sage: H = DirichletGroup(6027)
pari: g = idealstar(,6027,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 3360 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{840}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{6027}(4019,\cdot)$, $\chi_{6027}(493,\cdot)$, $\chi_{6027}(2794,\cdot)$ |
First 32 of 3360 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{6027}(1,\cdot)\) | 6027.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{6027}(2,\cdot)\) | 6027.eq | 420 | yes | \(-1\) | \(1\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{104}{105}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{26}{105}\right)\) | \(e\left(\frac{89}{420}\right)\) | \(e\left(\frac{81}{140}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{179}{420}\right)\) | \(e\left(\frac{31}{60}\right)\) |
\(\chi_{6027}(4,\cdot)\) | 6027.ef | 210 | no | \(1\) | \(1\) | \(e\left(\frac{104}{105}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{89}{210}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{179}{210}\right)\) | \(e\left(\frac{1}{30}\right)\) |
\(\chi_{6027}(5,\cdot)\) | 6027.er | 420 | yes | \(1\) | \(1\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{131}{210}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{79}{210}\right)\) | \(e\left(\frac{323}{420}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{383}{420}\right)\) | \(e\left(\frac{7}{60}\right)\) |
\(\chi_{6027}(8,\cdot)\) | 6027.ea | 140 | yes | \(-1\) | \(1\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{89}{140}\right)\) | \(e\left(\frac{103}{140}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{11}{20}\right)\) |
\(\chi_{6027}(10,\cdot)\) | 6027.eg | 210 | no | \(-1\) | \(1\) | \(e\left(\frac{26}{105}\right)\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{79}{210}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{131}{210}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{104}{105}\right)\) | \(e\left(\frac{71}{210}\right)\) | \(e\left(\frac{19}{30}\right)\) |
\(\chi_{6027}(11,\cdot)\) | 6027.eu | 840 | yes | \(1\) | \(1\) | \(e\left(\frac{89}{420}\right)\) | \(e\left(\frac{89}{210}\right)\) | \(e\left(\frac{323}{420}\right)\) | \(e\left(\frac{89}{140}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{689}{840}\right)\) | \(e\left(\frac{211}{280}\right)\) | \(e\left(\frac{89}{105}\right)\) | \(e\left(\frac{659}{840}\right)\) | \(e\left(\frac{1}{120}\right)\) |
\(\chi_{6027}(13,\cdot)\) | 6027.em | 280 | no | \(1\) | \(1\) | \(e\left(\frac{81}{140}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{103}{140}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{211}{280}\right)\) | \(e\left(\frac{267}{280}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{61}{280}\right)\) | \(e\left(\frac{19}{40}\right)\) |
\(\chi_{6027}(16,\cdot)\) | 6027.ds | 105 | no | \(1\) | \(1\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{104}{105}\right)\) | \(e\left(\frac{89}{105}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{97}{105}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{1}{15}\right)\) |
\(\chi_{6027}(17,\cdot)\) | 6027.ew | 840 | yes | \(-1\) | \(1\) | \(e\left(\frac{179}{420}\right)\) | \(e\left(\frac{179}{210}\right)\) | \(e\left(\frac{383}{420}\right)\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{71}{210}\right)\) | \(e\left(\frac{659}{840}\right)\) | \(e\left(\frac{61}{280}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{509}{840}\right)\) | \(e\left(\frac{31}{120}\right)\) |
\(\chi_{6027}(19,\cdot)\) | 6027.dt | 120 | no | \(1\) | \(1\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{23}{120}\right)\) |
\(\chi_{6027}(20,\cdot)\) | 6027.dz | 140 | yes | \(1\) | \(1\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{27}{140}\right)\) | \(e\left(\frac{139}{140}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{107}{140}\right)\) | \(e\left(\frac{3}{20}\right)\) |
\(\chi_{6027}(22,\cdot)\) | 6027.eo | 280 | no | \(-1\) | \(1\) | \(e\left(\frac{99}{140}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{73}{140}\right)\) | \(e\left(\frac{17}{140}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{9}{280}\right)\) | \(e\left(\frac{93}{280}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{59}{280}\right)\) | \(e\left(\frac{21}{40}\right)\) |
\(\chi_{6027}(23,\cdot)\) | 6027.ek | 210 | yes | \(-1\) | \(1\) | \(e\left(\frac{89}{210}\right)\) | \(e\left(\frac{89}{105}\right)\) | \(e\left(\frac{113}{210}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{41}{105}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{86}{105}\right)\) | \(e\left(\frac{23}{30}\right)\) |
\(\chi_{6027}(25,\cdot)\) | 6027.ef | 210 | no | \(1\) | \(1\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{26}{105}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{113}{210}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{173}{210}\right)\) | \(e\left(\frac{7}{30}\right)\) |
\(\chi_{6027}(26,\cdot)\) | 6027.ew | 840 | yes | \(-1\) | \(1\) | \(e\left(\frac{31}{420}\right)\) | \(e\left(\frac{31}{210}\right)\) | \(e\left(\frac{247}{420}\right)\) | \(e\left(\frac{31}{140}\right)\) | \(e\left(\frac{139}{210}\right)\) | \(e\left(\frac{811}{840}\right)\) | \(e\left(\frac{149}{280}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{541}{840}\right)\) | \(e\left(\frac{119}{120}\right)\) |
\(\chi_{6027}(29,\cdot)\) | 6027.ep | 280 | yes | \(1\) | \(1\) | \(e\left(\frac{27}{140}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{109}{140}\right)\) | \(e\left(\frac{81}{140}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{47}{280}\right)\) | \(e\left(\frac{159}{280}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{277}{280}\right)\) | \(e\left(\frac{23}{40}\right)\) |
\(\chi_{6027}(31,\cdot)\) | 6027.ck | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) |
\(\chi_{6027}(32,\cdot)\) | 6027.dr | 84 | yes | \(-1\) | \(1\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{6027}(34,\cdot)\) | 6027.em | 280 | no | \(1\) | \(1\) | \(e\left(\frac{129}{140}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{93}{140}\right)\) | \(e\left(\frac{107}{140}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{279}{280}\right)\) | \(e\left(\frac{223}{280}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{9}{280}\right)\) | \(e\left(\frac{31}{40}\right)\) |
\(\chi_{6027}(37,\cdot)\) | 6027.ds | 105 | no | \(1\) | \(1\) | \(e\left(\frac{64}{105}\right)\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{32}{105}\right)\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{46}{105}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{13}{15}\right)\) |
\(\chi_{6027}(38,\cdot)\) | 6027.ec | 168 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{73}{84}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{37}{168}\right)\) | \(e\left(\frac{3}{56}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{115}{168}\right)\) | \(e\left(\frac{17}{24}\right)\) |
\(\chi_{6027}(40,\cdot)\) | 6027.cw | 42 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{6027}(43,\cdot)\) | 6027.dx | 140 | no | \(1\) | \(1\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{93}{140}\right)\) | \(e\left(\frac{121}{140}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{3}{140}\right)\) | \(e\left(\frac{17}{20}\right)\) |
\(\chi_{6027}(44,\cdot)\) | 6027.ee | 168 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{41}{168}\right)\) | \(e\left(\frac{51}{56}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{107}{168}\right)\) | \(e\left(\frac{1}{24}\right)\) |
\(\chi_{6027}(46,\cdot)\) | 6027.et | 420 | no | \(1\) | \(1\) | \(e\left(\frac{193}{210}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{61}{210}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{253}{420}\right)\) | \(e\left(\frac{47}{140}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{103}{420}\right)\) | \(e\left(\frac{17}{60}\right)\) |
\(\chi_{6027}(47,\cdot)\) | 6027.ew | 840 | yes | \(-1\) | \(1\) | \(e\left(\frac{103}{420}\right)\) | \(e\left(\frac{103}{210}\right)\) | \(e\left(\frac{211}{420}\right)\) | \(e\left(\frac{103}{140}\right)\) | \(e\left(\frac{157}{210}\right)\) | \(e\left(\frac{283}{840}\right)\) | \(e\left(\frac{197}{280}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{253}{840}\right)\) | \(e\left(\frac{47}{120}\right)\) |
\(\chi_{6027}(50,\cdot)\) | 6027.m | 4 | no | \(-1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(-i\) | \(i\) | \(1\) | \(i\) | \(-i\) |
\(\chi_{6027}(52,\cdot)\) | 6027.ex | 840 | no | \(1\) | \(1\) | \(e\left(\frac{239}{420}\right)\) | \(e\left(\frac{29}{210}\right)\) | \(e\left(\frac{143}{420}\right)\) | \(e\left(\frac{99}{140}\right)\) | \(e\left(\frac{191}{210}\right)\) | \(e\left(\frac{149}{840}\right)\) | \(e\left(\frac{31}{280}\right)\) | \(e\left(\frac{29}{105}\right)\) | \(e\left(\frac{59}{840}\right)\) | \(e\left(\frac{61}{120}\right)\) |
\(\chi_{6027}(53,\cdot)\) | 6027.eu | 840 | yes | \(1\) | \(1\) | \(e\left(\frac{101}{420}\right)\) | \(e\left(\frac{101}{210}\right)\) | \(e\left(\frac{107}{420}\right)\) | \(e\left(\frac{101}{140}\right)\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{41}{840}\right)\) | \(e\left(\frac{219}{280}\right)\) | \(e\left(\frac{101}{105}\right)\) | \(e\left(\frac{611}{840}\right)\) | \(e\left(\frac{49}{120}\right)\) |
\(\chi_{6027}(55,\cdot)\) | 6027.dc | 56 | no | \(1\) | \(1\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{39}{56}\right)\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{6027}(58,\cdot)\) | 6027.ev | 840 | no | \(-1\) | \(1\) | \(e\left(\frac{289}{420}\right)\) | \(e\left(\frac{79}{210}\right)\) | \(e\left(\frac{223}{420}\right)\) | \(e\left(\frac{9}{140}\right)\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{319}{840}\right)\) | \(e\left(\frac{41}{280}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{349}{840}\right)\) | \(e\left(\frac{11}{120}\right)\) |