sage: H = DirichletGroup(3215)
pari: g = idealstar(,3215,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 2568 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{2}\times C_{1284}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{3215}(1287,\cdot)$, $\chi_{3215}(11,\cdot)$ |
First 32 of 2568 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{3215}(1,\cdot)\) | 3215.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{3215}(2,\cdot)\) | 3215.s | 428 | yes | \(1\) | \(1\) | \(e\left(\frac{381}{428}\right)\) | \(e\left(\frac{335}{428}\right)\) | \(e\left(\frac{167}{214}\right)\) | \(e\left(\frac{72}{107}\right)\) | \(e\left(\frac{95}{428}\right)\) | \(e\left(\frac{287}{428}\right)\) | \(e\left(\frac{121}{214}\right)\) | \(e\left(\frac{151}{214}\right)\) | \(e\left(\frac{241}{428}\right)\) | \(e\left(\frac{419}{428}\right)\) |
| \(\chi_{3215}(3,\cdot)\) | 3215.s | 428 | yes | \(1\) | \(1\) | \(e\left(\frac{335}{428}\right)\) | \(e\left(\frac{417}{428}\right)\) | \(e\left(\frac{121}{214}\right)\) | \(e\left(\frac{81}{107}\right)\) | \(e\left(\frac{361}{428}\right)\) | \(e\left(\frac{149}{428}\right)\) | \(e\left(\frac{203}{214}\right)\) | \(e\left(\frac{103}{214}\right)\) | \(e\left(\frac{231}{428}\right)\) | \(e\left(\frac{137}{428}\right)\) |
| \(\chi_{3215}(4,\cdot)\) | 3215.p | 214 | yes | \(1\) | \(1\) | \(e\left(\frac{167}{214}\right)\) | \(e\left(\frac{121}{214}\right)\) | \(e\left(\frac{60}{107}\right)\) | \(e\left(\frac{37}{107}\right)\) | \(e\left(\frac{95}{214}\right)\) | \(e\left(\frac{73}{214}\right)\) | \(e\left(\frac{14}{107}\right)\) | \(e\left(\frac{44}{107}\right)\) | \(e\left(\frac{27}{214}\right)\) | \(e\left(\frac{205}{214}\right)\) |
| \(\chi_{3215}(6,\cdot)\) | 3215.m | 107 | no | \(1\) | \(1\) | \(e\left(\frac{72}{107}\right)\) | \(e\left(\frac{81}{107}\right)\) | \(e\left(\frac{37}{107}\right)\) | \(e\left(\frac{46}{107}\right)\) | \(e\left(\frac{7}{107}\right)\) | \(e\left(\frac{2}{107}\right)\) | \(e\left(\frac{55}{107}\right)\) | \(e\left(\frac{20}{107}\right)\) | \(e\left(\frac{11}{107}\right)\) | \(e\left(\frac{32}{107}\right)\) |
| \(\chi_{3215}(7,\cdot)\) | 3215.x | 1284 | yes | \(-1\) | \(1\) | \(e\left(\frac{95}{428}\right)\) | \(e\left(\frac{361}{428}\right)\) | \(e\left(\frac{95}{214}\right)\) | \(e\left(\frac{7}{107}\right)\) | \(e\left(\frac{1013}{1284}\right)\) | \(e\left(\frac{285}{428}\right)\) | \(e\left(\frac{147}{214}\right)\) | \(e\left(\frac{265}{321}\right)\) | \(e\left(\frac{123}{428}\right)\) | \(e\left(\frac{947}{1284}\right)\) |
| \(\chi_{3215}(8,\cdot)\) | 3215.s | 428 | yes | \(1\) | \(1\) | \(e\left(\frac{287}{428}\right)\) | \(e\left(\frac{149}{428}\right)\) | \(e\left(\frac{73}{214}\right)\) | \(e\left(\frac{2}{107}\right)\) | \(e\left(\frac{285}{428}\right)\) | \(e\left(\frac{5}{428}\right)\) | \(e\left(\frac{149}{214}\right)\) | \(e\left(\frac{25}{214}\right)\) | \(e\left(\frac{295}{428}\right)\) | \(e\left(\frac{401}{428}\right)\) |
| \(\chi_{3215}(9,\cdot)\) | 3215.p | 214 | yes | \(1\) | \(1\) | \(e\left(\frac{121}{214}\right)\) | \(e\left(\frac{203}{214}\right)\) | \(e\left(\frac{14}{107}\right)\) | \(e\left(\frac{55}{107}\right)\) | \(e\left(\frac{147}{214}\right)\) | \(e\left(\frac{149}{214}\right)\) | \(e\left(\frac{96}{107}\right)\) | \(e\left(\frac{103}{107}\right)\) | \(e\left(\frac{17}{214}\right)\) | \(e\left(\frac{137}{214}\right)\) |
| \(\chi_{3215}(11,\cdot)\) | 3215.v | 642 | no | \(-1\) | \(1\) | \(e\left(\frac{151}{214}\right)\) | \(e\left(\frac{103}{214}\right)\) | \(e\left(\frac{44}{107}\right)\) | \(e\left(\frac{20}{107}\right)\) | \(e\left(\frac{265}{321}\right)\) | \(e\left(\frac{25}{214}\right)\) | \(e\left(\frac{103}{107}\right)\) | \(e\left(\frac{1}{642}\right)\) | \(e\left(\frac{191}{214}\right)\) | \(e\left(\frac{23}{642}\right)\) |
| \(\chi_{3215}(12,\cdot)\) | 3215.s | 428 | yes | \(1\) | \(1\) | \(e\left(\frac{241}{428}\right)\) | \(e\left(\frac{231}{428}\right)\) | \(e\left(\frac{27}{214}\right)\) | \(e\left(\frac{11}{107}\right)\) | \(e\left(\frac{123}{428}\right)\) | \(e\left(\frac{295}{428}\right)\) | \(e\left(\frac{17}{214}\right)\) | \(e\left(\frac{191}{214}\right)\) | \(e\left(\frac{285}{428}\right)\) | \(e\left(\frac{119}{428}\right)\) |
| \(\chi_{3215}(13,\cdot)\) | 3215.w | 1284 | yes | \(1\) | \(1\) | \(e\left(\frac{419}{428}\right)\) | \(e\left(\frac{137}{428}\right)\) | \(e\left(\frac{205}{214}\right)\) | \(e\left(\frac{32}{107}\right)\) | \(e\left(\frac{947}{1284}\right)\) | \(e\left(\frac{401}{428}\right)\) | \(e\left(\frac{137}{214}\right)\) | \(e\left(\frac{23}{642}\right)\) | \(e\left(\frac{119}{428}\right)\) | \(e\left(\frac{95}{1284}\right)\) |
| \(\chi_{3215}(14,\cdot)\) | 3215.t | 642 | yes | \(-1\) | \(1\) | \(e\left(\frac{12}{107}\right)\) | \(e\left(\frac{67}{107}\right)\) | \(e\left(\frac{24}{107}\right)\) | \(e\left(\frac{79}{107}\right)\) | \(e\left(\frac{7}{642}\right)\) | \(e\left(\frac{36}{107}\right)\) | \(e\left(\frac{27}{107}\right)\) | \(e\left(\frac{341}{642}\right)\) | \(e\left(\frac{91}{107}\right)\) | \(e\left(\frac{230}{321}\right)\) |
| \(\chi_{3215}(16,\cdot)\) | 3215.m | 107 | no | \(1\) | \(1\) | \(e\left(\frac{60}{107}\right)\) | \(e\left(\frac{14}{107}\right)\) | \(e\left(\frac{13}{107}\right)\) | \(e\left(\frac{74}{107}\right)\) | \(e\left(\frac{95}{107}\right)\) | \(e\left(\frac{73}{107}\right)\) | \(e\left(\frac{28}{107}\right)\) | \(e\left(\frac{88}{107}\right)\) | \(e\left(\frac{27}{107}\right)\) | \(e\left(\frac{98}{107}\right)\) |
| \(\chi_{3215}(17,\cdot)\) | 3215.w | 1284 | yes | \(1\) | \(1\) | \(e\left(\frac{137}{428}\right)\) | \(e\left(\frac{7}{428}\right)\) | \(e\left(\frac{137}{214}\right)\) | \(e\left(\frac{36}{107}\right)\) | \(e\left(\frac{517}{1284}\right)\) | \(e\left(\frac{411}{428}\right)\) | \(e\left(\frac{7}{214}\right)\) | \(e\left(\frac{601}{642}\right)\) | \(e\left(\frac{281}{428}\right)\) | \(e\left(\frac{361}{1284}\right)\) |
| \(\chi_{3215}(18,\cdot)\) | 3215.s | 428 | yes | \(1\) | \(1\) | \(e\left(\frac{195}{428}\right)\) | \(e\left(\frac{313}{428}\right)\) | \(e\left(\frac{195}{214}\right)\) | \(e\left(\frac{20}{107}\right)\) | \(e\left(\frac{389}{428}\right)\) | \(e\left(\frac{157}{428}\right)\) | \(e\left(\frac{99}{214}\right)\) | \(e\left(\frac{143}{214}\right)\) | \(e\left(\frac{275}{428}\right)\) | \(e\left(\frac{265}{428}\right)\) |
| \(\chi_{3215}(19,\cdot)\) | 3215.t | 642 | yes | \(-1\) | \(1\) | \(e\left(\frac{88}{107}\right)\) | \(e\left(\frac{99}{107}\right)\) | \(e\left(\frac{69}{107}\right)\) | \(e\left(\frac{80}{107}\right)\) | \(e\left(\frac{301}{642}\right)\) | \(e\left(\frac{50}{107}\right)\) | \(e\left(\frac{91}{107}\right)\) | \(e\left(\frac{539}{642}\right)\) | \(e\left(\frac{61}{107}\right)\) | \(e\left(\frac{260}{321}\right)\) |
| \(\chi_{3215}(21,\cdot)\) | 3215.v | 642 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{214}\right)\) | \(e\left(\frac{175}{214}\right)\) | \(e\left(\frac{1}{107}\right)\) | \(e\left(\frac{88}{107}\right)\) | \(e\left(\frac{203}{321}\right)\) | \(e\left(\frac{3}{214}\right)\) | \(e\left(\frac{68}{107}\right)\) | \(e\left(\frac{197}{642}\right)\) | \(e\left(\frac{177}{214}\right)\) | \(e\left(\frac{37}{642}\right)\) |
| \(\chi_{3215}(22,\cdot)\) | 3215.x | 1284 | yes | \(-1\) | \(1\) | \(e\left(\frac{255}{428}\right)\) | \(e\left(\frac{113}{428}\right)\) | \(e\left(\frac{41}{214}\right)\) | \(e\left(\frac{92}{107}\right)\) | \(e\left(\frac{61}{1284}\right)\) | \(e\left(\frac{337}{428}\right)\) | \(e\left(\frac{113}{214}\right)\) | \(e\left(\frac{227}{321}\right)\) | \(e\left(\frac{195}{428}\right)\) | \(e\left(\frac{19}{1284}\right)\) |
| \(\chi_{3215}(23,\cdot)\) | 3215.x | 1284 | yes | \(-1\) | \(1\) | \(e\left(\frac{213}{428}\right)\) | \(e\left(\frac{39}{428}\right)\) | \(e\left(\frac{213}{214}\right)\) | \(e\left(\frac{63}{107}\right)\) | \(e\left(\frac{343}{1284}\right)\) | \(e\left(\frac{211}{428}\right)\) | \(e\left(\frac{39}{214}\right)\) | \(e\left(\frac{245}{321}\right)\) | \(e\left(\frac{37}{428}\right)\) | \(e\left(\frac{1033}{1284}\right)\) |
| \(\chi_{3215}(24,\cdot)\) | 3215.p | 214 | yes | \(1\) | \(1\) | \(e\left(\frac{97}{214}\right)\) | \(e\left(\frac{69}{214}\right)\) | \(e\left(\frac{97}{107}\right)\) | \(e\left(\frac{83}{107}\right)\) | \(e\left(\frac{109}{214}\right)\) | \(e\left(\frac{77}{214}\right)\) | \(e\left(\frac{69}{107}\right)\) | \(e\left(\frac{64}{107}\right)\) | \(e\left(\frac{49}{214}\right)\) | \(e\left(\frac{55}{214}\right)\) |
| \(\chi_{3215}(26,\cdot)\) | 3215.q | 321 | no | \(1\) | \(1\) | \(e\left(\frac{93}{107}\right)\) | \(e\left(\frac{11}{107}\right)\) | \(e\left(\frac{79}{107}\right)\) | \(e\left(\frac{104}{107}\right)\) | \(e\left(\frac{308}{321}\right)\) | \(e\left(\frac{65}{107}\right)\) | \(e\left(\frac{22}{107}\right)\) | \(e\left(\frac{238}{321}\right)\) | \(e\left(\frac{90}{107}\right)\) | \(e\left(\frac{17}{321}\right)\) |
| \(\chi_{3215}(27,\cdot)\) | 3215.s | 428 | yes | \(1\) | \(1\) | \(e\left(\frac{149}{428}\right)\) | \(e\left(\frac{395}{428}\right)\) | \(e\left(\frac{149}{214}\right)\) | \(e\left(\frac{29}{107}\right)\) | \(e\left(\frac{227}{428}\right)\) | \(e\left(\frac{19}{428}\right)\) | \(e\left(\frac{181}{214}\right)\) | \(e\left(\frac{95}{214}\right)\) | \(e\left(\frac{265}{428}\right)\) | \(e\left(\frac{411}{428}\right)\) |
| \(\chi_{3215}(28,\cdot)\) | 3215.x | 1284 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{428}\right)\) | \(e\left(\frac{175}{428}\right)\) | \(e\left(\frac{1}{214}\right)\) | \(e\left(\frac{44}{107}\right)\) | \(e\left(\frac{299}{1284}\right)\) | \(e\left(\frac{3}{428}\right)\) | \(e\left(\frac{175}{214}\right)\) | \(e\left(\frac{76}{321}\right)\) | \(e\left(\frac{177}{428}\right)\) | \(e\left(\frac{893}{1284}\right)\) |
| \(\chi_{3215}(29,\cdot)\) | 3215.u | 642 | yes | \(1\) | \(1\) | \(e\left(\frac{151}{214}\right)\) | \(e\left(\frac{103}{214}\right)\) | \(e\left(\frac{44}{107}\right)\) | \(e\left(\frac{20}{107}\right)\) | \(e\left(\frac{637}{642}\right)\) | \(e\left(\frac{25}{214}\right)\) | \(e\left(\frac{103}{107}\right)\) | \(e\left(\frac{268}{321}\right)\) | \(e\left(\frac{191}{214}\right)\) | \(e\left(\frac{451}{642}\right)\) |
| \(\chi_{3215}(31,\cdot)\) | 3215.q | 321 | no | \(1\) | \(1\) | \(e\left(\frac{98}{107}\right)\) | \(e\left(\frac{30}{107}\right)\) | \(e\left(\frac{89}{107}\right)\) | \(e\left(\frac{21}{107}\right)\) | \(e\left(\frac{91}{321}\right)\) | \(e\left(\frac{80}{107}\right)\) | \(e\left(\frac{60}{107}\right)\) | \(e\left(\frac{260}{321}\right)\) | \(e\left(\frac{12}{107}\right)\) | \(e\left(\frac{202}{321}\right)\) |
| \(\chi_{3215}(32,\cdot)\) | 3215.s | 428 | yes | \(1\) | \(1\) | \(e\left(\frac{193}{428}\right)\) | \(e\left(\frac{391}{428}\right)\) | \(e\left(\frac{193}{214}\right)\) | \(e\left(\frac{39}{107}\right)\) | \(e\left(\frac{47}{428}\right)\) | \(e\left(\frac{151}{428}\right)\) | \(e\left(\frac{177}{214}\right)\) | \(e\left(\frac{113}{214}\right)\) | \(e\left(\frac{349}{428}\right)\) | \(e\left(\frac{383}{428}\right)\) |
| \(\chi_{3215}(33,\cdot)\) | 3215.x | 1284 | yes | \(-1\) | \(1\) | \(e\left(\frac{209}{428}\right)\) | \(e\left(\frac{195}{428}\right)\) | \(e\left(\frac{209}{214}\right)\) | \(e\left(\frac{101}{107}\right)\) | \(e\left(\frac{859}{1284}\right)\) | \(e\left(\frac{199}{428}\right)\) | \(e\left(\frac{195}{214}\right)\) | \(e\left(\frac{155}{321}\right)\) | \(e\left(\frac{185}{428}\right)\) | \(e\left(\frac{457}{1284}\right)\) |
| \(\chi_{3215}(34,\cdot)\) | 3215.u | 642 | yes | \(1\) | \(1\) | \(e\left(\frac{45}{214}\right)\) | \(e\left(\frac{171}{214}\right)\) | \(e\left(\frac{45}{107}\right)\) | \(e\left(\frac{1}{107}\right)\) | \(e\left(\frac{401}{642}\right)\) | \(e\left(\frac{135}{214}\right)\) | \(e\left(\frac{64}{107}\right)\) | \(e\left(\frac{206}{321}\right)\) | \(e\left(\frac{47}{214}\right)\) | \(e\left(\frac{167}{642}\right)\) |
| \(\chi_{3215}(36,\cdot)\) | 3215.m | 107 | no | \(1\) | \(1\) | \(e\left(\frac{37}{107}\right)\) | \(e\left(\frac{55}{107}\right)\) | \(e\left(\frac{74}{107}\right)\) | \(e\left(\frac{92}{107}\right)\) | \(e\left(\frac{14}{107}\right)\) | \(e\left(\frac{4}{107}\right)\) | \(e\left(\frac{3}{107}\right)\) | \(e\left(\frac{40}{107}\right)\) | \(e\left(\frac{22}{107}\right)\) | \(e\left(\frac{64}{107}\right)\) |
| \(\chi_{3215}(37,\cdot)\) | 3215.w | 1284 | yes | \(1\) | \(1\) | \(e\left(\frac{125}{428}\right)\) | \(e\left(\frac{47}{428}\right)\) | \(e\left(\frac{125}{214}\right)\) | \(e\left(\frac{43}{107}\right)\) | \(e\left(\frac{781}{1284}\right)\) | \(e\left(\frac{375}{428}\right)\) | \(e\left(\frac{47}{214}\right)\) | \(e\left(\frac{61}{642}\right)\) | \(e\left(\frac{297}{428}\right)\) | \(e\left(\frac{1201}{1284}\right)\) |
| \(\chi_{3215}(38,\cdot)\) | 3215.x | 1284 | yes | \(-1\) | \(1\) | \(e\left(\frac{305}{428}\right)\) | \(e\left(\frac{303}{428}\right)\) | \(e\left(\frac{91}{214}\right)\) | \(e\left(\frac{45}{107}\right)\) | \(e\left(\frac{887}{1284}\right)\) | \(e\left(\frac{59}{428}\right)\) | \(e\left(\frac{89}{214}\right)\) | \(e\left(\frac{175}{321}\right)\) | \(e\left(\frac{57}{428}\right)\) | \(e\left(\frac{1013}{1284}\right)\) |
| \(\chi_{3215}(39,\cdot)\) | 3215.u | 642 | yes | \(1\) | \(1\) | \(e\left(\frac{163}{214}\right)\) | \(e\left(\frac{63}{214}\right)\) | \(e\left(\frac{56}{107}\right)\) | \(e\left(\frac{6}{107}\right)\) | \(e\left(\frac{373}{642}\right)\) | \(e\left(\frac{61}{214}\right)\) | \(e\left(\frac{63}{107}\right)\) | \(e\left(\frac{166}{321}\right)\) | \(e\left(\frac{175}{214}\right)\) | \(e\left(\frac{253}{642}\right)\) |