sage: H = DirichletGroup(10537)
pari: g = idealstar(,10537,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 10240 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{8}\times C_{1280}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{10537}(8739,\cdot)$, $\chi_{10537}(2830,\cdot)$ |
First 32 of 10240 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{10537}(1,\cdot)\) | 10537.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{10537}(2,\cdot)\) | 10537.cx | 80 | yes | \(1\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{7}{10}\right)\) |
| \(\chi_{10537}(3,\cdot)\) | 10537.dt | 256 | yes | \(1\) | \(1\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{161}{256}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{119}{256}\right)\) | \(e\left(\frac{145}{256}\right)\) | \(e\left(\frac{245}{256}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{33}{128}\right)\) | \(e\left(\frac{103}{256}\right)\) | \(e\left(\frac{57}{64}\right)\) |
| \(\chi_{10537}(4,\cdot)\) | 10537.bw | 40 | yes | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(-i\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{2}{5}\right)\) |
| \(\chi_{10537}(5,\cdot)\) | 10537.er | 1280 | yes | \(-1\) | \(1\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{119}{256}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{1173}{1280}\right)\) | \(e\left(\frac{99}{1280}\right)\) | \(e\left(\frac{911}{1280}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{119}{128}\right)\) | \(e\left(\frac{677}{1280}\right)\) | \(e\left(\frac{243}{320}\right)\) |
| \(\chi_{10537}(6,\cdot)\) | 10537.em | 1280 | yes | \(1\) | \(1\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{145}{256}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{99}{1280}\right)\) | \(e\left(\frac{517}{1280}\right)\) | \(e\left(\frac{313}{1280}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{17}{128}\right)\) | \(e\left(\frac{1171}{1280}\right)\) | \(e\left(\frac{189}{320}\right)\) |
| \(\chi_{10537}(7,\cdot)\) | 10537.en | 1280 | yes | \(1\) | \(1\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{245}{256}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{911}{1280}\right)\) | \(e\left(\frac{313}{1280}\right)\) | \(e\left(\frac{317}{1280}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{117}{128}\right)\) | \(e\left(\frac{1279}{1280}\right)\) | \(e\left(\frac{1}{320}\right)\) |
| \(\chi_{10537}(8,\cdot)\) | 10537.cx | 80 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{1}{10}\right)\) |
| \(\chi_{10537}(9,\cdot)\) | 10537.cz | 128 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{33}{128}\right)\) | \(-i\) | \(e\left(\frac{119}{128}\right)\) | \(e\left(\frac{17}{128}\right)\) | \(e\left(\frac{117}{128}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{103}{128}\right)\) | \(e\left(\frac{25}{32}\right)\) |
| \(\chi_{10537}(10,\cdot)\) | 10537.ep | 1280 | yes | \(-1\) | \(1\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{103}{256}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{677}{1280}\right)\) | \(e\left(\frac{1171}{1280}\right)\) | \(e\left(\frac{1279}{1280}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{103}{128}\right)\) | \(e\left(\frac{53}{1280}\right)\) | \(e\left(\frac{147}{320}\right)\) |
| \(\chi_{10537}(11,\cdot)\) | 10537.ed | 320 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{57}{64}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{243}{320}\right)\) | \(e\left(\frac{189}{320}\right)\) | \(e\left(\frac{1}{320}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{147}{320}\right)\) | \(e\left(\frac{23}{80}\right)\) |
| \(\chi_{10537}(12,\cdot)\) | 10537.en | 1280 | yes | \(1\) | \(1\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{129}{256}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{883}{1280}\right)\) | \(e\left(\frac{309}{1280}\right)\) | \(e\left(\frac{681}{1280}\right)\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{1}{128}\right)\) | \(e\left(\frac{547}{1280}\right)\) | \(e\left(\frac{93}{320}\right)\) |
| \(\chi_{10537}(13,\cdot)\) | 10537.el | 640 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{5}{128}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{527}{640}\right)\) | \(e\left(\frac{41}{640}\right)\) | \(e\left(\frac{269}{640}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{5}{64}\right)\) | \(e\left(\frac{543}{640}\right)\) | \(e\left(\frac{77}{160}\right)\) |
| \(\chi_{10537}(14,\cdot)\) | 10537.do | 256 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{229}{256}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{83}{256}\right)\) | \(e\left(\frac{21}{256}\right)\) | \(e\left(\frac{137}{256}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{101}{128}\right)\) | \(e\left(\frac{131}{256}\right)\) | \(e\left(\frac{45}{64}\right)\) |
| \(\chi_{10537}(15,\cdot)\) | 10537.dj | 160 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{61}{160}\right)\) | \(e\left(\frac{103}{160}\right)\) | \(e\left(\frac{107}{160}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{149}{160}\right)\) | \(e\left(\frac{13}{20}\right)\) |
| \(\chi_{10537}(16,\cdot)\) | 10537.bi | 20 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(-i\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(-1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) |
| \(\chi_{10537}(17,\cdot)\) | 10537.dk | 160 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{149}{160}\right)\) | \(e\left(\frac{127}{160}\right)\) | \(e\left(\frac{3}{160}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{141}{160}\right)\) | \(e\left(\frac{7}{20}\right)\) |
| \(\chi_{10537}(18,\cdot)\) | 10537.ei | 640 | yes | \(1\) | \(1\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{25}{128}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{347}{640}\right)\) | \(e\left(\frac{621}{640}\right)\) | \(e\left(\frac{129}{640}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{25}{64}\right)\) | \(e\left(\frac{203}{640}\right)\) | \(e\left(\frac{77}{160}\right)\) |
| \(\chi_{10537}(19,\cdot)\) | 10537.et | 1280 | yes | \(1\) | \(1\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{221}{256}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{1031}{1280}\right)\) | \(e\left(\frac{193}{1280}\right)\) | \(e\left(\frac{357}{1280}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(e\left(\frac{93}{128}\right)\) | \(e\left(\frac{119}{1280}\right)\) | \(e\left(\frac{121}{320}\right)\) |
| \(\chi_{10537}(20,\cdot)\) | 10537.eq | 1280 | yes | \(-1\) | \(1\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{87}{256}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{181}{1280}\right)\) | \(e\left(\frac{963}{1280}\right)\) | \(e\left(\frac{367}{1280}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{87}{128}\right)\) | \(e\left(\frac{709}{1280}\right)\) | \(e\left(\frac{51}{320}\right)\) |
| \(\chi_{10537}(21,\cdot)\) | 10537.ef | 640 | yes | \(1\) | \(1\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{75}{128}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{113}{640}\right)\) | \(e\left(\frac{519}{640}\right)\) | \(e\left(\frac{131}{640}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{11}{64}\right)\) | \(e\left(\frac{257}{640}\right)\) | \(e\left(\frac{143}{160}\right)\) |
| \(\chi_{10537}(22,\cdot)\) | 10537.dw | 320 | yes | \(-1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{53}{64}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{119}{320}\right)\) | \(e\left(\frac{137}{320}\right)\) | \(e\left(\frac{93}{320}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{311}{320}\right)\) | \(e\left(\frac{79}{80}\right)\) |
| \(\chi_{10537}(23,\cdot)\) | 10537.dz | 320 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{39}{64}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{261}{320}\right)\) | \(e\left(\frac{83}{320}\right)\) | \(e\left(\frac{127}{320}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{149}{320}\right)\) | \(e\left(\frac{11}{80}\right)\) |
| \(\chi_{10537}(24,\cdot)\) | 10537.et | 1280 | yes | \(1\) | \(1\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{113}{256}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{387}{1280}\right)\) | \(e\left(\frac{101}{1280}\right)\) | \(e\left(\frac{1049}{1280}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{113}{128}\right)\) | \(e\left(\frac{1203}{1280}\right)\) | \(e\left(\frac{317}{320}\right)\) |
| \(\chi_{10537}(25,\cdot)\) | 10537.ej | 640 | yes | \(1\) | \(1\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{119}{128}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{533}{640}\right)\) | \(e\left(\frac{99}{640}\right)\) | \(e\left(\frac{271}{640}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{55}{64}\right)\) | \(e\left(\frac{37}{640}\right)\) | \(e\left(\frac{83}{160}\right)\) |
| \(\chi_{10537}(26,\cdot)\) | 10537.eh | 640 | yes | \(-1\) | \(1\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{125}{128}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{279}{640}\right)\) | \(e\left(\frac{577}{640}\right)\) | \(e\left(\frac{453}{640}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{61}{64}\right)\) | \(e\left(\frac{231}{640}\right)\) | \(e\left(\frac{29}{160}\right)\) |
| \(\chi_{10537}(27,\cdot)\) | 10537.dt | 256 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{227}{256}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{101}{256}\right)\) | \(e\left(\frac{179}{256}\right)\) | \(e\left(\frac{223}{256}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{99}{128}\right)\) | \(e\left(\frac{53}{256}\right)\) | \(e\left(\frac{43}{64}\right)\) |
| \(\chi_{10537}(28,\cdot)\) | 10537.eo | 1280 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{213}{256}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{1199}{1280}\right)\) | \(e\left(\frac{1177}{1280}\right)\) | \(e\left(\frac{1053}{1280}\right)\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{85}{128}\right)\) | \(e\left(\frac{31}{1280}\right)\) | \(e\left(\frac{129}{320}\right)\) |
| \(\chi_{10537}(29,\cdot)\) | 10537.eg | 640 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{127}{128}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{29}{640}\right)\) | \(e\left(\frac{107}{640}\right)\) | \(e\left(\frac{23}{640}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{63}{64}\right)\) | \(e\left(\frac{141}{640}\right)\) | \(e\left(\frac{79}{160}\right)\) |
| \(\chi_{10537}(30,\cdot)\) | 10537.dj | 160 | yes | \(-1\) | \(1\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{1}{32}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{159}{160}\right)\) | \(e\left(\frac{77}{160}\right)\) | \(e\left(\frac{153}{160}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{71}{160}\right)\) | \(e\left(\frac{7}{20}\right)\) |
| \(\chi_{10537}(31,\cdot)\) | 10537.ej | 640 | yes | \(1\) | \(1\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{57}{128}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{251}{640}\right)\) | \(e\left(\frac{13}{640}\right)\) | \(e\left(\frac{417}{640}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{57}{64}\right)\) | \(e\left(\frac{619}{640}\right)\) | \(e\left(\frac{61}{160}\right)\) |
| \(\chi_{10537}(32,\cdot)\) | 10537.ba | 16 | yes | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{11}{16}\right)\) | \(1\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(-1\) |