Properties

Modulus $483$
Structure \(C_{66}\times C_{2}\times C_{2}\)
Order $264$

Learn more about

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(483)
 
pari: g = idealstar(,483,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 264
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{66}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{483}(323,\cdot)$, $\chi_{483}(346,\cdot)$, $\chi_{483}(442,\cdot)$

First 32 of 264 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 \(-1\) \(1\) \(2\) \(4\) \(5\) \(8\) \(10\) \(11\) \(13\) \(16\) \(17\) \(19\)
\(\chi_{483}(1,\cdot)\) 483.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{483}(2,\cdot)\) 483.z 66 yes \(-1\) \(1\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{1}{33}\right)\)
\(\chi_{483}(4,\cdot)\) 483.y 33 no \(1\) \(1\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{2}{33}\right)\)
\(\chi_{483}(5,\cdot)\) 483.ba 66 yes \(-1\) \(1\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{28}{33}\right)\)
\(\chi_{483}(8,\cdot)\) 483.x 22 no \(-1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{483}(10,\cdot)\) 483.bf 66 no \(1\) \(1\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{29}{33}\right)\)
\(\chi_{483}(11,\cdot)\) 483.bc 66 yes \(1\) \(1\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{31}{66}\right)\)
\(\chi_{483}(13,\cdot)\) 483.s 22 no \(-1\) \(1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{483}(16,\cdot)\) 483.y 33 no \(1\) \(1\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{4}{33}\right)\)
\(\chi_{483}(17,\cdot)\) 483.ba 66 yes \(-1\) \(1\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{20}{33}\right)\)
\(\chi_{483}(19,\cdot)\) 483.bf 66 no \(1\) \(1\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{13}{33}\right)\)
\(\chi_{483}(20,\cdot)\) 483.w 22 yes \(-1\) \(1\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{483}(22,\cdot)\) 483.f 2 no \(-1\) \(1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\)
\(\chi_{483}(25,\cdot)\) 483.y 33 no \(1\) \(1\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{23}{33}\right)\)
\(\chi_{483}(26,\cdot)\) 483.bb 66 yes \(1\) \(1\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{5}{66}\right)\)
\(\chi_{483}(29,\cdot)\) 483.x 22 no \(-1\) \(1\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{483}(31,\cdot)\) 483.be 66 no \(-1\) \(1\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{61}{66}\right)\)
\(\chi_{483}(32,\cdot)\) 483.z 66 yes \(-1\) \(1\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{5}{33}\right)\)
\(\chi_{483}(34,\cdot)\) 483.r 22 no \(1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{483}(37,\cdot)\) 483.bd 66 no \(-1\) \(1\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{65}{66}\right)\)
\(\chi_{483}(38,\cdot)\) 483.ba 66 yes \(-1\) \(1\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{14}{33}\right)\)
\(\chi_{483}(40,\cdot)\) 483.bf 66 no \(1\) \(1\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{31}{33}\right)\)
\(\chi_{483}(41,\cdot)\) 483.v 22 yes \(1\) \(1\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{483}(43,\cdot)\) 483.t 22 no \(-1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{483}(44,\cdot)\) 483.bc 66 yes \(1\) \(1\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{35}{66}\right)\)
\(\chi_{483}(47,\cdot)\) 483.n 6 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{483}(50,\cdot)\) 483.x 22 no \(-1\) \(1\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{483}(52,\cdot)\) 483.be 66 no \(-1\) \(1\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{7}{66}\right)\)
\(\chi_{483}(53,\cdot)\) 483.bc 66 yes \(1\) \(1\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{19}{66}\right)\)
\(\chi_{483}(55,\cdot)\) 483.s 22 no \(-1\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{7}{22}\right)\)
\(\chi_{483}(58,\cdot)\) 483.y 33 no \(1\) \(1\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{10}{33}\right)\)
\(\chi_{483}(59,\cdot)\) 483.bb 66 yes \(1\) \(1\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{25}{66}\right)\)