LMFDB - Dirichlet character orbit 549261.hg

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(549261, base_ring=CyclotomicField(3390)) M = H._module chi = DirichletCharacter(H, M([565,2762])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(26, 549261)) 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("549261.26"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$549261$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$61029$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$3390$	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 61029.dx	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{1695})$	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 3390 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 896 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{549261}(26,\cdot)$	$-1$	$1$	$e\left(\frac{1109}{1130}\right)$	$e\left(\frac{544}{565}\right)$	$e\left(\frac{3043}{3390}\right)$	$e\left(\frac{187}{1695}\right)$	$e\left(\frac{1067}{1130}\right)$	$e\left(\frac{298}{339}\right)$	$e\left(\frac{853}{1130}\right)$	$e\left(\frac{328}{1695}\right)$	$e\left(\frac{311}{3390}\right)$	$e\left(\frac{523}{565}\right)$
$\chi_{549261}(539,\cdot)$	$-1$	$1$	$e\left(\frac{1051}{1130}\right)$	$e\left(\frac{486}{565}\right)$	$e\left(\frac{3107}{3390}\right)$	$e\left(\frac{1403}{1695}\right)$	$e\left(\frac{893}{1130}\right)$	$e\left(\frac{287}{339}\right)$	$e\left(\frac{357}{1130}\right)$	$e\left(\frac{77}{1695}\right)$	$e\left(\frac{2569}{3390}\right)$	$e\left(\frac{407}{565}\right)$
$\chi_{549261}(1079,\cdot)$	$-1$	$1$	$e\left(\frac{233}{1130}\right)$	$e\left(\frac{233}{565}\right)$	$e\left(\frac{1321}{3390}\right)$	$e\left(\frac{1369}{1695}\right)$	$e\left(\frac{699}{1130}\right)$	$e\left(\frac{202}{339}\right)$	$e\left(\frac{921}{1130}\right)$	$e\left(\frac{1096}{1695}\right)$	$e\left(\frac{47}{3390}\right)$	$e\left(\frac{466}{565}\right)$
$\chi_{549261}(1673,\cdot)$	$-1$	$1$	$e\left(\frac{1079}{1130}\right)$	$e\left(\frac{514}{565}\right)$	$e\left(\frac{2063}{3390}\right)$	$e\left(\frac{212}{1695}\right)$	$e\left(\frac{977}{1130}\right)$	$e\left(\frac{191}{339}\right)$	$e\left(\frac{1103}{1130}\right)$	$e\left(\frac{1523}{1695}\right)$	$e\left(\frac{271}{3390}\right)$	$e\left(\frac{463}{565}\right)$
$\chi_{549261}(2537,\cdot)$	$-1$	$1$	$e\left(\frac{769}{1130}\right)$	$e\left(\frac{204}{565}\right)$	$e\left(\frac{223}{3390}\right)$	$e\left(\frac{847}{1695}\right)$	$e\left(\frac{47}{1130}\right)$	$e\left(\frac{253}{339}\right)$	$e\left(\frac{673}{1130}\right)$	$e\left(\frac{688}{1695}\right)$	$e\left(\frac{611}{3390}\right)$	$e\left(\frac{408}{565}\right)$
$\chi_{549261}(2618,\cdot)$	$-1$	$1$	$e\left(\frac{703}{1130}\right)$	$e\left(\frac{138}{565}\right)$	$e\left(\frac{1231}{3390}\right)$	$e\left(\frac{1354}{1695}\right)$	$e\left(\frac{979}{1130}\right)$	$e\left(\frac{334}{339}\right)$	$e\left(\frac{771}{1130}\right)$	$e\left(\frac{1396}{1695}\right)$	$e\left(\frac{1427}{3390}\right)$	$e\left(\frac{276}{565}\right)$
$\chi_{549261}(2645,\cdot)$	$-1$	$1$	$e\left(\frac{687}{1130}\right)$	$e\left(\frac{122}{565}\right)$	$e\left(\frac{3119}{3390}\right)$	$e\left(\frac{1631}{1695}\right)$	$e\left(\frac{931}{1130}\right)$	$e\left(\frac{179}{339}\right)$	$e\left(\frac{829}{1130}\right)$	$e\left(\frac{1619}{1695}\right)$	$e\left(\frac{1933}{3390}\right)$	$e\left(\frac{244}{565}\right)$
$\chi_{549261}(3050,\cdot)$	$-1$	$1$	$e\left(\frac{247}{1130}\right)$	$e\left(\frac{247}{565}\right)$	$e\left(\frac{3059}{3390}\right)$	$e\left(\frac{491}{1695}\right)$	$e\left(\frac{741}{1130}\right)$	$e\left(\frac{41}{339}\right)$	$e\left(\frac{729}{1130}\right)$	$e\left(\frac{689}{1695}\right)$	$e\left(\frac{1723}{3390}\right)$	$e\left(\frac{494}{565}\right)$
$\chi_{549261}(4319,\cdot)$	$-1$	$1$	$e\left(\frac{537}{1130}\right)$	$e\left(\frac{537}{565}\right)$	$e\left(\frac{1609}{3390}\right)$	$e\left(\frac{61}{1695}\right)$	$e\left(\frac{481}{1130}\right)$	$e\left(\frac{322}{339}\right)$	$e\left(\frac{949}{1130}\right)$	$e\left(\frac{814}{1695}\right)$	$e\left(\frac{1733}{3390}\right)$	$e\left(\frac{509}{565}\right)$
$\chi_{549261}(4346,\cdot)$	$-1$	$1$	$e\left(\frac{717}{1130}\right)$	$e\left(\frac{152}{565}\right)$	$e\left(\frac{2969}{3390}\right)$	$e\left(\frac{476}{1695}\right)$	$e\left(\frac{1021}{1130}\right)$	$e\left(\frac{173}{339}\right)$	$e\left(\frac{579}{1130}\right)$	$e\left(\frac{989}{1695}\right)$	$e\left(\frac{3103}{3390}\right)$	$e\left(\frac{304}{565}\right)$
$\chi_{549261}(5777,\cdot)$	$-1$	$1$	$e\left(\frac{811}{1130}\right)$	$e\left(\frac{246}{565}\right)$	$e\left(\frac{2047}{3390}\right)$	$e\left(\frac{1603}{1695}\right)$	$e\left(\frac{173}{1130}\right)$	$e\left(\frac{109}{339}\right)$	$e\left(\frac{97}{1130}\right)$	$e\left(\frac{1162}{1695}\right)$	$e\left(\frac{2249}{3390}\right)$	$e\left(\frac{492}{565}\right)$
$\chi_{549261}(6020,\cdot)$	$-1$	$1$	$e\left(\frac{163}{1130}\right)$	$e\left(\frac{163}{565}\right)$	$e\left(\frac{541}{3390}\right)$	$e\left(\frac{109}{1695}\right)$	$e\left(\frac{489}{1130}\right)$	$e\left(\frac{103}{339}\right)$	$e\left(\frac{751}{1130}\right)$	$e\left(\frac{871}{1695}\right)$	$e\left(\frac{707}{3390}\right)$	$e\left(\frac{326}{565}\right)$
$\chi_{549261}(6668,\cdot)$	$-1$	$1$	$e\left(\frac{653}{1130}\right)$	$e\left(\frac{88}{565}\right)$	$e\left(\frac{2611}{3390}\right)$	$e\left(\frac{454}{1695}\right)$	$e\left(\frac{829}{1130}\right)$	$e\left(\frac{118}{339}\right)$	$e\left(\frac{811}{1130}\right)$	$e\left(\frac{751}{1695}\right)$	$e\left(\frac{2867}{3390}\right)$	$e\left(\frac{176}{565}\right)$
$\chi_{549261}(8126,\cdot)$	$-1$	$1$	$e\left(\frac{731}{1130}\right)$	$e\left(\frac{166}{565}\right)$	$e\left(\frac{187}{3390}\right)$	$e\left(\frac{163}{1695}\right)$	$e\left(\frac{1063}{1130}\right)$	$e\left(\frac{238}{339}\right)$	$e\left(\frac{387}{1130}\right)$	$e\left(\frac{1147}{1695}\right)$	$e\left(\frac{2519}{3390}\right)$	$e\left(\frac{332}{565}\right)$
$\chi_{549261}(9206,\cdot)$	$-1$	$1$	$e\left(\frac{173}{1130}\right)$	$e\left(\frac{173}{565}\right)$	$e\left(\frac{491}{3390}\right)$	$e\left(\frac{854}{1695}\right)$	$e\left(\frac{519}{1130}\right)$	$e\left(\frac{101}{339}\right)$	$e\left(\frac{291}{1130}\right)$	$e\left(\frac{1226}{1695}\right)$	$e\left(\frac{2227}{3390}\right)$	$e\left(\frac{346}{565}\right)$
$\chi_{549261}(9692,\cdot)$	$-1$	$1$	$e\left(\frac{217}{1130}\right)$	$e\left(\frac{217}{565}\right)$	$e\left(\frac{3209}{3390}\right)$	$e\left(\frac{1646}{1695}\right)$	$e\left(\frac{651}{1130}\right)$	$e\left(\frac{47}{339}\right)$	$e\left(\frac{979}{1130}\right)$	$e\left(\frac{1319}{1695}\right)$	$e\left(\frac{553}{3390}\right)$	$e\left(\frac{434}{565}\right)$
$\chi_{549261}(10583,\cdot)$	$-1$	$1$	$e\left(\frac{317}{1130}\right)$	$e\left(\frac{317}{565}\right)$	$e\left(\frac{449}{3390}\right)$	$e\left(\frac{56}{1695}\right)$	$e\left(\frac{951}{1130}\right)$	$e\left(\frac{140}{339}\right)$	$e\left(\frac{899}{1130}\right)$	$e\left(\frac{914}{1695}\right)$	$e\left(\frac{1063}{3390}\right)$	$e\left(\frac{69}{565}\right)$
$\chi_{549261}(11042,\cdot)$	$-1$	$1$	$e\left(\frac{931}{1130}\right)$	$e\left(\frac{366}{565}\right)$	$e\left(\frac{1447}{3390}\right)$	$e\left(\frac{373}{1695}\right)$	$e\left(\frac{533}{1130}\right)$	$e\left(\frac{85}{339}\right)$	$e\left(\frac{227}{1130}\right)$	$e\left(\frac{337}{1695}\right)$	$e\left(\frac{149}{3390}\right)$	$e\left(\frac{167}{565}\right)$
$\chi_{549261}(11879,\cdot)$	$-1$	$1$	$e\left(\frac{757}{1130}\right)$	$e\left(\frac{192}{565}\right)$	$e\left(\frac{509}{3390}\right)$	$e\left(\frac{1196}{1695}\right)$	$e\left(\frac{11}{1130}\right)$	$e\left(\frac{278}{339}\right)$	$e\left(\frac{999}{1130}\right)$	$e\left(\frac{149}{1695}\right)$	$e\left(\frac{1273}{3390}\right)$	$e\left(\frac{384}{565}\right)$
$\chi_{549261}(12500,\cdot)$	$-1$	$1$	$e\left(\frac{407}{1130}\right)$	$e\left(\frac{407}{565}\right)$	$e\left(\frac{1129}{3390}\right)$	$e\left(\frac{1111}{1695}\right)$	$e\left(\frac{91}{1130}\right)$	$e\left(\frac{235}{339}\right)$	$e\left(\frac{149}{1130}\right)$	$e\left(\frac{154}{1695}\right)$	$e\left(\frac{53}{3390}\right)$	$e\left(\frac{249}{565}\right)$
$\chi_{549261}(12905,\cdot)$	$-1$	$1$	$e\left(\frac{623}{1130}\right)$	$e\left(\frac{58}{565}\right)$	$e\left(\frac{2761}{3390}\right)$	$e\left(\frac{1609}{1695}\right)$	$e\left(\frac{739}{1130}\right)$	$e\left(\frac{124}{339}\right)$	$e\left(\frac{1061}{1130}\right)$	$e\left(\frac{1381}{1695}\right)$	$e\left(\frac{1697}{3390}\right)$	$e\left(\frac{116}{565}\right)$
$\chi_{549261}(12986,\cdot)$	$-1$	$1$	$e\left(\frac{1093}{1130}\right)$	$e\left(\frac{528}{565}\right)$	$e\left(\frac{2671}{3390}\right)$	$e\left(\frac{1594}{1695}\right)$	$e\left(\frac{1019}{1130}\right)$	$e\left(\frac{256}{339}\right)$	$e\left(\frac{911}{1130}\right)$	$e\left(\frac{1681}{1695}\right)$	$e\left(\frac{3077}{3390}\right)$	$e\left(\frac{491}{565}\right)$
$\chi_{549261}(13958,\cdot)$	$-1$	$1$	$e\left(\frac{821}{1130}\right)$	$e\left(\frac{256}{565}\right)$	$e\left(\frac{3127}{3390}\right)$	$e\left(\frac{88}{1695}\right)$	$e\left(\frac{203}{1130}\right)$	$e\left(\frac{220}{339}\right)$	$e\left(\frac{767}{1130}\right)$	$e\left(\frac{952}{1695}\right)$	$e\left(\frac{2639}{3390}\right)$	$e\left(\frac{512}{565}\right)$
$\chi_{549261}(15173,\cdot)$	$-1$	$1$	$e\left(\frac{429}{1130}\right)$	$e\left(\frac{429}{565}\right)$	$e\left(\frac{793}{3390}\right)$	$e\left(\frac{1507}{1695}\right)$	$e\left(\frac{157}{1130}\right)$	$e\left(\frac{208}{339}\right)$	$e\left(\frac{493}{1130}\right)$	$e\left(\frac{1048}{1695}\right)$	$e\left(\frac{911}{3390}\right)$	$e\left(\frac{293}{565}\right)$
$\chi_{549261}(15281,\cdot)$	$-1$	$1$	$e\left(\frac{1047}{1130}\right)$	$e\left(\frac{482}{565}\right)$	$e\left(\frac{1319}{3390}\right)$	$e\left(\frac{1331}{1695}\right)$	$e\left(\frac{881}{1130}\right)$	$e\left(\frac{107}{339}\right)$	$e\left(\frac{89}{1130}\right)$	$e\left(\frac{839}{1695}\right)$	$e\left(\frac{2413}{3390}\right)$	$e\left(\frac{399}{565}\right)$
$\chi_{549261}(15929,\cdot)$	$-1$	$1$	$e\left(\frac{139}{1130}\right)$	$e\left(\frac{139}{565}\right)$	$e\left(\frac{2243}{3390}\right)$	$e\left(\frac{242}{1695}\right)$	$e\left(\frac{417}{1130}\right)$	$e\left(\frac{266}{339}\right)$	$e\left(\frac{273}{1130}\right)$	$e\left(\frac{923}{1695}\right)$	$e\left(\frac{901}{3390}\right)$	$e\left(\frac{278}{565}\right)$
$\chi_{549261}(16010,\cdot)$	$-1$	$1$	$e\left(\frac{1029}{1130}\right)$	$e\left(\frac{464}{565}\right)$	$e\left(\frac{53}{3390}\right)$	$e\left(\frac{1007}{1695}\right)$	$e\left(\frac{827}{1130}\right)$	$e\left(\frac{314}{339}\right)$	$e\left(\frac{13}{1130}\right)$	$e\left(\frac{878}{1695}\right)$	$e\left(\frac{1711}{3390}\right)$	$e\left(\frac{363}{565}\right)$
$\chi_{549261}(17603,\cdot)$	$-1$	$1$	$e\left(\frac{617}{1130}\right)$	$e\left(\frac{52}{565}\right)$	$e\left(\frac{79}{3390}\right)$	$e\left(\frac{1501}{1695}\right)$	$e\left(\frac{721}{1130}\right)$	$e\left(\frac{193}{339}\right)$	$e\left(\frac{659}{1130}\right)$	$e\left(\frac{829}{1695}\right)$	$e\left(\frac{1463}{3390}\right)$	$e\left(\frac{104}{565}\right)$
$\chi_{549261}(17873,\cdot)$	$-1$	$1$	$e\left(\frac{273}{1130}\right)$	$e\left(\frac{273}{565}\right)$	$e\left(\frac{1121}{3390}\right)$	$e\left(\frac{959}{1695}\right)$	$e\left(\frac{819}{1130}\right)$	$e\left(\frac{194}{339}\right)$	$e\left(\frac{211}{1130}\right)$	$e\left(\frac{821}{1695}\right)$	$e\left(\frac{2737}{3390}\right)$	$e\left(\frac{546}{565}\right)$
$\chi_{549261}(18089,\cdot)$	$-1$	$1$	$e\left(\frac{759}{1130}\right)$	$e\left(\frac{194}{565}\right)$	$e\left(\frac{2533}{3390}\right)$	$e\left(\frac{667}{1695}\right)$	$e\left(\frac{17}{1130}\right)$	$e\left(\frac{142}{339}\right)$	$e\left(\frac{3}{1130}\right)$	$e\left(\frac{898}{1695}\right)$	$e\left(\frac{221}{3390}\right)$	$e\left(\frac{388}{565}\right)$
$\chi_{549261}(18332,\cdot)$	$-1$	$1$	$e\left(\frac{61}{1130}\right)$	$e\left(\frac{61}{565}\right)$	$e\left(\frac{2407}{3390}\right)$	$e\left(\frac{1663}{1695}\right)$	$e\left(\frac{183}{1130}\right)$	$e\left(\frac{259}{339}\right)$	$e\left(\frac{697}{1130}\right)$	$e\left(\frac{1657}{1695}\right)$	$e\left(\frac{119}{3390}\right)$	$e\left(\frac{122}{565}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{549261}(26,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1109}{1130}\right)\)	\(e\left(\frac{544}{565}\right)\)	\(e\left(\frac{3043}{3390}\right)\)	\(e\left(\frac{187}{1695}\right)\)	\(e\left(\frac{1067}{1130}\right)\)	\(e\left(\frac{298}{339}\right)\)	\(e\left(\frac{853}{1130}\right)\)	\(e\left(\frac{328}{1695}\right)\)	\(e\left(\frac{311}{3390}\right)\)	\(e\left(\frac{523}{565}\right)\)
\(\chi_{549261}(539,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1051}{1130}\right)\)	\(e\left(\frac{486}{565}\right)\)	\(e\left(\frac{3107}{3390}\right)\)	\(e\left(\frac{1403}{1695}\right)\)	\(e\left(\frac{893}{1130}\right)\)	\(e\left(\frac{287}{339}\right)\)	\(e\left(\frac{357}{1130}\right)\)	\(e\left(\frac{77}{1695}\right)\)	\(e\left(\frac{2569}{3390}\right)\)	\(e\left(\frac{407}{565}\right)\)
\(\chi_{549261}(1079,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{233}{1130}\right)\)	\(e\left(\frac{233}{565}\right)\)	\(e\left(\frac{1321}{3390}\right)\)	\(e\left(\frac{1369}{1695}\right)\)	\(e\left(\frac{699}{1130}\right)\)	\(e\left(\frac{202}{339}\right)\)	\(e\left(\frac{921}{1130}\right)\)	\(e\left(\frac{1096}{1695}\right)\)	\(e\left(\frac{47}{3390}\right)\)	\(e\left(\frac{466}{565}\right)\)
\(\chi_{549261}(1673,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1079}{1130}\right)\)	\(e\left(\frac{514}{565}\right)\)	\(e\left(\frac{2063}{3390}\right)\)	\(e\left(\frac{212}{1695}\right)\)	\(e\left(\frac{977}{1130}\right)\)	\(e\left(\frac{191}{339}\right)\)	\(e\left(\frac{1103}{1130}\right)\)	\(e\left(\frac{1523}{1695}\right)\)	\(e\left(\frac{271}{3390}\right)\)	\(e\left(\frac{463}{565}\right)\)
\(\chi_{549261}(2537,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{769}{1130}\right)\)	\(e\left(\frac{204}{565}\right)\)	\(e\left(\frac{223}{3390}\right)\)	\(e\left(\frac{847}{1695}\right)\)	\(e\left(\frac{47}{1130}\right)\)	\(e\left(\frac{253}{339}\right)\)	\(e\left(\frac{673}{1130}\right)\)	\(e\left(\frac{688}{1695}\right)\)	\(e\left(\frac{611}{3390}\right)\)	\(e\left(\frac{408}{565}\right)\)
\(\chi_{549261}(2618,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{703}{1130}\right)\)	\(e\left(\frac{138}{565}\right)\)	\(e\left(\frac{1231}{3390}\right)\)	\(e\left(\frac{1354}{1695}\right)\)	\(e\left(\frac{979}{1130}\right)\)	\(e\left(\frac{334}{339}\right)\)	\(e\left(\frac{771}{1130}\right)\)	\(e\left(\frac{1396}{1695}\right)\)	\(e\left(\frac{1427}{3390}\right)\)	\(e\left(\frac{276}{565}\right)\)
\(\chi_{549261}(2645,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{687}{1130}\right)\)	\(e\left(\frac{122}{565}\right)\)	\(e\left(\frac{3119}{3390}\right)\)	\(e\left(\frac{1631}{1695}\right)\)	\(e\left(\frac{931}{1130}\right)\)	\(e\left(\frac{179}{339}\right)\)	\(e\left(\frac{829}{1130}\right)\)	\(e\left(\frac{1619}{1695}\right)\)	\(e\left(\frac{1933}{3390}\right)\)	\(e\left(\frac{244}{565}\right)\)
\(\chi_{549261}(3050,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{247}{1130}\right)\)	\(e\left(\frac{247}{565}\right)\)	\(e\left(\frac{3059}{3390}\right)\)	\(e\left(\frac{491}{1695}\right)\)	\(e\left(\frac{741}{1130}\right)\)	\(e\left(\frac{41}{339}\right)\)	\(e\left(\frac{729}{1130}\right)\)	\(e\left(\frac{689}{1695}\right)\)	\(e\left(\frac{1723}{3390}\right)\)	\(e\left(\frac{494}{565}\right)\)
\(\chi_{549261}(4319,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{537}{1130}\right)\)	\(e\left(\frac{537}{565}\right)\)	\(e\left(\frac{1609}{3390}\right)\)	\(e\left(\frac{61}{1695}\right)\)	\(e\left(\frac{481}{1130}\right)\)	\(e\left(\frac{322}{339}\right)\)	\(e\left(\frac{949}{1130}\right)\)	\(e\left(\frac{814}{1695}\right)\)	\(e\left(\frac{1733}{3390}\right)\)	\(e\left(\frac{509}{565}\right)\)
\(\chi_{549261}(4346,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{717}{1130}\right)\)	\(e\left(\frac{152}{565}\right)\)	\(e\left(\frac{2969}{3390}\right)\)	\(e\left(\frac{476}{1695}\right)\)	\(e\left(\frac{1021}{1130}\right)\)	\(e\left(\frac{173}{339}\right)\)	\(e\left(\frac{579}{1130}\right)\)	\(e\left(\frac{989}{1695}\right)\)	\(e\left(\frac{3103}{3390}\right)\)	\(e\left(\frac{304}{565}\right)\)
\(\chi_{549261}(5777,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{811}{1130}\right)\)	\(e\left(\frac{246}{565}\right)\)	\(e\left(\frac{2047}{3390}\right)\)	\(e\left(\frac{1603}{1695}\right)\)	\(e\left(\frac{173}{1130}\right)\)	\(e\left(\frac{109}{339}\right)\)	\(e\left(\frac{97}{1130}\right)\)	\(e\left(\frac{1162}{1695}\right)\)	\(e\left(\frac{2249}{3390}\right)\)	\(e\left(\frac{492}{565}\right)\)
\(\chi_{549261}(6020,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{163}{1130}\right)\)	\(e\left(\frac{163}{565}\right)\)	\(e\left(\frac{541}{3390}\right)\)	\(e\left(\frac{109}{1695}\right)\)	\(e\left(\frac{489}{1130}\right)\)	\(e\left(\frac{103}{339}\right)\)	\(e\left(\frac{751}{1130}\right)\)	\(e\left(\frac{871}{1695}\right)\)	\(e\left(\frac{707}{3390}\right)\)	\(e\left(\frac{326}{565}\right)\)
\(\chi_{549261}(6668,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{653}{1130}\right)\)	\(e\left(\frac{88}{565}\right)\)	\(e\left(\frac{2611}{3390}\right)\)	\(e\left(\frac{454}{1695}\right)\)	\(e\left(\frac{829}{1130}\right)\)	\(e\left(\frac{118}{339}\right)\)	\(e\left(\frac{811}{1130}\right)\)	\(e\left(\frac{751}{1695}\right)\)	\(e\left(\frac{2867}{3390}\right)\)	\(e\left(\frac{176}{565}\right)\)
\(\chi_{549261}(8126,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{731}{1130}\right)\)	\(e\left(\frac{166}{565}\right)\)	\(e\left(\frac{187}{3390}\right)\)	\(e\left(\frac{163}{1695}\right)\)	\(e\left(\frac{1063}{1130}\right)\)	\(e\left(\frac{238}{339}\right)\)	\(e\left(\frac{387}{1130}\right)\)	\(e\left(\frac{1147}{1695}\right)\)	\(e\left(\frac{2519}{3390}\right)\)	\(e\left(\frac{332}{565}\right)\)
\(\chi_{549261}(9206,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{173}{1130}\right)\)	\(e\left(\frac{173}{565}\right)\)	\(e\left(\frac{491}{3390}\right)\)	\(e\left(\frac{854}{1695}\right)\)	\(e\left(\frac{519}{1130}\right)\)	\(e\left(\frac{101}{339}\right)\)	\(e\left(\frac{291}{1130}\right)\)	\(e\left(\frac{1226}{1695}\right)\)	\(e\left(\frac{2227}{3390}\right)\)	\(e\left(\frac{346}{565}\right)\)
\(\chi_{549261}(9692,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{217}{1130}\right)\)	\(e\left(\frac{217}{565}\right)\)	\(e\left(\frac{3209}{3390}\right)\)	\(e\left(\frac{1646}{1695}\right)\)	\(e\left(\frac{651}{1130}\right)\)	\(e\left(\frac{47}{339}\right)\)	\(e\left(\frac{979}{1130}\right)\)	\(e\left(\frac{1319}{1695}\right)\)	\(e\left(\frac{553}{3390}\right)\)	\(e\left(\frac{434}{565}\right)\)
\(\chi_{549261}(10583,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{317}{1130}\right)\)	\(e\left(\frac{317}{565}\right)\)	\(e\left(\frac{449}{3390}\right)\)	\(e\left(\frac{56}{1695}\right)\)	\(e\left(\frac{951}{1130}\right)\)	\(e\left(\frac{140}{339}\right)\)	\(e\left(\frac{899}{1130}\right)\)	\(e\left(\frac{914}{1695}\right)\)	\(e\left(\frac{1063}{3390}\right)\)	\(e\left(\frac{69}{565}\right)\)
\(\chi_{549261}(11042,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{931}{1130}\right)\)	\(e\left(\frac{366}{565}\right)\)	\(e\left(\frac{1447}{3390}\right)\)	\(e\left(\frac{373}{1695}\right)\)	\(e\left(\frac{533}{1130}\right)\)	\(e\left(\frac{85}{339}\right)\)	\(e\left(\frac{227}{1130}\right)\)	\(e\left(\frac{337}{1695}\right)\)	\(e\left(\frac{149}{3390}\right)\)	\(e\left(\frac{167}{565}\right)\)
\(\chi_{549261}(11879,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{757}{1130}\right)\)	\(e\left(\frac{192}{565}\right)\)	\(e\left(\frac{509}{3390}\right)\)	\(e\left(\frac{1196}{1695}\right)\)	\(e\left(\frac{11}{1130}\right)\)	\(e\left(\frac{278}{339}\right)\)	\(e\left(\frac{999}{1130}\right)\)	\(e\left(\frac{149}{1695}\right)\)	\(e\left(\frac{1273}{3390}\right)\)	\(e\left(\frac{384}{565}\right)\)
\(\chi_{549261}(12500,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{407}{1130}\right)\)	\(e\left(\frac{407}{565}\right)\)	\(e\left(\frac{1129}{3390}\right)\)	\(e\left(\frac{1111}{1695}\right)\)	\(e\left(\frac{91}{1130}\right)\)	\(e\left(\frac{235}{339}\right)\)	\(e\left(\frac{149}{1130}\right)\)	\(e\left(\frac{154}{1695}\right)\)	\(e\left(\frac{53}{3390}\right)\)	\(e\left(\frac{249}{565}\right)\)
\(\chi_{549261}(12905,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{623}{1130}\right)\)	\(e\left(\frac{58}{565}\right)\)	\(e\left(\frac{2761}{3390}\right)\)	\(e\left(\frac{1609}{1695}\right)\)	\(e\left(\frac{739}{1130}\right)\)	\(e\left(\frac{124}{339}\right)\)	\(e\left(\frac{1061}{1130}\right)\)	\(e\left(\frac{1381}{1695}\right)\)	\(e\left(\frac{1697}{3390}\right)\)	\(e\left(\frac{116}{565}\right)\)
\(\chi_{549261}(12986,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1093}{1130}\right)\)	\(e\left(\frac{528}{565}\right)\)	\(e\left(\frac{2671}{3390}\right)\)	\(e\left(\frac{1594}{1695}\right)\)	\(e\left(\frac{1019}{1130}\right)\)	\(e\left(\frac{256}{339}\right)\)	\(e\left(\frac{911}{1130}\right)\)	\(e\left(\frac{1681}{1695}\right)\)	\(e\left(\frac{3077}{3390}\right)\)	\(e\left(\frac{491}{565}\right)\)
\(\chi_{549261}(13958,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{821}{1130}\right)\)	\(e\left(\frac{256}{565}\right)\)	\(e\left(\frac{3127}{3390}\right)\)	\(e\left(\frac{88}{1695}\right)\)	\(e\left(\frac{203}{1130}\right)\)	\(e\left(\frac{220}{339}\right)\)	\(e\left(\frac{767}{1130}\right)\)	\(e\left(\frac{952}{1695}\right)\)	\(e\left(\frac{2639}{3390}\right)\)	\(e\left(\frac{512}{565}\right)\)
\(\chi_{549261}(15173,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{429}{1130}\right)\)	\(e\left(\frac{429}{565}\right)\)	\(e\left(\frac{793}{3390}\right)\)	\(e\left(\frac{1507}{1695}\right)\)	\(e\left(\frac{157}{1130}\right)\)	\(e\left(\frac{208}{339}\right)\)	\(e\left(\frac{493}{1130}\right)\)	\(e\left(\frac{1048}{1695}\right)\)	\(e\left(\frac{911}{3390}\right)\)	\(e\left(\frac{293}{565}\right)\)
\(\chi_{549261}(15281,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1047}{1130}\right)\)	\(e\left(\frac{482}{565}\right)\)	\(e\left(\frac{1319}{3390}\right)\)	\(e\left(\frac{1331}{1695}\right)\)	\(e\left(\frac{881}{1130}\right)\)	\(e\left(\frac{107}{339}\right)\)	\(e\left(\frac{89}{1130}\right)\)	\(e\left(\frac{839}{1695}\right)\)	\(e\left(\frac{2413}{3390}\right)\)	\(e\left(\frac{399}{565}\right)\)
\(\chi_{549261}(15929,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{139}{1130}\right)\)	\(e\left(\frac{139}{565}\right)\)	\(e\left(\frac{2243}{3390}\right)\)	\(e\left(\frac{242}{1695}\right)\)	\(e\left(\frac{417}{1130}\right)\)	\(e\left(\frac{266}{339}\right)\)	\(e\left(\frac{273}{1130}\right)\)	\(e\left(\frac{923}{1695}\right)\)	\(e\left(\frac{901}{3390}\right)\)	\(e\left(\frac{278}{565}\right)\)
\(\chi_{549261}(16010,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1029}{1130}\right)\)	\(e\left(\frac{464}{565}\right)\)	\(e\left(\frac{53}{3390}\right)\)	\(e\left(\frac{1007}{1695}\right)\)	\(e\left(\frac{827}{1130}\right)\)	\(e\left(\frac{314}{339}\right)\)	\(e\left(\frac{13}{1130}\right)\)	\(e\left(\frac{878}{1695}\right)\)	\(e\left(\frac{1711}{3390}\right)\)	\(e\left(\frac{363}{565}\right)\)
\(\chi_{549261}(17603,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{617}{1130}\right)\)	\(e\left(\frac{52}{565}\right)\)	\(e\left(\frac{79}{3390}\right)\)	\(e\left(\frac{1501}{1695}\right)\)	\(e\left(\frac{721}{1130}\right)\)	\(e\left(\frac{193}{339}\right)\)	\(e\left(\frac{659}{1130}\right)\)	\(e\left(\frac{829}{1695}\right)\)	\(e\left(\frac{1463}{3390}\right)\)	\(e\left(\frac{104}{565}\right)\)
\(\chi_{549261}(17873,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{273}{1130}\right)\)	\(e\left(\frac{273}{565}\right)\)	\(e\left(\frac{1121}{3390}\right)\)	\(e\left(\frac{959}{1695}\right)\)	\(e\left(\frac{819}{1130}\right)\)	\(e\left(\frac{194}{339}\right)\)	\(e\left(\frac{211}{1130}\right)\)	\(e\left(\frac{821}{1695}\right)\)	\(e\left(\frac{2737}{3390}\right)\)	\(e\left(\frac{546}{565}\right)\)
\(\chi_{549261}(18089,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{759}{1130}\right)\)	\(e\left(\frac{194}{565}\right)\)	\(e\left(\frac{2533}{3390}\right)\)	\(e\left(\frac{667}{1695}\right)\)	\(e\left(\frac{17}{1130}\right)\)	\(e\left(\frac{142}{339}\right)\)	\(e\left(\frac{3}{1130}\right)\)	\(e\left(\frac{898}{1695}\right)\)	\(e\left(\frac{221}{3390}\right)\)	\(e\left(\frac{388}{565}\right)\)
\(\chi_{549261}(18332,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{1130}\right)\)	\(e\left(\frac{61}{565}\right)\)	\(e\left(\frac{2407}{3390}\right)\)	\(e\left(\frac{1663}{1695}\right)\)	\(e\left(\frac{183}{1130}\right)\)	\(e\left(\frac{259}{339}\right)\)	\(e\left(\frac{697}{1130}\right)\)	\(e\left(\frac{1657}{1695}\right)\)	\(e\left(\frac{119}{3390}\right)\)	\(e\left(\frac{122}{565}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 896 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	549261.hg
Modulus	$549261$
Conductor	$61029$
Order	$3390$
Real	no
Primitive	no
Minimal	no
Parity	odd

Modulus:	\(549261\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(61029\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(3390\)	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 61029.dx	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);