Properties

Modulus $119$
Structure \(C_{48}\times C_{2}\)
Order $96$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(119)
 
pari: g = idealstar(,119,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 96
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{48}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{119}(52,\cdot)$, $\chi_{119}(71,\cdot)$

First 32 of 96 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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(8\) \(9\) \(10\) \(11\) \(12\)
\(\chi_{119}(1,\cdot)\) 119.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{119}(2,\cdot)\) 119.q 24 yes \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{24}\right)\)
\(\chi_{119}(3,\cdot)\) 119.s 48 yes \(1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{31}{48}\right)\)
\(\chi_{119}(4,\cdot)\) 119.n 12 yes \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(i\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{119}(5,\cdot)\) 119.s 48 yes \(1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{11}{48}\right)\)
\(\chi_{119}(6,\cdot)\) 119.p 16 yes \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(i\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{11}{16}\right)\)
\(\chi_{119}(8,\cdot)\) 119.k 8 no \(1\) \(1\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(i\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{119}(9,\cdot)\) 119.q 24 yes \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{7}{8}\right)\) \(i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{24}\right)\)
\(\chi_{119}(10,\cdot)\) 119.s 48 yes \(1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{13}{48}\right)\)
\(\chi_{119}(11,\cdot)\) 119.t 48 yes \(-1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{1}{48}\right)\)
\(\chi_{119}(12,\cdot)\) 119.s 48 yes \(1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{35}{48}\right)\)
\(\chi_{119}(13,\cdot)\) 119.f 4 yes \(-1\) \(1\) \(-1\) \(-i\) \(1\) \(-i\) \(i\) \(-1\) \(-1\) \(i\) \(-i\) \(-i\)
\(\chi_{119}(15,\cdot)\) 119.k 8 no \(1\) \(1\) \(i\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{119}(16,\cdot)\) 119.j 6 yes \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{119}(18,\cdot)\) 119.e 3 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{119}(19,\cdot)\) 119.r 24 yes \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{13}{24}\right)\)
\(\chi_{119}(20,\cdot)\) 119.p 16 yes \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(-i\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{119}(22,\cdot)\) 119.o 16 no \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(-i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{16}\right)\)
\(\chi_{119}(23,\cdot)\) 119.t 48 yes \(-1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{41}{48}\right)\)
\(\chi_{119}(24,\cdot)\) 119.s 48 yes \(1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{37}{48}\right)\)
\(\chi_{119}(25,\cdot)\) 119.q 24 yes \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{3}{8}\right)\) \(i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{11}{24}\right)\)
\(\chi_{119}(26,\cdot)\) 119.r 24 yes \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{3}{8}\right)\) \(i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{19}{24}\right)\)
\(\chi_{119}(27,\cdot)\) 119.p 16 yes \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(i\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{119}(29,\cdot)\) 119.o 16 no \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(-i\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{119}(30,\cdot)\) 119.n 12 yes \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{119}(31,\cdot)\) 119.s 48 yes \(1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{7}{48}\right)\)
\(\chi_{119}(32,\cdot)\) 119.q 24 yes \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{24}\right)\)
\(\chi_{119}(33,\cdot)\) 119.h 6 yes \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{119}(36,\cdot)\) 119.k 8 no \(1\) \(1\) \(i\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{119}(37,\cdot)\) 119.t 48 yes \(-1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{23}{48}\right)\)
\(\chi_{119}(38,\cdot)\) 119.m 12 yes \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{119}(39,\cdot)\) 119.t 48 yes \(-1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{19}{48}\right)\)