Properties

 Modulus 6042 Structure $$C_{468}\times C_{2}\times C_{2}$$ Order 1872

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(6042)

pari: g = idealstar(,6042,2)

Character group

 sage: G.order()  pari: g.no Order = 1872 sage: H.invariants()  pari: g.cyc Structure = $$C_{468}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{6042}(2917,\cdot)$, $\chi_{6042}(4027,\cdot)$, $\chi_{6042}(2015,\cdot)$

First 32 of 1872 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 5 7 11 13 17 23 25 29 31 35
$$\chi_{6042}(1,\cdot)$$ 6042.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{6042}(5,\cdot)$$ 6042.ct 468 no $$1$$ $$1$$ $$e\left(\frac{95}{468}\right)$$ $$e\left(\frac{77}{78}\right)$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{16}{117}\right)$$ $$e\left(\frac{50}{117}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{95}{234}\right)$$ $$e\left(\frac{22}{117}\right)$$ $$e\left(\frac{25}{156}\right)$$ $$e\left(\frac{89}{468}\right)$$
$$\chi_{6042}(7,\cdot)$$ 6042.by 78 no $$1$$ $$1$$ $$e\left(\frac{77}{78}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{5}{39}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{59}{78}\right)$$
$$\chi_{6042}(11,\cdot)$$ 6042.cd 78 no $$-1$$ $$1$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{25}{78}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{11}{78}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{8}{39}\right)$$
$$\chi_{6042}(13,\cdot)$$ 6042.co 234 no $$-1$$ $$1$$ $$e\left(\frac{16}{117}\right)$$ $$e\left(\frac{5}{39}\right)$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{109}{234}\right)$$ $$e\left(\frac{46}{117}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{32}{117}\right)$$ $$e\left(\frac{223}{234}\right)$$ $$e\left(\frac{31}{78}\right)$$ $$e\left(\frac{31}{117}\right)$$
$$\chi_{6042}(17,\cdot)$$ 6042.cj 234 no $$-1$$ $$1$$ $$e\left(\frac{50}{117}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{25}{78}\right)$$ $$e\left(\frac{46}{117}\right)$$ $$e\left(\frac{229}{234}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{100}{117}\right)$$ $$e\left(\frac{185}{234}\right)$$ $$e\left(\frac{53}{78}\right)$$ $$e\left(\frac{53}{117}\right)$$
$$\chi_{6042}(23,\cdot)$$ 6042.bo 36 no $$1$$ $$1$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{25}{36}\right)$$
$$\chi_{6042}(25,\cdot)$$ 6042.cn 234 no $$1$$ $$1$$ $$e\left(\frac{95}{234}\right)$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{32}{117}\right)$$ $$e\left(\frac{100}{117}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{95}{117}\right)$$ $$e\left(\frac{44}{117}\right)$$ $$e\left(\frac{25}{78}\right)$$ $$e\left(\frac{89}{234}\right)$$
$$\chi_{6042}(29,\cdot)$$ 6042.cm 234 no $$1$$ $$1$$ $$e\left(\frac{22}{117}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{11}{78}\right)$$ $$e\left(\frac{223}{234}\right)$$ $$e\left(\frac{185}{234}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{44}{117}\right)$$ $$e\left(\frac{29}{117}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{28}{117}\right)$$
$$\chi_{6042}(31,\cdot)$$ 6042.ch 156 no $$1$$ $$1$$ $$e\left(\frac{25}{156}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{31}{78}\right)$$ $$e\left(\frac{53}{78}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{25}{78}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{23}{52}\right)$$ $$e\left(\frac{7}{156}\right)$$
$$\chi_{6042}(35,\cdot)$$ 6042.ct 468 no $$1$$ $$1$$ $$e\left(\frac{89}{468}\right)$$ $$e\left(\frac{59}{78}\right)$$ $$e\left(\frac{8}{39}\right)$$ $$e\left(\frac{31}{117}\right)$$ $$e\left(\frac{53}{117}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{89}{234}\right)$$ $$e\left(\frac{28}{117}\right)$$ $$e\left(\frac{7}{156}\right)$$ $$e\left(\frac{443}{468}\right)$$
$$\chi_{6042}(37,\cdot)$$ 6042.bl 26 no $$-1$$ $$1$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$-1$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{5}{26}\right)$$
$$\chi_{6042}(41,\cdot)$$ 6042.cs 468 no $$-1$$ $$1$$ $$e\left(\frac{341}{468}\right)$$ $$e\left(\frac{35}{78}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{89}{234}\right)$$ $$e\left(\frac{44}{117}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{107}{234}\right)$$ $$e\left(\frac{137}{234}\right)$$ $$e\left(\frac{61}{156}\right)$$ $$e\left(\frac{83}{468}\right)$$
$$\chi_{6042}(43,\cdot)$$ 6042.cn 234 no $$1$$ $$1$$ $$e\left(\frac{25}{234}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{8}{39}\right)$$ $$e\left(\frac{70}{117}\right)$$ $$e\left(\frac{14}{117}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{25}{117}\right)$$ $$e\left(\frac{67}{117}\right)$$ $$e\left(\frac{23}{78}\right)$$ $$e\left(\frac{85}{234}\right)$$
$$\chi_{6042}(47,\cdot)$$ 6042.cl 234 no $$-1$$ $$1$$ $$e\left(\frac{89}{234}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{71}{78}\right)$$ $$e\left(\frac{62}{117}\right)$$ $$e\left(\frac{95}{234}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{89}{117}\right)$$ $$e\left(\frac{229}{234}\right)$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{209}{234}\right)$$
$$\chi_{6042}(49,\cdot)$$ 6042.bs 39 no $$1$$ $$1$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{20}{39}\right)$$
$$\chi_{6042}(55,\cdot)$$ 6042.cr 468 no $$-1$$ $$1$$ $$e\left(\frac{371}{468}\right)$$ $$e\left(\frac{47}{78}\right)$$ $$e\left(\frac{61}{78}\right)$$ $$e\left(\frac{28}{117}\right)$$ $$e\left(\frac{175}{234}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{137}{234}\right)$$ $$e\left(\frac{77}{234}\right)$$ $$e\left(\frac{151}{156}\right)$$ $$e\left(\frac{185}{468}\right)$$
$$\chi_{6042}(59,\cdot)$$ 6042.cm 234 no $$1$$ $$1$$ $$e\left(\frac{77}{117}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{19}{78}\right)$$ $$e\left(\frac{137}{234}\right)$$ $$e\left(\frac{121}{234}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{37}{117}\right)$$ $$e\left(\frac{43}{117}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{98}{117}\right)$$
$$\chi_{6042}(61,\cdot)$$ 6042.cr 468 no $$-1$$ $$1$$ $$e\left(\frac{229}{468}\right)$$ $$e\left(\frac{37}{78}\right)$$ $$e\left(\frac{53}{78}\right)$$ $$e\left(\frac{110}{117}\right)$$ $$e\left(\frac{161}{234}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{229}{234}\right)$$ $$e\left(\frac{127}{234}\right)$$ $$e\left(\frac{89}{156}\right)$$ $$e\left(\frac{451}{468}\right)$$
$$\chi_{6042}(65,\cdot)$$ 6042.cf 156 no $$-1$$ $$1$$ $$e\left(\frac{53}{156}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{47}{78}\right)$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{53}{78}\right)$$ $$e\left(\frac{11}{78}\right)$$ $$e\left(\frac{29}{52}\right)$$ $$e\left(\frac{71}{156}\right)$$
$$\chi_{6042}(67,\cdot)$$ 6042.cq 468 no $$1$$ $$1$$ $$e\left(\frac{313}{468}\right)$$ $$e\left(\frac{55}{78}\right)$$ $$e\left(\frac{5}{78}\right)$$ $$e\left(\frac{151}{234}\right)$$ $$e\left(\frac{77}{234}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{79}{234}\right)$$ $$e\left(\frac{38}{117}\right)$$ $$e\left(\frac{107}{156}\right)$$ $$e\left(\frac{175}{468}\right)$$
$$\chi_{6042}(71,\cdot)$$ 6042.cs 468 no $$-1$$ $$1$$ $$e\left(\frac{167}{468}\right)$$ $$e\left(\frac{59}{78}\right)$$ $$e\left(\frac{8}{39}\right)$$ $$e\left(\frac{23}{234}\right)$$ $$e\left(\frac{14}{117}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{167}{234}\right)$$ $$e\left(\frac{17}{234}\right)$$ $$e\left(\frac{7}{156}\right)$$ $$e\left(\frac{53}{468}\right)$$
$$\chi_{6042}(73,\cdot)$$ 6042.cr 468 no $$-1$$ $$1$$ $$e\left(\frac{395}{468}\right)$$ $$e\left(\frac{41}{78}\right)$$ $$e\left(\frac{25}{78}\right)$$ $$e\left(\frac{85}{117}\right)$$ $$e\left(\frac{151}{234}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{161}{234}\right)$$ $$e\left(\frac{29}{234}\right)$$ $$e\left(\frac{67}{156}\right)$$ $$e\left(\frac{173}{468}\right)$$
$$\chi_{6042}(77,\cdot)$$ 6042.bm 26 no $$-1$$ $$1$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$-1$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{25}{26}\right)$$
$$\chi_{6042}(79,\cdot)$$ 6042.cq 468 no $$1$$ $$1$$ $$e\left(\frac{71}{468}\right)$$ $$e\left(\frac{5}{78}\right)$$ $$e\left(\frac{43}{78}\right)$$ $$e\left(\frac{35}{234}\right)$$ $$e\left(\frac{7}{234}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{71}{234}\right)$$ $$e\left(\frac{46}{117}\right)$$ $$e\left(\frac{109}{156}\right)$$ $$e\left(\frac{101}{468}\right)$$
$$\chi_{6042}(83,\cdot)$$ 6042.x 12 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{6042}(85,\cdot)$$ 6042.cr 468 no $$-1$$ $$1$$ $$e\left(\frac{295}{468}\right)$$ $$e\left(\frac{1}{78}\right)$$ $$e\left(\frac{71}{78}\right)$$ $$e\left(\frac{62}{117}\right)$$ $$e\left(\frac{95}{234}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{61}{234}\right)$$ $$e\left(\frac{229}{234}\right)$$ $$e\left(\frac{131}{156}\right)$$ $$e\left(\frac{301}{468}\right)$$
$$\chi_{6042}(89,\cdot)$$ 6042.ck 234 no $$1$$ $$1$$ $$e\left(\frac{113}{234}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{77}{78}\right)$$ $$e\left(\frac{1}{234}\right)$$ $$e\left(\frac{47}{234}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{113}{117}\right)$$ $$e\left(\frac{8}{117}\right)$$ $$e\left(\frac{1}{78}\right)$$ $$e\left(\frac{197}{234}\right)$$
$$\chi_{6042}(91,\cdot)$$ 6042.cp 234 no $$-1$$ $$1$$ $$e\left(\frac{29}{234}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{139}{234}\right)$$ $$e\left(\frac{49}{117}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{29}{117}\right)$$ $$e\left(\frac{1}{234}\right)$$ $$e\left(\frac{11}{39}\right)$$ $$e\left(\frac{5}{234}\right)$$
$$\chi_{6042}(97,\cdot)$$ 6042.co 234 no $$-1$$ $$1$$ $$e\left(\frac{14}{117}\right)$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{227}{234}\right)$$ $$e\left(\frac{11}{117}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{28}{117}\right)$$ $$e\left(\frac{5}{234}\right)$$ $$e\left(\frac{71}{78}\right)$$ $$e\left(\frac{71}{117}\right)$$
$$\chi_{6042}(101,\cdot)$$ 6042.ct 468 no $$1$$ $$1$$ $$e\left(\frac{433}{468}\right)$$ $$e\left(\frac{25}{78}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{68}{117}\right)$$ $$e\left(\frac{37}{117}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{199}{234}\right)$$ $$e\left(\frac{35}{117}\right)$$ $$e\left(\frac{155}{156}\right)$$ $$e\left(\frac{115}{468}\right)$$
$$\chi_{6042}(103,\cdot)$$ 6042.ch 156 no $$1$$ $$1$$ $$e\left(\frac{83}{156}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{53}{78}\right)$$ $$e\left(\frac{73}{78}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{78}\right)$$ $$e\left(\frac{34}{39}\right)$$ $$e\left(\frac{41}{52}\right)$$ $$e\left(\frac{17}{156}\right)$$