Properties

Modulus $1078$
Structure \(C_{210}\times C_{2}\)
Order $420$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1078)
 
pari: g = idealstar(,1078,2)
 

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 = $\chi_{1078}(199,\cdot)$, $\chi_{1078}(981,\cdot)$

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 \(-1\) \(1\) \(3\) \(5\) \(9\) \(13\) \(15\) \(17\) \(19\) \(23\) \(25\) \(27\)
\(\chi_{1078}(1,\cdot)\) 1078.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1078}(3,\cdot)\) 1078.be 210 no \(-1\) \(1\) \(e\left(\frac{89}{210}\right)\) \(e\left(\frac{187}{210}\right)\) \(e\left(\frac{89}{105}\right)\) \(e\left(\frac{41}{70}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{167}{210}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{82}{105}\right)\) \(e\left(\frac{19}{70}\right)\)
\(\chi_{1078}(5,\cdot)\) 1078.be 210 no \(-1\) \(1\) \(e\left(\frac{187}{210}\right)\) \(e\left(\frac{131}{210}\right)\) \(e\left(\frac{82}{105}\right)\) \(e\left(\frac{13}{70}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{181}{210}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{26}{105}\right)\) \(e\left(\frac{47}{70}\right)\)
\(\chi_{1078}(9,\cdot)\) 1078.bc 105 no \(1\) \(1\) \(e\left(\frac{89}{105}\right)\) \(e\left(\frac{82}{105}\right)\) \(e\left(\frac{73}{105}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{62}{105}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{59}{105}\right)\) \(e\left(\frac{19}{35}\right)\)
\(\chi_{1078}(13,\cdot)\) 1078.ba 70 no \(1\) \(1\) \(e\left(\frac{41}{70}\right)\) \(e\left(\frac{13}{70}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{53}{70}\right)\)
\(\chi_{1078}(15,\cdot)\) 1078.v 35 no \(1\) \(1\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{33}{35}\right)\)
\(\chi_{1078}(17,\cdot)\) 1078.bf 210 no \(1\) \(1\) \(e\left(\frac{167}{210}\right)\) \(e\left(\frac{181}{210}\right)\) \(e\left(\frac{62}{105}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{103}{105}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{76}{105}\right)\) \(e\left(\frac{27}{70}\right)\)
\(\chi_{1078}(19,\cdot)\) 1078.s 30 no \(1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{1078}(23,\cdot)\) 1078.r 21 no \(1\) \(1\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{1078}(25,\cdot)\) 1078.bc 105 no \(1\) \(1\) \(e\left(\frac{82}{105}\right)\) \(e\left(\frac{26}{105}\right)\) \(e\left(\frac{59}{105}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{76}{105}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{52}{105}\right)\) \(e\left(\frac{12}{35}\right)\)
\(\chi_{1078}(27,\cdot)\) 1078.z 70 no \(-1\) \(1\) \(e\left(\frac{19}{70}\right)\) \(e\left(\frac{47}{70}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{53}{70}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{27}{70}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{57}{70}\right)\)
\(\chi_{1078}(29,\cdot)\) 1078.bb 70 no \(-1\) \(1\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{59}{70}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{1}{70}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{3}{35}\right)\)
\(\chi_{1078}(31,\cdot)\) 1078.t 30 no \(-1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{1078}(37,\cdot)\) 1078.bc 105 no \(1\) \(1\) \(e\left(\frac{38}{105}\right)\) \(e\left(\frac{94}{105}\right)\) \(e\left(\frac{76}{105}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{89}{105}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{83}{105}\right)\) \(e\left(\frac{3}{35}\right)\)
\(\chi_{1078}(39,\cdot)\) 1078.bd 210 no \(-1\) \(1\) \(e\left(\frac{1}{105}\right)\) \(e\left(\frac{8}{105}\right)\) \(e\left(\frac{2}{105}\right)\) \(e\left(\frac{43}{70}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{71}{210}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{16}{105}\right)\) \(e\left(\frac{1}{35}\right)\)
\(\chi_{1078}(41,\cdot)\) 1078.ba 70 no \(1\) \(1\) \(e\left(\frac{53}{70}\right)\) \(e\left(\frac{39}{70}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{19}{70}\right)\)
\(\chi_{1078}(43,\cdot)\) 1078.n 14 no \(-1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(-1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{1078}(45,\cdot)\) 1078.x 42 no \(-1\) \(1\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{3}{14}\right)\)
\(\chi_{1078}(47,\cdot)\) 1078.be 210 no \(-1\) \(1\) \(e\left(\frac{109}{210}\right)\) \(e\left(\frac{137}{210}\right)\) \(e\left(\frac{4}{105}\right)\) \(e\left(\frac{51}{70}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{37}{210}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{32}{105}\right)\) \(e\left(\frac{39}{70}\right)\)
\(\chi_{1078}(51,\cdot)\) 1078.bd 210 no \(-1\) \(1\) \(e\left(\frac{23}{105}\right)\) \(e\left(\frac{79}{105}\right)\) \(e\left(\frac{46}{105}\right)\) \(e\left(\frac{9}{70}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{163}{210}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{53}{105}\right)\) \(e\left(\frac{23}{35}\right)\)
\(\chi_{1078}(53,\cdot)\) 1078.bc 105 no \(1\) \(1\) \(e\left(\frac{4}{105}\right)\) \(e\left(\frac{32}{105}\right)\) \(e\left(\frac{8}{105}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{37}{105}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{64}{105}\right)\) \(e\left(\frac{4}{35}\right)\)
\(\chi_{1078}(57,\cdot)\) 1078.bb 70 no \(-1\) \(1\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{27}{70}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{23}{70}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{34}{35}\right)\)
\(\chi_{1078}(59,\cdot)\) 1078.be 210 no \(-1\) \(1\) \(e\left(\frac{191}{210}\right)\) \(e\left(\frac{163}{210}\right)\) \(e\left(\frac{86}{105}\right)\) \(e\left(\frac{29}{70}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{113}{210}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{58}{105}\right)\) \(e\left(\frac{51}{70}\right)\)
\(\chi_{1078}(61,\cdot)\) 1078.bf 210 no \(1\) \(1\) \(e\left(\frac{97}{210}\right)\) \(e\left(\frac{41}{210}\right)\) \(e\left(\frac{97}{105}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{68}{105}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{41}{105}\right)\) \(e\left(\frac{27}{70}\right)\)
\(\chi_{1078}(65,\cdot)\) 1078.y 42 no \(-1\) \(1\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{1078}(67,\cdot)\) 1078.e 3 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)
\(\chi_{1078}(69,\cdot)\) 1078.z 70 no \(-1\) \(1\) \(e\left(\frac{23}{70}\right)\) \(e\left(\frac{9}{70}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{31}{70}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{29}{70}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{69}{70}\right)\)
\(\chi_{1078}(71,\cdot)\) 1078.v 35 no \(1\) \(1\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{11}{35}\right)\)
\(\chi_{1078}(73,\cdot)\) 1078.bf 210 no \(1\) \(1\) \(e\left(\frac{101}{210}\right)\) \(e\left(\frac{73}{210}\right)\) \(e\left(\frac{101}{105}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{34}{105}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{73}{105}\right)\) \(e\left(\frac{31}{70}\right)\)
\(\chi_{1078}(75,\cdot)\) 1078.be 210 no \(-1\) \(1\) \(e\left(\frac{43}{210}\right)\) \(e\left(\frac{29}{210}\right)\) \(e\left(\frac{43}{105}\right)\) \(e\left(\frac{67}{70}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{109}{210}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{29}{105}\right)\) \(e\left(\frac{43}{70}\right)\)
\(\chi_{1078}(79,\cdot)\) 1078.u 30 no \(-1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{1078}(81,\cdot)\) 1078.bc 105 no \(1\) \(1\) \(e\left(\frac{73}{105}\right)\) \(e\left(\frac{59}{105}\right)\) \(e\left(\frac{41}{105}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{19}{105}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{13}{105}\right)\) \(e\left(\frac{3}{35}\right)\)