Properties

Modulus $460$
Structure \(C_{44}\times C_{2}\times C_{2}\)
Order $176$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(460)
 
pari: g = idealstar(,460,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 176
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{44}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{460}(231,\cdot)$, $\chi_{460}(277,\cdot)$, $\chi_{460}(281,\cdot)$

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 \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(17\) \(19\) \(21\) \(27\) \(29\)
\(\chi_{460}(1,\cdot)\) 460.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{460}(3,\cdot)\) 460.w 44 yes \(1\) \(1\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{460}(7,\cdot)\) 460.v 44 yes \(-1\) \(1\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{460}(9,\cdot)\) 460.s 22 no \(1\) \(1\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{460}(11,\cdot)\) 460.q 22 no \(1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{460}(13,\cdot)\) 460.u 44 no \(-1\) \(1\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{460}(17,\cdot)\) 460.x 44 no \(1\) \(1\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{460}(19,\cdot)\) 460.o 22 yes \(1\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{460}(21,\cdot)\) 460.p 22 no \(-1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{460}(27,\cdot)\) 460.w 44 yes \(1\) \(1\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{460}(29,\cdot)\) 460.s 22 no \(1\) \(1\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{460}(31,\cdot)\) 460.t 22 no \(-1\) \(1\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{460}(33,\cdot)\) 460.x 44 no \(1\) \(1\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{460}(37,\cdot)\) 460.x 44 no \(1\) \(1\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{460}(39,\cdot)\) 460.n 22 yes \(-1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{460}(41,\cdot)\) 460.m 11 no \(1\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{460}(43,\cdot)\) 460.v 44 yes \(-1\) \(1\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{460}(47,\cdot)\) 460.j 4 no \(1\) \(1\) \(i\) \(-i\) \(-1\) \(-1\) \(-i\) \(i\) \(1\) \(1\) \(-i\) \(-1\)
\(\chi_{460}(49,\cdot)\) 460.s 22 no \(1\) \(1\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{460}(51,\cdot)\) 460.q 22 no \(1\) \(1\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{460}(53,\cdot)\) 460.x 44 no \(1\) \(1\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{460}(57,\cdot)\) 460.x 44 no \(1\) \(1\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{460}(59,\cdot)\) 460.n 22 yes \(-1\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{460}(61,\cdot)\) 460.p 22 no \(-1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{460}(63,\cdot)\) 460.v 44 yes \(-1\) \(1\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{460}(67,\cdot)\) 460.v 44 yes \(-1\) \(1\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{460}(71,\cdot)\) 460.t 22 no \(-1\) \(1\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{460}(73,\cdot)\) 460.u 44 no \(-1\) \(1\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{460}(77,\cdot)\) 460.u 44 no \(-1\) \(1\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{460}(79,\cdot)\) 460.o 22 yes \(1\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{460}(81,\cdot)\) 460.m 11 no \(1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{460}(83,\cdot)\) 460.v 44 yes \(-1\) \(1\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{15}{22}\right)\)