sage: H = DirichletGroup(8023)
pari: g = idealstar(,8023,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 7840 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{14}\times C_{560}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{8023}(6894,\cdot)$, $\chi_{8023}(3054,\cdot)$ |
First 32 of 7840 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{8023}(1,\cdot)\) | 8023.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{8023}(2,\cdot)\) | 8023.fd | 140 | yes | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{47}{140}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{41}{140}\right)\) | \(e\left(\frac{19}{140}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{13}{140}\right)\) | \(e\left(\frac{41}{70}\right)\) |
| \(\chi_{8023}(3,\cdot)\) | 8023.gm | 560 | yes | \(-1\) | \(1\) | \(e\left(\frac{47}{140}\right)\) | \(e\left(\frac{373}{560}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{79}{560}\right)\) | \(e\left(\frac{1}{560}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{1}{140}\right)\) | \(e\left(\frac{93}{280}\right)\) | \(e\left(\frac{267}{560}\right)\) | \(e\left(\frac{7}{40}\right)\) |
| \(\chi_{8023}(4,\cdot)\) | 8023.dn | 70 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{6}{35}\right)\) |
| \(\chi_{8023}(5,\cdot)\) | 8023.gk | 560 | yes | \(-1\) | \(1\) | \(e\left(\frac{41}{140}\right)\) | \(e\left(\frac{79}{560}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{397}{560}\right)\) | \(e\left(\frac{243}{560}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{123}{140}\right)\) | \(e\left(\frac{79}{280}\right)\) | \(e\left(\frac{1}{560}\right)\) | \(e\left(\frac{67}{280}\right)\) |
| \(\chi_{8023}(6,\cdot)\) | 8023.gl | 560 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{140}\right)\) | \(e\left(\frac{1}{560}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{243}{560}\right)\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{57}{140}\right)\) | \(e\left(\frac{1}{280}\right)\) | \(e\left(\frac{319}{560}\right)\) | \(e\left(\frac{213}{280}\right)\) |
| \(\chi_{8023}(7,\cdot)\) | 8023.ds | 70 | yes | \(-1\) | \(1\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{51}{70}\right)\) |
| \(\chi_{8023}(8,\cdot)\) | 8023.fd | 140 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{140}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{123}{140}\right)\) | \(e\left(\frac{57}{140}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{53}{70}\right)\) |
| \(\chi_{8023}(9,\cdot)\) | 8023.gb | 280 | yes | \(1\) | \(1\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{93}{280}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{79}{280}\right)\) | \(e\left(\frac{1}{280}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{93}{140}\right)\) | \(e\left(\frac{267}{280}\right)\) | \(e\left(\frac{7}{20}\right)\) |
| \(\chi_{8023}(10,\cdot)\) | 8023.gm | 560 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{140}\right)\) | \(e\left(\frac{267}{560}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{1}{560}\right)\) | \(e\left(\frac{319}{560}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{267}{280}\right)\) | \(e\left(\frac{53}{560}\right)\) | \(e\left(\frac{33}{40}\right)\) |
| \(\chi_{8023}(11,\cdot)\) | 8023.fx | 280 | yes | \(-1\) | \(1\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{67}{280}\right)\) | \(e\left(\frac{213}{280}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{87}{140}\right)\) |
| \(\chi_{8023}(12,\cdot)\) | 8023.gj | 560 | yes | \(-1\) | \(1\) | \(e\left(\frac{131}{140}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{61}{70}\right)\) | \(e\left(\frac{407}{560}\right)\) | \(e\left(\frac{153}{560}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{113}{140}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{97}{280}\right)\) |
| \(\chi_{8023}(13,\cdot)\) | 8023.gg | 280 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{191}{280}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{253}{280}\right)\) | \(e\left(\frac{107}{280}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{51}{140}\right)\) | \(e\left(\frac{169}{280}\right)\) | \(e\left(\frac{113}{140}\right)\) |
| \(\chi_{8023}(14,\cdot)\) | 8023.fg | 140 | yes | \(-1\) | \(1\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{109}{140}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{87}{140}\right)\) | \(e\left(\frac{73}{140}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{51}{140}\right)\) | \(e\left(\frac{11}{35}\right)\) |
| \(\chi_{8023}(15,\cdot)\) | 8023.fl | 140 | yes | \(1\) | \(1\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{113}{140}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{61}{140}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{67}{140}\right)\) | \(e\left(\frac{29}{70}\right)\) |
| \(\chi_{8023}(16,\cdot)\) | 8023.cm | 35 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) |
| \(\chi_{8023}(17,\cdot)\) | 8023.gs | 560 | yes | \(1\) | \(1\) | \(e\left(\frac{103}{140}\right)\) | \(e\left(\frac{137}{560}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{171}{560}\right)\) | \(e\left(\frac{549}{560}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{29}{140}\right)\) | \(e\left(\frac{137}{280}\right)\) | \(e\left(\frac{23}{560}\right)\) | \(e\left(\frac{1}{280}\right)\) |
| \(\chi_{8023}(18,\cdot)\) | 8023.ge | 280 | yes | \(1\) | \(1\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{187}{280}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{39}{280}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{47}{140}\right)\) | \(e\left(\frac{13}{280}\right)\) | \(e\left(\frac{131}{140}\right)\) |
| \(\chi_{8023}(19,\cdot)\) | 8023.gv | 560 | yes | \(-1\) | \(1\) | \(e\left(\frac{137}{140}\right)\) | \(e\left(\frac{463}{560}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{429}{560}\right)\) | \(e\left(\frac{451}{560}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{131}{140}\right)\) | \(e\left(\frac{183}{280}\right)\) | \(e\left(\frac{417}{560}\right)\) | \(e\left(\frac{139}{280}\right)\) |
| \(\chi_{8023}(20,\cdot)\) | 8023.fa | 112 | yes | \(-1\) | \(1\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{33}{112}\right)\) | \(e\left(\frac{79}{112}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{23}{56}\right)\) |
| \(\chi_{8023}(21,\cdot)\) | 8023.gq | 560 | yes | \(1\) | \(1\) | \(e\left(\frac{39}{140}\right)\) | \(e\left(\frac{61}{560}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{263}{560}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{61}{280}\right)\) | \(e\left(\frac{419}{560}\right)\) | \(e\left(\frac{253}{280}\right)\) |
| \(\chi_{8023}(22,\cdot)\) | 8023.fw | 280 | yes | \(-1\) | \(1\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{143}{280}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{149}{280}\right)\) | \(e\left(\frac{251}{280}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{11}{70}\right)\) | \(e\left(\frac{3}{140}\right)\) | \(e\left(\frac{257}{280}\right)\) | \(e\left(\frac{29}{140}\right)\) |
| \(\chi_{8023}(23,\cdot)\) | 8023.ep | 112 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{43}{112}\right)\) | \(e\left(\frac{69}{112}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{41}{56}\right)\) |
| \(\chi_{8023}(24,\cdot)\) | 8023.go | 560 | yes | \(-1\) | \(1\) | \(e\left(\frac{103}{140}\right)\) | \(e\left(\frac{377}{560}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{11}{560}\right)\) | \(e\left(\frac{229}{560}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{29}{140}\right)\) | \(e\left(\frac{97}{280}\right)\) | \(e\left(\frac{423}{560}\right)\) | \(e\left(\frac{261}{280}\right)\) |
| \(\chi_{8023}(25,\cdot)\) | 8023.gd | 280 | yes | \(1\) | \(1\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{79}{280}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{117}{280}\right)\) | \(e\left(\frac{243}{280}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{79}{140}\right)\) | \(e\left(\frac{1}{280}\right)\) | \(e\left(\frac{67}{140}\right)\) |
| \(\chi_{8023}(26,\cdot)\) | 8023.cx | 56 | yes | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{56}\right)\) | \(1\) | \(e\left(\frac{11}{56}\right)\) | \(e\left(\frac{29}{56}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(-1\) | \(e\left(\frac{1}{28}\right)\) | \(e\left(\frac{39}{56}\right)\) | \(e\left(\frac{11}{28}\right)\) |
| \(\chi_{8023}(27,\cdot)\) | 8023.gm | 560 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{140}\right)\) | \(e\left(\frac{559}{560}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{237}{560}\right)\) | \(e\left(\frac{3}{560}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{3}{140}\right)\) | \(e\left(\frac{279}{280}\right)\) | \(e\left(\frac{241}{560}\right)\) | \(e\left(\frac{21}{40}\right)\) |
| \(\chi_{8023}(28,\cdot)\) | 8023.eg | 70 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{9}{10}\right)\) |
| \(\chi_{8023}(29,\cdot)\) | 8023.go | 560 | yes | \(-1\) | \(1\) | \(e\left(\frac{51}{140}\right)\) | \(e\left(\frac{29}{560}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{87}{560}\right)\) | \(e\left(\frac{233}{560}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{13}{140}\right)\) | \(e\left(\frac{29}{280}\right)\) | \(e\left(\frac{291}{560}\right)\) | \(e\left(\frac{257}{280}\right)\) |
| \(\chi_{8023}(30,\cdot)\) | 8023.j | 7 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(1\) |
| \(\chi_{8023}(31,\cdot)\) | 8023.gg | 280 | yes | \(-1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{149}{280}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{127}{280}\right)\) | \(e\left(\frac{233}{280}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{9}{140}\right)\) | \(e\left(\frac{211}{280}\right)\) | \(e\left(\frac{127}{140}\right)\) |
| \(\chi_{8023}(32,\cdot)\) | 8023.ck | 28 | yes | \(1\) | \(1\) | \(1\) | \(e\left(\frac{19}{28}\right)\) | \(1\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(1\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{13}{14}\right)\) |