Properties

Modulus $1455$
Structure \(C_{2}\times C_{4}\times C_{96}\)
Order $768$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(1455)
 
pari: g = idealstar(,1455,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 768
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{4}\times C_{96}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1455}(971,\cdot)$, $\chi_{1455}(292,\cdot)$, $\chi_{1455}(781,\cdot)$

First 32 of 768 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.

Character Orbit Order Primitive \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(13\) \(14\) \(16\) \(17\) \(19\)
\(\chi_{1455}(1,\cdot)\) 1455.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1455}(2,\cdot)\) 1455.cy 48 yes \(1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{1455}(4,\cdot)\) 1455.ch 24 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{24}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{1455}(7,\cdot)\) 1455.di 96 no \(1\) \(1\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{21}{32}\right)\)
\(\chi_{1455}(8,\cdot)\) 1455.by 16 yes \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(-1\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{1455}(11,\cdot)\) 1455.cv 48 no \(-1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{1455}(13,\cdot)\) 1455.di 96 no \(1\) \(1\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{73}{96}\right)\) \(e\left(\frac{41}{96}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{19}{32}\right)\)
\(\chi_{1455}(14,\cdot)\) 1455.dg 96 yes \(1\) \(1\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{41}{96}\right)\) \(e\left(\frac{49}{96}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{27}{32}\right)\)
\(\chi_{1455}(16,\cdot)\) 1455.bv 12 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\)
\(\chi_{1455}(17,\cdot)\) 1455.dc 96 yes \(-1\) \(1\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{19}{32}\right)\)
\(\chi_{1455}(19,\cdot)\) 1455.cr 32 no \(-1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(-i\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{11}{32}\right)\)
\(\chi_{1455}(22,\cdot)\) 1455.r 4 no \(-1\) \(1\) \(-i\) \(-1\) \(1\) \(i\) \(-1\) \(1\) \(-i\) \(1\) \(-1\) \(-i\)
\(\chi_{1455}(23,\cdot)\) 1455.dj 96 yes \(-1\) \(1\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{59}{96}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{15}{32}\right)\)
\(\chi_{1455}(26,\cdot)\) 1455.df 96 no \(1\) \(1\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{25}{32}\right)\)
\(\chi_{1455}(28,\cdot)\) 1455.cm 32 no \(1\) \(1\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(i\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{1}{32}\right)\)
\(\chi_{1455}(29,\cdot)\) 1455.dg 96 yes \(1\) \(1\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{31}{32}\right)\)
\(\chi_{1455}(31,\cdot)\) 1455.cu 48 no \(1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{13}{16}\right)\)
\(\chi_{1455}(32,\cdot)\) 1455.cy 48 yes \(1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{1455}(34,\cdot)\) 1455.cr 32 no \(-1\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(i\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{25}{32}\right)\)
\(\chi_{1455}(37,\cdot)\) 1455.di 96 no \(1\) \(1\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{11}{96}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{59}{96}\right)\) \(e\left(\frac{9}{32}\right)\)
\(\chi_{1455}(38,\cdot)\) 1455.dc 96 yes \(-1\) \(1\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{83}{96}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{83}{96}\right)\) \(e\left(\frac{17}{32}\right)\)
\(\chi_{1455}(41,\cdot)\) 1455.df 96 no \(1\) \(1\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{23}{32}\right)\)
\(\chi_{1455}(43,\cdot)\) 1455.cl 24 no \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{24}\right)\) \(-1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{1455}(44,\cdot)\) 1455.da 48 yes \(-1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{1455}(46,\cdot)\) 1455.co 32 no \(-1\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(i\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{21}{32}\right)\)
\(\chi_{1455}(47,\cdot)\) 1455.bd 8 yes \(1\) \(1\) \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{1455}(49,\cdot)\) 1455.db 48 no \(1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{1455}(52,\cdot)\) 1455.cm 32 no \(1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(-i\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{31}{32}\right)\)
\(\chi_{1455}(53,\cdot)\) 1455.cx 48 yes \(1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{1455}(56,\cdot)\) 1455.df 96 no \(1\) \(1\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{53}{96}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{77}{96}\right)\) \(e\left(\frac{7}{32}\right)\)
\(\chi_{1455}(58,\cdot)\) 1455.dd 96 no \(1\) \(1\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{5}{32}\right)\)
\(\chi_{1455}(59,\cdot)\) 1455.dg 96 yes \(1\) \(1\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{83}{96}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{96}\right)\) \(e\left(\frac{17}{32}\right)\)
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