sage: H = DirichletGroup(625)
pari: g = idealstar(,625,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 500 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{500}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{625}(2,\cdot)$ |
First 32 of 500 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{625}(1,\cdot)\) | 625.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{625}(2,\cdot)\) | 625.l | 500 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{500}\right)\) | \(e\left(\frac{107}{500}\right)\) | \(e\left(\frac{1}{250}\right)\) | \(e\left(\frac{27}{125}\right)\) | \(e\left(\frac{97}{100}\right)\) | \(e\left(\frac{3}{500}\right)\) | \(e\left(\frac{107}{250}\right)\) | \(e\left(\frac{119}{125}\right)\) | \(e\left(\frac{109}{500}\right)\) | \(e\left(\frac{139}{500}\right)\) |
\(\chi_{625}(3,\cdot)\) | 625.l | 500 | yes | \(-1\) | \(1\) | \(e\left(\frac{107}{500}\right)\) | \(e\left(\frac{449}{500}\right)\) | \(e\left(\frac{107}{250}\right)\) | \(e\left(\frac{14}{125}\right)\) | \(e\left(\frac{79}{100}\right)\) | \(e\left(\frac{321}{500}\right)\) | \(e\left(\frac{199}{250}\right)\) | \(e\left(\frac{108}{125}\right)\) | \(e\left(\frac{163}{500}\right)\) | \(e\left(\frac{373}{500}\right)\) |
\(\chi_{625}(4,\cdot)\) | 625.k | 250 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{250}\right)\) | \(e\left(\frac{107}{250}\right)\) | \(e\left(\frac{1}{125}\right)\) | \(e\left(\frac{54}{125}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{3}{250}\right)\) | \(e\left(\frac{107}{125}\right)\) | \(e\left(\frac{113}{125}\right)\) | \(e\left(\frac{109}{250}\right)\) | \(e\left(\frac{139}{250}\right)\) |
\(\chi_{625}(6,\cdot)\) | 625.j | 125 | yes | \(1\) | \(1\) | \(e\left(\frac{27}{125}\right)\) | \(e\left(\frac{14}{125}\right)\) | \(e\left(\frac{54}{125}\right)\) | \(e\left(\frac{41}{125}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{81}{125}\right)\) | \(e\left(\frac{28}{125}\right)\) | \(e\left(\frac{102}{125}\right)\) | \(e\left(\frac{68}{125}\right)\) | \(e\left(\frac{3}{125}\right)\) |
\(\chi_{625}(7,\cdot)\) | 625.i | 100 | no | \(-1\) | \(1\) | \(e\left(\frac{97}{100}\right)\) | \(e\left(\frac{79}{100}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{91}{100}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{73}{100}\right)\) | \(e\left(\frac{83}{100}\right)\) |
\(\chi_{625}(8,\cdot)\) | 625.l | 500 | yes | \(-1\) | \(1\) | \(e\left(\frac{3}{500}\right)\) | \(e\left(\frac{321}{500}\right)\) | \(e\left(\frac{3}{250}\right)\) | \(e\left(\frac{81}{125}\right)\) | \(e\left(\frac{91}{100}\right)\) | \(e\left(\frac{9}{500}\right)\) | \(e\left(\frac{71}{250}\right)\) | \(e\left(\frac{107}{125}\right)\) | \(e\left(\frac{327}{500}\right)\) | \(e\left(\frac{417}{500}\right)\) |
\(\chi_{625}(9,\cdot)\) | 625.k | 250 | yes | \(1\) | \(1\) | \(e\left(\frac{107}{250}\right)\) | \(e\left(\frac{199}{250}\right)\) | \(e\left(\frac{107}{125}\right)\) | \(e\left(\frac{28}{125}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{71}{250}\right)\) | \(e\left(\frac{74}{125}\right)\) | \(e\left(\frac{91}{125}\right)\) | \(e\left(\frac{163}{250}\right)\) | \(e\left(\frac{123}{250}\right)\) |
\(\chi_{625}(11,\cdot)\) | 625.j | 125 | yes | \(1\) | \(1\) | \(e\left(\frac{119}{125}\right)\) | \(e\left(\frac{108}{125}\right)\) | \(e\left(\frac{113}{125}\right)\) | \(e\left(\frac{102}{125}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{107}{125}\right)\) | \(e\left(\frac{91}{125}\right)\) | \(e\left(\frac{19}{125}\right)\) | \(e\left(\frac{96}{125}\right)\) | \(e\left(\frac{41}{125}\right)\) |
\(\chi_{625}(12,\cdot)\) | 625.l | 500 | yes | \(-1\) | \(1\) | \(e\left(\frac{109}{500}\right)\) | \(e\left(\frac{163}{500}\right)\) | \(e\left(\frac{109}{250}\right)\) | \(e\left(\frac{68}{125}\right)\) | \(e\left(\frac{73}{100}\right)\) | \(e\left(\frac{327}{500}\right)\) | \(e\left(\frac{163}{250}\right)\) | \(e\left(\frac{96}{125}\right)\) | \(e\left(\frac{381}{500}\right)\) | \(e\left(\frac{151}{500}\right)\) |
\(\chi_{625}(13,\cdot)\) | 625.l | 500 | yes | \(-1\) | \(1\) | \(e\left(\frac{139}{500}\right)\) | \(e\left(\frac{373}{500}\right)\) | \(e\left(\frac{139}{250}\right)\) | \(e\left(\frac{3}{125}\right)\) | \(e\left(\frac{83}{100}\right)\) | \(e\left(\frac{417}{500}\right)\) | \(e\left(\frac{123}{250}\right)\) | \(e\left(\frac{41}{125}\right)\) | \(e\left(\frac{151}{500}\right)\) | \(e\left(\frac{321}{500}\right)\) |
\(\chi_{625}(14,\cdot)\) | 625.k | 250 | yes | \(1\) | \(1\) | \(e\left(\frac{243}{250}\right)\) | \(e\left(\frac{1}{250}\right)\) | \(e\left(\frac{118}{125}\right)\) | \(e\left(\frac{122}{125}\right)\) | \(e\left(\frac{21}{50}\right)\) | \(e\left(\frac{229}{250}\right)\) | \(e\left(\frac{1}{125}\right)\) | \(e\left(\frac{84}{125}\right)\) | \(e\left(\frac{237}{250}\right)\) | \(e\left(\frac{27}{250}\right)\) |
\(\chi_{625}(16,\cdot)\) | 625.j | 125 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{125}\right)\) | \(e\left(\frac{107}{125}\right)\) | \(e\left(\frac{2}{125}\right)\) | \(e\left(\frac{108}{125}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{3}{125}\right)\) | \(e\left(\frac{89}{125}\right)\) | \(e\left(\frac{101}{125}\right)\) | \(e\left(\frac{109}{125}\right)\) | \(e\left(\frac{14}{125}\right)\) |
\(\chi_{625}(17,\cdot)\) | 625.l | 500 | yes | \(-1\) | \(1\) | \(e\left(\frac{173}{500}\right)\) | \(e\left(\frac{11}{500}\right)\) | \(e\left(\frac{173}{250}\right)\) | \(e\left(\frac{46}{125}\right)\) | \(e\left(\frac{81}{100}\right)\) | \(e\left(\frac{19}{500}\right)\) | \(e\left(\frac{11}{250}\right)\) | \(e\left(\frac{87}{125}\right)\) | \(e\left(\frac{357}{500}\right)\) | \(e\left(\frac{47}{500}\right)\) |
\(\chi_{625}(18,\cdot)\) | 625.i | 100 | no | \(-1\) | \(1\) | \(e\left(\frac{43}{100}\right)\) | \(e\left(\frac{1}{100}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{29}{100}\right)\) | \(e\left(\frac{1}{50}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{87}{100}\right)\) | \(e\left(\frac{77}{100}\right)\) |
\(\chi_{625}(19,\cdot)\) | 625.k | 250 | yes | \(1\) | \(1\) | \(e\left(\frac{209}{250}\right)\) | \(e\left(\frac{113}{250}\right)\) | \(e\left(\frac{84}{125}\right)\) | \(e\left(\frac{36}{125}\right)\) | \(e\left(\frac{23}{50}\right)\) | \(e\left(\frac{127}{250}\right)\) | \(e\left(\frac{113}{125}\right)\) | \(e\left(\frac{117}{125}\right)\) | \(e\left(\frac{31}{250}\right)\) | \(e\left(\frac{51}{250}\right)\) |
\(\chi_{625}(21,\cdot)\) | 625.j | 125 | yes | \(1\) | \(1\) | \(e\left(\frac{23}{125}\right)\) | \(e\left(\frac{86}{125}\right)\) | \(e\left(\frac{46}{125}\right)\) | \(e\left(\frac{109}{125}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{69}{125}\right)\) | \(e\left(\frac{47}{125}\right)\) | \(e\left(\frac{73}{125}\right)\) | \(e\left(\frac{7}{125}\right)\) | \(e\left(\frac{72}{125}\right)\) |
\(\chi_{625}(22,\cdot)\) | 625.l | 500 | yes | \(-1\) | \(1\) | \(e\left(\frac{477}{500}\right)\) | \(e\left(\frac{39}{500}\right)\) | \(e\left(\frac{227}{250}\right)\) | \(e\left(\frac{4}{125}\right)\) | \(e\left(\frac{69}{100}\right)\) | \(e\left(\frac{431}{500}\right)\) | \(e\left(\frac{39}{250}\right)\) | \(e\left(\frac{13}{125}\right)\) | \(e\left(\frac{493}{500}\right)\) | \(e\left(\frac{303}{500}\right)\) |
\(\chi_{625}(23,\cdot)\) | 625.l | 500 | yes | \(-1\) | \(1\) | \(e\left(\frac{431}{500}\right)\) | \(e\left(\frac{117}{500}\right)\) | \(e\left(\frac{181}{250}\right)\) | \(e\left(\frac{12}{125}\right)\) | \(e\left(\frac{7}{100}\right)\) | \(e\left(\frac{293}{500}\right)\) | \(e\left(\frac{117}{250}\right)\) | \(e\left(\frac{39}{125}\right)\) | \(e\left(\frac{479}{500}\right)\) | \(e\left(\frac{409}{500}\right)\) |
\(\chi_{625}(24,\cdot)\) | 625.h | 50 | no | \(1\) | \(1\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{33}{50}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{29}{50}\right)\) |
\(\chi_{625}(26,\cdot)\) | 625.g | 25 | no | \(1\) | \(1\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{23}{25}\right)\) |
\(\chi_{625}(27,\cdot)\) | 625.l | 500 | yes | \(-1\) | \(1\) | \(e\left(\frac{321}{500}\right)\) | \(e\left(\frac{347}{500}\right)\) | \(e\left(\frac{71}{250}\right)\) | \(e\left(\frac{42}{125}\right)\) | \(e\left(\frac{37}{100}\right)\) | \(e\left(\frac{463}{500}\right)\) | \(e\left(\frac{97}{250}\right)\) | \(e\left(\frac{74}{125}\right)\) | \(e\left(\frac{489}{500}\right)\) | \(e\left(\frac{119}{500}\right)\) |
\(\chi_{625}(28,\cdot)\) | 625.l | 500 | yes | \(-1\) | \(1\) | \(e\left(\frac{487}{500}\right)\) | \(e\left(\frac{109}{500}\right)\) | \(e\left(\frac{237}{250}\right)\) | \(e\left(\frac{24}{125}\right)\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{461}{500}\right)\) | \(e\left(\frac{109}{250}\right)\) | \(e\left(\frac{78}{125}\right)\) | \(e\left(\frac{83}{500}\right)\) | \(e\left(\frac{193}{500}\right)\) |
\(\chi_{625}(29,\cdot)\) | 625.k | 250 | yes | \(1\) | \(1\) | \(e\left(\frac{81}{250}\right)\) | \(e\left(\frac{167}{250}\right)\) | \(e\left(\frac{81}{125}\right)\) | \(e\left(\frac{124}{125}\right)\) | \(e\left(\frac{7}{50}\right)\) | \(e\left(\frac{243}{250}\right)\) | \(e\left(\frac{42}{125}\right)\) | \(e\left(\frac{28}{125}\right)\) | \(e\left(\frac{79}{250}\right)\) | \(e\left(\frac{9}{250}\right)\) |
\(\chi_{625}(31,\cdot)\) | 625.j | 125 | yes | \(1\) | \(1\) | \(e\left(\frac{12}{125}\right)\) | \(e\left(\frac{34}{125}\right)\) | \(e\left(\frac{24}{125}\right)\) | \(e\left(\frac{46}{125}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{36}{125}\right)\) | \(e\left(\frac{68}{125}\right)\) | \(e\left(\frac{87}{125}\right)\) | \(e\left(\frac{58}{125}\right)\) | \(e\left(\frac{43}{125}\right)\) |
\(\chi_{625}(32,\cdot)\) | 625.i | 100 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{100}\right)\) | \(e\left(\frac{7}{100}\right)\) | \(e\left(\frac{1}{50}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{3}{100}\right)\) | \(e\left(\frac{7}{50}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{9}{100}\right)\) | \(e\left(\frac{39}{100}\right)\) |
\(\chi_{625}(33,\cdot)\) | 625.l | 500 | yes | \(-1\) | \(1\) | \(e\left(\frac{83}{500}\right)\) | \(e\left(\frac{381}{500}\right)\) | \(e\left(\frac{83}{250}\right)\) | \(e\left(\frac{116}{125}\right)\) | \(e\left(\frac{51}{100}\right)\) | \(e\left(\frac{249}{500}\right)\) | \(e\left(\frac{131}{250}\right)\) | \(e\left(\frac{2}{125}\right)\) | \(e\left(\frac{47}{500}\right)\) | \(e\left(\frac{37}{500}\right)\) |
\(\chi_{625}(34,\cdot)\) | 625.k | 250 | yes | \(1\) | \(1\) | \(e\left(\frac{87}{250}\right)\) | \(e\left(\frac{59}{250}\right)\) | \(e\left(\frac{87}{125}\right)\) | \(e\left(\frac{73}{125}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{11}{250}\right)\) | \(e\left(\frac{59}{125}\right)\) | \(e\left(\frac{81}{125}\right)\) | \(e\left(\frac{233}{250}\right)\) | \(e\left(\frac{93}{250}\right)\) |
\(\chi_{625}(36,\cdot)\) | 625.j | 125 | yes | \(1\) | \(1\) | \(e\left(\frac{54}{125}\right)\) | \(e\left(\frac{28}{125}\right)\) | \(e\left(\frac{108}{125}\right)\) | \(e\left(\frac{82}{125}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{37}{125}\right)\) | \(e\left(\frac{56}{125}\right)\) | \(e\left(\frac{79}{125}\right)\) | \(e\left(\frac{11}{125}\right)\) | \(e\left(\frac{6}{125}\right)\) |
\(\chi_{625}(37,\cdot)\) | 625.l | 500 | yes | \(-1\) | \(1\) | \(e\left(\frac{329}{500}\right)\) | \(e\left(\frac{203}{500}\right)\) | \(e\left(\frac{79}{250}\right)\) | \(e\left(\frac{8}{125}\right)\) | \(e\left(\frac{13}{100}\right)\) | \(e\left(\frac{487}{500}\right)\) | \(e\left(\frac{203}{250}\right)\) | \(e\left(\frac{26}{125}\right)\) | \(e\left(\frac{361}{500}\right)\) | \(e\left(\frac{231}{500}\right)\) |
\(\chi_{625}(38,\cdot)\) | 625.l | 500 | yes | \(-1\) | \(1\) | \(e\left(\frac{419}{500}\right)\) | \(e\left(\frac{333}{500}\right)\) | \(e\left(\frac{169}{250}\right)\) | \(e\left(\frac{63}{125}\right)\) | \(e\left(\frac{43}{100}\right)\) | \(e\left(\frac{257}{500}\right)\) | \(e\left(\frac{83}{250}\right)\) | \(e\left(\frac{111}{125}\right)\) | \(e\left(\frac{171}{500}\right)\) | \(e\left(\frac{241}{500}\right)\) |
\(\chi_{625}(39,\cdot)\) | 625.k | 250 | yes | \(1\) | \(1\) | \(e\left(\frac{123}{250}\right)\) | \(e\left(\frac{161}{250}\right)\) | \(e\left(\frac{123}{125}\right)\) | \(e\left(\frac{17}{125}\right)\) | \(e\left(\frac{31}{50}\right)\) | \(e\left(\frac{119}{250}\right)\) | \(e\left(\frac{36}{125}\right)\) | \(e\left(\frac{24}{125}\right)\) | \(e\left(\frac{157}{250}\right)\) | \(e\left(\frac{97}{250}\right)\) |