Properties

Modulus $723$
Structure \(C_{240}\times C_{2}\)
Order $480$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(723)
 
pari: g = idealstar(,723,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 480
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{240}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{723}(242,\cdot)$, $\chi_{723}(7,\cdot)$

First 32 of 480 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 \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(13\) \(14\) \(16\)
\(\chi_{723}(1,\cdot)\) 723.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{723}(2,\cdot)\) 723.x 24 yes \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{19}{24}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{723}(4,\cdot)\) 723.r 12 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{723}(5,\cdot)\) 723.bc 40 yes \(-1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{23}{40}\right)\) \(i\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(1\)
\(\chi_{723}(7,\cdot)\) 723.bm 240 no \(-1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{1}{240}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{47}{240}\right)\) \(e\left(\frac{191}{240}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{723}(8,\cdot)\) 723.m 8 yes \(-1\) \(1\) \(-i\) \(-1\) \(i\) \(e\left(\frac{3}{8}\right)\) \(i\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\)
\(\chi_{723}(10,\cdot)\) 723.z 30 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{30}\right)\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{723}(11,\cdot)\) 723.be 48 yes \(1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{723}(13,\cdot)\) 723.bm 240 no \(-1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{47}{240}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{49}{240}\right)\) \(e\left(\frac{97}{240}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{723}(14,\cdot)\) 723.bn 240 yes \(1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{191}{240}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{97}{240}\right)\) \(e\left(\frac{121}{240}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{723}(16,\cdot)\) 723.i 6 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{723}(17,\cdot)\) 723.bj 80 yes \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{37}{80}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{59}{80}\right)\) \(e\left(\frac{67}{80}\right)\) \(-1\)
\(\chi_{723}(19,\cdot)\) 723.bf 48 no \(-1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{723}(20,\cdot)\) 723.bl 120 yes \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{19}{120}\right)\) \(-i\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{53}{120}\right)\) \(e\left(\frac{89}{120}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{723}(22,\cdot)\) 723.bf 48 no \(-1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{723}(23,\cdot)\) 723.bj 80 yes \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{19}{80}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{13}{80}\right)\) \(e\left(\frac{69}{80}\right)\) \(-1\)
\(\chi_{723}(25,\cdot)\) 723.v 20 no \(1\) \(1\) \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(-1\) \(e\left(\frac{1}{5}\right)\) \(-i\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(1\)
\(\chi_{723}(26,\cdot)\) 723.bj 80 yes \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{79}{80}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{33}{80}\right)\) \(e\left(\frac{9}{80}\right)\) \(-1\)
\(\chi_{723}(28,\cdot)\) 723.bi 80 no \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{47}{80}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{49}{80}\right)\) \(e\left(\frac{17}{80}\right)\) \(-1\)
\(\chi_{723}(29,\cdot)\) 723.bl 120 yes \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{77}{120}\right)\) \(i\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{19}{120}\right)\) \(e\left(\frac{7}{120}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{723}(31,\cdot)\) 723.bm 240 no \(-1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{151}{240}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{137}{240}\right)\) \(e\left(\frac{41}{240}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{723}(32,\cdot)\) 723.x 24 yes \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{23}{24}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{723}(34,\cdot)\) 723.bm 240 no \(-1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{61}{240}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{227}{240}\right)\) \(e\left(\frac{131}{240}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{723}(35,\cdot)\) 723.bn 240 yes \(1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{139}{240}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{53}{240}\right)\) \(e\left(\frac{29}{240}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{723}(37,\cdot)\) 723.bm 240 no \(-1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{73}{240}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{71}{240}\right)\) \(e\left(\frac{23}{240}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{723}(38,\cdot)\) 723.be 48 yes \(1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{723}(40,\cdot)\) 723.v 20 no \(1\) \(1\) \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(-1\) \(e\left(\frac{3}{5}\right)\) \(-i\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(1\)
\(\chi_{723}(41,\cdot)\) 723.bc 40 yes \(-1\) \(1\) \(i\) \(-1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{40}\right)\) \(-i\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(1\)
\(\chi_{723}(43,\cdot)\) 723.bi 80 no \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{73}{80}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{71}{80}\right)\) \(e\left(\frac{23}{80}\right)\) \(-1\)
\(\chi_{723}(44,\cdot)\) 723.t 16 yes \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(-1\)
\(\chi_{723}(46,\cdot)\) 723.bm 240 no \(-1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{7}{240}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{89}{240}\right)\) \(e\left(\frac{137}{240}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{723}(47,\cdot)\) 723.bc 40 yes \(-1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{19}{40}\right)\) \(i\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(1\)