Properties

Modulus 6048
Structure \(C_{72}\times C_{6}\times C_{2}\times C_{2}\)
Order 1728

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(6048)
 
pari: g = idealstar(,6048,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1728
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{72}\times C_{6}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{6048}(5645,\cdot)$, $\chi_{6048}(1745,\cdot)$, $\chi_{6048}(433,\cdot)$, $\chi_{6048}(4159,\cdot)$

First 32 of 1728 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 11 13 17 19 23 25 29 31 37
\(\chi_{6048}(1,\cdot)\) 6048.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{6048}(5,\cdot)\) 6048.iy 72 yes \(1\) \(1\) \(e\left(\frac{49}{72}\right)\) \(e\left(\frac{41}{72}\right)\) \(e\left(\frac{43}{72}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{47}{72}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{11}{24}\right)\)
\(\chi_{6048}(11,\cdot)\) 6048.jv 72 yes \(1\) \(1\) \(e\left(\frac{41}{72}\right)\) \(e\left(\frac{49}{72}\right)\) \(e\left(\frac{11}{72}\right)\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{43}{72}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{7}{24}\right)\)
\(\chi_{6048}(13,\cdot)\) 6048.jc 72 yes \(-1\) \(1\) \(e\left(\frac{43}{72}\right)\) \(e\left(\frac{11}{72}\right)\) \(e\left(\frac{13}{72}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{5}{72}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{13}{24}\right)\)
\(\chi_{6048}(17,\cdot)\) 6048.bg 6 no \(1\) \(1\) \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{6048}(19,\cdot)\) 6048.hd 24 no \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{19}{24}\right)\) \(-i\) \(-i\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{24}\right)\)
\(\chi_{6048}(23,\cdot)\) 6048.id 36 no \(1\) \(1\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(-1\) \(-i\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{6048}(25,\cdot)\) 6048.iv 36 no \(1\) \(1\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(1\) \(-i\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{6048}(29,\cdot)\) 6048.jd 72 no \(-1\) \(1\) \(e\left(\frac{47}{72}\right)\) \(e\left(\frac{43}{72}\right)\) \(e\left(\frac{5}{72}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{13}{72}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{17}{24}\right)\)
\(\chi_{6048}(31,\cdot)\) 6048.gd 18 no \(1\) \(1\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(1\)
\(\chi_{6048}(37,\cdot)\) 6048.hu 24 no \(1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{17}{24}\right)\) \(1\) \(e\left(\frac{19}{24}\right)\)
\(\chi_{6048}(41,\cdot)\) 6048.ij 36 no \(1\) \(1\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{6048}(43,\cdot)\) 6048.jp 72 no \(-1\) \(1\) \(e\left(\frac{53}{72}\right)\) \(e\left(\frac{37}{72}\right)\) \(e\left(\frac{11}{72}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{7}{72}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{23}{24}\right)\)
\(\chi_{6048}(47,\cdot)\) 6048.fp 18 no \(-1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(-1\)
\(\chi_{6048}(53,\cdot)\) 6048.hb 24 no \(-1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{23}{24}\right)\)
\(\chi_{6048}(55,\cdot)\) 6048.x 4 no \(1\) \(1\) \(i\) \(i\) \(-i\) \(-1\) \(i\) \(1\) \(-1\) \(i\) \(1\) \(-i\)
\(\chi_{6048}(59,\cdot)\) 6048.jr 72 yes \(-1\) \(1\) \(e\left(\frac{25}{72}\right)\) \(e\left(\frac{29}{72}\right)\) \(e\left(\frac{43}{72}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{47}{72}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{6048}(61,\cdot)\) 6048.jf 72 yes \(-1\) \(1\) \(e\left(\frac{71}{72}\right)\) \(e\left(\frac{55}{72}\right)\) \(e\left(\frac{17}{72}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{1}{72}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{6048}(65,\cdot)\) 6048.ge 18 no \(-1\) \(1\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(1\)
\(\chi_{6048}(67,\cdot)\) 6048.jq 72 yes \(-1\) \(1\) \(e\left(\frac{67}{72}\right)\) \(e\left(\frac{59}{72}\right)\) \(e\left(\frac{13}{72}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{41}{72}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{6048}(71,\cdot)\) 6048.dx 12 no \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(i\)
\(\chi_{6048}(73,\cdot)\) 6048.er 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{6048}(79,\cdot)\) 6048.fk 18 no \(-1\) \(1\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(-1\)
\(\chi_{6048}(83,\cdot)\) 6048.jo 72 yes \(-1\) \(1\) \(e\left(\frac{47}{72}\right)\) \(e\left(\frac{43}{72}\right)\) \(e\left(\frac{5}{72}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{49}{72}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{24}\right)\)
\(\chi_{6048}(85,\cdot)\) 6048.jn 72 no \(1\) \(1\) \(e\left(\frac{13}{72}\right)\) \(e\left(\frac{41}{72}\right)\) \(e\left(\frac{19}{72}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{71}{72}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{24}\right)\)
\(\chi_{6048}(89,\cdot)\) 6048.ej 12 no \(1\) \(1\) \(i\) \(-i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(1\) \(-1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{6048}(95,\cdot)\) 6048.gm 18 no \(1\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{18}\right)\) \(1\)
\(\chi_{6048}(97,\cdot)\) 6048.gi 18 no \(-1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{6048}(101,\cdot)\) 6048.iy 72 yes \(1\) \(1\) \(e\left(\frac{65}{72}\right)\) \(e\left(\frac{25}{72}\right)\) \(e\left(\frac{35}{72}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{55}{72}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{19}{24}\right)\)
\(\chi_{6048}(103,\cdot)\) 6048.ia 36 no \(1\) \(1\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(-1\) \(-i\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{6048}(107,\cdot)\) 6048.hh 24 no \(1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{24}\right)\)
\(\chi_{6048}(109,\cdot)\) 6048.hp 24 no \(1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{24}\right)\)