Properties

Modulus $368$
Structure \(C_{2}\times C_{2}\times C_{44}\)
Order $176$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(368)
 
pari: g = idealstar(,368,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 176
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{44}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{368}(47,\cdot)$, $\chi_{368}(277,\cdot)$, $\chi_{368}(97,\cdot)$

First 32 of 176 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 \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(21\)
\(\chi_{368}(1,\cdot)\) 368.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{368}(3,\cdot)\) 368.u 44 yes \(-1\) \(1\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{9}{44}\right)\)
\(\chi_{368}(5,\cdot)\) 368.v 44 yes \(-1\) \(1\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{37}{44}\right)\)
\(\chi_{368}(7,\cdot)\) 368.n 22 no \(1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{368}(9,\cdot)\) 368.t 22 no \(1\) \(1\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{368}(11,\cdot)\) 368.x 44 yes \(1\) \(1\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{25}{44}\right)\)
\(\chi_{368}(13,\cdot)\) 368.w 44 yes \(1\) \(1\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{1}{44}\right)\)
\(\chi_{368}(15,\cdot)\) 368.s 22 no \(1\) \(1\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{368}(17,\cdot)\) 368.p 22 no \(-1\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{368}(19,\cdot)\) 368.x 44 yes \(1\) \(1\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{27}{44}\right)\)
\(\chi_{368}(21,\cdot)\) 368.v 44 yes \(-1\) \(1\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{41}{44}\right)\)
\(\chi_{368}(25,\cdot)\) 368.t 22 no \(1\) \(1\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{368}(27,\cdot)\) 368.u 44 yes \(-1\) \(1\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{27}{44}\right)\)
\(\chi_{368}(29,\cdot)\) 368.w 44 yes \(1\) \(1\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{17}{44}\right)\)
\(\chi_{368}(31,\cdot)\) 368.r 22 no \(-1\) \(1\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{368}(33,\cdot)\) 368.p 22 no \(-1\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{368}(35,\cdot)\) 368.u 44 yes \(-1\) \(1\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{25}{44}\right)\)
\(\chi_{368}(37,\cdot)\) 368.v 44 yes \(-1\) \(1\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{29}{44}\right)\)
\(\chi_{368}(39,\cdot)\) 368.o 22 no \(-1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{368}(41,\cdot)\) 368.t 22 no \(1\) \(1\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{368}(43,\cdot)\) 368.x 44 yes \(1\) \(1\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{9}{44}\right)\)
\(\chi_{368}(45,\cdot)\) 368.k 4 yes \(-1\) \(1\) \(i\) \(i\) \(1\) \(-1\) \(i\) \(i\) \(-1\) \(-1\) \(-i\) \(i\)
\(\chi_{368}(47,\cdot)\) 368.d 2 no \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\)
\(\chi_{368}(49,\cdot)\) 368.m 11 no \(1\) \(1\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{368}(51,\cdot)\) 368.x 44 yes \(1\) \(1\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{15}{44}\right)\)
\(\chi_{368}(53,\cdot)\) 368.v 44 yes \(-1\) \(1\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{21}{44}\right)\)
\(\chi_{368}(55,\cdot)\) 368.o 22 no \(-1\) \(1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{368}(57,\cdot)\) 368.q 22 no \(-1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{368}(59,\cdot)\) 368.u 44 yes \(-1\) \(1\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{23}{44}\right)\)
\(\chi_{368}(61,\cdot)\) 368.v 44 yes \(-1\) \(1\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{35}{44}\right)\)
\(\chi_{368}(63,\cdot)\) 368.s 22 no \(1\) \(1\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{368}(65,\cdot)\) 368.p 22 no \(-1\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{19}{22}\right)\)
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