# Properties

 Modulus $5241$ Structure $$C_{1746}\times C_{2}$$ Order $3492$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(5241)

pari: g = idealstar(,5241,2)

## Character group

 sage: G.order()  pari: g.no Order = 3492 sage: H.invariants()  pari: g.cyc Structure = $$C_{1746}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{5241}(1748,\cdot)$, $\chi_{5241}(3496,\cdot)$

## First 32 of 3492 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$7$$ $$8$$ $$10$$ $$11$$ $$13$$ $$14$$ $$16$$
$$\chi_{5241}(1,\cdot)$$ 5241.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{5241}(2,\cdot)$$ 5241.x 1746 yes $$1$$ $$1$$ $$e\left(\frac{437}{873}\right)$$ $$e\left(\frac{1}{873}\right)$$ $$e\left(\frac{415}{873}\right)$$ $$e\left(\frac{307}{1746}\right)$$ $$e\left(\frac{146}{291}\right)$$ $$e\left(\frac{284}{291}\right)$$ $$e\left(\frac{70}{291}\right)$$ $$e\left(\frac{1255}{1746}\right)$$ $$e\left(\frac{1181}{1746}\right)$$ $$e\left(\frac{2}{873}\right)$$
$$\chi_{5241}(4,\cdot)$$ 5241.u 873 no $$1$$ $$1$$ $$e\left(\frac{1}{873}\right)$$ $$e\left(\frac{2}{873}\right)$$ $$e\left(\frac{830}{873}\right)$$ $$e\left(\frac{307}{873}\right)$$ $$e\left(\frac{1}{291}\right)$$ $$e\left(\frac{277}{291}\right)$$ $$e\left(\frac{140}{291}\right)$$ $$e\left(\frac{382}{873}\right)$$ $$e\left(\frac{308}{873}\right)$$ $$e\left(\frac{4}{873}\right)$$
$$\chi_{5241}(5,\cdot)$$ 5241.x 1746 yes $$1$$ $$1$$ $$e\left(\frac{415}{873}\right)$$ $$e\left(\frac{830}{873}\right)$$ $$e\left(\frac{488}{873}\right)$$ $$e\left(\frac{767}{1746}\right)$$ $$e\left(\frac{124}{291}\right)$$ $$e\left(\frac{10}{291}\right)$$ $$e\left(\frac{191}{291}\right)$$ $$e\left(\frac{161}{1746}\right)$$ $$e\left(\frac{1597}{1746}\right)$$ $$e\left(\frac{787}{873}\right)$$
$$\chi_{5241}(7,\cdot)$$ 5241.v 1746 no $$-1$$ $$1$$ $$e\left(\frac{307}{1746}\right)$$ $$e\left(\frac{307}{873}\right)$$ $$e\left(\frac{767}{1746}\right)$$ $$e\left(\frac{1711}{1746}\right)$$ $$e\left(\frac{307}{582}\right)$$ $$e\left(\frac{179}{291}\right)$$ $$e\left(\frac{203}{582}\right)$$ $$e\left(\frac{1165}{1746}\right)$$ $$e\left(\frac{136}{873}\right)$$ $$e\left(\frac{614}{873}\right)$$
$$\chi_{5241}(8,\cdot)$$ 5241.t 582 yes $$1$$ $$1$$ $$e\left(\frac{146}{291}\right)$$ $$e\left(\frac{1}{291}\right)$$ $$e\left(\frac{124}{291}\right)$$ $$e\left(\frac{307}{582}\right)$$ $$e\left(\frac{49}{97}\right)$$ $$e\left(\frac{90}{97}\right)$$ $$e\left(\frac{70}{97}\right)$$ $$e\left(\frac{91}{582}\right)$$ $$e\left(\frac{17}{582}\right)$$ $$e\left(\frac{2}{291}\right)$$
$$\chi_{5241}(10,\cdot)$$ 5241.q 291 no $$1$$ $$1$$ $$e\left(\frac{284}{291}\right)$$ $$e\left(\frac{277}{291}\right)$$ $$e\left(\frac{10}{291}\right)$$ $$e\left(\frac{179}{291}\right)$$ $$e\left(\frac{90}{97}\right)$$ $$e\left(\frac{1}{97}\right)$$ $$e\left(\frac{87}{97}\right)$$ $$e\left(\frac{236}{291}\right)$$ $$e\left(\frac{172}{291}\right)$$ $$e\left(\frac{263}{291}\right)$$
$$\chi_{5241}(11,\cdot)$$ 5241.t 582 yes $$1$$ $$1$$ $$e\left(\frac{70}{291}\right)$$ $$e\left(\frac{140}{291}\right)$$ $$e\left(\frac{191}{291}\right)$$ $$e\left(\frac{203}{582}\right)$$ $$e\left(\frac{70}{97}\right)$$ $$e\left(\frac{87}{97}\right)$$ $$e\left(\frac{3}{97}\right)$$ $$e\left(\frac{227}{582}\right)$$ $$e\left(\frac{343}{582}\right)$$ $$e\left(\frac{280}{291}\right)$$
$$\chi_{5241}(13,\cdot)$$ 5241.v 1746 no $$-1$$ $$1$$ $$e\left(\frac{1255}{1746}\right)$$ $$e\left(\frac{382}{873}\right)$$ $$e\left(\frac{161}{1746}\right)$$ $$e\left(\frac{1165}{1746}\right)$$ $$e\left(\frac{91}{582}\right)$$ $$e\left(\frac{236}{291}\right)$$ $$e\left(\frac{227}{582}\right)$$ $$e\left(\frac{133}{1746}\right)$$ $$e\left(\frac{337}{873}\right)$$ $$e\left(\frac{764}{873}\right)$$
$$\chi_{5241}(14,\cdot)$$ 5241.w 1746 yes $$-1$$ $$1$$ $$e\left(\frac{1181}{1746}\right)$$ $$e\left(\frac{308}{873}\right)$$ $$e\left(\frac{1597}{1746}\right)$$ $$e\left(\frac{136}{873}\right)$$ $$e\left(\frac{17}{582}\right)$$ $$e\left(\frac{172}{291}\right)$$ $$e\left(\frac{343}{582}\right)$$ $$e\left(\frac{337}{873}\right)$$ $$e\left(\frac{1453}{1746}\right)$$ $$e\left(\frac{616}{873}\right)$$
$$\chi_{5241}(16,\cdot)$$ 5241.u 873 no $$1$$ $$1$$ $$e\left(\frac{2}{873}\right)$$ $$e\left(\frac{4}{873}\right)$$ $$e\left(\frac{787}{873}\right)$$ $$e\left(\frac{614}{873}\right)$$ $$e\left(\frac{2}{291}\right)$$ $$e\left(\frac{263}{291}\right)$$ $$e\left(\frac{280}{291}\right)$$ $$e\left(\frac{764}{873}\right)$$ $$e\left(\frac{616}{873}\right)$$ $$e\left(\frac{8}{873}\right)$$
$$\chi_{5241}(17,\cdot)$$ 5241.w 1746 yes $$-1$$ $$1$$ $$e\left(\frac{101}{1746}\right)$$ $$e\left(\frac{101}{873}\right)$$ $$e\left(\frac{895}{1746}\right)$$ $$e\left(\frac{226}{873}\right)$$ $$e\left(\frac{101}{582}\right)$$ $$e\left(\frac{166}{291}\right)$$ $$e\left(\frac{463}{582}\right)$$ $$e\left(\frac{85}{873}\right)$$ $$e\left(\frac{553}{1746}\right)$$ $$e\left(\frac{202}{873}\right)$$
$$\chi_{5241}(19,\cdot)$$ 5241.q 291 no $$1$$ $$1$$ $$e\left(\frac{236}{291}\right)$$ $$e\left(\frac{181}{291}\right)$$ $$e\left(\frac{37}{291}\right)$$ $$e\left(\frac{284}{291}\right)$$ $$e\left(\frac{42}{97}\right)$$ $$e\left(\frac{91}{97}\right)$$ $$e\left(\frac{60}{97}\right)$$ $$e\left(\frac{233}{291}\right)$$ $$e\left(\frac{229}{291}\right)$$ $$e\left(\frac{71}{291}\right)$$
$$\chi_{5241}(20,\cdot)$$ 5241.x 1746 yes $$1$$ $$1$$ $$e\left(\frac{416}{873}\right)$$ $$e\left(\frac{832}{873}\right)$$ $$e\left(\frac{445}{873}\right)$$ $$e\left(\frac{1381}{1746}\right)$$ $$e\left(\frac{125}{291}\right)$$ $$e\left(\frac{287}{291}\right)$$ $$e\left(\frac{40}{291}\right)$$ $$e\left(\frac{925}{1746}\right)$$ $$e\left(\frac{467}{1746}\right)$$ $$e\left(\frac{791}{873}\right)$$
$$\chi_{5241}(22,\cdot)$$ 5241.u 873 no $$1$$ $$1$$ $$e\left(\frac{647}{873}\right)$$ $$e\left(\frac{421}{873}\right)$$ $$e\left(\frac{115}{873}\right)$$ $$e\left(\frac{458}{873}\right)$$ $$e\left(\frac{65}{291}\right)$$ $$e\left(\frac{254}{291}\right)$$ $$e\left(\frac{79}{291}\right)$$ $$e\left(\frac{95}{873}\right)$$ $$e\left(\frac{232}{873}\right)$$ $$e\left(\frac{842}{873}\right)$$
$$\chi_{5241}(23,\cdot)$$ 5241.w 1746 yes $$-1$$ $$1$$ $$e\left(\frac{1201}{1746}\right)$$ $$e\left(\frac{328}{873}\right)$$ $$e\left(\frac{737}{1746}\right)$$ $$e\left(\frac{587}{873}\right)$$ $$e\left(\frac{37}{582}\right)$$ $$e\left(\frac{32}{291}\right)$$ $$e\left(\frac{233}{582}\right)$$ $$e\left(\frac{665}{873}\right)$$ $$e\left(\frac{629}{1746}\right)$$ $$e\left(\frac{656}{873}\right)$$
$$\chi_{5241}(25,\cdot)$$ 5241.u 873 no $$1$$ $$1$$ $$e\left(\frac{830}{873}\right)$$ $$e\left(\frac{787}{873}\right)$$ $$e\left(\frac{103}{873}\right)$$ $$e\left(\frac{767}{873}\right)$$ $$e\left(\frac{248}{291}\right)$$ $$e\left(\frac{20}{291}\right)$$ $$e\left(\frac{91}{291}\right)$$ $$e\left(\frac{161}{873}\right)$$ $$e\left(\frac{724}{873}\right)$$ $$e\left(\frac{701}{873}\right)$$
$$\chi_{5241}(26,\cdot)$$ 5241.w 1746 yes $$-1$$ $$1$$ $$e\left(\frac{383}{1746}\right)$$ $$e\left(\frac{383}{873}\right)$$ $$e\left(\frac{991}{1746}\right)$$ $$e\left(\frac{736}{873}\right)$$ $$e\left(\frac{383}{582}\right)$$ $$e\left(\frac{229}{291}\right)$$ $$e\left(\frac{367}{582}\right)$$ $$e\left(\frac{694}{873}\right)$$ $$e\left(\frac{109}{1746}\right)$$ $$e\left(\frac{766}{873}\right)$$
$$\chi_{5241}(28,\cdot)$$ 5241.r 582 no $$-1$$ $$1$$ $$e\left(\frac{103}{582}\right)$$ $$e\left(\frac{103}{291}\right)$$ $$e\left(\frac{227}{582}\right)$$ $$e\left(\frac{193}{582}\right)$$ $$e\left(\frac{103}{194}\right)$$ $$e\left(\frac{55}{97}\right)$$ $$e\left(\frac{161}{194}\right)$$ $$e\left(\frac{61}{582}\right)$$ $$e\left(\frac{148}{291}\right)$$ $$e\left(\frac{206}{291}\right)$$
$$\chi_{5241}(29,\cdot)$$ 5241.w 1746 yes $$-1$$ $$1$$ $$e\left(\frac{169}{1746}\right)$$ $$e\left(\frac{169}{873}\right)$$ $$e\left(\frac{1463}{1746}\right)$$ $$e\left(\frac{188}{873}\right)$$ $$e\left(\frac{169}{582}\right)$$ $$e\left(\frac{272}{291}\right)$$ $$e\left(\frac{89}{582}\right)$$ $$e\left(\frac{851}{873}\right)$$ $$e\left(\frac{545}{1746}\right)$$ $$e\left(\frac{338}{873}\right)$$
$$\chi_{5241}(31,\cdot)$$ 5241.u 873 no $$1$$ $$1$$ $$e\left(\frac{55}{873}\right)$$ $$e\left(\frac{110}{873}\right)$$ $$e\left(\frac{254}{873}\right)$$ $$e\left(\frac{298}{873}\right)$$ $$e\left(\frac{55}{291}\right)$$ $$e\left(\frac{103}{291}\right)$$ $$e\left(\frac{134}{291}\right)$$ $$e\left(\frac{58}{873}\right)$$ $$e\left(\frac{353}{873}\right)$$ $$e\left(\frac{220}{873}\right)$$
$$\chi_{5241}(32,\cdot)$$ 5241.x 1746 yes $$1$$ $$1$$ $$e\left(\frac{439}{873}\right)$$ $$e\left(\frac{5}{873}\right)$$ $$e\left(\frac{329}{873}\right)$$ $$e\left(\frac{1535}{1746}\right)$$ $$e\left(\frac{148}{291}\right)$$ $$e\left(\frac{256}{291}\right)$$ $$e\left(\frac{59}{291}\right)$$ $$e\left(\frac{1037}{1746}\right)$$ $$e\left(\frac{667}{1746}\right)$$ $$e\left(\frac{10}{873}\right)$$
$$\chi_{5241}(34,\cdot)$$ 5241.r 582 no $$-1$$ $$1$$ $$e\left(\frac{325}{582}\right)$$ $$e\left(\frac{34}{291}\right)$$ $$e\left(\frac{575}{582}\right)$$ $$e\left(\frac{253}{582}\right)$$ $$e\left(\frac{131}{194}\right)$$ $$e\left(\frac{53}{97}\right)$$ $$e\left(\frac{7}{194}\right)$$ $$e\left(\frac{475}{582}\right)$$ $$e\left(\frac{289}{291}\right)$$ $$e\left(\frac{68}{291}\right)$$
$$\chi_{5241}(35,\cdot)$$ 5241.s 582 yes $$-1$$ $$1$$ $$e\left(\frac{379}{582}\right)$$ $$e\left(\frac{88}{291}\right)$$ $$e\left(\frac{581}{582}\right)$$ $$e\left(\frac{122}{291}\right)$$ $$e\left(\frac{185}{194}\right)$$ $$e\left(\frac{63}{97}\right)$$ $$e\left(\frac{1}{194}\right)$$ $$e\left(\frac{221}{291}\right)$$ $$e\left(\frac{41}{582}\right)$$ $$e\left(\frac{176}{291}\right)$$
$$\chi_{5241}(37,\cdot)$$ 5241.v 1746 no $$-1$$ $$1$$ $$e\left(\frac{859}{1746}\right)$$ $$e\left(\frac{859}{873}\right)$$ $$e\left(\frac{1475}{1746}\right)$$ $$e\left(\frac{67}{1746}\right)$$ $$e\left(\frac{277}{582}\right)$$ $$e\left(\frac{98}{291}\right)$$ $$e\left(\frac{77}{582}\right)$$ $$e\left(\frac{763}{1746}\right)$$ $$e\left(\frac{463}{873}\right)$$ $$e\left(\frac{845}{873}\right)$$
$$\chi_{5241}(38,\cdot)$$ 5241.x 1746 yes $$1$$ $$1$$ $$e\left(\frac{272}{873}\right)$$ $$e\left(\frac{544}{873}\right)$$ $$e\left(\frac{526}{873}\right)$$ $$e\left(\frac{265}{1746}\right)$$ $$e\left(\frac{272}{291}\right)$$ $$e\left(\frac{266}{291}\right)$$ $$e\left(\frac{250}{291}\right)$$ $$e\left(\frac{907}{1746}\right)$$ $$e\left(\frac{809}{1746}\right)$$ $$e\left(\frac{215}{873}\right)$$
$$\chi_{5241}(40,\cdot)$$ 5241.u 873 no $$1$$ $$1$$ $$e\left(\frac{853}{873}\right)$$ $$e\left(\frac{833}{873}\right)$$ $$e\left(\frac{860}{873}\right)$$ $$e\left(\frac{844}{873}\right)$$ $$e\left(\frac{271}{291}\right)$$ $$e\left(\frac{280}{291}\right)$$ $$e\left(\frac{110}{291}\right)$$ $$e\left(\frac{217}{873}\right)$$ $$e\left(\frac{824}{873}\right)$$ $$e\left(\frac{793}{873}\right)$$
$$\chi_{5241}(41,\cdot)$$ 5241.s 582 yes $$-1$$ $$1$$ $$e\left(\frac{391}{582}\right)$$ $$e\left(\frac{100}{291}\right)$$ $$e\left(\frac{65}{582}\right)$$ $$e\left(\frac{218}{291}\right)$$ $$e\left(\frac{3}{194}\right)$$ $$e\left(\frac{76}{97}\right)$$ $$e\left(\frac{129}{194}\right)$$ $$e\left(\frac{185}{291}\right)$$ $$e\left(\frac{245}{582}\right)$$ $$e\left(\frac{200}{291}\right)$$
$$\chi_{5241}(43,\cdot)$$ 5241.u 873 no $$1$$ $$1$$ $$e\left(\frac{725}{873}\right)$$ $$e\left(\frac{577}{873}\right)$$ $$e\left(\frac{253}{873}\right)$$ $$e\left(\frac{833}{873}\right)$$ $$e\left(\frac{143}{291}\right)$$ $$e\left(\frac{35}{291}\right)$$ $$e\left(\frac{232}{291}\right)$$ $$e\left(\frac{209}{873}\right)$$ $$e\left(\frac{685}{873}\right)$$ $$e\left(\frac{281}{873}\right)$$
$$\chi_{5241}(44,\cdot)$$ 5241.x 1746 yes $$1$$ $$1$$ $$e\left(\frac{211}{873}\right)$$ $$e\left(\frac{422}{873}\right)$$ $$e\left(\frac{530}{873}\right)$$ $$e\left(\frac{1223}{1746}\right)$$ $$e\left(\frac{211}{291}\right)$$ $$e\left(\frac{247}{291}\right)$$ $$e\left(\frac{149}{291}\right)$$ $$e\left(\frac{1445}{1746}\right)$$ $$e\left(\frac{1645}{1746}\right)$$ $$e\left(\frac{844}{873}\right)$$
$$\chi_{5241}(46,\cdot)$$ 5241.v 1746 no $$-1$$ $$1$$ $$e\left(\frac{329}{1746}\right)$$ $$e\left(\frac{329}{873}\right)$$ $$e\left(\frac{1567}{1746}\right)$$ $$e\left(\frac{1481}{1746}\right)$$ $$e\left(\frac{329}{582}\right)$$ $$e\left(\frac{25}{291}\right)$$ $$e\left(\frac{373}{582}\right)$$ $$e\left(\frac{839}{1746}\right)$$ $$e\left(\frac{32}{873}\right)$$ $$e\left(\frac{658}{873}\right)$$
$$\chi_{5241}(47,\cdot)$$ 5241.x 1746 yes $$1$$ $$1$$ $$e\left(\frac{445}{873}\right)$$ $$e\left(\frac{17}{873}\right)$$ $$e\left(\frac{71}{873}\right)$$ $$e\left(\frac{1727}{1746}\right)$$ $$e\left(\frac{154}{291}\right)$$ $$e\left(\frac{172}{291}\right)$$ $$e\left(\frac{26}{291}\right)$$ $$e\left(\frac{383}{1746}\right)$$ $$e\left(\frac{871}{1746}\right)$$ $$e\left(\frac{34}{873}\right)$$