sage: H = DirichletGroup(2883)
pari: g = idealstar(,2883,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 1860 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{2}\times C_{930}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{2883}(962,\cdot)$, $\chi_{2883}(964,\cdot)$ |
First 32 of 1860 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{2883}(1,\cdot)\) | 2883.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{2883}(2,\cdot)\) | 2883.z | 310 | yes | \(-1\) | \(1\) | \(e\left(\frac{57}{310}\right)\) | \(e\left(\frac{57}{155}\right)\) | \(e\left(\frac{45}{62}\right)\) | \(e\left(\frac{77}{155}\right)\) | \(e\left(\frac{171}{310}\right)\) | \(e\left(\frac{141}{155}\right)\) | \(e\left(\frac{69}{310}\right)\) | \(e\left(\frac{9}{155}\right)\) | \(e\left(\frac{211}{310}\right)\) | \(e\left(\frac{114}{155}\right)\) |
| \(\chi_{2883}(4,\cdot)\) | 2883.v | 155 | no | \(1\) | \(1\) | \(e\left(\frac{57}{155}\right)\) | \(e\left(\frac{114}{155}\right)\) | \(e\left(\frac{14}{31}\right)\) | \(e\left(\frac{154}{155}\right)\) | \(e\left(\frac{16}{155}\right)\) | \(e\left(\frac{127}{155}\right)\) | \(e\left(\frac{69}{155}\right)\) | \(e\left(\frac{18}{155}\right)\) | \(e\left(\frac{56}{155}\right)\) | \(e\left(\frac{73}{155}\right)\) |
| \(\chi_{2883}(5,\cdot)\) | 2883.x | 186 | yes | \(-1\) | \(1\) | \(e\left(\frac{45}{62}\right)\) | \(e\left(\frac{14}{31}\right)\) | \(e\left(\frac{125}{186}\right)\) | \(e\left(\frac{29}{93}\right)\) | \(e\left(\frac{11}{62}\right)\) | \(e\left(\frac{37}{93}\right)\) | \(e\left(\frac{59}{186}\right)\) | \(e\left(\frac{67}{93}\right)\) | \(e\left(\frac{7}{186}\right)\) | \(e\left(\frac{28}{31}\right)\) |
| \(\chi_{2883}(7,\cdot)\) | 2883.bc | 465 | no | \(1\) | \(1\) | \(e\left(\frac{77}{155}\right)\) | \(e\left(\frac{154}{155}\right)\) | \(e\left(\frac{29}{93}\right)\) | \(e\left(\frac{257}{465}\right)\) | \(e\left(\frac{76}{155}\right)\) | \(e\left(\frac{376}{465}\right)\) | \(e\left(\frac{247}{465}\right)\) | \(e\left(\frac{334}{465}\right)\) | \(e\left(\frac{23}{465}\right)\) | \(e\left(\frac{153}{155}\right)\) |
| \(\chi_{2883}(8,\cdot)\) | 2883.z | 310 | yes | \(-1\) | \(1\) | \(e\left(\frac{171}{310}\right)\) | \(e\left(\frac{16}{155}\right)\) | \(e\left(\frac{11}{62}\right)\) | \(e\left(\frac{76}{155}\right)\) | \(e\left(\frac{203}{310}\right)\) | \(e\left(\frac{113}{155}\right)\) | \(e\left(\frac{207}{310}\right)\) | \(e\left(\frac{27}{155}\right)\) | \(e\left(\frac{13}{310}\right)\) | \(e\left(\frac{32}{155}\right)\) |
| \(\chi_{2883}(10,\cdot)\) | 2883.bc | 465 | no | \(1\) | \(1\) | \(e\left(\frac{141}{155}\right)\) | \(e\left(\frac{127}{155}\right)\) | \(e\left(\frac{37}{93}\right)\) | \(e\left(\frac{376}{465}\right)\) | \(e\left(\frac{113}{155}\right)\) | \(e\left(\frac{143}{465}\right)\) | \(e\left(\frac{251}{465}\right)\) | \(e\left(\frac{362}{465}\right)\) | \(e\left(\frac{334}{465}\right)\) | \(e\left(\frac{99}{155}\right)\) |
| \(\chi_{2883}(11,\cdot)\) | 2883.bd | 930 | yes | \(1\) | \(1\) | \(e\left(\frac{69}{310}\right)\) | \(e\left(\frac{69}{155}\right)\) | \(e\left(\frac{59}{186}\right)\) | \(e\left(\frac{247}{465}\right)\) | \(e\left(\frac{207}{310}\right)\) | \(e\left(\frac{251}{465}\right)\) | \(e\left(\frac{317}{465}\right)\) | \(e\left(\frac{253}{930}\right)\) | \(e\left(\frac{701}{930}\right)\) | \(e\left(\frac{138}{155}\right)\) |
| \(\chi_{2883}(13,\cdot)\) | 2883.bf | 930 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{155}\right)\) | \(e\left(\frac{18}{155}\right)\) | \(e\left(\frac{67}{93}\right)\) | \(e\left(\frac{334}{465}\right)\) | \(e\left(\frac{27}{155}\right)\) | \(e\left(\frac{362}{465}\right)\) | \(e\left(\frac{253}{930}\right)\) | \(e\left(\frac{841}{930}\right)\) | \(e\left(\frac{361}{465}\right)\) | \(e\left(\frac{36}{155}\right)\) |
| \(\chi_{2883}(14,\cdot)\) | 2883.be | 930 | yes | \(-1\) | \(1\) | \(e\left(\frac{211}{310}\right)\) | \(e\left(\frac{56}{155}\right)\) | \(e\left(\frac{7}{186}\right)\) | \(e\left(\frac{23}{465}\right)\) | \(e\left(\frac{13}{310}\right)\) | \(e\left(\frac{334}{465}\right)\) | \(e\left(\frac{701}{930}\right)\) | \(e\left(\frac{361}{465}\right)\) | \(e\left(\frac{679}{930}\right)\) | \(e\left(\frac{112}{155}\right)\) |
| \(\chi_{2883}(16,\cdot)\) | 2883.v | 155 | no | \(1\) | \(1\) | \(e\left(\frac{114}{155}\right)\) | \(e\left(\frac{73}{155}\right)\) | \(e\left(\frac{28}{31}\right)\) | \(e\left(\frac{153}{155}\right)\) | \(e\left(\frac{32}{155}\right)\) | \(e\left(\frac{99}{155}\right)\) | \(e\left(\frac{138}{155}\right)\) | \(e\left(\frac{36}{155}\right)\) | \(e\left(\frac{112}{155}\right)\) | \(e\left(\frac{146}{155}\right)\) |
| \(\chi_{2883}(17,\cdot)\) | 2883.bd | 930 | yes | \(1\) | \(1\) | \(e\left(\frac{91}{310}\right)\) | \(e\left(\frac{91}{155}\right)\) | \(e\left(\frac{85}{186}\right)\) | \(e\left(\frac{173}{465}\right)\) | \(e\left(\frac{273}{310}\right)\) | \(e\left(\frac{349}{465}\right)\) | \(e\left(\frac{463}{465}\right)\) | \(e\left(\frac{437}{930}\right)\) | \(e\left(\frac{619}{930}\right)\) | \(e\left(\frac{27}{155}\right)\) |
| \(\chi_{2883}(19,\cdot)\) | 2883.bc | 465 | no | \(1\) | \(1\) | \(e\left(\frac{91}{155}\right)\) | \(e\left(\frac{27}{155}\right)\) | \(e\left(\frac{23}{93}\right)\) | \(e\left(\frac{191}{465}\right)\) | \(e\left(\frac{118}{155}\right)\) | \(e\left(\frac{388}{465}\right)\) | \(e\left(\frac{151}{465}\right)\) | \(e\left(\frac{127}{465}\right)\) | \(e\left(\frac{464}{465}\right)\) | \(e\left(\frac{54}{155}\right)\) |
| \(\chi_{2883}(20,\cdot)\) | 2883.be | 930 | yes | \(-1\) | \(1\) | \(e\left(\frac{29}{310}\right)\) | \(e\left(\frac{29}{155}\right)\) | \(e\left(\frac{23}{186}\right)\) | \(e\left(\frac{142}{465}\right)\) | \(e\left(\frac{87}{310}\right)\) | \(e\left(\frac{101}{465}\right)\) | \(e\left(\frac{709}{930}\right)\) | \(e\left(\frac{389}{465}\right)\) | \(e\left(\frac{371}{930}\right)\) | \(e\left(\frac{58}{155}\right)\) |
| \(\chi_{2883}(22,\cdot)\) | 2883.bf | 930 | no | \(-1\) | \(1\) | \(e\left(\frac{63}{155}\right)\) | \(e\left(\frac{126}{155}\right)\) | \(e\left(\frac{4}{93}\right)\) | \(e\left(\frac{13}{465}\right)\) | \(e\left(\frac{34}{155}\right)\) | \(e\left(\frac{209}{465}\right)\) | \(e\left(\frac{841}{930}\right)\) | \(e\left(\frac{307}{930}\right)\) | \(e\left(\frac{202}{465}\right)\) | \(e\left(\frac{97}{155}\right)\) |
| \(\chi_{2883}(23,\cdot)\) | 2883.ba | 310 | yes | \(1\) | \(1\) | \(e\left(\frac{271}{310}\right)\) | \(e\left(\frac{116}{155}\right)\) | \(e\left(\frac{41}{62}\right)\) | \(e\left(\frac{86}{155}\right)\) | \(e\left(\frac{193}{310}\right)\) | \(e\left(\frac{83}{155}\right)\) | \(e\left(\frac{111}{155}\right)\) | \(e\left(\frac{159}{310}\right)\) | \(e\left(\frac{133}{310}\right)\) | \(e\left(\frac{77}{155}\right)\) |
| \(\chi_{2883}(25,\cdot)\) | 2883.u | 93 | no | \(1\) | \(1\) | \(e\left(\frac{14}{31}\right)\) | \(e\left(\frac{28}{31}\right)\) | \(e\left(\frac{32}{93}\right)\) | \(e\left(\frac{58}{93}\right)\) | \(e\left(\frac{11}{31}\right)\) | \(e\left(\frac{74}{93}\right)\) | \(e\left(\frac{59}{93}\right)\) | \(e\left(\frac{41}{93}\right)\) | \(e\left(\frac{7}{93}\right)\) | \(e\left(\frac{25}{31}\right)\) |
| \(\chi_{2883}(26,\cdot)\) | 2883.y | 186 | yes | \(1\) | \(1\) | \(e\left(\frac{15}{62}\right)\) | \(e\left(\frac{15}{31}\right)\) | \(e\left(\frac{83}{186}\right)\) | \(e\left(\frac{20}{93}\right)\) | \(e\left(\frac{45}{62}\right)\) | \(e\left(\frac{64}{93}\right)\) | \(e\left(\frac{46}{93}\right)\) | \(e\left(\frac{179}{186}\right)\) | \(e\left(\frac{85}{186}\right)\) | \(e\left(\frac{30}{31}\right)\) |
| \(\chi_{2883}(28,\cdot)\) | 2883.bc | 465 | no | \(1\) | \(1\) | \(e\left(\frac{134}{155}\right)\) | \(e\left(\frac{113}{155}\right)\) | \(e\left(\frac{71}{93}\right)\) | \(e\left(\frac{254}{465}\right)\) | \(e\left(\frac{92}{155}\right)\) | \(e\left(\frac{292}{465}\right)\) | \(e\left(\frac{454}{465}\right)\) | \(e\left(\frac{388}{465}\right)\) | \(e\left(\frac{191}{465}\right)\) | \(e\left(\frac{71}{155}\right)\) |
| \(\chi_{2883}(29,\cdot)\) | 2883.ba | 310 | yes | \(1\) | \(1\) | \(e\left(\frac{147}{310}\right)\) | \(e\left(\frac{147}{155}\right)\) | \(e\left(\frac{41}{62}\right)\) | \(e\left(\frac{117}{155}\right)\) | \(e\left(\frac{131}{310}\right)\) | \(e\left(\frac{21}{155}\right)\) | \(e\left(\frac{142}{155}\right)\) | \(e\left(\frac{283}{310}\right)\) | \(e\left(\frac{71}{310}\right)\) | \(e\left(\frac{139}{155}\right)\) |
| \(\chi_{2883}(32,\cdot)\) | 2883.t | 62 | yes | \(-1\) | \(1\) | \(e\left(\frac{57}{62}\right)\) | \(e\left(\frac{26}{31}\right)\) | \(e\left(\frac{39}{62}\right)\) | \(e\left(\frac{15}{31}\right)\) | \(e\left(\frac{47}{62}\right)\) | \(e\left(\frac{17}{31}\right)\) | \(e\left(\frac{7}{62}\right)\) | \(e\left(\frac{9}{31}\right)\) | \(e\left(\frac{25}{62}\right)\) | \(e\left(\frac{21}{31}\right)\) |
| \(\chi_{2883}(34,\cdot)\) | 2883.bf | 930 | no | \(-1\) | \(1\) | \(e\left(\frac{74}{155}\right)\) | \(e\left(\frac{148}{155}\right)\) | \(e\left(\frac{17}{93}\right)\) | \(e\left(\frac{404}{465}\right)\) | \(e\left(\frac{67}{155}\right)\) | \(e\left(\frac{307}{465}\right)\) | \(e\left(\frac{203}{930}\right)\) | \(e\left(\frac{491}{930}\right)\) | \(e\left(\frac{161}{465}\right)\) | \(e\left(\frac{141}{155}\right)\) |
| \(\chi_{2883}(35,\cdot)\) | 2883.z | 310 | yes | \(-1\) | \(1\) | \(e\left(\frac{69}{310}\right)\) | \(e\left(\frac{69}{155}\right)\) | \(e\left(\frac{61}{62}\right)\) | \(e\left(\frac{134}{155}\right)\) | \(e\left(\frac{207}{310}\right)\) | \(e\left(\frac{32}{155}\right)\) | \(e\left(\frac{263}{310}\right)\) | \(e\left(\frac{68}{155}\right)\) | \(e\left(\frac{27}{310}\right)\) | \(e\left(\frac{138}{155}\right)\) |
| \(\chi_{2883}(37,\cdot)\) | 2883.w | 186 | no | \(-1\) | \(1\) | \(e\left(\frac{8}{31}\right)\) | \(e\left(\frac{16}{31}\right)\) | \(e\left(\frac{5}{93}\right)\) | \(e\left(\frac{73}{93}\right)\) | \(e\left(\frac{24}{31}\right)\) | \(e\left(\frac{29}{93}\right)\) | \(e\left(\frac{1}{186}\right)\) | \(e\left(\frac{7}{186}\right)\) | \(e\left(\frac{4}{93}\right)\) | \(e\left(\frac{1}{31}\right)\) |
| \(\chi_{2883}(38,\cdot)\) | 2883.be | 930 | yes | \(-1\) | \(1\) | \(e\left(\frac{239}{310}\right)\) | \(e\left(\frac{84}{155}\right)\) | \(e\left(\frac{181}{186}\right)\) | \(e\left(\frac{422}{465}\right)\) | \(e\left(\frac{97}{310}\right)\) | \(e\left(\frac{346}{465}\right)\) | \(e\left(\frac{509}{930}\right)\) | \(e\left(\frac{154}{465}\right)\) | \(e\left(\frac{631}{930}\right)\) | \(e\left(\frac{13}{155}\right)\) |
| \(\chi_{2883}(40,\cdot)\) | 2883.bc | 465 | no | \(1\) | \(1\) | \(e\left(\frac{43}{155}\right)\) | \(e\left(\frac{86}{155}\right)\) | \(e\left(\frac{79}{93}\right)\) | \(e\left(\frac{373}{465}\right)\) | \(e\left(\frac{129}{155}\right)\) | \(e\left(\frac{59}{465}\right)\) | \(e\left(\frac{458}{465}\right)\) | \(e\left(\frac{416}{465}\right)\) | \(e\left(\frac{37}{465}\right)\) | \(e\left(\frac{17}{155}\right)\) |
| \(\chi_{2883}(41,\cdot)\) | 2883.be | 930 | yes | \(-1\) | \(1\) | \(e\left(\frac{47}{310}\right)\) | \(e\left(\frac{47}{155}\right)\) | \(e\left(\frac{95}{186}\right)\) | \(e\left(\frac{166}{465}\right)\) | \(e\left(\frac{141}{310}\right)\) | \(e\left(\frac{308}{465}\right)\) | \(e\left(\frac{187}{930}\right)\) | \(e\left(\frac{422}{465}\right)\) | \(e\left(\frac{473}{930}\right)\) | \(e\left(\frac{94}{155}\right)\) |
| \(\chi_{2883}(43,\cdot)\) | 2883.bf | 930 | no | \(-1\) | \(1\) | \(e\left(\frac{76}{155}\right)\) | \(e\left(\frac{152}{155}\right)\) | \(e\left(\frac{56}{93}\right)\) | \(e\left(\frac{461}{465}\right)\) | \(e\left(\frac{73}{155}\right)\) | \(e\left(\frac{43}{465}\right)\) | \(e\left(\frac{707}{930}\right)\) | \(e\left(\frac{299}{930}\right)\) | \(e\left(\frac{224}{465}\right)\) | \(e\left(\frac{149}{155}\right)\) |
| \(\chi_{2883}(44,\cdot)\) | 2883.bd | 930 | yes | \(1\) | \(1\) | \(e\left(\frac{183}{310}\right)\) | \(e\left(\frac{28}{155}\right)\) | \(e\left(\frac{143}{186}\right)\) | \(e\left(\frac{244}{465}\right)\) | \(e\left(\frac{239}{310}\right)\) | \(e\left(\frac{167}{465}\right)\) | \(e\left(\frac{59}{465}\right)\) | \(e\left(\frac{361}{930}\right)\) | \(e\left(\frac{107}{930}\right)\) | \(e\left(\frac{56}{155}\right)\) |
| \(\chi_{2883}(46,\cdot)\) | 2883.bb | 310 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{155}\right)\) | \(e\left(\frac{18}{155}\right)\) | \(e\left(\frac{12}{31}\right)\) | \(e\left(\frac{8}{155}\right)\) | \(e\left(\frac{27}{155}\right)\) | \(e\left(\frac{69}{155}\right)\) | \(e\left(\frac{291}{310}\right)\) | \(e\left(\frac{177}{310}\right)\) | \(e\left(\frac{17}{155}\right)\) | \(e\left(\frac{36}{155}\right)\) |
| \(\chi_{2883}(47,\cdot)\) | 2883.z | 310 | yes | \(-1\) | \(1\) | \(e\left(\frac{23}{310}\right)\) | \(e\left(\frac{23}{155}\right)\) | \(e\left(\frac{41}{62}\right)\) | \(e\left(\frac{148}{155}\right)\) | \(e\left(\frac{69}{310}\right)\) | \(e\left(\frac{114}{155}\right)\) | \(e\left(\frac{191}{310}\right)\) | \(e\left(\frac{126}{155}\right)\) | \(e\left(\frac{9}{310}\right)\) | \(e\left(\frac{46}{155}\right)\) |
| \(\chi_{2883}(49,\cdot)\) | 2883.bc | 465 | no | \(1\) | \(1\) | \(e\left(\frac{154}{155}\right)\) | \(e\left(\frac{153}{155}\right)\) | \(e\left(\frac{58}{93}\right)\) | \(e\left(\frac{49}{465}\right)\) | \(e\left(\frac{152}{155}\right)\) | \(e\left(\frac{287}{465}\right)\) | \(e\left(\frac{29}{465}\right)\) | \(e\left(\frac{203}{465}\right)\) | \(e\left(\frac{46}{465}\right)\) | \(e\left(\frac{151}{155}\right)\) |