sage: H = DirichletGroup(4334)
pari: g = idealstar(,4334,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 1960 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{2}\times C_{980}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{4334}(1971,\cdot)$, $\chi_{4334}(199,\cdot)$ |
First 32 of 1960 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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{4334}(1,\cdot)\) | 4334.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{4334}(3,\cdot)\) | 4334.bi | 980 | no | \(-1\) | \(1\) | \(e\left(\frac{537}{980}\right)\) | \(e\left(\frac{381}{980}\right)\) | \(e\left(\frac{209}{490}\right)\) | \(e\left(\frac{47}{490}\right)\) | \(e\left(\frac{869}{980}\right)\) | \(e\left(\frac{459}{490}\right)\) | \(e\left(\frac{31}{980}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{191}{196}\right)\) | \(e\left(\frac{40}{49}\right)\) |
| \(\chi_{4334}(5,\cdot)\) | 4334.bi | 980 | no | \(-1\) | \(1\) | \(e\left(\frac{381}{980}\right)\) | \(e\left(\frac{13}{980}\right)\) | \(e\left(\frac{47}{490}\right)\) | \(e\left(\frac{381}{490}\right)\) | \(e\left(\frac{737}{980}\right)\) | \(e\left(\frac{197}{490}\right)\) | \(e\left(\frac{783}{980}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{95}{196}\right)\) | \(e\left(\frac{24}{49}\right)\) |
| \(\chi_{4334}(7,\cdot)\) | 4334.bf | 490 | no | \(-1\) | \(1\) | \(e\left(\frac{209}{490}\right)\) | \(e\left(\frac{47}{490}\right)\) | \(e\left(\frac{321}{490}\right)\) | \(e\left(\frac{209}{245}\right)\) | \(e\left(\frac{79}{245}\right)\) | \(e\left(\frac{128}{245}\right)\) | \(e\left(\frac{181}{245}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{4}{49}\right)\) | \(e\left(\frac{19}{49}\right)\) |
| \(\chi_{4334}(9,\cdot)\) | 4334.bh | 490 | no | \(1\) | \(1\) | \(e\left(\frac{47}{490}\right)\) | \(e\left(\frac{381}{490}\right)\) | \(e\left(\frac{209}{245}\right)\) | \(e\left(\frac{47}{245}\right)\) | \(e\left(\frac{379}{490}\right)\) | \(e\left(\frac{214}{245}\right)\) | \(e\left(\frac{31}{490}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{93}{98}\right)\) | \(e\left(\frac{31}{49}\right)\) |
| \(\chi_{4334}(13,\cdot)\) | 4334.bj | 980 | no | \(1\) | \(1\) | \(e\left(\frac{869}{980}\right)\) | \(e\left(\frac{737}{980}\right)\) | \(e\left(\frac{79}{245}\right)\) | \(e\left(\frac{379}{490}\right)\) | \(e\left(\frac{283}{980}\right)\) | \(e\left(\frac{313}{490}\right)\) | \(e\left(\frac{177}{980}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{41}{196}\right)\) | \(e\left(\frac{15}{49}\right)\) |
| \(\chi_{4334}(15,\cdot)\) | 4334.bh | 490 | no | \(1\) | \(1\) | \(e\left(\frac{459}{490}\right)\) | \(e\left(\frac{197}{490}\right)\) | \(e\left(\frac{128}{245}\right)\) | \(e\left(\frac{214}{245}\right)\) | \(e\left(\frac{313}{490}\right)\) | \(e\left(\frac{83}{245}\right)\) | \(e\left(\frac{407}{490}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{45}{98}\right)\) | \(e\left(\frac{15}{49}\right)\) |
| \(\chi_{4334}(17,\cdot)\) | 4334.bj | 980 | no | \(1\) | \(1\) | \(e\left(\frac{31}{980}\right)\) | \(e\left(\frac{783}{980}\right)\) | \(e\left(\frac{181}{245}\right)\) | \(e\left(\frac{31}{490}\right)\) | \(e\left(\frac{177}{980}\right)\) | \(e\left(\frac{407}{490}\right)\) | \(e\left(\frac{83}{980}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{151}{196}\right)\) | \(e\left(\frac{17}{49}\right)\) |
| \(\chi_{4334}(19,\cdot)\) | 4334.u | 70 | no | \(-1\) | \(1\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{2}{7}\right)\) |
| \(\chi_{4334}(21,\cdot)\) | 4334.bc | 196 | no | \(1\) | \(1\) | \(e\left(\frac{191}{196}\right)\) | \(e\left(\frac{95}{196}\right)\) | \(e\left(\frac{4}{49}\right)\) | \(e\left(\frac{93}{98}\right)\) | \(e\left(\frac{41}{196}\right)\) | \(e\left(\frac{45}{98}\right)\) | \(e\left(\frac{151}{196}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{11}{196}\right)\) | \(e\left(\frac{10}{49}\right)\) |
| \(\chi_{4334}(23,\cdot)\) | 4334.t | 49 | no | \(1\) | \(1\) | \(e\left(\frac{40}{49}\right)\) | \(e\left(\frac{24}{49}\right)\) | \(e\left(\frac{19}{49}\right)\) | \(e\left(\frac{31}{49}\right)\) | \(e\left(\frac{15}{49}\right)\) | \(e\left(\frac{15}{49}\right)\) | \(e\left(\frac{17}{49}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{10}{49}\right)\) | \(e\left(\frac{23}{49}\right)\) |
| \(\chi_{4334}(25,\cdot)\) | 4334.bh | 490 | no | \(1\) | \(1\) | \(e\left(\frac{381}{490}\right)\) | \(e\left(\frac{13}{490}\right)\) | \(e\left(\frac{47}{245}\right)\) | \(e\left(\frac{136}{245}\right)\) | \(e\left(\frac{247}{490}\right)\) | \(e\left(\frac{197}{245}\right)\) | \(e\left(\frac{293}{490}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{95}{98}\right)\) | \(e\left(\frac{48}{49}\right)\) |
| \(\chi_{4334}(27,\cdot)\) | 4334.bi | 980 | no | \(-1\) | \(1\) | \(e\left(\frac{631}{980}\right)\) | \(e\left(\frac{163}{980}\right)\) | \(e\left(\frac{137}{490}\right)\) | \(e\left(\frac{141}{490}\right)\) | \(e\left(\frac{647}{980}\right)\) | \(e\left(\frac{397}{490}\right)\) | \(e\left(\frac{93}{980}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{181}{196}\right)\) | \(e\left(\frac{22}{49}\right)\) |
| \(\chi_{4334}(29,\cdot)\) | 4334.bg | 490 | no | \(-1\) | \(1\) | \(e\left(\frac{207}{245}\right)\) | \(e\left(\frac{36}{245}\right)\) | \(e\left(\frac{351}{490}\right)\) | \(e\left(\frac{169}{245}\right)\) | \(e\left(\frac{143}{490}\right)\) | \(e\left(\frac{243}{245}\right)\) | \(e\left(\frac{247}{490}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{55}{98}\right)\) | \(e\left(\frac{2}{49}\right)\) |
| \(\chi_{4334}(31,\cdot)\) | 4334.bi | 980 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{980}\right)\) | \(e\left(\frac{417}{980}\right)\) | \(e\left(\frac{113}{490}\right)\) | \(e\left(\frac{9}{490}\right)\) | \(e\left(\frac{573}{980}\right)\) | \(e\left(\frac{213}{490}\right)\) | \(e\left(\frac{767}{980}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{47}{196}\right)\) | \(e\left(\frac{16}{49}\right)\) |
| \(\chi_{4334}(35,\cdot)\) | 4334.bj | 980 | no | \(1\) | \(1\) | \(e\left(\frac{799}{980}\right)\) | \(e\left(\frac{107}{980}\right)\) | \(e\left(\frac{184}{245}\right)\) | \(e\left(\frac{309}{490}\right)\) | \(e\left(\frac{73}{980}\right)\) | \(e\left(\frac{453}{490}\right)\) | \(e\left(\frac{527}{980}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{111}{196}\right)\) | \(e\left(\frac{43}{49}\right)\) |
| \(\chi_{4334}(37,\cdot)\) | 4334.be | 245 | no | \(1\) | \(1\) | \(e\left(\frac{222}{245}\right)\) | \(e\left(\frac{241}{245}\right)\) | \(e\left(\frac{103}{245}\right)\) | \(e\left(\frac{199}{245}\right)\) | \(e\left(\frac{169}{245}\right)\) | \(e\left(\frac{218}{245}\right)\) | \(e\left(\frac{136}{245}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{16}{49}\right)\) | \(e\left(\frac{27}{49}\right)\) |
| \(\chi_{4334}(39,\cdot)\) | 4334.bf | 490 | no | \(-1\) | \(1\) | \(e\left(\frac{213}{490}\right)\) | \(e\left(\frac{69}{490}\right)\) | \(e\left(\frac{367}{490}\right)\) | \(e\left(\frac{213}{245}\right)\) | \(e\left(\frac{43}{245}\right)\) | \(e\left(\frac{141}{245}\right)\) | \(e\left(\frac{52}{245}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{9}{49}\right)\) | \(e\left(\frac{6}{49}\right)\) |
| \(\chi_{4334}(41,\cdot)\) | 4334.bf | 490 | no | \(-1\) | \(1\) | \(e\left(\frac{481}{490}\right)\) | \(e\left(\frac{73}{490}\right)\) | \(e\left(\frac{19}{490}\right)\) | \(e\left(\frac{236}{245}\right)\) | \(e\left(\frac{81}{245}\right)\) | \(e\left(\frac{32}{245}\right)\) | \(e\left(\frac{229}{245}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{1}{49}\right)\) | \(e\left(\frac{17}{49}\right)\) |
| \(\chi_{4334}(43,\cdot)\) | 4334.z | 98 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{98}\right)\) | \(e\left(\frac{41}{98}\right)\) | \(e\left(\frac{59}{98}\right)\) | \(e\left(\frac{3}{49}\right)\) | \(e\left(\frac{22}{49}\right)\) | \(e\left(\frac{22}{49}\right)\) | \(e\left(\frac{38}{49}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{31}{49}\right)\) | \(e\left(\frac{37}{49}\right)\) |
| \(\chi_{4334}(45,\cdot)\) | 4334.bd | 196 | no | \(-1\) | \(1\) | \(e\left(\frac{95}{196}\right)\) | \(e\left(\frac{155}{196}\right)\) | \(e\left(\frac{93}{98}\right)\) | \(e\left(\frac{95}{98}\right)\) | \(e\left(\frac{103}{196}\right)\) | \(e\left(\frac{27}{98}\right)\) | \(e\left(\frac{169}{196}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{85}{196}\right)\) | \(e\left(\frac{6}{49}\right)\) |
| \(\chi_{4334}(47,\cdot)\) | 4334.bh | 490 | no | \(1\) | \(1\) | \(e\left(\frac{171}{490}\right)\) | \(e\left(\frac{83}{490}\right)\) | \(e\left(\frac{187}{245}\right)\) | \(e\left(\frac{171}{245}\right)\) | \(e\left(\frac{107}{490}\right)\) | \(e\left(\frac{127}{245}\right)\) | \(e\left(\frac{363}{490}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{11}{98}\right)\) | \(e\left(\frac{20}{49}\right)\) |
| \(\chi_{4334}(49,\cdot)\) | 4334.be | 245 | no | \(1\) | \(1\) | \(e\left(\frac{209}{245}\right)\) | \(e\left(\frac{47}{245}\right)\) | \(e\left(\frac{76}{245}\right)\) | \(e\left(\frac{173}{245}\right)\) | \(e\left(\frac{158}{245}\right)\) | \(e\left(\frac{11}{245}\right)\) | \(e\left(\frac{117}{245}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{8}{49}\right)\) | \(e\left(\frac{38}{49}\right)\) |
| \(\chi_{4334}(51,\cdot)\) | 4334.bg | 490 | no | \(-1\) | \(1\) | \(e\left(\frac{142}{245}\right)\) | \(e\left(\frac{46}{245}\right)\) | \(e\left(\frac{81}{490}\right)\) | \(e\left(\frac{39}{245}\right)\) | \(e\left(\frac{33}{490}\right)\) | \(e\left(\frac{188}{245}\right)\) | \(e\left(\frac{57}{490}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{73}{98}\right)\) | \(e\left(\frac{8}{49}\right)\) |
| \(\chi_{4334}(53,\cdot)\) | 4334.be | 245 | no | \(1\) | \(1\) | \(e\left(\frac{71}{245}\right)\) | \(e\left(\frac{23}{245}\right)\) | \(e\left(\frac{204}{245}\right)\) | \(e\left(\frac{142}{245}\right)\) | \(e\left(\frac{192}{245}\right)\) | \(e\left(\frac{94}{245}\right)\) | \(e\left(\frac{198}{245}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{6}{49}\right)\) | \(e\left(\frac{4}{49}\right)\) |
| \(\chi_{4334}(57,\cdot)\) | 4334.bj | 980 | no | \(1\) | \(1\) | \(e\left(\frac{159}{980}\right)\) | \(e\left(\frac{507}{980}\right)\) | \(e\left(\frac{59}{245}\right)\) | \(e\left(\frac{159}{490}\right)\) | \(e\left(\frac{813}{980}\right)\) | \(e\left(\frac{333}{490}\right)\) | \(e\left(\frac{647}{980}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{79}{196}\right)\) | \(e\left(\frac{5}{49}\right)\) |
| \(\chi_{4334}(59,\cdot)\) | 4334.be | 245 | no | \(1\) | \(1\) | \(e\left(\frac{242}{245}\right)\) | \(e\left(\frac{106}{245}\right)\) | \(e\left(\frac{88}{245}\right)\) | \(e\left(\frac{239}{245}\right)\) | \(e\left(\frac{54}{245}\right)\) | \(e\left(\frac{103}{245}\right)\) | \(e\left(\frac{71}{245}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{17}{49}\right)\) | \(e\left(\frac{44}{49}\right)\) |
| \(\chi_{4334}(61,\cdot)\) | 4334.bg | 490 | no | \(-1\) | \(1\) | \(e\left(\frac{74}{245}\right)\) | \(e\left(\frac{162}{245}\right)\) | \(e\left(\frac{477}{490}\right)\) | \(e\left(\frac{148}{245}\right)\) | \(e\left(\frac{31}{490}\right)\) | \(e\left(\frac{236}{245}\right)\) | \(e\left(\frac{9}{490}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{27}{98}\right)\) | \(e\left(\frac{9}{49}\right)\) |
| \(\chi_{4334}(63,\cdot)\) | 4334.bg | 490 | no | \(-1\) | \(1\) | \(e\left(\frac{128}{245}\right)\) | \(e\left(\frac{214}{245}\right)\) | \(e\left(\frac{249}{490}\right)\) | \(e\left(\frac{11}{245}\right)\) | \(e\left(\frac{47}{490}\right)\) | \(e\left(\frac{97}{245}\right)\) | \(e\left(\frac{393}{490}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{3}{98}\right)\) | \(e\left(\frac{1}{49}\right)\) |
| \(\chi_{4334}(65,\cdot)\) | 4334.z | 98 | no | \(-1\) | \(1\) | \(e\left(\frac{27}{98}\right)\) | \(e\left(\frac{75}{98}\right)\) | \(e\left(\frac{41}{98}\right)\) | \(e\left(\frac{27}{49}\right)\) | \(e\left(\frac{2}{49}\right)\) | \(e\left(\frac{2}{49}\right)\) | \(e\left(\frac{48}{49}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{34}{49}\right)\) | \(e\left(\frac{39}{49}\right)\) |
| \(\chi_{4334}(67,\cdot)\) | 4334.bd | 196 | no | \(-1\) | \(1\) | \(e\left(\frac{137}{196}\right)\) | \(e\left(\frac{141}{196}\right)\) | \(e\left(\frac{65}{98}\right)\) | \(e\left(\frac{39}{98}\right)\) | \(e\left(\frac{33}{196}\right)\) | \(e\left(\frac{41}{98}\right)\) | \(e\left(\frac{155}{196}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{71}{196}\right)\) | \(e\left(\frac{20}{49}\right)\) |
| \(\chi_{4334}(69,\cdot)\) | 4334.ba | 140 | no | \(-1\) | \(1\) | \(e\left(\frac{51}{140}\right)\) | \(e\left(\frac{123}{140}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{27}{140}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{53}{140}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{2}{7}\right)\) |