7,\cdot)$$ 6039.oo 60 Yes $$1$$ $$1$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{41}{60}\right)$$
$$\chi_{6039}(8,\cdot)$$ 6039.fm 20 No $$-1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{6039}(10,\cdot)$$ 6039.nt 60 No $$1$$ $$1$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{31}{60}\right)$$
$$\chi_{6039}(13,\cdot)$$ 6039.lt 30 Yes $$-1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{6039}(14,\cdot)$$ 6039.ku 30 Yes $$-1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{6039}(16,\cdot)$$ 6039.eq 15 Yes $$1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{6039}(17,\cdot)$$ 6039.mt 60 No $$-1$$ $$1$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{6039}(19,\cdot)$$ 6039.kj 30 No $$-1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{6039}(20,\cdot)$$ 6039.ma 30 Yes $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$-1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{6039}(23,\cdot)$$ 6039.nv 60 No $$1$$ $$1$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{3}{20}\right)$$
$$\chi_{6039}(25,\cdot)$$ 6039.eh 15 Yes $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{6039}(26,\cdot)$$ 6039.mu 60 No $$1$$ $$1$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{6039}(28,\cdot)$$ 6039.ff 20 No $$1$$ $$1$$ $$-i$$ $$-1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$i$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$1$$ $$e\left(\frac{1}{20}\right)$$
$$\chi_{6039}(29,\cdot)$$ 6039.pk 60 Yes $$-1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{60}\right)$$
$$\chi_{6039}(31,\cdot)$$ 6039.qc 60 Yes $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$-i$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{37}{60}\right)$$
$$\chi_{6039}(32,\cdot)$$ 6039.ec 12 Yes $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{6039}(34,\cdot)$$ 6039.ev 15 No $$1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{6039}(35,\cdot)$$ 6039.nz 60 No $$-1$$ $$1$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{60}\right)$$
$$\chi_{6039}(37,\cdot)$$ 6039.fr 20 No $$-1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$i$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$
$$\chi_{6039}(38,\cdot)$$ 6039.mv 60 Yes $$1$$ $$1$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$i$$
$$\chi_{6039}(40,\cdot)$$ 6039.pd 60 Yes $$1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{53}{60}\right)$$
$$\chi_{6039}(41,\cdot)$$ 6039.je 30 Yes $$1$$ $$1$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$-1$$
$$\chi_{6039}(43,\cdot)$$ 6039.ok 60 Yes $$1$$ $$1$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{11}{60}\right)$$
$$\chi_{6039}(46,\cdot)$$ 6039.jn 30 No $$-1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{6039}(47,\cdot)$$ 6039.lg 30 Yes $$-1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{6039}(49,\cdot)$$ 6039.ho 30 Yes $$1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{6039}(50,\cdot)$$ 6039.nx 60 Yes $$-1$$ $$1$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$-i$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{17}{20}\right)$$
$$\chi_{6039}(52,\cdot)$$ 6039.gj 30 Yes $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{3}{5}\right)$$