Properties

Modulus $2304$
Structure \(C_{192}\times C_{2}\times C_{2}\)
Order $768$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(2304)
 
pari: g = idealstar(,2304,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 768
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{192}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{2304}(1279,\cdot)$, $\chi_{2304}(2053,\cdot)$, $\chi_{2304}(1793,\cdot)$

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 \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\)
\(\chi_{2304}(1,\cdot)\) 2304.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{2304}(5,\cdot)\) 2304.cb 192 yes \(-1\) \(1\) \(e\left(\frac{35}{192}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{31}{192}\right)\) \(e\left(\frac{77}{192}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{37}{96}\right)\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{145}{192}\right)\) \(e\left(\frac{19}{24}\right)\)
\(\chi_{2304}(7,\cdot)\) 2304.by 96 no \(-1\) \(1\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{65}{96}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{2304}(11,\cdot)\) 2304.cd 192 yes \(1\) \(1\) \(e\left(\frac{31}{192}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{107}{192}\right)\) \(e\left(\frac{145}{192}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{101}{192}\right)\) \(e\left(\frac{11}{24}\right)\)
\(\chi_{2304}(13,\cdot)\) 2304.ca 192 yes \(1\) \(1\) \(e\left(\frac{77}{192}\right)\) \(e\left(\frac{65}{96}\right)\) \(e\left(\frac{145}{192}\right)\) \(e\left(\frac{35}{192}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{77}{96}\right)\) \(e\left(\frac{127}{192}\right)\) \(e\left(\frac{13}{24}\right)\)
\(\chi_{2304}(17,\cdot)\) 2304.bc 16 no \(-1\) \(1\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(-i\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(-1\)
\(\chi_{2304}(19,\cdot)\) 2304.bv 64 no \(-1\) \(1\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{2304}(23,\cdot)\) 2304.bw 96 no \(1\) \(1\) \(e\left(\frac{37}{96}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{71}{96}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{2304}(25,\cdot)\) 2304.bz 96 no \(1\) \(1\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{77}{96}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{49}{96}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{2304}(29,\cdot)\) 2304.cb 192 yes \(-1\) \(1\) \(e\left(\frac{145}{192}\right)\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{101}{192}\right)\) \(e\left(\frac{127}{192}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{71}{96}\right)\) \(e\left(\frac{49}{96}\right)\) \(e\left(\frac{107}{192}\right)\) \(e\left(\frac{17}{24}\right)\)
\(\chi_{2304}(31,\cdot)\) 2304.bh 24 no \(-1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{13}{24}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{2304}(35,\cdot)\) 2304.bu 64 no \(1\) \(1\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{2304}(37,\cdot)\) 2304.bt 64 no \(1\) \(1\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{2304}(41,\cdot)\) 2304.bx 96 no \(-1\) \(1\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{2304}(43,\cdot)\) 2304.cc 192 yes \(-1\) \(1\) \(e\left(\frac{55}{192}\right)\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{35}{192}\right)\) \(e\left(\frac{25}{192}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{55}{96}\right)\) \(e\left(\frac{173}{192}\right)\) \(e\left(\frac{11}{24}\right)\)
\(\chi_{2304}(47,\cdot)\) 2304.bp 48 no \(1\) \(1\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(-i\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2304}(49,\cdot)\) 2304.bq 48 no \(1\) \(1\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(-i\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{2304}(53,\cdot)\) 2304.bs 64 no \(-1\) \(1\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{2304}(55,\cdot)\) 2304.bk 32 no \(-1\) \(1\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{9}{32}\right)\) \(i\)
\(\chi_{2304}(59,\cdot)\) 2304.cd 192 yes \(1\) \(1\) \(e\left(\frac{83}{192}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{175}{192}\right)\) \(e\left(\frac{29}{192}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{37}{96}\right)\) \(e\left(\frac{83}{96}\right)\) \(e\left(\frac{97}{192}\right)\) \(e\left(\frac{7}{24}\right)\)
\(\chi_{2304}(61,\cdot)\) 2304.ca 192 yes \(1\) \(1\) \(e\left(\frac{121}{192}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{173}{192}\right)\) \(e\left(\frac{55}{192}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{35}{192}\right)\) \(e\left(\frac{17}{24}\right)\)
\(\chi_{2304}(65,\cdot)\) 2304.ba 12 no \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2304}(67,\cdot)\) 2304.cc 192 yes \(-1\) \(1\) \(e\left(\frac{89}{192}\right)\) \(e\left(\frac{77}{96}\right)\) \(e\left(\frac{109}{192}\right)\) \(e\left(\frac{23}{192}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{67}{192}\right)\) \(e\left(\frac{13}{24}\right)\)
\(\chi_{2304}(71,\cdot)\) 2304.bm 32 no \(1\) \(1\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{15}{32}\right)\) \(-i\)
\(\chi_{2304}(73,\cdot)\) 2304.bl 32 no \(1\) \(1\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{25}{32}\right)\) \(-i\)
\(\chi_{2304}(77,\cdot)\) 2304.cb 192 yes \(-1\) \(1\) \(e\left(\frac{125}{192}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{1}{192}\right)\) \(e\left(\frac{83}{192}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{79}{192}\right)\) \(e\left(\frac{13}{24}\right)\)
\(\chi_{2304}(79,\cdot)\) 2304.bo 48 no \(-1\) \(1\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(-i\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2304}(83,\cdot)\) 2304.cd 192 yes \(1\) \(1\) \(e\left(\frac{85}{192}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{89}{192}\right)\) \(e\left(\frac{187}{192}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{83}{96}\right)\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{23}{192}\right)\) \(e\left(\frac{17}{24}\right)\)
\(\chi_{2304}(85,\cdot)\) 2304.ca 192 yes \(1\) \(1\) \(e\left(\frac{23}{192}\right)\) \(e\left(\frac{83}{96}\right)\) \(e\left(\frac{163}{192}\right)\) \(e\left(\frac{185}{192}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{1}{96}\right)\) \(e\left(\frac{23}{96}\right)\) \(e\left(\frac{13}{192}\right)\) \(e\left(\frac{7}{24}\right)\)
\(\chi_{2304}(89,\cdot)\) 2304.bn 32 no \(-1\) \(1\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{19}{32}\right)\) \(i\)
\(\chi_{2304}(91,\cdot)\) 2304.bv 64 no \(-1\) \(1\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{2304}(95,\cdot)\) 2304.bj 24 no \(1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{24}\right)\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{6}\right)\)