LMFDB - Dirichlet character orbit 18225.cq

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(18225, base_ring=CyclotomicField(2430)) M = H._module chi = DirichletCharacter(H, M([1415,1944])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(11,18225)) 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:	$2430$	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:	$\Q(\zeta_{1215})$
Fixed field:	Number field defined by a degree 2430 polynomial (not computed)

First 31 of 648 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{18225}(11,\cdot)$	$-1$	$1$	$e\left(\frac{929}{2430}\right)$	$e\left(\frac{929}{1215}\right)$	$e\left(\frac{104}{243}\right)$	$e\left(\frac{119}{810}\right)$	$e\left(\frac{1439}{2430}\right)$	$e\left(\frac{638}{1215}\right)$	$e\left(\frac{1969}{2430}\right)$	$e\left(\frac{643}{1215}\right)$	$e\left(\frac{499}{810}\right)$	$e\left(\frac{232}{405}\right)$
$\chi_{18225}(41,\cdot)$	$-1$	$1$	$e\left(\frac{1561}{2430}\right)$	$e\left(\frac{346}{1215}\right)$	$e\left(\frac{73}{243}\right)$	$e\left(\frac{751}{810}\right)$	$e\left(\frac{961}{2430}\right)$	$e\left(\frac{817}{1215}\right)$	$e\left(\frac{2291}{2430}\right)$	$e\left(\frac{692}{1215}\right)$	$e\left(\frac{161}{810}\right)$	$e\left(\frac{113}{405}\right)$
$\chi_{18225}(56,\cdot)$	$-1$	$1$	$e\left(\frac{527}{2430}\right)$	$e\left(\frac{527}{1215}\right)$	$e\left(\frac{206}{243}\right)$	$e\left(\frac{527}{810}\right)$	$e\left(\frac{1397}{2430}\right)$	$e\left(\frac{974}{1215}\right)$	$e\left(\frac{157}{2430}\right)$	$e\left(\frac{1054}{1215}\right)$	$e\left(\frac{127}{810}\right)$	$e\left(\frac{391}{405}\right)$
$\chi_{18225}(86,\cdot)$	$-1$	$1$	$e\left(\frac{1789}{2430}\right)$	$e\left(\frac{574}{1215}\right)$	$e\left(\frac{211}{243}\right)$	$e\left(\frac{169}{810}\right)$	$e\left(\frac{1819}{2430}\right)$	$e\left(\frac{28}{1215}\right)$	$e\left(\frac{1469}{2430}\right)$	$e\left(\frac{1148}{1215}\right)$	$e\left(\frac{239}{810}\right)$	$e\left(\frac{47}{405}\right)$
$\chi_{18225}(131,\cdot)$	$-1$	$1$	$e\left(\frac{937}{2430}\right)$	$e\left(\frac{937}{1215}\right)$	$e\left(\frac{79}{243}\right)$	$e\left(\frac{127}{810}\right)$	$e\left(\frac{787}{2430}\right)$	$e\left(\frac{994}{1215}\right)$	$e\left(\frac{1727}{2430}\right)$	$e\left(\frac{659}{1215}\right)$	$e\left(\frac{587}{810}\right)$	$e\left(\frac{251}{405}\right)$
$\chi_{18225}(146,\cdot)$	$-1$	$1$	$e\left(\frac{1343}{2430}\right)$	$e\left(\frac{128}{1215}\right)$	$e\left(\frac{86}{243}\right)$	$e\left(\frac{533}{810}\right)$	$e\left(\frac{503}{2430}\right)$	$e\left(\frac{836}{1215}\right)$	$e\left(\frac{2203}{2430}\right)$	$e\left(\frac{256}{1215}\right)$	$e\left(\frac{193}{810}\right)$	$e\left(\frac{304}{405}\right)$
$\chi_{18225}(191,\cdot)$	$-1$	$1$	$e\left(\frac{131}{2430}\right)$	$e\left(\frac{131}{1215}\right)$	$e\left(\frac{107}{243}\right)$	$e\left(\frac{131}{810}\right)$	$e\left(\frac{2081}{2430}\right)$	$e\left(\frac{362}{1215}\right)$	$e\left(\frac{1201}{2430}\right)$	$e\left(\frac{262}{1215}\right)$	$e\left(\frac{631}{810}\right)$	$e\left(\frac{58}{405}\right)$
$\chi_{18225}(221,\cdot)$	$-1$	$1$	$e\left(\frac{853}{2430}\right)$	$e\left(\frac{853}{1215}\right)$	$e\left(\frac{220}{243}\right)$	$e\left(\frac{43}{810}\right)$	$e\left(\frac{343}{2430}\right)$	$e\left(\frac{901}{1215}\right)$	$e\left(\frac{623}{2430}\right)$	$e\left(\frac{491}{1215}\right)$	$e\left(\frac{473}{810}\right)$	$e\left(\frac{254}{405}\right)$
$\chi_{18225}(236,\cdot)$	$-1$	$1$	$e\left(\frac{1889}{2430}\right)$	$e\left(\frac{674}{1215}\right)$	$e\left(\frac{20}{243}\right)$	$e\left(\frac{269}{810}\right)$	$e\left(\frac{959}{2430}\right)$	$e\left(\frac{833}{1215}\right)$	$e\left(\frac{2089}{2430}\right)$	$e\left(\frac{133}{1215}\right)$	$e\left(\frac{529}{810}\right)$	$e\left(\frac{82}{405}\right)$
$\chi_{18225}(266,\cdot)$	$-1$	$1$	$e\left(\frac{1621}{2430}\right)$	$e\left(\frac{406}{1215}\right)$	$e\left(\frac{7}{243}\right)$	$e\left(\frac{1}{810}\right)$	$e\left(\frac{931}{2430}\right)$	$e\left(\frac{1057}{1215}\right)$	$e\left(\frac{1691}{2430}\right)$	$e\left(\frac{812}{1215}\right)$	$e\left(\frac{11}{810}\right)$	$e\left(\frac{53}{405}\right)$
$\chi_{18225}(281,\cdot)$	$-1$	$1$	$e\left(\frac{1757}{2430}\right)$	$e\left(\frac{542}{1215}\right)$	$e\left(\frac{68}{243}\right)$	$e\left(\frac{137}{810}\right)$	$e\left(\frac{1997}{2430}\right)$	$e\left(\frac{1034}{1215}\right)$	$e\left(\frac{7}{2430}\right)$	$e\left(\frac{1084}{1215}\right)$	$e\left(\frac{697}{810}\right)$	$e\left(\frac{376}{405}\right)$
$\chi_{18225}(311,\cdot)$	$-1$	$1$	$e\left(\frac{1309}{2430}\right)$	$e\left(\frac{94}{1215}\right)$	$e\left(\frac{10}{243}\right)$	$e\left(\frac{499}{810}\right)$	$e\left(\frac{2059}{2430}\right)$	$e\left(\frac{538}{1215}\right)$	$e\left(\frac{1409}{2430}\right)$	$e\left(\frac{188}{1215}\right)$	$e\left(\frac{629}{810}\right)$	$e\left(\frac{122}{405}\right)$
$\chi_{18225}(356,\cdot)$	$-1$	$1$	$e\left(\frac{2347}{2430}\right)$	$e\left(\frac{1132}{1215}\right)$	$e\left(\frac{229}{243}\right)$	$e\left(\frac{727}{810}\right)$	$e\left(\frac{1297}{2430}\right)$	$e\left(\frac{559}{1215}\right)$	$e\left(\frac{2207}{2430}\right)$	$e\left(\frac{1049}{1215}\right)$	$e\left(\frac{707}{810}\right)$	$e\left(\frac{56}{405}\right)$
$\chi_{18225}(371,\cdot)$	$-1$	$1$	$e\left(\frac{683}{2430}\right)$	$e\left(\frac{683}{1215}\right)$	$e\left(\frac{83}{243}\right)$	$e\left(\frac{683}{810}\right)$	$e\left(\frac{833}{2430}\right)$	$e\left(\frac{626}{1215}\right)$	$e\left(\frac{1513}{2430}\right)$	$e\left(\frac{151}{1215}\right)$	$e\left(\frac{223}{810}\right)$	$e\left(\frac{154}{405}\right)$
$\chi_{18225}(416,\cdot)$	$-1$	$1$	$e\left(\frac{2171}{2430}\right)$	$e\left(\frac{956}{1215}\right)$	$e\left(\frac{50}{243}\right)$	$e\left(\frac{551}{810}\right)$	$e\left(\frac{1061}{2430}\right)$	$e\left(\frac{17}{1215}\right)$	$e\left(\frac{241}{2430}\right)$	$e\left(\frac{697}{1215}\right)$	$e\left(\frac{391}{810}\right)$	$e\left(\frac{43}{405}\right)$
$\chi_{18225}(446,\cdot)$	$-1$	$1$	$e\left(\frac{1183}{2430}\right)$	$e\left(\frac{1183}{1215}\right)$	$e\left(\frac{100}{243}\right)$	$e\left(\frac{373}{810}\right)$	$e\left(\frac{1393}{2430}\right)$	$e\left(\frac{1006}{1215}\right)$	$e\left(\frac{2183}{2430}\right)$	$e\left(\frac{1151}{1215}\right)$	$e\left(\frac{53}{810}\right)$	$e\left(\frac{329}{405}\right)$
$\chi_{18225}(461,\cdot)$	$-1$	$1$	$e\left(\frac{1769}{2430}\right)$	$e\left(\frac{554}{1215}\right)$	$e\left(\frac{152}{243}\right)$	$e\left(\frac{149}{810}\right)$	$e\left(\frac{1019}{2430}\right)$	$e\left(\frac{353}{1215}\right)$	$e\left(\frac{859}{2430}\right)$	$e\left(\frac{1108}{1215}\right)$	$e\left(\frac{19}{810}\right)$	$e\left(\frac{202}{405}\right)$
$\chi_{18225}(491,\cdot)$	$-1$	$1$	$e\left(\frac{1411}{2430}\right)$	$e\left(\frac{196}{1215}\right)$	$e\left(\frac{238}{243}\right)$	$e\left(\frac{601}{810}\right)$	$e\left(\frac{2251}{2430}\right)$	$e\left(\frac{217}{1215}\right)$	$e\left(\frac{1361}{2430}\right)$	$e\left(\frac{392}{1215}\right)$	$e\left(\frac{131}{810}\right)$	$e\left(\frac{263}{405}\right)$
$\chi_{18225}(506,\cdot)$	$-1$	$1$	$e\left(\frac{1907}{2430}\right)$	$e\left(\frac{692}{1215}\right)$	$e\left(\frac{146}{243}\right)$	$e\left(\frac{287}{810}\right)$	$e\left(\frac{707}{2430}\right)$	$e\left(\frac{419}{1215}\right)$	$e\left(\frac{937}{2430}\right)$	$e\left(\frac{169}{1215}\right)$	$e\left(\frac{727}{810}\right)$	$e\left(\frac{226}{405}\right)$
$\chi_{18225}(536,\cdot)$	$-1$	$1$	$e\left(\frac{559}{2430}\right)$	$e\left(\frac{559}{1215}\right)$	$e\left(\frac{106}{243}\right)$	$e\left(\frac{559}{810}\right)$	$e\left(\frac{1219}{2430}\right)$	$e\left(\frac{1183}{1215}\right)$	$e\left(\frac{1619}{2430}\right)$	$e\left(\frac{1118}{1215}\right)$	$e\left(\frac{479}{810}\right)$	$e\left(\frac{62}{405}\right)$
$\chi_{18225}(581,\cdot)$	$-1$	$1$	$e\left(\frac{1057}{2430}\right)$	$e\left(\frac{1057}{1215}\right)$	$e\left(\frac{190}{243}\right)$	$e\left(\frac{247}{810}\right)$	$e\left(\frac{727}{2430}\right)$	$e\left(\frac{259}{1215}\right)$	$e\left(\frac{527}{2430}\right)$	$e\left(\frac{899}{1215}\right)$	$e\left(\frac{287}{810}\right)$	$e\left(\frac{131}{405}\right)$
$\chi_{18225}(596,\cdot)$	$-1$	$1$	$e\left(\frac{1373}{2430}\right)$	$e\left(\frac{158}{1215}\right)$	$e\left(\frac{53}{243}\right)$	$e\left(\frac{563}{810}\right)$	$e\left(\frac{1703}{2430}\right)$	$e\left(\frac{956}{1215}\right)$	$e\left(\frac{1903}{2430}\right)$	$e\left(\frac{316}{1215}\right)$	$e\left(\frac{523}{810}\right)$	$e\left(\frac{274}{405}\right)$
$\chi_{18225}(641,\cdot)$	$-1$	$1$	$e\left(\frac{701}{2430}\right)$	$e\left(\frac{701}{1215}\right)$	$e\left(\frac{209}{243}\right)$	$e\left(\frac{701}{810}\right)$	$e\left(\frac{581}{2430}\right)$	$e\left(\frac{212}{1215}\right)$	$e\left(\frac{361}{2430}\right)$	$e\left(\frac{187}{1215}\right)$	$e\left(\frac{421}{810}\right)$	$e\left(\frac{298}{405}\right)$
$\chi_{18225}(671,\cdot)$	$-1$	$1$	$e\left(\frac{1243}{2430}\right)$	$e\left(\frac{28}{1215}\right)$	$e\left(\frac{34}{243}\right)$	$e\left(\frac{433}{810}\right)$	$e\left(\frac{1363}{2430}\right)$	$e\left(\frac{31}{1215}\right)$	$e\left(\frac{1583}{2430}\right)$	$e\left(\frac{56}{1215}\right)$	$e\left(\frac{713}{810}\right)$	$e\left(\frac{269}{405}\right)$
$\chi_{18225}(686,\cdot)$	$-1$	$1$	$e\left(\frac{569}{2430}\right)$	$e\left(\frac{569}{1215}\right)$	$e\left(\frac{14}{243}\right)$	$e\left(\frac{569}{810}\right)$	$e\left(\frac{1619}{2430}\right)$	$e\left(\frac{413}{1215}\right)$	$e\left(\frac{709}{2430}\right)$	$e\left(\frac{1138}{1215}\right)$	$e\left(\frac{589}{810}\right)$	$e\left(\frac{187}{405}\right)$
$\chi_{18225}(716,\cdot)$	$-1$	$1$	$e\left(\frac{931}{2430}\right)$	$e\left(\frac{931}{1215}\right)$	$e\left(\frac{37}{243}\right)$	$e\left(\frac{121}{810}\right)$	$e\left(\frac{61}{2430}\right)$	$e\left(\frac{727}{1215}\right)$	$e\left(\frac{1301}{2430}\right)$	$e\left(\frac{647}{1215}\right)$	$e\left(\frac{521}{810}\right)$	$e\left(\frac{338}{405}\right)$
$\chi_{18225}(731,\cdot)$	$-1$	$1$	$e\left(\frac{977}{2430}\right)$	$e\left(\frac{977}{1215}\right)$	$e\left(\frac{197}{243}\right)$	$e\left(\frac{167}{810}\right)$	$e\left(\frac{2387}{2430}\right)$	$e\left(\frac{344}{1215}\right)$	$e\left(\frac{517}{2430}\right)$	$e\left(\frac{739}{1215}\right)$	$e\left(\frac{217}{810}\right)$	$e\left(\frac{346}{405}\right)$
$\chi_{18225}(761,\cdot)$	$-1$	$1$	$e\left(\frac{1969}{2430}\right)$	$e\left(\frac{754}{1215}\right)$	$e\left(\frac{13}{243}\right)$	$e\left(\frac{349}{810}\right)$	$e\left(\frac{1729}{2430}\right)$	$e\left(\frac{748}{1215}\right)$	$e\left(\frac{2099}{2430}\right)$	$e\left(\frac{293}{1215}\right)$	$e\left(\frac{599}{810}\right)$	$e\left(\frac{272}{405}\right)$
$\chi_{18225}(806,\cdot)$	$-1$	$1$	$e\left(\frac{1927}{2430}\right)$	$e\left(\frac{712}{1215}\right)$	$e\left(\frac{205}{243}\right)$	$e\left(\frac{307}{810}\right)$	$e\left(\frac{1507}{2430}\right)$	$e\left(\frac{94}{1215}\right)$	$e\left(\frac{1547}{2430}\right)$	$e\left(\frac{209}{1215}\right)$	$e\left(\frac{137}{810}\right)$	$e\left(\frac{71}{405}\right)$
$\chi_{18225}(821,\cdot)$	$-1$	$1$	$e\left(\frac{983}{2430}\right)$	$e\left(\frac{983}{1215}\right)$	$e\left(\frac{239}{243}\right)$	$e\left(\frac{173}{810}\right)$	$e\left(\frac{683}{2430}\right)$	$e\left(\frac{611}{1215}\right)$	$e\left(\frac{943}{2430}\right)$	$e\left(\frac{751}{1215}\right)$	$e\left(\frac{283}{810}\right)$	$e\left(\frac{259}{405}\right)$
$\chi_{18225}(866,\cdot)$	$-1$	$1$	$e\left(\frac{581}{2430}\right)$	$e\left(\frac{581}{1215}\right)$	$e\left(\frac{98}{243}\right)$	$e\left(\frac{581}{810}\right)$	$e\left(\frac{641}{2430}\right)$	$e\left(\frac{947}{1215}\right)$	$e\left(\frac{1561}{2430}\right)$	$e\left(\frac{1162}{1215}\right)$	$e\left(\frac{721}{810}\right)$	$e\left(\frac{13}{405}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{18225}(11,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{929}{2430}\right)\)	\(e\left(\frac{929}{1215}\right)\)	\(e\left(\frac{104}{243}\right)\)	\(e\left(\frac{119}{810}\right)\)	\(e\left(\frac{1439}{2430}\right)\)	\(e\left(\frac{638}{1215}\right)\)	\(e\left(\frac{1969}{2430}\right)\)	\(e\left(\frac{643}{1215}\right)\)	\(e\left(\frac{499}{810}\right)\)	\(e\left(\frac{232}{405}\right)\)
\(\chi_{18225}(41,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1561}{2430}\right)\)	\(e\left(\frac{346}{1215}\right)\)	\(e\left(\frac{73}{243}\right)\)	\(e\left(\frac{751}{810}\right)\)	\(e\left(\frac{961}{2430}\right)\)	\(e\left(\frac{817}{1215}\right)\)	\(e\left(\frac{2291}{2430}\right)\)	\(e\left(\frac{692}{1215}\right)\)	\(e\left(\frac{161}{810}\right)\)	\(e\left(\frac{113}{405}\right)\)
\(\chi_{18225}(56,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{527}{2430}\right)\)	\(e\left(\frac{527}{1215}\right)\)	\(e\left(\frac{206}{243}\right)\)	\(e\left(\frac{527}{810}\right)\)	\(e\left(\frac{1397}{2430}\right)\)	\(e\left(\frac{974}{1215}\right)\)	\(e\left(\frac{157}{2430}\right)\)	\(e\left(\frac{1054}{1215}\right)\)	\(e\left(\frac{127}{810}\right)\)	\(e\left(\frac{391}{405}\right)\)
\(\chi_{18225}(86,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1789}{2430}\right)\)	\(e\left(\frac{574}{1215}\right)\)	\(e\left(\frac{211}{243}\right)\)	\(e\left(\frac{169}{810}\right)\)	\(e\left(\frac{1819}{2430}\right)\)	\(e\left(\frac{28}{1215}\right)\)	\(e\left(\frac{1469}{2430}\right)\)	\(e\left(\frac{1148}{1215}\right)\)	\(e\left(\frac{239}{810}\right)\)	\(e\left(\frac{47}{405}\right)\)
\(\chi_{18225}(131,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{937}{2430}\right)\)	\(e\left(\frac{937}{1215}\right)\)	\(e\left(\frac{79}{243}\right)\)	\(e\left(\frac{127}{810}\right)\)	\(e\left(\frac{787}{2430}\right)\)	\(e\left(\frac{994}{1215}\right)\)	\(e\left(\frac{1727}{2430}\right)\)	\(e\left(\frac{659}{1215}\right)\)	\(e\left(\frac{587}{810}\right)\)	\(e\left(\frac{251}{405}\right)\)
\(\chi_{18225}(146,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1343}{2430}\right)\)	\(e\left(\frac{128}{1215}\right)\)	\(e\left(\frac{86}{243}\right)\)	\(e\left(\frac{533}{810}\right)\)	\(e\left(\frac{503}{2430}\right)\)	\(e\left(\frac{836}{1215}\right)\)	\(e\left(\frac{2203}{2430}\right)\)	\(e\left(\frac{256}{1215}\right)\)	\(e\left(\frac{193}{810}\right)\)	\(e\left(\frac{304}{405}\right)\)
\(\chi_{18225}(191,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{2430}\right)\)	\(e\left(\frac{131}{1215}\right)\)	\(e\left(\frac{107}{243}\right)\)	\(e\left(\frac{131}{810}\right)\)	\(e\left(\frac{2081}{2430}\right)\)	\(e\left(\frac{362}{1215}\right)\)	\(e\left(\frac{1201}{2430}\right)\)	\(e\left(\frac{262}{1215}\right)\)	\(e\left(\frac{631}{810}\right)\)	\(e\left(\frac{58}{405}\right)\)
\(\chi_{18225}(221,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{853}{2430}\right)\)	\(e\left(\frac{853}{1215}\right)\)	\(e\left(\frac{220}{243}\right)\)	\(e\left(\frac{43}{810}\right)\)	\(e\left(\frac{343}{2430}\right)\)	\(e\left(\frac{901}{1215}\right)\)	\(e\left(\frac{623}{2430}\right)\)	\(e\left(\frac{491}{1215}\right)\)	\(e\left(\frac{473}{810}\right)\)	\(e\left(\frac{254}{405}\right)\)
\(\chi_{18225}(236,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1889}{2430}\right)\)	\(e\left(\frac{674}{1215}\right)\)	\(e\left(\frac{20}{243}\right)\)	\(e\left(\frac{269}{810}\right)\)	\(e\left(\frac{959}{2430}\right)\)	\(e\left(\frac{833}{1215}\right)\)	\(e\left(\frac{2089}{2430}\right)\)	\(e\left(\frac{133}{1215}\right)\)	\(e\left(\frac{529}{810}\right)\)	\(e\left(\frac{82}{405}\right)\)
\(\chi_{18225}(266,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1621}{2430}\right)\)	\(e\left(\frac{406}{1215}\right)\)	\(e\left(\frac{7}{243}\right)\)	\(e\left(\frac{1}{810}\right)\)	\(e\left(\frac{931}{2430}\right)\)	\(e\left(\frac{1057}{1215}\right)\)	\(e\left(\frac{1691}{2430}\right)\)	\(e\left(\frac{812}{1215}\right)\)	\(e\left(\frac{11}{810}\right)\)	\(e\left(\frac{53}{405}\right)\)
\(\chi_{18225}(281,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1757}{2430}\right)\)	\(e\left(\frac{542}{1215}\right)\)	\(e\left(\frac{68}{243}\right)\)	\(e\left(\frac{137}{810}\right)\)	\(e\left(\frac{1997}{2430}\right)\)	\(e\left(\frac{1034}{1215}\right)\)	\(e\left(\frac{7}{2430}\right)\)	\(e\left(\frac{1084}{1215}\right)\)	\(e\left(\frac{697}{810}\right)\)	\(e\left(\frac{376}{405}\right)\)
\(\chi_{18225}(311,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1309}{2430}\right)\)	\(e\left(\frac{94}{1215}\right)\)	\(e\left(\frac{10}{243}\right)\)	\(e\left(\frac{499}{810}\right)\)	\(e\left(\frac{2059}{2430}\right)\)	\(e\left(\frac{538}{1215}\right)\)	\(e\left(\frac{1409}{2430}\right)\)	\(e\left(\frac{188}{1215}\right)\)	\(e\left(\frac{629}{810}\right)\)	\(e\left(\frac{122}{405}\right)\)
\(\chi_{18225}(356,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2347}{2430}\right)\)	\(e\left(\frac{1132}{1215}\right)\)	\(e\left(\frac{229}{243}\right)\)	\(e\left(\frac{727}{810}\right)\)	\(e\left(\frac{1297}{2430}\right)\)	\(e\left(\frac{559}{1215}\right)\)	\(e\left(\frac{2207}{2430}\right)\)	\(e\left(\frac{1049}{1215}\right)\)	\(e\left(\frac{707}{810}\right)\)	\(e\left(\frac{56}{405}\right)\)
\(\chi_{18225}(371,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{683}{2430}\right)\)	\(e\left(\frac{683}{1215}\right)\)	\(e\left(\frac{83}{243}\right)\)	\(e\left(\frac{683}{810}\right)\)	\(e\left(\frac{833}{2430}\right)\)	\(e\left(\frac{626}{1215}\right)\)	\(e\left(\frac{1513}{2430}\right)\)	\(e\left(\frac{151}{1215}\right)\)	\(e\left(\frac{223}{810}\right)\)	\(e\left(\frac{154}{405}\right)\)
\(\chi_{18225}(416,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2171}{2430}\right)\)	\(e\left(\frac{956}{1215}\right)\)	\(e\left(\frac{50}{243}\right)\)	\(e\left(\frac{551}{810}\right)\)	\(e\left(\frac{1061}{2430}\right)\)	\(e\left(\frac{17}{1215}\right)\)	\(e\left(\frac{241}{2430}\right)\)	\(e\left(\frac{697}{1215}\right)\)	\(e\left(\frac{391}{810}\right)\)	\(e\left(\frac{43}{405}\right)\)
\(\chi_{18225}(446,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1183}{2430}\right)\)	\(e\left(\frac{1183}{1215}\right)\)	\(e\left(\frac{100}{243}\right)\)	\(e\left(\frac{373}{810}\right)\)	\(e\left(\frac{1393}{2430}\right)\)	\(e\left(\frac{1006}{1215}\right)\)	\(e\left(\frac{2183}{2430}\right)\)	\(e\left(\frac{1151}{1215}\right)\)	\(e\left(\frac{53}{810}\right)\)	\(e\left(\frac{329}{405}\right)\)
\(\chi_{18225}(461,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1769}{2430}\right)\)	\(e\left(\frac{554}{1215}\right)\)	\(e\left(\frac{152}{243}\right)\)	\(e\left(\frac{149}{810}\right)\)	\(e\left(\frac{1019}{2430}\right)\)	\(e\left(\frac{353}{1215}\right)\)	\(e\left(\frac{859}{2430}\right)\)	\(e\left(\frac{1108}{1215}\right)\)	\(e\left(\frac{19}{810}\right)\)	\(e\left(\frac{202}{405}\right)\)
\(\chi_{18225}(491,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1411}{2430}\right)\)	\(e\left(\frac{196}{1215}\right)\)	\(e\left(\frac{238}{243}\right)\)	\(e\left(\frac{601}{810}\right)\)	\(e\left(\frac{2251}{2430}\right)\)	\(e\left(\frac{217}{1215}\right)\)	\(e\left(\frac{1361}{2430}\right)\)	\(e\left(\frac{392}{1215}\right)\)	\(e\left(\frac{131}{810}\right)\)	\(e\left(\frac{263}{405}\right)\)
\(\chi_{18225}(506,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1907}{2430}\right)\)	\(e\left(\frac{692}{1215}\right)\)	\(e\left(\frac{146}{243}\right)\)	\(e\left(\frac{287}{810}\right)\)	\(e\left(\frac{707}{2430}\right)\)	\(e\left(\frac{419}{1215}\right)\)	\(e\left(\frac{937}{2430}\right)\)	\(e\left(\frac{169}{1215}\right)\)	\(e\left(\frac{727}{810}\right)\)	\(e\left(\frac{226}{405}\right)\)
\(\chi_{18225}(536,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{559}{2430}\right)\)	\(e\left(\frac{559}{1215}\right)\)	\(e\left(\frac{106}{243}\right)\)	\(e\left(\frac{559}{810}\right)\)	\(e\left(\frac{1219}{2430}\right)\)	\(e\left(\frac{1183}{1215}\right)\)	\(e\left(\frac{1619}{2430}\right)\)	\(e\left(\frac{1118}{1215}\right)\)	\(e\left(\frac{479}{810}\right)\)	\(e\left(\frac{62}{405}\right)\)
\(\chi_{18225}(581,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1057}{2430}\right)\)	\(e\left(\frac{1057}{1215}\right)\)	\(e\left(\frac{190}{243}\right)\)	\(e\left(\frac{247}{810}\right)\)	\(e\left(\frac{727}{2430}\right)\)	\(e\left(\frac{259}{1215}\right)\)	\(e\left(\frac{527}{2430}\right)\)	\(e\left(\frac{899}{1215}\right)\)	\(e\left(\frac{287}{810}\right)\)	\(e\left(\frac{131}{405}\right)\)
\(\chi_{18225}(596,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1373}{2430}\right)\)	\(e\left(\frac{158}{1215}\right)\)	\(e\left(\frac{53}{243}\right)\)	\(e\left(\frac{563}{810}\right)\)	\(e\left(\frac{1703}{2430}\right)\)	\(e\left(\frac{956}{1215}\right)\)	\(e\left(\frac{1903}{2430}\right)\)	\(e\left(\frac{316}{1215}\right)\)	\(e\left(\frac{523}{810}\right)\)	\(e\left(\frac{274}{405}\right)\)
\(\chi_{18225}(641,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{701}{2430}\right)\)	\(e\left(\frac{701}{1215}\right)\)	\(e\left(\frac{209}{243}\right)\)	\(e\left(\frac{701}{810}\right)\)	\(e\left(\frac{581}{2430}\right)\)	\(e\left(\frac{212}{1215}\right)\)	\(e\left(\frac{361}{2430}\right)\)	\(e\left(\frac{187}{1215}\right)\)	\(e\left(\frac{421}{810}\right)\)	\(e\left(\frac{298}{405}\right)\)
\(\chi_{18225}(671,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1243}{2430}\right)\)	\(e\left(\frac{28}{1215}\right)\)	\(e\left(\frac{34}{243}\right)\)	\(e\left(\frac{433}{810}\right)\)	\(e\left(\frac{1363}{2430}\right)\)	\(e\left(\frac{31}{1215}\right)\)	\(e\left(\frac{1583}{2430}\right)\)	\(e\left(\frac{56}{1215}\right)\)	\(e\left(\frac{713}{810}\right)\)	\(e\left(\frac{269}{405}\right)\)
\(\chi_{18225}(686,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{569}{2430}\right)\)	\(e\left(\frac{569}{1215}\right)\)	\(e\left(\frac{14}{243}\right)\)	\(e\left(\frac{569}{810}\right)\)	\(e\left(\frac{1619}{2430}\right)\)	\(e\left(\frac{413}{1215}\right)\)	\(e\left(\frac{709}{2430}\right)\)	\(e\left(\frac{1138}{1215}\right)\)	\(e\left(\frac{589}{810}\right)\)	\(e\left(\frac{187}{405}\right)\)
\(\chi_{18225}(716,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{931}{2430}\right)\)	\(e\left(\frac{931}{1215}\right)\)	\(e\left(\frac{37}{243}\right)\)	\(e\left(\frac{121}{810}\right)\)	\(e\left(\frac{61}{2430}\right)\)	\(e\left(\frac{727}{1215}\right)\)	\(e\left(\frac{1301}{2430}\right)\)	\(e\left(\frac{647}{1215}\right)\)	\(e\left(\frac{521}{810}\right)\)	\(e\left(\frac{338}{405}\right)\)
\(\chi_{18225}(731,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{977}{2430}\right)\)	\(e\left(\frac{977}{1215}\right)\)	\(e\left(\frac{197}{243}\right)\)	\(e\left(\frac{167}{810}\right)\)	\(e\left(\frac{2387}{2430}\right)\)	\(e\left(\frac{344}{1215}\right)\)	\(e\left(\frac{517}{2430}\right)\)	\(e\left(\frac{739}{1215}\right)\)	\(e\left(\frac{217}{810}\right)\)	\(e\left(\frac{346}{405}\right)\)
\(\chi_{18225}(761,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1969}{2430}\right)\)	\(e\left(\frac{754}{1215}\right)\)	\(e\left(\frac{13}{243}\right)\)	\(e\left(\frac{349}{810}\right)\)	\(e\left(\frac{1729}{2430}\right)\)	\(e\left(\frac{748}{1215}\right)\)	\(e\left(\frac{2099}{2430}\right)\)	\(e\left(\frac{293}{1215}\right)\)	\(e\left(\frac{599}{810}\right)\)	\(e\left(\frac{272}{405}\right)\)
\(\chi_{18225}(806,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1927}{2430}\right)\)	\(e\left(\frac{712}{1215}\right)\)	\(e\left(\frac{205}{243}\right)\)	\(e\left(\frac{307}{810}\right)\)	\(e\left(\frac{1507}{2430}\right)\)	\(e\left(\frac{94}{1215}\right)\)	\(e\left(\frac{1547}{2430}\right)\)	\(e\left(\frac{209}{1215}\right)\)	\(e\left(\frac{137}{810}\right)\)	\(e\left(\frac{71}{405}\right)\)
\(\chi_{18225}(821,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{983}{2430}\right)\)	\(e\left(\frac{983}{1215}\right)\)	\(e\left(\frac{239}{243}\right)\)	\(e\left(\frac{173}{810}\right)\)	\(e\left(\frac{683}{2430}\right)\)	\(e\left(\frac{611}{1215}\right)\)	\(e\left(\frac{943}{2430}\right)\)	\(e\left(\frac{751}{1215}\right)\)	\(e\left(\frac{283}{810}\right)\)	\(e\left(\frac{259}{405}\right)\)
\(\chi_{18225}(866,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{581}{2430}\right)\)	\(e\left(\frac{581}{1215}\right)\)	\(e\left(\frac{98}{243}\right)\)	\(e\left(\frac{581}{810}\right)\)	\(e\left(\frac{641}{2430}\right)\)	\(e\left(\frac{947}{1215}\right)\)	\(e\left(\frac{1561}{2430}\right)\)	\(e\left(\frac{1162}{1215}\right)\)	\(e\left(\frac{721}{810}\right)\)	\(e\left(\frac{13}{405}\right)\)

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First 31 of 648 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.cq
Modulus	$18225$
Conductor	$18225$
Order	$2430$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(18225\)
Conductor:	\(18225\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(2430\)	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)