sage: H = DirichletGroup(1058)
pari: g = idealstar(,1058,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 506 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{506}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{1058}(5,\cdot)$ |
First 32 of 506 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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{1058}(1,\cdot)\) | 1058.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{1058}(3,\cdot)\) | 1058.g | 253 | no | \(1\) | \(1\) | \(e\left(\frac{128}{253}\right)\) | \(e\left(\frac{8}{253}\right)\) | \(e\left(\frac{20}{253}\right)\) | \(e\left(\frac{3}{253}\right)\) | \(e\left(\frac{50}{253}\right)\) | \(e\left(\frac{2}{253}\right)\) | \(e\left(\frac{136}{253}\right)\) | \(e\left(\frac{232}{253}\right)\) | \(e\left(\frac{197}{253}\right)\) | \(e\left(\frac{148}{253}\right)\) |
| \(\chi_{1058}(5,\cdot)\) | 1058.h | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{8}{253}\right)\) | \(e\left(\frac{1}{506}\right)\) | \(e\left(\frac{129}{506}\right)\) | \(e\left(\frac{16}{253}\right)\) | \(e\left(\frac{449}{506}\right)\) | \(e\left(\frac{95}{253}\right)\) | \(e\left(\frac{17}{506}\right)\) | \(e\left(\frac{29}{506}\right)\) | \(e\left(\frac{499}{506}\right)\) | \(e\left(\frac{145}{506}\right)\) |
| \(\chi_{1058}(7,\cdot)\) | 1058.h | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{20}{253}\right)\) | \(e\left(\frac{129}{506}\right)\) | \(e\left(\frac{449}{506}\right)\) | \(e\left(\frac{40}{253}\right)\) | \(e\left(\frac{237}{506}\right)\) | \(e\left(\frac{111}{253}\right)\) | \(e\left(\frac{169}{506}\right)\) | \(e\left(\frac{199}{506}\right)\) | \(e\left(\frac{109}{506}\right)\) | \(e\left(\frac{489}{506}\right)\) |
| \(\chi_{1058}(9,\cdot)\) | 1058.g | 253 | no | \(1\) | \(1\) | \(e\left(\frac{3}{253}\right)\) | \(e\left(\frac{16}{253}\right)\) | \(e\left(\frac{40}{253}\right)\) | \(e\left(\frac{6}{253}\right)\) | \(e\left(\frac{100}{253}\right)\) | \(e\left(\frac{4}{253}\right)\) | \(e\left(\frac{19}{253}\right)\) | \(e\left(\frac{211}{253}\right)\) | \(e\left(\frac{141}{253}\right)\) | \(e\left(\frac{43}{253}\right)\) |
| \(\chi_{1058}(11,\cdot)\) | 1058.h | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{50}{253}\right)\) | \(e\left(\frac{449}{506}\right)\) | \(e\left(\frac{237}{506}\right)\) | \(e\left(\frac{100}{253}\right)\) | \(e\left(\frac{213}{506}\right)\) | \(e\left(\frac{151}{253}\right)\) | \(e\left(\frac{43}{506}\right)\) | \(e\left(\frac{371}{506}\right)\) | \(e\left(\frac{399}{506}\right)\) | \(e\left(\frac{337}{506}\right)\) |
| \(\chi_{1058}(13,\cdot)\) | 1058.g | 253 | no | \(1\) | \(1\) | \(e\left(\frac{2}{253}\right)\) | \(e\left(\frac{95}{253}\right)\) | \(e\left(\frac{111}{253}\right)\) | \(e\left(\frac{4}{253}\right)\) | \(e\left(\frac{151}{253}\right)\) | \(e\left(\frac{87}{253}\right)\) | \(e\left(\frac{97}{253}\right)\) | \(e\left(\frac{225}{253}\right)\) | \(e\left(\frac{94}{253}\right)\) | \(e\left(\frac{113}{253}\right)\) |
| \(\chi_{1058}(15,\cdot)\) | 1058.h | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{136}{253}\right)\) | \(e\left(\frac{17}{506}\right)\) | \(e\left(\frac{169}{506}\right)\) | \(e\left(\frac{19}{253}\right)\) | \(e\left(\frac{43}{506}\right)\) | \(e\left(\frac{97}{253}\right)\) | \(e\left(\frac{289}{506}\right)\) | \(e\left(\frac{493}{506}\right)\) | \(e\left(\frac{387}{506}\right)\) | \(e\left(\frac{441}{506}\right)\) |
| \(\chi_{1058}(17,\cdot)\) | 1058.h | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{232}{253}\right)\) | \(e\left(\frac{29}{506}\right)\) | \(e\left(\frac{199}{506}\right)\) | \(e\left(\frac{211}{253}\right)\) | \(e\left(\frac{371}{506}\right)\) | \(e\left(\frac{225}{253}\right)\) | \(e\left(\frac{493}{506}\right)\) | \(e\left(\frac{335}{506}\right)\) | \(e\left(\frac{303}{506}\right)\) | \(e\left(\frac{157}{506}\right)\) |
| \(\chi_{1058}(19,\cdot)\) | 1058.h | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{197}{253}\right)\) | \(e\left(\frac{499}{506}\right)\) | \(e\left(\frac{109}{506}\right)\) | \(e\left(\frac{141}{253}\right)\) | \(e\left(\frac{399}{506}\right)\) | \(e\left(\frac{94}{253}\right)\) | \(e\left(\frac{387}{506}\right)\) | \(e\left(\frac{303}{506}\right)\) | \(e\left(\frac{49}{506}\right)\) | \(e\left(\frac{503}{506}\right)\) |
| \(\chi_{1058}(21,\cdot)\) | 1058.h | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{148}{253}\right)\) | \(e\left(\frac{145}{506}\right)\) | \(e\left(\frac{489}{506}\right)\) | \(e\left(\frac{43}{253}\right)\) | \(e\left(\frac{337}{506}\right)\) | \(e\left(\frac{113}{253}\right)\) | \(e\left(\frac{441}{506}\right)\) | \(e\left(\frac{157}{506}\right)\) | \(e\left(\frac{503}{506}\right)\) | \(e\left(\frac{279}{506}\right)\) |
| \(\chi_{1058}(25,\cdot)\) | 1058.g | 253 | no | \(1\) | \(1\) | \(e\left(\frac{16}{253}\right)\) | \(e\left(\frac{1}{253}\right)\) | \(e\left(\frac{129}{253}\right)\) | \(e\left(\frac{32}{253}\right)\) | \(e\left(\frac{196}{253}\right)\) | \(e\left(\frac{190}{253}\right)\) | \(e\left(\frac{17}{253}\right)\) | \(e\left(\frac{29}{253}\right)\) | \(e\left(\frac{246}{253}\right)\) | \(e\left(\frac{145}{253}\right)\) |
| \(\chi_{1058}(27,\cdot)\) | 1058.g | 253 | no | \(1\) | \(1\) | \(e\left(\frac{131}{253}\right)\) | \(e\left(\frac{24}{253}\right)\) | \(e\left(\frac{60}{253}\right)\) | \(e\left(\frac{9}{253}\right)\) | \(e\left(\frac{150}{253}\right)\) | \(e\left(\frac{6}{253}\right)\) | \(e\left(\frac{155}{253}\right)\) | \(e\left(\frac{190}{253}\right)\) | \(e\left(\frac{85}{253}\right)\) | \(e\left(\frac{191}{253}\right)\) |
| \(\chi_{1058}(29,\cdot)\) | 1058.g | 253 | no | \(1\) | \(1\) | \(e\left(\frac{188}{253}\right)\) | \(e\left(\frac{75}{253}\right)\) | \(e\left(\frac{61}{253}\right)\) | \(e\left(\frac{123}{253}\right)\) | \(e\left(\frac{26}{253}\right)\) | \(e\left(\frac{82}{253}\right)\) | \(e\left(\frac{10}{253}\right)\) | \(e\left(\frac{151}{253}\right)\) | \(e\left(\frac{234}{253}\right)\) | \(e\left(\frac{249}{253}\right)\) |
| \(\chi_{1058}(31,\cdot)\) | 1058.g | 253 | no | \(1\) | \(1\) | \(e\left(\frac{103}{253}\right)\) | \(e\left(\frac{212}{253}\right)\) | \(e\left(\frac{24}{253}\right)\) | \(e\left(\frac{206}{253}\right)\) | \(e\left(\frac{60}{253}\right)\) | \(e\left(\frac{53}{253}\right)\) | \(e\left(\frac{62}{253}\right)\) | \(e\left(\frac{76}{253}\right)\) | \(e\left(\frac{34}{253}\right)\) | \(e\left(\frac{127}{253}\right)\) |
| \(\chi_{1058}(33,\cdot)\) | 1058.h | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{178}{253}\right)\) | \(e\left(\frac{465}{506}\right)\) | \(e\left(\frac{277}{506}\right)\) | \(e\left(\frac{103}{253}\right)\) | \(e\left(\frac{313}{506}\right)\) | \(e\left(\frac{153}{253}\right)\) | \(e\left(\frac{315}{506}\right)\) | \(e\left(\frac{329}{506}\right)\) | \(e\left(\frac{287}{506}\right)\) | \(e\left(\frac{127}{506}\right)\) |
| \(\chi_{1058}(35,\cdot)\) | 1058.g | 253 | no | \(1\) | \(1\) | \(e\left(\frac{28}{253}\right)\) | \(e\left(\frac{65}{253}\right)\) | \(e\left(\frac{36}{253}\right)\) | \(e\left(\frac{56}{253}\right)\) | \(e\left(\frac{90}{253}\right)\) | \(e\left(\frac{206}{253}\right)\) | \(e\left(\frac{93}{253}\right)\) | \(e\left(\frac{114}{253}\right)\) | \(e\left(\frac{51}{253}\right)\) | \(e\left(\frac{64}{253}\right)\) |
| \(\chi_{1058}(37,\cdot)\) | 1058.h | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{201}{253}\right)\) | \(e\left(\frac{373}{506}\right)\) | \(e\left(\frac{47}{506}\right)\) | \(e\left(\frac{149}{253}\right)\) | \(e\left(\frac{497}{506}\right)\) | \(e\left(\frac{15}{253}\right)\) | \(e\left(\frac{269}{506}\right)\) | \(e\left(\frac{191}{506}\right)\) | \(e\left(\frac{425}{506}\right)\) | \(e\left(\frac{449}{506}\right)\) |
| \(\chi_{1058}(39,\cdot)\) | 1058.g | 253 | no | \(1\) | \(1\) | \(e\left(\frac{130}{253}\right)\) | \(e\left(\frac{103}{253}\right)\) | \(e\left(\frac{131}{253}\right)\) | \(e\left(\frac{7}{253}\right)\) | \(e\left(\frac{201}{253}\right)\) | \(e\left(\frac{89}{253}\right)\) | \(e\left(\frac{233}{253}\right)\) | \(e\left(\frac{204}{253}\right)\) | \(e\left(\frac{38}{253}\right)\) | \(e\left(\frac{8}{253}\right)\) |
| \(\chi_{1058}(41,\cdot)\) | 1058.g | 253 | no | \(1\) | \(1\) | \(e\left(\frac{162}{253}\right)\) | \(e\left(\frac{105}{253}\right)\) | \(e\left(\frac{136}{253}\right)\) | \(e\left(\frac{71}{253}\right)\) | \(e\left(\frac{87}{253}\right)\) | \(e\left(\frac{216}{253}\right)\) | \(e\left(\frac{14}{253}\right)\) | \(e\left(\frac{9}{253}\right)\) | \(e\left(\frac{24}{253}\right)\) | \(e\left(\frac{45}{253}\right)\) |
| \(\chi_{1058}(43,\cdot)\) | 1058.h | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{216}{253}\right)\) | \(e\left(\frac{27}{506}\right)\) | \(e\left(\frac{447}{506}\right)\) | \(e\left(\frac{179}{253}\right)\) | \(e\left(\frac{485}{506}\right)\) | \(e\left(\frac{35}{253}\right)\) | \(e\left(\frac{459}{506}\right)\) | \(e\left(\frac{277}{506}\right)\) | \(e\left(\frac{317}{506}\right)\) | \(e\left(\frac{373}{506}\right)\) |
| \(\chi_{1058}(45,\cdot)\) | 1058.f | 46 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(e\left(\frac{19}{46}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{5}{46}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{21}{46}\right)\) |
| \(\chi_{1058}(47,\cdot)\) | 1058.e | 23 | no | \(1\) | \(1\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{2}{23}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{9}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) |
| \(\chi_{1058}(49,\cdot)\) | 1058.g | 253 | no | \(1\) | \(1\) | \(e\left(\frac{40}{253}\right)\) | \(e\left(\frac{129}{253}\right)\) | \(e\left(\frac{196}{253}\right)\) | \(e\left(\frac{80}{253}\right)\) | \(e\left(\frac{237}{253}\right)\) | \(e\left(\frac{222}{253}\right)\) | \(e\left(\frac{169}{253}\right)\) | \(e\left(\frac{199}{253}\right)\) | \(e\left(\frac{109}{253}\right)\) | \(e\left(\frac{236}{253}\right)\) |
| \(\chi_{1058}(51,\cdot)\) | 1058.h | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{107}{253}\right)\) | \(e\left(\frac{45}{506}\right)\) | \(e\left(\frac{239}{506}\right)\) | \(e\left(\frac{214}{253}\right)\) | \(e\left(\frac{471}{506}\right)\) | \(e\left(\frac{227}{253}\right)\) | \(e\left(\frac{259}{506}\right)\) | \(e\left(\frac{293}{506}\right)\) | \(e\left(\frac{191}{506}\right)\) | \(e\left(\frac{453}{506}\right)\) |
| \(\chi_{1058}(53,\cdot)\) | 1058.h | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{163}{253}\right)\) | \(e\left(\frac{305}{506}\right)\) | \(e\left(\frac{383}{506}\right)\) | \(e\left(\frac{73}{253}\right)\) | \(e\left(\frac{325}{506}\right)\) | \(e\left(\frac{133}{253}\right)\) | \(e\left(\frac{125}{506}\right)\) | \(e\left(\frac{243}{506}\right)\) | \(e\left(\frac{395}{506}\right)\) | \(e\left(\frac{203}{506}\right)\) |
| \(\chi_{1058}(55,\cdot)\) | 1058.g | 253 | no | \(1\) | \(1\) | \(e\left(\frac{58}{253}\right)\) | \(e\left(\frac{225}{253}\right)\) | \(e\left(\frac{183}{253}\right)\) | \(e\left(\frac{116}{253}\right)\) | \(e\left(\frac{78}{253}\right)\) | \(e\left(\frac{246}{253}\right)\) | \(e\left(\frac{30}{253}\right)\) | \(e\left(\frac{200}{253}\right)\) | \(e\left(\frac{196}{253}\right)\) | \(e\left(\frac{241}{253}\right)\) |
| \(\chi_{1058}(57,\cdot)\) | 1058.h | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{72}{253}\right)\) | \(e\left(\frac{9}{506}\right)\) | \(e\left(\frac{149}{506}\right)\) | \(e\left(\frac{144}{253}\right)\) | \(e\left(\frac{499}{506}\right)\) | \(e\left(\frac{96}{253}\right)\) | \(e\left(\frac{153}{506}\right)\) | \(e\left(\frac{261}{506}\right)\) | \(e\left(\frac{443}{506}\right)\) | \(e\left(\frac{293}{506}\right)\) |
| \(\chi_{1058}(59,\cdot)\) | 1058.g | 253 | no | \(1\) | \(1\) | \(e\left(\frac{79}{253}\right)\) | \(e\left(\frac{84}{253}\right)\) | \(e\left(\frac{210}{253}\right)\) | \(e\left(\frac{158}{253}\right)\) | \(e\left(\frac{19}{253}\right)\) | \(e\left(\frac{21}{253}\right)\) | \(e\left(\frac{163}{253}\right)\) | \(e\left(\frac{159}{253}\right)\) | \(e\left(\frac{171}{253}\right)\) | \(e\left(\frac{36}{253}\right)\) |
| \(\chi_{1058}(61,\cdot)\) | 1058.h | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{169}{253}\right)\) | \(e\left(\frac{369}{506}\right)\) | \(e\left(\frac{37}{506}\right)\) | \(e\left(\frac{85}{253}\right)\) | \(e\left(\frac{219}{506}\right)\) | \(e\left(\frac{141}{253}\right)\) | \(e\left(\frac{201}{506}\right)\) | \(e\left(\frac{75}{506}\right)\) | \(e\left(\frac{453}{506}\right)\) | \(e\left(\frac{375}{506}\right)\) |
| \(\chi_{1058}(63,\cdot)\) | 1058.d | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{3}{22}\right)\) |
| \(\chi_{1058}(65,\cdot)\) | 1058.h | 506 | no | \(-1\) | \(1\) | \(e\left(\frac{10}{253}\right)\) | \(e\left(\frac{191}{506}\right)\) | \(e\left(\frac{351}{506}\right)\) | \(e\left(\frac{20}{253}\right)\) | \(e\left(\frac{245}{506}\right)\) | \(e\left(\frac{182}{253}\right)\) | \(e\left(\frac{211}{506}\right)\) | \(e\left(\frac{479}{506}\right)\) | \(e\left(\frac{181}{506}\right)\) | \(e\left(\frac{371}{506}\right)\) |