LMFDB - Dirichlet character orbit 58492.jh

Show commands: Magma / Pari/GP / SageMath

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([0,522,403])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(13, 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("58492.13"); 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.en	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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{58492}(13,\cdot)$	$-1$	$1$	$e\left(\frac{68}{261}\right)$	$e\left(\frac{35}{261}\right)$	$e\left(\frac{136}{261}\right)$	$e\left(\frac{541}{1044}\right)$	$e\left(\frac{164}{261}\right)$	$e\left(\frac{103}{261}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{277}{348}\right)$	$e\left(\frac{205}{348}\right)$	$e\left(\frac{70}{261}\right)$
$\chi_{58492}(153,\cdot)$	$-1$	$1$	$e\left(\frac{125}{261}\right)$	$e\left(\frac{191}{261}\right)$	$e\left(\frac{250}{261}\right)$	$e\left(\frac{223}{1044}\right)$	$e\left(\frac{194}{261}\right)$	$e\left(\frac{55}{261}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{55}{348}\right)$	$e\left(\frac{199}{348}\right)$	$e\left(\frac{121}{261}\right)$
$\chi_{58492}(209,\cdot)$	$-1$	$1$	$e\left(\frac{34}{261}\right)$	$e\left(\frac{148}{261}\right)$	$e\left(\frac{68}{261}\right)$	$e\left(\frac{401}{1044}\right)$	$e\left(\frac{82}{261}\right)$	$e\left(\frac{182}{261}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{269}{348}\right)$	$e\left(\frac{233}{348}\right)$	$e\left(\frac{35}{261}\right)$
$\chi_{58492}(293,\cdot)$	$-1$	$1$	$e\left(\frac{155}{261}\right)$	$e\left(\frac{122}{261}\right)$	$e\left(\frac{49}{261}\right)$	$e\left(\frac{193}{1044}\right)$	$e\left(\frac{251}{261}\right)$	$e\left(\frac{16}{261}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{277}{348}\right)$	$e\left(\frac{205}{348}\right)$	$e\left(\frac{244}{261}\right)$
$\chi_{58492}(377,\cdot)$	$-1$	$1$	$e\left(\frac{259}{261}\right)$	$e\left(\frac{22}{261}\right)$	$e\left(\frac{257}{261}\right)$	$e\left(\frac{437}{1044}\right)$	$e\left(\frac{118}{261}\right)$	$e\left(\frac{20}{261}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{281}{348}\right)$	$e\left(\frac{17}{348}\right)$	$e\left(\frac{44}{261}\right)$
$\chi_{58492}(405,\cdot)$	$-1$	$1$	$e\left(\frac{70}{261}\right)$	$e\left(\frac{13}{261}\right)$	$e\left(\frac{140}{261}\right)$	$e\left(\frac{887}{1044}\right)$	$e\left(\frac{46}{261}\right)$	$e\left(\frac{83}{261}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{83}{348}\right)$	$e\left(\frac{275}{348}\right)$	$e\left(\frac{26}{261}\right)$
$\chi_{58492}(713,\cdot)$	$-1$	$1$	$e\left(\frac{86}{261}\right)$	$e\left(\frac{98}{261}\right)$	$e\left(\frac{172}{261}\right)$	$e\left(\frac{1}{1044}\right)$	$e\left(\frac{146}{261}\right)$	$e\left(\frac{184}{261}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{97}{348}\right)$	$e\left(\frac{313}{348}\right)$	$e\left(\frac{196}{261}\right)$
$\chi_{58492}(1105,\cdot)$	$-1$	$1$	$e\left(\frac{62}{261}\right)$	$e\left(\frac{101}{261}\right)$	$e\left(\frac{124}{261}\right)$	$e\left(\frac{25}{1044}\right)$	$e\left(\frac{257}{261}\right)$	$e\left(\frac{163}{261}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{337}{348}\right)$	$e\left(\frac{169}{348}\right)$	$e\left(\frac{202}{261}\right)$
$\chi_{58492}(1917,\cdot)$	$-1$	$1$	$e\left(\frac{257}{261}\right)$	$e\left(\frac{44}{261}\right)$	$e\left(\frac{253}{261}\right)$	$e\left(\frac{613}{1044}\right)$	$e\left(\frac{236}{261}\right)$	$e\left(\frac{40}{261}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{301}{348}\right)$	$e\left(\frac{121}{348}\right)$	$e\left(\frac{88}{261}\right)$
$\chi_{58492}(2113,\cdot)$	$-1$	$1$	$e\left(\frac{80}{261}\right)$	$e\left(\frac{164}{261}\right)$	$e\left(\frac{160}{261}\right)$	$e\left(\frac{529}{1044}\right)$	$e\left(\frac{239}{261}\right)$	$e\left(\frac{244}{261}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{157}{348}\right)$	$e\left(\frac{277}{348}\right)$	$e\left(\frac{67}{261}\right)$
$\chi_{58492}(2141,\cdot)$	$-1$	$1$	$e\left(\frac{41}{261}\right)$	$e\left(\frac{71}{261}\right)$	$e\left(\frac{82}{261}\right)$	$e\left(\frac{829}{1044}\right)$	$e\left(\frac{191}{261}\right)$	$e\left(\frac{112}{261}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{25}{348}\right)$	$e\left(\frac{217}{348}\right)$	$e\left(\frac{142}{261}\right)$
$\chi_{58492}(2169,\cdot)$	$-1$	$1$	$e\left(\frac{56}{261}\right)$	$e\left(\frac{167}{261}\right)$	$e\left(\frac{112}{261}\right)$	$e\left(\frac{31}{1044}\right)$	$e\left(\frac{89}{261}\right)$	$e\left(\frac{223}{261}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{223}{348}\right)$	$e\left(\frac{307}{348}\right)$	$e\left(\frac{73}{261}\right)$
$\chi_{58492}(2225,\cdot)$	$-1$	$1$	$e\left(\frac{235}{261}\right)$	$e\left(\frac{25}{261}\right)$	$e\left(\frac{209}{261}\right)$	$e\left(\frac{461}{1044}\right)$	$e\left(\frac{229}{261}\right)$	$e\left(\frac{260}{261}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{173}{348}\right)$	$e\left(\frac{221}{348}\right)$	$e\left(\frac{50}{261}\right)$
$\chi_{58492}(2281,\cdot)$	$-1$	$1$	$e\left(\frac{170}{261}\right)$	$e\left(\frac{218}{261}\right)$	$e\left(\frac{79}{261}\right)$	$e\left(\frac{961}{1044}\right)$	$e\left(\frac{149}{261}\right)$	$e\left(\frac{127}{261}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{301}{348}\right)$	$e\left(\frac{121}{348}\right)$	$e\left(\frac{175}{261}\right)$
$\chi_{58492}(2505,\cdot)$	$-1$	$1$	$e\left(\frac{131}{261}\right)$	$e\left(\frac{125}{261}\right)$	$e\left(\frac{1}{261}\right)$	$e\left(\frac{217}{1044}\right)$	$e\left(\frac{101}{261}\right)$	$e\left(\frac{256}{261}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{169}{348}\right)$	$e\left(\frac{61}{348}\right)$	$e\left(\frac{250}{261}\right)$
$\chi_{58492}(2701,\cdot)$	$-1$	$1$	$e\left(\frac{98}{261}\right)$	$e\left(\frac{227}{261}\right)$	$e\left(\frac{196}{261}\right)$	$e\left(\frac{511}{1044}\right)$	$e\left(\frac{221}{261}\right)$	$e\left(\frac{64}{261}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{151}{348}\right)$	$e\left(\frac{211}{348}\right)$	$e\left(\frac{193}{261}\right)$
$\chi_{58492}(2729,\cdot)$	$-1$	$1$	$e\left(\frac{146}{261}\right)$	$e\left(\frac{221}{261}\right)$	$e\left(\frac{31}{261}\right)$	$e\left(\frac{463}{1044}\right)$	$e\left(\frac{260}{261}\right)$	$e\left(\frac{106}{261}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{19}{348}\right)$	$e\left(\frac{151}{348}\right)$	$e\left(\frac{181}{261}\right)$
$\chi_{58492}(2757,\cdot)$	$-1$	$1$	$e\left(\frac{4}{261}\right)$	$e\left(\frac{217}{261}\right)$	$e\left(\frac{8}{261}\right)$	$e\left(\frac{953}{1044}\right)$	$e\left(\frac{25}{261}\right)$	$e\left(\frac{221}{261}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{221}{348}\right)$	$e\left(\frac{53}{348}\right)$	$e\left(\frac{173}{261}\right)$
$\chi_{58492}(2785,\cdot)$	$-1$	$1$	$e\left(\frac{10}{261}\right)$	$e\left(\frac{151}{261}\right)$	$e\left(\frac{20}{261}\right)$	$e\left(\frac{425}{1044}\right)$	$e\left(\frac{193}{261}\right)$	$e\left(\frac{161}{261}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{161}{348}\right)$	$e\left(\frac{89}{348}\right)$	$e\left(\frac{41}{261}\right)$
$\chi_{58492}(2925,\cdot)$	$-1$	$1$	$e\left(\frac{7}{261}\right)$	$e\left(\frac{184}{261}\right)$	$e\left(\frac{14}{261}\right)$	$e\left(\frac{689}{1044}\right)$	$e\left(\frac{109}{261}\right)$	$e\left(\frac{191}{261}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{17}{348}\right)$	$e\left(\frac{245}{348}\right)$	$e\left(\frac{107}{261}\right)$
$\chi_{58492}(3177,\cdot)$	$-1$	$1$	$e\left(\frac{64}{261}\right)$	$e\left(\frac{79}{261}\right)$	$e\left(\frac{128}{261}\right)$	$e\left(\frac{893}{1044}\right)$	$e\left(\frac{139}{261}\right)$	$e\left(\frac{143}{261}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{317}{348}\right)$	$e\left(\frac{65}{348}\right)$	$e\left(\frac{158}{261}\right)$
$\chi_{58492}(3261,\cdot)$	$-1$	$1$	$e\left(\frac{128}{261}\right)$	$e\left(\frac{158}{261}\right)$	$e\left(\frac{256}{261}\right)$	$e\left(\frac{481}{1044}\right)$	$e\left(\frac{17}{261}\right)$	$e\left(\frac{25}{261}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{25}{348}\right)$	$e\left(\frac{217}{348}\right)$	$e\left(\frac{55}{261}\right)$
$\chi_{58492}(3625,\cdot)$	$-1$	$1$	$e\left(\frac{260}{261}\right)$	$e\left(\frac{11}{261}\right)$	$e\left(\frac{259}{261}\right)$	$e\left(\frac{349}{1044}\right)$	$e\left(\frac{59}{261}\right)$	$e\left(\frac{10}{261}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{97}{348}\right)$	$e\left(\frac{313}{348}\right)$	$e\left(\frac{22}{261}\right)$
$\chi_{58492}(3709,\cdot)$	$-1$	$1$	$e\left(\frac{43}{261}\right)$	$e\left(\frac{49}{261}\right)$	$e\left(\frac{86}{261}\right)$	$e\left(\frac{131}{1044}\right)$	$e\left(\frac{73}{261}\right)$	$e\left(\frac{92}{261}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{179}{348}\right)$	$e\left(\frac{287}{348}\right)$	$e\left(\frac{98}{261}\right)$
$\chi_{58492}(3793,\cdot)$	$-1$	$1$	$e\left(\frac{106}{261}\right)$	$e\left(\frac{139}{261}\right)$	$e\left(\frac{212}{261}\right)$	$e\left(\frac{851}{1044}\right)$	$e\left(\frac{10}{261}\right)$	$e\left(\frac{245}{261}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{71}{348}\right)$	$e\left(\frac{143}{348}\right)$	$e\left(\frac{17}{261}\right)$
$\chi_{58492}(4017,\cdot)$	$-1$	$1$	$e\left(\frac{166}{261}\right)$	$e\left(\frac{1}{261}\right)$	$e\left(\frac{71}{261}\right)$	$e\left(\frac{269}{1044}\right)$	$e\left(\frac{124}{261}\right)$	$e\left(\frac{167}{261}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{341}{348}\right)$	$e\left(\frac{329}{348}\right)$	$e\left(\frac{2}{261}\right)$
$\chi_{58492}(4129,\cdot)$	$-1$	$1$	$e\left(\frac{74}{261}\right)$	$e\left(\frac{230}{261}\right)$	$e\left(\frac{148}{261}\right)$	$e\left(\frac{13}{1044}\right)$	$e\left(\frac{71}{261}\right)$	$e\left(\frac{43}{261}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{217}{348}\right)$	$e\left(\frac{241}{348}\right)$	$e\left(\frac{199}{261}\right)$
$\chi_{58492}(4409,\cdot)$	$-1$	$1$	$e\left(\frac{247}{261}\right)$	$e\left(\frac{154}{261}\right)$	$e\left(\frac{233}{261}\right)$	$e\left(\frac{971}{1044}\right)$	$e\left(\frac{43}{261}\right)$	$e\left(\frac{140}{261}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{227}{348}\right)$	$e\left(\frac{119}{348}\right)$	$e\left(\frac{47}{261}\right)$
$\chi_{58492}(4437,\cdot)$	$-1$	$1$	$e\left(\frac{55}{261}\right)$	$e\left(\frac{178}{261}\right)$	$e\left(\frac{110}{261}\right)$	$e\left(\frac{119}{1044}\right)$	$e\left(\frac{148}{261}\right)$	$e\left(\frac{233}{261}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{59}{348}\right)$	$e\left(\frac{11}{348}\right)$	$e\left(\frac{95}{261}\right)$
$\chi_{58492}(4885,\cdot)$	$-1$	$1$	$e\left(\frac{73}{261}\right)$	$e\left(\frac{241}{261}\right)$	$e\left(\frac{146}{261}\right)$	$e\left(\frac{623}{1044}\right)$	$e\left(\frac{130}{261}\right)$	$e\left(\frac{53}{261}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{227}{348}\right)$	$e\left(\frac{119}{348}\right)$	$e\left(\frac{221}{261}\right)$
$\chi_{58492}(4941,\cdot)$	$-1$	$1$	$e\left(\frac{59}{261}\right)$	$e\left(\frac{134}{261}\right)$	$e\left(\frac{118}{261}\right)$	$e\left(\frac{289}{1044}\right)$	$e\left(\frac{173}{261}\right)$	$e\left(\frac{193}{261}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{193}{348}\right)$	$e\left(\frac{325}{348}\right)$	$e\left(\frac{7}{261}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{58492}(13,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{68}{261}\right)\)	\(e\left(\frac{35}{261}\right)\)	\(e\left(\frac{136}{261}\right)\)	\(e\left(\frac{541}{1044}\right)\)	\(e\left(\frac{164}{261}\right)\)	\(e\left(\frac{103}{261}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{277}{348}\right)\)	\(e\left(\frac{205}{348}\right)\)	\(e\left(\frac{70}{261}\right)\)
\(\chi_{58492}(153,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{125}{261}\right)\)	\(e\left(\frac{191}{261}\right)\)	\(e\left(\frac{250}{261}\right)\)	\(e\left(\frac{223}{1044}\right)\)	\(e\left(\frac{194}{261}\right)\)	\(e\left(\frac{55}{261}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{55}{348}\right)\)	\(e\left(\frac{199}{348}\right)\)	\(e\left(\frac{121}{261}\right)\)
\(\chi_{58492}(209,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{34}{261}\right)\)	\(e\left(\frac{148}{261}\right)\)	\(e\left(\frac{68}{261}\right)\)	\(e\left(\frac{401}{1044}\right)\)	\(e\left(\frac{82}{261}\right)\)	\(e\left(\frac{182}{261}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{269}{348}\right)\)	\(e\left(\frac{233}{348}\right)\)	\(e\left(\frac{35}{261}\right)\)
\(\chi_{58492}(293,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{155}{261}\right)\)	\(e\left(\frac{122}{261}\right)\)	\(e\left(\frac{49}{261}\right)\)	\(e\left(\frac{193}{1044}\right)\)	\(e\left(\frac{251}{261}\right)\)	\(e\left(\frac{16}{261}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{277}{348}\right)\)	\(e\left(\frac{205}{348}\right)\)	\(e\left(\frac{244}{261}\right)\)
\(\chi_{58492}(377,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{259}{261}\right)\)	\(e\left(\frac{22}{261}\right)\)	\(e\left(\frac{257}{261}\right)\)	\(e\left(\frac{437}{1044}\right)\)	\(e\left(\frac{118}{261}\right)\)	\(e\left(\frac{20}{261}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{281}{348}\right)\)	\(e\left(\frac{17}{348}\right)\)	\(e\left(\frac{44}{261}\right)\)
\(\chi_{58492}(405,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{70}{261}\right)\)	\(e\left(\frac{13}{261}\right)\)	\(e\left(\frac{140}{261}\right)\)	\(e\left(\frac{887}{1044}\right)\)	\(e\left(\frac{46}{261}\right)\)	\(e\left(\frac{83}{261}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{83}{348}\right)\)	\(e\left(\frac{275}{348}\right)\)	\(e\left(\frac{26}{261}\right)\)
\(\chi_{58492}(713,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{86}{261}\right)\)	\(e\left(\frac{98}{261}\right)\)	\(e\left(\frac{172}{261}\right)\)	\(e\left(\frac{1}{1044}\right)\)	\(e\left(\frac{146}{261}\right)\)	\(e\left(\frac{184}{261}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{97}{348}\right)\)	\(e\left(\frac{313}{348}\right)\)	\(e\left(\frac{196}{261}\right)\)
\(\chi_{58492}(1105,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{62}{261}\right)\)	\(e\left(\frac{101}{261}\right)\)	\(e\left(\frac{124}{261}\right)\)	\(e\left(\frac{25}{1044}\right)\)	\(e\left(\frac{257}{261}\right)\)	\(e\left(\frac{163}{261}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{337}{348}\right)\)	\(e\left(\frac{169}{348}\right)\)	\(e\left(\frac{202}{261}\right)\)
\(\chi_{58492}(1917,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{257}{261}\right)\)	\(e\left(\frac{44}{261}\right)\)	\(e\left(\frac{253}{261}\right)\)	\(e\left(\frac{613}{1044}\right)\)	\(e\left(\frac{236}{261}\right)\)	\(e\left(\frac{40}{261}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{301}{348}\right)\)	\(e\left(\frac{121}{348}\right)\)	\(e\left(\frac{88}{261}\right)\)
\(\chi_{58492}(2113,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{80}{261}\right)\)	\(e\left(\frac{164}{261}\right)\)	\(e\left(\frac{160}{261}\right)\)	\(e\left(\frac{529}{1044}\right)\)	\(e\left(\frac{239}{261}\right)\)	\(e\left(\frac{244}{261}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{157}{348}\right)\)	\(e\left(\frac{277}{348}\right)\)	\(e\left(\frac{67}{261}\right)\)
\(\chi_{58492}(2141,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{261}\right)\)	\(e\left(\frac{71}{261}\right)\)	\(e\left(\frac{82}{261}\right)\)	\(e\left(\frac{829}{1044}\right)\)	\(e\left(\frac{191}{261}\right)\)	\(e\left(\frac{112}{261}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{25}{348}\right)\)	\(e\left(\frac{217}{348}\right)\)	\(e\left(\frac{142}{261}\right)\)
\(\chi_{58492}(2169,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{56}{261}\right)\)	\(e\left(\frac{167}{261}\right)\)	\(e\left(\frac{112}{261}\right)\)	\(e\left(\frac{31}{1044}\right)\)	\(e\left(\frac{89}{261}\right)\)	\(e\left(\frac{223}{261}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{223}{348}\right)\)	\(e\left(\frac{307}{348}\right)\)	\(e\left(\frac{73}{261}\right)\)
\(\chi_{58492}(2225,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{235}{261}\right)\)	\(e\left(\frac{25}{261}\right)\)	\(e\left(\frac{209}{261}\right)\)	\(e\left(\frac{461}{1044}\right)\)	\(e\left(\frac{229}{261}\right)\)	\(e\left(\frac{260}{261}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{173}{348}\right)\)	\(e\left(\frac{221}{348}\right)\)	\(e\left(\frac{50}{261}\right)\)
\(\chi_{58492}(2281,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{170}{261}\right)\)	\(e\left(\frac{218}{261}\right)\)	\(e\left(\frac{79}{261}\right)\)	\(e\left(\frac{961}{1044}\right)\)	\(e\left(\frac{149}{261}\right)\)	\(e\left(\frac{127}{261}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{301}{348}\right)\)	\(e\left(\frac{121}{348}\right)\)	\(e\left(\frac{175}{261}\right)\)
\(\chi_{58492}(2505,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{261}\right)\)	\(e\left(\frac{125}{261}\right)\)	\(e\left(\frac{1}{261}\right)\)	\(e\left(\frac{217}{1044}\right)\)	\(e\left(\frac{101}{261}\right)\)	\(e\left(\frac{256}{261}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{169}{348}\right)\)	\(e\left(\frac{61}{348}\right)\)	\(e\left(\frac{250}{261}\right)\)
\(\chi_{58492}(2701,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{98}{261}\right)\)	\(e\left(\frac{227}{261}\right)\)	\(e\left(\frac{196}{261}\right)\)	\(e\left(\frac{511}{1044}\right)\)	\(e\left(\frac{221}{261}\right)\)	\(e\left(\frac{64}{261}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{151}{348}\right)\)	\(e\left(\frac{211}{348}\right)\)	\(e\left(\frac{193}{261}\right)\)
\(\chi_{58492}(2729,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{146}{261}\right)\)	\(e\left(\frac{221}{261}\right)\)	\(e\left(\frac{31}{261}\right)\)	\(e\left(\frac{463}{1044}\right)\)	\(e\left(\frac{260}{261}\right)\)	\(e\left(\frac{106}{261}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{19}{348}\right)\)	\(e\left(\frac{151}{348}\right)\)	\(e\left(\frac{181}{261}\right)\)
\(\chi_{58492}(2757,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{261}\right)\)	\(e\left(\frac{217}{261}\right)\)	\(e\left(\frac{8}{261}\right)\)	\(e\left(\frac{953}{1044}\right)\)	\(e\left(\frac{25}{261}\right)\)	\(e\left(\frac{221}{261}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{221}{348}\right)\)	\(e\left(\frac{53}{348}\right)\)	\(e\left(\frac{173}{261}\right)\)
\(\chi_{58492}(2785,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{10}{261}\right)\)	\(e\left(\frac{151}{261}\right)\)	\(e\left(\frac{20}{261}\right)\)	\(e\left(\frac{425}{1044}\right)\)	\(e\left(\frac{193}{261}\right)\)	\(e\left(\frac{161}{261}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{161}{348}\right)\)	\(e\left(\frac{89}{348}\right)\)	\(e\left(\frac{41}{261}\right)\)
\(\chi_{58492}(2925,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{261}\right)\)	\(e\left(\frac{184}{261}\right)\)	\(e\left(\frac{14}{261}\right)\)	\(e\left(\frac{689}{1044}\right)\)	\(e\left(\frac{109}{261}\right)\)	\(e\left(\frac{191}{261}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{17}{348}\right)\)	\(e\left(\frac{245}{348}\right)\)	\(e\left(\frac{107}{261}\right)\)
\(\chi_{58492}(3177,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{64}{261}\right)\)	\(e\left(\frac{79}{261}\right)\)	\(e\left(\frac{128}{261}\right)\)	\(e\left(\frac{893}{1044}\right)\)	\(e\left(\frac{139}{261}\right)\)	\(e\left(\frac{143}{261}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{317}{348}\right)\)	\(e\left(\frac{65}{348}\right)\)	\(e\left(\frac{158}{261}\right)\)
\(\chi_{58492}(3261,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{128}{261}\right)\)	\(e\left(\frac{158}{261}\right)\)	\(e\left(\frac{256}{261}\right)\)	\(e\left(\frac{481}{1044}\right)\)	\(e\left(\frac{17}{261}\right)\)	\(e\left(\frac{25}{261}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{25}{348}\right)\)	\(e\left(\frac{217}{348}\right)\)	\(e\left(\frac{55}{261}\right)\)
\(\chi_{58492}(3625,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{260}{261}\right)\)	\(e\left(\frac{11}{261}\right)\)	\(e\left(\frac{259}{261}\right)\)	\(e\left(\frac{349}{1044}\right)\)	\(e\left(\frac{59}{261}\right)\)	\(e\left(\frac{10}{261}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{97}{348}\right)\)	\(e\left(\frac{313}{348}\right)\)	\(e\left(\frac{22}{261}\right)\)
\(\chi_{58492}(3709,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{261}\right)\)	\(e\left(\frac{49}{261}\right)\)	\(e\left(\frac{86}{261}\right)\)	\(e\left(\frac{131}{1044}\right)\)	\(e\left(\frac{73}{261}\right)\)	\(e\left(\frac{92}{261}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{179}{348}\right)\)	\(e\left(\frac{287}{348}\right)\)	\(e\left(\frac{98}{261}\right)\)
\(\chi_{58492}(3793,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{106}{261}\right)\)	\(e\left(\frac{139}{261}\right)\)	\(e\left(\frac{212}{261}\right)\)	\(e\left(\frac{851}{1044}\right)\)	\(e\left(\frac{10}{261}\right)\)	\(e\left(\frac{245}{261}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{71}{348}\right)\)	\(e\left(\frac{143}{348}\right)\)	\(e\left(\frac{17}{261}\right)\)
\(\chi_{58492}(4017,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{166}{261}\right)\)	\(e\left(\frac{1}{261}\right)\)	\(e\left(\frac{71}{261}\right)\)	\(e\left(\frac{269}{1044}\right)\)	\(e\left(\frac{124}{261}\right)\)	\(e\left(\frac{167}{261}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{341}{348}\right)\)	\(e\left(\frac{329}{348}\right)\)	\(e\left(\frac{2}{261}\right)\)
\(\chi_{58492}(4129,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{74}{261}\right)\)	\(e\left(\frac{230}{261}\right)\)	\(e\left(\frac{148}{261}\right)\)	\(e\left(\frac{13}{1044}\right)\)	\(e\left(\frac{71}{261}\right)\)	\(e\left(\frac{43}{261}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{217}{348}\right)\)	\(e\left(\frac{241}{348}\right)\)	\(e\left(\frac{199}{261}\right)\)
\(\chi_{58492}(4409,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{247}{261}\right)\)	\(e\left(\frac{154}{261}\right)\)	\(e\left(\frac{233}{261}\right)\)	\(e\left(\frac{971}{1044}\right)\)	\(e\left(\frac{43}{261}\right)\)	\(e\left(\frac{140}{261}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{227}{348}\right)\)	\(e\left(\frac{119}{348}\right)\)	\(e\left(\frac{47}{261}\right)\)
\(\chi_{58492}(4437,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{261}\right)\)	\(e\left(\frac{178}{261}\right)\)	\(e\left(\frac{110}{261}\right)\)	\(e\left(\frac{119}{1044}\right)\)	\(e\left(\frac{148}{261}\right)\)	\(e\left(\frac{233}{261}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{59}{348}\right)\)	\(e\left(\frac{11}{348}\right)\)	\(e\left(\frac{95}{261}\right)\)
\(\chi_{58492}(4885,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{261}\right)\)	\(e\left(\frac{241}{261}\right)\)	\(e\left(\frac{146}{261}\right)\)	\(e\left(\frac{623}{1044}\right)\)	\(e\left(\frac{130}{261}\right)\)	\(e\left(\frac{53}{261}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{227}{348}\right)\)	\(e\left(\frac{119}{348}\right)\)	\(e\left(\frac{221}{261}\right)\)
\(\chi_{58492}(4941,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{261}\right)\)	\(e\left(\frac{134}{261}\right)\)	\(e\left(\frac{118}{261}\right)\)	\(e\left(\frac{289}{1044}\right)\)	\(e\left(\frac{173}{261}\right)\)	\(e\left(\frac{193}{261}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{193}{348}\right)\)	\(e\left(\frac{325}{348}\right)\)	\(e\left(\frac{7}{261}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

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.jh
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.en	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);