Properties

Modulus $324$
Structure \(C_{2}\times C_{54}\)
Order $108$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(324)
 
pari: g = idealstar(,324,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 108
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{54}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{324}(163,\cdot)$, $\chi_{324}(245,\cdot)$

First 32 of 108 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 \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\)
\(\chi_{324}(1,\cdot)\) 324.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{324}(5,\cdot)\) 324.o 54 no \(-1\) \(1\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{37}{54}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{14}{27}\right)\)
\(\chi_{324}(7,\cdot)\) 324.n 54 yes \(-1\) \(1\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{23}{54}\right)\)
\(\chi_{324}(11,\cdot)\) 324.p 54 yes \(1\) \(1\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{17}{54}\right)\)
\(\chi_{324}(13,\cdot)\) 324.m 27 no \(1\) \(1\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{26}{27}\right)\)
\(\chi_{324}(17,\cdot)\) 324.k 18 no \(-1\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{324}(19,\cdot)\) 324.j 18 no \(-1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{18}\right)\)
\(\chi_{324}(23,\cdot)\) 324.p 54 yes \(1\) \(1\) \(e\left(\frac{37}{54}\right)\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{31}{54}\right)\)
\(\chi_{324}(25,\cdot)\) 324.m 27 no \(1\) \(1\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{1}{27}\right)\)
\(\chi_{324}(29,\cdot)\) 324.o 54 no \(-1\) \(1\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{19}{27}\right)\)
\(\chi_{324}(31,\cdot)\) 324.n 54 yes \(-1\) \(1\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{23}{54}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{49}{54}\right)\)
\(\chi_{324}(35,\cdot)\) 324.l 18 no \(1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{17}{18}\right)\)
\(\chi_{324}(37,\cdot)\) 324.i 9 no \(1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{324}(41,\cdot)\) 324.o 54 no \(-1\) \(1\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{17}{27}\right)\)
\(\chi_{324}(43,\cdot)\) 324.n 54 yes \(-1\) \(1\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{1}{54}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{35}{54}\right)\)
\(\chi_{324}(47,\cdot)\) 324.p 54 yes \(1\) \(1\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{5}{54}\right)\)
\(\chi_{324}(49,\cdot)\) 324.m 27 no \(1\) \(1\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{23}{27}\right)\)
\(\chi_{324}(53,\cdot)\) 324.g 6 no \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{324}(55,\cdot)\) 324.f 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{324}(59,\cdot)\) 324.p 54 yes \(1\) \(1\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{37}{54}\right)\)
\(\chi_{324}(61,\cdot)\) 324.m 27 no \(1\) \(1\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{7}{27}\right)\)
\(\chi_{324}(65,\cdot)\) 324.o 54 no \(-1\) \(1\) \(e\left(\frac{11}{54}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{13}{27}\right)\)
\(\chi_{324}(67,\cdot)\) 324.n 54 yes \(-1\) \(1\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{43}{54}\right)\)
\(\chi_{324}(71,\cdot)\) 324.l 18 no \(1\) \(1\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{7}{18}\right)\)
\(\chi_{324}(73,\cdot)\) 324.i 9 no \(1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{324}(77,\cdot)\) 324.o 54 no \(-1\) \(1\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{47}{54}\right)\) \(e\left(\frac{20}{27}\right)\)
\(\chi_{324}(79,\cdot)\) 324.n 54 yes \(-1\) \(1\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{11}{54}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{47}{54}\right)\)
\(\chi_{324}(83,\cdot)\) 324.p 54 yes \(1\) \(1\) \(e\left(\frac{23}{54}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{37}{54}\right)\) \(e\left(\frac{47}{54}\right)\)
\(\chi_{324}(85,\cdot)\) 324.m 27 no \(1\) \(1\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{20}{27}\right)\)
\(\chi_{324}(89,\cdot)\) 324.k 18 no \(-1\) \(1\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{324}(91,\cdot)\) 324.j 18 no \(-1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{18}\right)\)
\(\chi_{324}(95,\cdot)\) 324.p 54 yes \(1\) \(1\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{43}{54}\right)\)
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