LMFDB - Dirichlet character orbit 508288.wa

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(508288, base_ring=CyclotomicField(27360)) M = H._module chi = DirichletCharacter(H, M([0,4275,16416,6640])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(53,508288)) 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 20 of 6912 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$21$	$23$	$25$
$\chi_{508288}(53,\cdot)$	$-1$	$1$	$e\left(\frac{73}{27360}\right)$	$e\left(\frac{23539}{27360}\right)$	$e\left(\frac{757}{4560}\right)$	$e\left(\frac{73}{13680}\right)$	$e\left(\frac{21581}{27360}\right)$	$e\left(\frac{5903}{6840}\right)$	$e\left(\frac{4261}{6840}\right)$	$e\left(\frac{923}{5472}\right)$	$e\left(\frac{1697}{2736}\right)$	$e\left(\frac{9859}{13680}\right)$
$\chi_{508288}(181,\cdot)$	$-1$	$1$	$e\left(\frac{7177}{27360}\right)$	$e\left(\frac{2131}{27360}\right)$	$e\left(\frac{4213}{4560}\right)$	$e\left(\frac{7177}{13680}\right)$	$e\left(\frac{21389}{27360}\right)$	$e\left(\frac{2327}{6840}\right)$	$e\left(\frac{2149}{6840}\right)$	$e\left(\frac{1019}{5472}\right)$	$e\left(\frac{2081}{2736}\right)$	$e\left(\frac{2131}{13680}\right)$
$\chi_{508288}(269,\cdot)$	$-1$	$1$	$e\left(\frac{7067}{27360}\right)$	$e\left(\frac{12761}{27360}\right)$	$e\left(\frac{1823}{4560}\right)$	$e\left(\frac{7067}{13680}\right)$	$e\left(\frac{8359}{27360}\right)$	$e\left(\frac{4957}{6840}\right)$	$e\left(\frac{3599}{6840}\right)$	$e\left(\frac{3601}{5472}\right)$	$e\left(\frac{2035}{2736}\right)$	$e\left(\frac{12761}{13680}\right)$
$\chi_{508288}(317,\cdot)$	$-1$	$1$	$e\left(\frac{9583}{27360}\right)$	$e\left(\frac{14869}{27360}\right)$	$e\left(\frac{3427}{4560}\right)$	$e\left(\frac{9583}{13680}\right)$	$e\left(\frac{1451}{27360}\right)$	$e\left(\frac{6113}{6840}\right)$	$e\left(\frac{5131}{6840}\right)$	$e\left(\frac{557}{5472}\right)$	$e\left(\frac{1943}{2736}\right)$	$e\left(\frac{1189}{13680}\right)$
$\chi_{508288}(357,\cdot)$	$-1$	$1$	$e\left(\frac{9757}{27360}\right)$	$e\left(\frac{6511}{27360}\right)$	$e\left(\frac{2233}{4560}\right)$	$e\left(\frac{9757}{13680}\right)$	$e\left(\frac{1169}{27360}\right)$	$e\left(\frac{4067}{6840}\right)$	$e\left(\frac{5449}{6840}\right)$	$e\left(\frac{4631}{5472}\right)$	$e\left(\frac{2165}{2736}\right)$	$e\left(\frac{6511}{13680}\right)$
$\chi_{508288}(421,\cdot)$	$-1$	$1$	$e\left(\frac{9389}{27360}\right)$	$e\left(\frac{287}{27360}\right)$	$e\left(\frac{41}{4560}\right)$	$e\left(\frac{9389}{13680}\right)$	$e\left(\frac{9313}{27360}\right)$	$e\left(\frac{2419}{6840}\right)$	$e\left(\frac{3833}{6840}\right)$	$e\left(\frac{1927}{5472}\right)$	$e\left(\frac{469}{2736}\right)$	$e\left(\frac{287}{13680}\right)$
$\chi_{508288}(509,\cdot)$	$-1$	$1$	$e\left(\frac{21439}{27360}\right)$	$e\left(\frac{4837}{27360}\right)$	$e\left(\frac{691}{4560}\right)$	$e\left(\frac{7759}{13680}\right)$	$e\left(\frac{11483}{27360}\right)$	$e\left(\frac{6569}{6840}\right)$	$e\left(\frac{6043}{6840}\right)$	$e\left(\frac{5117}{5472}\right)$	$e\left(\frac{1031}{2736}\right)$	$e\left(\frac{4837}{13680}\right)$
$\chi_{508288}(565,\cdot)$	$-1$	$1$	$e\left(\frac{6281}{27360}\right)$	$e\left(\frac{25043}{27360}\right)$	$e\left(\frac{4229}{4560}\right)$	$e\left(\frac{6281}{13680}\right)$	$e\left(\frac{16237}{27360}\right)$	$e\left(\frac{991}{6840}\right)$	$e\left(\frac{4757}{6840}\right)$	$e\left(\frac{859}{5472}\right)$	$e\left(\frac{2353}{2736}\right)$	$e\left(\frac{11363}{13680}\right)$
$\chi_{508288}(621,\cdot)$	$-1$	$1$	$e\left(\frac{4867}{27360}\right)$	$e\left(\frac{6481}{27360}\right)$	$e\left(\frac{4183}{4560}\right)$	$e\left(\frac{4867}{13680}\right)$	$e\left(\frac{21359}{27360}\right)$	$e\left(\frac{2837}{6840}\right)$	$e\left(\frac{5239}{6840}\right)$	$e\left(\frac{521}{5472}\right)$	$e\left(\frac{1115}{2736}\right)$	$e\left(\frac{6481}{13680}\right)$
$\chi_{508288}(773,\cdot)$	$-1$	$1$	$e\left(\frac{23029}{27360}\right)$	$e\left(\frac{22807}{27360}\right)$	$e\left(\frac{1}{4560}\right)$	$e\left(\frac{9349}{13680}\right)$	$e\left(\frac{10793}{27360}\right)$	$e\left(\frac{4619}{6840}\right)$	$e\left(\frac{1873}{6840}\right)$	$e\left(\frac{4607}{5472}\right)$	$e\left(\frac{701}{2736}\right)$	$e\left(\frac{9127}{13680}\right)$
$\chi_{508288}(933,\cdot)$	$-1$	$1$	$e\left(\frac{3533}{27360}\right)$	$e\left(\frac{24959}{27360}\right)$	$e\left(\frac{4217}{4560}\right)$	$e\left(\frac{3533}{13680}\right)$	$e\left(\frac{23521}{27360}\right)$	$e\left(\frac{283}{6840}\right)$	$e\left(\frac{2801}{6840}\right)$	$e\left(\frac{295}{5472}\right)$	$e\left(\frac{2149}{2736}\right)$	$e\left(\frac{11279}{13680}\right)$
$\chi_{508288}(1093,\cdot)$	$-1$	$1$	$e\left(\frac{24421}{27360}\right)$	$e\left(\frac{10663}{27360}\right)$	$e\left(\frac{4129}{4560}\right)$	$e\left(\frac{10741}{13680}\right)$	$e\left(\frac{8537}{27360}\right)$	$e\left(\frac{1931}{6840}\right)$	$e\left(\frac{4417}{6840}\right)$	$e\left(\frac{4367}{5472}\right)$	$e\left(\frac{2477}{2736}\right)$	$e\left(\frac{10663}{13680}\right)$
$\chi_{508288}(1181,\cdot)$	$-1$	$1$	$e\left(\frac{12791}{27360}\right)$	$e\left(\frac{22733}{27360}\right)$	$e\left(\frac{3899}{4560}\right)$	$e\left(\frac{12791}{13680}\right)$	$e\left(\frac{11347}{27360}\right)$	$e\left(\frac{2041}{6840}\right)$	$e\left(\frac{2267}{6840}\right)$	$e\left(\frac{1765}{5472}\right)$	$e\left(\frac{847}{2736}\right)$	$e\left(\frac{9053}{13680}\right)$
$\chi_{508288}(1237,\cdot)$	$-1$	$1$	$e\left(\frac{20417}{27360}\right)$	$e\left(\frac{3611}{27360}\right)$	$e\left(\frac{3773}{4560}\right)$	$e\left(\frac{6737}{13680}\right)$	$e\left(\frac{10309}{27360}\right)$	$e\left(\frac{6007}{6840}\right)$	$e\left(\frac{1109}{6840}\right)$	$e\left(\frac{3139}{5472}\right)$	$e\left(\frac{1897}{2736}\right)$	$e\left(\frac{3611}{13680}\right)$
$\chi_{508288}(1269,\cdot)$	$-1$	$1$	$e\left(\frac{16921}{27360}\right)$	$e\left(\frac{26563}{27360}\right)$	$e\left(\frac{1189}{4560}\right)$	$e\left(\frac{3241}{13680}\right)$	$e\left(\frac{5597}{27360}\right)$	$e\left(\frac{4031}{6840}\right)$	$e\left(\frac{6277}{6840}\right)$	$e\left(\frac{4811}{5472}\right)$	$e\left(\frac{833}{2736}\right)$	$e\left(\frac{12883}{13680}\right)$
$\chi_{508288}(1325,\cdot)$	$-1$	$1$	$e\left(\frac{4787}{27360}\right)$	$e\left(\frac{24161}{27360}\right)$	$e\left(\frac{4103}{4560}\right)$	$e\left(\frac{4787}{13680}\right)$	$e\left(\frac{24319}{27360}\right)$	$e\left(\frac{397}{6840}\right)$	$e\left(\frac{1319}{6840}\right)$	$e\left(\frac{409}{5472}\right)$	$e\left(\frac{1579}{2736}\right)$	$e\left(\frac{10481}{13680}\right)$
$\chi_{508288}(1389,\cdot)$	$-1$	$1$	$e\left(\frac{22019}{27360}\right)$	$e\left(\frac{13457}{27360}\right)$	$e\left(\frac{1271}{4560}\right)$	$e\left(\frac{8339}{13680}\right)$	$e\left(\frac{10543}{27360}\right)$	$e\left(\frac{2029}{6840}\right)$	$e\left(\frac{263}{6840}\right)$	$e\left(\frac{457}{5472}\right)$	$e\left(\frac{1771}{2736}\right)$	$e\left(\frac{13457}{13680}\right)$
$\chi_{508288}(1477,\cdot)$	$-1$	$1$	$e\left(\frac{25829}{27360}\right)$	$e\left(\frac{5927}{27360}\right)$	$e\left(\frac{2801}{4560}\right)$	$e\left(\frac{12149}{13680}\right)$	$e\left(\frac{16633}{27360}\right)$	$e\left(\frac{1099}{6840}\right)$	$e\left(\frac{2273}{6840}\right)$	$e\left(\frac{3055}{5472}\right)$	$e\left(\frac{877}{2736}\right)$	$e\left(\frac{5927}{13680}\right)$
$\chi_{508288}(1533,\cdot)$	$-1$	$1$	$e\left(\frac{23551}{27360}\right)$	$e\left(\frac{25093}{27360}\right)$	$e\left(\frac{979}{4560}\right)$	$e\left(\frac{9871}{13680}\right)$	$e\left(\frac{9947}{27360}\right)$	$e\left(\frac{5321}{6840}\right)$	$e\left(\frac{2827}{6840}\right)$	$e\left(\frac{413}{5472}\right)$	$e\left(\frac{1367}{2736}\right)$	$e\left(\frac{11413}{13680}\right)$
$\chi_{508288}(1549,\cdot)$	$-1$	$1$	$e\left(\frac{26203}{27360}\right)$	$e\left(\frac{8089}{27360}\right)$	$e\left(\frac{1807}{4560}\right)$	$e\left(\frac{12523}{13680}\right)$	$e\left(\frac{22631}{27360}\right)$	$e\left(\frac{1733}{6840}\right)$	$e\left(\frac{5551}{6840}\right)$	$e\left(\frac{1937}{5472}\right)$	$e\left(\frac{2675}{2736}\right)$	$e\left(\frac{8089}{13680}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)	\(25\)
\(\chi_{508288}(53,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{27360}\right)\)	\(e\left(\frac{23539}{27360}\right)\)	\(e\left(\frac{757}{4560}\right)\)	\(e\left(\frac{73}{13680}\right)\)	\(e\left(\frac{21581}{27360}\right)\)	\(e\left(\frac{5903}{6840}\right)\)	\(e\left(\frac{4261}{6840}\right)\)	\(e\left(\frac{923}{5472}\right)\)	\(e\left(\frac{1697}{2736}\right)\)	\(e\left(\frac{9859}{13680}\right)\)
\(\chi_{508288}(181,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7177}{27360}\right)\)	\(e\left(\frac{2131}{27360}\right)\)	\(e\left(\frac{4213}{4560}\right)\)	\(e\left(\frac{7177}{13680}\right)\)	\(e\left(\frac{21389}{27360}\right)\)	\(e\left(\frac{2327}{6840}\right)\)	\(e\left(\frac{2149}{6840}\right)\)	\(e\left(\frac{1019}{5472}\right)\)	\(e\left(\frac{2081}{2736}\right)\)	\(e\left(\frac{2131}{13680}\right)\)
\(\chi_{508288}(269,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7067}{27360}\right)\)	\(e\left(\frac{12761}{27360}\right)\)	\(e\left(\frac{1823}{4560}\right)\)	\(e\left(\frac{7067}{13680}\right)\)	\(e\left(\frac{8359}{27360}\right)\)	\(e\left(\frac{4957}{6840}\right)\)	\(e\left(\frac{3599}{6840}\right)\)	\(e\left(\frac{3601}{5472}\right)\)	\(e\left(\frac{2035}{2736}\right)\)	\(e\left(\frac{12761}{13680}\right)\)
\(\chi_{508288}(317,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9583}{27360}\right)\)	\(e\left(\frac{14869}{27360}\right)\)	\(e\left(\frac{3427}{4560}\right)\)	\(e\left(\frac{9583}{13680}\right)\)	\(e\left(\frac{1451}{27360}\right)\)	\(e\left(\frac{6113}{6840}\right)\)	\(e\left(\frac{5131}{6840}\right)\)	\(e\left(\frac{557}{5472}\right)\)	\(e\left(\frac{1943}{2736}\right)\)	\(e\left(\frac{1189}{13680}\right)\)
\(\chi_{508288}(357,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9757}{27360}\right)\)	\(e\left(\frac{6511}{27360}\right)\)	\(e\left(\frac{2233}{4560}\right)\)	\(e\left(\frac{9757}{13680}\right)\)	\(e\left(\frac{1169}{27360}\right)\)	\(e\left(\frac{4067}{6840}\right)\)	\(e\left(\frac{5449}{6840}\right)\)	\(e\left(\frac{4631}{5472}\right)\)	\(e\left(\frac{2165}{2736}\right)\)	\(e\left(\frac{6511}{13680}\right)\)
\(\chi_{508288}(421,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9389}{27360}\right)\)	\(e\left(\frac{287}{27360}\right)\)	\(e\left(\frac{41}{4560}\right)\)	\(e\left(\frac{9389}{13680}\right)\)	\(e\left(\frac{9313}{27360}\right)\)	\(e\left(\frac{2419}{6840}\right)\)	\(e\left(\frac{3833}{6840}\right)\)	\(e\left(\frac{1927}{5472}\right)\)	\(e\left(\frac{469}{2736}\right)\)	\(e\left(\frac{287}{13680}\right)\)
\(\chi_{508288}(509,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21439}{27360}\right)\)	\(e\left(\frac{4837}{27360}\right)\)	\(e\left(\frac{691}{4560}\right)\)	\(e\left(\frac{7759}{13680}\right)\)	\(e\left(\frac{11483}{27360}\right)\)	\(e\left(\frac{6569}{6840}\right)\)	\(e\left(\frac{6043}{6840}\right)\)	\(e\left(\frac{5117}{5472}\right)\)	\(e\left(\frac{1031}{2736}\right)\)	\(e\left(\frac{4837}{13680}\right)\)
\(\chi_{508288}(565,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{6281}{27360}\right)\)	\(e\left(\frac{25043}{27360}\right)\)	\(e\left(\frac{4229}{4560}\right)\)	\(e\left(\frac{6281}{13680}\right)\)	\(e\left(\frac{16237}{27360}\right)\)	\(e\left(\frac{991}{6840}\right)\)	\(e\left(\frac{4757}{6840}\right)\)	\(e\left(\frac{859}{5472}\right)\)	\(e\left(\frac{2353}{2736}\right)\)	\(e\left(\frac{11363}{13680}\right)\)
\(\chi_{508288}(621,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4867}{27360}\right)\)	\(e\left(\frac{6481}{27360}\right)\)	\(e\left(\frac{4183}{4560}\right)\)	\(e\left(\frac{4867}{13680}\right)\)	\(e\left(\frac{21359}{27360}\right)\)	\(e\left(\frac{2837}{6840}\right)\)	\(e\left(\frac{5239}{6840}\right)\)	\(e\left(\frac{521}{5472}\right)\)	\(e\left(\frac{1115}{2736}\right)\)	\(e\left(\frac{6481}{13680}\right)\)
\(\chi_{508288}(773,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23029}{27360}\right)\)	\(e\left(\frac{22807}{27360}\right)\)	\(e\left(\frac{1}{4560}\right)\)	\(e\left(\frac{9349}{13680}\right)\)	\(e\left(\frac{10793}{27360}\right)\)	\(e\left(\frac{4619}{6840}\right)\)	\(e\left(\frac{1873}{6840}\right)\)	\(e\left(\frac{4607}{5472}\right)\)	\(e\left(\frac{701}{2736}\right)\)	\(e\left(\frac{9127}{13680}\right)\)
\(\chi_{508288}(933,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3533}{27360}\right)\)	\(e\left(\frac{24959}{27360}\right)\)	\(e\left(\frac{4217}{4560}\right)\)	\(e\left(\frac{3533}{13680}\right)\)	\(e\left(\frac{23521}{27360}\right)\)	\(e\left(\frac{283}{6840}\right)\)	\(e\left(\frac{2801}{6840}\right)\)	\(e\left(\frac{295}{5472}\right)\)	\(e\left(\frac{2149}{2736}\right)\)	\(e\left(\frac{11279}{13680}\right)\)
\(\chi_{508288}(1093,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{24421}{27360}\right)\)	\(e\left(\frac{10663}{27360}\right)\)	\(e\left(\frac{4129}{4560}\right)\)	\(e\left(\frac{10741}{13680}\right)\)	\(e\left(\frac{8537}{27360}\right)\)	\(e\left(\frac{1931}{6840}\right)\)	\(e\left(\frac{4417}{6840}\right)\)	\(e\left(\frac{4367}{5472}\right)\)	\(e\left(\frac{2477}{2736}\right)\)	\(e\left(\frac{10663}{13680}\right)\)
\(\chi_{508288}(1181,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{12791}{27360}\right)\)	\(e\left(\frac{22733}{27360}\right)\)	\(e\left(\frac{3899}{4560}\right)\)	\(e\left(\frac{12791}{13680}\right)\)	\(e\left(\frac{11347}{27360}\right)\)	\(e\left(\frac{2041}{6840}\right)\)	\(e\left(\frac{2267}{6840}\right)\)	\(e\left(\frac{1765}{5472}\right)\)	\(e\left(\frac{847}{2736}\right)\)	\(e\left(\frac{9053}{13680}\right)\)
\(\chi_{508288}(1237,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{20417}{27360}\right)\)	\(e\left(\frac{3611}{27360}\right)\)	\(e\left(\frac{3773}{4560}\right)\)	\(e\left(\frac{6737}{13680}\right)\)	\(e\left(\frac{10309}{27360}\right)\)	\(e\left(\frac{6007}{6840}\right)\)	\(e\left(\frac{1109}{6840}\right)\)	\(e\left(\frac{3139}{5472}\right)\)	\(e\left(\frac{1897}{2736}\right)\)	\(e\left(\frac{3611}{13680}\right)\)
\(\chi_{508288}(1269,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{16921}{27360}\right)\)	\(e\left(\frac{26563}{27360}\right)\)	\(e\left(\frac{1189}{4560}\right)\)	\(e\left(\frac{3241}{13680}\right)\)	\(e\left(\frac{5597}{27360}\right)\)	\(e\left(\frac{4031}{6840}\right)\)	\(e\left(\frac{6277}{6840}\right)\)	\(e\left(\frac{4811}{5472}\right)\)	\(e\left(\frac{833}{2736}\right)\)	\(e\left(\frac{12883}{13680}\right)\)
\(\chi_{508288}(1325,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4787}{27360}\right)\)	\(e\left(\frac{24161}{27360}\right)\)	\(e\left(\frac{4103}{4560}\right)\)	\(e\left(\frac{4787}{13680}\right)\)	\(e\left(\frac{24319}{27360}\right)\)	\(e\left(\frac{397}{6840}\right)\)	\(e\left(\frac{1319}{6840}\right)\)	\(e\left(\frac{409}{5472}\right)\)	\(e\left(\frac{1579}{2736}\right)\)	\(e\left(\frac{10481}{13680}\right)\)
\(\chi_{508288}(1389,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{22019}{27360}\right)\)	\(e\left(\frac{13457}{27360}\right)\)	\(e\left(\frac{1271}{4560}\right)\)	\(e\left(\frac{8339}{13680}\right)\)	\(e\left(\frac{10543}{27360}\right)\)	\(e\left(\frac{2029}{6840}\right)\)	\(e\left(\frac{263}{6840}\right)\)	\(e\left(\frac{457}{5472}\right)\)	\(e\left(\frac{1771}{2736}\right)\)	\(e\left(\frac{13457}{13680}\right)\)
\(\chi_{508288}(1477,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25829}{27360}\right)\)	\(e\left(\frac{5927}{27360}\right)\)	\(e\left(\frac{2801}{4560}\right)\)	\(e\left(\frac{12149}{13680}\right)\)	\(e\left(\frac{16633}{27360}\right)\)	\(e\left(\frac{1099}{6840}\right)\)	\(e\left(\frac{2273}{6840}\right)\)	\(e\left(\frac{3055}{5472}\right)\)	\(e\left(\frac{877}{2736}\right)\)	\(e\left(\frac{5927}{13680}\right)\)
\(\chi_{508288}(1533,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23551}{27360}\right)\)	\(e\left(\frac{25093}{27360}\right)\)	\(e\left(\frac{979}{4560}\right)\)	\(e\left(\frac{9871}{13680}\right)\)	\(e\left(\frac{9947}{27360}\right)\)	\(e\left(\frac{5321}{6840}\right)\)	\(e\left(\frac{2827}{6840}\right)\)	\(e\left(\frac{413}{5472}\right)\)	\(e\left(\frac{1367}{2736}\right)\)	\(e\left(\frac{11413}{13680}\right)\)
\(\chi_{508288}(1549,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{26203}{27360}\right)\)	\(e\left(\frac{8089}{27360}\right)\)	\(e\left(\frac{1807}{4560}\right)\)	\(e\left(\frac{12523}{13680}\right)\)	\(e\left(\frac{22631}{27360}\right)\)	\(e\left(\frac{1733}{6840}\right)\)	\(e\left(\frac{5551}{6840}\right)\)	\(e\left(\frac{1937}{5472}\right)\)	\(e\left(\frac{2675}{2736}\right)\)	\(e\left(\frac{8089}{13680}\right)\)

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First 20 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.wa
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)