Properties

Modulus 4028
Structure \(C_{468}\times C_{2}\times C_{2}\)
Order 1872

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(4028)
pari: g = idealstar(,4028,2)

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 = $\chi_{4028}(2917,\cdot)$, $\chi_{4028}(2013,\cdot)$, $\chi_{4028}(2015,\cdot)$

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 3 5 7 9 11 13 15 17 21 23
\(\chi_{4028}(1,\cdot)\) 4028.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{4028}(3,\cdot)\) 4028.cs 468 Yes \(-1\) \(1\) \(e\left(\frac{209}{468}\right)\) \(e\left(\frac{431}{468}\right)\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{209}{234}\right)\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{107}{234}\right)\) \(e\left(\frac{43}{117}\right)\) \(e\left(\frac{115}{234}\right)\) \(e\left(\frac{401}{468}\right)\) \(e\left(\frac{25}{36}\right)\)
\(\chi_{4028}(5,\cdot)\) 4028.cr 468 No \(-1\) \(1\) \(e\left(\frac{431}{468}\right)\) \(e\left(\frac{329}{468}\right)\) \(e\left(\frac{77}{78}\right)\) \(e\left(\frac{197}{234}\right)\) \(e\left(\frac{7}{78}\right)\) \(e\left(\frac{16}{117}\right)\) \(e\left(\frac{73}{117}\right)\) \(e\left(\frac{217}{234}\right)\) \(e\left(\frac{425}{468}\right)\) \(e\left(\frac{1}{36}\right)\)
\(\chi_{4028}(7,\cdot)\) 4028.cc 78 Yes \(-1\) \(1\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{77}{78}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{31}{78}\right)\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{53}{78}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{4028}(9,\cdot)\) 4028.cn 234 No \(1\) \(1\) \(e\left(\frac{209}{234}\right)\) \(e\left(\frac{197}{234}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{92}{117}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{107}{117}\right)\) \(e\left(\frac{86}{117}\right)\) \(e\left(\frac{115}{117}\right)\) \(e\left(\frac{167}{234}\right)\) \(e\left(\frac{7}{18}\right)\)
\(\chi_{4028}(11,\cdot)\) 4028.cc 78 Yes \(-1\) \(1\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{7}{78}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{17}{78}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{19}{78}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{4028}(13,\cdot)\) 4028.co 234 No \(-1\) \(1\) \(e\left(\frac{107}{234}\right)\) \(e\left(\frac{16}{117}\right)\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{107}{117}\right)\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{109}{234}\right)\) \(e\left(\frac{139}{234}\right)\) \(e\left(\frac{46}{117}\right)\) \(e\left(\frac{137}{234}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{4028}(15,\cdot)\) 4028.cm 234 Yes \(1\) \(1\) \(e\left(\frac{43}{117}\right)\) \(e\left(\frac{73}{117}\right)\) \(e\left(\frac{31}{78}\right)\) \(e\left(\frac{86}{117}\right)\) \(e\left(\frac{17}{78}\right)\) \(e\left(\frac{139}{234}\right)\) \(e\left(\frac{116}{117}\right)\) \(e\left(\frac{49}{117}\right)\) \(e\left(\frac{179}{234}\right)\) \(e\left(\frac{13}{18}\right)\)
\(\chi_{4028}(17,\cdot)\) 4028.cn 234 No \(1\) \(1\) \(e\left(\frac{115}{234}\right)\) \(e\left(\frac{217}{234}\right)\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{115}{117}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{46}{117}\right)\) \(e\left(\frac{49}{117}\right)\) \(e\left(\frac{56}{117}\right)\) \(e\left(\frac{121}{234}\right)\) \(e\left(\frac{11}{18}\right)\)
\(\chi_{4028}(21,\cdot)\) 4028.cq 468 No \(1\) \(1\) \(e\left(\frac{401}{468}\right)\) \(e\left(\frac{425}{468}\right)\) \(e\left(\frac{53}{78}\right)\) \(e\left(\frac{167}{234}\right)\) \(e\left(\frac{19}{78}\right)\) \(e\left(\frac{137}{234}\right)\) \(e\left(\frac{179}{234}\right)\) \(e\left(\frac{121}{234}\right)\) \(e\left(\frac{251}{468}\right)\) \(e\left(\frac{13}{36}\right)\)
\(\chi_{4028}(23,\cdot)\) 4028.bo 36 Yes \(1\) \(1\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{35}{36}\right)\)
\(\chi_{4028}(25,\cdot)\) 4028.cn 234 No \(1\) \(1\) \(e\left(\frac{197}{234}\right)\) \(e\left(\frac{95}{234}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{80}{117}\right)\) \(e\left(\frac{7}{39}\right)\) \(e\left(\frac{32}{117}\right)\) \(e\left(\frac{29}{117}\right)\) \(e\left(\frac{100}{117}\right)\) \(e\left(\frac{191}{234}\right)\) \(e\left(\frac{1}{18}\right)\)
\(\chi_{4028}(27,\cdot)\) 4028.cf 156 Yes \(-1\) \(1\) \(e\left(\frac{53}{156}\right)\) \(e\left(\frac{119}{156}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{53}{78}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{29}{78}\right)\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{37}{78}\right)\) \(e\left(\frac{89}{156}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{4028}(29,\cdot)\) 4028.cp 234 No \(-1\) \(1\) \(e\left(\frac{37}{117}\right)\) \(e\left(\frac{161}{234}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{74}{117}\right)\) \(e\left(\frac{25}{39}\right)\) \(e\left(\frac{223}{234}\right)\) \(e\left(\frac{1}{234}\right)\) \(e\left(\frac{34}{117}\right)\) \(e\left(\frac{43}{117}\right)\) \(e\left(\frac{7}{18}\right)\)
\(\chi_{4028}(31,\cdot)\) 4028.cf 156 Yes \(-1\) \(1\) \(e\left(\frac{19}{156}\right)\) \(e\left(\frac{25}{156}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{19}{78}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{31}{78}\right)\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{53}{78}\right)\) \(e\left(\frac{79}{156}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{4028}(33,\cdot)\) 4028.cq 468 No \(1\) \(1\) \(e\left(\frac{269}{468}\right)\) \(e\left(\frac{5}{468}\right)\) \(e\left(\frac{41}{78}\right)\) \(e\left(\frac{35}{234}\right)\) \(e\left(\frac{25}{78}\right)\) \(e\left(\frac{131}{234}\right)\) \(e\left(\frac{137}{234}\right)\) \(e\left(\frac{73}{234}\right)\) \(e\left(\frac{47}{468}\right)\) \(e\left(\frac{1}{36}\right)\)
\(\chi_{4028}(35,\cdot)\) 4028.ct 468 Yes \(1\) \(1\) \(e\left(\frac{155}{468}\right)\) \(e\left(\frac{323}{468}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{155}{234}\right)\) \(e\left(\frac{8}{39}\right)\) \(e\left(\frac{31}{117}\right)\) \(e\left(\frac{5}{234}\right)\) \(e\left(\frac{223}{234}\right)\) \(e\left(\frac{275}{468}\right)\) \(e\left(\frac{25}{36}\right)\)
\(\chi_{4028}(37,\cdot)\) 4028.bi 26 No \(-1\) \(1\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(-1\)
\(\chi_{4028}(39,\cdot)\) 4028.bt 52 No \(1\) \(1\) \(e\left(\frac{47}{52}\right)\) \(e\left(\frac{3}{52}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{23}{52}\right)\) \(i\)
\(\chi_{4028}(41,\cdot)\) 4028.cq 468 No \(1\) \(1\) \(e\left(\frac{47}{468}\right)\) \(e\left(\frac{107}{468}\right)\) \(e\left(\frac{35}{78}\right)\) \(e\left(\frac{47}{234}\right)\) \(e\left(\frac{67}{78}\right)\) \(e\left(\frac{89}{234}\right)\) \(e\left(\frac{77}{234}\right)\) \(e\left(\frac{205}{234}\right)\) \(e\left(\frac{257}{468}\right)\) \(e\left(\frac{7}{36}\right)\)
\(\chi_{4028}(43,\cdot)\) 4028.cl 234 Yes \(-1\) \(1\) \(e\left(\frac{29}{117}\right)\) \(e\left(\frac{25}{234}\right)\) \(e\left(\frac{59}{78}\right)\) \(e\left(\frac{58}{117}\right)\) \(e\left(\frac{55}{78}\right)\) \(e\left(\frac{70}{117}\right)\) \(e\left(\frac{83}{234}\right)\) \(e\left(\frac{14}{117}\right)\) \(e\left(\frac{1}{234}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{4028}(45,\cdot)\) 4028.ci 156 No \(-1\) \(1\) \(e\left(\frac{127}{156}\right)\) \(e\left(\frac{85}{156}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{49}{78}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{14}{39}\right)\) \(e\left(\frac{71}{78}\right)\) \(e\left(\frac{97}{156}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{4028}(47,\cdot)\) 4028.cj 234 Yes \(-1\) \(1\) \(e\left(\frac{155}{234}\right)\) \(e\left(\frac{103}{117}\right)\) \(e\left(\frac{1}{78}\right)\) \(e\left(\frac{38}{117}\right)\) \(e\left(\frac{71}{78}\right)\) \(e\left(\frac{62}{117}\right)\) \(e\left(\frac{127}{234}\right)\) \(e\left(\frac{106}{117}\right)\) \(e\left(\frac{79}{117}\right)\) \(e\left(\frac{7}{18}\right)\)
\(\chi_{4028}(49,\cdot)\) 4028.bs 39 No \(1\) \(1\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{25}{39}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{14}{39}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{4028}(51,\cdot)\) 4028.cs 468 Yes \(-1\) \(1\) \(e\left(\frac{439}{468}\right)\) \(e\left(\frac{397}{468}\right)\) \(e\left(\frac{17}{39}\right)\) \(e\left(\frac{205}{234}\right)\) \(e\left(\frac{37}{39}\right)\) \(e\left(\frac{199}{234}\right)\) \(e\left(\frac{92}{117}\right)\) \(e\left(\frac{227}{234}\right)\) \(e\left(\frac{175}{468}\right)\) \(e\left(\frac{11}{36}\right)\)
\(\chi_{4028}(55,\cdot)\) 4028.ct 468 Yes \(1\) \(1\) \(e\left(\frac{23}{468}\right)\) \(e\left(\frac{371}{468}\right)\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{23}{234}\right)\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{28}{117}\right)\) \(e\left(\frac{197}{234}\right)\) \(e\left(\frac{175}{234}\right)\) \(e\left(\frac{71}{468}\right)\) \(e\left(\frac{13}{36}\right)\)
\(\chi_{4028}(59,\cdot)\) 4028.ck 234 Yes \(1\) \(1\) \(e\left(\frac{25}{234}\right)\) \(e\left(\frac{37}{234}\right)\) \(e\left(\frac{53}{78}\right)\) \(e\left(\frac{25}{117}\right)\) \(e\left(\frac{19}{78}\right)\) \(e\left(\frac{137}{234}\right)\) \(e\left(\frac{31}{117}\right)\) \(e\left(\frac{2}{117}\right)\) \(e\left(\frac{92}{117}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{4028}(61,\cdot)\) 4028.cr 468 No \(-1\) \(1\) \(e\left(\frac{199}{468}\right)\) \(e\left(\frac{229}{468}\right)\) \(e\left(\frac{37}{78}\right)\) \(e\left(\frac{199}{234}\right)\) \(e\left(\frac{53}{78}\right)\) \(e\left(\frac{110}{117}\right)\) \(e\left(\frac{107}{117}\right)\) \(e\left(\frac{161}{234}\right)\) \(e\left(\frac{421}{468}\right)\) \(e\left(\frac{17}{36}\right)\)
\(\chi_{4028}(63,\cdot)\) 4028.cj 234 Yes \(-1\) \(1\) \(e\left(\frac{71}{234}\right)\) \(e\left(\frac{97}{117}\right)\) \(e\left(\frac{7}{78}\right)\) \(e\left(\frac{71}{117}\right)\) \(e\left(\frac{29}{78}\right)\) \(e\left(\frac{5}{117}\right)\) \(e\left(\frac{31}{234}\right)\) \(e\left(\frac{1}{117}\right)\) \(e\left(\frac{46}{117}\right)\) \(e\left(\frac{1}{18}\right)\)
\(\chi_{4028}(65,\cdot)\) 4028.ch 156 No \(1\) \(1\) \(e\left(\frac{59}{156}\right)\) \(e\left(\frac{131}{156}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{59}{78}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{47}{78}\right)\) \(e\left(\frac{17}{78}\right)\) \(e\left(\frac{25}{78}\right)\) \(e\left(\frac{77}{156}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{4028}(67,\cdot)\) 4028.cs 468 Yes \(-1\) \(1\) \(e\left(\frac{319}{468}\right)\) \(e\left(\frac{313}{468}\right)\) \(e\left(\frac{8}{39}\right)\) \(e\left(\frac{85}{234}\right)\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{151}{234}\right)\) \(e\left(\frac{41}{117}\right)\) \(e\left(\frac{77}{234}\right)\) \(e\left(\frac{415}{468}\right)\) \(e\left(\frac{23}{36}\right)\)
\(\chi_{4028}(69,\cdot)\) 4028.bz 78 No \(-1\) \(1\) \(e\left(\frac{11}{78}\right)\) \(e\left(\frac{37}{39}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{1}{78}\right)\) \(e\left(\frac{7}{78}\right)\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{17}{78}\right)\) \(e\left(\frac{2}{3}\right)\)