Properties

Modulus 4032
Structure \(C_{48}\times C_{6}\times C_{2}\times C_{2}\)
Order 1152

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(4032)
pari: g = idealstar(,4032,2)

Character group

sage: G.order()
pari: g.no
Order = 1152
sage: H.invariants()
pari: g.cyc
Structure = \(C_{48}\times C_{6}\times C_{2}\times C_{2}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{4032}(901,\cdot)$, $\chi_{4032}(1793,\cdot)$, $\chi_{4032}(1441,\cdot)$, $\chi_{4032}(127,\cdot)$

First 32 of 1152 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
\(\chi_{4032}(1,\cdot)\) 4032.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{4032}(5,\cdot)\) 4032.hp 48 Yes \(1\) \(1\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{25}{48}\right)\) \(1\) \(e\left(\frac{11}{48}\right)\)
\(\chi_{4032}(11,\cdot)\) 4032.ho 48 Yes \(1\) \(1\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{29}{48}\right)\) \(1\) \(e\left(\frac{7}{48}\right)\)
\(\chi_{4032}(13,\cdot)\) 4032.gu 48 Yes \(-1\) \(1\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(-i\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{16}\right)\)
\(\chi_{4032}(17,\cdot)\) 4032.ea 12 No \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{4032}(19,\cdot)\) 4032.he 48 No \(1\) \(1\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{29}{48}\right)\)
\(\chi_{4032}(23,\cdot)\) 4032.fk 24 No \(1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{24}\right)\) \(-1\) \(e\left(\frac{13}{24}\right)\)
\(\chi_{4032}(25,\cdot)\) 4032.gg 24 No \(1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{24}\right)\) \(1\) \(e\left(\frac{11}{24}\right)\)
\(\chi_{4032}(29,\cdot)\) 4032.hk 48 No \(-1\) \(1\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(-i\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{4032}(31,\cdot)\) 4032.dh 6 No \(1\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{4032}(37,\cdot)\) 4032.hf 48 No \(1\) \(1\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{35}{48}\right)\)
\(\chi_{4032}(41,\cdot)\) 4032.fj 24 No \(1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{24}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{4032}(43,\cdot)\) 4032.gr 48 No \(-1\) \(1\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(-i\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{4032}(47,\cdot)\) 4032.dx 12 No \(-1\) \(1\) \(-i\) \(-i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{4032}(53,\cdot)\) 4032.hi 48 No \(-1\) \(1\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{48}\right)\)
\(\chi_{4032}(55,\cdot)\) 4032.dq 8 No \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(1\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{4032}(59,\cdot)\) 4032.hm 48 Yes \(-1\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{43}{48}\right)\)
\(\chi_{4032}(61,\cdot)\) 4032.gt 48 Yes \(-1\) \(1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{48}\right)\)
\(\chi_{4032}(65,\cdot)\) 4032.bd 6 No \(-1\) \(1\) \(-1\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{4032}(67,\cdot)\) 4032.gs 48 Yes \(-1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{48}\right)\)
\(\chi_{4032}(71,\cdot)\) 4032.do 8 No \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(i\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{4032}(73,\cdot)\) 4032.fq 24 No \(-1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{24}\right)\)
\(\chi_{4032}(79,\cdot)\) 4032.eh 12 No \(-1\) \(1\) \(i\) \(-i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(1\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{4032}(83,\cdot)\) 4032.hl 48 Yes \(-1\) \(1\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(i\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{4032}(85,\cdot)\) 4032.hg 48 No \(1\) \(1\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(-i\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{4032}(89,\cdot)\) 4032.ge 24 No \(1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{24}\right)\)
\(\chi_{4032}(95,\cdot)\) 4032.dg 6 No \(1\) \(1\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{4032}(97,\cdot)\) 4032.bv 6 No \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\)
\(\chi_{4032}(101,\cdot)\) 4032.hp 48 Yes \(1\) \(1\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{17}{48}\right)\) \(1\) \(e\left(\frac{19}{48}\right)\)
\(\chi_{4032}(103,\cdot)\) 4032.fu 24 No \(1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{17}{24}\right)\) \(1\) \(e\left(\frac{19}{24}\right)\)
\(\chi_{4032}(107,\cdot)\) 4032.gz 48 No \(1\) \(1\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{47}{48}\right)\)
\(\chi_{4032}(109,\cdot)\) 4032.hf 48 No \(1\) \(1\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{48}\right)\)