# Properties

 Modulus $1137$ Structure $$C_{378}\times C_{2}$$ Order $756$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(1137)

pari: g = idealstar(,1137,2)

## Character group

 sage: G.order()  pari: g.no Order = 756 sage: H.invariants()  pari: g.cyc Structure = $$C_{378}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1137}(380,\cdot)$, $\chi_{1137}(760,\cdot)$

## First 32 of 756 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$7$$ $$8$$ $$10$$ $$11$$ $$13$$ $$14$$ $$16$$
$$\chi_{1137}(1,\cdot)$$ 1137.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1137}(2,\cdot)$$ 1137.be 378 yes $$1$$ $$1$$ $$e\left(\frac{95}{189}\right)$$ $$e\left(\frac{1}{189}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{155}{378}\right)$$ $$e\left(\frac{32}{63}\right)$$ $$e\left(\frac{145}{378}\right)$$ $$e\left(\frac{2}{27}\right)$$ $$e\left(\frac{313}{378}\right)$$ $$e\left(\frac{115}{126}\right)$$ $$e\left(\frac{2}{189}\right)$$
$$\chi_{1137}(4,\cdot)$$ 1137.bc 189 no $$1$$ $$1$$ $$e\left(\frac{1}{189}\right)$$ $$e\left(\frac{2}{189}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{155}{189}\right)$$ $$e\left(\frac{1}{63}\right)$$ $$e\left(\frac{145}{189}\right)$$ $$e\left(\frac{4}{27}\right)$$ $$e\left(\frac{124}{189}\right)$$ $$e\left(\frac{52}{63}\right)$$ $$e\left(\frac{4}{189}\right)$$
$$\chi_{1137}(5,\cdot)$$ 1137.t 42 yes $$-1$$ $$1$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{11}{21}\right)$$
$$\chi_{1137}(7,\cdot)$$ 1137.bf 378 no $$-1$$ $$1$$ $$e\left(\frac{155}{378}\right)$$ $$e\left(\frac{155}{189}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{211}{378}\right)$$ $$e\left(\frac{29}{126}\right)$$ $$e\left(\frac{173}{378}\right)$$ $$e\left(\frac{53}{54}\right)$$ $$e\left(\frac{131}{378}\right)$$ $$e\left(\frac{61}{63}\right)$$ $$e\left(\frac{121}{189}\right)$$
$$\chi_{1137}(8,\cdot)$$ 1137.bb 126 yes $$1$$ $$1$$ $$e\left(\frac{32}{63}\right)$$ $$e\left(\frac{1}{63}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{29}{126}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{19}{126}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{61}{126}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{2}{63}\right)$$
$$\chi_{1137}(10,\cdot)$$ 1137.bf 378 no $$-1$$ $$1$$ $$e\left(\frac{145}{378}\right)$$ $$e\left(\frac{145}{189}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{173}{378}\right)$$ $$e\left(\frac{19}{126}\right)$$ $$e\left(\frac{235}{378}\right)$$ $$e\left(\frac{13}{54}\right)$$ $$e\left(\frac{25}{378}\right)$$ $$e\left(\frac{53}{63}\right)$$ $$e\left(\frac{101}{189}\right)$$
$$\chi_{1137}(11,\cdot)$$ 1137.x 54 yes $$1$$ $$1$$ $$e\left(\frac{2}{27}\right)$$ $$e\left(\frac{4}{27}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{53}{54}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{13}{54}\right)$$ $$e\left(\frac{2}{27}\right)$$ $$e\left(\frac{37}{54}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{8}{27}\right)$$
$$\chi_{1137}(13,\cdot)$$ 1137.bf 378 no $$-1$$ $$1$$ $$e\left(\frac{313}{378}\right)$$ $$e\left(\frac{124}{189}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{131}{378}\right)$$ $$e\left(\frac{61}{126}\right)$$ $$e\left(\frac{25}{378}\right)$$ $$e\left(\frac{37}{54}\right)$$ $$e\left(\frac{67}{378}\right)$$ $$e\left(\frac{11}{63}\right)$$ $$e\left(\frac{59}{189}\right)$$
$$\chi_{1137}(14,\cdot)$$ 1137.ba 126 yes $$-1$$ $$1$$ $$e\left(\frac{115}{126}\right)$$ $$e\left(\frac{52}{63}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{61}{63}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{53}{63}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{11}{63}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{41}{63}\right)$$
$$\chi_{1137}(16,\cdot)$$ 1137.bc 189 no $$1$$ $$1$$ $$e\left(\frac{2}{189}\right)$$ $$e\left(\frac{4}{189}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{121}{189}\right)$$ $$e\left(\frac{2}{63}\right)$$ $$e\left(\frac{101}{189}\right)$$ $$e\left(\frac{8}{27}\right)$$ $$e\left(\frac{59}{189}\right)$$ $$e\left(\frac{41}{63}\right)$$ $$e\left(\frac{8}{189}\right)$$
$$\chi_{1137}(17,\cdot)$$ 1137.be 378 yes $$1$$ $$1$$ $$e\left(\frac{152}{189}\right)$$ $$e\left(\frac{115}{189}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{59}{378}\right)$$ $$e\left(\frac{26}{63}\right)$$ $$e\left(\frac{43}{378}\right)$$ $$e\left(\frac{14}{27}\right)$$ $$e\left(\frac{85}{378}\right)$$ $$e\left(\frac{121}{126}\right)$$ $$e\left(\frac{41}{189}\right)$$
$$\chi_{1137}(19,\cdot)$$ 1137.bc 189 no $$1$$ $$1$$ $$e\left(\frac{116}{189}\right)$$ $$e\left(\frac{43}{189}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{25}{189}\right)$$ $$e\left(\frac{53}{63}\right)$$ $$e\left(\frac{188}{189}\right)$$ $$e\left(\frac{5}{27}\right)$$ $$e\left(\frac{20}{189}\right)$$ $$e\left(\frac{47}{63}\right)$$ $$e\left(\frac{86}{189}\right)$$
$$\chi_{1137}(20,\cdot)$$ 1137.bd 378 yes $$-1$$ $$1$$ $$e\left(\frac{335}{378}\right)$$ $$e\left(\frac{146}{189}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{164}{189}\right)$$ $$e\left(\frac{83}{126}\right)$$ $$e\left(\frac{1}{189}\right)$$ $$e\left(\frac{17}{54}\right)$$ $$e\left(\frac{169}{189}\right)$$ $$e\left(\frac{95}{126}\right)$$ $$e\left(\frac{103}{189}\right)$$
$$\chi_{1137}(22,\cdot)$$ 1137.bc 189 no $$1$$ $$1$$ $$e\left(\frac{109}{189}\right)$$ $$e\left(\frac{29}{189}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{74}{189}\right)$$ $$e\left(\frac{46}{63}\right)$$ $$e\left(\frac{118}{189}\right)$$ $$e\left(\frac{4}{27}\right)$$ $$e\left(\frac{97}{189}\right)$$ $$e\left(\frac{61}{63}\right)$$ $$e\left(\frac{58}{189}\right)$$
$$\chi_{1137}(23,\cdot)$$ 1137.ba 126 yes $$-1$$ $$1$$ $$e\left(\frac{71}{126}\right)$$ $$e\left(\frac{8}{63}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{53}{63}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{13}{63}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{55}{63}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{16}{63}\right)$$
$$\chi_{1137}(25,\cdot)$$ 1137.q 21 no $$1$$ $$1$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{21}\right)$$
$$\chi_{1137}(26,\cdot)$$ 1137.bd 378 yes $$-1$$ $$1$$ $$e\left(\frac{125}{378}\right)$$ $$e\left(\frac{125}{189}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{143}{189}\right)$$ $$e\left(\frac{125}{126}\right)$$ $$e\left(\frac{85}{189}\right)$$ $$e\left(\frac{41}{54}\right)$$ $$e\left(\frac{1}{189}\right)$$ $$e\left(\frac{11}{126}\right)$$ $$e\left(\frac{61}{189}\right)$$
$$\chi_{1137}(28,\cdot)$$ 1137.bf 378 no $$-1$$ $$1$$ $$e\left(\frac{157}{378}\right)$$ $$e\left(\frac{157}{189}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{143}{378}\right)$$ $$e\left(\frac{31}{126}\right)$$ $$e\left(\frac{85}{378}\right)$$ $$e\left(\frac{7}{54}\right)$$ $$e\left(\frac{1}{378}\right)$$ $$e\left(\frac{50}{63}\right)$$ $$e\left(\frac{125}{189}\right)$$
$$\chi_{1137}(29,\cdot)$$ 1137.bb 126 yes $$1$$ $$1$$ $$e\left(\frac{11}{63}\right)$$ $$e\left(\frac{22}{63}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{71}{126}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{103}{126}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{19}{126}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{44}{63}\right)$$
$$\chi_{1137}(31,\cdot)$$ 1137.bf 378 no $$-1$$ $$1$$ $$e\left(\frac{205}{378}\right)$$ $$e\left(\frac{16}{189}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{23}{378}\right)$$ $$e\left(\frac{79}{126}\right)$$ $$e\left(\frac{241}{378}\right)$$ $$e\left(\frac{37}{54}\right)$$ $$e\left(\frac{283}{378}\right)$$ $$e\left(\frac{38}{63}\right)$$ $$e\left(\frac{32}{189}\right)$$
$$\chi_{1137}(32,\cdot)$$ 1137.be 378 yes $$1$$ $$1$$ $$e\left(\frac{97}{189}\right)$$ $$e\left(\frac{5}{189}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{19}{378}\right)$$ $$e\left(\frac{34}{63}\right)$$ $$e\left(\frac{347}{378}\right)$$ $$e\left(\frac{10}{27}\right)$$ $$e\left(\frac{53}{378}\right)$$ $$e\left(\frac{71}{126}\right)$$ $$e\left(\frac{10}{189}\right)$$
$$\chi_{1137}(34,\cdot)$$ 1137.bc 189 no $$1$$ $$1$$ $$e\left(\frac{58}{189}\right)$$ $$e\left(\frac{116}{189}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{107}{189}\right)$$ $$e\left(\frac{58}{63}\right)$$ $$e\left(\frac{94}{189}\right)$$ $$e\left(\frac{16}{27}\right)$$ $$e\left(\frac{10}{189}\right)$$ $$e\left(\frac{55}{63}\right)$$ $$e\left(\frac{43}{189}\right)$$
$$\chi_{1137}(35,\cdot)$$ 1137.be 378 yes $$1$$ $$1$$ $$e\left(\frac{55}{189}\right)$$ $$e\left(\frac{110}{189}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{229}{378}\right)$$ $$e\left(\frac{55}{63}\right)$$ $$e\left(\frac{263}{378}\right)$$ $$e\left(\frac{4}{27}\right)$$ $$e\left(\frac{221}{378}\right)$$ $$e\left(\frac{113}{126}\right)$$ $$e\left(\frac{31}{189}\right)$$
$$\chi_{1137}(37,\cdot)$$ 1137.y 63 no $$1$$ $$1$$ $$e\left(\frac{53}{63}\right)$$ $$e\left(\frac{43}{63}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{25}{63}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{62}{63}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{20}{63}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{23}{63}\right)$$
$$\chi_{1137}(38,\cdot)$$ 1137.be 378 yes $$1$$ $$1$$ $$e\left(\frac{22}{189}\right)$$ $$e\left(\frac{44}{189}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{205}{378}\right)$$ $$e\left(\frac{22}{63}\right)$$ $$e\left(\frac{143}{378}\right)$$ $$e\left(\frac{7}{27}\right)$$ $$e\left(\frac{353}{378}\right)$$ $$e\left(\frac{83}{126}\right)$$ $$e\left(\frac{88}{189}\right)$$
$$\chi_{1137}(40,\cdot)$$ 1137.p 18 no $$-1$$ $$1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$1$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{9}\right)$$
$$\chi_{1137}(41,\cdot)$$ 1137.ba 126 yes $$-1$$ $$1$$ $$e\left(\frac{83}{126}\right)$$ $$e\left(\frac{20}{63}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{38}{63}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{1}{63}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{43}{63}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{40}{63}\right)$$
$$\chi_{1137}(43,\cdot)$$ 1137.bf 378 no $$-1$$ $$1$$ $$e\left(\frac{107}{378}\right)$$ $$e\left(\frac{107}{189}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{331}{378}\right)$$ $$e\left(\frac{107}{126}\right)$$ $$e\left(\frac{17}{378}\right)$$ $$e\left(\frac{23}{54}\right)$$ $$e\left(\frac{227}{378}\right)$$ $$e\left(\frac{10}{63}\right)$$ $$e\left(\frac{25}{189}\right)$$
$$\chi_{1137}(44,\cdot)$$ 1137.bb 126 yes $$1$$ $$1$$ $$e\left(\frac{5}{63}\right)$$ $$e\left(\frac{10}{63}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{101}{126}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{1}{126}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{43}{126}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{20}{63}\right)$$
$$\chi_{1137}(46,\cdot)$$ 1137.bf 378 no $$-1$$ $$1$$ $$e\left(\frac{25}{378}\right)$$ $$e\left(\frac{25}{189}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{95}{378}\right)$$ $$e\left(\frac{25}{126}\right)$$ $$e\left(\frac{223}{378}\right)$$ $$e\left(\frac{19}{54}\right)$$ $$e\left(\frac{265}{378}\right)$$ $$e\left(\frac{20}{63}\right)$$ $$e\left(\frac{50}{189}\right)$$
$$\chi_{1137}(47,\cdot)$$ 1137.be 378 yes $$1$$ $$1$$ $$e\left(\frac{67}{189}\right)$$ $$e\left(\frac{134}{189}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{169}{378}\right)$$ $$e\left(\frac{4}{63}\right)$$ $$e\left(\frac{341}{378}\right)$$ $$e\left(\frac{25}{27}\right)$$ $$e\left(\frac{173}{378}\right)$$ $$e\left(\frac{101}{126}\right)$$ $$e\left(\frac{79}{189}\right)$$