LMFDB - Dirichlet character orbit 549261.jx

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(549261, base_ring=CyclotomicField(30510)) M = H._module chi = DirichletCharacter(H, M([1130,9])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(4, 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("549261.4"); 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:	$549261$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$30510$	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:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{15255})$	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 30510 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 20 of 8064 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{549261}(4,\cdot)$	$1$	$1$	$e\left(\frac{1139}{30510}\right)$	$e\left(\frac{1139}{15255}\right)$	$e\left(\frac{11123}{15255}\right)$	$e\left(\frac{13103}{30510}\right)$	$e\left(\frac{1139}{10170}\right)$	$e\left(\frac{1559}{2034}\right)$	$e\left(\frac{19}{15255}\right)$	$e\left(\frac{28237}{30510}\right)$	$e\left(\frac{7121}{15255}\right)$	$e\left(\frac{2278}{15255}\right)$
$\chi_{549261}(76,\cdot)$	$1$	$1$	$e\left(\frac{17729}{30510}\right)$	$e\left(\frac{2474}{15255}\right)$	$e\left(\frac{11423}{15255}\right)$	$e\left(\frac{15563}{30510}\right)$	$e\left(\frac{7559}{10170}\right)$	$e\left(\frac{671}{2034}\right)$	$e\left(\frac{6604}{15255}\right)$	$e\left(\frac{26497}{30510}\right)$	$e\left(\frac{1391}{15255}\right)$	$e\left(\frac{4948}{15255}\right)$
$\chi_{549261}(94,\cdot)$	$1$	$1$	$e\left(\frac{4961}{30510}\right)$	$e\left(\frac{4961}{15255}\right)$	$e\left(\frac{6017}{15255}\right)$	$e\left(\frac{11507}{30510}\right)$	$e\left(\frac{4961}{10170}\right)$	$e\left(\frac{1133}{2034}\right)$	$e\left(\frac{6016}{15255}\right)$	$e\left(\frac{493}{30510}\right)$	$e\left(\frac{8234}{15255}\right)$	$e\left(\frac{9922}{15255}\right)$
$\chi_{549261}(130,\cdot)$	$1$	$1$	$e\left(\frac{25811}{30510}\right)$	$e\left(\frac{10556}{15255}\right)$	$e\left(\frac{3332}{15255}\right)$	$e\left(\frac{10847}{30510}\right)$	$e\left(\frac{5471}{10170}\right)$	$e\left(\frac{131}{2034}\right)$	$e\left(\frac{2761}{15255}\right)$	$e\left(\frac{6913}{30510}\right)$	$e\left(\frac{3074}{15255}\right)$	$e\left(\frac{5857}{15255}\right)$
$\chi_{549261}(157,\cdot)$	$1$	$1$	$e\left(\frac{27287}{30510}\right)$	$e\left(\frac{12032}{15255}\right)$	$e\left(\frac{6509}{15255}\right)$	$e\left(\frac{8219}{30510}\right)$	$e\left(\frac{6947}{10170}\right)$	$e\left(\frac{653}{2034}\right)$	$e\left(\frac{6442}{15255}\right)$	$e\left(\frac{2521}{30510}\right)$	$e\left(\frac{2498}{15255}\right)$	$e\left(\frac{8809}{15255}\right)$
$\chi_{549261}(166,\cdot)$	$1$	$1$	$e\left(\frac{7997}{30510}\right)$	$e\left(\frac{7997}{15255}\right)$	$e\left(\frac{3374}{15255}\right)$	$e\left(\frac{3869}{30510}\right)$	$e\left(\frac{7997}{10170}\right)$	$e\left(\frac{983}{2034}\right)$	$e\left(\frac{937}{15255}\right)$	$e\left(\frac{11551}{30510}\right)$	$e\left(\frac{5933}{15255}\right)$	$e\left(\frac{739}{15255}\right)$
$\chi_{549261}(184,\cdot)$	$1$	$1$	$e\left(\frac{13049}{30510}\right)$	$e\left(\frac{13049}{15255}\right)$	$e\left(\frac{13628}{15255}\right)$	$e\left(\frac{83}{30510}\right)$	$e\left(\frac{2879}{10170}\right)$	$e\left(\frac{653}{2034}\right)$	$e\left(\frac{2374}{15255}\right)$	$e\left(\frac{10657}{30510}\right)$	$e\left(\frac{6566}{15255}\right)$	$e\left(\frac{10843}{15255}\right)$
$\chi_{549261}(463,\cdot)$	$1$	$1$	$e\left(\frac{23423}{30510}\right)$	$e\left(\frac{8168}{15255}\right)$	$e\left(\frac{8486}{15255}\right)$	$e\left(\frac{26261}{30510}\right)$	$e\left(\frac{3083}{10170}\right)$	$e\left(\frac{659}{2034}\right)$	$e\left(\frac{14293}{15255}\right)$	$e\left(\frac{5089}{30510}\right)$	$e\left(\frac{9587}{15255}\right)$	$e\left(\frac{1081}{15255}\right)$
$\chi_{549261}(484,\cdot)$	$1$	$1$	$e\left(\frac{1177}{30510}\right)$	$e\left(\frac{1177}{15255}\right)$	$e\left(\frac{8869}{15255}\right)$	$e\left(\frac{21469}{30510}\right)$	$e\left(\frac{1177}{10170}\right)$	$e\left(\frac{1261}{2034}\right)$	$e\left(\frac{1292}{15255}\right)$	$e\left(\frac{13241}{30510}\right)$	$e\left(\frac{11323}{15255}\right)$	$e\left(\frac{2354}{15255}\right)$
$\chi_{549261}(529,\cdot)$	$1$	$1$	$e\left(\frac{22681}{30510}\right)$	$e\left(\frac{7426}{15255}\right)$	$e\left(\frac{9142}{15255}\right)$	$e\left(\frac{21877}{30510}\right)$	$e\left(\frac{2341}{10170}\right)$	$e\left(\frac{697}{2034}\right)$	$e\left(\frac{4691}{15255}\right)$	$e\left(\frac{28133}{30510}\right)$	$e\left(\frac{7024}{15255}\right)$	$e\left(\frac{14852}{15255}\right)$
$\chi_{549261}(580,\cdot)$	$1$	$1$	$e\left(\frac{27803}{30510}\right)$	$e\left(\frac{12548}{15255}\right)$	$e\left(\frac{14441}{15255}\right)$	$e\left(\frac{11021}{30510}\right)$	$e\left(\frac{7463}{10170}\right)$	$e\left(\frac{1745}{2034}\right)$	$e\left(\frac{8473}{15255}\right)$	$e\left(\frac{28519}{30510}\right)$	$e\left(\frac{4157}{15255}\right)$	$e\left(\frac{9841}{15255}\right)$
$\chi_{549261}(607,\cdot)$	$1$	$1$	$e\left(\frac{16373}{30510}\right)$	$e\left(\frac{1118}{15255}\right)$	$e\left(\frac{1931}{15255}\right)$	$e\left(\frac{6071}{30510}\right)$	$e\left(\frac{6203}{10170}\right)$	$e\left(\frac{1349}{2034}\right)$	$e\left(\frac{6943}{15255}\right)$	$e\left(\frac{15649}{30510}\right)$	$e\left(\frac{11222}{15255}\right)$	$e\left(\frac{2236}{15255}\right)$
$\chi_{549261}(610,\cdot)$	$1$	$1$	$e\left(\frac{10801}{30510}\right)$	$e\left(\frac{10801}{15255}\right)$	$e\left(\frac{8872}{15255}\right)$	$e\left(\frac{1357}{30510}\right)$	$e\left(\frac{631}{10170}\right)$	$e\left(\frac{1903}{2034}\right)$	$e\left(\frac{3341}{15255}\right)$	$e\left(\frac{11393}{30510}\right)$	$e\left(\frac{6079}{15255}\right)$	$e\left(\frac{6347}{15255}\right)$
$\chi_{549261}(997,\cdot)$	$1$	$1$	$e\left(\frac{30301}{30510}\right)$	$e\left(\frac{15046}{15255}\right)$	$e\left(\frac{12397}{15255}\right)$	$e\left(\frac{15007}{30510}\right)$	$e\left(\frac{9961}{10170}\right)$	$e\left(\frac{1639}{2034}\right)$	$e\left(\frac{626}{15255}\right)$	$e\left(\frac{6203}{30510}\right)$	$e\left(\frac{7399}{15255}\right)$	$e\left(\frac{14837}{15255}\right)$
$\chi_{549261}(1156,\cdot)$	$1$	$1$	$e\left(\frac{24821}{30510}\right)$	$e\left(\frac{9566}{15255}\right)$	$e\left(\frac{5852}{15255}\right)$	$e\left(\frac{19307}{30510}\right)$	$e\left(\frac{4481}{10170}\right)$	$e\left(\frac{401}{2034}\right)$	$e\left(\frac{106}{15255}\right)$	$e\left(\frac{10603}{30510}\right)$	$e\left(\frac{6809}{15255}\right)$	$e\left(\frac{3877}{15255}\right)$
$\chi_{549261}(1282,\cdot)$	$1$	$1$	$e\left(\frac{13529}{30510}\right)$	$e\left(\frac{13529}{15255}\right)$	$e\left(\frac{3623}{15255}\right)$	$e\left(\frac{12623}{30510}\right)$	$e\left(\frac{3359}{10170}\right)$	$e\left(\frac{1385}{2034}\right)$	$e\left(\frac{3199}{15255}\right)$	$e\left(\frac{10717}{30510}\right)$	$e\left(\frac{13076}{15255}\right)$	$e\left(\frac{11803}{15255}\right)$
$\chi_{549261}(1321,\cdot)$	$1$	$1$	$e\left(\frac{5299}{30510}\right)$	$e\left(\frac{5299}{15255}\right)$	$e\left(\frac{10858}{15255}\right)$	$e\left(\frac{20083}{30510}\right)$	$e\left(\frac{5299}{10170}\right)$	$e\left(\frac{1801}{2034}\right)$	$e\left(\frac{2084}{15255}\right)$	$e\left(\frac{8417}{30510}\right)$	$e\left(\frac{12691}{15255}\right)$	$e\left(\frac{10598}{15255}\right)$
$\chi_{549261}(1444,\cdot)$	$1$	$1$	$e\left(\frac{3809}{30510}\right)$	$e\left(\frac{3809}{15255}\right)$	$e\left(\frac{11723}{15255}\right)$	$e\left(\frac{18023}{30510}\right)$	$e\left(\frac{3809}{10170}\right)$	$e\left(\frac{1817}{2034}\right)$	$e\left(\frac{13189}{15255}\right)$	$e\left(\frac{24757}{30510}\right)$	$e\left(\frac{10916}{15255}\right)$	$e\left(\frac{7618}{15255}\right)$
$\chi_{549261}(1447,\cdot)$	$1$	$1$	$e\left(\frac{1153}{30510}\right)$	$e\left(\frac{1153}{15255}\right)$	$e\left(\frac{7081}{15255}\right)$	$e\left(\frac{17791}{30510}\right)$	$e\left(\frac{1153}{10170}\right)$	$e\left(\frac{1021}{2034}\right)$	$e\left(\frac{488}{15255}\right)$	$e\left(\frac{16289}{30510}\right)$	$e\left(\frac{9472}{15255}\right)$	$e\left(\frac{2306}{15255}\right)$
$\chi_{549261}(1471,\cdot)$	$1$	$1$	$e\left(\frac{23807}{30510}\right)$	$e\left(\frac{8552}{15255}\right)$	$e\left(\frac{6584}{15255}\right)$	$e\left(\frac{24089}{30510}\right)$	$e\left(\frac{3467}{10170}\right)$	$e\left(\frac{431}{2034}\right)$	$e\left(\frac{11902}{15255}\right)$	$e\left(\frac{17341}{30510}\right)$	$e\left(\frac{8693}{15255}\right)$	$e\left(\frac{1849}{15255}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{549261}(4,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1139}{30510}\right)\)	\(e\left(\frac{1139}{15255}\right)\)	\(e\left(\frac{11123}{15255}\right)\)	\(e\left(\frac{13103}{30510}\right)\)	\(e\left(\frac{1139}{10170}\right)\)	\(e\left(\frac{1559}{2034}\right)\)	\(e\left(\frac{19}{15255}\right)\)	\(e\left(\frac{28237}{30510}\right)\)	\(e\left(\frac{7121}{15255}\right)\)	\(e\left(\frac{2278}{15255}\right)\)
\(\chi_{549261}(76,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17729}{30510}\right)\)	\(e\left(\frac{2474}{15255}\right)\)	\(e\left(\frac{11423}{15255}\right)\)	\(e\left(\frac{15563}{30510}\right)\)	\(e\left(\frac{7559}{10170}\right)\)	\(e\left(\frac{671}{2034}\right)\)	\(e\left(\frac{6604}{15255}\right)\)	\(e\left(\frac{26497}{30510}\right)\)	\(e\left(\frac{1391}{15255}\right)\)	\(e\left(\frac{4948}{15255}\right)\)
\(\chi_{549261}(94,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4961}{30510}\right)\)	\(e\left(\frac{4961}{15255}\right)\)	\(e\left(\frac{6017}{15255}\right)\)	\(e\left(\frac{11507}{30510}\right)\)	\(e\left(\frac{4961}{10170}\right)\)	\(e\left(\frac{1133}{2034}\right)\)	\(e\left(\frac{6016}{15255}\right)\)	\(e\left(\frac{493}{30510}\right)\)	\(e\left(\frac{8234}{15255}\right)\)	\(e\left(\frac{9922}{15255}\right)\)
\(\chi_{549261}(130,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25811}{30510}\right)\)	\(e\left(\frac{10556}{15255}\right)\)	\(e\left(\frac{3332}{15255}\right)\)	\(e\left(\frac{10847}{30510}\right)\)	\(e\left(\frac{5471}{10170}\right)\)	\(e\left(\frac{131}{2034}\right)\)	\(e\left(\frac{2761}{15255}\right)\)	\(e\left(\frac{6913}{30510}\right)\)	\(e\left(\frac{3074}{15255}\right)\)	\(e\left(\frac{5857}{15255}\right)\)
\(\chi_{549261}(157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27287}{30510}\right)\)	\(e\left(\frac{12032}{15255}\right)\)	\(e\left(\frac{6509}{15255}\right)\)	\(e\left(\frac{8219}{30510}\right)\)	\(e\left(\frac{6947}{10170}\right)\)	\(e\left(\frac{653}{2034}\right)\)	\(e\left(\frac{6442}{15255}\right)\)	\(e\left(\frac{2521}{30510}\right)\)	\(e\left(\frac{2498}{15255}\right)\)	\(e\left(\frac{8809}{15255}\right)\)
\(\chi_{549261}(166,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7997}{30510}\right)\)	\(e\left(\frac{7997}{15255}\right)\)	\(e\left(\frac{3374}{15255}\right)\)	\(e\left(\frac{3869}{30510}\right)\)	\(e\left(\frac{7997}{10170}\right)\)	\(e\left(\frac{983}{2034}\right)\)	\(e\left(\frac{937}{15255}\right)\)	\(e\left(\frac{11551}{30510}\right)\)	\(e\left(\frac{5933}{15255}\right)\)	\(e\left(\frac{739}{15255}\right)\)
\(\chi_{549261}(184,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13049}{30510}\right)\)	\(e\left(\frac{13049}{15255}\right)\)	\(e\left(\frac{13628}{15255}\right)\)	\(e\left(\frac{83}{30510}\right)\)	\(e\left(\frac{2879}{10170}\right)\)	\(e\left(\frac{653}{2034}\right)\)	\(e\left(\frac{2374}{15255}\right)\)	\(e\left(\frac{10657}{30510}\right)\)	\(e\left(\frac{6566}{15255}\right)\)	\(e\left(\frac{10843}{15255}\right)\)
\(\chi_{549261}(463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23423}{30510}\right)\)	\(e\left(\frac{8168}{15255}\right)\)	\(e\left(\frac{8486}{15255}\right)\)	\(e\left(\frac{26261}{30510}\right)\)	\(e\left(\frac{3083}{10170}\right)\)	\(e\left(\frac{659}{2034}\right)\)	\(e\left(\frac{14293}{15255}\right)\)	\(e\left(\frac{5089}{30510}\right)\)	\(e\left(\frac{9587}{15255}\right)\)	\(e\left(\frac{1081}{15255}\right)\)
\(\chi_{549261}(484,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1177}{30510}\right)\)	\(e\left(\frac{1177}{15255}\right)\)	\(e\left(\frac{8869}{15255}\right)\)	\(e\left(\frac{21469}{30510}\right)\)	\(e\left(\frac{1177}{10170}\right)\)	\(e\left(\frac{1261}{2034}\right)\)	\(e\left(\frac{1292}{15255}\right)\)	\(e\left(\frac{13241}{30510}\right)\)	\(e\left(\frac{11323}{15255}\right)\)	\(e\left(\frac{2354}{15255}\right)\)
\(\chi_{549261}(529,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22681}{30510}\right)\)	\(e\left(\frac{7426}{15255}\right)\)	\(e\left(\frac{9142}{15255}\right)\)	\(e\left(\frac{21877}{30510}\right)\)	\(e\left(\frac{2341}{10170}\right)\)	\(e\left(\frac{697}{2034}\right)\)	\(e\left(\frac{4691}{15255}\right)\)	\(e\left(\frac{28133}{30510}\right)\)	\(e\left(\frac{7024}{15255}\right)\)	\(e\left(\frac{14852}{15255}\right)\)
\(\chi_{549261}(580,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27803}{30510}\right)\)	\(e\left(\frac{12548}{15255}\right)\)	\(e\left(\frac{14441}{15255}\right)\)	\(e\left(\frac{11021}{30510}\right)\)	\(e\left(\frac{7463}{10170}\right)\)	\(e\left(\frac{1745}{2034}\right)\)	\(e\left(\frac{8473}{15255}\right)\)	\(e\left(\frac{28519}{30510}\right)\)	\(e\left(\frac{4157}{15255}\right)\)	\(e\left(\frac{9841}{15255}\right)\)
\(\chi_{549261}(607,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16373}{30510}\right)\)	\(e\left(\frac{1118}{15255}\right)\)	\(e\left(\frac{1931}{15255}\right)\)	\(e\left(\frac{6071}{30510}\right)\)	\(e\left(\frac{6203}{10170}\right)\)	\(e\left(\frac{1349}{2034}\right)\)	\(e\left(\frac{6943}{15255}\right)\)	\(e\left(\frac{15649}{30510}\right)\)	\(e\left(\frac{11222}{15255}\right)\)	\(e\left(\frac{2236}{15255}\right)\)
\(\chi_{549261}(610,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10801}{30510}\right)\)	\(e\left(\frac{10801}{15255}\right)\)	\(e\left(\frac{8872}{15255}\right)\)	\(e\left(\frac{1357}{30510}\right)\)	\(e\left(\frac{631}{10170}\right)\)	\(e\left(\frac{1903}{2034}\right)\)	\(e\left(\frac{3341}{15255}\right)\)	\(e\left(\frac{11393}{30510}\right)\)	\(e\left(\frac{6079}{15255}\right)\)	\(e\left(\frac{6347}{15255}\right)\)
\(\chi_{549261}(997,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{30301}{30510}\right)\)	\(e\left(\frac{15046}{15255}\right)\)	\(e\left(\frac{12397}{15255}\right)\)	\(e\left(\frac{15007}{30510}\right)\)	\(e\left(\frac{9961}{10170}\right)\)	\(e\left(\frac{1639}{2034}\right)\)	\(e\left(\frac{626}{15255}\right)\)	\(e\left(\frac{6203}{30510}\right)\)	\(e\left(\frac{7399}{15255}\right)\)	\(e\left(\frac{14837}{15255}\right)\)
\(\chi_{549261}(1156,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24821}{30510}\right)\)	\(e\left(\frac{9566}{15255}\right)\)	\(e\left(\frac{5852}{15255}\right)\)	\(e\left(\frac{19307}{30510}\right)\)	\(e\left(\frac{4481}{10170}\right)\)	\(e\left(\frac{401}{2034}\right)\)	\(e\left(\frac{106}{15255}\right)\)	\(e\left(\frac{10603}{30510}\right)\)	\(e\left(\frac{6809}{15255}\right)\)	\(e\left(\frac{3877}{15255}\right)\)
\(\chi_{549261}(1282,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13529}{30510}\right)\)	\(e\left(\frac{13529}{15255}\right)\)	\(e\left(\frac{3623}{15255}\right)\)	\(e\left(\frac{12623}{30510}\right)\)	\(e\left(\frac{3359}{10170}\right)\)	\(e\left(\frac{1385}{2034}\right)\)	\(e\left(\frac{3199}{15255}\right)\)	\(e\left(\frac{10717}{30510}\right)\)	\(e\left(\frac{13076}{15255}\right)\)	\(e\left(\frac{11803}{15255}\right)\)
\(\chi_{549261}(1321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5299}{30510}\right)\)	\(e\left(\frac{5299}{15255}\right)\)	\(e\left(\frac{10858}{15255}\right)\)	\(e\left(\frac{20083}{30510}\right)\)	\(e\left(\frac{5299}{10170}\right)\)	\(e\left(\frac{1801}{2034}\right)\)	\(e\left(\frac{2084}{15255}\right)\)	\(e\left(\frac{8417}{30510}\right)\)	\(e\left(\frac{12691}{15255}\right)\)	\(e\left(\frac{10598}{15255}\right)\)
\(\chi_{549261}(1444,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3809}{30510}\right)\)	\(e\left(\frac{3809}{15255}\right)\)	\(e\left(\frac{11723}{15255}\right)\)	\(e\left(\frac{18023}{30510}\right)\)	\(e\left(\frac{3809}{10170}\right)\)	\(e\left(\frac{1817}{2034}\right)\)	\(e\left(\frac{13189}{15255}\right)\)	\(e\left(\frac{24757}{30510}\right)\)	\(e\left(\frac{10916}{15255}\right)\)	\(e\left(\frac{7618}{15255}\right)\)
\(\chi_{549261}(1447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1153}{30510}\right)\)	\(e\left(\frac{1153}{15255}\right)\)	\(e\left(\frac{7081}{15255}\right)\)	\(e\left(\frac{17791}{30510}\right)\)	\(e\left(\frac{1153}{10170}\right)\)	\(e\left(\frac{1021}{2034}\right)\)	\(e\left(\frac{488}{15255}\right)\)	\(e\left(\frac{16289}{30510}\right)\)	\(e\left(\frac{9472}{15255}\right)\)	\(e\left(\frac{2306}{15255}\right)\)
\(\chi_{549261}(1471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23807}{30510}\right)\)	\(e\left(\frac{8552}{15255}\right)\)	\(e\left(\frac{6584}{15255}\right)\)	\(e\left(\frac{24089}{30510}\right)\)	\(e\left(\frac{3467}{10170}\right)\)	\(e\left(\frac{431}{2034}\right)\)	\(e\left(\frac{11902}{15255}\right)\)	\(e\left(\frac{17341}{30510}\right)\)	\(e\left(\frac{8693}{15255}\right)\)	\(e\left(\frac{1849}{15255}\right)\)

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First 20 of 8064 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.jx
Modulus	$549261$
Conductor	$549261$
Order	$30510$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(549261\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(549261\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(30510\)	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:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);