sage: H = DirichletGroup(4018)
pari: g = idealstar(,4018,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 1680 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{2}\times C_{840}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{4018}(493,\cdot)$, $\chi_{4018}(785,\cdot)$ |
First 32 of 1680 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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{4018}(1,\cdot)\) | 4018.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{4018}(3,\cdot)\) | 4018.cb | 168 | no | \(1\) | \(1\) | \(e\left(\frac{109}{168}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{13}{168}\right)\) | \(e\left(\frac{23}{56}\right)\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{163}{168}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{37}{42}\right)\) |
| \(\chi_{4018}(5,\cdot)\) | 4018.ci | 420 | no | \(-1\) | \(1\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{13}{105}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{113}{420}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{9}{140}\right)\) | \(e\left(\frac{173}{420}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{26}{105}\right)\) |
| \(\chi_{4018}(9,\cdot)\) | 4018.bu | 84 | no | \(1\) | \(1\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) |
| \(\chi_{4018}(11,\cdot)\) | 4018.ck | 840 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{168}\right)\) | \(e\left(\frac{113}{420}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{269}{840}\right)\) | \(e\left(\frac{211}{280}\right)\) | \(e\left(\frac{97}{280}\right)\) | \(e\left(\frac{239}{840}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{187}{210}\right)\) | \(e\left(\frac{113}{210}\right)\) |
| \(\chi_{4018}(13,\cdot)\) | 4018.cg | 280 | no | \(1\) | \(1\) | \(e\left(\frac{23}{56}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{211}{280}\right)\) | \(e\left(\frac{267}{280}\right)\) | \(e\left(\frac{69}{280}\right)\) | \(e\left(\frac{61}{280}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{47}{70}\right)\) |
| \(\chi_{4018}(15,\cdot)\) | 4018.ch | 280 | no | \(-1\) | \(1\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{9}{140}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{97}{280}\right)\) | \(e\left(\frac{69}{280}\right)\) | \(e\left(\frac{183}{280}\right)\) | \(e\left(\frac{107}{280}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{9}{70}\right)\) |
| \(\chi_{4018}(17,\cdot)\) | 4018.cl | 840 | no | \(1\) | \(1\) | \(e\left(\frac{163}{168}\right)\) | \(e\left(\frac{173}{420}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{239}{840}\right)\) | \(e\left(\frac{61}{280}\right)\) | \(e\left(\frac{107}{280}\right)\) | \(e\left(\frac{89}{840}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{67}{210}\right)\) | \(e\left(\frac{173}{210}\right)\) |
| \(\chi_{4018}(19,\cdot)\) | 4018.by | 120 | no | \(1\) | \(1\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{7}{30}\right)\) |
| \(\chi_{4018}(23,\cdot)\) | 4018.cd | 210 | no | \(1\) | \(1\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{4}{105}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{187}{210}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{67}{210}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{8}{105}\right)\) |
| \(\chi_{4018}(25,\cdot)\) | 4018.cd | 210 | no | \(1\) | \(1\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{26}{105}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{113}{210}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{173}{210}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{8}{105}\right)\) | \(e\left(\frac{52}{105}\right)\) |
| \(\chi_{4018}(27,\cdot)\) | 4018.bo | 56 | no | \(1\) | \(1\) | \(e\left(\frac{53}{56}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{43}{56}\right)\) | \(e\left(\frac{51}{56}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{9}{14}\right)\) |
| \(\chi_{4018}(29,\cdot)\) | 4018.ch | 280 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{56}\right)\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{187}{280}\right)\) | \(e\left(\frac{159}{280}\right)\) | \(e\left(\frac{93}{280}\right)\) | \(e\left(\frac{137}{280}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{39}{70}\right)\) |
| \(\chi_{4018}(31,\cdot)\) | 4018.be | 30 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) |
| \(\chi_{4018}(33,\cdot)\) | 4018.ci | 420 | no | \(-1\) | \(1\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{167}{420}\right)\) | \(e\left(\frac{23}{140}\right)\) | \(e\left(\frac{131}{140}\right)\) | \(e\left(\frac{107}{420}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{44}{105}\right)\) |
| \(\chi_{4018}(37,\cdot)\) | 4018.bw | 105 | no | \(1\) | \(1\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{73}{105}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{41}{105}\right)\) |
| \(\chi_{4018}(39,\cdot)\) | 4018.cj | 420 | no | \(1\) | \(1\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{163}{210}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{349}{420}\right)\) | \(e\left(\frac{51}{140}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{79}{420}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{58}{105}\right)\) |
| \(\chi_{4018}(43,\cdot)\) | 4018.bz | 140 | no | \(1\) | \(1\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{93}{140}\right)\) | \(e\left(\frac{121}{140}\right)\) | \(e\left(\frac{47}{140}\right)\) | \(e\left(\frac{3}{140}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{31}{35}\right)\) |
| \(\chi_{4018}(45,\cdot)\) | 4018.cf | 210 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{1}{210}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{89}{210}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{89}{105}\right)\) | \(e\left(\frac{1}{105}\right)\) |
| \(\chi_{4018}(47,\cdot)\) | 4018.cl | 840 | no | \(1\) | \(1\) | \(e\left(\frac{83}{168}\right)\) | \(e\left(\frac{1}{420}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{703}{840}\right)\) | \(e\left(\frac{197}{280}\right)\) | \(e\left(\frac{139}{280}\right)\) | \(e\left(\frac{673}{840}\right)\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{89}{210}\right)\) | \(e\left(\frac{1}{210}\right)\) |
| \(\chi_{4018}(51,\cdot)\) | 4018.bw | 105 | no | \(1\) | \(1\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{8}{105}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{76}{105}\right)\) | \(e\left(\frac{74}{105}\right)\) |
| \(\chi_{4018}(53,\cdot)\) | 4018.ck | 840 | no | \(-1\) | \(1\) | \(e\left(\frac{61}{168}\right)\) | \(e\left(\frac{317}{420}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{461}{840}\right)\) | \(e\left(\frac{219}{280}\right)\) | \(e\left(\frac{33}{280}\right)\) | \(e\left(\frac{191}{840}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{73}{210}\right)\) | \(e\left(\frac{107}{210}\right)\) |
| \(\chi_{4018}(55,\cdot)\) | 4018.bo | 56 | no | \(1\) | \(1\) | \(e\left(\frac{1}{56}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{23}{56}\right)\) | \(e\left(\frac{39}{56}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{11}{14}\right)\) |
| \(\chi_{4018}(57,\cdot)\) | 4018.bh | 35 | no | \(1\) | \(1\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) |
| \(\chi_{4018}(59,\cdot)\) | 4018.ce | 210 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{163}{210}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{61}{105}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{197}{210}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{58}{105}\right)\) |
| \(\chi_{4018}(61,\cdot)\) | 4018.ci | 420 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{84}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{11}{420}\right)\) | \(e\left(\frac{139}{140}\right)\) | \(e\left(\frac{43}{140}\right)\) | \(e\left(\frac{251}{420}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{62}{105}\right)\) |
| \(\chi_{4018}(65,\cdot)\) | 4018.ck | 840 | no | \(-1\) | \(1\) | \(e\left(\frac{59}{168}\right)\) | \(e\left(\frac{403}{420}\right)\) | \(e\left(\frac{59}{84}\right)\) | \(e\left(\frac{19}{840}\right)\) | \(e\left(\frac{221}{280}\right)\) | \(e\left(\frac{87}{280}\right)\) | \(e\left(\frac{529}{840}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{167}{210}\right)\) | \(e\left(\frac{193}{210}\right)\) |
| \(\chi_{4018}(67,\cdot)\) | 4018.bx | 120 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) |
| \(\chi_{4018}(69,\cdot)\) | 4018.cg | 280 | no | \(1\) | \(1\) | \(e\left(\frac{3}{56}\right)\) | \(e\left(\frac{137}{140}\right)\) | \(e\left(\frac{3}{28}\right)\) | \(e\left(\frac{271}{280}\right)\) | \(e\left(\frac{47}{280}\right)\) | \(e\left(\frac{9}{280}\right)\) | \(e\left(\frac{81}{280}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{67}{70}\right)\) |
| \(\chi_{4018}(71,\cdot)\) | 4018.ch | 280 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{56}\right)\) | \(e\left(\frac{31}{140}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{163}{280}\right)\) | \(e\left(\frac{191}{280}\right)\) | \(e\left(\frac{117}{280}\right)\) | \(e\left(\frac{73}{280}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{31}{70}\right)\) |
| \(\chi_{4018}(73,\cdot)\) | 4018.bv | 84 | no | \(-1\) | \(1\) | \(e\left(\frac{53}{84}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{23}{84}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{2}{21}\right)\) |
| \(\chi_{4018}(75,\cdot)\) | 4018.cl | 840 | no | \(1\) | \(1\) | \(e\left(\frac{89}{168}\right)\) | \(e\left(\frac{79}{420}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{517}{840}\right)\) | \(e\left(\frac{23}{280}\right)\) | \(e\left(\frac{201}{280}\right)\) | \(e\left(\frac{667}{840}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{101}{210}\right)\) | \(e\left(\frac{79}{210}\right)\) |