sage: H = DirichletGroup(4504)
pari: g = idealstar(,4504,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 2248 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{562}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{4504}(1127,\cdot)$, $\chi_{4504}(2253,\cdot)$, $\chi_{4504}(2817,\cdot)$ |
First 32 of 2248 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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{4504}(1,\cdot)\) | 4504.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{4504}(3,\cdot)\) | 4504.l | 562 | yes | \(-1\) | \(1\) | \(e\left(\frac{231}{281}\right)\) | \(e\left(\frac{535}{562}\right)\) | \(e\left(\frac{55}{562}\right)\) | \(e\left(\frac{181}{281}\right)\) | \(e\left(\frac{128}{281}\right)\) | \(e\left(\frac{451}{562}\right)\) | \(e\left(\frac{435}{562}\right)\) | \(e\left(\frac{187}{281}\right)\) | \(e\left(\frac{107}{281}\right)\) | \(e\left(\frac{517}{562}\right)\) |
\(\chi_{4504}(5,\cdot)\) | 4504.m | 562 | yes | \(-1\) | \(1\) | \(e\left(\frac{535}{562}\right)\) | \(e\left(\frac{9}{281}\right)\) | \(e\left(\frac{169}{281}\right)\) | \(e\left(\frac{254}{281}\right)\) | \(e\left(\frac{485}{562}\right)\) | \(e\left(\frac{355}{562}\right)\) | \(e\left(\frac{553}{562}\right)\) | \(e\left(\frac{250}{281}\right)\) | \(e\left(\frac{513}{562}\right)\) | \(e\left(\frac{311}{562}\right)\) |
\(\chi_{4504}(7,\cdot)\) | 4504.n | 562 | no | \(-1\) | \(1\) | \(e\left(\frac{55}{562}\right)\) | \(e\left(\frac{169}{281}\right)\) | \(e\left(\frac{321}{562}\right)\) | \(e\left(\frac{55}{281}\right)\) | \(e\left(\frac{365}{562}\right)\) | \(e\left(\frac{164}{281}\right)\) | \(e\left(\frac{393}{562}\right)\) | \(e\left(\frac{136}{281}\right)\) | \(e\left(\frac{79}{562}\right)\) | \(e\left(\frac{188}{281}\right)\) |
\(\chi_{4504}(9,\cdot)\) | 4504.i | 281 | no | \(1\) | \(1\) | \(e\left(\frac{181}{281}\right)\) | \(e\left(\frac{254}{281}\right)\) | \(e\left(\frac{55}{281}\right)\) | \(e\left(\frac{81}{281}\right)\) | \(e\left(\frac{256}{281}\right)\) | \(e\left(\frac{170}{281}\right)\) | \(e\left(\frac{154}{281}\right)\) | \(e\left(\frac{93}{281}\right)\) | \(e\left(\frac{214}{281}\right)\) | \(e\left(\frac{236}{281}\right)\) |
\(\chi_{4504}(11,\cdot)\) | 4504.l | 562 | yes | \(-1\) | \(1\) | \(e\left(\frac{128}{281}\right)\) | \(e\left(\frac{485}{562}\right)\) | \(e\left(\frac{365}{562}\right)\) | \(e\left(\frac{256}{281}\right)\) | \(e\left(\frac{32}{281}\right)\) | \(e\left(\frac{183}{562}\right)\) | \(e\left(\frac{179}{562}\right)\) | \(e\left(\frac{117}{281}\right)\) | \(e\left(\frac{97}{281}\right)\) | \(e\left(\frac{59}{562}\right)\) |
\(\chi_{4504}(13,\cdot)\) | 4504.o | 562 | yes | \(1\) | \(1\) | \(e\left(\frac{451}{562}\right)\) | \(e\left(\frac{355}{562}\right)\) | \(e\left(\frac{164}{281}\right)\) | \(e\left(\frac{170}{281}\right)\) | \(e\left(\frac{183}{562}\right)\) | \(e\left(\frac{273}{562}\right)\) | \(e\left(\frac{122}{281}\right)\) | \(e\left(\frac{216}{281}\right)\) | \(e\left(\frac{423}{562}\right)\) | \(e\left(\frac{217}{562}\right)\) |
\(\chi_{4504}(15,\cdot)\) | 4504.p | 562 | no | \(1\) | \(1\) | \(e\left(\frac{435}{562}\right)\) | \(e\left(\frac{553}{562}\right)\) | \(e\left(\frac{393}{562}\right)\) | \(e\left(\frac{154}{281}\right)\) | \(e\left(\frac{179}{562}\right)\) | \(e\left(\frac{122}{281}\right)\) | \(e\left(\frac{213}{281}\right)\) | \(e\left(\frac{156}{281}\right)\) | \(e\left(\frac{165}{562}\right)\) | \(e\left(\frac{133}{281}\right)\) |
\(\chi_{4504}(17,\cdot)\) | 4504.i | 281 | no | \(1\) | \(1\) | \(e\left(\frac{187}{281}\right)\) | \(e\left(\frac{250}{281}\right)\) | \(e\left(\frac{136}{281}\right)\) | \(e\left(\frac{93}{281}\right)\) | \(e\left(\frac{117}{281}\right)\) | \(e\left(\frac{216}{281}\right)\) | \(e\left(\frac{156}{281}\right)\) | \(e\left(\frac{138}{281}\right)\) | \(e\left(\frac{100}{281}\right)\) | \(e\left(\frac{42}{281}\right)\) |
\(\chi_{4504}(19,\cdot)\) | 4504.l | 562 | yes | \(-1\) | \(1\) | \(e\left(\frac{107}{281}\right)\) | \(e\left(\frac{513}{562}\right)\) | \(e\left(\frac{79}{562}\right)\) | \(e\left(\frac{214}{281}\right)\) | \(e\left(\frac{97}{281}\right)\) | \(e\left(\frac{423}{562}\right)\) | \(e\left(\frac{165}{562}\right)\) | \(e\left(\frac{100}{281}\right)\) | \(e\left(\frac{215}{281}\right)\) | \(e\left(\frac{293}{562}\right)\) |
\(\chi_{4504}(21,\cdot)\) | 4504.o | 562 | yes | \(1\) | \(1\) | \(e\left(\frac{517}{562}\right)\) | \(e\left(\frac{311}{562}\right)\) | \(e\left(\frac{188}{281}\right)\) | \(e\left(\frac{236}{281}\right)\) | \(e\left(\frac{59}{562}\right)\) | \(e\left(\frac{217}{562}\right)\) | \(e\left(\frac{133}{281}\right)\) | \(e\left(\frac{42}{281}\right)\) | \(e\left(\frac{293}{562}\right)\) | \(e\left(\frac{331}{562}\right)\) |
\(\chi_{4504}(23,\cdot)\) | 4504.n | 562 | no | \(-1\) | \(1\) | \(e\left(\frac{171}{562}\right)\) | \(e\left(\frac{224}{281}\right)\) | \(e\left(\frac{201}{562}\right)\) | \(e\left(\frac{171}{281}\right)\) | \(e\left(\frac{113}{562}\right)\) | \(e\left(\frac{234}{281}\right)\) | \(e\left(\frac{57}{562}\right)\) | \(e\left(\frac{9}{281}\right)\) | \(e\left(\frac{123}{562}\right)\) | \(e\left(\frac{186}{281}\right)\) |
\(\chi_{4504}(25,\cdot)\) | 4504.i | 281 | no | \(1\) | \(1\) | \(e\left(\frac{254}{281}\right)\) | \(e\left(\frac{18}{281}\right)\) | \(e\left(\frac{57}{281}\right)\) | \(e\left(\frac{227}{281}\right)\) | \(e\left(\frac{204}{281}\right)\) | \(e\left(\frac{74}{281}\right)\) | \(e\left(\frac{272}{281}\right)\) | \(e\left(\frac{219}{281}\right)\) | \(e\left(\frac{232}{281}\right)\) | \(e\left(\frac{30}{281}\right)\) |
\(\chi_{4504}(27,\cdot)\) | 4504.l | 562 | yes | \(-1\) | \(1\) | \(e\left(\frac{131}{281}\right)\) | \(e\left(\frac{481}{562}\right)\) | \(e\left(\frac{165}{562}\right)\) | \(e\left(\frac{262}{281}\right)\) | \(e\left(\frac{103}{281}\right)\) | \(e\left(\frac{229}{562}\right)\) | \(e\left(\frac{181}{562}\right)\) | \(e\left(\frac{280}{281}\right)\) | \(e\left(\frac{40}{281}\right)\) | \(e\left(\frac{427}{562}\right)\) |
\(\chi_{4504}(29,\cdot)\) | 4504.m | 562 | yes | \(-1\) | \(1\) | \(e\left(\frac{465}{562}\right)\) | \(e\left(\frac{126}{281}\right)\) | \(e\left(\frac{118}{281}\right)\) | \(e\left(\frac{184}{281}\right)\) | \(e\left(\frac{327}{562}\right)\) | \(e\left(\frac{193}{562}\right)\) | \(e\left(\frac{155}{562}\right)\) | \(e\left(\frac{128}{281}\right)\) | \(e\left(\frac{157}{562}\right)\) | \(e\left(\frac{139}{562}\right)\) |
\(\chi_{4504}(31,\cdot)\) | 4504.p | 562 | no | \(1\) | \(1\) | \(e\left(\frac{205}{562}\right)\) | \(e\left(\frac{519}{562}\right)\) | \(e\left(\frac{379}{562}\right)\) | \(e\left(\frac{205}{281}\right)\) | \(e\left(\frac{543}{562}\right)\) | \(e\left(\frac{177}{281}\right)\) | \(e\left(\frac{81}{281}\right)\) | \(e\left(\frac{277}{281}\right)\) | \(e\left(\frac{39}{562}\right)\) | \(e\left(\frac{11}{281}\right)\) |
\(\chi_{4504}(33,\cdot)\) | 4504.i | 281 | no | \(1\) | \(1\) | \(e\left(\frac{78}{281}\right)\) | \(e\left(\frac{229}{281}\right)\) | \(e\left(\frac{210}{281}\right)\) | \(e\left(\frac{156}{281}\right)\) | \(e\left(\frac{160}{281}\right)\) | \(e\left(\frac{36}{281}\right)\) | \(e\left(\frac{26}{281}\right)\) | \(e\left(\frac{23}{281}\right)\) | \(e\left(\frac{204}{281}\right)\) | \(e\left(\frac{7}{281}\right)\) |
\(\chi_{4504}(35,\cdot)\) | 4504.j | 562 | yes | \(1\) | \(1\) | \(e\left(\frac{14}{281}\right)\) | \(e\left(\frac{178}{281}\right)\) | \(e\left(\frac{97}{562}\right)\) | \(e\left(\frac{28}{281}\right)\) | \(e\left(\frac{144}{281}\right)\) | \(e\left(\frac{121}{562}\right)\) | \(e\left(\frac{192}{281}\right)\) | \(e\left(\frac{105}{281}\right)\) | \(e\left(\frac{15}{281}\right)\) | \(e\left(\frac{125}{562}\right)\) |
\(\chi_{4504}(37,\cdot)\) | 4504.m | 562 | yes | \(-1\) | \(1\) | \(e\left(\frac{31}{562}\right)\) | \(e\left(\frac{177}{281}\right)\) | \(e\left(\frac{139}{281}\right)\) | \(e\left(\frac{31}{281}\right)\) | \(e\left(\frac{359}{562}\right)\) | \(e\left(\frac{425}{562}\right)\) | \(e\left(\frac{385}{562}\right)\) | \(e\left(\frac{46}{281}\right)\) | \(e\left(\frac{535}{562}\right)\) | \(e\left(\frac{309}{562}\right)\) |
\(\chi_{4504}(39,\cdot)\) | 4504.n | 562 | no | \(-1\) | \(1\) | \(e\left(\frac{351}{562}\right)\) | \(e\left(\frac{164}{281}\right)\) | \(e\left(\frac{383}{562}\right)\) | \(e\left(\frac{70}{281}\right)\) | \(e\left(\frac{439}{562}\right)\) | \(e\left(\frac{81}{281}\right)\) | \(e\left(\frac{117}{562}\right)\) | \(e\left(\frac{122}{281}\right)\) | \(e\left(\frac{75}{562}\right)\) | \(e\left(\frac{86}{281}\right)\) |
\(\chi_{4504}(41,\cdot)\) | 4504.k | 562 | no | \(-1\) | \(1\) | \(e\left(\frac{257}{281}\right)\) | \(e\left(\frac{313}{562}\right)\) | \(e\left(\frac{238}{281}\right)\) | \(e\left(\frac{233}{281}\right)\) | \(e\left(\frac{275}{281}\right)\) | \(e\left(\frac{97}{281}\right)\) | \(e\left(\frac{265}{562}\right)\) | \(e\left(\frac{101}{281}\right)\) | \(e\left(\frac{175}{281}\right)\) | \(e\left(\frac{214}{281}\right)\) |
\(\chi_{4504}(43,\cdot)\) | 4504.j | 562 | yes | \(1\) | \(1\) | \(e\left(\frac{164}{281}\right)\) | \(e\left(\frac{78}{281}\right)\) | \(e\left(\frac{213}{562}\right)\) | \(e\left(\frac{47}{281}\right)\) | \(e\left(\frac{41}{281}\right)\) | \(e\left(\frac{173}{562}\right)\) | \(e\left(\frac{242}{281}\right)\) | \(e\left(\frac{106}{281}\right)\) | \(e\left(\frac{256}{281}\right)\) | \(e\left(\frac{541}{562}\right)\) |
\(\chi_{4504}(45,\cdot)\) | 4504.m | 562 | yes | \(-1\) | \(1\) | \(e\left(\frac{335}{562}\right)\) | \(e\left(\frac{263}{281}\right)\) | \(e\left(\frac{224}{281}\right)\) | \(e\left(\frac{54}{281}\right)\) | \(e\left(\frac{435}{562}\right)\) | \(e\left(\frac{133}{562}\right)\) | \(e\left(\frac{299}{562}\right)\) | \(e\left(\frac{62}{281}\right)\) | \(e\left(\frac{379}{562}\right)\) | \(e\left(\frac{221}{562}\right)\) |
\(\chi_{4504}(47,\cdot)\) | 4504.n | 562 | no | \(-1\) | \(1\) | \(e\left(\frac{445}{562}\right)\) | \(e\left(\frac{39}{281}\right)\) | \(e\left(\frac{247}{562}\right)\) | \(e\left(\frac{164}{281}\right)\) | \(e\left(\frac{41}{562}\right)\) | \(e\left(\frac{254}{281}\right)\) | \(e\left(\frac{523}{562}\right)\) | \(e\left(\frac{53}{281}\right)\) | \(e\left(\frac{537}{562}\right)\) | \(e\left(\frac{65}{281}\right)\) |
\(\chi_{4504}(49,\cdot)\) | 4504.i | 281 | no | \(1\) | \(1\) | \(e\left(\frac{55}{281}\right)\) | \(e\left(\frac{57}{281}\right)\) | \(e\left(\frac{40}{281}\right)\) | \(e\left(\frac{110}{281}\right)\) | \(e\left(\frac{84}{281}\right)\) | \(e\left(\frac{47}{281}\right)\) | \(e\left(\frac{112}{281}\right)\) | \(e\left(\frac{272}{281}\right)\) | \(e\left(\frac{79}{281}\right)\) | \(e\left(\frac{95}{281}\right)\) |
\(\chi_{4504}(51,\cdot)\) | 4504.l | 562 | yes | \(-1\) | \(1\) | \(e\left(\frac{137}{281}\right)\) | \(e\left(\frac{473}{562}\right)\) | \(e\left(\frac{327}{562}\right)\) | \(e\left(\frac{274}{281}\right)\) | \(e\left(\frac{245}{281}\right)\) | \(e\left(\frac{321}{562}\right)\) | \(e\left(\frac{185}{562}\right)\) | \(e\left(\frac{44}{281}\right)\) | \(e\left(\frac{207}{281}\right)\) | \(e\left(\frac{39}{562}\right)\) |
\(\chi_{4504}(53,\cdot)\) | 4504.m | 562 | yes | \(-1\) | \(1\) | \(e\left(\frac{215}{562}\right)\) | \(e\left(\frac{22}{281}\right)\) | \(e\left(\frac{257}{281}\right)\) | \(e\left(\frac{215}{281}\right)\) | \(e\left(\frac{405}{562}\right)\) | \(e\left(\frac{337}{562}\right)\) | \(e\left(\frac{259}{562}\right)\) | \(e\left(\frac{174}{281}\right)\) | \(e\left(\frac{411}{562}\right)\) | \(e\left(\frac{167}{562}\right)\) |
\(\chi_{4504}(55,\cdot)\) | 4504.p | 562 | no | \(1\) | \(1\) | \(e\left(\frac{229}{562}\right)\) | \(e\left(\frac{503}{562}\right)\) | \(e\left(\frac{141}{562}\right)\) | \(e\left(\frac{229}{281}\right)\) | \(e\left(\frac{549}{562}\right)\) | \(e\left(\frac{269}{281}\right)\) | \(e\left(\frac{85}{281}\right)\) | \(e\left(\frac{86}{281}\right)\) | \(e\left(\frac{145}{562}\right)\) | \(e\left(\frac{185}{281}\right)\) |
\(\chi_{4504}(57,\cdot)\) | 4504.i | 281 | no | \(1\) | \(1\) | \(e\left(\frac{57}{281}\right)\) | \(e\left(\frac{243}{281}\right)\) | \(e\left(\frac{67}{281}\right)\) | \(e\left(\frac{114}{281}\right)\) | \(e\left(\frac{225}{281}\right)\) | \(e\left(\frac{156}{281}\right)\) | \(e\left(\frac{19}{281}\right)\) | \(e\left(\frac{6}{281}\right)\) | \(e\left(\frac{41}{281}\right)\) | \(e\left(\frac{124}{281}\right)\) |
\(\chi_{4504}(59,\cdot)\) | 4504.l | 562 | yes | \(-1\) | \(1\) | \(e\left(\frac{20}{281}\right)\) | \(e\left(\frac{67}{562}\right)\) | \(e\left(\frac{259}{562}\right)\) | \(e\left(\frac{40}{281}\right)\) | \(e\left(\frac{5}{281}\right)\) | \(e\left(\frac{213}{562}\right)\) | \(e\left(\frac{107}{562}\right)\) | \(e\left(\frac{150}{281}\right)\) | \(e\left(\frac{182}{281}\right)\) | \(e\left(\frac{299}{562}\right)\) |
\(\chi_{4504}(61,\cdot)\) | 4504.o | 562 | yes | \(1\) | \(1\) | \(e\left(\frac{223}{562}\right)\) | \(e\left(\frac{507}{562}\right)\) | \(e\left(\frac{30}{281}\right)\) | \(e\left(\frac{223}{281}\right)\) | \(e\left(\frac{407}{562}\right)\) | \(e\left(\frac{211}{562}\right)\) | \(e\left(\frac{84}{281}\right)\) | \(e\left(\frac{204}{281}\right)\) | \(e\left(\frac{259}{562}\right)\) | \(e\left(\frac{283}{562}\right)\) |
\(\chi_{4504}(63,\cdot)\) | 4504.n | 562 | no | \(-1\) | \(1\) | \(e\left(\frac{417}{562}\right)\) | \(e\left(\frac{142}{281}\right)\) | \(e\left(\frac{431}{562}\right)\) | \(e\left(\frac{136}{281}\right)\) | \(e\left(\frac{315}{562}\right)\) | \(e\left(\frac{53}{281}\right)\) | \(e\left(\frac{139}{562}\right)\) | \(e\left(\frac{229}{281}\right)\) | \(e\left(\frac{507}{562}\right)\) | \(e\left(\frac{143}{281}\right)\) |