sage: H = DirichletGroup(2675)
pari: g = idealstar(,2675,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 2120 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{1060}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{2675}(1927,\cdot)$, $\chi_{2675}(751,\cdot)$ |
First 32 of 2120 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{2675}(1,\cdot)\) | 2675.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{2675}(2,\cdot)\) | 2675.w | 1060 | yes | \(1\) | \(1\) | \(e\left(\frac{63}{1060}\right)\) | \(e\left(\frac{11}{1060}\right)\) | \(e\left(\frac{63}{530}\right)\) | \(e\left(\frac{37}{530}\right)\) | \(e\left(\frac{139}{212}\right)\) | \(e\left(\frac{189}{1060}\right)\) | \(e\left(\frac{11}{530}\right)\) | \(e\left(\frac{2}{265}\right)\) | \(e\left(\frac{137}{1060}\right)\) | \(e\left(\frac{87}{1060}\right)\) |
\(\chi_{2675}(3,\cdot)\) | 2675.x | 1060 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{1060}\right)\) | \(e\left(\frac{717}{1060}\right)\) | \(e\left(\frac{11}{530}\right)\) | \(e\left(\frac{182}{265}\right)\) | \(e\left(\frac{31}{212}\right)\) | \(e\left(\frac{33}{1060}\right)\) | \(e\left(\frac{187}{530}\right)\) | \(e\left(\frac{34}{265}\right)\) | \(e\left(\frac{739}{1060}\right)\) | \(e\left(\frac{949}{1060}\right)\) |
\(\chi_{2675}(4,\cdot)\) | 2675.t | 530 | yes | \(1\) | \(1\) | \(e\left(\frac{63}{530}\right)\) | \(e\left(\frac{11}{530}\right)\) | \(e\left(\frac{63}{265}\right)\) | \(e\left(\frac{37}{265}\right)\) | \(e\left(\frac{33}{106}\right)\) | \(e\left(\frac{189}{530}\right)\) | \(e\left(\frac{11}{265}\right)\) | \(e\left(\frac{4}{265}\right)\) | \(e\left(\frac{137}{530}\right)\) | \(e\left(\frac{87}{530}\right)\) |
\(\chi_{2675}(6,\cdot)\) | 2675.u | 530 | yes | \(-1\) | \(1\) | \(e\left(\frac{37}{530}\right)\) | \(e\left(\frac{182}{265}\right)\) | \(e\left(\frac{37}{265}\right)\) | \(e\left(\frac{401}{530}\right)\) | \(e\left(\frac{85}{106}\right)\) | \(e\left(\frac{111}{530}\right)\) | \(e\left(\frac{99}{265}\right)\) | \(e\left(\frac{36}{265}\right)\) | \(e\left(\frac{219}{265}\right)\) | \(e\left(\frac{259}{265}\right)\) |
\(\chi_{2675}(7,\cdot)\) | 2675.r | 212 | no | \(1\) | \(1\) | \(e\left(\frac{139}{212}\right)\) | \(e\left(\frac{31}{212}\right)\) | \(e\left(\frac{33}{106}\right)\) | \(e\left(\frac{85}{106}\right)\) | \(e\left(\frac{147}{212}\right)\) | \(e\left(\frac{205}{212}\right)\) | \(e\left(\frac{31}{106}\right)\) | \(e\left(\frac{49}{53}\right)\) | \(e\left(\frac{97}{212}\right)\) | \(e\left(\frac{91}{212}\right)\) |
\(\chi_{2675}(8,\cdot)\) | 2675.w | 1060 | yes | \(1\) | \(1\) | \(e\left(\frac{189}{1060}\right)\) | \(e\left(\frac{33}{1060}\right)\) | \(e\left(\frac{189}{530}\right)\) | \(e\left(\frac{111}{530}\right)\) | \(e\left(\frac{205}{212}\right)\) | \(e\left(\frac{567}{1060}\right)\) | \(e\left(\frac{33}{530}\right)\) | \(e\left(\frac{6}{265}\right)\) | \(e\left(\frac{411}{1060}\right)\) | \(e\left(\frac{261}{1060}\right)\) |
\(\chi_{2675}(9,\cdot)\) | 2675.t | 530 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{530}\right)\) | \(e\left(\frac{187}{530}\right)\) | \(e\left(\frac{11}{265}\right)\) | \(e\left(\frac{99}{265}\right)\) | \(e\left(\frac{31}{106}\right)\) | \(e\left(\frac{33}{530}\right)\) | \(e\left(\frac{187}{265}\right)\) | \(e\left(\frac{68}{265}\right)\) | \(e\left(\frac{209}{530}\right)\) | \(e\left(\frac{419}{530}\right)\) |
\(\chi_{2675}(11,\cdot)\) | 2675.s | 265 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{265}\right)\) | \(e\left(\frac{34}{265}\right)\) | \(e\left(\frac{4}{265}\right)\) | \(e\left(\frac{36}{265}\right)\) | \(e\left(\frac{49}{53}\right)\) | \(e\left(\frac{6}{265}\right)\) | \(e\left(\frac{68}{265}\right)\) | \(e\left(\frac{97}{265}\right)\) | \(e\left(\frac{38}{265}\right)\) | \(e\left(\frac{28}{265}\right)\) |
\(\chi_{2675}(12,\cdot)\) | 2675.x | 1060 | yes | \(-1\) | \(1\) | \(e\left(\frac{137}{1060}\right)\) | \(e\left(\frac{739}{1060}\right)\) | \(e\left(\frac{137}{530}\right)\) | \(e\left(\frac{219}{265}\right)\) | \(e\left(\frac{97}{212}\right)\) | \(e\left(\frac{411}{1060}\right)\) | \(e\left(\frac{209}{530}\right)\) | \(e\left(\frac{38}{265}\right)\) | \(e\left(\frac{1013}{1060}\right)\) | \(e\left(\frac{63}{1060}\right)\) |
\(\chi_{2675}(13,\cdot)\) | 2675.x | 1060 | yes | \(-1\) | \(1\) | \(e\left(\frac{87}{1060}\right)\) | \(e\left(\frac{949}{1060}\right)\) | \(e\left(\frac{87}{530}\right)\) | \(e\left(\frac{259}{265}\right)\) | \(e\left(\frac{91}{212}\right)\) | \(e\left(\frac{261}{1060}\right)\) | \(e\left(\frac{419}{530}\right)\) | \(e\left(\frac{28}{265}\right)\) | \(e\left(\frac{63}{1060}\right)\) | \(e\left(\frac{953}{1060}\right)\) |
\(\chi_{2675}(14,\cdot)\) | 2675.t | 530 | yes | \(1\) | \(1\) | \(e\left(\frac{379}{530}\right)\) | \(e\left(\frac{83}{530}\right)\) | \(e\left(\frac{114}{265}\right)\) | \(e\left(\frac{231}{265}\right)\) | \(e\left(\frac{37}{106}\right)\) | \(e\left(\frac{77}{530}\right)\) | \(e\left(\frac{83}{265}\right)\) | \(e\left(\frac{247}{265}\right)\) | \(e\left(\frac{311}{530}\right)\) | \(e\left(\frac{271}{530}\right)\) |
\(\chi_{2675}(16,\cdot)\) | 2675.s | 265 | yes | \(1\) | \(1\) | \(e\left(\frac{63}{265}\right)\) | \(e\left(\frac{11}{265}\right)\) | \(e\left(\frac{126}{265}\right)\) | \(e\left(\frac{74}{265}\right)\) | \(e\left(\frac{33}{53}\right)\) | \(e\left(\frac{189}{265}\right)\) | \(e\left(\frac{22}{265}\right)\) | \(e\left(\frac{8}{265}\right)\) | \(e\left(\frac{137}{265}\right)\) | \(e\left(\frac{87}{265}\right)\) |
\(\chi_{2675}(17,\cdot)\) | 2675.w | 1060 | yes | \(1\) | \(1\) | \(e\left(\frac{979}{1060}\right)\) | \(e\left(\frac{743}{1060}\right)\) | \(e\left(\frac{449}{530}\right)\) | \(e\left(\frac{331}{530}\right)\) | \(e\left(\frac{3}{212}\right)\) | \(e\left(\frac{817}{1060}\right)\) | \(e\left(\frac{213}{530}\right)\) | \(e\left(\frac{111}{265}\right)\) | \(e\left(\frac{581}{1060}\right)\) | \(e\left(\frac{191}{1060}\right)\) |
\(\chi_{2675}(18,\cdot)\) | 2675.r | 212 | no | \(1\) | \(1\) | \(e\left(\frac{17}{212}\right)\) | \(e\left(\frac{77}{212}\right)\) | \(e\left(\frac{17}{106}\right)\) | \(e\left(\frac{47}{106}\right)\) | \(e\left(\frac{201}{212}\right)\) | \(e\left(\frac{51}{212}\right)\) | \(e\left(\frac{77}{106}\right)\) | \(e\left(\frac{14}{53}\right)\) | \(e\left(\frac{111}{212}\right)\) | \(e\left(\frac{185}{212}\right)\) |
\(\chi_{2675}(19,\cdot)\) | 2675.t | 530 | yes | \(1\) | \(1\) | \(e\left(\frac{337}{530}\right)\) | \(e\left(\frac{429}{530}\right)\) | \(e\left(\frac{72}{265}\right)\) | \(e\left(\frac{118}{265}\right)\) | \(e\left(\frac{15}{106}\right)\) | \(e\left(\frac{481}{530}\right)\) | \(e\left(\frac{164}{265}\right)\) | \(e\left(\frac{156}{265}\right)\) | \(e\left(\frac{43}{530}\right)\) | \(e\left(\frac{213}{530}\right)\) |
\(\chi_{2675}(21,\cdot)\) | 2675.u | 530 | yes | \(-1\) | \(1\) | \(e\left(\frac{353}{530}\right)\) | \(e\left(\frac{218}{265}\right)\) | \(e\left(\frac{88}{265}\right)\) | \(e\left(\frac{259}{530}\right)\) | \(e\left(\frac{89}{106}\right)\) | \(e\left(\frac{529}{530}\right)\) | \(e\left(\frac{171}{265}\right)\) | \(e\left(\frac{14}{265}\right)\) | \(e\left(\frac{41}{265}\right)\) | \(e\left(\frac{86}{265}\right)\) |
\(\chi_{2675}(22,\cdot)\) | 2675.w | 1060 | yes | \(1\) | \(1\) | \(e\left(\frac{71}{1060}\right)\) | \(e\left(\frac{147}{1060}\right)\) | \(e\left(\frac{71}{530}\right)\) | \(e\left(\frac{109}{530}\right)\) | \(e\left(\frac{123}{212}\right)\) | \(e\left(\frac{213}{1060}\right)\) | \(e\left(\frac{147}{530}\right)\) | \(e\left(\frac{99}{265}\right)\) | \(e\left(\frac{289}{1060}\right)\) | \(e\left(\frac{199}{1060}\right)\) |
\(\chi_{2675}(23,\cdot)\) | 2675.x | 1060 | yes | \(-1\) | \(1\) | \(e\left(\frac{143}{1060}\right)\) | \(e\left(\frac{841}{1060}\right)\) | \(e\left(\frac{143}{530}\right)\) | \(e\left(\frac{246}{265}\right)\) | \(e\left(\frac{191}{212}\right)\) | \(e\left(\frac{429}{1060}\right)\) | \(e\left(\frac{311}{530}\right)\) | \(e\left(\frac{177}{265}\right)\) | \(e\left(\frac{67}{1060}\right)\) | \(e\left(\frac{677}{1060}\right)\) |
\(\chi_{2675}(24,\cdot)\) | 2675.n | 106 | no | \(-1\) | \(1\) | \(e\left(\frac{10}{53}\right)\) | \(e\left(\frac{75}{106}\right)\) | \(e\left(\frac{20}{53}\right)\) | \(e\left(\frac{95}{106}\right)\) | \(e\left(\frac{6}{53}\right)\) | \(e\left(\frac{30}{53}\right)\) | \(e\left(\frac{22}{53}\right)\) | \(e\left(\frac{8}{53}\right)\) | \(e\left(\frac{9}{106}\right)\) | \(e\left(\frac{15}{106}\right)\) |
\(\chi_{2675}(26,\cdot)\) | 2675.o | 106 | no | \(-1\) | \(1\) | \(e\left(\frac{15}{106}\right)\) | \(e\left(\frac{48}{53}\right)\) | \(e\left(\frac{15}{53}\right)\) | \(e\left(\frac{5}{106}\right)\) | \(e\left(\frac{9}{106}\right)\) | \(e\left(\frac{45}{106}\right)\) | \(e\left(\frac{43}{53}\right)\) | \(e\left(\frac{6}{53}\right)\) | \(e\left(\frac{10}{53}\right)\) | \(e\left(\frac{52}{53}\right)\) |
\(\chi_{2675}(27,\cdot)\) | 2675.x | 1060 | yes | \(-1\) | \(1\) | \(e\left(\frac{33}{1060}\right)\) | \(e\left(\frac{31}{1060}\right)\) | \(e\left(\frac{33}{530}\right)\) | \(e\left(\frac{16}{265}\right)\) | \(e\left(\frac{93}{212}\right)\) | \(e\left(\frac{99}{1060}\right)\) | \(e\left(\frac{31}{530}\right)\) | \(e\left(\frac{102}{265}\right)\) | \(e\left(\frac{97}{1060}\right)\) | \(e\left(\frac{727}{1060}\right)\) |
\(\chi_{2675}(28,\cdot)\) | 2675.w | 1060 | yes | \(1\) | \(1\) | \(e\left(\frac{821}{1060}\right)\) | \(e\left(\frac{177}{1060}\right)\) | \(e\left(\frac{291}{530}\right)\) | \(e\left(\frac{499}{530}\right)\) | \(e\left(\frac{1}{212}\right)\) | \(e\left(\frac{343}{1060}\right)\) | \(e\left(\frac{177}{530}\right)\) | \(e\left(\frac{249}{265}\right)\) | \(e\left(\frac{759}{1060}\right)\) | \(e\left(\frac{629}{1060}\right)\) |
\(\chi_{2675}(29,\cdot)\) | 2675.t | 530 | yes | \(1\) | \(1\) | \(e\left(\frac{213}{530}\right)\) | \(e\left(\frac{441}{530}\right)\) | \(e\left(\frac{213}{265}\right)\) | \(e\left(\frac{62}{265}\right)\) | \(e\left(\frac{51}{106}\right)\) | \(e\left(\frac{109}{530}\right)\) | \(e\left(\frac{176}{265}\right)\) | \(e\left(\frac{64}{265}\right)\) | \(e\left(\frac{337}{530}\right)\) | \(e\left(\frac{67}{530}\right)\) |
\(\chi_{2675}(31,\cdot)\) | 2675.u | 530 | yes | \(-1\) | \(1\) | \(e\left(\frac{347}{530}\right)\) | \(e\left(\frac{167}{265}\right)\) | \(e\left(\frac{82}{265}\right)\) | \(e\left(\frac{151}{530}\right)\) | \(e\left(\frac{101}{106}\right)\) | \(e\left(\frac{511}{530}\right)\) | \(e\left(\frac{69}{265}\right)\) | \(e\left(\frac{1}{265}\right)\) | \(e\left(\frac{249}{265}\right)\) | \(e\left(\frac{44}{265}\right)\) |
\(\chi_{2675}(32,\cdot)\) | 2675.r | 212 | no | \(1\) | \(1\) | \(e\left(\frac{63}{212}\right)\) | \(e\left(\frac{11}{212}\right)\) | \(e\left(\frac{63}{106}\right)\) | \(e\left(\frac{37}{106}\right)\) | \(e\left(\frac{59}{212}\right)\) | \(e\left(\frac{189}{212}\right)\) | \(e\left(\frac{11}{106}\right)\) | \(e\left(\frac{2}{53}\right)\) | \(e\left(\frac{137}{212}\right)\) | \(e\left(\frac{87}{212}\right)\) |
\(\chi_{2675}(33,\cdot)\) | 2675.x | 1060 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{1060}\right)\) | \(e\left(\frac{853}{1060}\right)\) | \(e\left(\frac{19}{530}\right)\) | \(e\left(\frac{218}{265}\right)\) | \(e\left(\frac{15}{212}\right)\) | \(e\left(\frac{57}{1060}\right)\) | \(e\left(\frac{323}{530}\right)\) | \(e\left(\frac{131}{265}\right)\) | \(e\left(\frac{891}{1060}\right)\) | \(e\left(\frac{1}{1060}\right)\) |
\(\chi_{2675}(34,\cdot)\) | 2675.t | 530 | yes | \(1\) | \(1\) | \(e\left(\frac{521}{530}\right)\) | \(e\left(\frac{377}{530}\right)\) | \(e\left(\frac{256}{265}\right)\) | \(e\left(\frac{184}{265}\right)\) | \(e\left(\frac{71}{106}\right)\) | \(e\left(\frac{503}{530}\right)\) | \(e\left(\frac{112}{265}\right)\) | \(e\left(\frac{113}{265}\right)\) | \(e\left(\frac{359}{530}\right)\) | \(e\left(\frac{139}{530}\right)\) |
\(\chi_{2675}(36,\cdot)\) | 2675.s | 265 | yes | \(1\) | \(1\) | \(e\left(\frac{37}{265}\right)\) | \(e\left(\frac{99}{265}\right)\) | \(e\left(\frac{74}{265}\right)\) | \(e\left(\frac{136}{265}\right)\) | \(e\left(\frac{32}{53}\right)\) | \(e\left(\frac{111}{265}\right)\) | \(e\left(\frac{198}{265}\right)\) | \(e\left(\frac{72}{265}\right)\) | \(e\left(\frac{173}{265}\right)\) | \(e\left(\frac{253}{265}\right)\) |
\(\chi_{2675}(37,\cdot)\) | 2675.x | 1060 | yes | \(-1\) | \(1\) | \(e\left(\frac{857}{1060}\right)\) | \(e\left(\frac{259}{1060}\right)\) | \(e\left(\frac{327}{530}\right)\) | \(e\left(\frac{14}{265}\right)\) | \(e\left(\frac{141}{212}\right)\) | \(e\left(\frac{451}{1060}\right)\) | \(e\left(\frac{259}{530}\right)\) | \(e\left(\frac{23}{265}\right)\) | \(e\left(\frac{913}{1060}\right)\) | \(e\left(\frac{603}{1060}\right)\) |
\(\chi_{2675}(38,\cdot)\) | 2675.w | 1060 | yes | \(1\) | \(1\) | \(e\left(\frac{737}{1060}\right)\) | \(e\left(\frac{869}{1060}\right)\) | \(e\left(\frac{207}{530}\right)\) | \(e\left(\frac{273}{530}\right)\) | \(e\left(\frac{169}{212}\right)\) | \(e\left(\frac{91}{1060}\right)\) | \(e\left(\frac{339}{530}\right)\) | \(e\left(\frac{158}{265}\right)\) | \(e\left(\frac{223}{1060}\right)\) | \(e\left(\frac{513}{1060}\right)\) |
\(\chi_{2675}(39,\cdot)\) | 2675.t | 530 | yes | \(1\) | \(1\) | \(e\left(\frac{49}{530}\right)\) | \(e\left(\frac{303}{530}\right)\) | \(e\left(\frac{49}{265}\right)\) | \(e\left(\frac{176}{265}\right)\) | \(e\left(\frac{61}{106}\right)\) | \(e\left(\frac{147}{530}\right)\) | \(e\left(\frac{38}{265}\right)\) | \(e\left(\frac{62}{265}\right)\) | \(e\left(\frac{401}{530}\right)\) | \(e\left(\frac{421}{530}\right)\) |