Properties

Modulus $322$
Structure \(C_{66}\times C_{2}\)
Order $132$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(322)
 
pari: g = idealstar(,322,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 132
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{66}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{322}(185,\cdot)$, $\chi_{322}(281,\cdot)$

First 32 of 132 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 \(-1\) \(1\) \(3\) \(5\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(25\) \(27\)
\(\chi_{322}(1,\cdot)\) 322.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{322}(3,\cdot)\) 322.n 66 no \(-1\) \(1\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{322}(5,\cdot)\) 322.o 66 no \(1\) \(1\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{322}(9,\cdot)\) 322.m 33 no \(1\) \(1\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{322}(11,\cdot)\) 322.p 66 no \(-1\) \(1\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{322}(13,\cdot)\) 322.l 22 no \(-1\) \(1\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{322}(15,\cdot)\) 322.j 22 no \(-1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{322}(17,\cdot)\) 322.o 66 no \(1\) \(1\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{322}(19,\cdot)\) 322.o 66 no \(1\) \(1\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{322}(25,\cdot)\) 322.m 33 no \(1\) \(1\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{322}(27,\cdot)\) 322.l 22 no \(-1\) \(1\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{322}(29,\cdot)\) 322.i 11 no \(1\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{322}(31,\cdot)\) 322.n 66 no \(-1\) \(1\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{322}(33,\cdot)\) 322.o 66 no \(1\) \(1\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{322}(37,\cdot)\) 322.p 66 no \(-1\) \(1\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{322}(39,\cdot)\) 322.m 33 no \(1\) \(1\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{322}(41,\cdot)\) 322.l 22 no \(-1\) \(1\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{322}(43,\cdot)\) 322.j 22 no \(-1\) \(1\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{322}(45,\cdot)\) 322.g 6 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\)
\(\chi_{322}(47,\cdot)\) 322.h 6 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\)
\(\chi_{322}(51,\cdot)\) 322.p 66 no \(-1\) \(1\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{322}(53,\cdot)\) 322.p 66 no \(-1\) \(1\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{322}(55,\cdot)\) 322.l 22 no \(-1\) \(1\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{22}\right)\)
\(\chi_{322}(57,\cdot)\) 322.j 22 no \(-1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{322}(59,\cdot)\) 322.n 66 no \(-1\) \(1\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{322}(61,\cdot)\) 322.o 66 no \(1\) \(1\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{322}(65,\cdot)\) 322.p 66 no \(-1\) \(1\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{322}(67,\cdot)\) 322.p 66 no \(-1\) \(1\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{322}(71,\cdot)\) 322.i 11 no \(1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{322}(73,\cdot)\) 322.n 66 no \(-1\) \(1\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{322}(75,\cdot)\) 322.n 66 no \(-1\) \(1\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{322}(79,\cdot)\) 322.p 66 no \(-1\) \(1\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{6}{11}\right)\)