sage: H = DirichletGroup(946)
pari: g = idealstar(,946,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 420 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{210}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{946}(431,\cdot)$, $\chi_{946}(89,\cdot)$ |
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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{946}(1,\cdot)\) | 946.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{946}(3,\cdot)\) | 946.be | 210 | no | \(-1\) | \(1\) | \(e\left(\frac{89}{210}\right)\) | \(e\left(\frac{167}{210}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{89}{105}\right)\) | \(e\left(\frac{59}{105}\right)\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{11}{105}\right)\) | \(e\left(\frac{179}{210}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{8}{21}\right)\) |
\(\chi_{946}(5,\cdot)\) | 946.be | 210 | no | \(-1\) | \(1\) | \(e\left(\frac{167}{210}\right)\) | \(e\left(\frac{101}{210}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{62}{105}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{29}{105}\right)\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{107}{210}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{11}{21}\right)\) |
\(\chi_{946}(7,\cdot)\) | 946.t | 30 | no | \(1\) | \(1\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{946}(9,\cdot)\) | 946.bc | 105 | no | \(1\) | \(1\) | \(e\left(\frac{89}{105}\right)\) | \(e\left(\frac{62}{105}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{13}{105}\right)\) | \(e\left(\frac{46}{105}\right)\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{16}{21}\right)\) |
\(\chi_{946}(13,\cdot)\) | 946.bd | 210 | no | \(-1\) | \(1\) | \(e\left(\frac{59}{105}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{13}{105}\right)\) | \(e\left(\frac{101}{210}\right)\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{179}{210}\right)\) | \(e\left(\frac{163}{210}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{4}{21}\right)\) |
\(\chi_{946}(15,\cdot)\) | 946.bc | 105 | no | \(1\) | \(1\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{29}{105}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{46}{105}\right)\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{19}{21}\right)\) |
\(\chi_{946}(17,\cdot)\) | 946.bd | 210 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{105}\right)\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{179}{210}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{101}{210}\right)\) | \(e\left(\frac{187}{210}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{10}{21}\right)\) |
\(\chi_{946}(19,\cdot)\) | 946.bf | 210 | no | \(1\) | \(1\) | \(e\left(\frac{179}{210}\right)\) | \(e\left(\frac{107}{210}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{163}{210}\right)\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{187}{210}\right)\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{5}{21}\right)\) |
\(\chi_{946}(21,\cdot)\) | 946.n | 14 | no | \(-1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(-1\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{5}{7}\right)\) |
\(\chi_{946}(23,\cdot)\) | 946.r | 21 | no | \(1\) | \(1\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{2}{21}\right)\) |
\(\chi_{946}(25,\cdot)\) | 946.bc | 105 | no | \(1\) | \(1\) | \(e\left(\frac{62}{105}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{46}{105}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{21}\right)\) |
\(\chi_{946}(27,\cdot)\) | 946.ba | 70 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) |
\(\chi_{946}(29,\cdot)\) | 946.bf | 210 | no | \(1\) | \(1\) | \(e\left(\frac{121}{210}\right)\) | \(e\left(\frac{43}{210}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{16}{105}\right)\) | \(e\left(\frac{197}{210}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{83}{210}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{13}{21}\right)\) |
\(\chi_{946}(31,\cdot)\) | 946.bc | 105 | no | \(1\) | \(1\) | \(e\left(\frac{64}{105}\right)\) | \(e\left(\frac{67}{105}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{26}{105}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{20}{21}\right)\) |
\(\chi_{946}(35,\cdot)\) | 946.bb | 70 | no | \(-1\) | \(1\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) |
\(\chi_{946}(37,\cdot)\) | 946.s | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{946}(39,\cdot)\) | 946.z | 70 | no | \(1\) | \(1\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{4}{7}\right)\) |
\(\chi_{946}(41,\cdot)\) | 946.bb | 70 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) |
\(\chi_{946}(45,\cdot)\) | 946.o | 14 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(-1\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) |
\(\chi_{946}(47,\cdot)\) | 946.v | 35 | no | \(1\) | \(1\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) |
\(\chi_{946}(49,\cdot)\) | 946.q | 15 | no | \(1\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{946}(51,\cdot)\) | 946.z | 70 | no | \(1\) | \(1\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) |
\(\chi_{946}(53,\cdot)\) | 946.bc | 105 | no | \(1\) | \(1\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{8}{105}\right)\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{41}{105}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{34}{105}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{17}{21}\right)\) |
\(\chi_{946}(57,\cdot)\) | 946.bd | 210 | no | \(-1\) | \(1\) | \(e\left(\frac{29}{105}\right)\) | \(e\left(\frac{32}{105}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{71}{210}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{209}{210}\right)\) | \(e\left(\frac{73}{210}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{13}{21}\right)\) |
\(\chi_{946}(59,\cdot)\) | 946.v | 35 | no | \(1\) | \(1\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) |
\(\chi_{946}(61,\cdot)\) | 946.bf | 210 | no | \(1\) | \(1\) | \(e\left(\frac{187}{210}\right)\) | \(e\left(\frac{181}{210}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{209}{210}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{71}{210}\right)\) | \(e\left(\frac{86}{105}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{1}{21}\right)\) |
\(\chi_{946}(63,\cdot)\) | 946.bf | 210 | no | \(1\) | \(1\) | \(e\left(\frac{59}{210}\right)\) | \(e\left(\frac{47}{210}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{59}{105}\right)\) | \(e\left(\frac{103}{210}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{37}{210}\right)\) | \(e\left(\frac{67}{105}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{2}{21}\right)\) |
\(\chi_{946}(65,\cdot)\) | 946.p | 14 | no | \(1\) | \(1\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(1\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{5}{7}\right)\) |
\(\chi_{946}(67,\cdot)\) | 946.r | 21 | no | \(1\) | \(1\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{5}{21}\right)\) |
\(\chi_{946}(69,\cdot)\) | 946.be | 210 | no | \(-1\) | \(1\) | \(e\left(\frac{169}{210}\right)\) | \(e\left(\frac{67}{210}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{64}{105}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{13}{105}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{19}{210}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{10}{21}\right)\) |
\(\chi_{946}(71,\cdot)\) | 946.be | 210 | no | \(-1\) | \(1\) | \(e\left(\frac{67}{210}\right)\) | \(e\left(\frac{121}{210}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{67}{105}\right)\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{94}{105}\right)\) | \(e\left(\frac{13}{105}\right)\) | \(e\left(\frac{97}{210}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{19}{21}\right)\) |