# Properties

 Modulus 8015 Structure $$C_{228}\times C_{12}\times C_{2}$$ Order 5472

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(8015)

pari: g = idealstar(,8015,2)

## Character group

 sage: G.order()  pari: g.no Order = 5472 sage: H.invariants()  pari: g.cyc Structure = $$C_{228}\times C_{12}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{8015}(4586,\cdot)$, $\chi_{8015}(2978,\cdot)$, $\chi_{8015}(5039,\cdot)$

## First 32 of 5472 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 3 4 6 8 9 11 12 13 16
$$\chi_{8015}(1,\cdot)$$ 8015.a 1 No $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{8015}(2,\cdot)$$ 8015.fy 228 Yes $$1$$ $$1$$ $$e\left(\frac{97}{114}\right)$$ $$e\left(\frac{55}{228}\right)$$ $$e\left(\frac{40}{57}\right)$$ $$e\left(\frac{7}{76}\right)$$ $$e\left(\frac{21}{38}\right)$$ $$e\left(\frac{55}{114}\right)$$ $$e\left(\frac{29}{114}\right)$$ $$e\left(\frac{215}{228}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{23}{57}\right)$$
$$\chi_{8015}(3,\cdot)$$ 8015.gq 228 Yes $$1$$ $$1$$ $$e\left(\frac{55}{228}\right)$$ $$e\left(\frac{13}{76}\right)$$ $$e\left(\frac{55}{114}\right)$$ $$e\left(\frac{47}{114}\right)$$ $$e\left(\frac{55}{76}\right)$$ $$e\left(\frac{13}{38}\right)$$ $$e\left(\frac{26}{57}\right)$$ $$e\left(\frac{149}{228}\right)$$ $$e\left(\frac{37}{76}\right)$$ $$e\left(\frac{55}{57}\right)$$
$$\chi_{8015}(4,\cdot)$$ 8015.fm 114 Yes $$1$$ $$1$$ $$e\left(\frac{40}{57}\right)$$ $$e\left(\frac{55}{114}\right)$$ $$e\left(\frac{23}{57}\right)$$ $$e\left(\frac{7}{38}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{55}{57}\right)$$ $$e\left(\frac{29}{57}\right)$$ $$e\left(\frac{101}{114}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{46}{57}\right)$$
$$\chi_{8015}(6,\cdot)$$ 8015.gk 228 No $$1$$ $$1$$ $$e\left(\frac{7}{76}\right)$$ $$e\left(\frac{47}{114}\right)$$ $$e\left(\frac{7}{38}\right)$$ $$e\left(\frac{115}{228}\right)$$ $$e\left(\frac{21}{76}\right)$$ $$e\left(\frac{47}{57}\right)$$ $$e\left(\frac{27}{38}\right)$$ $$e\left(\frac{34}{57}\right)$$ $$e\left(\frac{1}{76}\right)$$ $$e\left(\frac{7}{19}\right)$$
$$\chi_{8015}(8,\cdot)$$ 8015.es 76 No $$1$$ $$1$$ $$e\left(\frac{21}{38}\right)$$ $$e\left(\frac{55}{76}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{21}{76}\right)$$ $$e\left(\frac{25}{38}\right)$$ $$e\left(\frac{17}{38}\right)$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{63}{76}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{4}{19}\right)$$
$$\chi_{8015}(9,\cdot)$$ 8015.fi 114 Yes $$1$$ $$1$$ $$e\left(\frac{55}{114}\right)$$ $$e\left(\frac{13}{38}\right)$$ $$e\left(\frac{55}{57}\right)$$ $$e\left(\frac{47}{57}\right)$$ $$e\left(\frac{17}{38}\right)$$ $$e\left(\frac{13}{19}\right)$$ $$e\left(\frac{52}{57}\right)$$ $$e\left(\frac{35}{114}\right)$$ $$e\left(\frac{37}{38}\right)$$ $$e\left(\frac{53}{57}\right)$$
$$\chi_{8015}(11,\cdot)$$ 8015.fg 114 No $$1$$ $$1$$ $$e\left(\frac{29}{114}\right)$$ $$e\left(\frac{26}{57}\right)$$ $$e\left(\frac{29}{57}\right)$$ $$e\left(\frac{27}{38}\right)$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{52}{57}\right)$$ $$e\left(\frac{44}{57}\right)$$ $$e\left(\frac{55}{57}\right)$$ $$e\left(\frac{5}{38}\right)$$ $$e\left(\frac{1}{57}\right)$$
$$\chi_{8015}(12,\cdot)$$ 8015.gt 228 Yes $$1$$ $$1$$ $$e\left(\frac{215}{228}\right)$$ $$e\left(\frac{149}{228}\right)$$ $$e\left(\frac{101}{114}\right)$$ $$e\left(\frac{34}{57}\right)$$ $$e\left(\frac{63}{76}\right)$$ $$e\left(\frac{35}{114}\right)$$ $$e\left(\frac{55}{57}\right)$$ $$e\left(\frac{41}{76}\right)$$ $$e\left(\frac{41}{76}\right)$$ $$e\left(\frac{44}{57}\right)$$
$$\chi_{8015}(13,\cdot)$$ 8015.ei 76 Yes $$-1$$ $$1$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{37}{76}\right)$$ $$e\left(\frac{1}{19}\right)$$ $$e\left(\frac{1}{76}\right)$$ $$e\left(\frac{11}{19}\right)$$ $$e\left(\frac{37}{38}\right)$$ $$e\left(\frac{5}{38}\right)$$ $$e\left(\frac{41}{76}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{2}{19}\right)$$
$$\chi_{8015}(16,\cdot)$$ 8015.eg 57 No $$1$$ $$1$$ $$e\left(\frac{23}{57}\right)$$ $$e\left(\frac{55}{57}\right)$$ $$e\left(\frac{46}{57}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{53}{57}\right)$$ $$e\left(\frac{1}{57}\right)$$ $$e\left(\frac{44}{57}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{35}{57}\right)$$
$$\chi_{8015}(17,\cdot)$$ 8015.gx 228 Yes $$1$$ $$1$$ $$e\left(\frac{25}{228}\right)$$ $$e\left(\frac{149}{228}\right)$$ $$e\left(\frac{25}{114}\right)$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{25}{76}\right)$$ $$e\left(\frac{35}{114}\right)$$ $$e\left(\frac{17}{57}\right)$$ $$e\left(\frac{199}{228}\right)$$ $$e\left(\frac{3}{76}\right)$$ $$e\left(\frac{25}{57}\right)$$
$$\chi_{8015}(18,\cdot)$$ 8015.ce 12 Yes $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{8015}(19,\cdot)$$ 8015.ex 114 Yes $$-1$$ $$1$$ $$e\left(\frac{73}{114}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{16}{57}\right)$$ $$e\left(\frac{103}{114}\right)$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{40}{57}\right)$$ $$e\left(\frac{31}{57}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{32}{57}\right)$$
$$\chi_{8015}(22,\cdot)$$ 8015.ej 76 No $$1$$ $$1$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{53}{76}\right)$$ $$e\left(\frac{4}{19}\right)$$ $$e\left(\frac{61}{76}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{15}{38}\right)$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{69}{76}\right)$$ $$e\left(\frac{25}{38}\right)$$ $$e\left(\frac{8}{19}\right)$$
$$\chi_{8015}(23,\cdot)$$ 8015.hm 228 Yes $$1$$ $$1$$ $$e\left(\frac{26}{57}\right)$$ $$e\left(\frac{5}{228}\right)$$ $$e\left(\frac{52}{57}\right)$$ $$e\left(\frac{109}{228}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{5}{114}\right)$$ $$e\left(\frac{89}{114}\right)$$ $$e\left(\frac{71}{76}\right)$$ $$e\left(\frac{7}{38}\right)$$ $$e\left(\frac{47}{57}\right)$$
$$\chi_{8015}(24,\cdot)$$ 8015.gf 228 Yes $$1$$ $$1$$ $$e\left(\frac{181}{228}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{67}{114}\right)$$ $$e\left(\frac{157}{228}\right)$$ $$e\left(\frac{29}{76}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{25}{114}\right)$$ $$e\left(\frac{55}{114}\right)$$ $$e\left(\frac{5}{76}\right)$$ $$e\left(\frac{10}{57}\right)$$
$$\chi_{8015}(26,\cdot)$$ 8015.ez 114 No $$-1$$ $$1$$ $$e\left(\frac{43}{114}\right)$$ $$e\left(\frac{83}{114}\right)$$ $$e\left(\frac{43}{57}\right)$$ $$e\left(\frac{2}{19}\right)$$ $$e\left(\frac{5}{38}\right)$$ $$e\left(\frac{26}{57}\right)$$ $$e\left(\frac{22}{57}\right)$$ $$e\left(\frac{55}{114}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{29}{57}\right)$$
$$\chi_{8015}(27,\cdot)$$ 8015.eo 76 Yes $$1$$ $$1$$ $$e\left(\frac{55}{76}\right)$$ $$e\left(\frac{39}{76}\right)$$ $$e\left(\frac{17}{38}\right)$$ $$e\left(\frac{9}{38}\right)$$ $$e\left(\frac{13}{76}\right)$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{73}{76}\right)$$ $$e\left(\frac{35}{76}\right)$$ $$e\left(\frac{17}{19}\right)$$
$$\chi_{8015}(29,\cdot)$$ 8015.gl 228 No $$-1$$ $$1$$ $$e\left(\frac{65}{76}\right)$$ $$e\left(\frac{89}{114}\right)$$ $$e\left(\frac{27}{38}\right)$$ $$e\left(\frac{145}{228}\right)$$ $$e\left(\frac{43}{76}\right)$$ $$e\left(\frac{32}{57}\right)$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{28}{57}\right)$$ $$e\left(\frac{69}{76}\right)$$ $$e\left(\frac{8}{19}\right)$$
$$\chi_{8015}(31,\cdot)$$ 8015.gg 228 No $$1$$ $$1$$ $$e\left(\frac{1}{228}\right)$$ $$e\left(\frac{71}{114}\right)$$ $$e\left(\frac{1}{114}\right)$$ $$e\left(\frac{143}{228}\right)$$ $$e\left(\frac{1}{76}\right)$$ $$e\left(\frac{14}{57}\right)$$ $$e\left(\frac{31}{114}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{29}{76}\right)$$ $$e\left(\frac{1}{57}\right)$$
$$\chi_{8015}(32,\cdot)$$ 8015.fy 228 Yes $$1$$ $$1$$ $$e\left(\frac{29}{114}\right)$$ $$e\left(\frac{47}{228}\right)$$ $$e\left(\frac{29}{57}\right)$$ $$e\left(\frac{35}{76}\right)$$ $$e\left(\frac{29}{38}\right)$$ $$e\left(\frac{47}{114}\right)$$ $$e\left(\frac{31}{114}\right)$$ $$e\left(\frac{163}{228}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{1}{57}\right)$$
$$\chi_{8015}(33,\cdot)$$ 8015.gt 228 Yes $$1$$ $$1$$ $$e\left(\frac{113}{228}\right)$$ $$e\left(\frac{143}{228}\right)$$ $$e\left(\frac{113}{114}\right)$$ $$e\left(\frac{7}{57}\right)$$ $$e\left(\frac{37}{76}\right)$$ $$e\left(\frac{29}{114}\right)$$ $$e\left(\frac{13}{57}\right)$$ $$e\left(\frac{47}{76}\right)$$ $$e\left(\frac{47}{76}\right)$$ $$e\left(\frac{56}{57}\right)$$
$$\chi_{8015}(34,\cdot)$$ 8015.el 76 Yes $$1$$ $$1$$ $$e\left(\frac{73}{76}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{65}{76}\right)$$ $$e\left(\frac{67}{76}\right)$$ $$e\left(\frac{15}{19}\right)$$ $$e\left(\frac{21}{38}\right)$$ $$e\left(\frac{31}{38}\right)$$ $$e\left(\frac{43}{76}\right)$$ $$e\left(\frac{16}{19}\right)$$
$$\chi_{8015}(36,\cdot)$$ 8015.fv 114 No $$1$$ $$1$$ $$e\left(\frac{7}{38}\right)$$ $$e\left(\frac{47}{57}\right)$$ $$e\left(\frac{7}{19}\right)$$ $$e\left(\frac{1}{114}\right)$$ $$e\left(\frac{21}{38}\right)$$ $$e\left(\frac{37}{57}\right)$$ $$e\left(\frac{8}{19}\right)$$ $$e\left(\frac{11}{57}\right)$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{14}{19}\right)$$
$$\chi_{8015}(37,\cdot)$$ 8015.gs 228 Yes $$-1$$ $$1$$ $$e\left(\frac{41}{228}\right)$$ $$e\left(\frac{179}{228}\right)$$ $$e\left(\frac{41}{114}\right)$$ $$e\left(\frac{55}{57}\right)$$ $$e\left(\frac{41}{76}\right)$$ $$e\left(\frac{65}{114}\right)$$ $$e\left(\frac{37}{57}\right)$$ $$e\left(\frac{11}{76}\right)$$ $$e\left(\frac{49}{76}\right)$$ $$e\left(\frac{41}{57}\right)$$
$$\chi_{8015}(38,\cdot)$$ 8015.hk 228 Yes $$-1$$ $$1$$ $$e\left(\frac{28}{57}\right)$$ $$e\left(\frac{115}{228}\right)$$ $$e\left(\frac{56}{57}\right)$$ $$e\left(\frac{227}{228}\right)$$ $$e\left(\frac{9}{19}\right)$$ $$e\left(\frac{1}{114}\right)$$ $$e\left(\frac{109}{114}\right)$$ $$e\left(\frac{37}{76}\right)$$ $$e\left(\frac{14}{19}\right)$$ $$e\left(\frac{55}{57}\right)$$
$$\chi_{8015}(39,\cdot)$$ 8015.hi 228 Yes $$-1$$ $$1$$ $$e\left(\frac{175}{228}\right)$$ $$e\left(\frac{25}{38}\right)$$ $$e\left(\frac{61}{114}\right)$$ $$e\left(\frac{97}{228}\right)$$ $$e\left(\frac{23}{76}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{67}{114}\right)$$ $$e\left(\frac{11}{57}\right)$$ $$e\left(\frac{21}{76}\right)$$ $$e\left(\frac{4}{57}\right)$$
$$\chi_{8015}(41,\cdot)$$ 8015.gk 228 No $$1$$ $$1$$ $$e\left(\frac{33}{76}\right)$$ $$e\left(\frac{37}{114}\right)$$ $$e\left(\frac{33}{38}\right)$$ $$e\left(\frac{173}{228}\right)$$ $$e\left(\frac{23}{76}\right)$$ $$e\left(\frac{37}{57}\right)$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{11}{57}\right)$$ $$e\left(\frac{59}{76}\right)$$ $$e\left(\frac{14}{19}\right)$$
$$\chi_{8015}(43,\cdot)$$ 8015.en 76 No $$-1$$ $$1$$ $$e\left(\frac{1}{76}\right)$$ $$e\left(\frac{47}{76}\right)$$ $$e\left(\frac{1}{38}\right)$$ $$e\left(\frac{12}{19}\right)$$ $$e\left(\frac{3}{76}\right)$$ $$e\left(\frac{9}{38}\right)$$ $$e\left(\frac{6}{19}\right)$$ $$e\left(\frac{49}{76}\right)$$ $$e\left(\frac{11}{76}\right)$$ $$e\left(\frac{1}{19}\right)$$
$$\chi_{8015}(44,\cdot)$$ 8015.fa 114 Yes $$1$$ $$1$$ $$e\left(\frac{109}{114}\right)$$ $$e\left(\frac{107}{114}\right)$$ $$e\left(\frac{52}{57}\right)$$ $$e\left(\frac{17}{19}\right)$$ $$e\left(\frac{33}{38}\right)$$ $$e\left(\frac{50}{57}\right)$$ $$e\left(\frac{16}{57}\right)$$ $$e\left(\frac{97}{114}\right)$$ $$e\left(\frac{7}{38}\right)$$ $$e\left(\frac{47}{57}\right)$$
$$\chi_{8015}(46,\cdot)$$ 8015.ey 114 No $$1$$ $$1$$ $$e\left(\frac{35}{114}\right)$$ $$e\left(\frac{5}{19}\right)$$ $$e\left(\frac{35}{57}\right)$$ $$e\left(\frac{65}{114}\right)$$ $$e\left(\frac{35}{38}\right)$$ $$e\left(\frac{10}{19}\right)$$ $$e\left(\frac{2}{57}\right)$$ $$e\left(\frac{50}{57}\right)$$ $$e\left(\frac{27}{38}\right)$$ $$e\left(\frac{13}{57}\right)$$