sage: H = DirichletGroup(16900)
pari: g = idealstar(,16900,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 6240 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{4}\times C_{780}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{16900}(8451,\cdot)$, $\chi_{16900}(677,\cdot)$, $\chi_{16900}(12001,\cdot)$ |
First 32 of 6240 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 | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{16900}(1,\cdot)\) | 16900.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{16900}(3,\cdot)\) | 16900.fz | 780 | yes | \(1\) | \(1\) | \(e\left(\frac{401}{780}\right)\) | \(e\left(\frac{47}{156}\right)\) | \(e\left(\frac{11}{390}\right)\) | \(e\left(\frac{379}{390}\right)\) | \(e\left(\frac{469}{780}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{141}{260}\right)\) | \(e\left(\frac{193}{390}\right)\) |
\(\chi_{16900}(7,\cdot)\) | 16900.eo | 156 | no | \(-1\) | \(1\) | \(e\left(\frac{47}{156}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{61}{156}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{73}{78}\right)\) |
\(\chi_{16900}(9,\cdot)\) | 16900.fo | 390 | no | \(1\) | \(1\) | \(e\left(\frac{11}{390}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{11}{195}\right)\) | \(e\left(\frac{184}{195}\right)\) | \(e\left(\frac{79}{390}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{11}{130}\right)\) | \(e\left(\frac{193}{195}\right)\) |
\(\chi_{16900}(11,\cdot)\) | 16900.gd | 780 | yes | \(1\) | \(1\) | \(e\left(\frac{379}{390}\right)\) | \(e\left(\frac{23}{156}\right)\) | \(e\left(\frac{184}{195}\right)\) | \(e\left(\frac{239}{780}\right)\) | \(e\left(\frac{311}{390}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{31}{260}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{119}{130}\right)\) | \(e\left(\frac{2}{195}\right)\) |
\(\chi_{16900}(17,\cdot)\) | 16900.fy | 780 | no | \(-1\) | \(1\) | \(e\left(\frac{469}{780}\right)\) | \(e\left(\frac{61}{156}\right)\) | \(e\left(\frac{79}{390}\right)\) | \(e\left(\frac{311}{390}\right)\) | \(e\left(\frac{71}{780}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{129}{130}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{209}{260}\right)\) | \(e\left(\frac{287}{390}\right)\) |
\(\chi_{16900}(19,\cdot)\) | 16900.dw | 60 | no | \(1\) | \(1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{15}\right)\) |
\(\chi_{16900}(21,\cdot)\) | 16900.fj | 260 | no | \(-1\) | \(1\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{23}{52}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{31}{260}\right)\) | \(e\left(\frac{129}{130}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{67}{260}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{28}{65}\right)\) |
\(\chi_{16900}(23,\cdot)\) | 16900.ds | 60 | no | \(1\) | \(1\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{13}{30}\right)\) |
\(\chi_{16900}(27,\cdot)\) | 16900.fe | 260 | yes | \(1\) | \(1\) | \(e\left(\frac{141}{260}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{11}{130}\right)\) | \(e\left(\frac{119}{130}\right)\) | \(e\left(\frac{209}{260}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{163}{260}\right)\) | \(e\left(\frac{63}{130}\right)\) |
\(\chi_{16900}(29,\cdot)\) | 16900.fo | 390 | no | \(1\) | \(1\) | \(e\left(\frac{193}{390}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{193}{195}\right)\) | \(e\left(\frac{2}{195}\right)\) | \(e\left(\frac{287}{390}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{63}{130}\right)\) | \(e\left(\frac{89}{195}\right)\) |
\(\chi_{16900}(31,\cdot)\) | 16900.ez | 260 | yes | \(1\) | \(1\) | \(e\left(\frac{129}{130}\right)\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{64}{65}\right)\) | \(e\left(\frac{199}{260}\right)\) | \(e\left(\frac{111}{130}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{233}{260}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{127}{130}\right)\) | \(e\left(\frac{12}{65}\right)\) |
\(\chi_{16900}(33,\cdot)\) | 16900.fu | 780 | no | \(1\) | \(1\) | \(e\left(\frac{379}{780}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{379}{390}\right)\) | \(e\left(\frac{217}{780}\right)\) | \(e\left(\frac{311}{780}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{243}{260}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{119}{260}\right)\) | \(e\left(\frac{197}{390}\right)\) |
\(\chi_{16900}(37,\cdot)\) | 16900.gb | 780 | no | \(1\) | \(1\) | \(e\left(\frac{137}{780}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{137}{390}\right)\) | \(e\left(\frac{701}{780}\right)\) | \(e\left(\frac{133}{780}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{259}{260}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{137}{260}\right)\) | \(e\left(\frac{241}{390}\right)\) |
\(\chi_{16900}(41,\cdot)\) | 16900.ft | 780 | no | \(-1\) | \(1\) | \(e\left(\frac{188}{195}\right)\) | \(e\left(\frac{47}{156}\right)\) | \(e\left(\frac{181}{195}\right)\) | \(e\left(\frac{251}{780}\right)\) | \(e\left(\frac{59}{390}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{69}{260}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{38}{195}\right)\) |
\(\chi_{16900}(43,\cdot)\) | 16900.et | 156 | no | \(1\) | \(1\) | \(e\left(\frac{113}{156}\right)\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{145}{156}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{61}{78}\right)\) |
\(\chi_{16900}(47,\cdot)\) | 16900.fh | 260 | yes | \(-1\) | \(1\) | \(e\left(\frac{137}{260}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{7}{130}\right)\) | \(e\left(\frac{181}{260}\right)\) | \(e\left(\frac{3}{260}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{127}{260}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{151}{260}\right)\) | \(e\left(\frac{111}{130}\right)\) |
\(\chi_{16900}(49,\cdot)\) | 16900.ea | 78 | no | \(1\) | \(1\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{34}{39}\right)\) |
\(\chi_{16900}(51,\cdot)\) | 16900.cn | 26 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(1\) | \(e\left(\frac{21}{26}\right)\) | \(-1\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{3}{13}\right)\) |
\(\chi_{16900}(53,\cdot)\) | 16900.fg | 260 | no | \(-1\) | \(1\) | \(e\left(\frac{217}{260}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{87}{130}\right)\) | \(e\left(\frac{54}{65}\right)\) | \(e\left(\frac{223}{260}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{131}{260}\right)\) | \(e\left(\frac{61}{130}\right)\) |
\(\chi_{16900}(57,\cdot)\) | 16900.dh | 52 | no | \(1\) | \(1\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{7}{52}\right)\) | \(i\) | \(e\left(\frac{45}{52}\right)\) | \(i\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{25}{26}\right)\) |
\(\chi_{16900}(59,\cdot)\) | 16900.fs | 780 | yes | \(1\) | \(1\) | \(e\left(\frac{43}{195}\right)\) | \(e\left(\frac{1}{156}\right)\) | \(e\left(\frac{86}{195}\right)\) | \(e\left(\frac{631}{780}\right)\) | \(e\left(\frac{167}{195}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{59}{260}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{43}{65}\right)\) | \(e\left(\frac{73}{195}\right)\) |
\(\chi_{16900}(61,\cdot)\) | 16900.ey | 195 | no | \(1\) | \(1\) | \(e\left(\frac{172}{195}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{149}{195}\right)\) | \(e\left(\frac{46}{195}\right)\) | \(e\left(\frac{83}{195}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{42}{65}\right)\) | \(e\left(\frac{97}{195}\right)\) |
\(\chi_{16900}(63,\cdot)\) | 16900.ga | 780 | yes | \(-1\) | \(1\) | \(e\left(\frac{257}{780}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{257}{390}\right)\) | \(e\left(\frac{71}{780}\right)\) | \(e\left(\frac{463}{780}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{19}{260}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{257}{260}\right)\) | \(e\left(\frac{361}{390}\right)\) |
\(\chi_{16900}(67,\cdot)\) | 16900.ga | 780 | yes | \(-1\) | \(1\) | \(e\left(\frac{359}{780}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{359}{390}\right)\) | \(e\left(\frac{257}{780}\right)\) | \(e\left(\frac{61}{780}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{153}{260}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{99}{260}\right)\) | \(e\left(\frac{307}{390}\right)\) |
\(\chi_{16900}(69,\cdot)\) | 16900.fr | 390 | no | \(1\) | \(1\) | \(e\left(\frac{77}{390}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{77}{195}\right)\) | \(e\left(\frac{41}{390}\right)\) | \(e\left(\frac{163}{390}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{119}{130}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{77}{130}\right)\) | \(e\left(\frac{181}{195}\right)\) |
\(\chi_{16900}(71,\cdot)\) | 16900.gd | 780 | yes | \(1\) | \(1\) | \(e\left(\frac{233}{390}\right)\) | \(e\left(\frac{73}{156}\right)\) | \(e\left(\frac{38}{195}\right)\) | \(e\left(\frac{433}{780}\right)\) | \(e\left(\frac{7}{390}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{17}{260}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{103}{130}\right)\) | \(e\left(\frac{64}{195}\right)\) |
\(\chi_{16900}(73,\cdot)\) | 16900.fi | 260 | no | \(1\) | \(1\) | \(e\left(\frac{101}{260}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{101}{130}\right)\) | \(e\left(\frac{123}{260}\right)\) | \(e\left(\frac{229}{260}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{31}{260}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{43}{260}\right)\) | \(e\left(\frac{23}{130}\right)\) |
\(\chi_{16900}(77,\cdot)\) | 16900.fd | 260 | no | \(-1\) | \(1\) | \(e\left(\frac{71}{260}\right)\) | \(e\left(\frac{15}{52}\right)\) | \(e\left(\frac{71}{130}\right)\) | \(e\left(\frac{59}{130}\right)\) | \(e\left(\frac{49}{260}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{73}{130}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{213}{260}\right)\) | \(e\left(\frac{123}{130}\right)\) |
\(\chi_{16900}(79,\cdot)\) | 16900.ej | 130 | yes | \(-1\) | \(1\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{123}{130}\right)\) | \(e\left(\frac{99}{130}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{54}{65}\right)\) | \(e\left(\frac{23}{65}\right)\) |
\(\chi_{16900}(81,\cdot)\) | 16900.ey | 195 | no | \(1\) | \(1\) | \(e\left(\frac{11}{195}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{22}{195}\right)\) | \(e\left(\frac{173}{195}\right)\) | \(e\left(\frac{79}{195}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{11}{65}\right)\) | \(e\left(\frac{191}{195}\right)\) |
\(\chi_{16900}(83,\cdot)\) | 16900.fh | 260 | yes | \(-1\) | \(1\) | \(e\left(\frac{83}{260}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{83}{130}\right)\) | \(e\left(\frac{159}{260}\right)\) | \(e\left(\frac{17}{260}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{113}{260}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{249}{260}\right)\) | \(e\left(\frac{109}{130}\right)\) |