sage: H = DirichletGroup(529)
pari: g = idealstar(,529,2)
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 | = | $\chi_{529}(5,\cdot)$ |
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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{529}(1,\cdot)\) | 529.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{529}(2,\cdot)\) | 529.g | 253 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{253}\right)\) | \(e\left(\frac{82}{253}\right)\) | \(e\left(\frac{26}{253}\right)\) | \(e\left(\frac{100}{253}\right)\) | \(e\left(\frac{95}{253}\right)\) | \(e\left(\frac{250}{253}\right)\) | \(e\left(\frac{39}{253}\right)\) | \(e\left(\frac{164}{253}\right)\) | \(e\left(\frac{113}{253}\right)\) | \(e\left(\frac{119}{253}\right)\) |
| \(\chi_{529}(3,\cdot)\) | 529.g | 253 | yes | \(1\) | \(1\) | \(e\left(\frac{82}{253}\right)\) | \(e\left(\frac{128}{253}\right)\) | \(e\left(\frac{164}{253}\right)\) | \(e\left(\frac{8}{253}\right)\) | \(e\left(\frac{210}{253}\right)\) | \(e\left(\frac{20}{253}\right)\) | \(e\left(\frac{246}{253}\right)\) | \(e\left(\frac{3}{253}\right)\) | \(e\left(\frac{90}{253}\right)\) | \(e\left(\frac{50}{253}\right)\) |
| \(\chi_{529}(4,\cdot)\) | 529.g | 253 | yes | \(1\) | \(1\) | \(e\left(\frac{26}{253}\right)\) | \(e\left(\frac{164}{253}\right)\) | \(e\left(\frac{52}{253}\right)\) | \(e\left(\frac{200}{253}\right)\) | \(e\left(\frac{190}{253}\right)\) | \(e\left(\frac{247}{253}\right)\) | \(e\left(\frac{78}{253}\right)\) | \(e\left(\frac{75}{253}\right)\) | \(e\left(\frac{226}{253}\right)\) | \(e\left(\frac{238}{253}\right)\) |
| \(\chi_{529}(5,\cdot)\) | 529.h | 506 | yes | \(-1\) | \(1\) | \(e\left(\frac{100}{253}\right)\) | \(e\left(\frac{8}{253}\right)\) | \(e\left(\frac{200}{253}\right)\) | \(e\left(\frac{1}{506}\right)\) | \(e\left(\frac{108}{253}\right)\) | \(e\left(\frac{129}{506}\right)\) | \(e\left(\frac{47}{253}\right)\) | \(e\left(\frac{16}{253}\right)\) | \(e\left(\frac{201}{506}\right)\) | \(e\left(\frac{449}{506}\right)\) |
| \(\chi_{529}(6,\cdot)\) | 529.g | 253 | yes | \(1\) | \(1\) | \(e\left(\frac{95}{253}\right)\) | \(e\left(\frac{210}{253}\right)\) | \(e\left(\frac{190}{253}\right)\) | \(e\left(\frac{108}{253}\right)\) | \(e\left(\frac{52}{253}\right)\) | \(e\left(\frac{17}{253}\right)\) | \(e\left(\frac{32}{253}\right)\) | \(e\left(\frac{167}{253}\right)\) | \(e\left(\frac{203}{253}\right)\) | \(e\left(\frac{169}{253}\right)\) |
| \(\chi_{529}(7,\cdot)\) | 529.h | 506 | yes | \(-1\) | \(1\) | \(e\left(\frac{250}{253}\right)\) | \(e\left(\frac{20}{253}\right)\) | \(e\left(\frac{247}{253}\right)\) | \(e\left(\frac{129}{506}\right)\) | \(e\left(\frac{17}{253}\right)\) | \(e\left(\frac{449}{506}\right)\) | \(e\left(\frac{244}{253}\right)\) | \(e\left(\frac{40}{253}\right)\) | \(e\left(\frac{123}{506}\right)\) | \(e\left(\frac{237}{506}\right)\) |
| \(\chi_{529}(8,\cdot)\) | 529.g | 253 | yes | \(1\) | \(1\) | \(e\left(\frac{39}{253}\right)\) | \(e\left(\frac{246}{253}\right)\) | \(e\left(\frac{78}{253}\right)\) | \(e\left(\frac{47}{253}\right)\) | \(e\left(\frac{32}{253}\right)\) | \(e\left(\frac{244}{253}\right)\) | \(e\left(\frac{117}{253}\right)\) | \(e\left(\frac{239}{253}\right)\) | \(e\left(\frac{86}{253}\right)\) | \(e\left(\frac{104}{253}\right)\) |
| \(\chi_{529}(9,\cdot)\) | 529.g | 253 | yes | \(1\) | \(1\) | \(e\left(\frac{164}{253}\right)\) | \(e\left(\frac{3}{253}\right)\) | \(e\left(\frac{75}{253}\right)\) | \(e\left(\frac{16}{253}\right)\) | \(e\left(\frac{167}{253}\right)\) | \(e\left(\frac{40}{253}\right)\) | \(e\left(\frac{239}{253}\right)\) | \(e\left(\frac{6}{253}\right)\) | \(e\left(\frac{180}{253}\right)\) | \(e\left(\frac{100}{253}\right)\) |
| \(\chi_{529}(10,\cdot)\) | 529.h | 506 | yes | \(-1\) | \(1\) | \(e\left(\frac{113}{253}\right)\) | \(e\left(\frac{90}{253}\right)\) | \(e\left(\frac{226}{253}\right)\) | \(e\left(\frac{201}{506}\right)\) | \(e\left(\frac{203}{253}\right)\) | \(e\left(\frac{123}{506}\right)\) | \(e\left(\frac{86}{253}\right)\) | \(e\left(\frac{180}{253}\right)\) | \(e\left(\frac{427}{506}\right)\) | \(e\left(\frac{181}{506}\right)\) |
| \(\chi_{529}(11,\cdot)\) | 529.h | 506 | yes | \(-1\) | \(1\) | \(e\left(\frac{119}{253}\right)\) | \(e\left(\frac{50}{253}\right)\) | \(e\left(\frac{238}{253}\right)\) | \(e\left(\frac{449}{506}\right)\) | \(e\left(\frac{169}{253}\right)\) | \(e\left(\frac{237}{506}\right)\) | \(e\left(\frac{104}{253}\right)\) | \(e\left(\frac{100}{253}\right)\) | \(e\left(\frac{181}{506}\right)\) | \(e\left(\frac{213}{506}\right)\) |
| \(\chi_{529}(12,\cdot)\) | 529.g | 253 | yes | \(1\) | \(1\) | \(e\left(\frac{108}{253}\right)\) | \(e\left(\frac{39}{253}\right)\) | \(e\left(\frac{216}{253}\right)\) | \(e\left(\frac{208}{253}\right)\) | \(e\left(\frac{147}{253}\right)\) | \(e\left(\frac{14}{253}\right)\) | \(e\left(\frac{71}{253}\right)\) | \(e\left(\frac{78}{253}\right)\) | \(e\left(\frac{63}{253}\right)\) | \(e\left(\frac{35}{253}\right)\) |
| \(\chi_{529}(13,\cdot)\) | 529.g | 253 | yes | \(1\) | \(1\) | \(e\left(\frac{25}{253}\right)\) | \(e\left(\frac{2}{253}\right)\) | \(e\left(\frac{50}{253}\right)\) | \(e\left(\frac{95}{253}\right)\) | \(e\left(\frac{27}{253}\right)\) | \(e\left(\frac{111}{253}\right)\) | \(e\left(\frac{75}{253}\right)\) | \(e\left(\frac{4}{253}\right)\) | \(e\left(\frac{120}{253}\right)\) | \(e\left(\frac{151}{253}\right)\) |
| \(\chi_{529}(14,\cdot)\) | 529.h | 506 | yes | \(-1\) | \(1\) | \(e\left(\frac{10}{253}\right)\) | \(e\left(\frac{102}{253}\right)\) | \(e\left(\frac{20}{253}\right)\) | \(e\left(\frac{329}{506}\right)\) | \(e\left(\frac{112}{253}\right)\) | \(e\left(\frac{443}{506}\right)\) | \(e\left(\frac{30}{253}\right)\) | \(e\left(\frac{204}{253}\right)\) | \(e\left(\frac{349}{506}\right)\) | \(e\left(\frac{475}{506}\right)\) |
| \(\chi_{529}(15,\cdot)\) | 529.h | 506 | yes | \(-1\) | \(1\) | \(e\left(\frac{182}{253}\right)\) | \(e\left(\frac{136}{253}\right)\) | \(e\left(\frac{111}{253}\right)\) | \(e\left(\frac{17}{506}\right)\) | \(e\left(\frac{65}{253}\right)\) | \(e\left(\frac{169}{506}\right)\) | \(e\left(\frac{40}{253}\right)\) | \(e\left(\frac{19}{253}\right)\) | \(e\left(\frac{381}{506}\right)\) | \(e\left(\frac{43}{506}\right)\) |
| \(\chi_{529}(16,\cdot)\) | 529.g | 253 | yes | \(1\) | \(1\) | \(e\left(\frac{52}{253}\right)\) | \(e\left(\frac{75}{253}\right)\) | \(e\left(\frac{104}{253}\right)\) | \(e\left(\frac{147}{253}\right)\) | \(e\left(\frac{127}{253}\right)\) | \(e\left(\frac{241}{253}\right)\) | \(e\left(\frac{156}{253}\right)\) | \(e\left(\frac{150}{253}\right)\) | \(e\left(\frac{199}{253}\right)\) | \(e\left(\frac{223}{253}\right)\) |
| \(\chi_{529}(17,\cdot)\) | 529.h | 506 | yes | \(-1\) | \(1\) | \(e\left(\frac{117}{253}\right)\) | \(e\left(\frac{232}{253}\right)\) | \(e\left(\frac{234}{253}\right)\) | \(e\left(\frac{29}{506}\right)\) | \(e\left(\frac{96}{253}\right)\) | \(e\left(\frac{199}{506}\right)\) | \(e\left(\frac{98}{253}\right)\) | \(e\left(\frac{211}{253}\right)\) | \(e\left(\frac{263}{506}\right)\) | \(e\left(\frac{371}{506}\right)\) |
| \(\chi_{529}(18,\cdot)\) | 529.g | 253 | yes | \(1\) | \(1\) | \(e\left(\frac{177}{253}\right)\) | \(e\left(\frac{85}{253}\right)\) | \(e\left(\frac{101}{253}\right)\) | \(e\left(\frac{116}{253}\right)\) | \(e\left(\frac{9}{253}\right)\) | \(e\left(\frac{37}{253}\right)\) | \(e\left(\frac{25}{253}\right)\) | \(e\left(\frac{170}{253}\right)\) | \(e\left(\frac{40}{253}\right)\) | \(e\left(\frac{219}{253}\right)\) |
| \(\chi_{529}(19,\cdot)\) | 529.h | 506 | yes | \(-1\) | \(1\) | \(e\left(\frac{59}{253}\right)\) | \(e\left(\frac{197}{253}\right)\) | \(e\left(\frac{118}{253}\right)\) | \(e\left(\frac{499}{506}\right)\) | \(e\left(\frac{3}{253}\right)\) | \(e\left(\frac{109}{506}\right)\) | \(e\left(\frac{177}{253}\right)\) | \(e\left(\frac{141}{253}\right)\) | \(e\left(\frac{111}{506}\right)\) | \(e\left(\frac{399}{506}\right)\) |
| \(\chi_{529}(20,\cdot)\) | 529.h | 506 | yes | \(-1\) | \(1\) | \(e\left(\frac{126}{253}\right)\) | \(e\left(\frac{172}{253}\right)\) | \(e\left(\frac{252}{253}\right)\) | \(e\left(\frac{401}{506}\right)\) | \(e\left(\frac{45}{253}\right)\) | \(e\left(\frac{117}{506}\right)\) | \(e\left(\frac{125}{253}\right)\) | \(e\left(\frac{91}{253}\right)\) | \(e\left(\frac{147}{506}\right)\) | \(e\left(\frac{419}{506}\right)\) |
| \(\chi_{529}(21,\cdot)\) | 529.h | 506 | yes | \(-1\) | \(1\) | \(e\left(\frac{79}{253}\right)\) | \(e\left(\frac{148}{253}\right)\) | \(e\left(\frac{158}{253}\right)\) | \(e\left(\frac{145}{506}\right)\) | \(e\left(\frac{227}{253}\right)\) | \(e\left(\frac{489}{506}\right)\) | \(e\left(\frac{237}{253}\right)\) | \(e\left(\frac{43}{253}\right)\) | \(e\left(\frac{303}{506}\right)\) | \(e\left(\frac{337}{506}\right)\) |
| \(\chi_{529}(22,\cdot)\) | 529.f | 46 | yes | \(-1\) | \(1\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{13}{46}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{13}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{37}{46}\right)\) | \(e\left(\frac{41}{46}\right)\) |
| \(\chi_{529}(24,\cdot)\) | 529.e | 23 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{14}{23}\right)\) |
| \(\chi_{529}(25,\cdot)\) | 529.g | 253 | yes | \(1\) | \(1\) | \(e\left(\frac{200}{253}\right)\) | \(e\left(\frac{16}{253}\right)\) | \(e\left(\frac{147}{253}\right)\) | \(e\left(\frac{1}{253}\right)\) | \(e\left(\frac{216}{253}\right)\) | \(e\left(\frac{129}{253}\right)\) | \(e\left(\frac{94}{253}\right)\) | \(e\left(\frac{32}{253}\right)\) | \(e\left(\frac{201}{253}\right)\) | \(e\left(\frac{196}{253}\right)\) |
| \(\chi_{529}(26,\cdot)\) | 529.g | 253 | yes | \(1\) | \(1\) | \(e\left(\frac{38}{253}\right)\) | \(e\left(\frac{84}{253}\right)\) | \(e\left(\frac{76}{253}\right)\) | \(e\left(\frac{195}{253}\right)\) | \(e\left(\frac{122}{253}\right)\) | \(e\left(\frac{108}{253}\right)\) | \(e\left(\frac{114}{253}\right)\) | \(e\left(\frac{168}{253}\right)\) | \(e\left(\frac{233}{253}\right)\) | \(e\left(\frac{17}{253}\right)\) |
| \(\chi_{529}(27,\cdot)\) | 529.g | 253 | yes | \(1\) | \(1\) | \(e\left(\frac{246}{253}\right)\) | \(e\left(\frac{131}{253}\right)\) | \(e\left(\frac{239}{253}\right)\) | \(e\left(\frac{24}{253}\right)\) | \(e\left(\frac{124}{253}\right)\) | \(e\left(\frac{60}{253}\right)\) | \(e\left(\frac{232}{253}\right)\) | \(e\left(\frac{9}{253}\right)\) | \(e\left(\frac{17}{253}\right)\) | \(e\left(\frac{150}{253}\right)\) |
| \(\chi_{529}(28,\cdot)\) | 529.d | 22 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{9}{22}\right)\) |
| \(\chi_{529}(29,\cdot)\) | 529.g | 253 | yes | \(1\) | \(1\) | \(e\left(\frac{73}{253}\right)\) | \(e\left(\frac{188}{253}\right)\) | \(e\left(\frac{146}{253}\right)\) | \(e\left(\frac{75}{253}\right)\) | \(e\left(\frac{8}{253}\right)\) | \(e\left(\frac{61}{253}\right)\) | \(e\left(\frac{219}{253}\right)\) | \(e\left(\frac{123}{253}\right)\) | \(e\left(\frac{148}{253}\right)\) | \(e\left(\frac{26}{253}\right)\) |
| \(\chi_{529}(30,\cdot)\) | 529.h | 506 | yes | \(-1\) | \(1\) | \(e\left(\frac{195}{253}\right)\) | \(e\left(\frac{218}{253}\right)\) | \(e\left(\frac{137}{253}\right)\) | \(e\left(\frac{217}{506}\right)\) | \(e\left(\frac{160}{253}\right)\) | \(e\left(\frac{163}{506}\right)\) | \(e\left(\frac{79}{253}\right)\) | \(e\left(\frac{183}{253}\right)\) | \(e\left(\frac{101}{506}\right)\) | \(e\left(\frac{281}{506}\right)\) |
| \(\chi_{529}(31,\cdot)\) | 529.g | 253 | yes | \(1\) | \(1\) | \(e\left(\frac{149}{253}\right)\) | \(e\left(\frac{103}{253}\right)\) | \(e\left(\frac{45}{253}\right)\) | \(e\left(\frac{212}{253}\right)\) | \(e\left(\frac{252}{253}\right)\) | \(e\left(\frac{24}{253}\right)\) | \(e\left(\frac{194}{253}\right)\) | \(e\left(\frac{206}{253}\right)\) | \(e\left(\frac{108}{253}\right)\) | \(e\left(\frac{60}{253}\right)\) |
| \(\chi_{529}(32,\cdot)\) | 529.g | 253 | yes | \(1\) | \(1\) | \(e\left(\frac{65}{253}\right)\) | \(e\left(\frac{157}{253}\right)\) | \(e\left(\frac{130}{253}\right)\) | \(e\left(\frac{247}{253}\right)\) | \(e\left(\frac{222}{253}\right)\) | \(e\left(\frac{238}{253}\right)\) | \(e\left(\frac{195}{253}\right)\) | \(e\left(\frac{61}{253}\right)\) | \(e\left(\frac{59}{253}\right)\) | \(e\left(\frac{89}{253}\right)\) |
| \(\chi_{529}(33,\cdot)\) | 529.h | 506 | yes | \(-1\) | \(1\) | \(e\left(\frac{201}{253}\right)\) | \(e\left(\frac{178}{253}\right)\) | \(e\left(\frac{149}{253}\right)\) | \(e\left(\frac{465}{506}\right)\) | \(e\left(\frac{126}{253}\right)\) | \(e\left(\frac{277}{506}\right)\) | \(e\left(\frac{97}{253}\right)\) | \(e\left(\frac{103}{253}\right)\) | \(e\left(\frac{361}{506}\right)\) | \(e\left(\frac{313}{506}\right)\) |