LMFDB - Dirichlet character orbit 18225.cr

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(18225, base_ring=CyclotomicField(2430)) M = H._module chi = DirichletCharacter(H, M([1975,729])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(14,18225)) 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{18225}(14,\cdot)$	$-1$	$1$	$e\left(\frac{137}{1215}\right)$	$e\left(\frac{274}{1215}\right)$	$e\left(\frac{353}{486}\right)$	$e\left(\frac{137}{405}\right)$	$e\left(\frac{1969}{2430}\right)$	$e\left(\frac{1301}{2430}\right)$	$e\left(\frac{2039}{2430}\right)$	$e\left(\frac{548}{1215}\right)$	$e\left(\frac{292}{405}\right)$	$e\left(\frac{347}{405}\right)$
$\chi_{18225}(29,\cdot)$	$-1$	$1$	$e\left(\frac{619}{1215}\right)$	$e\left(\frac{23}{1215}\right)$	$e\left(\frac{403}{486}\right)$	$e\left(\frac{214}{405}\right)$	$e\left(\frac{1163}{2430}\right)$	$e\left(\frac{2047}{2430}\right)$	$e\left(\frac{823}{2430}\right)$	$e\left(\frac{46}{1215}\right)$	$e\left(\frac{329}{405}\right)$	$e\left(\frac{4}{405}\right)$
$\chi_{18225}(59,\cdot)$	$-1$	$1$	$e\left(\frac{818}{1215}\right)$	$e\left(\frac{421}{1215}\right)$	$e\left(\frac{467}{486}\right)$	$e\left(\frac{8}{405}\right)$	$e\left(\frac{1531}{2430}\right)$	$e\left(\frac{1019}{2430}\right)$	$e\left(\frac{1541}{2430}\right)$	$e\left(\frac{842}{1215}\right)$	$e\left(\frac{88}{405}\right)$	$e\left(\frac{38}{405}\right)$
$\chi_{18225}(104,\cdot)$	$-1$	$1$	$e\left(\frac{959}{1215}\right)$	$e\left(\frac{703}{1215}\right)$	$e\left(\frac{41}{486}\right)$	$e\left(\frac{149}{405}\right)$	$e\left(\frac{1633}{2430}\right)$	$e\left(\frac{1817}{2430}\right)$	$e\left(\frac{2123}{2430}\right)$	$e\left(\frac{191}{1215}\right)$	$e\left(\frac{19}{405}\right)$	$e\left(\frac{404}{405}\right)$
$\chi_{18225}(119,\cdot)$	$-1$	$1$	$e\left(\frac{946}{1215}\right)$	$e\left(\frac{677}{1215}\right)$	$e\left(\frac{325}{486}\right)$	$e\left(\frac{136}{405}\right)$	$e\left(\frac{107}{2430}\right)$	$e\left(\frac{1933}{2430}\right)$	$e\left(\frac{1087}{2430}\right)$	$e\left(\frac{139}{1215}\right)$	$e\left(\frac{281}{405}\right)$	$e\left(\frac{241}{405}\right)$
$\chi_{18225}(164,\cdot)$	$-1$	$1$	$e\left(\frac{907}{1215}\right)$	$e\left(\frac{599}{1215}\right)$	$e\left(\frac{205}{486}\right)$	$e\left(\frac{97}{405}\right)$	$e\left(\frac{389}{2430}\right)$	$e\left(\frac{2281}{2430}\right)$	$e\left(\frac{409}{2430}\right)$	$e\left(\frac{1198}{1215}\right)$	$e\left(\frac{257}{405}\right)$	$e\left(\frac{157}{405}\right)$
$\chi_{18225}(194,\cdot)$	$-1$	$1$	$e\left(\frac{836}{1215}\right)$	$e\left(\frac{457}{1215}\right)$	$e\left(\frac{485}{486}\right)$	$e\left(\frac{26}{405}\right)$	$e\left(\frac{1027}{2430}\right)$	$e\left(\frac{1793}{2430}\right)$	$e\left(\frac{1667}{2430}\right)$	$e\left(\frac{914}{1215}\right)$	$e\left(\frac{286}{405}\right)$	$e\left(\frac{326}{405}\right)$
$\chi_{18225}(209,\cdot)$	$-1$	$1$	$e\left(\frac{1138}{1215}\right)$	$e\left(\frac{1061}{1215}\right)$	$e\left(\frac{355}{486}\right)$	$e\left(\frac{328}{405}\right)$	$e\left(\frac{401}{2430}\right)$	$e\left(\frac{2089}{2430}\right)$	$e\left(\frac{1621}{2430}\right)$	$e\left(\frac{907}{1215}\right)$	$e\left(\frac{368}{405}\right)$	$e\left(\frac{343}{405}\right)$
$\chi_{18225}(239,\cdot)$	$-1$	$1$	$e\left(\frac{572}{1215}\right)$	$e\left(\frac{1144}{1215}\right)$	$e\left(\frac{383}{486}\right)$	$e\left(\frac{167}{405}\right)$	$e\left(\frac{319}{2430}\right)$	$e\left(\frac{971}{2430}\right)$	$e\left(\frac{629}{2430}\right)$	$e\left(\frac{1073}{1215}\right)$	$e\left(\frac{217}{405}\right)$	$e\left(\frac{287}{405}\right)$
$\chi_{18225}(254,\cdot)$	$-1$	$1$	$e\left(\frac{424}{1215}\right)$	$e\left(\frac{848}{1215}\right)$	$e\left(\frac{289}{486}\right)$	$e\left(\frac{19}{405}\right)$	$e\left(\frac{143}{2430}\right)$	$e\left(\frac{1357}{2430}\right)$	$e\left(\frac{2293}{2430}\right)$	$e\left(\frac{481}{1215}\right)$	$e\left(\frac{209}{405}\right)$	$e\left(\frac{394}{405}\right)$
$\chi_{18225}(284,\cdot)$	$-1$	$1$	$e\left(\frac{983}{1215}\right)$	$e\left(\frac{751}{1215}\right)$	$e\left(\frac{227}{486}\right)$	$e\left(\frac{173}{405}\right)$	$e\left(\frac{151}{2430}\right)$	$e\left(\frac{1229}{2430}\right)$	$e\left(\frac{671}{2430}\right)$	$e\left(\frac{287}{1215}\right)$	$e\left(\frac{283}{405}\right)$	$e\left(\frac{113}{405}\right)$
$\chi_{18225}(329,\cdot)$	$-1$	$1$	$e\left(\frac{854}{1215}\right)$	$e\left(\frac{493}{1215}\right)$	$e\left(\frac{17}{486}\right)$	$e\left(\frac{44}{405}\right)$	$e\left(\frac{523}{2430}\right)$	$e\left(\frac{137}{2430}\right)$	$e\left(\frac{1793}{2430}\right)$	$e\left(\frac{986}{1215}\right)$	$e\left(\frac{79}{405}\right)$	$e\left(\frac{209}{405}\right)$
$\chi_{18225}(344,\cdot)$	$-1$	$1$	$e\left(\frac{1021}{1215}\right)$	$e\left(\frac{827}{1215}\right)$	$e\left(\frac{481}{486}\right)$	$e\left(\frac{211}{405}\right)$	$e\left(\frac{1247}{2430}\right)$	$e\left(\frac{703}{2430}\right)$	$e\left(\frac{2017}{2430}\right)$	$e\left(\frac{439}{1215}\right)$	$e\left(\frac{296}{405}\right)$	$e\left(\frac{91}{405}\right)$
$\chi_{18225}(389,\cdot)$	$-1$	$1$	$e\left(\frac{1117}{1215}\right)$	$e\left(\frac{1019}{1215}\right)$	$e\left(\frac{253}{486}\right)$	$e\left(\frac{307}{405}\right)$	$e\left(\frac{179}{2430}\right)$	$e\left(\frac{781}{2430}\right)$	$e\left(\frac{1069}{2430}\right)$	$e\left(\frac{823}{1215}\right)$	$e\left(\frac{137}{405}\right)$	$e\left(\frac{142}{405}\right)$
$\chi_{18225}(419,\cdot)$	$-1$	$1$	$e\left(\frac{191}{1215}\right)$	$e\left(\frac{382}{1215}\right)$	$e\left(\frac{407}{486}\right)$	$e\left(\frac{191}{405}\right)$	$e\left(\frac{457}{2430}\right)$	$e\left(\frac{1193}{2430}\right)$	$e\left(\frac{2417}{2430}\right)$	$e\left(\frac{764}{1215}\right)$	$e\left(\frac{76}{405}\right)$	$e\left(\frac{401}{405}\right)$
$\chi_{18225}(434,\cdot)$	$-1$	$1$	$e\left(\frac{268}{1215}\right)$	$e\left(\frac{536}{1215}\right)$	$e\left(\frac{295}{486}\right)$	$e\left(\frac{268}{405}\right)$	$e\left(\frac{1271}{2430}\right)$	$e\left(\frac{319}{2430}\right)$	$e\left(\frac{2011}{2430}\right)$	$e\left(\frac{1072}{1215}\right)$	$e\left(\frac{113}{405}\right)$	$e\left(\frac{58}{405}\right)$
$\chi_{18225}(464,\cdot)$	$-1$	$1$	$e\left(\frac{872}{1215}\right)$	$e\left(\frac{529}{1215}\right)$	$e\left(\frac{35}{486}\right)$	$e\left(\frac{62}{405}\right)$	$e\left(\frac{19}{2430}\right)$	$e\left(\frac{911}{2430}\right)$	$e\left(\frac{1919}{2430}\right)$	$e\left(\frac{1058}{1215}\right)$	$e\left(\frac{277}{405}\right)$	$e\left(\frac{92}{405}\right)$
$\chi_{18225}(479,\cdot)$	$-1$	$1$	$e\left(\frac{904}{1215}\right)$	$e\left(\frac{593}{1215}\right)$	$e\left(\frac{121}{486}\right)$	$e\left(\frac{94}{405}\right)$	$e\left(\frac{2093}{2430}\right)$	$e\left(\frac{1747}{2430}\right)$	$e\left(\frac{2413}{2430}\right)$	$e\left(\frac{1186}{1215}\right)$	$e\left(\frac{224}{405}\right)$	$e\left(\frac{244}{405}\right)$
$\chi_{18225}(509,\cdot)$	$-1$	$1$	$e\left(\frac{1013}{1215}\right)$	$e\left(\frac{811}{1215}\right)$	$e\left(\frac{95}{486}\right)$	$e\left(\frac{203}{405}\right)$	$e\left(\frac{121}{2430}\right)$	$e\left(\frac{1709}{2430}\right)$	$e\left(\frac{71}{2430}\right)$	$e\left(\frac{407}{1215}\right)$	$e\left(\frac{208}{405}\right)$	$e\left(\frac{53}{405}\right)$
$\chi_{18225}(554,\cdot)$	$-1$	$1$	$e\left(\frac{614}{1215}\right)$	$e\left(\frac{13}{1215}\right)$	$e\left(\frac{101}{486}\right)$	$e\left(\frac{209}{405}\right)$	$e\left(\frac{763}{2430}\right)$	$e\left(\frac{1157}{2430}\right)$	$e\left(\frac{1733}{2430}\right)$	$e\left(\frac{26}{1215}\right)$	$e\left(\frac{274}{405}\right)$	$e\left(\frac{284}{405}\right)$
$\chi_{18225}(569,\cdot)$	$-1$	$1$	$e\left(\frac{556}{1215}\right)$	$e\left(\frac{1112}{1215}\right)$	$e\left(\frac{97}{486}\right)$	$e\left(\frac{151}{405}\right)$	$e\left(\frac{497}{2430}\right)$	$e\left(\frac{553}{2430}\right)$	$e\left(\frac{1597}{2430}\right)$	$e\left(\frac{1009}{1215}\right)$	$e\left(\frac{41}{405}\right)$	$e\left(\frac{211}{405}\right)$
$\chi_{18225}(614,\cdot)$	$-1$	$1$	$e\left(\frac{787}{1215}\right)$	$e\left(\frac{359}{1215}\right)$	$e\left(\frac{247}{486}\right)$	$e\left(\frac{382}{405}\right)$	$e\left(\frac{509}{2430}\right)$	$e\left(\frac{361}{2430}\right)$	$e\left(\frac{379}{2430}\right)$	$e\left(\frac{718}{1215}\right)$	$e\left(\frac{152}{405}\right)$	$e\left(\frac{397}{405}\right)$
$\chi_{18225}(644,\cdot)$	$-1$	$1$	$e\left(\frac{626}{1215}\right)$	$e\left(\frac{37}{1215}\right)$	$e\left(\frac{437}{486}\right)$	$e\left(\frac{221}{405}\right)$	$e\left(\frac{1237}{2430}\right)$	$e\left(\frac{863}{2430}\right)$	$e\left(\frac{1007}{2430}\right)$	$e\left(\frac{74}{1215}\right)$	$e\left(\frac{1}{405}\right)$	$e\left(\frac{341}{405}\right)$
$\chi_{18225}(659,\cdot)$	$-1$	$1$	$e\left(\frac{73}{1215}\right)$	$e\left(\frac{146}{1215}\right)$	$e\left(\frac{181}{486}\right)$	$e\left(\frac{73}{405}\right)$	$e\left(\frac{251}{2430}\right)$	$e\left(\frac{2059}{2430}\right)$	$e\left(\frac{1051}{2430}\right)$	$e\left(\frac{292}{1215}\right)$	$e\left(\frac{398}{405}\right)$	$e\left(\frac{43}{405}\right)$
$\chi_{18225}(689,\cdot)$	$-1$	$1$	$e\left(\frac{1037}{1215}\right)$	$e\left(\frac{859}{1215}\right)$	$e\left(\frac{281}{486}\right)$	$e\left(\frac{227}{405}\right)$	$e\left(\frac{1069}{2430}\right)$	$e\left(\frac{1121}{2430}\right)$	$e\left(\frac{1049}{2430}\right)$	$e\left(\frac{503}{1215}\right)$	$e\left(\frac{67}{405}\right)$	$e\left(\frac{167}{405}\right)$
$\chi_{18225}(704,\cdot)$	$-1$	$1$	$e\left(\frac{844}{1215}\right)$	$e\left(\frac{473}{1215}\right)$	$e\left(\frac{385}{486}\right)$	$e\left(\frac{34}{405}\right)$	$e\left(\frac{2153}{2430}\right)$	$e\left(\frac{787}{2430}\right)$	$e\left(\frac{1183}{2430}\right)$	$e\left(\frac{946}{1215}\right)$	$e\left(\frac{374}{405}\right)$	$e\left(\frac{364}{405}\right)$
$\chi_{18225}(734,\cdot)$	$-1$	$1$	$e\left(\frac{908}{1215}\right)$	$e\left(\frac{601}{1215}\right)$	$e\left(\frac{71}{486}\right)$	$e\left(\frac{98}{405}\right)$	$e\left(\frac{1441}{2430}\right)$	$e\left(\frac{29}{2430}\right)$	$e\left(\frac{2171}{2430}\right)$	$e\left(\frac{1202}{1215}\right)$	$e\left(\frac{268}{405}\right)$	$e\left(\frac{263}{405}\right)$
$\chi_{18225}(779,\cdot)$	$-1$	$1$	$e\left(\frac{239}{1215}\right)$	$e\left(\frac{478}{1215}\right)$	$e\left(\frac{293}{486}\right)$	$e\left(\frac{239}{405}\right)$	$e\left(\frac{2353}{2430}\right)$	$e\left(\frac{17}{2430}\right)$	$e\left(\frac{1943}{2430}\right)$	$e\left(\frac{956}{1215}\right)$	$e\left(\frac{199}{405}\right)$	$e\left(\frac{224}{405}\right)$
$\chi_{18225}(794,\cdot)$	$-1$	$1$	$e\left(\frac{766}{1215}\right)$	$e\left(\frac{317}{1215}\right)$	$e\left(\frac{145}{486}\right)$	$e\left(\frac{361}{405}\right)$	$e\left(\frac{287}{2430}\right)$	$e\left(\frac{1483}{2430}\right)$	$e\left(\frac{2257}{2430}\right)$	$e\left(\frac{634}{1215}\right)$	$e\left(\frac{326}{405}\right)$	$e\left(\frac{196}{405}\right)$
$\chi_{18225}(839,\cdot)$	$-1$	$1$	$e\left(\frac{1132}{1215}\right)$	$e\left(\frac{1049}{1215}\right)$	$e\left(\frac{187}{486}\right)$	$e\left(\frac{322}{405}\right)$	$e\left(\frac{1379}{2430}\right)$	$e\left(\frac{1021}{2430}\right)$	$e\left(\frac{769}{2430}\right)$	$e\left(\frac{883}{1215}\right)$	$e\left(\frac{302}{405}\right)$	$e\left(\frac{112}{405}\right)$
$\chi_{18225}(869,\cdot)$	$-1$	$1$	$e\left(\frac{926}{1215}\right)$	$e\left(\frac{637}{1215}\right)$	$e\left(\frac{89}{486}\right)$	$e\left(\frac{116}{405}\right)$	$e\left(\frac{937}{2430}\right)$	$e\left(\frac{803}{2430}\right)$	$e\left(\frac{2297}{2430}\right)$	$e\left(\frac{59}{1215}\right)$	$e\left(\frac{61}{405}\right)$	$e\left(\frac{146}{405}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{18225}(14,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{1215}\right)\)	\(e\left(\frac{274}{1215}\right)\)	\(e\left(\frac{353}{486}\right)\)	\(e\left(\frac{137}{405}\right)\)	\(e\left(\frac{1969}{2430}\right)\)	\(e\left(\frac{1301}{2430}\right)\)	\(e\left(\frac{2039}{2430}\right)\)	\(e\left(\frac{548}{1215}\right)\)	\(e\left(\frac{292}{405}\right)\)	\(e\left(\frac{347}{405}\right)\)
\(\chi_{18225}(29,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{619}{1215}\right)\)	\(e\left(\frac{23}{1215}\right)\)	\(e\left(\frac{403}{486}\right)\)	\(e\left(\frac{214}{405}\right)\)	\(e\left(\frac{1163}{2430}\right)\)	\(e\left(\frac{2047}{2430}\right)\)	\(e\left(\frac{823}{2430}\right)\)	\(e\left(\frac{46}{1215}\right)\)	\(e\left(\frac{329}{405}\right)\)	\(e\left(\frac{4}{405}\right)\)
\(\chi_{18225}(59,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{818}{1215}\right)\)	\(e\left(\frac{421}{1215}\right)\)	\(e\left(\frac{467}{486}\right)\)	\(e\left(\frac{8}{405}\right)\)	\(e\left(\frac{1531}{2430}\right)\)	\(e\left(\frac{1019}{2430}\right)\)	\(e\left(\frac{1541}{2430}\right)\)	\(e\left(\frac{842}{1215}\right)\)	\(e\left(\frac{88}{405}\right)\)	\(e\left(\frac{38}{405}\right)\)
\(\chi_{18225}(104,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{959}{1215}\right)\)	\(e\left(\frac{703}{1215}\right)\)	\(e\left(\frac{41}{486}\right)\)	\(e\left(\frac{149}{405}\right)\)	\(e\left(\frac{1633}{2430}\right)\)	\(e\left(\frac{1817}{2430}\right)\)	\(e\left(\frac{2123}{2430}\right)\)	\(e\left(\frac{191}{1215}\right)\)	\(e\left(\frac{19}{405}\right)\)	\(e\left(\frac{404}{405}\right)\)
\(\chi_{18225}(119,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{946}{1215}\right)\)	\(e\left(\frac{677}{1215}\right)\)	\(e\left(\frac{325}{486}\right)\)	\(e\left(\frac{136}{405}\right)\)	\(e\left(\frac{107}{2430}\right)\)	\(e\left(\frac{1933}{2430}\right)\)	\(e\left(\frac{1087}{2430}\right)\)	\(e\left(\frac{139}{1215}\right)\)	\(e\left(\frac{281}{405}\right)\)	\(e\left(\frac{241}{405}\right)\)
\(\chi_{18225}(164,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{907}{1215}\right)\)	\(e\left(\frac{599}{1215}\right)\)	\(e\left(\frac{205}{486}\right)\)	\(e\left(\frac{97}{405}\right)\)	\(e\left(\frac{389}{2430}\right)\)	\(e\left(\frac{2281}{2430}\right)\)	\(e\left(\frac{409}{2430}\right)\)	\(e\left(\frac{1198}{1215}\right)\)	\(e\left(\frac{257}{405}\right)\)	\(e\left(\frac{157}{405}\right)\)
\(\chi_{18225}(194,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{836}{1215}\right)\)	\(e\left(\frac{457}{1215}\right)\)	\(e\left(\frac{485}{486}\right)\)	\(e\left(\frac{26}{405}\right)\)	\(e\left(\frac{1027}{2430}\right)\)	\(e\left(\frac{1793}{2430}\right)\)	\(e\left(\frac{1667}{2430}\right)\)	\(e\left(\frac{914}{1215}\right)\)	\(e\left(\frac{286}{405}\right)\)	\(e\left(\frac{326}{405}\right)\)
\(\chi_{18225}(209,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1138}{1215}\right)\)	\(e\left(\frac{1061}{1215}\right)\)	\(e\left(\frac{355}{486}\right)\)	\(e\left(\frac{328}{405}\right)\)	\(e\left(\frac{401}{2430}\right)\)	\(e\left(\frac{2089}{2430}\right)\)	\(e\left(\frac{1621}{2430}\right)\)	\(e\left(\frac{907}{1215}\right)\)	\(e\left(\frac{368}{405}\right)\)	\(e\left(\frac{343}{405}\right)\)
\(\chi_{18225}(239,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{572}{1215}\right)\)	\(e\left(\frac{1144}{1215}\right)\)	\(e\left(\frac{383}{486}\right)\)	\(e\left(\frac{167}{405}\right)\)	\(e\left(\frac{319}{2430}\right)\)	\(e\left(\frac{971}{2430}\right)\)	\(e\left(\frac{629}{2430}\right)\)	\(e\left(\frac{1073}{1215}\right)\)	\(e\left(\frac{217}{405}\right)\)	\(e\left(\frac{287}{405}\right)\)
\(\chi_{18225}(254,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{424}{1215}\right)\)	\(e\left(\frac{848}{1215}\right)\)	\(e\left(\frac{289}{486}\right)\)	\(e\left(\frac{19}{405}\right)\)	\(e\left(\frac{143}{2430}\right)\)	\(e\left(\frac{1357}{2430}\right)\)	\(e\left(\frac{2293}{2430}\right)\)	\(e\left(\frac{481}{1215}\right)\)	\(e\left(\frac{209}{405}\right)\)	\(e\left(\frac{394}{405}\right)\)
\(\chi_{18225}(284,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{983}{1215}\right)\)	\(e\left(\frac{751}{1215}\right)\)	\(e\left(\frac{227}{486}\right)\)	\(e\left(\frac{173}{405}\right)\)	\(e\left(\frac{151}{2430}\right)\)	\(e\left(\frac{1229}{2430}\right)\)	\(e\left(\frac{671}{2430}\right)\)	\(e\left(\frac{287}{1215}\right)\)	\(e\left(\frac{283}{405}\right)\)	\(e\left(\frac{113}{405}\right)\)
\(\chi_{18225}(329,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{854}{1215}\right)\)	\(e\left(\frac{493}{1215}\right)\)	\(e\left(\frac{17}{486}\right)\)	\(e\left(\frac{44}{405}\right)\)	\(e\left(\frac{523}{2430}\right)\)	\(e\left(\frac{137}{2430}\right)\)	\(e\left(\frac{1793}{2430}\right)\)	\(e\left(\frac{986}{1215}\right)\)	\(e\left(\frac{79}{405}\right)\)	\(e\left(\frac{209}{405}\right)\)
\(\chi_{18225}(344,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1021}{1215}\right)\)	\(e\left(\frac{827}{1215}\right)\)	\(e\left(\frac{481}{486}\right)\)	\(e\left(\frac{211}{405}\right)\)	\(e\left(\frac{1247}{2430}\right)\)	\(e\left(\frac{703}{2430}\right)\)	\(e\left(\frac{2017}{2430}\right)\)	\(e\left(\frac{439}{1215}\right)\)	\(e\left(\frac{296}{405}\right)\)	\(e\left(\frac{91}{405}\right)\)
\(\chi_{18225}(389,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1117}{1215}\right)\)	\(e\left(\frac{1019}{1215}\right)\)	\(e\left(\frac{253}{486}\right)\)	\(e\left(\frac{307}{405}\right)\)	\(e\left(\frac{179}{2430}\right)\)	\(e\left(\frac{781}{2430}\right)\)	\(e\left(\frac{1069}{2430}\right)\)	\(e\left(\frac{823}{1215}\right)\)	\(e\left(\frac{137}{405}\right)\)	\(e\left(\frac{142}{405}\right)\)
\(\chi_{18225}(419,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{191}{1215}\right)\)	\(e\left(\frac{382}{1215}\right)\)	\(e\left(\frac{407}{486}\right)\)	\(e\left(\frac{191}{405}\right)\)	\(e\left(\frac{457}{2430}\right)\)	\(e\left(\frac{1193}{2430}\right)\)	\(e\left(\frac{2417}{2430}\right)\)	\(e\left(\frac{764}{1215}\right)\)	\(e\left(\frac{76}{405}\right)\)	\(e\left(\frac{401}{405}\right)\)
\(\chi_{18225}(434,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{268}{1215}\right)\)	\(e\left(\frac{536}{1215}\right)\)	\(e\left(\frac{295}{486}\right)\)	\(e\left(\frac{268}{405}\right)\)	\(e\left(\frac{1271}{2430}\right)\)	\(e\left(\frac{319}{2430}\right)\)	\(e\left(\frac{2011}{2430}\right)\)	\(e\left(\frac{1072}{1215}\right)\)	\(e\left(\frac{113}{405}\right)\)	\(e\left(\frac{58}{405}\right)\)
\(\chi_{18225}(464,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{872}{1215}\right)\)	\(e\left(\frac{529}{1215}\right)\)	\(e\left(\frac{35}{486}\right)\)	\(e\left(\frac{62}{405}\right)\)	\(e\left(\frac{19}{2430}\right)\)	\(e\left(\frac{911}{2430}\right)\)	\(e\left(\frac{1919}{2430}\right)\)	\(e\left(\frac{1058}{1215}\right)\)	\(e\left(\frac{277}{405}\right)\)	\(e\left(\frac{92}{405}\right)\)
\(\chi_{18225}(479,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{904}{1215}\right)\)	\(e\left(\frac{593}{1215}\right)\)	\(e\left(\frac{121}{486}\right)\)	\(e\left(\frac{94}{405}\right)\)	\(e\left(\frac{2093}{2430}\right)\)	\(e\left(\frac{1747}{2430}\right)\)	\(e\left(\frac{2413}{2430}\right)\)	\(e\left(\frac{1186}{1215}\right)\)	\(e\left(\frac{224}{405}\right)\)	\(e\left(\frac{244}{405}\right)\)
\(\chi_{18225}(509,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1013}{1215}\right)\)	\(e\left(\frac{811}{1215}\right)\)	\(e\left(\frac{95}{486}\right)\)	\(e\left(\frac{203}{405}\right)\)	\(e\left(\frac{121}{2430}\right)\)	\(e\left(\frac{1709}{2430}\right)\)	\(e\left(\frac{71}{2430}\right)\)	\(e\left(\frac{407}{1215}\right)\)	\(e\left(\frac{208}{405}\right)\)	\(e\left(\frac{53}{405}\right)\)
\(\chi_{18225}(554,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{614}{1215}\right)\)	\(e\left(\frac{13}{1215}\right)\)	\(e\left(\frac{101}{486}\right)\)	\(e\left(\frac{209}{405}\right)\)	\(e\left(\frac{763}{2430}\right)\)	\(e\left(\frac{1157}{2430}\right)\)	\(e\left(\frac{1733}{2430}\right)\)	\(e\left(\frac{26}{1215}\right)\)	\(e\left(\frac{274}{405}\right)\)	\(e\left(\frac{284}{405}\right)\)
\(\chi_{18225}(569,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{556}{1215}\right)\)	\(e\left(\frac{1112}{1215}\right)\)	\(e\left(\frac{97}{486}\right)\)	\(e\left(\frac{151}{405}\right)\)	\(e\left(\frac{497}{2430}\right)\)	\(e\left(\frac{553}{2430}\right)\)	\(e\left(\frac{1597}{2430}\right)\)	\(e\left(\frac{1009}{1215}\right)\)	\(e\left(\frac{41}{405}\right)\)	\(e\left(\frac{211}{405}\right)\)
\(\chi_{18225}(614,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{787}{1215}\right)\)	\(e\left(\frac{359}{1215}\right)\)	\(e\left(\frac{247}{486}\right)\)	\(e\left(\frac{382}{405}\right)\)	\(e\left(\frac{509}{2430}\right)\)	\(e\left(\frac{361}{2430}\right)\)	\(e\left(\frac{379}{2430}\right)\)	\(e\left(\frac{718}{1215}\right)\)	\(e\left(\frac{152}{405}\right)\)	\(e\left(\frac{397}{405}\right)\)
\(\chi_{18225}(644,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{626}{1215}\right)\)	\(e\left(\frac{37}{1215}\right)\)	\(e\left(\frac{437}{486}\right)\)	\(e\left(\frac{221}{405}\right)\)	\(e\left(\frac{1237}{2430}\right)\)	\(e\left(\frac{863}{2430}\right)\)	\(e\left(\frac{1007}{2430}\right)\)	\(e\left(\frac{74}{1215}\right)\)	\(e\left(\frac{1}{405}\right)\)	\(e\left(\frac{341}{405}\right)\)
\(\chi_{18225}(659,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{1215}\right)\)	\(e\left(\frac{146}{1215}\right)\)	\(e\left(\frac{181}{486}\right)\)	\(e\left(\frac{73}{405}\right)\)	\(e\left(\frac{251}{2430}\right)\)	\(e\left(\frac{2059}{2430}\right)\)	\(e\left(\frac{1051}{2430}\right)\)	\(e\left(\frac{292}{1215}\right)\)	\(e\left(\frac{398}{405}\right)\)	\(e\left(\frac{43}{405}\right)\)
\(\chi_{18225}(689,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1037}{1215}\right)\)	\(e\left(\frac{859}{1215}\right)\)	\(e\left(\frac{281}{486}\right)\)	\(e\left(\frac{227}{405}\right)\)	\(e\left(\frac{1069}{2430}\right)\)	\(e\left(\frac{1121}{2430}\right)\)	\(e\left(\frac{1049}{2430}\right)\)	\(e\left(\frac{503}{1215}\right)\)	\(e\left(\frac{67}{405}\right)\)	\(e\left(\frac{167}{405}\right)\)
\(\chi_{18225}(704,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{844}{1215}\right)\)	\(e\left(\frac{473}{1215}\right)\)	\(e\left(\frac{385}{486}\right)\)	\(e\left(\frac{34}{405}\right)\)	\(e\left(\frac{2153}{2430}\right)\)	\(e\left(\frac{787}{2430}\right)\)	\(e\left(\frac{1183}{2430}\right)\)	\(e\left(\frac{946}{1215}\right)\)	\(e\left(\frac{374}{405}\right)\)	\(e\left(\frac{364}{405}\right)\)
\(\chi_{18225}(734,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{908}{1215}\right)\)	\(e\left(\frac{601}{1215}\right)\)	\(e\left(\frac{71}{486}\right)\)	\(e\left(\frac{98}{405}\right)\)	\(e\left(\frac{1441}{2430}\right)\)	\(e\left(\frac{29}{2430}\right)\)	\(e\left(\frac{2171}{2430}\right)\)	\(e\left(\frac{1202}{1215}\right)\)	\(e\left(\frac{268}{405}\right)\)	\(e\left(\frac{263}{405}\right)\)
\(\chi_{18225}(779,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{239}{1215}\right)\)	\(e\left(\frac{478}{1215}\right)\)	\(e\left(\frac{293}{486}\right)\)	\(e\left(\frac{239}{405}\right)\)	\(e\left(\frac{2353}{2430}\right)\)	\(e\left(\frac{17}{2430}\right)\)	\(e\left(\frac{1943}{2430}\right)\)	\(e\left(\frac{956}{1215}\right)\)	\(e\left(\frac{199}{405}\right)\)	\(e\left(\frac{224}{405}\right)\)
\(\chi_{18225}(794,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{766}{1215}\right)\)	\(e\left(\frac{317}{1215}\right)\)	\(e\left(\frac{145}{486}\right)\)	\(e\left(\frac{361}{405}\right)\)	\(e\left(\frac{287}{2430}\right)\)	\(e\left(\frac{1483}{2430}\right)\)	\(e\left(\frac{2257}{2430}\right)\)	\(e\left(\frac{634}{1215}\right)\)	\(e\left(\frac{326}{405}\right)\)	\(e\left(\frac{196}{405}\right)\)
\(\chi_{18225}(839,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1132}{1215}\right)\)	\(e\left(\frac{1049}{1215}\right)\)	\(e\left(\frac{187}{486}\right)\)	\(e\left(\frac{322}{405}\right)\)	\(e\left(\frac{1379}{2430}\right)\)	\(e\left(\frac{1021}{2430}\right)\)	\(e\left(\frac{769}{2430}\right)\)	\(e\left(\frac{883}{1215}\right)\)	\(e\left(\frac{302}{405}\right)\)	\(e\left(\frac{112}{405}\right)\)
\(\chi_{18225}(869,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{926}{1215}\right)\)	\(e\left(\frac{637}{1215}\right)\)	\(e\left(\frac{89}{486}\right)\)	\(e\left(\frac{116}{405}\right)\)	\(e\left(\frac{937}{2430}\right)\)	\(e\left(\frac{803}{2430}\right)\)	\(e\left(\frac{2297}{2430}\right)\)	\(e\left(\frac{59}{1215}\right)\)	\(e\left(\frac{61}{405}\right)\)	\(e\left(\frac{146}{405}\right)\)

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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.cr
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)