Properties

Modulus $405$
Structure \(C_{108}\times C_{2}\)
Order $216$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(405)
 
pari: g = idealstar(,405,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 216
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{108}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{405}(326,\cdot)$, $\chi_{405}(82,\cdot)$

First 32 of 216 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 \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(13\) \(14\) \(16\) \(17\) \(19\)
\(\chi_{405}(1,\cdot)\) 405.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{405}(2,\cdot)\) 405.x 108 yes \(1\) \(1\) \(e\left(\frac{29}{108}\right)\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{59}{108}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{97}{108}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{7}{18}\right)\)
\(\chi_{405}(4,\cdot)\) 405.t 54 yes \(1\) \(1\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{405}(7,\cdot)\) 405.w 108 yes \(-1\) \(1\) \(e\left(\frac{59}{108}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{107}{108}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{13}{108}\right)\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{13}{18}\right)\)
\(\chi_{405}(8,\cdot)\) 405.r 36 no \(1\) \(1\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{405}(11,\cdot)\) 405.u 54 no \(-1\) \(1\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{54}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{405}(13,\cdot)\) 405.w 108 yes \(-1\) \(1\) \(e\left(\frac{97}{108}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{13}{108}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{47}{108}\right)\) \(e\left(\frac{1}{54}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{11}{18}\right)\)
\(\chi_{405}(14,\cdot)\) 405.v 54 yes \(-1\) \(1\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{1}{54}\right)\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{405}(16,\cdot)\) 405.q 27 no \(1\) \(1\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{405}(17,\cdot)\) 405.r 36 no \(1\) \(1\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{405}(19,\cdot)\) 405.p 18 no \(1\) \(1\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{405}(22,\cdot)\) 405.w 108 yes \(-1\) \(1\) \(e\left(\frac{55}{108}\right)\) \(e\left(\frac{1}{54}\right)\) \(e\left(\frac{43}{108}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{89}{108}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{17}{18}\right)\)
\(\chi_{405}(23,\cdot)\) 405.x 108 yes \(1\) \(1\) \(e\left(\frac{103}{108}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{1}{108}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{95}{108}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{5}{18}\right)\)
\(\chi_{405}(26,\cdot)\) 405.i 6 no \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\)
\(\chi_{405}(28,\cdot)\) 405.l 12 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(-1\)
\(\chi_{405}(29,\cdot)\) 405.v 54 yes \(-1\) \(1\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{405}(31,\cdot)\) 405.q 27 no \(1\) \(1\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{405}(32,\cdot)\) 405.x 108 yes \(1\) \(1\) \(e\left(\frac{37}{108}\right)\) \(e\left(\frac{37}{54}\right)\) \(e\left(\frac{79}{108}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{11}{54}\right)\) \(e\left(\frac{53}{108}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{17}{18}\right)\)
\(\chi_{405}(34,\cdot)\) 405.t 54 yes \(1\) \(1\) \(e\left(\frac{7}{54}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{405}(37,\cdot)\) 405.s 36 no \(-1\) \(1\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{405}(38,\cdot)\) 405.x 108 yes \(1\) \(1\) \(e\left(\frac{71}{108}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{29}{108}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{55}{108}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{1}{18}\right)\)
\(\chi_{405}(41,\cdot)\) 405.u 54 no \(-1\) \(1\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{37}{54}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{405}(43,\cdot)\) 405.w 108 yes \(-1\) \(1\) \(e\left(\frac{17}{108}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{29}{108}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{55}{108}\right)\) \(e\left(\frac{23}{54}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{1}{18}\right)\)
\(\chi_{405}(44,\cdot)\) 405.n 18 no \(-1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{405}(46,\cdot)\) 405.k 9 no \(1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{405}(47,\cdot)\) 405.x 108 yes \(1\) \(1\) \(e\left(\frac{41}{108}\right)\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{35}{108}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{37}{54}\right)\) \(e\left(\frac{85}{108}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{13}{18}\right)\)
\(\chi_{405}(49,\cdot)\) 405.t 54 yes \(1\) \(1\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{405}(52,\cdot)\) 405.w 108 yes \(-1\) \(1\) \(e\left(\frac{47}{108}\right)\) \(e\left(\frac{47}{54}\right)\) \(e\left(\frac{23}{108}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{25}{108}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{7}{18}\right)\)
\(\chi_{405}(53,\cdot)\) 405.m 12 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(i\) \(-1\)
\(\chi_{405}(56,\cdot)\) 405.u 54 no \(-1\) \(1\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{405}(58,\cdot)\) 405.w 108 yes \(-1\) \(1\) \(e\left(\frac{49}{108}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{1}{108}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{95}{108}\right)\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{5}{18}\right)\)
\(\chi_{405}(59,\cdot)\) 405.v 54 yes \(-1\) \(1\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{47}{54}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{4}{9}\right)\)