Properties

Modulus $232$
Structure \(C_{28}\times C_{2}\times C_{2}\)
Order $112$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(232)
 
pari: g = idealstar(,232,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 112
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{28}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{232}(175,\cdot)$, $\chi_{232}(117,\cdot)$, $\chi_{232}(89,\cdot)$

First 32 of 112 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 \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(21\)
\(\chi_{232}(1,\cdot)\) 232.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{232}(3,\cdot)\) 232.v 28 yes \(1\) \(1\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{9}{28}\right)\) \(-i\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{15}{28}\right)\)
\(\chi_{232}(5,\cdot)\) 232.o 14 yes \(1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(-1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{232}(7,\cdot)\) 232.r 14 no \(-1\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{232}(9,\cdot)\) 232.q 14 no \(1\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(-1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{14}\right)\)
\(\chi_{232}(11,\cdot)\) 232.v 28 yes \(1\) \(1\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{17}{28}\right)\) \(-i\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{19}{28}\right)\)
\(\chi_{232}(13,\cdot)\) 232.o 14 yes \(1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(-1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{232}(15,\cdot)\) 232.x 28 no \(1\) \(1\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(i\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{11}{28}\right)\)
\(\chi_{232}(17,\cdot)\) 232.j 4 no \(-1\) \(1\) \(-i\) \(-1\) \(1\) \(-1\) \(-i\) \(-1\) \(i\) \(-i\) \(-i\) \(-i\)
\(\chi_{232}(19,\cdot)\) 232.v 28 yes \(1\) \(1\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{28}\right)\) \(-i\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{27}{28}\right)\)
\(\chi_{232}(21,\cdot)\) 232.u 28 yes \(-1\) \(1\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{11}{28}\right)\) \(-i\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{23}{28}\right)\)
\(\chi_{232}(23,\cdot)\) 232.r 14 no \(-1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{232}(25,\cdot)\) 232.m 7 no \(1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{232}(27,\cdot)\) 232.v 28 yes \(1\) \(1\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{27}{28}\right)\) \(i\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{17}{28}\right)\)
\(\chi_{232}(31,\cdot)\) 232.x 28 no \(1\) \(1\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{13}{28}\right)\) \(-i\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{17}{28}\right)\)
\(\chi_{232}(33,\cdot)\) 232.q 14 no \(1\) \(1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(-1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{14}\right)\)
\(\chi_{232}(35,\cdot)\) 232.t 14 yes \(-1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(-1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{232}(37,\cdot)\) 232.u 28 yes \(-1\) \(1\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{25}{28}\right)\) \(i\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{9}{28}\right)\)
\(\chi_{232}(39,\cdot)\) 232.x 28 no \(1\) \(1\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{19}{28}\right)\) \(i\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{27}{28}\right)\)
\(\chi_{232}(41,\cdot)\) 232.j 4 no \(-1\) \(1\) \(i\) \(-1\) \(1\) \(-1\) \(i\) \(-1\) \(-i\) \(i\) \(i\) \(i\)
\(\chi_{232}(43,\cdot)\) 232.v 28 yes \(1\) \(1\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{28}\right)\) \(-i\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{11}{28}\right)\)
\(\chi_{232}(45,\cdot)\) 232.s 14 yes \(1\) \(1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{13}{14}\right)\)
\(\chi_{232}(47,\cdot)\) 232.x 28 no \(1\) \(1\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{28}\right)\) \(i\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{19}{28}\right)\)
\(\chi_{232}(49,\cdot)\) 232.m 7 no \(1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{232}(51,\cdot)\) 232.t 14 yes \(-1\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(-1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{232}(53,\cdot)\) 232.s 14 yes \(1\) \(1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{14}\right)\)
\(\chi_{232}(55,\cdot)\) 232.x 28 no \(1\) \(1\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{23}{28}\right)\) \(i\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{15}{28}\right)\)
\(\chi_{232}(57,\cdot)\) 232.e 2 no \(1\) \(1\) \(-1\) \(1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(-1\) \(-1\)
\(\chi_{232}(59,\cdot)\) 232.f 2 no \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\)
\(\chi_{232}(61,\cdot)\) 232.u 28 yes \(-1\) \(1\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{23}{28}\right)\) \(-i\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{15}{28}\right)\)
\(\chi_{232}(63,\cdot)\) 232.n 14 no \(-1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(-1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{14}\right)\)
\(\chi_{232}(65,\cdot)\) 232.m 7 no \(1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{2}{7}\right)\)