LMFDB - Dirichlet character orbit 58492.jj

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(58492, base_ring=CyclotomicField(1044)) M = H._module chi = DirichletCharacter(H, M([0,870,721])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(5, 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("58492.5"); 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:	$14623$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$1044$	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 14623.er	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:	$\Q(\zeta_{1044})$	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 1044 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 336 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{58492}(5,\cdot)$	$-1$	$1$	$e\left(\frac{197}{261}\right)$	$e\left(\frac{8}{261}\right)$	$e\left(\frac{133}{261}\right)$	$e\left(\frac{847}{1044}\right)$	$e\left(\frac{35}{261}\right)$	$e\left(\frac{205}{261}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{263}{348}\right)$	$e\left(\frac{167}{348}\right)$	$e\left(\frac{16}{261}\right)$
$\chi_{58492}(213,\cdot)$	$-1$	$1$	$e\left(\frac{190}{261}\right)$	$e\left(\frac{172}{261}\right)$	$e\left(\frac{119}{261}\right)$	$e\left(\frac{71}{1044}\right)$	$e\left(\frac{100}{261}\right)$	$e\left(\frac{101}{261}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{43}{348}\right)$	$e\left(\frac{67}{348}\right)$	$e\left(\frac{83}{261}\right)$
$\chi_{58492}(241,\cdot)$	$-1$	$1$	$e\left(\frac{250}{261}\right)$	$e\left(\frac{34}{261}\right)$	$e\left(\frac{239}{261}\right)$	$e\left(\frac{533}{1044}\right)$	$e\left(\frac{214}{261}\right)$	$e\left(\frac{23}{261}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{313}{348}\right)$	$e\left(\frac{253}{348}\right)$	$e\left(\frac{68}{261}\right)$
$\chi_{58492}(425,\cdot)$	$-1$	$1$	$e\left(\frac{191}{261}\right)$	$e\left(\frac{74}{261}\right)$	$e\left(\frac{121}{261}\right)$	$e\left(\frac{331}{1044}\right)$	$e\left(\frac{128}{261}\right)$	$e\left(\frac{4}{261}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{323}{348}\right)$	$e\left(\frac{131}{348}\right)$	$e\left(\frac{148}{261}\right)$
$\chi_{58492}(549,\cdot)$	$-1$	$1$	$e\left(\frac{253}{261}\right)$	$e\left(\frac{1}{261}\right)$	$e\left(\frac{245}{261}\right)$	$e\left(\frac{791}{1044}\right)$	$e\left(\frac{37}{261}\right)$	$e\left(\frac{254}{261}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{283}{348}\right)$	$e\left(\frac{271}{348}\right)$	$e\left(\frac{2}{261}\right)$
$\chi_{58492}(801,\cdot)$	$-1$	$1$	$e\left(\frac{169}{261}\right)$	$e\left(\frac{142}{261}\right)$	$e\left(\frac{77}{261}\right)$	$e\left(\frac{353}{1044}\right)$	$e\left(\frac{34}{261}\right)$	$e\left(\frac{50}{261}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{253}{348}\right)$	$e\left(\frac{289}{348}\right)$	$e\left(\frac{23}{261}\right)$
$\chi_{58492}(1053,\cdot)$	$-1$	$1$	$e\left(\frac{202}{261}\right)$	$e\left(\frac{40}{261}\right)$	$e\left(\frac{143}{261}\right)$	$e\left(\frac{581}{1044}\right)$	$e\left(\frac{175}{261}\right)$	$e\left(\frac{242}{261}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{97}{348}\right)$	$e\left(\frac{313}{348}\right)$	$e\left(\frac{80}{261}\right)$
$\chi_{58492}(1069,\cdot)$	$-1$	$1$	$e\left(\frac{44}{261}\right)$	$e\left(\frac{125}{261}\right)$	$e\left(\frac{88}{261}\right)$	$e\left(\frac{739}{1044}\right)$	$e\left(\frac{188}{261}\right)$	$e\left(\frac{169}{261}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{227}{348}\right)$	$e\left(\frac{119}{348}\right)$	$e\left(\frac{250}{261}\right)$
$\chi_{58492}(1165,\cdot)$	$-1$	$1$	$e\left(\frac{133}{261}\right)$	$e\left(\frac{16}{261}\right)$	$e\left(\frac{5}{261}\right)$	$e\left(\frac{389}{1044}\right)$	$e\left(\frac{70}{261}\right)$	$e\left(\frac{149}{261}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{265}{348}\right)$	$e\left(\frac{73}{348}\right)$	$e\left(\frac{32}{261}\right)$
$\chi_{58492}(1321,\cdot)$	$-1$	$1$	$e\left(\frac{230}{261}\right)$	$e\left(\frac{167}{261}\right)$	$e\left(\frac{199}{261}\right)$	$e\left(\frac{31}{1044}\right)$	$e\left(\frac{176}{261}\right)$	$e\left(\frac{136}{261}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{107}{348}\right)$	$e\left(\frac{191}{348}\right)$	$e\left(\frac{73}{261}\right)$
$\chi_{58492}(1445,\cdot)$	$-1$	$1$	$e\left(\frac{52}{261}\right)$	$e\left(\frac{124}{261}\right)$	$e\left(\frac{104}{261}\right)$	$e\left(\frac{209}{1044}\right)$	$e\left(\frac{151}{261}\right)$	$e\left(\frac{176}{261}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{205}{348}\right)$	$e\left(\frac{109}{348}\right)$	$e\left(\frac{248}{261}\right)$
$\chi_{58492}(1881,\cdot)$	$-1$	$1$	$e\left(\frac{101}{261}\right)$	$e\left(\frac{20}{261}\right)$	$e\left(\frac{202}{261}\right)$	$e\left(\frac{943}{1044}\right)$	$e\left(\frac{218}{261}\right)$	$e\left(\frac{121}{261}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{179}{348}\right)$	$e\left(\frac{287}{348}\right)$	$e\left(\frac{40}{261}\right)$
$\chi_{58492}(1993,\cdot)$	$-1$	$1$	$e\left(\frac{140}{261}\right)$	$e\left(\frac{113}{261}\right)$	$e\left(\frac{19}{261}\right)$	$e\left(\frac{643}{1044}\right)$	$e\left(\frac{5}{261}\right)$	$e\left(\frac{253}{261}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{311}{348}\right)$	$e\left(\frac{347}{348}\right)$	$e\left(\frac{226}{261}\right)$
$\chi_{58492}(2049,\cdot)$	$-1$	$1$	$e\left(\frac{26}{261}\right)$	$e\left(\frac{62}{261}\right)$	$e\left(\frac{52}{261}\right)$	$e\left(\frac{757}{1044}\right)$	$e\left(\frac{206}{261}\right)$	$e\left(\frac{88}{261}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{233}{348}\right)$	$e\left(\frac{185}{348}\right)$	$e\left(\frac{124}{261}\right)$
$\chi_{58492}(2077,\cdot)$	$-1$	$1$	$e\left(\frac{50}{261}\right)$	$e\left(\frac{59}{261}\right)$	$e\left(\frac{100}{261}\right)$	$e\left(\frac{211}{1044}\right)$	$e\left(\frac{95}{261}\right)$	$e\left(\frac{109}{261}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{167}{348}\right)$	$e\left(\frac{155}{348}\right)$	$e\left(\frac{118}{261}\right)$
$\chi_{58492}(2581,\cdot)$	$-1$	$1$	$e\left(\frac{32}{261}\right)$	$e\left(\frac{257}{261}\right)$	$e\left(\frac{64}{261}\right)$	$e\left(\frac{751}{1044}\right)$	$e\left(\frac{113}{261}\right)$	$e\left(\frac{28}{261}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{347}{348}\right)$	$e\left(\frac{47}{348}\right)$	$e\left(\frac{253}{261}\right)$
$\chi_{58492}(2733,\cdot)$	$-1$	$1$	$e\left(\frac{52}{261}\right)$	$e\left(\frac{124}{261}\right)$	$e\left(\frac{104}{261}\right)$	$e\left(\frac{731}{1044}\right)$	$e\left(\frac{151}{261}\right)$	$e\left(\frac{176}{261}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{31}{348}\right)$	$e\left(\frac{283}{348}\right)$	$e\left(\frac{248}{261}\right)$
$\chi_{58492}(2777,\cdot)$	$-1$	$1$	$e\left(\frac{56}{261}\right)$	$e\left(\frac{254}{261}\right)$	$e\left(\frac{112}{261}\right)$	$e\left(\frac{727}{1044}\right)$	$e\left(\frac{2}{261}\right)$	$e\left(\frac{49}{261}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{107}{348}\right)$	$e\left(\frac{191}{348}\right)$	$e\left(\frac{247}{261}\right)$
$\chi_{58492}(3013,\cdot)$	$-1$	$1$	$e\left(\frac{133}{261}\right)$	$e\left(\frac{16}{261}\right)$	$e\left(\frac{5}{261}\right)$	$e\left(\frac{911}{1044}\right)$	$e\left(\frac{70}{261}\right)$	$e\left(\frac{149}{261}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{91}{348}\right)$	$e\left(\frac{247}{348}\right)$	$e\left(\frac{32}{261}\right)$
$\chi_{58492}(3057,\cdot)$	$-1$	$1$	$e\left(\frac{95}{261}\right)$	$e\left(\frac{86}{261}\right)$	$e\left(\frac{190}{261}\right)$	$e\left(\frac{949}{1044}\right)$	$e\left(\frac{50}{261}\right)$	$e\left(\frac{181}{261}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{65}{348}\right)$	$e\left(\frac{77}{348}\right)$	$e\left(\frac{172}{261}\right)$
$\chi_{58492}(3125,\cdot)$	$-1$	$1$	$e\left(\frac{202}{261}\right)$	$e\left(\frac{40}{261}\right)$	$e\left(\frac{143}{261}\right)$	$e\left(\frac{59}{1044}\right)$	$e\left(\frac{175}{261}\right)$	$e\left(\frac{242}{261}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{271}{348}\right)$	$e\left(\frac{139}{348}\right)$	$e\left(\frac{80}{261}\right)$
$\chi_{58492}(3377,\cdot)$	$-1$	$1$	$e\left(\frac{169}{261}\right)$	$e\left(\frac{142}{261}\right)$	$e\left(\frac{77}{261}\right)$	$e\left(\frac{875}{1044}\right)$	$e\left(\frac{34}{261}\right)$	$e\left(\frac{50}{261}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{79}{348}\right)$	$e\left(\frac{115}{348}\right)$	$e\left(\frac{23}{261}\right)$
$\chi_{58492}(3393,\cdot)$	$-1$	$1$	$e\left(\frac{65}{261}\right)$	$e\left(\frac{155}{261}\right)$	$e\left(\frac{130}{261}\right)$	$e\left(\frac{979}{1044}\right)$	$e\left(\frac{254}{261}\right)$	$e\left(\frac{220}{261}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{191}{348}\right)$	$e\left(\frac{71}{348}\right)$	$e\left(\frac{49}{261}\right)$
$\chi_{58492}(3629,\cdot)$	$-1$	$1$	$e\left(\frac{253}{261}\right)$	$e\left(\frac{1}{261}\right)$	$e\left(\frac{245}{261}\right)$	$e\left(\frac{269}{1044}\right)$	$e\left(\frac{37}{261}\right)$	$e\left(\frac{254}{261}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{109}{348}\right)$	$e\left(\frac{97}{348}\right)$	$e\left(\frac{2}{261}\right)$
$\chi_{58492}(3645,\cdot)$	$-1$	$1$	$e\left(\frac{137}{261}\right)$	$e\left(\frac{146}{261}\right)$	$e\left(\frac{13}{261}\right)$	$e\left(\frac{385}{1044}\right)$	$e\left(\frac{182}{261}\right)$	$e\left(\frac{22}{261}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{341}{348}\right)$	$e\left(\frac{329}{348}\right)$	$e\left(\frac{31}{261}\right)$
$\chi_{58492}(3729,\cdot)$	$-1$	$1$	$e\left(\frac{8}{261}\right)$	$e\left(\frac{260}{261}\right)$	$e\left(\frac{16}{261}\right)$	$e\left(\frac{253}{1044}\right)$	$e\left(\frac{224}{261}\right)$	$e\left(\frac{7}{261}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{65}{348}\right)$	$e\left(\frac{77}{348}\right)$	$e\left(\frac{259}{261}\right)$
$\chi_{58492}(3937,\cdot)$	$-1$	$1$	$e\left(\frac{250}{261}\right)$	$e\left(\frac{34}{261}\right)$	$e\left(\frac{239}{261}\right)$	$e\left(\frac{11}{1044}\right)$	$e\left(\frac{214}{261}\right)$	$e\left(\frac{23}{261}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{139}{348}\right)$	$e\left(\frac{79}{348}\right)$	$e\left(\frac{68}{261}\right)$
$\chi_{58492}(3965,\cdot)$	$-1$	$1$	$e\left(\frac{190}{261}\right)$	$e\left(\frac{172}{261}\right)$	$e\left(\frac{119}{261}\right)$	$e\left(\frac{593}{1044}\right)$	$e\left(\frac{100}{261}\right)$	$e\left(\frac{101}{261}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{217}{348}\right)$	$e\left(\frac{241}{348}\right)$	$e\left(\frac{83}{261}\right)$
$\chi_{58492}(4413,\cdot)$	$-1$	$1$	$e\left(\frac{118}{261}\right)$	$e\left(\frac{181}{261}\right)$	$e\left(\frac{236}{261}\right)$	$e\left(\frac{143}{1044}\right)$	$e\left(\frac{172}{261}\right)$	$e\left(\frac{38}{261}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{67}{348}\right)$	$e\left(\frac{331}{348}\right)$	$e\left(\frac{101}{261}\right)$
$\chi_{58492}(4665,\cdot)$	$-1$	$1$	$e\left(\frac{25}{261}\right)$	$e\left(\frac{160}{261}\right)$	$e\left(\frac{50}{261}\right)$	$e\left(\frac{1019}{1044}\right)$	$e\left(\frac{178}{261}\right)$	$e\left(\frac{185}{261}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{127}{348}\right)$	$e\left(\frac{295}{348}\right)$	$e\left(\frac{59}{261}\right)$
$\chi_{58492}(4917,\cdot)$	$-1$	$1$	$e\left(\frac{220}{261}\right)$	$e\left(\frac{103}{261}\right)$	$e\left(\frac{179}{261}\right)$	$e\left(\frac{563}{1044}\right)$	$e\left(\frac{157}{261}\right)$	$e\left(\frac{62}{261}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{91}{348}\right)$	$e\left(\frac{247}{348}\right)$	$e\left(\frac{206}{261}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{58492}(5,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{197}{261}\right)\)	\(e\left(\frac{8}{261}\right)\)	\(e\left(\frac{133}{261}\right)\)	\(e\left(\frac{847}{1044}\right)\)	\(e\left(\frac{35}{261}\right)\)	\(e\left(\frac{205}{261}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{263}{348}\right)\)	\(e\left(\frac{167}{348}\right)\)	\(e\left(\frac{16}{261}\right)\)
\(\chi_{58492}(213,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{190}{261}\right)\)	\(e\left(\frac{172}{261}\right)\)	\(e\left(\frac{119}{261}\right)\)	\(e\left(\frac{71}{1044}\right)\)	\(e\left(\frac{100}{261}\right)\)	\(e\left(\frac{101}{261}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{43}{348}\right)\)	\(e\left(\frac{67}{348}\right)\)	\(e\left(\frac{83}{261}\right)\)
\(\chi_{58492}(241,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{250}{261}\right)\)	\(e\left(\frac{34}{261}\right)\)	\(e\left(\frac{239}{261}\right)\)	\(e\left(\frac{533}{1044}\right)\)	\(e\left(\frac{214}{261}\right)\)	\(e\left(\frac{23}{261}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{313}{348}\right)\)	\(e\left(\frac{253}{348}\right)\)	\(e\left(\frac{68}{261}\right)\)
\(\chi_{58492}(425,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{191}{261}\right)\)	\(e\left(\frac{74}{261}\right)\)	\(e\left(\frac{121}{261}\right)\)	\(e\left(\frac{331}{1044}\right)\)	\(e\left(\frac{128}{261}\right)\)	\(e\left(\frac{4}{261}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{323}{348}\right)\)	\(e\left(\frac{131}{348}\right)\)	\(e\left(\frac{148}{261}\right)\)
\(\chi_{58492}(549,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{253}{261}\right)\)	\(e\left(\frac{1}{261}\right)\)	\(e\left(\frac{245}{261}\right)\)	\(e\left(\frac{791}{1044}\right)\)	\(e\left(\frac{37}{261}\right)\)	\(e\left(\frac{254}{261}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{283}{348}\right)\)	\(e\left(\frac{271}{348}\right)\)	\(e\left(\frac{2}{261}\right)\)
\(\chi_{58492}(801,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{169}{261}\right)\)	\(e\left(\frac{142}{261}\right)\)	\(e\left(\frac{77}{261}\right)\)	\(e\left(\frac{353}{1044}\right)\)	\(e\left(\frac{34}{261}\right)\)	\(e\left(\frac{50}{261}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{253}{348}\right)\)	\(e\left(\frac{289}{348}\right)\)	\(e\left(\frac{23}{261}\right)\)
\(\chi_{58492}(1053,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{202}{261}\right)\)	\(e\left(\frac{40}{261}\right)\)	\(e\left(\frac{143}{261}\right)\)	\(e\left(\frac{581}{1044}\right)\)	\(e\left(\frac{175}{261}\right)\)	\(e\left(\frac{242}{261}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{97}{348}\right)\)	\(e\left(\frac{313}{348}\right)\)	\(e\left(\frac{80}{261}\right)\)
\(\chi_{58492}(1069,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{44}{261}\right)\)	\(e\left(\frac{125}{261}\right)\)	\(e\left(\frac{88}{261}\right)\)	\(e\left(\frac{739}{1044}\right)\)	\(e\left(\frac{188}{261}\right)\)	\(e\left(\frac{169}{261}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{227}{348}\right)\)	\(e\left(\frac{119}{348}\right)\)	\(e\left(\frac{250}{261}\right)\)
\(\chi_{58492}(1165,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{133}{261}\right)\)	\(e\left(\frac{16}{261}\right)\)	\(e\left(\frac{5}{261}\right)\)	\(e\left(\frac{389}{1044}\right)\)	\(e\left(\frac{70}{261}\right)\)	\(e\left(\frac{149}{261}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{265}{348}\right)\)	\(e\left(\frac{73}{348}\right)\)	\(e\left(\frac{32}{261}\right)\)
\(\chi_{58492}(1321,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{230}{261}\right)\)	\(e\left(\frac{167}{261}\right)\)	\(e\left(\frac{199}{261}\right)\)	\(e\left(\frac{31}{1044}\right)\)	\(e\left(\frac{176}{261}\right)\)	\(e\left(\frac{136}{261}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{107}{348}\right)\)	\(e\left(\frac{191}{348}\right)\)	\(e\left(\frac{73}{261}\right)\)
\(\chi_{58492}(1445,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{52}{261}\right)\)	\(e\left(\frac{124}{261}\right)\)	\(e\left(\frac{104}{261}\right)\)	\(e\left(\frac{209}{1044}\right)\)	\(e\left(\frac{151}{261}\right)\)	\(e\left(\frac{176}{261}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{205}{348}\right)\)	\(e\left(\frac{109}{348}\right)\)	\(e\left(\frac{248}{261}\right)\)
\(\chi_{58492}(1881,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{101}{261}\right)\)	\(e\left(\frac{20}{261}\right)\)	\(e\left(\frac{202}{261}\right)\)	\(e\left(\frac{943}{1044}\right)\)	\(e\left(\frac{218}{261}\right)\)	\(e\left(\frac{121}{261}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{179}{348}\right)\)	\(e\left(\frac{287}{348}\right)\)	\(e\left(\frac{40}{261}\right)\)
\(\chi_{58492}(1993,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{140}{261}\right)\)	\(e\left(\frac{113}{261}\right)\)	\(e\left(\frac{19}{261}\right)\)	\(e\left(\frac{643}{1044}\right)\)	\(e\left(\frac{5}{261}\right)\)	\(e\left(\frac{253}{261}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{311}{348}\right)\)	\(e\left(\frac{347}{348}\right)\)	\(e\left(\frac{226}{261}\right)\)
\(\chi_{58492}(2049,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{26}{261}\right)\)	\(e\left(\frac{62}{261}\right)\)	\(e\left(\frac{52}{261}\right)\)	\(e\left(\frac{757}{1044}\right)\)	\(e\left(\frac{206}{261}\right)\)	\(e\left(\frac{88}{261}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{233}{348}\right)\)	\(e\left(\frac{185}{348}\right)\)	\(e\left(\frac{124}{261}\right)\)
\(\chi_{58492}(2077,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{50}{261}\right)\)	\(e\left(\frac{59}{261}\right)\)	\(e\left(\frac{100}{261}\right)\)	\(e\left(\frac{211}{1044}\right)\)	\(e\left(\frac{95}{261}\right)\)	\(e\left(\frac{109}{261}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{167}{348}\right)\)	\(e\left(\frac{155}{348}\right)\)	\(e\left(\frac{118}{261}\right)\)
\(\chi_{58492}(2581,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{32}{261}\right)\)	\(e\left(\frac{257}{261}\right)\)	\(e\left(\frac{64}{261}\right)\)	\(e\left(\frac{751}{1044}\right)\)	\(e\left(\frac{113}{261}\right)\)	\(e\left(\frac{28}{261}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{347}{348}\right)\)	\(e\left(\frac{47}{348}\right)\)	\(e\left(\frac{253}{261}\right)\)
\(\chi_{58492}(2733,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{52}{261}\right)\)	\(e\left(\frac{124}{261}\right)\)	\(e\left(\frac{104}{261}\right)\)	\(e\left(\frac{731}{1044}\right)\)	\(e\left(\frac{151}{261}\right)\)	\(e\left(\frac{176}{261}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{31}{348}\right)\)	\(e\left(\frac{283}{348}\right)\)	\(e\left(\frac{248}{261}\right)\)
\(\chi_{58492}(2777,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{56}{261}\right)\)	\(e\left(\frac{254}{261}\right)\)	\(e\left(\frac{112}{261}\right)\)	\(e\left(\frac{727}{1044}\right)\)	\(e\left(\frac{2}{261}\right)\)	\(e\left(\frac{49}{261}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{107}{348}\right)\)	\(e\left(\frac{191}{348}\right)\)	\(e\left(\frac{247}{261}\right)\)
\(\chi_{58492}(3013,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{133}{261}\right)\)	\(e\left(\frac{16}{261}\right)\)	\(e\left(\frac{5}{261}\right)\)	\(e\left(\frac{911}{1044}\right)\)	\(e\left(\frac{70}{261}\right)\)	\(e\left(\frac{149}{261}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{91}{348}\right)\)	\(e\left(\frac{247}{348}\right)\)	\(e\left(\frac{32}{261}\right)\)
\(\chi_{58492}(3057,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{95}{261}\right)\)	\(e\left(\frac{86}{261}\right)\)	\(e\left(\frac{190}{261}\right)\)	\(e\left(\frac{949}{1044}\right)\)	\(e\left(\frac{50}{261}\right)\)	\(e\left(\frac{181}{261}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{65}{348}\right)\)	\(e\left(\frac{77}{348}\right)\)	\(e\left(\frac{172}{261}\right)\)
\(\chi_{58492}(3125,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{202}{261}\right)\)	\(e\left(\frac{40}{261}\right)\)	\(e\left(\frac{143}{261}\right)\)	\(e\left(\frac{59}{1044}\right)\)	\(e\left(\frac{175}{261}\right)\)	\(e\left(\frac{242}{261}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{271}{348}\right)\)	\(e\left(\frac{139}{348}\right)\)	\(e\left(\frac{80}{261}\right)\)
\(\chi_{58492}(3377,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{169}{261}\right)\)	\(e\left(\frac{142}{261}\right)\)	\(e\left(\frac{77}{261}\right)\)	\(e\left(\frac{875}{1044}\right)\)	\(e\left(\frac{34}{261}\right)\)	\(e\left(\frac{50}{261}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{79}{348}\right)\)	\(e\left(\frac{115}{348}\right)\)	\(e\left(\frac{23}{261}\right)\)
\(\chi_{58492}(3393,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{65}{261}\right)\)	\(e\left(\frac{155}{261}\right)\)	\(e\left(\frac{130}{261}\right)\)	\(e\left(\frac{979}{1044}\right)\)	\(e\left(\frac{254}{261}\right)\)	\(e\left(\frac{220}{261}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{191}{348}\right)\)	\(e\left(\frac{71}{348}\right)\)	\(e\left(\frac{49}{261}\right)\)
\(\chi_{58492}(3629,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{253}{261}\right)\)	\(e\left(\frac{1}{261}\right)\)	\(e\left(\frac{245}{261}\right)\)	\(e\left(\frac{269}{1044}\right)\)	\(e\left(\frac{37}{261}\right)\)	\(e\left(\frac{254}{261}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{109}{348}\right)\)	\(e\left(\frac{97}{348}\right)\)	\(e\left(\frac{2}{261}\right)\)
\(\chi_{58492}(3645,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{261}\right)\)	\(e\left(\frac{146}{261}\right)\)	\(e\left(\frac{13}{261}\right)\)	\(e\left(\frac{385}{1044}\right)\)	\(e\left(\frac{182}{261}\right)\)	\(e\left(\frac{22}{261}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{341}{348}\right)\)	\(e\left(\frac{329}{348}\right)\)	\(e\left(\frac{31}{261}\right)\)
\(\chi_{58492}(3729,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8}{261}\right)\)	\(e\left(\frac{260}{261}\right)\)	\(e\left(\frac{16}{261}\right)\)	\(e\left(\frac{253}{1044}\right)\)	\(e\left(\frac{224}{261}\right)\)	\(e\left(\frac{7}{261}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{65}{348}\right)\)	\(e\left(\frac{77}{348}\right)\)	\(e\left(\frac{259}{261}\right)\)
\(\chi_{58492}(3937,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{250}{261}\right)\)	\(e\left(\frac{34}{261}\right)\)	\(e\left(\frac{239}{261}\right)\)	\(e\left(\frac{11}{1044}\right)\)	\(e\left(\frac{214}{261}\right)\)	\(e\left(\frac{23}{261}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{139}{348}\right)\)	\(e\left(\frac{79}{348}\right)\)	\(e\left(\frac{68}{261}\right)\)
\(\chi_{58492}(3965,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{190}{261}\right)\)	\(e\left(\frac{172}{261}\right)\)	\(e\left(\frac{119}{261}\right)\)	\(e\left(\frac{593}{1044}\right)\)	\(e\left(\frac{100}{261}\right)\)	\(e\left(\frac{101}{261}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{217}{348}\right)\)	\(e\left(\frac{241}{348}\right)\)	\(e\left(\frac{83}{261}\right)\)
\(\chi_{58492}(4413,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{118}{261}\right)\)	\(e\left(\frac{181}{261}\right)\)	\(e\left(\frac{236}{261}\right)\)	\(e\left(\frac{143}{1044}\right)\)	\(e\left(\frac{172}{261}\right)\)	\(e\left(\frac{38}{261}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{67}{348}\right)\)	\(e\left(\frac{331}{348}\right)\)	\(e\left(\frac{101}{261}\right)\)
\(\chi_{58492}(4665,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{261}\right)\)	\(e\left(\frac{160}{261}\right)\)	\(e\left(\frac{50}{261}\right)\)	\(e\left(\frac{1019}{1044}\right)\)	\(e\left(\frac{178}{261}\right)\)	\(e\left(\frac{185}{261}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{127}{348}\right)\)	\(e\left(\frac{295}{348}\right)\)	\(e\left(\frac{59}{261}\right)\)
\(\chi_{58492}(4917,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{220}{261}\right)\)	\(e\left(\frac{103}{261}\right)\)	\(e\left(\frac{179}{261}\right)\)	\(e\left(\frac{563}{1044}\right)\)	\(e\left(\frac{157}{261}\right)\)	\(e\left(\frac{62}{261}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{91}{348}\right)\)	\(e\left(\frac{247}{348}\right)\)	\(e\left(\frac{206}{261}\right)\)

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First 31 of 336 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.jj
Modulus	$58492$
Conductor	$14623$
Order	$1044$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(58492\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(14623\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(1044\)	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 14623.er	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);