Properties

Modulus $539$
Structure \(C_{210}\times C_{2}\)
Order $420$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(539)
 
pari: g = idealstar(,539,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 420
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{210}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{539}(199,\cdot)$, $\chi_{539}(442,\cdot)$

First 32 of 420 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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(8\) \(9\) \(10\) \(12\) \(13\)
\(\chi_{539}(1,\cdot)\) 539.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{539}(2,\cdot)\) 539.be 210 yes \(-1\) \(1\) \(e\left(\frac{41}{210}\right)\) \(e\left(\frac{44}{105}\right)\) \(e\left(\frac{41}{105}\right)\) \(e\left(\frac{37}{105}\right)\) \(e\left(\frac{43}{70}\right)\) \(e\left(\frac{41}{70}\right)\) \(e\left(\frac{88}{105}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{37}{70}\right)\)
\(\chi_{539}(3,\cdot)\) 539.bd 210 yes \(-1\) \(1\) \(e\left(\frac{44}{105}\right)\) \(e\left(\frac{89}{210}\right)\) \(e\left(\frac{88}{105}\right)\) \(e\left(\frac{187}{210}\right)\) \(e\left(\frac{59}{70}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{89}{105}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{41}{70}\right)\)
\(\chi_{539}(4,\cdot)\) 539.bc 105 yes \(1\) \(1\) \(e\left(\frac{41}{105}\right)\) \(e\left(\frac{88}{105}\right)\) \(e\left(\frac{82}{105}\right)\) \(e\left(\frac{74}{105}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{71}{105}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{2}{35}\right)\)
\(\chi_{539}(5,\cdot)\) 539.bd 210 yes \(-1\) \(1\) \(e\left(\frac{37}{105}\right)\) \(e\left(\frac{187}{210}\right)\) \(e\left(\frac{74}{105}\right)\) \(e\left(\frac{131}{210}\right)\) \(e\left(\frac{17}{70}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{82}{105}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{13}{70}\right)\)
\(\chi_{539}(6,\cdot)\) 539.z 70 yes \(1\) \(1\) \(e\left(\frac{43}{70}\right)\) \(e\left(\frac{59}{70}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{17}{70}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{59}{70}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{4}{35}\right)\)
\(\chi_{539}(8,\cdot)\) 539.ba 70 yes \(-1\) \(1\) \(e\left(\frac{41}{70}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{59}{70}\right)\) \(e\left(\frac{53}{70}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{41}{70}\right)\)
\(\chi_{539}(9,\cdot)\) 539.bc 105 yes \(1\) \(1\) \(e\left(\frac{88}{105}\right)\) \(e\left(\frac{89}{105}\right)\) \(e\left(\frac{71}{105}\right)\) \(e\left(\frac{82}{105}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{73}{105}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{6}{35}\right)\)
\(\chi_{539}(10,\cdot)\) 539.w 42 yes \(1\) \(1\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{539}(12,\cdot)\) 539.y 42 no \(-1\) \(1\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{9}{14}\right)\)
\(\chi_{539}(13,\cdot)\) 539.z 70 yes \(1\) \(1\) \(e\left(\frac{37}{70}\right)\) \(e\left(\frac{41}{70}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{13}{70}\right)\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{41}{70}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{35}\right)\)
\(\chi_{539}(15,\cdot)\) 539.v 35 yes \(1\) \(1\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{27}{35}\right)\)
\(\chi_{539}(16,\cdot)\) 539.bc 105 yes \(1\) \(1\) \(e\left(\frac{82}{105}\right)\) \(e\left(\frac{71}{105}\right)\) \(e\left(\frac{59}{105}\right)\) \(e\left(\frac{43}{105}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{37}{105}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{4}{35}\right)\)
\(\chi_{539}(17,\cdot)\) 539.bf 210 yes \(1\) \(1\) \(e\left(\frac{79}{210}\right)\) \(e\left(\frac{167}{210}\right)\) \(e\left(\frac{79}{105}\right)\) \(e\left(\frac{181}{210}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{9}{70}\right)\) \(e\left(\frac{62}{105}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{19}{35}\right)\)
\(\chi_{539}(18,\cdot)\) 539.t 30 no \(-1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{539}(19,\cdot)\) 539.s 30 no \(1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{539}(20,\cdot)\) 539.bb 70 yes \(-1\) \(1\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{51}{70}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{23}{70}\right)\) \(e\left(\frac{33}{70}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{17}{70}\right)\)
\(\chi_{539}(23,\cdot)\) 539.r 21 no \(1\) \(1\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{539}(24,\cdot)\) 539.bf 210 yes \(1\) \(1\) \(e\left(\frac{1}{210}\right)\) \(e\left(\frac{143}{210}\right)\) \(e\left(\frac{1}{105}\right)\) \(e\left(\frac{199}{210}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{1}{70}\right)\) \(e\left(\frac{38}{105}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{6}{35}\right)\)
\(\chi_{539}(25,\cdot)\) 539.bc 105 yes \(1\) \(1\) \(e\left(\frac{74}{105}\right)\) \(e\left(\frac{82}{105}\right)\) \(e\left(\frac{43}{105}\right)\) \(e\left(\frac{26}{105}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{59}{105}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{13}{35}\right)\)
\(\chi_{539}(26,\cdot)\) 539.bd 210 yes \(-1\) \(1\) \(e\left(\frac{76}{105}\right)\) \(e\left(\frac{1}{210}\right)\) \(e\left(\frac{47}{105}\right)\) \(e\left(\frac{113}{210}\right)\) \(e\left(\frac{51}{70}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{1}{105}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{39}{70}\right)\)
\(\chi_{539}(27,\cdot)\) 539.bb 70 yes \(-1\) \(1\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{19}{70}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{47}{70}\right)\) \(e\left(\frac{37}{70}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{53}{70}\right)\)
\(\chi_{539}(29,\cdot)\) 539.ba 70 yes \(-1\) \(1\) \(e\left(\frac{59}{70}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{61}{70}\right)\) \(e\left(\frac{37}{70}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{59}{70}\right)\)
\(\chi_{539}(30,\cdot)\) 539.t 30 no \(-1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{539}(31,\cdot)\) 539.u 30 no \(-1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{539}(32,\cdot)\) 539.x 42 yes \(-1\) \(1\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{9}{14}\right)\)
\(\chi_{539}(34,\cdot)\) 539.n 14 no \(-1\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{14}\right)\)
\(\chi_{539}(36,\cdot)\) 539.v 35 yes \(1\) \(1\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{8}{35}\right)\)
\(\chi_{539}(37,\cdot)\) 539.bc 105 yes \(1\) \(1\) \(e\left(\frac{1}{105}\right)\) \(e\left(\frac{38}{105}\right)\) \(e\left(\frac{2}{105}\right)\) \(e\left(\frac{94}{105}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{76}{105}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{12}{35}\right)\)
\(\chi_{539}(38,\cdot)\) 539.bd 210 yes \(-1\) \(1\) \(e\left(\frac{17}{105}\right)\) \(e\left(\frac{137}{210}\right)\) \(e\left(\frac{34}{105}\right)\) \(e\left(\frac{151}{210}\right)\) \(e\left(\frac{57}{70}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{32}{105}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{23}{70}\right)\)
\(\chi_{539}(39,\cdot)\) 539.be 210 yes \(-1\) \(1\) \(e\left(\frac{199}{210}\right)\) \(e\left(\frac{1}{105}\right)\) \(e\left(\frac{94}{105}\right)\) \(e\left(\frac{8}{105}\right)\) \(e\left(\frac{67}{70}\right)\) \(e\left(\frac{59}{70}\right)\) \(e\left(\frac{2}{105}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{43}{70}\right)\)
\(\chi_{539}(40,\cdot)\) 539.bf 210 yes \(1\) \(1\) \(e\left(\frac{197}{210}\right)\) \(e\left(\frac{31}{210}\right)\) \(e\left(\frac{92}{105}\right)\) \(e\left(\frac{143}{210}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{57}{70}\right)\) \(e\left(\frac{31}{105}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{27}{35}\right)\)