# Properties

 Modulus $1296$ Structure $$C_{2}\times C_{2}\times C_{108}$$ Order $432$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1296)

pari: g = idealstar(,1296,2)

## Character group

 sage: G.order()  pari: g.no Order = 432 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{108}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1296}(1135,\cdot)$, $\chi_{1296}(325,\cdot)$, $\chi_{1296}(1217,\cdot)$

## First 32 of 432 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 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$
$$\chi_{1296}(1,\cdot)$$ 1296.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1296}(5,\cdot)$$ 1296.bu 108 yes $$-1$$ $$1$$ $$e\left(\frac{5}{108}\right)$$ $$e\left(\frac{17}{54}\right)$$ $$e\left(\frac{85}{108}\right)$$ $$e\left(\frac{17}{108}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{5}{27}\right)$$ $$e\left(\frac{5}{54}\right)$$ $$e\left(\frac{55}{108}\right)$$ $$e\left(\frac{14}{27}\right)$$
$$\chi_{1296}(7,\cdot)$$ 1296.br 54 no $$-1$$ $$1$$ $$e\left(\frac{17}{54}\right)$$ $$e\left(\frac{13}{54}\right)$$ $$e\left(\frac{23}{27}\right)$$ $$e\left(\frac{47}{54}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{41}{54}\right)$$ $$e\left(\frac{17}{27}\right)$$ $$e\left(\frac{25}{54}\right)$$ $$e\left(\frac{23}{54}\right)$$
$$\chi_{1296}(11,\cdot)$$ 1296.bs 108 yes $$1$$ $$1$$ $$e\left(\frac{85}{108}\right)$$ $$e\left(\frac{23}{27}\right)$$ $$e\left(\frac{95}{108}\right)$$ $$e\left(\frac{73}{108}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{35}{54}\right)$$ $$e\left(\frac{31}{54}\right)$$ $$e\left(\frac{71}{108}\right)$$ $$e\left(\frac{17}{54}\right)$$
$$\chi_{1296}(13,\cdot)$$ 1296.bv 108 yes $$1$$ $$1$$ $$e\left(\frac{17}{108}\right)$$ $$e\left(\frac{47}{54}\right)$$ $$e\left(\frac{73}{108}\right)$$ $$e\left(\frac{47}{108}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{7}{54}\right)$$ $$e\left(\frac{17}{54}\right)$$ $$e\left(\frac{79}{108}\right)$$ $$e\left(\frac{26}{27}\right)$$
$$\chi_{1296}(17,\cdot)$$ 1296.bc 18 no $$-1$$ $$1$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$
$$\chi_{1296}(19,\cdot)$$ 1296.bi 36 no $$-1$$ $$1$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{5}{18}\right)$$
$$\chi_{1296}(23,\cdot)$$ 1296.bn 54 no $$1$$ $$1$$ $$e\left(\frac{5}{27}\right)$$ $$e\left(\frac{41}{54}\right)$$ $$e\left(\frac{35}{54}\right)$$ $$e\left(\frac{7}{54}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{20}{27}\right)$$ $$e\left(\frac{10}{27}\right)$$ $$e\left(\frac{1}{27}\right)$$ $$e\left(\frac{31}{54}\right)$$
$$\chi_{1296}(25,\cdot)$$ 1296.bp 54 no $$1$$ $$1$$ $$e\left(\frac{5}{54}\right)$$ $$e\left(\frac{17}{27}\right)$$ $$e\left(\frac{31}{54}\right)$$ $$e\left(\frac{17}{54}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{10}{27}\right)$$ $$e\left(\frac{5}{27}\right)$$ $$e\left(\frac{1}{54}\right)$$ $$e\left(\frac{1}{27}\right)$$
$$\chi_{1296}(29,\cdot)$$ 1296.bu 108 yes $$-1$$ $$1$$ $$e\left(\frac{55}{108}\right)$$ $$e\left(\frac{25}{54}\right)$$ $$e\left(\frac{71}{108}\right)$$ $$e\left(\frac{79}{108}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{1}{27}\right)$$ $$e\left(\frac{1}{54}\right)$$ $$e\left(\frac{65}{108}\right)$$ $$e\left(\frac{19}{27}\right)$$
$$\chi_{1296}(31,\cdot)$$ 1296.bm 54 no $$-1$$ $$1$$ $$e\left(\frac{14}{27}\right)$$ $$e\left(\frac{23}{54}\right)$$ $$e\left(\frac{17}{54}\right)$$ $$e\left(\frac{26}{27}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{31}{54}\right)$$ $$e\left(\frac{1}{27}\right)$$ $$e\left(\frac{19}{27}\right)$$ $$e\left(\frac{49}{54}\right)$$
$$\chi_{1296}(35,\cdot)$$ 1296.bk 36 no $$1$$ $$1$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{17}{18}\right)$$
$$\chi_{1296}(37,\cdot)$$ 1296.bh 36 no $$1$$ $$1$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{5}{9}\right)$$
$$\chi_{1296}(41,\cdot)$$ 1296.bl 54 no $$-1$$ $$1$$ $$e\left(\frac{2}{27}\right)$$ $$e\left(\frac{19}{27}\right)$$ $$e\left(\frac{7}{27}\right)$$ $$e\left(\frac{19}{54}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{43}{54}\right)$$ $$e\left(\frac{4}{27}\right)$$ $$e\left(\frac{22}{27}\right)$$ $$e\left(\frac{17}{27}\right)$$
$$\chi_{1296}(43,\cdot)$$ 1296.bt 108 yes $$-1$$ $$1$$ $$e\left(\frac{67}{108}\right)$$ $$e\left(\frac{14}{27}\right)$$ $$e\left(\frac{5}{108}\right)$$ $$e\left(\frac{1}{108}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{13}{27}\right)$$ $$e\left(\frac{13}{54}\right)$$ $$e\left(\frac{89}{108}\right)$$ $$e\left(\frac{35}{54}\right)$$
$$\chi_{1296}(47,\cdot)$$ 1296.bq 54 no $$1$$ $$1$$ $$e\left(\frac{53}{54}\right)$$ $$e\left(\frac{31}{54}\right)$$ $$e\left(\frac{5}{27}\right)$$ $$e\left(\frac{1}{27}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{25}{27}\right)$$ $$e\left(\frac{26}{27}\right)$$ $$e\left(\frac{43}{54}\right)$$ $$e\left(\frac{5}{54}\right)$$
$$\chi_{1296}(49,\cdot)$$ 1296.bg 27 no $$1$$ $$1$$ $$e\left(\frac{17}{27}\right)$$ $$e\left(\frac{13}{27}\right)$$ $$e\left(\frac{19}{27}\right)$$ $$e\left(\frac{20}{27}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{14}{27}\right)$$ $$e\left(\frac{7}{27}\right)$$ $$e\left(\frac{25}{27}\right)$$ $$e\left(\frac{23}{27}\right)$$
$$\chi_{1296}(53,\cdot)$$ 1296.x 12 no $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1296}(55,\cdot)$$ 1296.t 6 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1296}(59,\cdot)$$ 1296.bs 108 yes $$1$$ $$1$$ $$e\left(\frac{77}{108}\right)$$ $$e\left(\frac{4}{27}\right)$$ $$e\left(\frac{67}{108}\right)$$ $$e\left(\frac{89}{108}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{19}{54}\right)$$ $$e\left(\frac{23}{54}\right)$$ $$e\left(\frac{91}{108}\right)$$ $$e\left(\frac{37}{54}\right)$$
$$\chi_{1296}(61,\cdot)$$ 1296.bv 108 yes $$1$$ $$1$$ $$e\left(\frac{97}{108}\right)$$ $$e\left(\frac{49}{54}\right)$$ $$e\left(\frac{29}{108}\right)$$ $$e\left(\frac{103}{108}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{5}{54}\right)$$ $$e\left(\frac{43}{54}\right)$$ $$e\left(\frac{95}{108}\right)$$ $$e\left(\frac{7}{27}\right)$$
$$\chi_{1296}(65,\cdot)$$ 1296.bo 54 no $$-1$$ $$1$$ $$e\left(\frac{11}{54}\right)$$ $$e\left(\frac{5}{27}\right)$$ $$e\left(\frac{25}{54}\right)$$ $$e\left(\frac{16}{27}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{17}{54}\right)$$ $$e\left(\frac{11}{27}\right)$$ $$e\left(\frac{13}{54}\right)$$ $$e\left(\frac{13}{27}\right)$$
$$\chi_{1296}(67,\cdot)$$ 1296.bt 108 yes $$-1$$ $$1$$ $$e\left(\frac{53}{108}\right)$$ $$e\left(\frac{1}{27}\right)$$ $$e\left(\frac{91}{108}\right)$$ $$e\left(\frac{83}{108}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{26}{27}\right)$$ $$e\left(\frac{53}{54}\right)$$ $$e\left(\frac{43}{108}\right)$$ $$e\left(\frac{43}{54}\right)$$
$$\chi_{1296}(71,\cdot)$$ 1296.bd 18 no $$1$$ $$1$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$
$$\chi_{1296}(73,\cdot)$$ 1296.bb 18 no $$1$$ $$1$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$
$$\chi_{1296}(77,\cdot)$$ 1296.bu 108 yes $$-1$$ $$1$$ $$e\left(\frac{11}{108}\right)$$ $$e\left(\frac{5}{54}\right)$$ $$e\left(\frac{79}{108}\right)$$ $$e\left(\frac{59}{108}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{11}{27}\right)$$ $$e\left(\frac{11}{54}\right)$$ $$e\left(\frac{13}{108}\right)$$ $$e\left(\frac{20}{27}\right)$$
$$\chi_{1296}(79,\cdot)$$ 1296.bm 54 no $$-1$$ $$1$$ $$e\left(\frac{25}{27}\right)$$ $$e\left(\frac{43}{54}\right)$$ $$e\left(\frac{13}{54}\right)$$ $$e\left(\frac{4}{27}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{11}{54}\right)$$ $$e\left(\frac{23}{27}\right)$$ $$e\left(\frac{5}{27}\right)$$ $$e\left(\frac{47}{54}\right)$$
$$\chi_{1296}(83,\cdot)$$ 1296.bs 108 yes $$1$$ $$1$$ $$e\left(\frac{19}{108}\right)$$ $$e\left(\frac{8}{27}\right)$$ $$e\left(\frac{53}{108}\right)$$ $$e\left(\frac{43}{108}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{11}{54}\right)$$ $$e\left(\frac{19}{54}\right)$$ $$e\left(\frac{101}{108}\right)$$ $$e\left(\frac{47}{54}\right)$$
$$\chi_{1296}(85,\cdot)$$ 1296.bv 108 yes $$1$$ $$1$$ $$e\left(\frac{11}{108}\right)$$ $$e\left(\frac{5}{54}\right)$$ $$e\left(\frac{79}{108}\right)$$ $$e\left(\frac{5}{108}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{49}{54}\right)$$ $$e\left(\frac{11}{54}\right)$$ $$e\left(\frac{13}{108}\right)$$ $$e\left(\frac{20}{27}\right)$$
$$\chi_{1296}(89,\cdot)$$ 1296.bf 18 no $$-1$$ $$1$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$
$$\chi_{1296}(91,\cdot)$$ 1296.bi 36 no $$-1$$ $$1$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{7}{18}\right)$$
$$\chi_{1296}(95,\cdot)$$ 1296.bq 54 no $$1$$ $$1$$ $$e\left(\frac{13}{54}\right)$$ $$e\left(\frac{29}{54}\right)$$ $$e\left(\frac{16}{27}\right)$$ $$e\left(\frac{14}{27}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{26}{27}\right)$$ $$e\left(\frac{13}{27}\right)$$ $$e\left(\frac{35}{54}\right)$$ $$e\left(\frac{43}{54}\right)$$