LMFDB - Dirichlet character orbit 508288.tj

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(508288, base_ring=CyclotomicField(2280)) M = H._module chi = DirichletCharacter(H, M([0,1425,912,2000])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(49,508288)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$508288$
Conductor:	$127072$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$2280$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 127072.od	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{2280})$
Fixed field:	Number field defined by a degree 2280 polynomial (not computed)

First 31 of 576 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$21$	$23$	$25$
$\chi_{508288}(49,\cdot)$	$1$	$1$	$e\left(\frac{11}{2280}\right)$	$e\left(\frac{1673}{2280}\right)$	$e\left(\frac{239}{380}\right)$	$e\left(\frac{11}{1140}\right)$	$e\left(\frac{847}{2280}\right)$	$e\left(\frac{421}{570}\right)$	$e\left(\frac{197}{570}\right)$	$e\left(\frac{289}{456}\right)$	$e\left(\frac{187}{228}\right)$	$e\left(\frac{533}{1140}\right)$
$\chi_{508288}(273,\cdot)$	$1$	$1$	$e\left(\frac{1369}{2280}\right)$	$e\left(\frac{1147}{2280}\right)$	$e\left(\frac{1}{380}\right)$	$e\left(\frac{229}{1140}\right)$	$e\left(\frac{533}{2280}\right)$	$e\left(\frac{59}{570}\right)$	$e\left(\frac{163}{570}\right)$	$e\left(\frac{275}{456}\right)$	$e\left(\frac{17}{228}\right)$	$e\left(\frac{7}{1140}\right)$
$\chi_{508288}(1489,\cdot)$	$1$	$1$	$e\left(\frac{13}{2280}\right)$	$e\left(\frac{319}{2280}\right)$	$e\left(\frac{317}{380}\right)$	$e\left(\frac{13}{1140}\right)$	$e\left(\frac{1001}{2280}\right)$	$e\left(\frac{83}{570}\right)$	$e\left(\frac{181}{570}\right)$	$e\left(\frac{383}{456}\right)$	$e\left(\frac{221}{228}\right)$	$e\left(\frac{319}{1140}\right)$
$\chi_{508288}(3089,\cdot)$	$1$	$1$	$e\left(\frac{569}{2280}\right)$	$e\left(\frac{107}{2280}\right)$	$e\left(\frac{341}{380}\right)$	$e\left(\frac{569}{1140}\right)$	$e\left(\frac{493}{2280}\right)$	$e\left(\frac{169}{570}\right)$	$e\left(\frac{293}{570}\right)$	$e\left(\frac{67}{456}\right)$	$e\left(\frac{97}{228}\right)$	$e\left(\frac{107}{1140}\right)$
$\chi_{508288}(3921,\cdot)$	$1$	$1$	$e\left(\frac{1861}{2280}\right)$	$e\left(\frac{943}{2280}\right)$	$e\left(\frac{189}{380}\right)$	$e\left(\frac{721}{1140}\right)$	$e\left(\frac{1937}{2280}\right)$	$e\left(\frac{131}{570}\right)$	$e\left(\frac{217}{570}\right)$	$e\left(\frac{143}{456}\right)$	$e\left(\frac{173}{228}\right)$	$e\left(\frac{943}{1140}\right)$
$\chi_{508288}(4305,\cdot)$	$1$	$1$	$e\left(\frac{1613}{2280}\right)$	$e\left(\frac{119}{2280}\right)$	$e\left(\frac{17}{380}\right)$	$e\left(\frac{473}{1140}\right)$	$e\left(\frac{1081}{2280}\right)$	$e\left(\frac{433}{570}\right)$	$e\left(\frac{491}{570}\right)$	$e\left(\frac{343}{456}\right)$	$e\left(\frac{61}{228}\right)$	$e\left(\frac{119}{1140}\right)$
$\chi_{508288}(5745,\cdot)$	$1$	$1$	$e\left(\frac{967}{2280}\right)$	$e\left(\frac{1981}{2280}\right)$	$e\left(\frac{283}{380}\right)$	$e\left(\frac{967}{1140}\right)$	$e\left(\frac{1499}{2280}\right)$	$e\left(\frac{167}{570}\right)$	$e\left(\frac{529}{570}\right)$	$e\left(\frac{77}{456}\right)$	$e\left(\frac{23}{228}\right)$	$e\left(\frac{841}{1140}\right)$
$\chi_{508288}(6737,\cdot)$	$1$	$1$	$e\left(\frac{1421}{2280}\right)$	$e\left(\frac{143}{2280}\right)$	$e\left(\frac{129}{380}\right)$	$e\left(\frac{281}{1140}\right)$	$e\left(\frac{2257}{2280}\right)$	$e\left(\frac{391}{570}\right)$	$e\left(\frac{317}{570}\right)$	$e\left(\frac{439}{456}\right)$	$e\left(\frac{217}{228}\right)$	$e\left(\frac{143}{1140}\right)$
$\chi_{508288}(6961,\cdot)$	$1$	$1$	$e\left(\frac{979}{2280}\right)$	$e\left(\frac{697}{2280}\right)$	$e\left(\frac{371}{380}\right)$	$e\left(\frac{979}{1140}\right)$	$e\left(\frac{143}{2280}\right)$	$e\left(\frac{419}{570}\right)$	$e\left(\frac{433}{570}\right)$	$e\left(\frac{185}{456}\right)$	$e\left(\frac{227}{228}\right)$	$e\left(\frac{697}{1140}\right)$
$\chi_{508288}(8177,\cdot)$	$1$	$1$	$e\left(\frac{1903}{2280}\right)$	$e\left(\frac{2149}{2280}\right)$	$e\left(\frac{307}{380}\right)$	$e\left(\frac{763}{1140}\right)$	$e\left(\frac{611}{2280}\right)$	$e\left(\frac{443}{570}\right)$	$e\left(\frac{451}{570}\right)$	$e\left(\frac{293}{456}\right)$	$e\left(\frac{203}{228}\right)$	$e\left(\frac{1009}{1140}\right)$
$\chi_{508288}(8561,\cdot)$	$1$	$1$	$e\left(\frac{1847}{2280}\right)$	$e\left(\frac{1301}{2280}\right)$	$e\left(\frac{23}{380}\right)$	$e\left(\frac{707}{1140}\right)$	$e\left(\frac{859}{2280}\right)$	$e\left(\frac{217}{570}\right)$	$e\left(\frac{329}{570}\right)$	$e\left(\frac{397}{456}\right)$	$e\left(\frac{163}{228}\right)$	$e\left(\frac{161}{1140}\right)$
$\chi_{508288}(9777,\cdot)$	$1$	$1$	$e\left(\frac{1979}{2280}\right)$	$e\left(\frac{857}{2280}\right)$	$e\left(\frac{231}{380}\right)$	$e\left(\frac{839}{1140}\right)$	$e\left(\frac{1903}{2280}\right)$	$e\left(\frac{139}{570}\right)$	$e\left(\frac{413}{570}\right)$	$e\left(\frac{217}{456}\right)$	$e\left(\frac{127}{228}\right)$	$e\left(\frac{857}{1140}\right)$
$\chi_{508288}(10609,\cdot)$	$1$	$1$	$e\left(\frac{1471}{2280}\right)$	$e\left(\frac{493}{2280}\right)$	$e\left(\frac{179}{380}\right)$	$e\left(\frac{331}{1140}\right)$	$e\left(\frac{1547}{2280}\right)$	$e\left(\frac{491}{570}\right)$	$e\left(\frac{487}{570}\right)$	$e\left(\frac{53}{456}\right)$	$e\left(\frac{155}{228}\right)$	$e\left(\frac{493}{1140}\right)$
$\chi_{508288}(10993,\cdot)$	$1$	$1$	$e\left(\frac{743}{2280}\right)$	$e\left(\frac{869}{2280}\right)$	$e\left(\frac{287}{380}\right)$	$e\left(\frac{743}{1140}\right)$	$e\left(\frac{211}{2280}\right)$	$e\left(\frac{403}{570}\right)$	$e\left(\frac{41}{570}\right)$	$e\left(\frac{37}{456}\right)$	$e\left(\frac{91}{228}\right)$	$e\left(\frac{869}{1140}\right)$
$\chi_{508288}(12433,\cdot)$	$1$	$1$	$e\left(\frac{577}{2280}\right)$	$e\left(\frac{1531}{2280}\right)$	$e\left(\frac{273}{380}\right)$	$e\left(\frac{577}{1140}\right)$	$e\left(\frac{1109}{2280}\right)$	$e\left(\frac{527}{570}\right)$	$e\left(\frac{229}{570}\right)$	$e\left(\frac{443}{456}\right)$	$e\left(\frac{5}{228}\right)$	$e\left(\frac{391}{1140}\right)$
$\chi_{508288}(14865,\cdot)$	$1$	$1$	$e\left(\frac{1513}{2280}\right)$	$e\left(\frac{1699}{2280}\right)$	$e\left(\frac{297}{380}\right)$	$e\left(\frac{373}{1140}\right)$	$e\left(\frac{221}{2280}\right)$	$e\left(\frac{233}{570}\right)$	$e\left(\frac{151}{570}\right)$	$e\left(\frac{203}{456}\right)$	$e\left(\frac{185}{228}\right)$	$e\left(\frac{559}{1140}\right)$
$\chi_{508288}(15249,\cdot)$	$1$	$1$	$e\left(\frac{977}{2280}\right)$	$e\left(\frac{2051}{2280}\right)$	$e\left(\frac{293}{380}\right)$	$e\left(\frac{977}{1140}\right)$	$e\left(\frac{2269}{2280}\right)$	$e\left(\frac{187}{570}\right)$	$e\left(\frac{449}{570}\right)$	$e\left(\frac{91}{456}\right)$	$e\left(\frac{193}{228}\right)$	$e\left(\frac{911}{1140}\right)$
$\chi_{508288}(16465,\cdot)$	$1$	$1$	$e\left(\frac{1109}{2280}\right)$	$e\left(\frac{1607}{2280}\right)$	$e\left(\frac{121}{380}\right)$	$e\left(\frac{1109}{1140}\right)$	$e\left(\frac{1033}{2280}\right)$	$e\left(\frac{109}{570}\right)$	$e\left(\frac{533}{570}\right)$	$e\left(\frac{367}{456}\right)$	$e\left(\frac{157}{228}\right)$	$e\left(\frac{467}{1140}\right)$
$\chi_{508288}(17297,\cdot)$	$1$	$1$	$e\left(\frac{1081}{2280}\right)$	$e\left(\frac{43}{2280}\right)$	$e\left(\frac{169}{380}\right)$	$e\left(\frac{1081}{1140}\right)$	$e\left(\frac{1157}{2280}\right)$	$e\left(\frac{281}{570}\right)$	$e\left(\frac{187}{570}\right)$	$e\left(\frac{419}{456}\right)$	$e\left(\frac{137}{228}\right)$	$e\left(\frac{43}{1140}\right)$
$\chi_{508288}(17681,\cdot)$	$1$	$1$	$e\left(\frac{2153}{2280}\right)$	$e\left(\frac{1619}{2280}\right)$	$e\left(\frac{177}{380}\right)$	$e\left(\frac{1013}{1140}\right)$	$e\left(\frac{1621}{2280}\right)$	$e\left(\frac{373}{570}\right)$	$e\left(\frac{161}{570}\right)$	$e\left(\frac{187}{456}\right)$	$e\left(\frac{121}{228}\right)$	$e\left(\frac{479}{1140}\right)$
$\chi_{508288}(19121,\cdot)$	$1$	$1$	$e\left(\frac{187}{2280}\right)$	$e\left(\frac{1081}{2280}\right)$	$e\left(\frac{263}{380}\right)$	$e\left(\frac{187}{1140}\right)$	$e\left(\frac{719}{2280}\right)$	$e\left(\frac{317}{570}\right)$	$e\left(\frac{499}{570}\right)$	$e\left(\frac{353}{456}\right)$	$e\left(\frac{215}{228}\right)$	$e\left(\frac{1081}{1140}\right)$
$\chi_{508288}(20113,\cdot)$	$1$	$1$	$e\left(\frac{1961}{2280}\right)$	$e\left(\frac{1643}{2280}\right)$	$e\left(\frac{289}{380}\right)$	$e\left(\frac{821}{1140}\right)$	$e\left(\frac{517}{2280}\right)$	$e\left(\frac{331}{570}\right)$	$e\left(\frac{557}{570}\right)$	$e\left(\frac{283}{456}\right)$	$e\left(\frac{49}{228}\right)$	$e\left(\frac{503}{1140}\right)$
$\chi_{508288}(20337,\cdot)$	$1$	$1$	$e\left(\frac{199}{2280}\right)$	$e\left(\frac{2077}{2280}\right)$	$e\left(\frac{351}{380}\right)$	$e\left(\frac{199}{1140}\right)$	$e\left(\frac{1643}{2280}\right)$	$e\left(\frac{569}{570}\right)$	$e\left(\frac{403}{570}\right)$	$e\left(\frac{5}{456}\right)$	$e\left(\frac{191}{228}\right)$	$e\left(\frac{937}{1140}\right)$
$\chi_{508288}(21553,\cdot)$	$1$	$1$	$e\left(\frac{1123}{2280}\right)$	$e\left(\frac{1249}{2280}\right)$	$e\left(\frac{287}{380}\right)$	$e\left(\frac{1123}{1140}\right)$	$e\left(\frac{2111}{2280}\right)$	$e\left(\frac{23}{570}\right)$	$e\left(\frac{421}{570}\right)$	$e\left(\frac{113}{456}\right)$	$e\left(\frac{167}{228}\right)$	$e\left(\frac{109}{1140}\right)$
$\chi_{508288}(21937,\cdot)$	$1$	$1$	$e\left(\frac{107}{2280}\right)$	$e\left(\frac{521}{2280}\right)$	$e\left(\frac{183}{380}\right)$	$e\left(\frac{107}{1140}\right)$	$e\left(\frac{1399}{2280}\right)$	$e\left(\frac{157}{570}\right)$	$e\left(\frac{569}{570}\right)$	$e\left(\frac{241}{456}\right)$	$e\left(\frac{223}{228}\right)$	$e\left(\frac{521}{1140}\right)$
$\chi_{508288}(23153,\cdot)$	$1$	$1$	$e\left(\frac{239}{2280}\right)$	$e\left(\frac{77}{2280}\right)$	$e\left(\frac{11}{380}\right)$	$e\left(\frac{239}{1140}\right)$	$e\left(\frac{163}{2280}\right)$	$e\left(\frac{79}{570}\right)$	$e\left(\frac{83}{570}\right)$	$e\left(\frac{61}{456}\right)$	$e\left(\frac{187}{228}\right)$	$e\left(\frac{77}{1140}\right)$
$\chi_{508288}(23985,\cdot)$	$1$	$1$	$e\left(\frac{691}{2280}\right)$	$e\left(\frac{1873}{2280}\right)$	$e\left(\frac{159}{380}\right)$	$e\left(\frac{691}{1140}\right)$	$e\left(\frac{767}{2280}\right)$	$e\left(\frac{71}{570}\right)$	$e\left(\frac{457}{570}\right)$	$e\left(\frac{329}{456}\right)$	$e\left(\frac{119}{228}\right)$	$e\left(\frac{733}{1140}\right)$
$\chi_{508288}(24369,\cdot)$	$1$	$1$	$e\left(\frac{1283}{2280}\right)$	$e\left(\frac{89}{2280}\right)$	$e\left(\frac{67}{380}\right)$	$e\left(\frac{143}{1140}\right)$	$e\left(\frac{751}{2280}\right)$	$e\left(\frac{343}{570}\right)$	$e\left(\frac{281}{570}\right)$	$e\left(\frac{337}{456}\right)$	$e\left(\frac{151}{228}\right)$	$e\left(\frac{89}{1140}\right)$
$\chi_{508288}(25809,\cdot)$	$1$	$1$	$e\left(\frac{2077}{2280}\right)$	$e\left(\frac{631}{2280}\right)$	$e\left(\frac{253}{380}\right)$	$e\left(\frac{937}{1140}\right)$	$e\left(\frac{329}{2280}\right)$	$e\left(\frac{107}{570}\right)$	$e\left(\frac{199}{570}\right)$	$e\left(\frac{263}{456}\right)$	$e\left(\frac{197}{228}\right)$	$e\left(\frac{631}{1140}\right)$
$\chi_{508288}(26801,\cdot)$	$1$	$1$	$e\left(\frac{1091}{2280}\right)$	$e\left(\frac{113}{2280}\right)$	$e\left(\frac{179}{380}\right)$	$e\left(\frac{1091}{1140}\right)$	$e\left(\frac{1927}{2280}\right)$	$e\left(\frac{301}{570}\right)$	$e\left(\frac{107}{570}\right)$	$e\left(\frac{433}{456}\right)$	$e\left(\frac{79}{228}\right)$	$e\left(\frac{113}{1140}\right)$
$\chi_{508288}(27025,\cdot)$	$1$	$1$	$e\left(\frac{2089}{2280}\right)$	$e\left(\frac{1627}{2280}\right)$	$e\left(\frac{341}{380}\right)$	$e\left(\frac{949}{1140}\right)$	$e\left(\frac{1253}{2280}\right)$	$e\left(\frac{359}{570}\right)$	$e\left(\frac{103}{570}\right)$	$e\left(\frac{371}{456}\right)$	$e\left(\frac{173}{228}\right)$	$e\left(\frac{487}{1140}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)	\(25\)
\(\chi_{508288}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{2280}\right)\)	\(e\left(\frac{1673}{2280}\right)\)	\(e\left(\frac{239}{380}\right)\)	\(e\left(\frac{11}{1140}\right)\)	\(e\left(\frac{847}{2280}\right)\)	\(e\left(\frac{421}{570}\right)\)	\(e\left(\frac{197}{570}\right)\)	\(e\left(\frac{289}{456}\right)\)	\(e\left(\frac{187}{228}\right)\)	\(e\left(\frac{533}{1140}\right)\)
\(\chi_{508288}(273,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1369}{2280}\right)\)	\(e\left(\frac{1147}{2280}\right)\)	\(e\left(\frac{1}{380}\right)\)	\(e\left(\frac{229}{1140}\right)\)	\(e\left(\frac{533}{2280}\right)\)	\(e\left(\frac{59}{570}\right)\)	\(e\left(\frac{163}{570}\right)\)	\(e\left(\frac{275}{456}\right)\)	\(e\left(\frac{17}{228}\right)\)	\(e\left(\frac{7}{1140}\right)\)
\(\chi_{508288}(1489,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{2280}\right)\)	\(e\left(\frac{319}{2280}\right)\)	\(e\left(\frac{317}{380}\right)\)	\(e\left(\frac{13}{1140}\right)\)	\(e\left(\frac{1001}{2280}\right)\)	\(e\left(\frac{83}{570}\right)\)	\(e\left(\frac{181}{570}\right)\)	\(e\left(\frac{383}{456}\right)\)	\(e\left(\frac{221}{228}\right)\)	\(e\left(\frac{319}{1140}\right)\)
\(\chi_{508288}(3089,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{569}{2280}\right)\)	\(e\left(\frac{107}{2280}\right)\)	\(e\left(\frac{341}{380}\right)\)	\(e\left(\frac{569}{1140}\right)\)	\(e\left(\frac{493}{2280}\right)\)	\(e\left(\frac{169}{570}\right)\)	\(e\left(\frac{293}{570}\right)\)	\(e\left(\frac{67}{456}\right)\)	\(e\left(\frac{97}{228}\right)\)	\(e\left(\frac{107}{1140}\right)\)
\(\chi_{508288}(3921,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1861}{2280}\right)\)	\(e\left(\frac{943}{2280}\right)\)	\(e\left(\frac{189}{380}\right)\)	\(e\left(\frac{721}{1140}\right)\)	\(e\left(\frac{1937}{2280}\right)\)	\(e\left(\frac{131}{570}\right)\)	\(e\left(\frac{217}{570}\right)\)	\(e\left(\frac{143}{456}\right)\)	\(e\left(\frac{173}{228}\right)\)	\(e\left(\frac{943}{1140}\right)\)
\(\chi_{508288}(4305,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1613}{2280}\right)\)	\(e\left(\frac{119}{2280}\right)\)	\(e\left(\frac{17}{380}\right)\)	\(e\left(\frac{473}{1140}\right)\)	\(e\left(\frac{1081}{2280}\right)\)	\(e\left(\frac{433}{570}\right)\)	\(e\left(\frac{491}{570}\right)\)	\(e\left(\frac{343}{456}\right)\)	\(e\left(\frac{61}{228}\right)\)	\(e\left(\frac{119}{1140}\right)\)
\(\chi_{508288}(5745,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{967}{2280}\right)\)	\(e\left(\frac{1981}{2280}\right)\)	\(e\left(\frac{283}{380}\right)\)	\(e\left(\frac{967}{1140}\right)\)	\(e\left(\frac{1499}{2280}\right)\)	\(e\left(\frac{167}{570}\right)\)	\(e\left(\frac{529}{570}\right)\)	\(e\left(\frac{77}{456}\right)\)	\(e\left(\frac{23}{228}\right)\)	\(e\left(\frac{841}{1140}\right)\)
\(\chi_{508288}(6737,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1421}{2280}\right)\)	\(e\left(\frac{143}{2280}\right)\)	\(e\left(\frac{129}{380}\right)\)	\(e\left(\frac{281}{1140}\right)\)	\(e\left(\frac{2257}{2280}\right)\)	\(e\left(\frac{391}{570}\right)\)	\(e\left(\frac{317}{570}\right)\)	\(e\left(\frac{439}{456}\right)\)	\(e\left(\frac{217}{228}\right)\)	\(e\left(\frac{143}{1140}\right)\)
\(\chi_{508288}(6961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{979}{2280}\right)\)	\(e\left(\frac{697}{2280}\right)\)	\(e\left(\frac{371}{380}\right)\)	\(e\left(\frac{979}{1140}\right)\)	\(e\left(\frac{143}{2280}\right)\)	\(e\left(\frac{419}{570}\right)\)	\(e\left(\frac{433}{570}\right)\)	\(e\left(\frac{185}{456}\right)\)	\(e\left(\frac{227}{228}\right)\)	\(e\left(\frac{697}{1140}\right)\)
\(\chi_{508288}(8177,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1903}{2280}\right)\)	\(e\left(\frac{2149}{2280}\right)\)	\(e\left(\frac{307}{380}\right)\)	\(e\left(\frac{763}{1140}\right)\)	\(e\left(\frac{611}{2280}\right)\)	\(e\left(\frac{443}{570}\right)\)	\(e\left(\frac{451}{570}\right)\)	\(e\left(\frac{293}{456}\right)\)	\(e\left(\frac{203}{228}\right)\)	\(e\left(\frac{1009}{1140}\right)\)
\(\chi_{508288}(8561,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1847}{2280}\right)\)	\(e\left(\frac{1301}{2280}\right)\)	\(e\left(\frac{23}{380}\right)\)	\(e\left(\frac{707}{1140}\right)\)	\(e\left(\frac{859}{2280}\right)\)	\(e\left(\frac{217}{570}\right)\)	\(e\left(\frac{329}{570}\right)\)	\(e\left(\frac{397}{456}\right)\)	\(e\left(\frac{163}{228}\right)\)	\(e\left(\frac{161}{1140}\right)\)
\(\chi_{508288}(9777,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1979}{2280}\right)\)	\(e\left(\frac{857}{2280}\right)\)	\(e\left(\frac{231}{380}\right)\)	\(e\left(\frac{839}{1140}\right)\)	\(e\left(\frac{1903}{2280}\right)\)	\(e\left(\frac{139}{570}\right)\)	\(e\left(\frac{413}{570}\right)\)	\(e\left(\frac{217}{456}\right)\)	\(e\left(\frac{127}{228}\right)\)	\(e\left(\frac{857}{1140}\right)\)
\(\chi_{508288}(10609,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1471}{2280}\right)\)	\(e\left(\frac{493}{2280}\right)\)	\(e\left(\frac{179}{380}\right)\)	\(e\left(\frac{331}{1140}\right)\)	\(e\left(\frac{1547}{2280}\right)\)	\(e\left(\frac{491}{570}\right)\)	\(e\left(\frac{487}{570}\right)\)	\(e\left(\frac{53}{456}\right)\)	\(e\left(\frac{155}{228}\right)\)	\(e\left(\frac{493}{1140}\right)\)
\(\chi_{508288}(10993,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{743}{2280}\right)\)	\(e\left(\frac{869}{2280}\right)\)	\(e\left(\frac{287}{380}\right)\)	\(e\left(\frac{743}{1140}\right)\)	\(e\left(\frac{211}{2280}\right)\)	\(e\left(\frac{403}{570}\right)\)	\(e\left(\frac{41}{570}\right)\)	\(e\left(\frac{37}{456}\right)\)	\(e\left(\frac{91}{228}\right)\)	\(e\left(\frac{869}{1140}\right)\)
\(\chi_{508288}(12433,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{577}{2280}\right)\)	\(e\left(\frac{1531}{2280}\right)\)	\(e\left(\frac{273}{380}\right)\)	\(e\left(\frac{577}{1140}\right)\)	\(e\left(\frac{1109}{2280}\right)\)	\(e\left(\frac{527}{570}\right)\)	\(e\left(\frac{229}{570}\right)\)	\(e\left(\frac{443}{456}\right)\)	\(e\left(\frac{5}{228}\right)\)	\(e\left(\frac{391}{1140}\right)\)
\(\chi_{508288}(14865,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1513}{2280}\right)\)	\(e\left(\frac{1699}{2280}\right)\)	\(e\left(\frac{297}{380}\right)\)	\(e\left(\frac{373}{1140}\right)\)	\(e\left(\frac{221}{2280}\right)\)	\(e\left(\frac{233}{570}\right)\)	\(e\left(\frac{151}{570}\right)\)	\(e\left(\frac{203}{456}\right)\)	\(e\left(\frac{185}{228}\right)\)	\(e\left(\frac{559}{1140}\right)\)
\(\chi_{508288}(15249,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{977}{2280}\right)\)	\(e\left(\frac{2051}{2280}\right)\)	\(e\left(\frac{293}{380}\right)\)	\(e\left(\frac{977}{1140}\right)\)	\(e\left(\frac{2269}{2280}\right)\)	\(e\left(\frac{187}{570}\right)\)	\(e\left(\frac{449}{570}\right)\)	\(e\left(\frac{91}{456}\right)\)	\(e\left(\frac{193}{228}\right)\)	\(e\left(\frac{911}{1140}\right)\)
\(\chi_{508288}(16465,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1109}{2280}\right)\)	\(e\left(\frac{1607}{2280}\right)\)	\(e\left(\frac{121}{380}\right)\)	\(e\left(\frac{1109}{1140}\right)\)	\(e\left(\frac{1033}{2280}\right)\)	\(e\left(\frac{109}{570}\right)\)	\(e\left(\frac{533}{570}\right)\)	\(e\left(\frac{367}{456}\right)\)	\(e\left(\frac{157}{228}\right)\)	\(e\left(\frac{467}{1140}\right)\)
\(\chi_{508288}(17297,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1081}{2280}\right)\)	\(e\left(\frac{43}{2280}\right)\)	\(e\left(\frac{169}{380}\right)\)	\(e\left(\frac{1081}{1140}\right)\)	\(e\left(\frac{1157}{2280}\right)\)	\(e\left(\frac{281}{570}\right)\)	\(e\left(\frac{187}{570}\right)\)	\(e\left(\frac{419}{456}\right)\)	\(e\left(\frac{137}{228}\right)\)	\(e\left(\frac{43}{1140}\right)\)
\(\chi_{508288}(17681,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2153}{2280}\right)\)	\(e\left(\frac{1619}{2280}\right)\)	\(e\left(\frac{177}{380}\right)\)	\(e\left(\frac{1013}{1140}\right)\)	\(e\left(\frac{1621}{2280}\right)\)	\(e\left(\frac{373}{570}\right)\)	\(e\left(\frac{161}{570}\right)\)	\(e\left(\frac{187}{456}\right)\)	\(e\left(\frac{121}{228}\right)\)	\(e\left(\frac{479}{1140}\right)\)
\(\chi_{508288}(19121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{187}{2280}\right)\)	\(e\left(\frac{1081}{2280}\right)\)	\(e\left(\frac{263}{380}\right)\)	\(e\left(\frac{187}{1140}\right)\)	\(e\left(\frac{719}{2280}\right)\)	\(e\left(\frac{317}{570}\right)\)	\(e\left(\frac{499}{570}\right)\)	\(e\left(\frac{353}{456}\right)\)	\(e\left(\frac{215}{228}\right)\)	\(e\left(\frac{1081}{1140}\right)\)
\(\chi_{508288}(20113,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1961}{2280}\right)\)	\(e\left(\frac{1643}{2280}\right)\)	\(e\left(\frac{289}{380}\right)\)	\(e\left(\frac{821}{1140}\right)\)	\(e\left(\frac{517}{2280}\right)\)	\(e\left(\frac{331}{570}\right)\)	\(e\left(\frac{557}{570}\right)\)	\(e\left(\frac{283}{456}\right)\)	\(e\left(\frac{49}{228}\right)\)	\(e\left(\frac{503}{1140}\right)\)
\(\chi_{508288}(20337,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{2280}\right)\)	\(e\left(\frac{2077}{2280}\right)\)	\(e\left(\frac{351}{380}\right)\)	\(e\left(\frac{199}{1140}\right)\)	\(e\left(\frac{1643}{2280}\right)\)	\(e\left(\frac{569}{570}\right)\)	\(e\left(\frac{403}{570}\right)\)	\(e\left(\frac{5}{456}\right)\)	\(e\left(\frac{191}{228}\right)\)	\(e\left(\frac{937}{1140}\right)\)
\(\chi_{508288}(21553,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1123}{2280}\right)\)	\(e\left(\frac{1249}{2280}\right)\)	\(e\left(\frac{287}{380}\right)\)	\(e\left(\frac{1123}{1140}\right)\)	\(e\left(\frac{2111}{2280}\right)\)	\(e\left(\frac{23}{570}\right)\)	\(e\left(\frac{421}{570}\right)\)	\(e\left(\frac{113}{456}\right)\)	\(e\left(\frac{167}{228}\right)\)	\(e\left(\frac{109}{1140}\right)\)
\(\chi_{508288}(21937,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{2280}\right)\)	\(e\left(\frac{521}{2280}\right)\)	\(e\left(\frac{183}{380}\right)\)	\(e\left(\frac{107}{1140}\right)\)	\(e\left(\frac{1399}{2280}\right)\)	\(e\left(\frac{157}{570}\right)\)	\(e\left(\frac{569}{570}\right)\)	\(e\left(\frac{241}{456}\right)\)	\(e\left(\frac{223}{228}\right)\)	\(e\left(\frac{521}{1140}\right)\)
\(\chi_{508288}(23153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{239}{2280}\right)\)	\(e\left(\frac{77}{2280}\right)\)	\(e\left(\frac{11}{380}\right)\)	\(e\left(\frac{239}{1140}\right)\)	\(e\left(\frac{163}{2280}\right)\)	\(e\left(\frac{79}{570}\right)\)	\(e\left(\frac{83}{570}\right)\)	\(e\left(\frac{61}{456}\right)\)	\(e\left(\frac{187}{228}\right)\)	\(e\left(\frac{77}{1140}\right)\)
\(\chi_{508288}(23985,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{691}{2280}\right)\)	\(e\left(\frac{1873}{2280}\right)\)	\(e\left(\frac{159}{380}\right)\)	\(e\left(\frac{691}{1140}\right)\)	\(e\left(\frac{767}{2280}\right)\)	\(e\left(\frac{71}{570}\right)\)	\(e\left(\frac{457}{570}\right)\)	\(e\left(\frac{329}{456}\right)\)	\(e\left(\frac{119}{228}\right)\)	\(e\left(\frac{733}{1140}\right)\)
\(\chi_{508288}(24369,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1283}{2280}\right)\)	\(e\left(\frac{89}{2280}\right)\)	\(e\left(\frac{67}{380}\right)\)	\(e\left(\frac{143}{1140}\right)\)	\(e\left(\frac{751}{2280}\right)\)	\(e\left(\frac{343}{570}\right)\)	\(e\left(\frac{281}{570}\right)\)	\(e\left(\frac{337}{456}\right)\)	\(e\left(\frac{151}{228}\right)\)	\(e\left(\frac{89}{1140}\right)\)
\(\chi_{508288}(25809,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2077}{2280}\right)\)	\(e\left(\frac{631}{2280}\right)\)	\(e\left(\frac{253}{380}\right)\)	\(e\left(\frac{937}{1140}\right)\)	\(e\left(\frac{329}{2280}\right)\)	\(e\left(\frac{107}{570}\right)\)	\(e\left(\frac{199}{570}\right)\)	\(e\left(\frac{263}{456}\right)\)	\(e\left(\frac{197}{228}\right)\)	\(e\left(\frac{631}{1140}\right)\)
\(\chi_{508288}(26801,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1091}{2280}\right)\)	\(e\left(\frac{113}{2280}\right)\)	\(e\left(\frac{179}{380}\right)\)	\(e\left(\frac{1091}{1140}\right)\)	\(e\left(\frac{1927}{2280}\right)\)	\(e\left(\frac{301}{570}\right)\)	\(e\left(\frac{107}{570}\right)\)	\(e\left(\frac{433}{456}\right)\)	\(e\left(\frac{79}{228}\right)\)	\(e\left(\frac{113}{1140}\right)\)
\(\chi_{508288}(27025,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2089}{2280}\right)\)	\(e\left(\frac{1627}{2280}\right)\)	\(e\left(\frac{341}{380}\right)\)	\(e\left(\frac{949}{1140}\right)\)	\(e\left(\frac{1253}{2280}\right)\)	\(e\left(\frac{359}{570}\right)\)	\(e\left(\frac{103}{570}\right)\)	\(e\left(\frac{371}{456}\right)\)	\(e\left(\frac{173}{228}\right)\)	\(e\left(\frac{487}{1140}\right)\)

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First 31 of 576 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.tj
Modulus	$508288$
Conductor	$127072$
Order	$2280$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(508288\)
Conductor:	\(127072\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(2280\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 127072.od	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)