sage: H = DirichletGroup(10015)
pari: g = idealstar(,10015,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 8008 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{2}\times C_{4004}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{10015}(4007,\cdot)$, $\chi_{10015}(4011,\cdot)$ |
First 32 of 8008 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{10015}(1,\cdot)\) | 10015.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{10015}(2,\cdot)\) | 10015.bp | 572 | yes | \(1\) | \(1\) | \(e\left(\frac{81}{572}\right)\) | \(e\left(\frac{469}{572}\right)\) | \(e\left(\frac{81}{286}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{225}{572}\right)\) | \(e\left(\frac{243}{572}\right)\) | \(e\left(\frac{183}{286}\right)\) | \(e\left(\frac{207}{286}\right)\) | \(e\left(\frac{59}{572}\right)\) | \(e\left(\frac{281}{572}\right)\) |
| \(\chi_{10015}(3,\cdot)\) | 10015.bv | 4004 | yes | \(-1\) | \(1\) | \(e\left(\frac{469}{572}\right)\) | \(e\left(\frac{193}{4004}\right)\) | \(e\left(\frac{183}{286}\right)\) | \(e\left(\frac{79}{91}\right)\) | \(e\left(\frac{31}{4004}\right)\) | \(e\left(\frac{263}{572}\right)\) | \(e\left(\frac{193}{2002}\right)\) | \(e\left(\frac{67}{143}\right)\) | \(e\left(\frac{2755}{4004}\right)\) | \(e\left(\frac{1817}{4004}\right)\) |
| \(\chi_{10015}(4,\cdot)\) | 10015.bh | 286 | yes | \(1\) | \(1\) | \(e\left(\frac{81}{286}\right)\) | \(e\left(\frac{183}{286}\right)\) | \(e\left(\frac{81}{143}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{225}{286}\right)\) | \(e\left(\frac{243}{286}\right)\) | \(e\left(\frac{40}{143}\right)\) | \(e\left(\frac{64}{143}\right)\) | \(e\left(\frac{59}{286}\right)\) | \(e\left(\frac{281}{286}\right)\) |
| \(\chi_{10015}(6,\cdot)\) | 10015.bg | 182 | no | \(-1\) | \(1\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{79}{91}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{151}{182}\right)\) | \(e\left(\frac{73}{182}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{67}{91}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{72}{91}\right)\) | \(e\left(\frac{86}{91}\right)\) |
| \(\chi_{10015}(7,\cdot)\) | 10015.bu | 4004 | yes | \(1\) | \(1\) | \(e\left(\frac{225}{572}\right)\) | \(e\left(\frac{31}{4004}\right)\) | \(e\left(\frac{225}{286}\right)\) | \(e\left(\frac{73}{182}\right)\) | \(e\left(\frac{3231}{4004}\right)\) | \(e\left(\frac{103}{572}\right)\) | \(e\left(\frac{31}{2002}\right)\) | \(e\left(\frac{3}{286}\right)\) | \(e\left(\frac{3181}{4004}\right)\) | \(e\left(\frac{2159}{4004}\right)\) |
| \(\chi_{10015}(8,\cdot)\) | 10015.bp | 572 | yes | \(1\) | \(1\) | \(e\left(\frac{243}{572}\right)\) | \(e\left(\frac{263}{572}\right)\) | \(e\left(\frac{243}{286}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{103}{572}\right)\) | \(e\left(\frac{157}{572}\right)\) | \(e\left(\frac{263}{286}\right)\) | \(e\left(\frac{49}{286}\right)\) | \(e\left(\frac{177}{572}\right)\) | \(e\left(\frac{271}{572}\right)\) |
| \(\chi_{10015}(9,\cdot)\) | 10015.bs | 2002 | yes | \(1\) | \(1\) | \(e\left(\frac{183}{286}\right)\) | \(e\left(\frac{193}{2002}\right)\) | \(e\left(\frac{40}{143}\right)\) | \(e\left(\frac{67}{91}\right)\) | \(e\left(\frac{31}{2002}\right)\) | \(e\left(\frac{263}{286}\right)\) | \(e\left(\frac{193}{1001}\right)\) | \(e\left(\frac{134}{143}\right)\) | \(e\left(\frac{753}{2002}\right)\) | \(e\left(\frac{1817}{2002}\right)\) |
| \(\chi_{10015}(11,\cdot)\) | 10015.bi | 286 | no | \(-1\) | \(1\) | \(e\left(\frac{207}{286}\right)\) | \(e\left(\frac{67}{143}\right)\) | \(e\left(\frac{64}{143}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{3}{286}\right)\) | \(e\left(\frac{49}{286}\right)\) | \(e\left(\frac{134}{143}\right)\) | \(e\left(\frac{57}{286}\right)\) | \(e\left(\frac{131}{143}\right)\) | \(e\left(\frac{81}{143}\right)\) |
| \(\chi_{10015}(12,\cdot)\) | 10015.bv | 4004 | yes | \(-1\) | \(1\) | \(e\left(\frac{59}{572}\right)\) | \(e\left(\frac{2755}{4004}\right)\) | \(e\left(\frac{59}{286}\right)\) | \(e\left(\frac{72}{91}\right)\) | \(e\left(\frac{3181}{4004}\right)\) | \(e\left(\frac{177}{572}\right)\) | \(e\left(\frac{753}{2002}\right)\) | \(e\left(\frac{131}{143}\right)\) | \(e\left(\frac{3581}{4004}\right)\) | \(e\left(\frac{1747}{4004}\right)\) |
| \(\chi_{10015}(13,\cdot)\) | 10015.bv | 4004 | yes | \(-1\) | \(1\) | \(e\left(\frac{281}{572}\right)\) | \(e\left(\frac{1817}{4004}\right)\) | \(e\left(\frac{281}{286}\right)\) | \(e\left(\frac{86}{91}\right)\) | \(e\left(\frac{2159}{4004}\right)\) | \(e\left(\frac{271}{572}\right)\) | \(e\left(\frac{1817}{2002}\right)\) | \(e\left(\frac{81}{143}\right)\) | \(e\left(\frac{1747}{4004}\right)\) | \(e\left(\frac{613}{4004}\right)\) |
| \(\chi_{10015}(14,\cdot)\) | 10015.bs | 2002 | yes | \(1\) | \(1\) | \(e\left(\frac{153}{286}\right)\) | \(e\left(\frac{1657}{2002}\right)\) | \(e\left(\frac{10}{143}\right)\) | \(e\left(\frac{33}{91}\right)\) | \(e\left(\frac{401}{2002}\right)\) | \(e\left(\frac{173}{286}\right)\) | \(e\left(\frac{656}{1001}\right)\) | \(e\left(\frac{105}{143}\right)\) | \(e\left(\frac{1797}{2002}\right)\) | \(e\left(\frac{61}{2002}\right)\) |
| \(\chi_{10015}(16,\cdot)\) | 10015.ba | 143 | no | \(1\) | \(1\) | \(e\left(\frac{81}{143}\right)\) | \(e\left(\frac{40}{143}\right)\) | \(e\left(\frac{19}{143}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{82}{143}\right)\) | \(e\left(\frac{100}{143}\right)\) | \(e\left(\frac{80}{143}\right)\) | \(e\left(\frac{128}{143}\right)\) | \(e\left(\frac{59}{143}\right)\) | \(e\left(\frac{138}{143}\right)\) |
| \(\chi_{10015}(17,\cdot)\) | 10015.bm | 364 | yes | \(1\) | \(1\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{101}{364}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{33}{182}\right)\) | \(e\left(\frac{53}{364}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{101}{182}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{31}{364}\right)\) | \(e\left(\frac{353}{364}\right)\) |
| \(\chi_{10015}(18,\cdot)\) | 10015.bu | 4004 | yes | \(1\) | \(1\) | \(e\left(\frac{447}{572}\right)\) | \(e\left(\frac{3669}{4004}\right)\) | \(e\left(\frac{161}{286}\right)\) | \(e\left(\frac{127}{182}\right)\) | \(e\left(\frac{1637}{4004}\right)\) | \(e\left(\frac{197}{572}\right)\) | \(e\left(\frac{1667}{2002}\right)\) | \(e\left(\frac{189}{286}\right)\) | \(e\left(\frac{1919}{4004}\right)\) | \(e\left(\frac{1597}{4004}\right)\) |
| \(\chi_{10015}(19,\cdot)\) | 10015.bs | 2002 | yes | \(1\) | \(1\) | \(e\left(\frac{227}{286}\right)\) | \(e\left(\frac{963}{2002}\right)\) | \(e\left(\frac{84}{143}\right)\) | \(e\left(\frac{25}{91}\right)\) | \(e\left(\frac{1109}{2002}\right)\) | \(e\left(\frac{109}{286}\right)\) | \(e\left(\frac{963}{1001}\right)\) | \(e\left(\frac{24}{143}\right)\) | \(e\left(\frac{137}{2002}\right)\) | \(e\left(\frac{1971}{2002}\right)\) |
| \(\chi_{10015}(21,\cdot)\) | 10015.bi | 286 | no | \(-1\) | \(1\) | \(e\left(\frac{61}{286}\right)\) | \(e\left(\frac{8}{143}\right)\) | \(e\left(\frac{61}{143}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{233}{286}\right)\) | \(e\left(\frac{183}{286}\right)\) | \(e\left(\frac{16}{143}\right)\) | \(e\left(\frac{137}{286}\right)\) | \(e\left(\frac{69}{143}\right)\) | \(e\left(\frac{142}{143}\right)\) |
| \(\chi_{10015}(22,\cdot)\) | 10015.w | 52 | yes | \(-1\) | \(1\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{3}{52}\right)\) |
| \(\chi_{10015}(23,\cdot)\) | 10015.bp | 572 | yes | \(1\) | \(1\) | \(e\left(\frac{323}{572}\right)\) | \(e\left(\frac{359}{572}\right)\) | \(e\left(\frac{37}{286}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{71}{572}\right)\) | \(e\left(\frac{397}{572}\right)\) | \(e\left(\frac{73}{286}\right)\) | \(e\left(\frac{31}{286}\right)\) | \(e\left(\frac{433}{572}\right)\) | \(e\left(\frac{259}{572}\right)\) |
| \(\chi_{10015}(24,\cdot)\) | 10015.bt | 2002 | yes | \(-1\) | \(1\) | \(e\left(\frac{35}{143}\right)\) | \(e\left(\frac{1017}{2002}\right)\) | \(e\left(\frac{70}{143}\right)\) | \(e\left(\frac{137}{182}\right)\) | \(e\left(\frac{188}{1001}\right)\) | \(e\left(\frac{105}{143}\right)\) | \(e\left(\frac{16}{1001}\right)\) | \(e\left(\frac{183}{286}\right)\) | \(e\left(\frac{1997}{2002}\right)\) | \(e\left(\frac{1857}{2002}\right)\) |
| \(\chi_{10015}(26,\cdot)\) | 10015.br | 2002 | no | \(-1\) | \(1\) | \(e\left(\frac{181}{286}\right)\) | \(e\left(\frac{274}{1001}\right)\) | \(e\left(\frac{38}{143}\right)\) | \(e\left(\frac{165}{182}\right)\) | \(e\left(\frac{1867}{2002}\right)\) | \(e\left(\frac{257}{286}\right)\) | \(e\left(\frac{548}{1001}\right)\) | \(e\left(\frac{83}{286}\right)\) | \(e\left(\frac{540}{1001}\right)\) | \(e\left(\frac{645}{1001}\right)\) |
| \(\chi_{10015}(27,\cdot)\) | 10015.bv | 4004 | yes | \(-1\) | \(1\) | \(e\left(\frac{263}{572}\right)\) | \(e\left(\frac{579}{4004}\right)\) | \(e\left(\frac{263}{286}\right)\) | \(e\left(\frac{55}{91}\right)\) | \(e\left(\frac{93}{4004}\right)\) | \(e\left(\frac{217}{572}\right)\) | \(e\left(\frac{579}{2002}\right)\) | \(e\left(\frac{58}{143}\right)\) | \(e\left(\frac{257}{4004}\right)\) | \(e\left(\frac{1447}{4004}\right)\) |
| \(\chi_{10015}(28,\cdot)\) | 10015.bu | 4004 | yes | \(1\) | \(1\) | \(e\left(\frac{387}{572}\right)\) | \(e\left(\frac{2593}{4004}\right)\) | \(e\left(\frac{101}{286}\right)\) | \(e\left(\frac{59}{182}\right)\) | \(e\left(\frac{2377}{4004}\right)\) | \(e\left(\frac{17}{572}\right)\) | \(e\left(\frac{591}{2002}\right)\) | \(e\left(\frac{131}{286}\right)\) | \(e\left(\frac{3}{4004}\right)\) | \(e\left(\frac{2089}{4004}\right)\) |
| \(\chi_{10015}(29,\cdot)\) | 10015.bt | 2002 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{143}\right)\) | \(e\left(\frac{789}{2002}\right)\) | \(e\left(\frac{2}{143}\right)\) | \(e\left(\frac{73}{182}\right)\) | \(e\left(\frac{512}{1001}\right)\) | \(e\left(\frac{3}{143}\right)\) | \(e\left(\frac{789}{1001}\right)\) | \(e\left(\frac{185}{286}\right)\) | \(e\left(\frac{817}{2002}\right)\) | \(e\left(\frac{1671}{2002}\right)\) |
| \(\chi_{10015}(31,\cdot)\) | 10015.br | 2002 | no | \(-1\) | \(1\) | \(e\left(\frac{127}{286}\right)\) | \(e\left(\frac{562}{1001}\right)\) | \(e\left(\frac{127}{143}\right)\) | \(e\left(\frac{1}{182}\right)\) | \(e\left(\frac{1389}{2002}\right)\) | \(e\left(\frac{95}{286}\right)\) | \(e\left(\frac{123}{1001}\right)\) | \(e\left(\frac{93}{286}\right)\) | \(e\left(\frac{450}{1001}\right)\) | \(e\left(\frac{37}{1001}\right)\) |
| \(\chi_{10015}(32,\cdot)\) | 10015.bp | 572 | yes | \(1\) | \(1\) | \(e\left(\frac{405}{572}\right)\) | \(e\left(\frac{57}{572}\right)\) | \(e\left(\frac{119}{286}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{553}{572}\right)\) | \(e\left(\frac{71}{572}\right)\) | \(e\left(\frac{57}{286}\right)\) | \(e\left(\frac{177}{286}\right)\) | \(e\left(\frac{295}{572}\right)\) | \(e\left(\frac{261}{572}\right)\) |
| \(\chi_{10015}(33,\cdot)\) | 10015.bu | 4004 | yes | \(1\) | \(1\) | \(e\left(\frac{311}{572}\right)\) | \(e\left(\frac{2069}{4004}\right)\) | \(e\left(\frac{25}{286}\right)\) | \(e\left(\frac{11}{182}\right)\) | \(e\left(\frac{73}{4004}\right)\) | \(e\left(\frac{361}{572}\right)\) | \(e\left(\frac{67}{2002}\right)\) | \(e\left(\frac{191}{286}\right)\) | \(e\left(\frac{2419}{4004}\right)\) | \(e\left(\frac{81}{4004}\right)\) |
| \(\chi_{10015}(34,\cdot)\) | 10015.bc | 154 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{15}{154}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{83}{154}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{15}{77}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{29}{154}\right)\) | \(e\left(\frac{71}{154}\right)\) |
| \(\chi_{10015}(36,\cdot)\) | 10015.z | 91 | no | \(1\) | \(1\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{67}{91}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{60}{91}\right)\) | \(e\left(\frac{73}{91}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{43}{91}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{53}{91}\right)\) | \(e\left(\frac{81}{91}\right)\) |
| \(\chi_{10015}(37,\cdot)\) | 10015.bu | 4004 | yes | \(1\) | \(1\) | \(e\left(\frac{181}{572}\right)\) | \(e\left(\frac{1835}{4004}\right)\) | \(e\left(\frac{181}{286}\right)\) | \(e\left(\frac{141}{182}\right)\) | \(e\left(\frac{3583}{4004}\right)\) | \(e\left(\frac{543}{572}\right)\) | \(e\left(\frac{1835}{2002}\right)\) | \(e\left(\frac{113}{286}\right)\) | \(e\left(\frac{365}{4004}\right)\) | \(e\left(\frac{575}{4004}\right)\) |
| \(\chi_{10015}(38,\cdot)\) | 10015.bu | 4004 | yes | \(1\) | \(1\) | \(e\left(\frac{535}{572}\right)\) | \(e\left(\frac{1205}{4004}\right)\) | \(e\left(\frac{249}{286}\right)\) | \(e\left(\frac{43}{182}\right)\) | \(e\left(\frac{3793}{4004}\right)\) | \(e\left(\frac{461}{572}\right)\) | \(e\left(\frac{1205}{2002}\right)\) | \(e\left(\frac{255}{286}\right)\) | \(e\left(\frac{687}{4004}\right)\) | \(e\left(\frac{1905}{4004}\right)\) |
| \(\chi_{10015}(39,\cdot)\) | 10015.bs | 2002 | yes | \(1\) | \(1\) | \(e\left(\frac{89}{286}\right)\) | \(e\left(\frac{1005}{2002}\right)\) | \(e\left(\frac{89}{143}\right)\) | \(e\left(\frac{74}{91}\right)\) | \(e\left(\frac{1095}{2002}\right)\) | \(e\left(\frac{267}{286}\right)\) | \(e\left(\frac{4}{1001}\right)\) | \(e\left(\frac{5}{143}\right)\) | \(e\left(\frac{249}{2002}\right)\) | \(e\left(\frac{1215}{2002}\right)\) |