LMFDB - Dirichlet character orbit 508288.vy

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(508288, base_ring=CyclotomicField(27360)) M = H._module chi = DirichletCharacter(H, M([13680,26505,19152,1840])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(51,508288)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$508288$
Conductor:	$508288$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$27360$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{27360})$
Fixed field:	Number field defined by a degree 27360 polynomial (not computed)

First 21 of 6912 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$21$	$23$	$25$
$\chi_{508288}(51,\cdot)$	$-1$	$1$	$e\left(\frac{9691}{27360}\right)$	$e\left(\frac{10153}{27360}\right)$	$e\left(\frac{799}{4560}\right)$	$e\left(\frac{9691}{13680}\right)$	$e\left(\frac{9767}{27360}\right)$	$e\left(\frac{4961}{6840}\right)$	$e\left(\frac{4267}{6840}\right)$	$e\left(\frac{2897}{5472}\right)$	$e\left(\frac{2411}{2736}\right)$	$e\left(\frac{10153}{13680}\right)$
$\chi_{508288}(211,\cdot)$	$-1$	$1$	$e\left(\frac{25763}{27360}\right)$	$e\left(\frac{9569}{27360}\right)$	$e\left(\frac{1367}{4560}\right)$	$e\left(\frac{12083}{13680}\right)$	$e\left(\frac{25231}{27360}\right)$	$e\left(\frac{1993}{6840}\right)$	$e\left(\frac{1091}{6840}\right)$	$e\left(\frac{1321}{5472}\right)$	$e\left(\frac{1123}{2736}\right)$	$e\left(\frac{9569}{13680}\right)$
$\chi_{508288}(371,\cdot)$	$-1$	$1$	$e\left(\frac{139}{27360}\right)$	$e\left(\frac{19897}{27360}\right)$	$e\left(\frac{2191}{4560}\right)$	$e\left(\frac{139}{13680}\right)$	$e\left(\frac{12983}{27360}\right)$	$e\left(\frac{5009}{6840}\right)$	$e\left(\frac{5443}{6840}\right)$	$e\left(\frac{2657}{5472}\right)$	$e\left(\frac{1451}{2736}\right)$	$e\left(\frac{6217}{13680}\right)$
$\chi_{508288}(459,\cdot)$	$-1$	$1$	$e\left(\frac{19289}{27360}\right)$	$e\left(\frac{14867}{27360}\right)$	$e\left(\frac{821}{4560}\right)$	$e\left(\frac{5609}{13680}\right)$	$e\left(\frac{5533}{27360}\right)$	$e\left(\frac{1699}{6840}\right)$	$e\left(\frac{6713}{6840}\right)$	$e\left(\frac{4843}{5472}\right)$	$e\left(\frac{505}{2736}\right)$	$e\left(\frac{1187}{13680}\right)$
$\chi_{508288}(523,\cdot)$	$-1$	$1$	$e\left(\frac{1417}{27360}\right)$	$e\left(\frac{2851}{27360}\right)$	$e\left(\frac{3013}{4560}\right)$	$e\left(\frac{1417}{13680}\right)$	$e\left(\frac{15629}{27360}\right)$	$e\left(\frac{1067}{6840}\right)$	$e\left(\frac{3769}{6840}\right)$	$e\left(\frac{3899}{5472}\right)$	$e\left(\frac{1289}{2736}\right)$	$e\left(\frac{2851}{13680}\right)$
$\chi_{508288}(547,\cdot)$	$-1$	$1$	$e\left(\frac{26839}{27360}\right)$	$e\left(\frac{1597}{27360}\right)$	$e\left(\frac{1531}{4560}\right)$	$e\left(\frac{13159}{13680}\right)$	$e\left(\frac{16883}{27360}\right)$	$e\left(\frac{269}{6840}\right)$	$e\left(\frac{463}{6840}\right)$	$e\left(\frac{1733}{5472}\right)$	$e\left(\frac{1175}{2736}\right)$	$e\left(\frac{1597}{13680}\right)$
$\chi_{508288}(611,\cdot)$	$-1$	$1$	$e\left(\frac{14087}{27360}\right)$	$e\left(\frac{7181}{27360}\right)$	$e\left(\frac{4283}{4560}\right)$	$e\left(\frac{407}{13680}\right)$	$e\left(\frac{1699}{27360}\right)$	$e\left(\frac{5317}{6840}\right)$	$e\left(\frac{2159}{6840}\right)$	$e\left(\frac{2485}{5472}\right)$	$e\left(\frac{2359}{2736}\right)$	$e\left(\frac{7181}{13680}\right)$
$\chi_{508288}(667,\cdot)$	$-1$	$1$	$e\left(\frac{5261}{27360}\right)$	$e\left(\frac{17903}{27360}\right)$	$e\left(\frac{3209}{4560}\right)$	$e\left(\frac{5261}{13680}\right)$	$e\left(\frac{19777}{27360}\right)$	$e\left(\frac{5791}{6840}\right)$	$e\left(\frac{6077}{6840}\right)$	$e\left(\frac{4903}{5472}\right)$	$e\left(\frac{61}{2736}\right)$	$e\left(\frac{4223}{13680}\right)$
$\chi_{508288}(699,\cdot)$	$-1$	$1$	$e\left(\frac{3637}{27360}\right)$	$e\left(\frac{4711}{27360}\right)$	$e\left(\frac{673}{4560}\right)$	$e\left(\frac{3637}{13680}\right)$	$e\left(\frac{22409}{27360}\right)$	$e\left(\frac{2087}{6840}\right)$	$e\left(\frac{3109}{6840}\right)$	$e\left(\frac{1535}{5472}\right)$	$e\left(\frac{725}{2736}\right)$	$e\left(\frac{4711}{13680}\right)$
$\chi_{508288}(755,\cdot)$	$-1$	$1$	$e\left(\frac{12491}{27360}\right)$	$e\left(\frac{20633}{27360}\right)$	$e\left(\frac{3599}{4560}\right)$	$e\left(\frac{12491}{13680}\right)$	$e\left(\frac{15607}{27360}\right)$	$e\left(\frac{1441}{6840}\right)$	$e\left(\frac{4667}{6840}\right)$	$e\left(\frac{1345}{5472}\right)$	$e\left(\frac{2587}{2736}\right)$	$e\left(\frac{6953}{13680}\right)$
$\chi_{508288}(811,\cdot)$	$-1$	$1$	$e\left(\frac{16369}{27360}\right)$	$e\left(\frac{3547}{27360}\right)$	$e\left(\frac{2461}{4560}\right)$	$e\left(\frac{2689}{13680}\right)$	$e\left(\frac{17813}{27360}\right)$	$e\left(\frac{4979}{6840}\right)$	$e\left(\frac{433}{6840}\right)$	$e\left(\frac{755}{5472}\right)$	$e\left(\frac{1025}{2736}\right)$	$e\left(\frac{3547}{13680}\right)$
$\chi_{508288}(827,\cdot)$	$-1$	$1$	$e\left(\frac{17653}{27360}\right)$	$e\left(\frac{9799}{27360}\right)$	$e\left(\frac{97}{4560}\right)$	$e\left(\frac{3973}{13680}\right)$	$e\left(\frac{7241}{27360}\right)$	$e\left(\frac{23}{6840}\right)$	$e\left(\frac{421}{6840}\right)$	$e\left(\frac{3647}{5472}\right)$	$e\left(\frac{965}{2736}\right)$	$e\left(\frac{9799}{13680}\right)$
$\chi_{508288}(915,\cdot)$	$-1$	$1$	$e\left(\frac{17363}{27360}\right)$	$e\left(\frac{5489}{27360}\right)$	$e\left(\frac{2087}{4560}\right)$	$e\left(\frac{3683}{13680}\right)$	$e\left(\frac{7711}{27360}\right)$	$e\left(\frac{5713}{6840}\right)$	$e\left(\frac{6731}{6840}\right)$	$e\left(\frac{505}{5472}\right)$	$e\left(\frac{595}{2736}\right)$	$e\left(\frac{5489}{13680}\right)$
$\chi_{508288}(963,\cdot)$	$-1$	$1$	$e\left(\frac{27007}{27360}\right)$	$e\left(\frac{24661}{27360}\right)$	$e\left(\frac{3523}{4560}\right)$	$e\left(\frac{13327}{13680}\right)$	$e\left(\frac{2459}{27360}\right)$	$e\left(\frac{6077}{6840}\right)$	$e\left(\frac{5959}{6840}\right)$	$e\left(\frac{4157}{5472}\right)$	$e\left(\frac{1295}{2736}\right)$	$e\left(\frac{10981}{13680}\right)$
$\chi_{508288}(1003,\cdot)$	$-1$	$1$	$e\left(\frac{25633}{27360}\right)$	$e\left(\frac{24619}{27360}\right)$	$e\left(\frac{3517}{4560}\right)$	$e\left(\frac{11953}{13680}\right)$	$e\left(\frac{19781}{27360}\right)$	$e\left(\frac{5723}{6840}\right)$	$e\left(\frac{1561}{6840}\right)$	$e\left(\frac{3875}{5472}\right)$	$e\left(\frac{2561}{2736}\right)$	$e\left(\frac{10939}{13680}\right)$
$\chi_{508288}(1267,\cdot)$	$-1$	$1$	$e\left(\frac{7243}{27360}\right)$	$e\left(\frac{25849}{27360}\right)$	$e\left(\frac{1087}{4560}\right)$	$e\left(\frac{7243}{13680}\right)$	$e\left(\frac{12791}{27360}\right)$	$e\left(\frac{1433}{6840}\right)$	$e\left(\frac{3331}{6840}\right)$	$e\left(\frac{2753}{5472}\right)$	$e\left(\frac{1835}{2736}\right)$	$e\left(\frac{12169}{13680}\right)$
$\chi_{508288}(1283,\cdot)$	$-1$	$1$	$e\left(\frac{5071}{27360}\right)$	$e\left(\frac{18853}{27360}\right)$	$e\left(\frac{739}{4560}\right)$	$e\left(\frac{5071}{13680}\right)$	$e\left(\frac{9707}{27360}\right)$	$e\left(\frac{5981}{6840}\right)$	$e\left(\frac{3607}{6840}\right)$	$e\left(\frac{1901}{5472}\right)$	$e\left(\frac{479}{2736}\right)$	$e\left(\frac{5173}{13680}\right)$
$\chi_{508288}(1371,\cdot)$	$-1$	$1$	$e\left(\frac{12701}{27360}\right)$	$e\left(\frac{15263}{27360}\right)$	$e\left(\frac{1529}{4560}\right)$	$e\left(\frac{12701}{13680}\right)$	$e\left(\frac{18097}{27360}\right)$	$e\left(\frac{151}{6840}\right)$	$e\left(\frac{1277}{6840}\right)$	$e\left(\frac{4375}{5472}\right)$	$e\left(\frac{685}{2736}\right)$	$e\left(\frac{1583}{13680}\right)$
$\chi_{508288}(1427,\cdot)$	$-1$	$1$	$e\left(\frac{11219}{27360}\right)$	$e\left(\frac{6257}{27360}\right)$	$e\left(\frac{4151}{4560}\right)$	$e\left(\frac{11219}{13680}\right)$	$e\left(\frac{27103}{27360}\right)$	$e\left(\frac{4369}{6840}\right)$	$e\left(\frac{1163}{6840}\right)$	$e\left(\frac{1753}{5472}\right)$	$e\left(\frac{115}{2736}\right)$	$e\left(\frac{6257}{13680}\right)$
$\chi_{508288}(1459,\cdot)$	$-1$	$1$	$e\left(\frac{21691}{27360}\right)$	$e\left(\frac{12073}{27360}\right)$	$e\left(\frac{3679}{4560}\right)$	$e\left(\frac{8011}{13680}\right)$	$e\left(\frac{3527}{27360}\right)$	$e\left(\frac{1601}{6840}\right)$	$e\left(\frac{4027}{6840}\right)$	$e\left(\frac{3281}{5472}\right)$	$e\left(\frac{1211}{2736}\right)$	$e\left(\frac{12073}{13680}\right)$
$\chi_{508288}(1515,\cdot)$	$-1$	$1$	$e\left(\frac{6209}{27360}\right)$	$e\left(\frac{5387}{27360}\right)$	$e\left(\frac{1421}{4560}\right)$	$e\left(\frac{6209}{13680}\right)$	$e\left(\frac{10693}{27360}\right)$	$e\left(\frac{2899}{6840}\right)$	$e\left(\frac{1913}{6840}\right)$	$e\left(\frac{2947}{5472}\right)$	$e\left(\frac{2497}{2736}\right)$	$e\left(\frac{5387}{13680}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)	\(25\)
\(\chi_{508288}(51,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9691}{27360}\right)\)	\(e\left(\frac{10153}{27360}\right)\)	\(e\left(\frac{799}{4560}\right)\)	\(e\left(\frac{9691}{13680}\right)\)	\(e\left(\frac{9767}{27360}\right)\)	\(e\left(\frac{4961}{6840}\right)\)	\(e\left(\frac{4267}{6840}\right)\)	\(e\left(\frac{2897}{5472}\right)\)	\(e\left(\frac{2411}{2736}\right)\)	\(e\left(\frac{10153}{13680}\right)\)
\(\chi_{508288}(211,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25763}{27360}\right)\)	\(e\left(\frac{9569}{27360}\right)\)	\(e\left(\frac{1367}{4560}\right)\)	\(e\left(\frac{12083}{13680}\right)\)	\(e\left(\frac{25231}{27360}\right)\)	\(e\left(\frac{1993}{6840}\right)\)	\(e\left(\frac{1091}{6840}\right)\)	\(e\left(\frac{1321}{5472}\right)\)	\(e\left(\frac{1123}{2736}\right)\)	\(e\left(\frac{9569}{13680}\right)\)
\(\chi_{508288}(371,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{139}{27360}\right)\)	\(e\left(\frac{19897}{27360}\right)\)	\(e\left(\frac{2191}{4560}\right)\)	\(e\left(\frac{139}{13680}\right)\)	\(e\left(\frac{12983}{27360}\right)\)	\(e\left(\frac{5009}{6840}\right)\)	\(e\left(\frac{5443}{6840}\right)\)	\(e\left(\frac{2657}{5472}\right)\)	\(e\left(\frac{1451}{2736}\right)\)	\(e\left(\frac{6217}{13680}\right)\)
\(\chi_{508288}(459,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19289}{27360}\right)\)	\(e\left(\frac{14867}{27360}\right)\)	\(e\left(\frac{821}{4560}\right)\)	\(e\left(\frac{5609}{13680}\right)\)	\(e\left(\frac{5533}{27360}\right)\)	\(e\left(\frac{1699}{6840}\right)\)	\(e\left(\frac{6713}{6840}\right)\)	\(e\left(\frac{4843}{5472}\right)\)	\(e\left(\frac{505}{2736}\right)\)	\(e\left(\frac{1187}{13680}\right)\)
\(\chi_{508288}(523,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1417}{27360}\right)\)	\(e\left(\frac{2851}{27360}\right)\)	\(e\left(\frac{3013}{4560}\right)\)	\(e\left(\frac{1417}{13680}\right)\)	\(e\left(\frac{15629}{27360}\right)\)	\(e\left(\frac{1067}{6840}\right)\)	\(e\left(\frac{3769}{6840}\right)\)	\(e\left(\frac{3899}{5472}\right)\)	\(e\left(\frac{1289}{2736}\right)\)	\(e\left(\frac{2851}{13680}\right)\)
\(\chi_{508288}(547,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{26839}{27360}\right)\)	\(e\left(\frac{1597}{27360}\right)\)	\(e\left(\frac{1531}{4560}\right)\)	\(e\left(\frac{13159}{13680}\right)\)	\(e\left(\frac{16883}{27360}\right)\)	\(e\left(\frac{269}{6840}\right)\)	\(e\left(\frac{463}{6840}\right)\)	\(e\left(\frac{1733}{5472}\right)\)	\(e\left(\frac{1175}{2736}\right)\)	\(e\left(\frac{1597}{13680}\right)\)
\(\chi_{508288}(611,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{14087}{27360}\right)\)	\(e\left(\frac{7181}{27360}\right)\)	\(e\left(\frac{4283}{4560}\right)\)	\(e\left(\frac{407}{13680}\right)\)	\(e\left(\frac{1699}{27360}\right)\)	\(e\left(\frac{5317}{6840}\right)\)	\(e\left(\frac{2159}{6840}\right)\)	\(e\left(\frac{2485}{5472}\right)\)	\(e\left(\frac{2359}{2736}\right)\)	\(e\left(\frac{7181}{13680}\right)\)
\(\chi_{508288}(667,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5261}{27360}\right)\)	\(e\left(\frac{17903}{27360}\right)\)	\(e\left(\frac{3209}{4560}\right)\)	\(e\left(\frac{5261}{13680}\right)\)	\(e\left(\frac{19777}{27360}\right)\)	\(e\left(\frac{5791}{6840}\right)\)	\(e\left(\frac{6077}{6840}\right)\)	\(e\left(\frac{4903}{5472}\right)\)	\(e\left(\frac{61}{2736}\right)\)	\(e\left(\frac{4223}{13680}\right)\)
\(\chi_{508288}(699,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3637}{27360}\right)\)	\(e\left(\frac{4711}{27360}\right)\)	\(e\left(\frac{673}{4560}\right)\)	\(e\left(\frac{3637}{13680}\right)\)	\(e\left(\frac{22409}{27360}\right)\)	\(e\left(\frac{2087}{6840}\right)\)	\(e\left(\frac{3109}{6840}\right)\)	\(e\left(\frac{1535}{5472}\right)\)	\(e\left(\frac{725}{2736}\right)\)	\(e\left(\frac{4711}{13680}\right)\)
\(\chi_{508288}(755,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{12491}{27360}\right)\)	\(e\left(\frac{20633}{27360}\right)\)	\(e\left(\frac{3599}{4560}\right)\)	\(e\left(\frac{12491}{13680}\right)\)	\(e\left(\frac{15607}{27360}\right)\)	\(e\left(\frac{1441}{6840}\right)\)	\(e\left(\frac{4667}{6840}\right)\)	\(e\left(\frac{1345}{5472}\right)\)	\(e\left(\frac{2587}{2736}\right)\)	\(e\left(\frac{6953}{13680}\right)\)
\(\chi_{508288}(811,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{16369}{27360}\right)\)	\(e\left(\frac{3547}{27360}\right)\)	\(e\left(\frac{2461}{4560}\right)\)	\(e\left(\frac{2689}{13680}\right)\)	\(e\left(\frac{17813}{27360}\right)\)	\(e\left(\frac{4979}{6840}\right)\)	\(e\left(\frac{433}{6840}\right)\)	\(e\left(\frac{755}{5472}\right)\)	\(e\left(\frac{1025}{2736}\right)\)	\(e\left(\frac{3547}{13680}\right)\)
\(\chi_{508288}(827,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17653}{27360}\right)\)	\(e\left(\frac{9799}{27360}\right)\)	\(e\left(\frac{97}{4560}\right)\)	\(e\left(\frac{3973}{13680}\right)\)	\(e\left(\frac{7241}{27360}\right)\)	\(e\left(\frac{23}{6840}\right)\)	\(e\left(\frac{421}{6840}\right)\)	\(e\left(\frac{3647}{5472}\right)\)	\(e\left(\frac{965}{2736}\right)\)	\(e\left(\frac{9799}{13680}\right)\)
\(\chi_{508288}(915,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17363}{27360}\right)\)	\(e\left(\frac{5489}{27360}\right)\)	\(e\left(\frac{2087}{4560}\right)\)	\(e\left(\frac{3683}{13680}\right)\)	\(e\left(\frac{7711}{27360}\right)\)	\(e\left(\frac{5713}{6840}\right)\)	\(e\left(\frac{6731}{6840}\right)\)	\(e\left(\frac{505}{5472}\right)\)	\(e\left(\frac{595}{2736}\right)\)	\(e\left(\frac{5489}{13680}\right)\)
\(\chi_{508288}(963,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27007}{27360}\right)\)	\(e\left(\frac{24661}{27360}\right)\)	\(e\left(\frac{3523}{4560}\right)\)	\(e\left(\frac{13327}{13680}\right)\)	\(e\left(\frac{2459}{27360}\right)\)	\(e\left(\frac{6077}{6840}\right)\)	\(e\left(\frac{5959}{6840}\right)\)	\(e\left(\frac{4157}{5472}\right)\)	\(e\left(\frac{1295}{2736}\right)\)	\(e\left(\frac{10981}{13680}\right)\)
\(\chi_{508288}(1003,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25633}{27360}\right)\)	\(e\left(\frac{24619}{27360}\right)\)	\(e\left(\frac{3517}{4560}\right)\)	\(e\left(\frac{11953}{13680}\right)\)	\(e\left(\frac{19781}{27360}\right)\)	\(e\left(\frac{5723}{6840}\right)\)	\(e\left(\frac{1561}{6840}\right)\)	\(e\left(\frac{3875}{5472}\right)\)	\(e\left(\frac{2561}{2736}\right)\)	\(e\left(\frac{10939}{13680}\right)\)
\(\chi_{508288}(1267,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7243}{27360}\right)\)	\(e\left(\frac{25849}{27360}\right)\)	\(e\left(\frac{1087}{4560}\right)\)	\(e\left(\frac{7243}{13680}\right)\)	\(e\left(\frac{12791}{27360}\right)\)	\(e\left(\frac{1433}{6840}\right)\)	\(e\left(\frac{3331}{6840}\right)\)	\(e\left(\frac{2753}{5472}\right)\)	\(e\left(\frac{1835}{2736}\right)\)	\(e\left(\frac{12169}{13680}\right)\)
\(\chi_{508288}(1283,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5071}{27360}\right)\)	\(e\left(\frac{18853}{27360}\right)\)	\(e\left(\frac{739}{4560}\right)\)	\(e\left(\frac{5071}{13680}\right)\)	\(e\left(\frac{9707}{27360}\right)\)	\(e\left(\frac{5981}{6840}\right)\)	\(e\left(\frac{3607}{6840}\right)\)	\(e\left(\frac{1901}{5472}\right)\)	\(e\left(\frac{479}{2736}\right)\)	\(e\left(\frac{5173}{13680}\right)\)
\(\chi_{508288}(1371,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{12701}{27360}\right)\)	\(e\left(\frac{15263}{27360}\right)\)	\(e\left(\frac{1529}{4560}\right)\)	\(e\left(\frac{12701}{13680}\right)\)	\(e\left(\frac{18097}{27360}\right)\)	\(e\left(\frac{151}{6840}\right)\)	\(e\left(\frac{1277}{6840}\right)\)	\(e\left(\frac{4375}{5472}\right)\)	\(e\left(\frac{685}{2736}\right)\)	\(e\left(\frac{1583}{13680}\right)\)
\(\chi_{508288}(1427,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11219}{27360}\right)\)	\(e\left(\frac{6257}{27360}\right)\)	\(e\left(\frac{4151}{4560}\right)\)	\(e\left(\frac{11219}{13680}\right)\)	\(e\left(\frac{27103}{27360}\right)\)	\(e\left(\frac{4369}{6840}\right)\)	\(e\left(\frac{1163}{6840}\right)\)	\(e\left(\frac{1753}{5472}\right)\)	\(e\left(\frac{115}{2736}\right)\)	\(e\left(\frac{6257}{13680}\right)\)
\(\chi_{508288}(1459,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21691}{27360}\right)\)	\(e\left(\frac{12073}{27360}\right)\)	\(e\left(\frac{3679}{4560}\right)\)	\(e\left(\frac{8011}{13680}\right)\)	\(e\left(\frac{3527}{27360}\right)\)	\(e\left(\frac{1601}{6840}\right)\)	\(e\left(\frac{4027}{6840}\right)\)	\(e\left(\frac{3281}{5472}\right)\)	\(e\left(\frac{1211}{2736}\right)\)	\(e\left(\frac{12073}{13680}\right)\)
\(\chi_{508288}(1515,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{6209}{27360}\right)\)	\(e\left(\frac{5387}{27360}\right)\)	\(e\left(\frac{1421}{4560}\right)\)	\(e\left(\frac{6209}{13680}\right)\)	\(e\left(\frac{10693}{27360}\right)\)	\(e\left(\frac{2899}{6840}\right)\)	\(e\left(\frac{1913}{6840}\right)\)	\(e\left(\frac{2947}{5472}\right)\)	\(e\left(\frac{2497}{2736}\right)\)	\(e\left(\frac{5387}{13680}\right)\)

Introduction

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Basic properties

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First 21 of 6912 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	508288.vy
Modulus	$508288$
Conductor	$508288$
Order	$27360$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(508288\)
Conductor:	\(508288\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(27360\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)