sage: H = DirichletGroup(668)
pari: g = idealstar(,668,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 332 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{166}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{668}(335,\cdot)$, $\chi_{668}(5,\cdot)$ |
First 32 of 332 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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{668}(1,\cdot)\) | 668.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{668}(3,\cdot)\) | 668.g | 166 | yes | \(-1\) | \(1\) | \(e\left(\frac{121}{166}\right)\) | \(e\left(\frac{47}{83}\right)\) | \(e\left(\frac{53}{166}\right)\) | \(e\left(\frac{38}{83}\right)\) | \(e\left(\frac{59}{166}\right)\) | \(e\left(\frac{27}{83}\right)\) | \(e\left(\frac{49}{166}\right)\) | \(e\left(\frac{1}{83}\right)\) | \(e\left(\frac{57}{166}\right)\) | \(e\left(\frac{4}{83}\right)\) |
\(\chi_{668}(5,\cdot)\) | 668.f | 166 | no | \(-1\) | \(1\) | \(e\left(\frac{47}{83}\right)\) | \(e\left(\frac{1}{166}\right)\) | \(e\left(\frac{59}{83}\right)\) | \(e\left(\frac{11}{83}\right)\) | \(e\left(\frac{14}{83}\right)\) | \(e\left(\frac{103}{166}\right)\) | \(e\left(\frac{95}{166}\right)\) | \(e\left(\frac{53}{166}\right)\) | \(e\left(\frac{29}{83}\right)\) | \(e\left(\frac{23}{83}\right)\) |
\(\chi_{668}(7,\cdot)\) | 668.g | 166 | yes | \(-1\) | \(1\) | \(e\left(\frac{53}{166}\right)\) | \(e\left(\frac{59}{83}\right)\) | \(e\left(\frac{63}{166}\right)\) | \(e\left(\frac{53}{83}\right)\) | \(e\left(\frac{67}{166}\right)\) | \(e\left(\frac{18}{83}\right)\) | \(e\left(\frac{5}{166}\right)\) | \(e\left(\frac{56}{83}\right)\) | \(e\left(\frac{121}{166}\right)\) | \(e\left(\frac{58}{83}\right)\) |
\(\chi_{668}(9,\cdot)\) | 668.e | 83 | no | \(1\) | \(1\) | \(e\left(\frac{38}{83}\right)\) | \(e\left(\frac{11}{83}\right)\) | \(e\left(\frac{53}{83}\right)\) | \(e\left(\frac{76}{83}\right)\) | \(e\left(\frac{59}{83}\right)\) | \(e\left(\frac{54}{83}\right)\) | \(e\left(\frac{49}{83}\right)\) | \(e\left(\frac{2}{83}\right)\) | \(e\left(\frac{57}{83}\right)\) | \(e\left(\frac{8}{83}\right)\) |
\(\chi_{668}(11,\cdot)\) | 668.g | 166 | yes | \(-1\) | \(1\) | \(e\left(\frac{59}{166}\right)\) | \(e\left(\frac{14}{83}\right)\) | \(e\left(\frac{67}{166}\right)\) | \(e\left(\frac{59}{83}\right)\) | \(e\left(\frac{37}{166}\right)\) | \(e\left(\frac{31}{83}\right)\) | \(e\left(\frac{87}{166}\right)\) | \(e\left(\frac{78}{83}\right)\) | \(e\left(\frac{47}{166}\right)\) | \(e\left(\frac{63}{83}\right)\) |
\(\chi_{668}(13,\cdot)\) | 668.f | 166 | no | \(-1\) | \(1\) | \(e\left(\frac{27}{83}\right)\) | \(e\left(\frac{103}{166}\right)\) | \(e\left(\frac{18}{83}\right)\) | \(e\left(\frac{54}{83}\right)\) | \(e\left(\frac{31}{83}\right)\) | \(e\left(\frac{151}{166}\right)\) | \(e\left(\frac{157}{166}\right)\) | \(e\left(\frac{147}{166}\right)\) | \(e\left(\frac{82}{83}\right)\) | \(e\left(\frac{45}{83}\right)\) |
\(\chi_{668}(15,\cdot)\) | 668.h | 166 | yes | \(1\) | \(1\) | \(e\left(\frac{49}{166}\right)\) | \(e\left(\frac{95}{166}\right)\) | \(e\left(\frac{5}{166}\right)\) | \(e\left(\frac{49}{83}\right)\) | \(e\left(\frac{87}{166}\right)\) | \(e\left(\frac{157}{166}\right)\) | \(e\left(\frac{72}{83}\right)\) | \(e\left(\frac{55}{166}\right)\) | \(e\left(\frac{115}{166}\right)\) | \(e\left(\frac{27}{83}\right)\) |
\(\chi_{668}(17,\cdot)\) | 668.f | 166 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{83}\right)\) | \(e\left(\frac{53}{166}\right)\) | \(e\left(\frac{56}{83}\right)\) | \(e\left(\frac{2}{83}\right)\) | \(e\left(\frac{78}{83}\right)\) | \(e\left(\frac{147}{166}\right)\) | \(e\left(\frac{55}{166}\right)\) | \(e\left(\frac{153}{166}\right)\) | \(e\left(\frac{43}{83}\right)\) | \(e\left(\frac{57}{83}\right)\) |
\(\chi_{668}(19,\cdot)\) | 668.g | 166 | yes | \(-1\) | \(1\) | \(e\left(\frac{57}{166}\right)\) | \(e\left(\frac{29}{83}\right)\) | \(e\left(\frac{121}{166}\right)\) | \(e\left(\frac{57}{83}\right)\) | \(e\left(\frac{47}{166}\right)\) | \(e\left(\frac{82}{83}\right)\) | \(e\left(\frac{115}{166}\right)\) | \(e\left(\frac{43}{83}\right)\) | \(e\left(\frac{127}{166}\right)\) | \(e\left(\frac{6}{83}\right)\) |
\(\chi_{668}(21,\cdot)\) | 668.e | 83 | no | \(1\) | \(1\) | \(e\left(\frac{4}{83}\right)\) | \(e\left(\frac{23}{83}\right)\) | \(e\left(\frac{58}{83}\right)\) | \(e\left(\frac{8}{83}\right)\) | \(e\left(\frac{63}{83}\right)\) | \(e\left(\frac{45}{83}\right)\) | \(e\left(\frac{27}{83}\right)\) | \(e\left(\frac{57}{83}\right)\) | \(e\left(\frac{6}{83}\right)\) | \(e\left(\frac{62}{83}\right)\) |
\(\chi_{668}(23,\cdot)\) | 668.h | 166 | yes | \(1\) | \(1\) | \(e\left(\frac{93}{166}\right)\) | \(e\left(\frac{99}{166}\right)\) | \(e\left(\frac{145}{166}\right)\) | \(e\left(\frac{10}{83}\right)\) | \(e\left(\frac{33}{166}\right)\) | \(e\left(\frac{71}{166}\right)\) | \(e\left(\frac{13}{83}\right)\) | \(e\left(\frac{101}{166}\right)\) | \(e\left(\frac{15}{166}\right)\) | \(e\left(\frac{36}{83}\right)\) |
\(\chi_{668}(25,\cdot)\) | 668.e | 83 | no | \(1\) | \(1\) | \(e\left(\frac{11}{83}\right)\) | \(e\left(\frac{1}{83}\right)\) | \(e\left(\frac{35}{83}\right)\) | \(e\left(\frac{22}{83}\right)\) | \(e\left(\frac{28}{83}\right)\) | \(e\left(\frac{20}{83}\right)\) | \(e\left(\frac{12}{83}\right)\) | \(e\left(\frac{53}{83}\right)\) | \(e\left(\frac{58}{83}\right)\) | \(e\left(\frac{46}{83}\right)\) |
\(\chi_{668}(27,\cdot)\) | 668.g | 166 | yes | \(-1\) | \(1\) | \(e\left(\frac{31}{166}\right)\) | \(e\left(\frac{58}{83}\right)\) | \(e\left(\frac{159}{166}\right)\) | \(e\left(\frac{31}{83}\right)\) | \(e\left(\frac{11}{166}\right)\) | \(e\left(\frac{81}{83}\right)\) | \(e\left(\frac{147}{166}\right)\) | \(e\left(\frac{3}{83}\right)\) | \(e\left(\frac{5}{166}\right)\) | \(e\left(\frac{12}{83}\right)\) |
\(\chi_{668}(29,\cdot)\) | 668.e | 83 | no | \(1\) | \(1\) | \(e\left(\frac{78}{83}\right)\) | \(e\left(\frac{75}{83}\right)\) | \(e\left(\frac{52}{83}\right)\) | \(e\left(\frac{73}{83}\right)\) | \(e\left(\frac{25}{83}\right)\) | \(e\left(\frac{6}{83}\right)\) | \(e\left(\frac{70}{83}\right)\) | \(e\left(\frac{74}{83}\right)\) | \(e\left(\frac{34}{83}\right)\) | \(e\left(\frac{47}{83}\right)\) |
\(\chi_{668}(31,\cdot)\) | 668.g | 166 | yes | \(-1\) | \(1\) | \(e\left(\frac{77}{166}\right)\) | \(e\left(\frac{45}{83}\right)\) | \(e\left(\frac{79}{166}\right)\) | \(e\left(\frac{77}{83}\right)\) | \(e\left(\frac{113}{166}\right)\) | \(e\left(\frac{70}{83}\right)\) | \(e\left(\frac{1}{166}\right)\) | \(e\left(\frac{61}{83}\right)\) | \(e\left(\frac{157}{166}\right)\) | \(e\left(\frac{78}{83}\right)\) |
\(\chi_{668}(33,\cdot)\) | 668.e | 83 | no | \(1\) | \(1\) | \(e\left(\frac{7}{83}\right)\) | \(e\left(\frac{61}{83}\right)\) | \(e\left(\frac{60}{83}\right)\) | \(e\left(\frac{14}{83}\right)\) | \(e\left(\frac{48}{83}\right)\) | \(e\left(\frac{58}{83}\right)\) | \(e\left(\frac{68}{83}\right)\) | \(e\left(\frac{79}{83}\right)\) | \(e\left(\frac{52}{83}\right)\) | \(e\left(\frac{67}{83}\right)\) |
\(\chi_{668}(35,\cdot)\) | 668.h | 166 | yes | \(1\) | \(1\) | \(e\left(\frac{147}{166}\right)\) | \(e\left(\frac{119}{166}\right)\) | \(e\left(\frac{15}{166}\right)\) | \(e\left(\frac{64}{83}\right)\) | \(e\left(\frac{95}{166}\right)\) | \(e\left(\frac{139}{166}\right)\) | \(e\left(\frac{50}{83}\right)\) | \(e\left(\frac{165}{166}\right)\) | \(e\left(\frac{13}{166}\right)\) | \(e\left(\frac{81}{83}\right)\) |
\(\chi_{668}(37,\cdot)\) | 668.f | 166 | no | \(-1\) | \(1\) | \(e\left(\frac{45}{83}\right)\) | \(e\left(\frac{61}{166}\right)\) | \(e\left(\frac{30}{83}\right)\) | \(e\left(\frac{7}{83}\right)\) | \(e\left(\frac{24}{83}\right)\) | \(e\left(\frac{141}{166}\right)\) | \(e\left(\frac{151}{166}\right)\) | \(e\left(\frac{79}{166}\right)\) | \(e\left(\frac{26}{83}\right)\) | \(e\left(\frac{75}{83}\right)\) |
\(\chi_{668}(39,\cdot)\) | 668.h | 166 | yes | \(1\) | \(1\) | \(e\left(\frac{9}{166}\right)\) | \(e\left(\frac{31}{166}\right)\) | \(e\left(\frac{89}{166}\right)\) | \(e\left(\frac{9}{83}\right)\) | \(e\left(\frac{121}{166}\right)\) | \(e\left(\frac{39}{166}\right)\) | \(e\left(\frac{20}{83}\right)\) | \(e\left(\frac{149}{166}\right)\) | \(e\left(\frac{55}{166}\right)\) | \(e\left(\frac{49}{83}\right)\) |
\(\chi_{668}(41,\cdot)\) | 668.f | 166 | no | \(-1\) | \(1\) | \(e\left(\frac{77}{83}\right)\) | \(e\left(\frac{97}{166}\right)\) | \(e\left(\frac{79}{83}\right)\) | \(e\left(\frac{71}{83}\right)\) | \(e\left(\frac{30}{83}\right)\) | \(e\left(\frac{31}{166}\right)\) | \(e\left(\frac{85}{166}\right)\) | \(e\left(\frac{161}{166}\right)\) | \(e\left(\frac{74}{83}\right)\) | \(e\left(\frac{73}{83}\right)\) |
\(\chi_{668}(43,\cdot)\) | 668.h | 166 | yes | \(1\) | \(1\) | \(e\left(\frac{127}{166}\right)\) | \(e\left(\frac{87}{166}\right)\) | \(e\left(\frac{57}{166}\right)\) | \(e\left(\frac{44}{83}\right)\) | \(e\left(\frac{29}{166}\right)\) | \(e\left(\frac{163}{166}\right)\) | \(e\left(\frac{24}{83}\right)\) | \(e\left(\frac{129}{166}\right)\) | \(e\left(\frac{149}{166}\right)\) | \(e\left(\frac{9}{83}\right)\) |
\(\chi_{668}(45,\cdot)\) | 668.f | 166 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{83}\right)\) | \(e\left(\frac{23}{166}\right)\) | \(e\left(\frac{29}{83}\right)\) | \(e\left(\frac{4}{83}\right)\) | \(e\left(\frac{73}{83}\right)\) | \(e\left(\frac{45}{166}\right)\) | \(e\left(\frac{27}{166}\right)\) | \(e\left(\frac{57}{166}\right)\) | \(e\left(\frac{3}{83}\right)\) | \(e\left(\frac{31}{83}\right)\) |
\(\chi_{668}(47,\cdot)\) | 668.g | 166 | yes | \(-1\) | \(1\) | \(e\left(\frac{41}{166}\right)\) | \(e\left(\frac{66}{83}\right)\) | \(e\left(\frac{55}{166}\right)\) | \(e\left(\frac{41}{83}\right)\) | \(e\left(\frac{127}{166}\right)\) | \(e\left(\frac{75}{83}\right)\) | \(e\left(\frac{7}{166}\right)\) | \(e\left(\frac{12}{83}\right)\) | \(e\left(\frac{103}{166}\right)\) | \(e\left(\frac{48}{83}\right)\) |
\(\chi_{668}(49,\cdot)\) | 668.e | 83 | no | \(1\) | \(1\) | \(e\left(\frac{53}{83}\right)\) | \(e\left(\frac{35}{83}\right)\) | \(e\left(\frac{63}{83}\right)\) | \(e\left(\frac{23}{83}\right)\) | \(e\left(\frac{67}{83}\right)\) | \(e\left(\frac{36}{83}\right)\) | \(e\left(\frac{5}{83}\right)\) | \(e\left(\frac{29}{83}\right)\) | \(e\left(\frac{38}{83}\right)\) | \(e\left(\frac{33}{83}\right)\) |
\(\chi_{668}(51,\cdot)\) | 668.h | 166 | yes | \(1\) | \(1\) | \(e\left(\frac{123}{166}\right)\) | \(e\left(\frac{147}{166}\right)\) | \(e\left(\frac{165}{166}\right)\) | \(e\left(\frac{40}{83}\right)\) | \(e\left(\frac{49}{166}\right)\) | \(e\left(\frac{35}{166}\right)\) | \(e\left(\frac{52}{83}\right)\) | \(e\left(\frac{155}{166}\right)\) | \(e\left(\frac{143}{166}\right)\) | \(e\left(\frac{61}{83}\right)\) |
\(\chi_{668}(53,\cdot)\) | 668.f | 166 | no | \(-1\) | \(1\) | \(e\left(\frac{60}{83}\right)\) | \(e\left(\frac{109}{166}\right)\) | \(e\left(\frac{40}{83}\right)\) | \(e\left(\frac{37}{83}\right)\) | \(e\left(\frac{32}{83}\right)\) | \(e\left(\frac{105}{166}\right)\) | \(e\left(\frac{63}{166}\right)\) | \(e\left(\frac{133}{166}\right)\) | \(e\left(\frac{7}{83}\right)\) | \(e\left(\frac{17}{83}\right)\) |
\(\chi_{668}(55,\cdot)\) | 668.h | 166 | yes | \(1\) | \(1\) | \(e\left(\frac{153}{166}\right)\) | \(e\left(\frac{29}{166}\right)\) | \(e\left(\frac{19}{166}\right)\) | \(e\left(\frac{70}{83}\right)\) | \(e\left(\frac{65}{166}\right)\) | \(e\left(\frac{165}{166}\right)\) | \(e\left(\frac{8}{83}\right)\) | \(e\left(\frac{43}{166}\right)\) | \(e\left(\frac{105}{166}\right)\) | \(e\left(\frac{3}{83}\right)\) |
\(\chi_{668}(57,\cdot)\) | 668.e | 83 | no | \(1\) | \(1\) | \(e\left(\frac{6}{83}\right)\) | \(e\left(\frac{76}{83}\right)\) | \(e\left(\frac{4}{83}\right)\) | \(e\left(\frac{12}{83}\right)\) | \(e\left(\frac{53}{83}\right)\) | \(e\left(\frac{26}{83}\right)\) | \(e\left(\frac{82}{83}\right)\) | \(e\left(\frac{44}{83}\right)\) | \(e\left(\frac{9}{83}\right)\) | \(e\left(\frac{10}{83}\right)\) |
\(\chi_{668}(59,\cdot)\) | 668.h | 166 | yes | \(1\) | \(1\) | \(e\left(\frac{81}{166}\right)\) | \(e\left(\frac{113}{166}\right)\) | \(e\left(\frac{137}{166}\right)\) | \(e\left(\frac{81}{83}\right)\) | \(e\left(\frac{93}{166}\right)\) | \(e\left(\frac{19}{166}\right)\) | \(e\left(\frac{14}{83}\right)\) | \(e\left(\frac{13}{166}\right)\) | \(e\left(\frac{163}{166}\right)\) | \(e\left(\frac{26}{83}\right)\) |
\(\chi_{668}(61,\cdot)\) | 668.e | 83 | no | \(1\) | \(1\) | \(e\left(\frac{31}{83}\right)\) | \(e\left(\frac{33}{83}\right)\) | \(e\left(\frac{76}{83}\right)\) | \(e\left(\frac{62}{83}\right)\) | \(e\left(\frac{11}{83}\right)\) | \(e\left(\frac{79}{83}\right)\) | \(e\left(\frac{64}{83}\right)\) | \(e\left(\frac{6}{83}\right)\) | \(e\left(\frac{5}{83}\right)\) | \(e\left(\frac{24}{83}\right)\) |
\(\chi_{668}(63,\cdot)\) | 668.g | 166 | yes | \(-1\) | \(1\) | \(e\left(\frac{129}{166}\right)\) | \(e\left(\frac{70}{83}\right)\) | \(e\left(\frac{3}{166}\right)\) | \(e\left(\frac{46}{83}\right)\) | \(e\left(\frac{19}{166}\right)\) | \(e\left(\frac{72}{83}\right)\) | \(e\left(\frac{103}{166}\right)\) | \(e\left(\frac{58}{83}\right)\) | \(e\left(\frac{69}{166}\right)\) | \(e\left(\frac{66}{83}\right)\) |