LMFDB - Dirichlet character orbit 58492.gv

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(58492, base_ring=CyclotomicField(522)) M = H._module chi = DirichletCharacter(H, M([0,0,518])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(29, 58492)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("58492.29"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$58492$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$2089$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$261$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 2089.s	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{261})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 261 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 168 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{58492}(29,\cdot)$	$1$	$1$	$e\left(\frac{191}{261}\right)$	$e\left(\frac{248}{261}\right)$	$e\left(\frac{121}{261}\right)$	$e\left(\frac{235}{261}\right)$	$e\left(\frac{215}{261}\right)$	$e\left(\frac{178}{261}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{235}{261}\right)$
$\chi_{58492}(225,\cdot)$	$1$	$1$	$e\left(\frac{200}{261}\right)$	$e\left(\frac{149}{261}\right)$	$e\left(\frac{139}{261}\right)$	$e\left(\frac{37}{261}\right)$	$e\left(\frac{206}{261}\right)$	$e\left(\frac{88}{261}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{22}{87}\right)$	$e\left(\frac{10}{87}\right)$	$e\left(\frac{37}{261}\right)$
$\chi_{58492}(309,\cdot)$	$1$	$1$	$e\left(\frac{98}{261}\right)$	$e\left(\frac{227}{261}\right)$	$e\left(\frac{196}{261}\right)$	$e\left(\frac{193}{261}\right)$	$e\left(\frac{221}{261}\right)$	$e\left(\frac{64}{261}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{16}{87}\right)$	$e\left(\frac{31}{87}\right)$	$e\left(\frac{193}{261}\right)$
$\chi_{58492}(589,\cdot)$	$1$	$1$	$e\left(\frac{32}{261}\right)$	$e\left(\frac{170}{261}\right)$	$e\left(\frac{64}{261}\right)$	$e\left(\frac{79}{261}\right)$	$e\left(\frac{200}{261}\right)$	$e\left(\frac{202}{261}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{87}\right)$	$e\left(\frac{19}{87}\right)$	$e\left(\frac{79}{261}\right)$
$\chi_{58492}(841,\cdot)$	$1$	$1$	$e\left(\frac{121}{261}\right)$	$e\left(\frac{235}{261}\right)$	$e\left(\frac{242}{261}\right)$	$e\left(\frac{209}{261}\right)$	$e\left(\frac{169}{261}\right)$	$e\left(\frac{95}{261}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{209}{261}\right)$
$\chi_{58492}(953,\cdot)$	$1$	$1$	$e\left(\frac{233}{261}\right)$	$e\left(\frac{47}{261}\right)$	$e\left(\frac{205}{261}\right)$	$e\left(\frac{94}{261}\right)$	$e\left(\frac{86}{261}\right)$	$e\left(\frac{19}{261}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{16}{87}\right)$	$e\left(\frac{94}{261}\right)$
$\chi_{58492}(1009,\cdot)$	$1$	$1$	$e\left(\frac{170}{261}\right)$	$e\left(\frac{218}{261}\right)$	$e\left(\frac{79}{261}\right)$	$e\left(\frac{175}{261}\right)$	$e\left(\frac{149}{261}\right)$	$e\left(\frac{127}{261}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{10}{87}\right)$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{175}{261}\right)$
$\chi_{58492}(1289,\cdot)$	$1$	$1$	$e\left(\frac{22}{261}\right)$	$e\left(\frac{19}{261}\right)$	$e\left(\frac{44}{261}\right)$	$e\left(\frac{38}{261}\right)$	$e\left(\frac{7}{261}\right)$	$e\left(\frac{41}{261}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{32}{87}\right)$	$e\left(\frac{62}{87}\right)$	$e\left(\frac{38}{261}\right)$
$\chi_{58492}(1513,\cdot)$	$1$	$1$	$e\left(\frac{160}{261}\right)$	$e\left(\frac{67}{261}\right)$	$e\left(\frac{59}{261}\right)$	$e\left(\frac{134}{261}\right)$	$e\left(\frac{217}{261}\right)$	$e\left(\frac{227}{261}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{35}{87}\right)$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{134}{261}\right)$
$\chi_{58492}(1933,\cdot)$	$1$	$1$	$e\left(\frac{31}{261}\right)$	$e\left(\frac{181}{261}\right)$	$e\left(\frac{62}{261}\right)$	$e\left(\frac{101}{261}\right)$	$e\left(\frac{259}{261}\right)$	$e\left(\frac{212}{261}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{53}{87}\right)$	$e\left(\frac{32}{87}\right)$	$e\left(\frac{101}{261}\right)$
$\chi_{58492}(1989,\cdot)$	$1$	$1$	$e\left(\frac{193}{261}\right)$	$e\left(\frac{226}{261}\right)$	$e\left(\frac{125}{261}\right)$	$e\left(\frac{191}{261}\right)$	$e\left(\frac{97}{261}\right)$	$e\left(\frac{158}{261}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{14}{87}\right)$	$e\left(\frac{191}{261}\right)$
$\chi_{58492}(2017,\cdot)$	$1$	$1$	$e\left(\frac{70}{261}\right)$	$e\left(\frac{13}{261}\right)$	$e\left(\frac{140}{261}\right)$	$e\left(\frac{26}{261}\right)$	$e\left(\frac{46}{261}\right)$	$e\left(\frac{83}{261}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{86}{87}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{26}{261}\right)$
$\chi_{58492}(2465,\cdot)$	$1$	$1$	$e\left(\frac{185}{261}\right)$	$e\left(\frac{53}{261}\right)$	$e\left(\frac{109}{261}\right)$	$e\left(\frac{106}{261}\right)$	$e\left(\frac{47}{261}\right)$	$e\left(\frac{238}{261}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{16}{87}\right)$	$e\left(\frac{31}{87}\right)$	$e\left(\frac{106}{261}\right)$
$\chi_{58492}(2605,\cdot)$	$1$	$1$	$e\left(\frac{247}{261}\right)$	$e\left(\frac{154}{261}\right)$	$e\left(\frac{233}{261}\right)$	$e\left(\frac{47}{261}\right)$	$e\left(\frac{43}{261}\right)$	$e\left(\frac{140}{261}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{35}{87}\right)$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{47}{261}\right)$
$\chi_{58492}(4509,\cdot)$	$1$	$1$	$e\left(\frac{1}{261}\right)$	$e\left(\frac{250}{261}\right)$	$e\left(\frac{2}{261}\right)$	$e\left(\frac{239}{261}\right)$	$e\left(\frac{202}{261}\right)$	$e\left(\frac{251}{261}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{41}{87}\right)$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{239}{261}\right)$
$\chi_{58492}(5041,\cdot)$	$1$	$1$	$e\left(\frac{52}{261}\right)$	$e\left(\frac{211}{261}\right)$	$e\left(\frac{104}{261}\right)$	$e\left(\frac{161}{261}\right)$	$e\left(\frac{64}{261}\right)$	$e\left(\frac{2}{261}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{20}{87}\right)$	$e\left(\frac{161}{261}\right)$
$\chi_{58492}(5097,\cdot)$	$1$	$1$	$e\left(\frac{14}{261}\right)$	$e\left(\frac{107}{261}\right)$	$e\left(\frac{28}{261}\right)$	$e\left(\frac{214}{261}\right)$	$e\left(\frac{218}{261}\right)$	$e\left(\frac{121}{261}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{79}{87}\right)$	$e\left(\frac{214}{261}\right)$
$\chi_{58492}(5153,\cdot)$	$1$	$1$	$e\left(\frac{17}{261}\right)$	$e\left(\frac{74}{261}\right)$	$e\left(\frac{34}{261}\right)$	$e\left(\frac{148}{261}\right)$	$e\left(\frac{41}{261}\right)$	$e\left(\frac{91}{261}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{148}{261}\right)$
$\chi_{58492}(5237,\cdot)$	$1$	$1$	$e\left(\frac{74}{261}\right)$	$e\left(\frac{230}{261}\right)$	$e\left(\frac{148}{261}\right)$	$e\left(\frac{199}{261}\right)$	$e\left(\frac{71}{261}\right)$	$e\left(\frac{43}{261}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{76}{87}\right)$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{199}{261}\right)$
$\chi_{58492}(5377,\cdot)$	$1$	$1$	$e\left(\frac{242}{261}\right)$	$e\left(\frac{209}{261}\right)$	$e\left(\frac{223}{261}\right)$	$e\left(\frac{157}{261}\right)$	$e\left(\frac{77}{261}\right)$	$e\left(\frac{190}{261}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{87}\right)$	$e\left(\frac{73}{87}\right)$	$e\left(\frac{157}{261}\right)$
$\chi_{58492}(5517,\cdot)$	$1$	$1$	$e\left(\frac{176}{261}\right)$	$e\left(\frac{152}{261}\right)$	$e\left(\frac{91}{261}\right)$	$e\left(\frac{43}{261}\right)$	$e\left(\frac{56}{261}\right)$	$e\left(\frac{67}{261}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{61}{87}\right)$	$e\left(\frac{43}{261}\right)$
$\chi_{58492}(6189,\cdot)$	$1$	$1$	$e\left(\frac{175}{261}\right)$	$e\left(\frac{163}{261}\right)$	$e\left(\frac{89}{261}\right)$	$e\left(\frac{65}{261}\right)$	$e\left(\frac{115}{261}\right)$	$e\left(\frac{77}{261}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{41}{87}\right)$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{65}{261}\right)$
$\chi_{58492}(6217,\cdot)$	$1$	$1$	$e\left(\frac{76}{261}\right)$	$e\left(\frac{208}{261}\right)$	$e\left(\frac{152}{261}\right)$	$e\left(\frac{155}{261}\right)$	$e\left(\frac{214}{261}\right)$	$e\left(\frac{23}{261}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{155}{261}\right)$
$\chi_{58492}(6525,\cdot)$	$1$	$1$	$e\left(\frac{130}{261}\right)$	$e\left(\frac{136}{261}\right)$	$e\left(\frac{260}{261}\right)$	$e\left(\frac{11}{261}\right)$	$e\left(\frac{160}{261}\right)$	$e\left(\frac{5}{261}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{23}{87}\right)$	$e\left(\frac{50}{87}\right)$	$e\left(\frac{11}{261}\right)$
$\chi_{58492}(7841,\cdot)$	$1$	$1$	$e\left(\frac{218}{261}\right)$	$e\left(\frac{212}{261}\right)$	$e\left(\frac{175}{261}\right)$	$e\left(\frac{163}{261}\right)$	$e\left(\frac{188}{261}\right)$	$e\left(\frac{169}{261}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{64}{87}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{163}{261}\right)$
$\chi_{58492}(7981,\cdot)$	$1$	$1$	$e\left(\frac{59}{261}\right)$	$e\left(\frac{134}{261}\right)$	$e\left(\frac{118}{261}\right)$	$e\left(\frac{7}{261}\right)$	$e\left(\frac{173}{261}\right)$	$e\left(\frac{193}{261}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{16}{87}\right)$	$e\left(\frac{7}{261}\right)$
$\chi_{58492}(8485,\cdot)$	$1$	$1$	$e\left(\frac{13}{261}\right)$	$e\left(\frac{118}{261}\right)$	$e\left(\frac{26}{261}\right)$	$e\left(\frac{236}{261}\right)$	$e\left(\frac{16}{261}\right)$	$e\left(\frac{131}{261}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{5}{87}\right)$	$e\left(\frac{236}{261}\right)$
$\chi_{58492}(8961,\cdot)$	$1$	$1$	$e\left(\frac{28}{261}\right)$	$e\left(\frac{214}{261}\right)$	$e\left(\frac{56}{261}\right)$	$e\left(\frac{167}{261}\right)$	$e\left(\frac{175}{261}\right)$	$e\left(\frac{242}{261}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{167}{261}\right)$
$\chi_{58492}(9381,\cdot)$	$1$	$1$	$e\left(\frac{202}{261}\right)$	$e\left(\frac{127}{261}\right)$	$e\left(\frac{143}{261}\right)$	$e\left(\frac{254}{261}\right)$	$e\left(\frac{88}{261}\right)$	$e\left(\frac{68}{261}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{254}{261}\right)$
$\chi_{58492}(9465,\cdot)$	$1$	$1$	$e\left(\frac{157}{261}\right)$	$e\left(\frac{100}{261}\right)$	$e\left(\frac{53}{261}\right)$	$e\left(\frac{200}{261}\right)$	$e\left(\frac{133}{261}\right)$	$e\left(\frac{257}{261}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{86}{87}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{200}{261}\right)$
$\chi_{58492}(9829,\cdot)$	$1$	$1$	$e\left(\frac{86}{261}\right)$	$e\left(\frac{98}{261}\right)$	$e\left(\frac{172}{261}\right)$	$e\left(\frac{196}{261}\right)$	$e\left(\frac{146}{261}\right)$	$e\left(\frac{184}{261}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{13}{87}\right)$	$e\left(\frac{196}{261}\right)$

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{58492}(29,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{261}\right)\)	\(e\left(\frac{248}{261}\right)\)	\(e\left(\frac{121}{261}\right)\)	\(e\left(\frac{235}{261}\right)\)	\(e\left(\frac{215}{261}\right)\)	\(e\left(\frac{178}{261}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{235}{261}\right)\)
\(\chi_{58492}(225,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{200}{261}\right)\)	\(e\left(\frac{149}{261}\right)\)	\(e\left(\frac{139}{261}\right)\)	\(e\left(\frac{37}{261}\right)\)	\(e\left(\frac{206}{261}\right)\)	\(e\left(\frac{88}{261}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{22}{87}\right)\)	\(e\left(\frac{10}{87}\right)\)	\(e\left(\frac{37}{261}\right)\)
\(\chi_{58492}(309,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{98}{261}\right)\)	\(e\left(\frac{227}{261}\right)\)	\(e\left(\frac{196}{261}\right)\)	\(e\left(\frac{193}{261}\right)\)	\(e\left(\frac{221}{261}\right)\)	\(e\left(\frac{64}{261}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{16}{87}\right)\)	\(e\left(\frac{31}{87}\right)\)	\(e\left(\frac{193}{261}\right)\)
\(\chi_{58492}(589,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{261}\right)\)	\(e\left(\frac{170}{261}\right)\)	\(e\left(\frac{64}{261}\right)\)	\(e\left(\frac{79}{261}\right)\)	\(e\left(\frac{200}{261}\right)\)	\(e\left(\frac{202}{261}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{87}\right)\)	\(e\left(\frac{19}{87}\right)\)	\(e\left(\frac{79}{261}\right)\)
\(\chi_{58492}(841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{261}\right)\)	\(e\left(\frac{235}{261}\right)\)	\(e\left(\frac{242}{261}\right)\)	\(e\left(\frac{209}{261}\right)\)	\(e\left(\frac{169}{261}\right)\)	\(e\left(\frac{95}{261}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{209}{261}\right)\)
\(\chi_{58492}(953,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{233}{261}\right)\)	\(e\left(\frac{47}{261}\right)\)	\(e\left(\frac{205}{261}\right)\)	\(e\left(\frac{94}{261}\right)\)	\(e\left(\frac{86}{261}\right)\)	\(e\left(\frac{19}{261}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{16}{87}\right)\)	\(e\left(\frac{94}{261}\right)\)
\(\chi_{58492}(1009,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{170}{261}\right)\)	\(e\left(\frac{218}{261}\right)\)	\(e\left(\frac{79}{261}\right)\)	\(e\left(\frac{175}{261}\right)\)	\(e\left(\frac{149}{261}\right)\)	\(e\left(\frac{127}{261}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{10}{87}\right)\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{175}{261}\right)\)
\(\chi_{58492}(1289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{261}\right)\)	\(e\left(\frac{19}{261}\right)\)	\(e\left(\frac{44}{261}\right)\)	\(e\left(\frac{38}{261}\right)\)	\(e\left(\frac{7}{261}\right)\)	\(e\left(\frac{41}{261}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{32}{87}\right)\)	\(e\left(\frac{62}{87}\right)\)	\(e\left(\frac{38}{261}\right)\)
\(\chi_{58492}(1513,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{160}{261}\right)\)	\(e\left(\frac{67}{261}\right)\)	\(e\left(\frac{59}{261}\right)\)	\(e\left(\frac{134}{261}\right)\)	\(e\left(\frac{217}{261}\right)\)	\(e\left(\frac{227}{261}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{35}{87}\right)\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{134}{261}\right)\)
\(\chi_{58492}(1933,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{261}\right)\)	\(e\left(\frac{181}{261}\right)\)	\(e\left(\frac{62}{261}\right)\)	\(e\left(\frac{101}{261}\right)\)	\(e\left(\frac{259}{261}\right)\)	\(e\left(\frac{212}{261}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{53}{87}\right)\)	\(e\left(\frac{32}{87}\right)\)	\(e\left(\frac{101}{261}\right)\)
\(\chi_{58492}(1989,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{261}\right)\)	\(e\left(\frac{226}{261}\right)\)	\(e\left(\frac{125}{261}\right)\)	\(e\left(\frac{191}{261}\right)\)	\(e\left(\frac{97}{261}\right)\)	\(e\left(\frac{158}{261}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{14}{87}\right)\)	\(e\left(\frac{191}{261}\right)\)
\(\chi_{58492}(2017,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{70}{261}\right)\)	\(e\left(\frac{13}{261}\right)\)	\(e\left(\frac{140}{261}\right)\)	\(e\left(\frac{26}{261}\right)\)	\(e\left(\frac{46}{261}\right)\)	\(e\left(\frac{83}{261}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{86}{87}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{26}{261}\right)\)
\(\chi_{58492}(2465,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{185}{261}\right)\)	\(e\left(\frac{53}{261}\right)\)	\(e\left(\frac{109}{261}\right)\)	\(e\left(\frac{106}{261}\right)\)	\(e\left(\frac{47}{261}\right)\)	\(e\left(\frac{238}{261}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{16}{87}\right)\)	\(e\left(\frac{31}{87}\right)\)	\(e\left(\frac{106}{261}\right)\)
\(\chi_{58492}(2605,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{247}{261}\right)\)	\(e\left(\frac{154}{261}\right)\)	\(e\left(\frac{233}{261}\right)\)	\(e\left(\frac{47}{261}\right)\)	\(e\left(\frac{43}{261}\right)\)	\(e\left(\frac{140}{261}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{35}{87}\right)\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{47}{261}\right)\)
\(\chi_{58492}(4509,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{261}\right)\)	\(e\left(\frac{250}{261}\right)\)	\(e\left(\frac{2}{261}\right)\)	\(e\left(\frac{239}{261}\right)\)	\(e\left(\frac{202}{261}\right)\)	\(e\left(\frac{251}{261}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{41}{87}\right)\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{239}{261}\right)\)
\(\chi_{58492}(5041,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{261}\right)\)	\(e\left(\frac{211}{261}\right)\)	\(e\left(\frac{104}{261}\right)\)	\(e\left(\frac{161}{261}\right)\)	\(e\left(\frac{64}{261}\right)\)	\(e\left(\frac{2}{261}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{20}{87}\right)\)	\(e\left(\frac{161}{261}\right)\)
\(\chi_{58492}(5097,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{261}\right)\)	\(e\left(\frac{107}{261}\right)\)	\(e\left(\frac{28}{261}\right)\)	\(e\left(\frac{214}{261}\right)\)	\(e\left(\frac{218}{261}\right)\)	\(e\left(\frac{121}{261}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{79}{87}\right)\)	\(e\left(\frac{214}{261}\right)\)
\(\chi_{58492}(5153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{261}\right)\)	\(e\left(\frac{74}{261}\right)\)	\(e\left(\frac{34}{261}\right)\)	\(e\left(\frac{148}{261}\right)\)	\(e\left(\frac{41}{261}\right)\)	\(e\left(\frac{91}{261}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{148}{261}\right)\)
\(\chi_{58492}(5237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{74}{261}\right)\)	\(e\left(\frac{230}{261}\right)\)	\(e\left(\frac{148}{261}\right)\)	\(e\left(\frac{199}{261}\right)\)	\(e\left(\frac{71}{261}\right)\)	\(e\left(\frac{43}{261}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{76}{87}\right)\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{199}{261}\right)\)
\(\chi_{58492}(5377,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{242}{261}\right)\)	\(e\left(\frac{209}{261}\right)\)	\(e\left(\frac{223}{261}\right)\)	\(e\left(\frac{157}{261}\right)\)	\(e\left(\frac{77}{261}\right)\)	\(e\left(\frac{190}{261}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{87}\right)\)	\(e\left(\frac{73}{87}\right)\)	\(e\left(\frac{157}{261}\right)\)
\(\chi_{58492}(5517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{176}{261}\right)\)	\(e\left(\frac{152}{261}\right)\)	\(e\left(\frac{91}{261}\right)\)	\(e\left(\frac{43}{261}\right)\)	\(e\left(\frac{56}{261}\right)\)	\(e\left(\frac{67}{261}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{61}{87}\right)\)	\(e\left(\frac{43}{261}\right)\)
\(\chi_{58492}(6189,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{175}{261}\right)\)	\(e\left(\frac{163}{261}\right)\)	\(e\left(\frac{89}{261}\right)\)	\(e\left(\frac{65}{261}\right)\)	\(e\left(\frac{115}{261}\right)\)	\(e\left(\frac{77}{261}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{41}{87}\right)\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{65}{261}\right)\)
\(\chi_{58492}(6217,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{76}{261}\right)\)	\(e\left(\frac{208}{261}\right)\)	\(e\left(\frac{152}{261}\right)\)	\(e\left(\frac{155}{261}\right)\)	\(e\left(\frac{214}{261}\right)\)	\(e\left(\frac{23}{261}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{155}{261}\right)\)
\(\chi_{58492}(6525,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{130}{261}\right)\)	\(e\left(\frac{136}{261}\right)\)	\(e\left(\frac{260}{261}\right)\)	\(e\left(\frac{11}{261}\right)\)	\(e\left(\frac{160}{261}\right)\)	\(e\left(\frac{5}{261}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{23}{87}\right)\)	\(e\left(\frac{50}{87}\right)\)	\(e\left(\frac{11}{261}\right)\)
\(\chi_{58492}(7841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{218}{261}\right)\)	\(e\left(\frac{212}{261}\right)\)	\(e\left(\frac{175}{261}\right)\)	\(e\left(\frac{163}{261}\right)\)	\(e\left(\frac{188}{261}\right)\)	\(e\left(\frac{169}{261}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{64}{87}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{163}{261}\right)\)
\(\chi_{58492}(7981,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{261}\right)\)	\(e\left(\frac{134}{261}\right)\)	\(e\left(\frac{118}{261}\right)\)	\(e\left(\frac{7}{261}\right)\)	\(e\left(\frac{173}{261}\right)\)	\(e\left(\frac{193}{261}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{16}{87}\right)\)	\(e\left(\frac{7}{261}\right)\)
\(\chi_{58492}(8485,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{261}\right)\)	\(e\left(\frac{118}{261}\right)\)	\(e\left(\frac{26}{261}\right)\)	\(e\left(\frac{236}{261}\right)\)	\(e\left(\frac{16}{261}\right)\)	\(e\left(\frac{131}{261}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{5}{87}\right)\)	\(e\left(\frac{236}{261}\right)\)
\(\chi_{58492}(8961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{261}\right)\)	\(e\left(\frac{214}{261}\right)\)	\(e\left(\frac{56}{261}\right)\)	\(e\left(\frac{167}{261}\right)\)	\(e\left(\frac{175}{261}\right)\)	\(e\left(\frac{242}{261}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{167}{261}\right)\)
\(\chi_{58492}(9381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{202}{261}\right)\)	\(e\left(\frac{127}{261}\right)\)	\(e\left(\frac{143}{261}\right)\)	\(e\left(\frac{254}{261}\right)\)	\(e\left(\frac{88}{261}\right)\)	\(e\left(\frac{68}{261}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{254}{261}\right)\)
\(\chi_{58492}(9465,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{261}\right)\)	\(e\left(\frac{100}{261}\right)\)	\(e\left(\frac{53}{261}\right)\)	\(e\left(\frac{200}{261}\right)\)	\(e\left(\frac{133}{261}\right)\)	\(e\left(\frac{257}{261}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{86}{87}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{200}{261}\right)\)
\(\chi_{58492}(9829,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{86}{261}\right)\)	\(e\left(\frac{98}{261}\right)\)	\(e\left(\frac{172}{261}\right)\)	\(e\left(\frac{196}{261}\right)\)	\(e\left(\frac{146}{261}\right)\)	\(e\left(\frac{184}{261}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{13}{87}\right)\)	\(e\left(\frac{196}{261}\right)\)

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First 31 of 168 characters in Galois orbit

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	58492.gv
Modulus	$58492$
Conductor	$2089$
Order	$261$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(58492\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(2089\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(261\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 2089.s	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);