LMFDB - Dirichlet character orbit 58492.hq

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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([261,0,304])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(15, 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("58492.15"); 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:	$8356$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$522$	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 8356.bn	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	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 522 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 168 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{58492}(15,\cdot)$	$-1$	$1$	$e\left(\frac{461}{522}\right)$	$e\left(\frac{205}{261}\right)$	$e\left(\frac{200}{261}\right)$	$e\left(\frac{37}{522}\right)$	$e\left(\frac{103}{261}\right)$	$e\left(\frac{349}{522}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{109}{174}\right)$	$e\left(\frac{97}{174}\right)$	$e\left(\frac{149}{261}\right)$
$\chi_{58492}(267,\cdot)$	$-1$	$1$	$e\left(\frac{271}{522}\right)$	$e\left(\frac{206}{261}\right)$	$e\left(\frac{10}{261}\right)$	$e\left(\frac{41}{522}\right)$	$e\left(\frac{227}{261}\right)$	$e\left(\frac{161}{522}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{149}{174}\right)$	$e\left(\frac{131}{174}\right)$	$e\left(\frac{151}{261}\right)$
$\chi_{58492}(351,\cdot)$	$-1$	$1$	$e\left(\frac{337}{522}\right)$	$e\left(\frac{104}{261}\right)$	$e\left(\frac{76}{261}\right)$	$e\left(\frac{155}{522}\right)$	$e\left(\frac{107}{261}\right)$	$e\left(\frac{23}{522}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{71}{174}\right)$	$e\left(\frac{143}{174}\right)$	$e\left(\frac{208}{261}\right)$
$\chi_{58492}(1275,\cdot)$	$-1$	$1$	$e\left(\frac{449}{522}\right)$	$e\left(\frac{10}{261}\right)$	$e\left(\frac{188}{261}\right)$	$e\left(\frac{301}{522}\right)$	$e\left(\frac{196}{261}\right)$	$e\left(\frac{469}{522}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{139}{174}\right)$	$e\left(\frac{79}{174}\right)$	$e\left(\frac{20}{261}\right)$
$\chi_{58492}(1583,\cdot)$	$-1$	$1$	$e\left(\frac{149}{522}\right)$	$e\left(\frac{94}{261}\right)$	$e\left(\frac{149}{261}\right)$	$e\left(\frac{115}{522}\right)$	$e\left(\frac{172}{261}\right)$	$e\left(\frac{337}{522}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{19}{174}\right)$	$e\left(\frac{151}{174}\right)$	$e\left(\frac{188}{261}\right)$
$\chi_{58492}(1723,\cdot)$	$-1$	$1$	$e\left(\frac{151}{522}\right)$	$e\left(\frac{83}{261}\right)$	$e\left(\frac{151}{261}\right)$	$e\left(\frac{71}{522}\right)$	$e\left(\frac{113}{261}\right)$	$e\left(\frac{317}{522}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{101}{174}\right)$	$e\left(\frac{125}{174}\right)$	$e\left(\frac{166}{261}\right)$
$\chi_{58492}(1751,\cdot)$	$-1$	$1$	$e\left(\frac{245}{522}\right)$	$e\left(\frac{88}{261}\right)$	$e\left(\frac{245}{261}\right)$	$e\left(\frac{91}{522}\right)$	$e\left(\frac{211}{261}\right)$	$e\left(\frac{421}{522}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{127}{174}\right)$	$e\left(\frac{121}{174}\right)$	$e\left(\frac{176}{261}\right)$
$\chi_{58492}(1947,\cdot)$	$-1$	$1$	$e\left(\frac{25}{522}\right)$	$e\left(\frac{254}{261}\right)$	$e\left(\frac{25}{261}\right)$	$e\left(\frac{233}{522}\right)$	$e\left(\frac{176}{261}\right)$	$e\left(\frac{11}{522}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{155}{174}\right)$	$e\left(\frac{23}{174}\right)$	$e\left(\frac{247}{261}\right)$
$\chi_{58492}(3011,\cdot)$	$-1$	$1$	$e\left(\frac{395}{522}\right)$	$e\left(\frac{46}{261}\right)$	$e\left(\frac{134}{261}\right)$	$e\left(\frac{445}{522}\right)$	$e\left(\frac{223}{261}\right)$	$e\left(\frac{487}{522}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{13}{174}\right)$	$e\left(\frac{85}{174}\right)$	$e\left(\frac{92}{261}\right)$
$\chi_{58492}(3067,\cdot)$	$-1$	$1$	$e\left(\frac{251}{522}\right)$	$e\left(\frac{55}{261}\right)$	$e\left(\frac{251}{261}\right)$	$e\left(\frac{481}{522}\right)$	$e\left(\frac{34}{261}\right)$	$e\left(\frac{361}{522}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{25}{174}\right)$	$e\left(\frac{43}{174}\right)$	$e\left(\frac{110}{261}\right)$
$\chi_{58492}(3095,\cdot)$	$-1$	$1$	$e\left(\frac{19}{522}\right)$	$e\left(\frac{26}{261}\right)$	$e\left(\frac{19}{261}\right)$	$e\left(\frac{365}{522}\right)$	$e\left(\frac{92}{261}\right)$	$e\left(\frac{71}{522}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{83}{174}\right)$	$e\left(\frac{101}{174}\right)$	$e\left(\frac{52}{261}\right)$
$\chi_{58492}(3207,\cdot)$	$-1$	$1$	$e\left(\frac{155}{522}\right)$	$e\left(\frac{61}{261}\right)$	$e\left(\frac{155}{261}\right)$	$e\left(\frac{505}{522}\right)$	$e\left(\frac{256}{261}\right)$	$e\left(\frac{277}{522}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{91}{174}\right)$	$e\left(\frac{73}{174}\right)$	$e\left(\frac{122}{261}\right)$
$\chi_{58492}(3963,\cdot)$	$-1$	$1$	$e\left(\frac{5}{522}\right)$	$e\left(\frac{103}{261}\right)$	$e\left(\frac{5}{261}\right)$	$e\left(\frac{151}{522}\right)$	$e\left(\frac{244}{261}\right)$	$e\left(\frac{211}{522}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{31}{174}\right)$	$e\left(\frac{109}{174}\right)$	$e\left(\frac{206}{261}\right)$
$\chi_{58492}(4243,\cdot)$	$-1$	$1$	$e\left(\frac{95}{522}\right)$	$e\left(\frac{130}{261}\right)$	$e\left(\frac{95}{261}\right)$	$e\left(\frac{259}{522}\right)$	$e\left(\frac{199}{261}\right)$	$e\left(\frac{355}{522}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{67}{174}\right)$	$e\left(\frac{157}{174}\right)$	$e\left(\frac{260}{261}\right)$
$\chi_{58492}(4803,\cdot)$	$-1$	$1$	$e\left(\frac{97}{522}\right)$	$e\left(\frac{119}{261}\right)$	$e\left(\frac{97}{261}\right)$	$e\left(\frac{215}{522}\right)$	$e\left(\frac{140}{261}\right)$	$e\left(\frac{335}{522}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{149}{174}\right)$	$e\left(\frac{131}{174}\right)$	$e\left(\frac{238}{261}\right)$
$\chi_{58492}(4915,\cdot)$	$-1$	$1$	$e\left(\frac{191}{522}\right)$	$e\left(\frac{124}{261}\right)$	$e\left(\frac{191}{261}\right)$	$e\left(\frac{235}{522}\right)$	$e\left(\frac{238}{261}\right)$	$e\left(\frac{439}{522}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{174}\right)$	$e\left(\frac{127}{174}\right)$	$e\left(\frac{248}{261}\right)$
$\chi_{58492}(5111,\cdot)$	$-1$	$1$	$e\left(\frac{265}{522}\right)$	$e\left(\frac{239}{261}\right)$	$e\left(\frac{4}{261}\right)$	$e\left(\frac{173}{522}\right)$	$e\left(\frac{143}{261}\right)$	$e\left(\frac{221}{522}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{77}{174}\right)$	$e\left(\frac{35}{174}\right)$	$e\left(\frac{217}{261}\right)$
$\chi_{58492}(5335,\cdot)$	$-1$	$1$	$e\left(\frac{427}{522}\right)$	$e\left(\frac{131}{261}\right)$	$e\left(\frac{166}{261}\right)$	$e\left(\frac{263}{522}\right)$	$e\left(\frac{62}{261}\right)$	$e\left(\frac{167}{522}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{107}{174}\right)$	$e\left(\frac{17}{174}\right)$	$e\left(\frac{1}{261}\right)$
$\chi_{58492}(5643,\cdot)$	$-1$	$1$	$e\left(\frac{269}{522}\right)$	$e\left(\frac{217}{261}\right)$	$e\left(\frac{8}{261}\right)$	$e\left(\frac{85}{522}\right)$	$e\left(\frac{25}{261}\right)$	$e\left(\frac{181}{522}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{67}{174}\right)$	$e\left(\frac{157}{174}\right)$	$e\left(\frac{173}{261}\right)$
$\chi_{58492}(5727,\cdot)$	$-1$	$1$	$e\left(\frac{367}{522}\right)$	$e\left(\frac{200}{261}\right)$	$e\left(\frac{106}{261}\right)$	$e\left(\frac{17}{522}\right)$	$e\left(\frac{5}{261}\right)$	$e\left(\frac{245}{522}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{83}{174}\right)$	$e\left(\frac{101}{174}\right)$	$e\left(\frac{139}{261}\right)$
$\chi_{58492}(5867,\cdot)$	$-1$	$1$	$e\left(\frac{71}{522}\right)$	$e\left(\frac{1}{261}\right)$	$e\left(\frac{71}{261}\right)$	$e\left(\frac{265}{522}\right)$	$e\left(\frac{124}{261}\right)$	$e\left(\frac{73}{522}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{127}{174}\right)$	$e\left(\frac{121}{174}\right)$	$e\left(\frac{2}{261}\right)$
$\chi_{58492}(5979,\cdot)$	$-1$	$1$	$e\left(\frac{347}{522}\right)$	$e\left(\frac{49}{261}\right)$	$e\left(\frac{86}{261}\right)$	$e\left(\frac{457}{522}\right)$	$e\left(\frac{73}{261}\right)$	$e\left(\frac{445}{522}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{133}{174}\right)$	$e\left(\frac{13}{174}\right)$	$e\left(\frac{98}{261}\right)$
$\chi_{58492}(6231,\cdot)$	$-1$	$1$	$e\left(\frac{167}{522}\right)$	$e\left(\frac{256}{261}\right)$	$e\left(\frac{167}{261}\right)$	$e\left(\frac{241}{522}\right)$	$e\left(\frac{163}{261}\right)$	$e\left(\frac{157}{522}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{61}{174}\right)$	$e\left(\frac{91}{174}\right)$	$e\left(\frac{251}{261}\right)$
$\chi_{58492}(6455,\cdot)$	$-1$	$1$	$e\left(\frac{397}{522}\right)$	$e\left(\frac{35}{261}\right)$	$e\left(\frac{136}{261}\right)$	$e\left(\frac{401}{522}\right)$	$e\left(\frac{164}{261}\right)$	$e\left(\frac{467}{522}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{95}{174}\right)$	$e\left(\frac{59}{174}\right)$	$e\left(\frac{70}{261}\right)$
$\chi_{58492}(7743,\cdot)$	$-1$	$1$	$e\left(\frac{131}{522}\right)$	$e\left(\frac{193}{261}\right)$	$e\left(\frac{131}{261}\right)$	$e\left(\frac{511}{522}\right)$	$e\left(\frac{181}{261}\right)$	$e\left(\frac{517}{522}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{151}{174}\right)$	$e\left(\frac{37}{174}\right)$	$e\left(\frac{125}{261}\right)$
$\chi_{58492}(7771,\cdot)$	$-1$	$1$	$e\left(\frac{55}{522}\right)$	$e\left(\frac{89}{261}\right)$	$e\left(\frac{55}{261}\right)$	$e\left(\frac{95}{522}\right)$	$e\left(\frac{74}{261}\right)$	$e\left(\frac{233}{522}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{167}{174}\right)$	$e\left(\frac{155}{174}\right)$	$e\left(\frac{178}{261}\right)$
$\chi_{58492}(7799,\cdot)$	$-1$	$1$	$e\left(\frac{61}{522}\right)$	$e\left(\frac{56}{261}\right)$	$e\left(\frac{61}{261}\right)$	$e\left(\frac{485}{522}\right)$	$e\left(\frac{158}{261}\right)$	$e\left(\frac{173}{522}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{65}{174}\right)$	$e\left(\frac{77}{174}\right)$	$e\left(\frac{112}{261}\right)$
$\chi_{58492}(7911,\cdot)$	$-1$	$1$	$e\left(\frac{511}{522}\right)$	$e\left(\frac{191}{261}\right)$	$e\left(\frac{250}{261}\right)$	$e\left(\frac{503}{522}\right)$	$e\left(\frac{194}{261}\right)$	$e\left(\frac{371}{522}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{71}{174}\right)$	$e\left(\frac{143}{174}\right)$	$e\left(\frac{121}{261}\right)$
$\chi_{58492}(8331,\cdot)$	$-1$	$1$	$e\left(\frac{179}{522}\right)$	$e\left(\frac{190}{261}\right)$	$e\left(\frac{179}{261}\right)$	$e\left(\frac{499}{522}\right)$	$e\left(\frac{70}{261}\right)$	$e\left(\frac{37}{522}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{31}{174}\right)$	$e\left(\frac{109}{174}\right)$	$e\left(\frac{119}{261}\right)$
$\chi_{58492}(9143,\cdot)$	$-1$	$1$	$e\left(\frac{463}{522}\right)$	$e\left(\frac{194}{261}\right)$	$e\left(\frac{202}{261}\right)$	$e\left(\frac{515}{522}\right)$	$e\left(\frac{44}{261}\right)$	$e\left(\frac{329}{522}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{174}\right)$	$e\left(\frac{71}{174}\right)$	$e\left(\frac{127}{261}\right)$
$\chi_{58492}(9703,\cdot)$	$-1$	$1$	$e\left(\frac{83}{522}\right)$	$e\left(\frac{196}{261}\right)$	$e\left(\frac{83}{261}\right)$	$e\left(\frac{1}{522}\right)$	$e\left(\frac{31}{261}\right)$	$e\left(\frac{475}{522}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{97}{174}\right)$	$e\left(\frac{139}{174}\right)$	$e\left(\frac{131}{261}\right)$

Overview	Random
Universe	Knowledge

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{58492}(15,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{461}{522}\right)\)	\(e\left(\frac{205}{261}\right)\)	\(e\left(\frac{200}{261}\right)\)	\(e\left(\frac{37}{522}\right)\)	\(e\left(\frac{103}{261}\right)\)	\(e\left(\frac{349}{522}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{109}{174}\right)\)	\(e\left(\frac{97}{174}\right)\)	\(e\left(\frac{149}{261}\right)\)
\(\chi_{58492}(267,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{271}{522}\right)\)	\(e\left(\frac{206}{261}\right)\)	\(e\left(\frac{10}{261}\right)\)	\(e\left(\frac{41}{522}\right)\)	\(e\left(\frac{227}{261}\right)\)	\(e\left(\frac{161}{522}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{149}{174}\right)\)	\(e\left(\frac{131}{174}\right)\)	\(e\left(\frac{151}{261}\right)\)
\(\chi_{58492}(351,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{337}{522}\right)\)	\(e\left(\frac{104}{261}\right)\)	\(e\left(\frac{76}{261}\right)\)	\(e\left(\frac{155}{522}\right)\)	\(e\left(\frac{107}{261}\right)\)	\(e\left(\frac{23}{522}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{71}{174}\right)\)	\(e\left(\frac{143}{174}\right)\)	\(e\left(\frac{208}{261}\right)\)
\(\chi_{58492}(1275,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{449}{522}\right)\)	\(e\left(\frac{10}{261}\right)\)	\(e\left(\frac{188}{261}\right)\)	\(e\left(\frac{301}{522}\right)\)	\(e\left(\frac{196}{261}\right)\)	\(e\left(\frac{469}{522}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{139}{174}\right)\)	\(e\left(\frac{79}{174}\right)\)	\(e\left(\frac{20}{261}\right)\)
\(\chi_{58492}(1583,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{522}\right)\)	\(e\left(\frac{94}{261}\right)\)	\(e\left(\frac{149}{261}\right)\)	\(e\left(\frac{115}{522}\right)\)	\(e\left(\frac{172}{261}\right)\)	\(e\left(\frac{337}{522}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{19}{174}\right)\)	\(e\left(\frac{151}{174}\right)\)	\(e\left(\frac{188}{261}\right)\)
\(\chi_{58492}(1723,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{151}{522}\right)\)	\(e\left(\frac{83}{261}\right)\)	\(e\left(\frac{151}{261}\right)\)	\(e\left(\frac{71}{522}\right)\)	\(e\left(\frac{113}{261}\right)\)	\(e\left(\frac{317}{522}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{101}{174}\right)\)	\(e\left(\frac{125}{174}\right)\)	\(e\left(\frac{166}{261}\right)\)
\(\chi_{58492}(1751,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{245}{522}\right)\)	\(e\left(\frac{88}{261}\right)\)	\(e\left(\frac{245}{261}\right)\)	\(e\left(\frac{91}{522}\right)\)	\(e\left(\frac{211}{261}\right)\)	\(e\left(\frac{421}{522}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{127}{174}\right)\)	\(e\left(\frac{121}{174}\right)\)	\(e\left(\frac{176}{261}\right)\)
\(\chi_{58492}(1947,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{522}\right)\)	\(e\left(\frac{254}{261}\right)\)	\(e\left(\frac{25}{261}\right)\)	\(e\left(\frac{233}{522}\right)\)	\(e\left(\frac{176}{261}\right)\)	\(e\left(\frac{11}{522}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{155}{174}\right)\)	\(e\left(\frac{23}{174}\right)\)	\(e\left(\frac{247}{261}\right)\)
\(\chi_{58492}(3011,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{395}{522}\right)\)	\(e\left(\frac{46}{261}\right)\)	\(e\left(\frac{134}{261}\right)\)	\(e\left(\frac{445}{522}\right)\)	\(e\left(\frac{223}{261}\right)\)	\(e\left(\frac{487}{522}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{13}{174}\right)\)	\(e\left(\frac{85}{174}\right)\)	\(e\left(\frac{92}{261}\right)\)
\(\chi_{58492}(3067,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{251}{522}\right)\)	\(e\left(\frac{55}{261}\right)\)	\(e\left(\frac{251}{261}\right)\)	\(e\left(\frac{481}{522}\right)\)	\(e\left(\frac{34}{261}\right)\)	\(e\left(\frac{361}{522}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{25}{174}\right)\)	\(e\left(\frac{43}{174}\right)\)	\(e\left(\frac{110}{261}\right)\)
\(\chi_{58492}(3095,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{522}\right)\)	\(e\left(\frac{26}{261}\right)\)	\(e\left(\frac{19}{261}\right)\)	\(e\left(\frac{365}{522}\right)\)	\(e\left(\frac{92}{261}\right)\)	\(e\left(\frac{71}{522}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{83}{174}\right)\)	\(e\left(\frac{101}{174}\right)\)	\(e\left(\frac{52}{261}\right)\)
\(\chi_{58492}(3207,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{155}{522}\right)\)	\(e\left(\frac{61}{261}\right)\)	\(e\left(\frac{155}{261}\right)\)	\(e\left(\frac{505}{522}\right)\)	\(e\left(\frac{256}{261}\right)\)	\(e\left(\frac{277}{522}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{91}{174}\right)\)	\(e\left(\frac{73}{174}\right)\)	\(e\left(\frac{122}{261}\right)\)
\(\chi_{58492}(3963,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{522}\right)\)	\(e\left(\frac{103}{261}\right)\)	\(e\left(\frac{5}{261}\right)\)	\(e\left(\frac{151}{522}\right)\)	\(e\left(\frac{244}{261}\right)\)	\(e\left(\frac{211}{522}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{31}{174}\right)\)	\(e\left(\frac{109}{174}\right)\)	\(e\left(\frac{206}{261}\right)\)
\(\chi_{58492}(4243,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{95}{522}\right)\)	\(e\left(\frac{130}{261}\right)\)	\(e\left(\frac{95}{261}\right)\)	\(e\left(\frac{259}{522}\right)\)	\(e\left(\frac{199}{261}\right)\)	\(e\left(\frac{355}{522}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{67}{174}\right)\)	\(e\left(\frac{157}{174}\right)\)	\(e\left(\frac{260}{261}\right)\)
\(\chi_{58492}(4803,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{522}\right)\)	\(e\left(\frac{119}{261}\right)\)	\(e\left(\frac{97}{261}\right)\)	\(e\left(\frac{215}{522}\right)\)	\(e\left(\frac{140}{261}\right)\)	\(e\left(\frac{335}{522}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{149}{174}\right)\)	\(e\left(\frac{131}{174}\right)\)	\(e\left(\frac{238}{261}\right)\)
\(\chi_{58492}(4915,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{191}{522}\right)\)	\(e\left(\frac{124}{261}\right)\)	\(e\left(\frac{191}{261}\right)\)	\(e\left(\frac{235}{522}\right)\)	\(e\left(\frac{238}{261}\right)\)	\(e\left(\frac{439}{522}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{174}\right)\)	\(e\left(\frac{127}{174}\right)\)	\(e\left(\frac{248}{261}\right)\)
\(\chi_{58492}(5111,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{265}{522}\right)\)	\(e\left(\frac{239}{261}\right)\)	\(e\left(\frac{4}{261}\right)\)	\(e\left(\frac{173}{522}\right)\)	\(e\left(\frac{143}{261}\right)\)	\(e\left(\frac{221}{522}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{77}{174}\right)\)	\(e\left(\frac{35}{174}\right)\)	\(e\left(\frac{217}{261}\right)\)
\(\chi_{58492}(5335,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{427}{522}\right)\)	\(e\left(\frac{131}{261}\right)\)	\(e\left(\frac{166}{261}\right)\)	\(e\left(\frac{263}{522}\right)\)	\(e\left(\frac{62}{261}\right)\)	\(e\left(\frac{167}{522}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{107}{174}\right)\)	\(e\left(\frac{17}{174}\right)\)	\(e\left(\frac{1}{261}\right)\)
\(\chi_{58492}(5643,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{269}{522}\right)\)	\(e\left(\frac{217}{261}\right)\)	\(e\left(\frac{8}{261}\right)\)	\(e\left(\frac{85}{522}\right)\)	\(e\left(\frac{25}{261}\right)\)	\(e\left(\frac{181}{522}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{67}{174}\right)\)	\(e\left(\frac{157}{174}\right)\)	\(e\left(\frac{173}{261}\right)\)
\(\chi_{58492}(5727,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{367}{522}\right)\)	\(e\left(\frac{200}{261}\right)\)	\(e\left(\frac{106}{261}\right)\)	\(e\left(\frac{17}{522}\right)\)	\(e\left(\frac{5}{261}\right)\)	\(e\left(\frac{245}{522}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{83}{174}\right)\)	\(e\left(\frac{101}{174}\right)\)	\(e\left(\frac{139}{261}\right)\)
\(\chi_{58492}(5867,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{522}\right)\)	\(e\left(\frac{1}{261}\right)\)	\(e\left(\frac{71}{261}\right)\)	\(e\left(\frac{265}{522}\right)\)	\(e\left(\frac{124}{261}\right)\)	\(e\left(\frac{73}{522}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{127}{174}\right)\)	\(e\left(\frac{121}{174}\right)\)	\(e\left(\frac{2}{261}\right)\)
\(\chi_{58492}(5979,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{347}{522}\right)\)	\(e\left(\frac{49}{261}\right)\)	\(e\left(\frac{86}{261}\right)\)	\(e\left(\frac{457}{522}\right)\)	\(e\left(\frac{73}{261}\right)\)	\(e\left(\frac{445}{522}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{133}{174}\right)\)	\(e\left(\frac{13}{174}\right)\)	\(e\left(\frac{98}{261}\right)\)
\(\chi_{58492}(6231,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{167}{522}\right)\)	\(e\left(\frac{256}{261}\right)\)	\(e\left(\frac{167}{261}\right)\)	\(e\left(\frac{241}{522}\right)\)	\(e\left(\frac{163}{261}\right)\)	\(e\left(\frac{157}{522}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{61}{174}\right)\)	\(e\left(\frac{91}{174}\right)\)	\(e\left(\frac{251}{261}\right)\)
\(\chi_{58492}(6455,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{397}{522}\right)\)	\(e\left(\frac{35}{261}\right)\)	\(e\left(\frac{136}{261}\right)\)	\(e\left(\frac{401}{522}\right)\)	\(e\left(\frac{164}{261}\right)\)	\(e\left(\frac{467}{522}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{95}{174}\right)\)	\(e\left(\frac{59}{174}\right)\)	\(e\left(\frac{70}{261}\right)\)
\(\chi_{58492}(7743,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{522}\right)\)	\(e\left(\frac{193}{261}\right)\)	\(e\left(\frac{131}{261}\right)\)	\(e\left(\frac{511}{522}\right)\)	\(e\left(\frac{181}{261}\right)\)	\(e\left(\frac{517}{522}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{151}{174}\right)\)	\(e\left(\frac{37}{174}\right)\)	\(e\left(\frac{125}{261}\right)\)
\(\chi_{58492}(7771,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{522}\right)\)	\(e\left(\frac{89}{261}\right)\)	\(e\left(\frac{55}{261}\right)\)	\(e\left(\frac{95}{522}\right)\)	\(e\left(\frac{74}{261}\right)\)	\(e\left(\frac{233}{522}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{167}{174}\right)\)	\(e\left(\frac{155}{174}\right)\)	\(e\left(\frac{178}{261}\right)\)
\(\chi_{58492}(7799,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{522}\right)\)	\(e\left(\frac{56}{261}\right)\)	\(e\left(\frac{61}{261}\right)\)	\(e\left(\frac{485}{522}\right)\)	\(e\left(\frac{158}{261}\right)\)	\(e\left(\frac{173}{522}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{65}{174}\right)\)	\(e\left(\frac{77}{174}\right)\)	\(e\left(\frac{112}{261}\right)\)
\(\chi_{58492}(7911,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{511}{522}\right)\)	\(e\left(\frac{191}{261}\right)\)	\(e\left(\frac{250}{261}\right)\)	\(e\left(\frac{503}{522}\right)\)	\(e\left(\frac{194}{261}\right)\)	\(e\left(\frac{371}{522}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{71}{174}\right)\)	\(e\left(\frac{143}{174}\right)\)	\(e\left(\frac{121}{261}\right)\)
\(\chi_{58492}(8331,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{179}{522}\right)\)	\(e\left(\frac{190}{261}\right)\)	\(e\left(\frac{179}{261}\right)\)	\(e\left(\frac{499}{522}\right)\)	\(e\left(\frac{70}{261}\right)\)	\(e\left(\frac{37}{522}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{31}{174}\right)\)	\(e\left(\frac{109}{174}\right)\)	\(e\left(\frac{119}{261}\right)\)
\(\chi_{58492}(9143,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{463}{522}\right)\)	\(e\left(\frac{194}{261}\right)\)	\(e\left(\frac{202}{261}\right)\)	\(e\left(\frac{515}{522}\right)\)	\(e\left(\frac{44}{261}\right)\)	\(e\left(\frac{329}{522}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{174}\right)\)	\(e\left(\frac{71}{174}\right)\)	\(e\left(\frac{127}{261}\right)\)
\(\chi_{58492}(9703,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{522}\right)\)	\(e\left(\frac{196}{261}\right)\)	\(e\left(\frac{83}{261}\right)\)	\(e\left(\frac{1}{522}\right)\)	\(e\left(\frac{31}{261}\right)\)	\(e\left(\frac{475}{522}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{97}{174}\right)\)	\(e\left(\frac{139}{174}\right)\)	\(e\left(\frac{131}{261}\right)\)

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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.hq
Modulus	$58492$
Conductor	$8356$
Order	$522$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(58492\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(8356\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(522\)	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 8356.bn	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);