LMFDB - Dirichlet character orbit 18225.ct

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(18225, base_ring=CyclotomicField(4860)) M = H._module chi = DirichletCharacter(H, M([3320,4617])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(13,18225)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$18225$
Conductor:	$18225$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$4860$	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:	$\Q(\zeta_{4860})$
Fixed field:	Number field defined by a degree 4860 polynomial (not computed)

First 31 of 1296 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{18225}(13,\cdot)$	$-1$	$1$	$e\left(\frac{3077}{4860}\right)$	$e\left(\frac{647}{2430}\right)$	$e\left(\frac{877}{972}\right)$	$e\left(\frac{1457}{1620}\right)$	$e\left(\frac{638}{1215}\right)$	$e\left(\frac{4123}{4860}\right)$	$e\left(\frac{1301}{2430}\right)$	$e\left(\frac{647}{1215}\right)$	$e\left(\frac{1447}{1620}\right)$	$e\left(\frac{271}{810}\right)$
$\chi_{18225}(22,\cdot)$	$-1$	$1$	$e\left(\frac{2111}{4860}\right)$	$e\left(\frac{2111}{2430}\right)$	$e\left(\frac{475}{972}\right)$	$e\left(\frac{491}{1620}\right)$	$e\left(\frac{1184}{1215}\right)$	$e\left(\frac{769}{4860}\right)$	$e\left(\frac{2243}{2430}\right)$	$e\left(\frac{896}{1215}\right)$	$e\left(\frac{541}{1620}\right)$	$e\left(\frac{103}{810}\right)$
$\chi_{18225}(52,\cdot)$	$-1$	$1$	$e\left(\frac{3583}{4860}\right)$	$e\left(\frac{1153}{2430}\right)$	$e\left(\frac{23}{972}\right)$	$e\left(\frac{343}{1620}\right)$	$e\left(\frac{352}{1215}\right)$	$e\left(\frac{557}{4860}\right)$	$e\left(\frac{1849}{2430}\right)$	$e\left(\frac{1153}{1215}\right)$	$e\left(\frac{533}{1620}\right)$	$e\left(\frac{359}{810}\right)$
$\chi_{18225}(58,\cdot)$	$-1$	$1$	$e\left(\frac{2729}{4860}\right)$	$e\left(\frac{299}{2430}\right)$	$e\left(\frac{865}{972}\right)$	$e\left(\frac{1109}{1620}\right)$	$e\left(\frac{1046}{1215}\right)$	$e\left(\frac{2311}{4860}\right)$	$e\left(\frac{1097}{2430}\right)$	$e\left(\frac{299}{1215}\right)$	$e\left(\frac{859}{1620}\right)$	$e\left(\frac{457}{810}\right)$
$\chi_{18225}(67,\cdot)$	$-1$	$1$	$e\left(\frac{359}{4860}\right)$	$e\left(\frac{359}{2430}\right)$	$e\left(\frac{247}{972}\right)$	$e\left(\frac{359}{1620}\right)$	$e\left(\frac{431}{1215}\right)$	$e\left(\frac{361}{4860}\right)$	$e\left(\frac{797}{2430}\right)$	$e\left(\frac{359}{1215}\right)$	$e\left(\frac{709}{1620}\right)$	$e\left(\frac{397}{810}\right)$
$\chi_{18225}(88,\cdot)$	$-1$	$1$	$e\left(\frac{2617}{4860}\right)$	$e\left(\frac{187}{2430}\right)$	$e\left(\frac{593}{972}\right)$	$e\left(\frac{997}{1620}\right)$	$e\left(\frac{898}{1215}\right)$	$e\left(\frac{2063}{4860}\right)$	$e\left(\frac{361}{2430}\right)$	$e\left(\frac{187}{1215}\right)$	$e\left(\frac{1247}{1620}\right)$	$e\left(\frac{191}{810}\right)$
$\chi_{18225}(97,\cdot)$	$-1$	$1$	$e\left(\frac{3091}{4860}\right)$	$e\left(\frac{661}{2430}\right)$	$e\left(\frac{911}{972}\right)$	$e\left(\frac{1471}{1620}\right)$	$e\left(\frac{49}{1215}\right)$	$e\left(\frac{509}{4860}\right)$	$e\left(\frac{1393}{2430}\right)$	$e\left(\frac{661}{1215}\right)$	$e\left(\frac{1601}{1620}\right)$	$e\left(\frac{203}{810}\right)$
$\chi_{18225}(103,\cdot)$	$-1$	$1$	$e\left(\frac{221}{4860}\right)$	$e\left(\frac{221}{2430}\right)$	$e\left(\frac{745}{972}\right)$	$e\left(\frac{221}{1620}\right)$	$e\left(\frac{509}{1215}\right)$	$e\left(\frac{2659}{4860}\right)$	$e\left(\frac{1973}{2430}\right)$	$e\left(\frac{221}{1215}\right)$	$e\left(\frac{811}{1620}\right)$	$e\left(\frac{373}{810}\right)$
$\chi_{18225}(112,\cdot)$	$-1$	$1$	$e\left(\frac{1307}{4860}\right)$	$e\left(\frac{1307}{2430}\right)$	$e\left(\frac{883}{972}\right)$	$e\left(\frac{1307}{1620}\right)$	$e\left(\frac{1163}{1215}\right)$	$e\left(\frac{2113}{4860}\right)$	$e\left(\frac{431}{2430}\right)$	$e\left(\frac{92}{1215}\right)$	$e\left(\frac{1417}{1620}\right)$	$e\left(\frac{421}{810}\right)$
$\chi_{18225}(133,\cdot)$	$-1$	$1$	$e\left(\frac{2989}{4860}\right)$	$e\left(\frac{559}{2430}\right)$	$e\left(\frac{941}{972}\right)$	$e\left(\frac{1369}{1620}\right)$	$e\left(\frac{1}{1215}\right)$	$e\left(\frac{1151}{4860}\right)$	$e\left(\frac{1417}{2430}\right)$	$e\left(\frac{559}{1215}\right)$	$e\left(\frac{479}{1620}\right)$	$e\left(\frac{467}{810}\right)$
$\chi_{18225}(142,\cdot)$	$-1$	$1$	$e\left(\frac{3679}{4860}\right)$	$e\left(\frac{1249}{2430}\right)$	$e\left(\frac{395}{972}\right)$	$e\left(\frac{439}{1620}\right)$	$e\left(\frac{826}{1215}\right)$	$e\left(\frac{4241}{4860}\right)$	$e\left(\frac{397}{2430}\right)$	$e\left(\frac{34}{1215}\right)$	$e\left(\frac{1589}{1620}\right)$	$e\left(\frac{587}{810}\right)$
$\chi_{18225}(148,\cdot)$	$-1$	$1$	$e\left(\frac{413}{4860}\right)$	$e\left(\frac{413}{2430}\right)$	$e\left(\frac{517}{972}\right)$	$e\left(\frac{413}{1620}\right)$	$e\left(\frac{242}{1215}\right)$	$e\left(\frac{307}{4860}\right)$	$e\left(\frac{1499}{2430}\right)$	$e\left(\frac{413}{1215}\right)$	$e\left(\frac{1303}{1620}\right)$	$e\left(\frac{19}{810}\right)$
$\chi_{18225}(178,\cdot)$	$-1$	$1$	$e\left(\frac{4441}{4860}\right)$	$e\left(\frac{2011}{2430}\right)$	$e\left(\frac{857}{972}\right)$	$e\left(\frac{1201}{1620}\right)$	$e\left(\frac{184}{1215}\right)$	$e\left(\frac{4019}{4860}\right)$	$e\left(\frac{1933}{2430}\right)$	$e\left(\frac{796}{1215}\right)$	$e\left(\frac{251}{1620}\right)$	$e\left(\frac{473}{810}\right)$
$\chi_{18225}(187,\cdot)$	$-1$	$1$	$e\left(\frac{487}{4860}\right)$	$e\left(\frac{487}{2430}\right)$	$e\left(\frac{419}{972}\right)$	$e\left(\frac{487}{1620}\right)$	$e\left(\frac{253}{1215}\right)$	$e\left(\frac{2033}{4860}\right)$	$e\left(\frac{1291}{2430}\right)$	$e\left(\frac{487}{1215}\right)$	$e\left(\frac{497}{1620}\right)$	$e\left(\frac{701}{810}\right)$
$\chi_{18225}(202,\cdot)$	$-1$	$1$	$e\left(\frac{1583}{4860}\right)$	$e\left(\frac{1583}{2430}\right)$	$e\left(\frac{859}{972}\right)$	$e\left(\frac{1583}{1620}\right)$	$e\left(\frac{1007}{1215}\right)$	$e\left(\frac{2377}{4860}\right)$	$e\left(\frac{509}{2430}\right)$	$e\left(\frac{368}{1215}\right)$	$e\left(\frac{1213}{1620}\right)$	$e\left(\frac{469}{810}\right)$
$\chi_{18225}(223,\cdot)$	$-1$	$1$	$e\left(\frac{2113}{4860}\right)$	$e\left(\frac{2113}{2430}\right)$	$e\left(\frac{341}{972}\right)$	$e\left(\frac{493}{1620}\right)$	$e\left(\frac{232}{1215}\right)$	$e\left(\frac{947}{4860}\right)$	$e\left(\frac{1909}{2430}\right)$	$e\left(\frac{898}{1215}\right)$	$e\left(\frac{563}{1620}\right)$	$e\left(\frac{209}{810}\right)$
$\chi_{18225}(238,\cdot)$	$-1$	$1$	$e\left(\frac{4037}{4860}\right)$	$e\left(\frac{1607}{2430}\right)$	$e\left(\frac{709}{972}\right)$	$e\left(\frac{797}{1620}\right)$	$e\left(\frac{518}{1215}\right)$	$e\left(\frac{2083}{4860}\right)$	$e\left(\frac{1361}{2430}\right)$	$e\left(\frac{392}{1215}\right)$	$e\left(\frac{667}{1620}\right)$	$e\left(\frac{121}{810}\right)$
$\chi_{18225}(247,\cdot)$	$-1$	$1$	$e\left(\frac{911}{4860}\right)$	$e\left(\frac{911}{2430}\right)$	$e\left(\frac{199}{972}\right)$	$e\left(\frac{911}{1620}\right)$	$e\left(\frac{119}{1215}\right)$	$e\left(\frac{889}{4860}\right)$	$e\left(\frac{953}{2430}\right)$	$e\left(\frac{911}{1215}\right)$	$e\left(\frac{301}{1620}\right)$	$e\left(\frac{493}{810}\right)$
$\chi_{18225}(277,\cdot)$	$-1$	$1$	$e\left(\frac{2203}{4860}\right)$	$e\left(\frac{2203}{2430}\right)$	$e\left(\frac{143}{972}\right)$	$e\left(\frac{583}{1620}\right)$	$e\left(\frac{1132}{1215}\right)$	$e\left(\frac{4097}{4860}\right)$	$e\left(\frac{1459}{2430}\right)$	$e\left(\frac{988}{1215}\right)$	$e\left(\frac{1553}{1620}\right)$	$e\left(\frac{119}{810}\right)$
$\chi_{18225}(283,\cdot)$	$-1$	$1$	$e\left(\frac{2609}{4860}\right)$	$e\left(\frac{179}{2430}\right)$	$e\left(\frac{157}{972}\right)$	$e\left(\frac{989}{1620}\right)$	$e\left(\frac{1061}{1215}\right)$	$e\left(\frac{1351}{4860}\right)$	$e\left(\frac{1697}{2430}\right)$	$e\left(\frac{179}{1215}\right)$	$e\left(\frac{1159}{1620}\right)$	$e\left(\frac{577}{810}\right)$
$\chi_{18225}(292,\cdot)$	$-1$	$1$	$e\left(\frac{2939}{4860}\right)$	$e\left(\frac{509}{2430}\right)$	$e\left(\frac{403}{972}\right)$	$e\left(\frac{1319}{1620}\right)$	$e\left(\frac{716}{1215}\right)$	$e\left(\frac{1561}{4860}\right)$	$e\left(\frac{47}{2430}\right)$	$e\left(\frac{509}{1215}\right)$	$e\left(\frac{1549}{1620}\right)$	$e\left(\frac{247}{810}\right)$
$\chi_{18225}(313,\cdot)$	$-1$	$1$	$e\left(\frac{697}{4860}\right)$	$e\left(\frac{697}{2430}\right)$	$e\left(\frac{929}{972}\right)$	$e\left(\frac{697}{1620}\right)$	$e\left(\frac{1138}{1215}\right)$	$e\left(\frac{1283}{4860}\right)$	$e\left(\frac{241}{2430}\right)$	$e\left(\frac{697}{1215}\right)$	$e\left(\frac{1187}{1620}\right)$	$e\left(\frac{491}{810}\right)$
$\chi_{18225}(322,\cdot)$	$-1$	$1$	$e\left(\frac{2251}{4860}\right)$	$e\left(\frac{2251}{2430}\right)$	$e\left(\frac{815}{972}\right)$	$e\left(\frac{631}{1620}\right)$	$e\left(\frac{154}{1215}\right)$	$e\left(\frac{3509}{4860}\right)$	$e\left(\frac{733}{2430}\right)$	$e\left(\frac{1036}{1215}\right)$	$e\left(\frac{461}{1620}\right)$	$e\left(\frac{233}{810}\right)$
$\chi_{18225}(328,\cdot)$	$-1$	$1$	$e\left(\frac{3881}{4860}\right)$	$e\left(\frac{1451}{2430}\right)$	$e\left(\frac{469}{972}\right)$	$e\left(\frac{641}{1620}\right)$	$e\left(\frac{659}{1215}\right)$	$e\left(\frac{2779}{4860}\right)$	$e\left(\frac{683}{2430}\right)$	$e\left(\frac{236}{1215}\right)$	$e\left(\frac{571}{1620}\right)$	$e\left(\frac{763}{810}\right)$
$\chi_{18225}(337,\cdot)$	$-1$	$1$	$e\left(\frac{2807}{4860}\right)$	$e\left(\frac{377}{2430}\right)$	$e\left(\frac{499}{972}\right)$	$e\left(\frac{1187}{1620}\right)$	$e\left(\frac{368}{1215}\right)$	$e\left(\frac{4393}{4860}\right)$	$e\left(\frac{221}{2430}\right)$	$e\left(\frac{377}{1215}\right)$	$e\left(\frac{97}{1620}\right)$	$e\left(\frac{541}{810}\right)$
$\chi_{18225}(358,\cdot)$	$-1$	$1$	$e\left(\frac{1609}{4860}\right)$	$e\left(\frac{1609}{2430}\right)$	$e\left(\frac{89}{972}\right)$	$e\left(\frac{1609}{1620}\right)$	$e\left(\frac{781}{1215}\right)$	$e\left(\frac{4691}{4860}\right)$	$e\left(\frac{1027}{2430}\right)$	$e\left(\frac{394}{1215}\right)$	$e\left(\frac{1499}{1620}\right)$	$e\left(\frac{227}{810}\right)$
$\chi_{18225}(367,\cdot)$	$-1$	$1$	$e\left(\frac{3379}{4860}\right)$	$e\left(\frac{949}{2430}\right)$	$e\left(\frac{83}{972}\right)$	$e\left(\frac{139}{1620}\right)$	$e\left(\frac{256}{1215}\right)$	$e\left(\frac{1841}{4860}\right)$	$e\left(\frac{1897}{2430}\right)$	$e\left(\frac{949}{1215}\right)$	$e\left(\frac{1529}{1620}\right)$	$e\left(\frac{77}{810}\right)$
$\chi_{18225}(373,\cdot)$	$-1$	$1$	$e\left(\frac{2993}{4860}\right)$	$e\left(\frac{563}{2430}\right)$	$e\left(\frac{673}{972}\right)$	$e\left(\frac{1373}{1620}\right)$	$e\left(\frac{527}{1215}\right)$	$e\left(\frac{1507}{4860}\right)$	$e\left(\frac{749}{2430}\right)$	$e\left(\frac{563}{1215}\right)$	$e\left(\frac{523}{1620}\right)$	$e\left(\frac{679}{810}\right)$
$\chi_{18225}(403,\cdot)$	$-1$	$1$	$e\left(\frac{3601}{4860}\right)$	$e\left(\frac{1171}{2430}\right)$	$e\left(\frac{761}{972}\right)$	$e\left(\frac{361}{1620}\right)$	$e\left(\frac{289}{1215}\right)$	$e\left(\frac{2159}{4860}\right)$	$e\left(\frac{1273}{2430}\right)$	$e\left(\frac{1171}{1215}\right)$	$e\left(\frac{731}{1620}\right)$	$e\left(\frac{503}{810}\right)$
$\chi_{18225}(412,\cdot)$	$-1$	$1$	$e\left(\frac{727}{4860}\right)$	$e\left(\frac{727}{2430}\right)$	$e\left(\frac{863}{972}\right)$	$e\left(\frac{727}{1620}\right)$	$e\left(\frac{223}{1215}\right)$	$e\left(\frac{3953}{4860}\right)$	$e\left(\frac{91}{2430}\right)$	$e\left(\frac{727}{1215}\right)$	$e\left(\frac{1517}{1620}\right)$	$e\left(\frac{461}{810}\right)$
$\chi_{18225}(427,\cdot)$	$-1$	$1$	$e\left(\frac{923}{4860}\right)$	$e\left(\frac{923}{2430}\right)$	$e\left(\frac{367}{972}\right)$	$e\left(\frac{923}{1620}\right)$	$e\left(\frac{482}{1215}\right)$	$e\left(\frac{1957}{4860}\right)$	$e\left(\frac{1379}{2430}\right)$	$e\left(\frac{923}{1215}\right)$	$e\left(\frac{433}{1620}\right)$	$e\left(\frac{319}{810}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{18225}(13,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3077}{4860}\right)\)	\(e\left(\frac{647}{2430}\right)\)	\(e\left(\frac{877}{972}\right)\)	\(e\left(\frac{1457}{1620}\right)\)	\(e\left(\frac{638}{1215}\right)\)	\(e\left(\frac{4123}{4860}\right)\)	\(e\left(\frac{1301}{2430}\right)\)	\(e\left(\frac{647}{1215}\right)\)	\(e\left(\frac{1447}{1620}\right)\)	\(e\left(\frac{271}{810}\right)\)
\(\chi_{18225}(22,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2111}{4860}\right)\)	\(e\left(\frac{2111}{2430}\right)\)	\(e\left(\frac{475}{972}\right)\)	\(e\left(\frac{491}{1620}\right)\)	\(e\left(\frac{1184}{1215}\right)\)	\(e\left(\frac{769}{4860}\right)\)	\(e\left(\frac{2243}{2430}\right)\)	\(e\left(\frac{896}{1215}\right)\)	\(e\left(\frac{541}{1620}\right)\)	\(e\left(\frac{103}{810}\right)\)
\(\chi_{18225}(52,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3583}{4860}\right)\)	\(e\left(\frac{1153}{2430}\right)\)	\(e\left(\frac{23}{972}\right)\)	\(e\left(\frac{343}{1620}\right)\)	\(e\left(\frac{352}{1215}\right)\)	\(e\left(\frac{557}{4860}\right)\)	\(e\left(\frac{1849}{2430}\right)\)	\(e\left(\frac{1153}{1215}\right)\)	\(e\left(\frac{533}{1620}\right)\)	\(e\left(\frac{359}{810}\right)\)
\(\chi_{18225}(58,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2729}{4860}\right)\)	\(e\left(\frac{299}{2430}\right)\)	\(e\left(\frac{865}{972}\right)\)	\(e\left(\frac{1109}{1620}\right)\)	\(e\left(\frac{1046}{1215}\right)\)	\(e\left(\frac{2311}{4860}\right)\)	\(e\left(\frac{1097}{2430}\right)\)	\(e\left(\frac{299}{1215}\right)\)	\(e\left(\frac{859}{1620}\right)\)	\(e\left(\frac{457}{810}\right)\)
\(\chi_{18225}(67,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{359}{4860}\right)\)	\(e\left(\frac{359}{2430}\right)\)	\(e\left(\frac{247}{972}\right)\)	\(e\left(\frac{359}{1620}\right)\)	\(e\left(\frac{431}{1215}\right)\)	\(e\left(\frac{361}{4860}\right)\)	\(e\left(\frac{797}{2430}\right)\)	\(e\left(\frac{359}{1215}\right)\)	\(e\left(\frac{709}{1620}\right)\)	\(e\left(\frac{397}{810}\right)\)
\(\chi_{18225}(88,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2617}{4860}\right)\)	\(e\left(\frac{187}{2430}\right)\)	\(e\left(\frac{593}{972}\right)\)	\(e\left(\frac{997}{1620}\right)\)	\(e\left(\frac{898}{1215}\right)\)	\(e\left(\frac{2063}{4860}\right)\)	\(e\left(\frac{361}{2430}\right)\)	\(e\left(\frac{187}{1215}\right)\)	\(e\left(\frac{1247}{1620}\right)\)	\(e\left(\frac{191}{810}\right)\)
\(\chi_{18225}(97,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3091}{4860}\right)\)	\(e\left(\frac{661}{2430}\right)\)	\(e\left(\frac{911}{972}\right)\)	\(e\left(\frac{1471}{1620}\right)\)	\(e\left(\frac{49}{1215}\right)\)	\(e\left(\frac{509}{4860}\right)\)	\(e\left(\frac{1393}{2430}\right)\)	\(e\left(\frac{661}{1215}\right)\)	\(e\left(\frac{1601}{1620}\right)\)	\(e\left(\frac{203}{810}\right)\)
\(\chi_{18225}(103,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{221}{4860}\right)\)	\(e\left(\frac{221}{2430}\right)\)	\(e\left(\frac{745}{972}\right)\)	\(e\left(\frac{221}{1620}\right)\)	\(e\left(\frac{509}{1215}\right)\)	\(e\left(\frac{2659}{4860}\right)\)	\(e\left(\frac{1973}{2430}\right)\)	\(e\left(\frac{221}{1215}\right)\)	\(e\left(\frac{811}{1620}\right)\)	\(e\left(\frac{373}{810}\right)\)
\(\chi_{18225}(112,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1307}{4860}\right)\)	\(e\left(\frac{1307}{2430}\right)\)	\(e\left(\frac{883}{972}\right)\)	\(e\left(\frac{1307}{1620}\right)\)	\(e\left(\frac{1163}{1215}\right)\)	\(e\left(\frac{2113}{4860}\right)\)	\(e\left(\frac{431}{2430}\right)\)	\(e\left(\frac{92}{1215}\right)\)	\(e\left(\frac{1417}{1620}\right)\)	\(e\left(\frac{421}{810}\right)\)
\(\chi_{18225}(133,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2989}{4860}\right)\)	\(e\left(\frac{559}{2430}\right)\)	\(e\left(\frac{941}{972}\right)\)	\(e\left(\frac{1369}{1620}\right)\)	\(e\left(\frac{1}{1215}\right)\)	\(e\left(\frac{1151}{4860}\right)\)	\(e\left(\frac{1417}{2430}\right)\)	\(e\left(\frac{559}{1215}\right)\)	\(e\left(\frac{479}{1620}\right)\)	\(e\left(\frac{467}{810}\right)\)
\(\chi_{18225}(142,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3679}{4860}\right)\)	\(e\left(\frac{1249}{2430}\right)\)	\(e\left(\frac{395}{972}\right)\)	\(e\left(\frac{439}{1620}\right)\)	\(e\left(\frac{826}{1215}\right)\)	\(e\left(\frac{4241}{4860}\right)\)	\(e\left(\frac{397}{2430}\right)\)	\(e\left(\frac{34}{1215}\right)\)	\(e\left(\frac{1589}{1620}\right)\)	\(e\left(\frac{587}{810}\right)\)
\(\chi_{18225}(148,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{413}{4860}\right)\)	\(e\left(\frac{413}{2430}\right)\)	\(e\left(\frac{517}{972}\right)\)	\(e\left(\frac{413}{1620}\right)\)	\(e\left(\frac{242}{1215}\right)\)	\(e\left(\frac{307}{4860}\right)\)	\(e\left(\frac{1499}{2430}\right)\)	\(e\left(\frac{413}{1215}\right)\)	\(e\left(\frac{1303}{1620}\right)\)	\(e\left(\frac{19}{810}\right)\)
\(\chi_{18225}(178,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4441}{4860}\right)\)	\(e\left(\frac{2011}{2430}\right)\)	\(e\left(\frac{857}{972}\right)\)	\(e\left(\frac{1201}{1620}\right)\)	\(e\left(\frac{184}{1215}\right)\)	\(e\left(\frac{4019}{4860}\right)\)	\(e\left(\frac{1933}{2430}\right)\)	\(e\left(\frac{796}{1215}\right)\)	\(e\left(\frac{251}{1620}\right)\)	\(e\left(\frac{473}{810}\right)\)
\(\chi_{18225}(187,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{487}{4860}\right)\)	\(e\left(\frac{487}{2430}\right)\)	\(e\left(\frac{419}{972}\right)\)	\(e\left(\frac{487}{1620}\right)\)	\(e\left(\frac{253}{1215}\right)\)	\(e\left(\frac{2033}{4860}\right)\)	\(e\left(\frac{1291}{2430}\right)\)	\(e\left(\frac{487}{1215}\right)\)	\(e\left(\frac{497}{1620}\right)\)	\(e\left(\frac{701}{810}\right)\)
\(\chi_{18225}(202,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1583}{4860}\right)\)	\(e\left(\frac{1583}{2430}\right)\)	\(e\left(\frac{859}{972}\right)\)	\(e\left(\frac{1583}{1620}\right)\)	\(e\left(\frac{1007}{1215}\right)\)	\(e\left(\frac{2377}{4860}\right)\)	\(e\left(\frac{509}{2430}\right)\)	\(e\left(\frac{368}{1215}\right)\)	\(e\left(\frac{1213}{1620}\right)\)	\(e\left(\frac{469}{810}\right)\)
\(\chi_{18225}(223,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2113}{4860}\right)\)	\(e\left(\frac{2113}{2430}\right)\)	\(e\left(\frac{341}{972}\right)\)	\(e\left(\frac{493}{1620}\right)\)	\(e\left(\frac{232}{1215}\right)\)	\(e\left(\frac{947}{4860}\right)\)	\(e\left(\frac{1909}{2430}\right)\)	\(e\left(\frac{898}{1215}\right)\)	\(e\left(\frac{563}{1620}\right)\)	\(e\left(\frac{209}{810}\right)\)
\(\chi_{18225}(238,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4037}{4860}\right)\)	\(e\left(\frac{1607}{2430}\right)\)	\(e\left(\frac{709}{972}\right)\)	\(e\left(\frac{797}{1620}\right)\)	\(e\left(\frac{518}{1215}\right)\)	\(e\left(\frac{2083}{4860}\right)\)	\(e\left(\frac{1361}{2430}\right)\)	\(e\left(\frac{392}{1215}\right)\)	\(e\left(\frac{667}{1620}\right)\)	\(e\left(\frac{121}{810}\right)\)
\(\chi_{18225}(247,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{911}{4860}\right)\)	\(e\left(\frac{911}{2430}\right)\)	\(e\left(\frac{199}{972}\right)\)	\(e\left(\frac{911}{1620}\right)\)	\(e\left(\frac{119}{1215}\right)\)	\(e\left(\frac{889}{4860}\right)\)	\(e\left(\frac{953}{2430}\right)\)	\(e\left(\frac{911}{1215}\right)\)	\(e\left(\frac{301}{1620}\right)\)	\(e\left(\frac{493}{810}\right)\)
\(\chi_{18225}(277,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2203}{4860}\right)\)	\(e\left(\frac{2203}{2430}\right)\)	\(e\left(\frac{143}{972}\right)\)	\(e\left(\frac{583}{1620}\right)\)	\(e\left(\frac{1132}{1215}\right)\)	\(e\left(\frac{4097}{4860}\right)\)	\(e\left(\frac{1459}{2430}\right)\)	\(e\left(\frac{988}{1215}\right)\)	\(e\left(\frac{1553}{1620}\right)\)	\(e\left(\frac{119}{810}\right)\)
\(\chi_{18225}(283,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2609}{4860}\right)\)	\(e\left(\frac{179}{2430}\right)\)	\(e\left(\frac{157}{972}\right)\)	\(e\left(\frac{989}{1620}\right)\)	\(e\left(\frac{1061}{1215}\right)\)	\(e\left(\frac{1351}{4860}\right)\)	\(e\left(\frac{1697}{2430}\right)\)	\(e\left(\frac{179}{1215}\right)\)	\(e\left(\frac{1159}{1620}\right)\)	\(e\left(\frac{577}{810}\right)\)
\(\chi_{18225}(292,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2939}{4860}\right)\)	\(e\left(\frac{509}{2430}\right)\)	\(e\left(\frac{403}{972}\right)\)	\(e\left(\frac{1319}{1620}\right)\)	\(e\left(\frac{716}{1215}\right)\)	\(e\left(\frac{1561}{4860}\right)\)	\(e\left(\frac{47}{2430}\right)\)	\(e\left(\frac{509}{1215}\right)\)	\(e\left(\frac{1549}{1620}\right)\)	\(e\left(\frac{247}{810}\right)\)
\(\chi_{18225}(313,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{697}{4860}\right)\)	\(e\left(\frac{697}{2430}\right)\)	\(e\left(\frac{929}{972}\right)\)	\(e\left(\frac{697}{1620}\right)\)	\(e\left(\frac{1138}{1215}\right)\)	\(e\left(\frac{1283}{4860}\right)\)	\(e\left(\frac{241}{2430}\right)\)	\(e\left(\frac{697}{1215}\right)\)	\(e\left(\frac{1187}{1620}\right)\)	\(e\left(\frac{491}{810}\right)\)
\(\chi_{18225}(322,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2251}{4860}\right)\)	\(e\left(\frac{2251}{2430}\right)\)	\(e\left(\frac{815}{972}\right)\)	\(e\left(\frac{631}{1620}\right)\)	\(e\left(\frac{154}{1215}\right)\)	\(e\left(\frac{3509}{4860}\right)\)	\(e\left(\frac{733}{2430}\right)\)	\(e\left(\frac{1036}{1215}\right)\)	\(e\left(\frac{461}{1620}\right)\)	\(e\left(\frac{233}{810}\right)\)
\(\chi_{18225}(328,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3881}{4860}\right)\)	\(e\left(\frac{1451}{2430}\right)\)	\(e\left(\frac{469}{972}\right)\)	\(e\left(\frac{641}{1620}\right)\)	\(e\left(\frac{659}{1215}\right)\)	\(e\left(\frac{2779}{4860}\right)\)	\(e\left(\frac{683}{2430}\right)\)	\(e\left(\frac{236}{1215}\right)\)	\(e\left(\frac{571}{1620}\right)\)	\(e\left(\frac{763}{810}\right)\)
\(\chi_{18225}(337,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2807}{4860}\right)\)	\(e\left(\frac{377}{2430}\right)\)	\(e\left(\frac{499}{972}\right)\)	\(e\left(\frac{1187}{1620}\right)\)	\(e\left(\frac{368}{1215}\right)\)	\(e\left(\frac{4393}{4860}\right)\)	\(e\left(\frac{221}{2430}\right)\)	\(e\left(\frac{377}{1215}\right)\)	\(e\left(\frac{97}{1620}\right)\)	\(e\left(\frac{541}{810}\right)\)
\(\chi_{18225}(358,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1609}{4860}\right)\)	\(e\left(\frac{1609}{2430}\right)\)	\(e\left(\frac{89}{972}\right)\)	\(e\left(\frac{1609}{1620}\right)\)	\(e\left(\frac{781}{1215}\right)\)	\(e\left(\frac{4691}{4860}\right)\)	\(e\left(\frac{1027}{2430}\right)\)	\(e\left(\frac{394}{1215}\right)\)	\(e\left(\frac{1499}{1620}\right)\)	\(e\left(\frac{227}{810}\right)\)
\(\chi_{18225}(367,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3379}{4860}\right)\)	\(e\left(\frac{949}{2430}\right)\)	\(e\left(\frac{83}{972}\right)\)	\(e\left(\frac{139}{1620}\right)\)	\(e\left(\frac{256}{1215}\right)\)	\(e\left(\frac{1841}{4860}\right)\)	\(e\left(\frac{1897}{2430}\right)\)	\(e\left(\frac{949}{1215}\right)\)	\(e\left(\frac{1529}{1620}\right)\)	\(e\left(\frac{77}{810}\right)\)
\(\chi_{18225}(373,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2993}{4860}\right)\)	\(e\left(\frac{563}{2430}\right)\)	\(e\left(\frac{673}{972}\right)\)	\(e\left(\frac{1373}{1620}\right)\)	\(e\left(\frac{527}{1215}\right)\)	\(e\left(\frac{1507}{4860}\right)\)	\(e\left(\frac{749}{2430}\right)\)	\(e\left(\frac{563}{1215}\right)\)	\(e\left(\frac{523}{1620}\right)\)	\(e\left(\frac{679}{810}\right)\)
\(\chi_{18225}(403,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3601}{4860}\right)\)	\(e\left(\frac{1171}{2430}\right)\)	\(e\left(\frac{761}{972}\right)\)	\(e\left(\frac{361}{1620}\right)\)	\(e\left(\frac{289}{1215}\right)\)	\(e\left(\frac{2159}{4860}\right)\)	\(e\left(\frac{1273}{2430}\right)\)	\(e\left(\frac{1171}{1215}\right)\)	\(e\left(\frac{731}{1620}\right)\)	\(e\left(\frac{503}{810}\right)\)
\(\chi_{18225}(412,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{727}{4860}\right)\)	\(e\left(\frac{727}{2430}\right)\)	\(e\left(\frac{863}{972}\right)\)	\(e\left(\frac{727}{1620}\right)\)	\(e\left(\frac{223}{1215}\right)\)	\(e\left(\frac{3953}{4860}\right)\)	\(e\left(\frac{91}{2430}\right)\)	\(e\left(\frac{727}{1215}\right)\)	\(e\left(\frac{1517}{1620}\right)\)	\(e\left(\frac{461}{810}\right)\)
\(\chi_{18225}(427,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{923}{4860}\right)\)	\(e\left(\frac{923}{2430}\right)\)	\(e\left(\frac{367}{972}\right)\)	\(e\left(\frac{923}{1620}\right)\)	\(e\left(\frac{482}{1215}\right)\)	\(e\left(\frac{1957}{4860}\right)\)	\(e\left(\frac{1379}{2430}\right)\)	\(e\left(\frac{923}{1215}\right)\)	\(e\left(\frac{433}{1620}\right)\)	\(e\left(\frac{319}{810}\right)\)

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First 31 of 1296 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	18225.ct
Modulus	$18225$
Conductor	$18225$
Order	$4860$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(18225\)
Conductor:	\(18225\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(4860\)	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)