Properties

Modulus 2432
Structure \(C_{288}\times C_{2}\times C_{2}\)
Order 1152

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Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(2432)
 
pari: g = idealstar(,2432,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1152
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{288}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{2432}(2309,\cdot)$, $\chi_{2432}(1025,\cdot)$, $\chi_{2432}(1407,\cdot)$

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 3 5 7 9 11 13 15 17 21 23
\(\chi_{2432}(1,\cdot)\) 2432.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{2432}(3,\cdot)\) 2432.cr 288 yes \(1\) \(1\) \(e\left(\frac{49}{288}\right)\) \(e\left(\frac{187}{288}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{49}{144}\right)\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{5}{288}\right)\) \(e\left(\frac{59}{72}\right)\) \(e\left(\frac{61}{72}\right)\) \(e\left(\frac{271}{288}\right)\) \(e\left(\frac{37}{144}\right)\)
\(\chi_{2432}(5,\cdot)\) 2432.cs 288 yes \(1\) \(1\) \(e\left(\frac{187}{288}\right)\) \(e\left(\frac{73}{288}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{43}{144}\right)\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{263}{288}\right)\) \(e\left(\frac{65}{72}\right)\) \(e\left(\frac{55}{72}\right)\) \(e\left(\frac{85}{288}\right)\) \(e\left(\frac{31}{144}\right)\)
\(\chi_{2432}(7,\cdot)\) 2432.cd 48 no \(-1\) \(1\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{13}{24}\right)\)
\(\chi_{2432}(9,\cdot)\) 2432.co 144 no \(1\) \(1\) \(e\left(\frac{49}{144}\right)\) \(e\left(\frac{43}{144}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{49}{72}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{5}{144}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{127}{144}\right)\) \(e\left(\frac{37}{72}\right)\)
\(\chi_{2432}(11,\cdot)\) 2432.ci 96 yes \(-1\) \(1\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{1}{48}\right)\)
\(\chi_{2432}(13,\cdot)\) 2432.cq 288 yes \(-1\) \(1\) \(e\left(\frac{5}{288}\right)\) \(e\left(\frac{263}{288}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{5}{144}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{121}{288}\right)\) \(e\left(\frac{67}{72}\right)\) \(e\left(\frac{65}{72}\right)\) \(e\left(\frac{107}{288}\right)\) \(e\left(\frac{17}{144}\right)\)
\(\chi_{2432}(15,\cdot)\) 2432.cf 72 no \(1\) \(1\) \(e\left(\frac{59}{72}\right)\) \(e\left(\frac{65}{72}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{67}{72}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{17}{72}\right)\) \(e\left(\frac{17}{36}\right)\)
\(\chi_{2432}(17,\cdot)\) 2432.ce 72 no \(1\) \(1\) \(e\left(\frac{61}{72}\right)\) \(e\left(\frac{55}{72}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{65}{72}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{67}{72}\right)\) \(e\left(\frac{13}{36}\right)\)
\(\chi_{2432}(21,\cdot)\) 2432.cq 288 yes \(-1\) \(1\) \(e\left(\frac{271}{288}\right)\) \(e\left(\frac{85}{288}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{127}{144}\right)\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{107}{288}\right)\) \(e\left(\frac{17}{72}\right)\) \(e\left(\frac{67}{72}\right)\) \(e\left(\frac{97}{288}\right)\) \(e\left(\frac{115}{144}\right)\)
\(\chi_{2432}(23,\cdot)\) 2432.cm 144 no \(-1\) \(1\) \(e\left(\frac{37}{144}\right)\) \(e\left(\frac{31}{144}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{37}{72}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{17}{144}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{115}{144}\right)\) \(e\left(\frac{61}{72}\right)\)
\(\chi_{2432}(25,\cdot)\) 2432.co 144 no \(1\) \(1\) \(e\left(\frac{43}{144}\right)\) \(e\left(\frac{73}{144}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{43}{72}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{119}{144}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{85}{144}\right)\) \(e\left(\frac{31}{72}\right)\)
\(\chi_{2432}(27,\cdot)\) 2432.cj 96 yes \(1\) \(1\) \(e\left(\frac{49}{96}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{37}{48}\right)\)
\(\chi_{2432}(29,\cdot)\) 2432.cq 288 yes \(-1\) \(1\) \(e\left(\frac{233}{288}\right)\) \(e\left(\frac{275}{288}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{89}{144}\right)\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{109}{288}\right)\) \(e\left(\frac{55}{72}\right)\) \(e\left(\frac{5}{72}\right)\) \(e\left(\frac{263}{288}\right)\) \(e\left(\frac{101}{144}\right)\)
\(\chi_{2432}(31,\cdot)\) 2432.bb 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2432}(33,\cdot)\) 2432.bz 36 no \(-1\) \(1\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{5}{18}\right)\)
\(\chi_{2432}(35,\cdot)\) 2432.ct 288 yes \(-1\) \(1\) \(e\left(\frac{121}{288}\right)\) \(e\left(\frac{259}{288}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{121}{144}\right)\) \(e\left(\frac{37}{96}\right)\) \(e\left(\frac{77}{288}\right)\) \(e\left(\frac{23}{72}\right)\) \(e\left(\frac{61}{72}\right)\) \(e\left(\frac{199}{288}\right)\) \(e\left(\frac{109}{144}\right)\)
\(\chi_{2432}(37,\cdot)\) 2432.bt 32 yes \(-1\) \(1\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{2432}(39,\cdot)\) 2432.bf 16 no \(-1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(-i\) \(-i\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{2432}(41,\cdot)\) 2432.cn 144 no \(-1\) \(1\) \(e\left(\frac{29}{144}\right)\) \(e\left(\frac{71}{144}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{29}{72}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{97}{144}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{131}{144}\right)\) \(e\left(\frac{41}{72}\right)\)
\(\chi_{2432}(43,\cdot)\) 2432.ct 288 yes \(-1\) \(1\) \(e\left(\frac{223}{288}\right)\) \(e\left(\frac{37}{288}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{79}{144}\right)\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{11}{288}\right)\) \(e\left(\frac{65}{72}\right)\) \(e\left(\frac{19}{72}\right)\) \(e\left(\frac{193}{288}\right)\) \(e\left(\frac{139}{144}\right)\)
\(\chi_{2432}(45,\cdot)\) 2432.ck 96 yes \(1\) \(1\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{53}{96}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{35}{48}\right)\)
\(\chi_{2432}(47,\cdot)\) 2432.cg 72 no \(-1\) \(1\) \(e\left(\frac{29}{72}\right)\) \(e\left(\frac{35}{72}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{61}{72}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{23}{72}\right)\) \(e\left(\frac{23}{36}\right)\)
\(\chi_{2432}(49,\cdot)\) 2432.bq 24 no \(1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{7}{24}\right)\) \(i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{2432}(51,\cdot)\) 2432.cr 288 yes \(1\) \(1\) \(e\left(\frac{5}{288}\right)\) \(e\left(\frac{119}{288}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{5}{144}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{265}{288}\right)\) \(e\left(\frac{31}{72}\right)\) \(e\left(\frac{65}{72}\right)\) \(e\left(\frac{251}{288}\right)\) \(e\left(\frac{89}{144}\right)\)
\(\chi_{2432}(53,\cdot)\) 2432.cq 288 yes \(-1\) \(1\) \(e\left(\frac{119}{288}\right)\) \(e\left(\frac{269}{288}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{119}{144}\right)\) \(e\left(\frac{59}{96}\right)\) \(e\left(\frac{115}{288}\right)\) \(e\left(\frac{25}{72}\right)\) \(e\left(\frac{35}{72}\right)\) \(e\left(\frac{185}{288}\right)\) \(e\left(\frac{59}{144}\right)\)
\(\chi_{2432}(55,\cdot)\) 2432.cm 144 no \(-1\) \(1\) \(e\left(\frac{113}{144}\right)\) \(e\left(\frac{83}{144}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{41}{72}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{13}{144}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{71}{144}\right)\) \(e\left(\frac{17}{72}\right)\)
\(\chi_{2432}(59,\cdot)\) 2432.cr 288 yes \(1\) \(1\) \(e\left(\frac{235}{288}\right)\) \(e\left(\frac{121}{288}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{91}{144}\right)\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{71}{288}\right)\) \(e\left(\frac{17}{72}\right)\) \(e\left(\frac{31}{72}\right)\) \(e\left(\frac{277}{288}\right)\) \(e\left(\frac{7}{144}\right)\)
\(\chi_{2432}(61,\cdot)\) 2432.cs 288 yes \(1\) \(1\) \(e\left(\frac{65}{288}\right)\) \(e\left(\frac{107}{288}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{65}{144}\right)\) \(e\left(\frac{77}{96}\right)\) \(e\left(\frac{133}{288}\right)\) \(e\left(\frac{43}{72}\right)\) \(e\left(\frac{53}{72}\right)\) \(e\left(\frac{239}{288}\right)\) \(e\left(\frac{77}{144}\right)\)
\(\chi_{2432}(63,\cdot)\) 2432.bk 18 no \(-1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{18}\right)\)
\(\chi_{2432}(65,\cdot)\) 2432.p 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2432}(67,\cdot)\) 2432.cr 288 yes \(1\) \(1\) \(e\left(\frac{161}{288}\right)\) \(e\left(\frac{203}{288}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{17}{144}\right)\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{181}{288}\right)\) \(e\left(\frac{19}{72}\right)\) \(e\left(\frac{5}{72}\right)\) \(e\left(\frac{191}{288}\right)\) \(e\left(\frac{101}{144}\right)\)