Properties

Modulus $176$
Structure \(C_{2}\times C_{2}\times C_{20}\)
Order $80$

Learn more

Show commands: PariGP / SageMath

sage: H = DirichletGroup(176)
 
pari: g = idealstar(,176,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 80
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{20}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{176}(111,\cdot)$, $\chi_{176}(133,\cdot)$, $\chi_{176}(145,\cdot)$

First 32 of 80 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 \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(13\) \(15\) \(17\) \(19\) \(21\) \(23\)
\(\chi_{176}(1,\cdot)\) 176.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{176}(3,\cdot)\) 176.v 20 yes \(-1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(-i\) \(1\)
\(\chi_{176}(5,\cdot)\) 176.w 20 yes \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(i\) \(-1\)
\(\chi_{176}(7,\cdot)\) 176.o 10 no \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(1\) \(-1\)
\(\chi_{176}(9,\cdot)\) 176.s 10 no \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(-1\) \(1\)
\(\chi_{176}(13,\cdot)\) 176.u 20 yes \(-1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(i\) \(-1\)
\(\chi_{176}(15,\cdot)\) 176.r 10 no \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(1\) \(-1\)
\(\chi_{176}(17,\cdot)\) 176.n 10 no \(-1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(-1\) \(1\)
\(\chi_{176}(19,\cdot)\) 176.x 20 yes \(1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(i\) \(1\)
\(\chi_{176}(21,\cdot)\) 176.l 4 yes \(-1\) \(1\) \(-i\) \(i\) \(1\) \(-1\) \(i\) \(1\) \(-1\) \(i\) \(-i\) \(-1\)
\(\chi_{176}(23,\cdot)\) 176.f 2 no \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\)
\(\chi_{176}(25,\cdot)\) 176.s 10 no \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(-1\) \(1\)
\(\chi_{176}(27,\cdot)\) 176.v 20 yes \(-1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(i\) \(1\)
\(\chi_{176}(29,\cdot)\) 176.u 20 yes \(-1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(i\) \(-1\)
\(\chi_{176}(31,\cdot)\) 176.r 10 no \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(1\) \(-1\)
\(\chi_{176}(35,\cdot)\) 176.x 20 yes \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(i\) \(1\)
\(\chi_{176}(37,\cdot)\) 176.w 20 yes \(1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(i\) \(-1\)
\(\chi_{176}(39,\cdot)\) 176.o 10 no \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(1\) \(-1\)
\(\chi_{176}(41,\cdot)\) 176.t 10 no \(-1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(1\)
\(\chi_{176}(43,\cdot)\) 176.i 4 yes \(1\) \(1\) \(i\) \(i\) \(-1\) \(-1\) \(i\) \(-1\) \(-1\) \(-i\) \(-i\) \(1\)
\(\chi_{176}(45,\cdot)\) 176.j 4 no \(1\) \(1\) \(i\) \(-i\) \(-1\) \(-1\) \(i\) \(1\) \(1\) \(i\) \(-i\) \(-1\)
\(\chi_{176}(47,\cdot)\) 176.r 10 no \(-1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(1\) \(-1\)
\(\chi_{176}(49,\cdot)\) 176.m 5 no \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(1\)
\(\chi_{176}(51,\cdot)\) 176.x 20 yes \(1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(i\) \(1\)
\(\chi_{176}(53,\cdot)\) 176.w 20 yes \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(i\) \(-1\)
\(\chi_{176}(57,\cdot)\) 176.t 10 no \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(1\)
\(\chi_{176}(59,\cdot)\) 176.v 20 yes \(-1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(i\) \(1\)
\(\chi_{176}(61,\cdot)\) 176.u 20 yes \(-1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(i\) \(-1\)
\(\chi_{176}(63,\cdot)\) 176.q 10 no \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(-1\)
\(\chi_{176}(65,\cdot)\) 176.h 2 no \(-1\) \(1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\)
\(\chi_{176}(67,\cdot)\) 176.k 4 no \(-1\) \(1\) \(-i\) \(-i\) \(1\) \(-1\) \(i\) \(-1\) \(1\) \(-i\) \(-i\) \(1\)
\(\chi_{176}(69,\cdot)\) 176.w 20 yes \(1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(i\) \(-1\)
Click here to search among the remaining 48 characters.