LMFDB - Dirichlet character orbit 18225.cl

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(18225, base_ring=CyclotomicField(972)) M = H._module chi = DirichletCharacter(H, M([10,243])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(32,18225)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$18225$
Conductor:	$3645$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$972$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 3645.bj	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{972})$
Fixed field:	Number field defined by a degree 972 polynomial (not computed)

First 27 of 324 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{18225}(32,\cdot)$	$1$	$1$	$e\left(\frac{253}{972}\right)$	$e\left(\frac{253}{486}\right)$	$e\left(\frac{295}{972}\right)$	$e\left(\frac{253}{324}\right)$	$e\left(\frac{443}{486}\right)$	$e\left(\frac{161}{972}\right)$	$e\left(\frac{137}{243}\right)$	$e\left(\frac{10}{243}\right)$	$e\left(\frac{191}{324}\right)$	$e\left(\frac{125}{162}\right)$
$\chi_{18225}(68,\cdot)$	$1$	$1$	$e\left(\frac{799}{972}\right)$	$e\left(\frac{313}{486}\right)$	$e\left(\frac{121}{972}\right)$	$e\left(\frac{151}{324}\right)$	$e\left(\frac{185}{486}\right)$	$e\left(\frac{155}{972}\right)$	$e\left(\frac{230}{243}\right)$	$e\left(\frac{70}{243}\right)$	$e\left(\frac{41}{324}\right)$	$e\left(\frac{65}{162}\right)$
$\chi_{18225}(182,\cdot)$	$1$	$1$	$e\left(\frac{725}{972}\right)$	$e\left(\frac{239}{486}\right)$	$e\left(\frac{611}{972}\right)$	$e\left(\frac{77}{324}\right)$	$e\left(\frac{163}{486}\right)$	$e\left(\frac{373}{972}\right)$	$e\left(\frac{91}{243}\right)$	$e\left(\frac{239}{243}\right)$	$e\left(\frac{199}{324}\right)$	$e\left(\frac{31}{162}\right)$
$\chi_{18225}(218,\cdot)$	$1$	$1$	$e\left(\frac{11}{972}\right)$	$e\left(\frac{11}{486}\right)$	$e\left(\frac{689}{972}\right)$	$e\left(\frac{11}{324}\right)$	$e\left(\frac{463}{486}\right)$	$e\left(\frac{7}{972}\right)$	$e\left(\frac{175}{243}\right)$	$e\left(\frac{11}{243}\right)$	$e\left(\frac{121}{324}\right)$	$e\left(\frac{97}{162}\right)$
$\chi_{18225}(257,\cdot)$	$1$	$1$	$e\left(\frac{709}{972}\right)$	$e\left(\frac{223}{486}\right)$	$e\left(\frac{139}{972}\right)$	$e\left(\frac{61}{324}\right)$	$e\left(\frac{329}{486}\right)$	$e\left(\frac{893}{972}\right)$	$e\left(\frac{212}{243}\right)$	$e\left(\frac{223}{243}\right)$	$e\left(\frac{23}{324}\right)$	$e\left(\frac{155}{162}\right)$
$\chi_{18225}(293,\cdot)$	$1$	$1$	$e\left(\frac{499}{972}\right)$	$e\left(\frac{13}{486}\right)$	$e\left(\frac{505}{972}\right)$	$e\left(\frac{175}{324}\right)$	$e\left(\frac{17}{486}\right)$	$e\left(\frac{671}{972}\right)$	$e\left(\frac{8}{243}\right)$	$e\left(\frac{13}{243}\right)$	$e\left(\frac{305}{324}\right)$	$e\left(\frac{41}{162}\right)$
$\chi_{18225}(407,\cdot)$	$1$	$1$	$e\left(\frac{353}{972}\right)$	$e\left(\frac{353}{486}\right)$	$e\left(\frac{815}{972}\right)$	$e\left(\frac{29}{324}\right)$	$e\left(\frac{13}{486}\right)$	$e\left(\frac{313}{972}\right)$	$e\left(\frac{49}{243}\right)$	$e\left(\frac{110}{243}\right)$	$e\left(\frac{319}{324}\right)$	$e\left(\frac{79}{162}\right)$
$\chi_{18225}(443,\cdot)$	$1$	$1$	$e\left(\frac{503}{972}\right)$	$e\left(\frac{17}{486}\right)$	$e\left(\frac{137}{972}\right)$	$e\left(\frac{179}{324}\right)$	$e\left(\frac{97}{486}\right)$	$e\left(\frac{55}{972}\right)$	$e\left(\frac{160}{243}\right)$	$e\left(\frac{17}{243}\right)$	$e\left(\frac{25}{324}\right)$	$e\left(\frac{91}{162}\right)$
$\chi_{18225}(482,\cdot)$	$1$	$1$	$e\left(\frac{85}{972}\right)$	$e\left(\frac{85}{486}\right)$	$e\left(\frac{199}{972}\right)$	$e\left(\frac{85}{324}\right)$	$e\left(\frac{485}{486}\right)$	$e\left(\frac{761}{972}\right)$	$e\left(\frac{71}{243}\right)$	$e\left(\frac{85}{243}\right)$	$e\left(\frac{287}{324}\right)$	$e\left(\frac{131}{162}\right)$
$\chi_{18225}(518,\cdot)$	$1$	$1$	$e\left(\frac{91}{972}\right)$	$e\left(\frac{91}{486}\right)$	$e\left(\frac{133}{972}\right)$	$e\left(\frac{91}{324}\right)$	$e\left(\frac{119}{486}\right)$	$e\left(\frac{323}{972}\right)$	$e\left(\frac{56}{243}\right)$	$e\left(\frac{91}{243}\right)$	$e\left(\frac{29}{324}\right)$	$e\left(\frac{125}{162}\right)$
$\chi_{18225}(632,\cdot)$	$1$	$1$	$e\left(\frac{521}{972}\right)$	$e\left(\frac{35}{486}\right)$	$e\left(\frac{911}{972}\right)$	$e\left(\frac{197}{324}\right)$	$e\left(\frac{457}{486}\right)$	$e\left(\frac{685}{972}\right)$	$e\left(\frac{115}{243}\right)$	$e\left(\frac{35}{243}\right)$	$e\left(\frac{223}{324}\right)$	$e\left(\frac{73}{162}\right)$
$\chi_{18225}(668,\cdot)$	$1$	$1$	$e\left(\frac{563}{972}\right)$	$e\left(\frac{77}{486}\right)$	$e\left(\frac{449}{972}\right)$	$e\left(\frac{239}{324}\right)$	$e\left(\frac{325}{486}\right)$	$e\left(\frac{535}{972}\right)$	$e\left(\frac{10}{243}\right)$	$e\left(\frac{77}{243}\right)$	$e\left(\frac{37}{324}\right)$	$e\left(\frac{31}{162}\right)$
$\chi_{18225}(707,\cdot)$	$1$	$1$	$e\left(\frac{325}{972}\right)$	$e\left(\frac{325}{486}\right)$	$e\left(\frac{475}{972}\right)$	$e\left(\frac{1}{324}\right)$	$e\left(\frac{425}{486}\right)$	$e\left(\frac{737}{972}\right)$	$e\left(\frac{200}{243}\right)$	$e\left(\frac{82}{243}\right)$	$e\left(\frac{11}{324}\right)$	$e\left(\frac{53}{162}\right)$
$\chi_{18225}(743,\cdot)$	$1$	$1$	$e\left(\frac{547}{972}\right)$	$e\left(\frac{61}{486}\right)$	$e\left(\frac{949}{972}\right)$	$e\left(\frac{223}{324}\right)$	$e\left(\frac{5}{486}\right)$	$e\left(\frac{83}{972}\right)$	$e\left(\frac{131}{243}\right)$	$e\left(\frac{61}{243}\right)$	$e\left(\frac{185}{324}\right)$	$e\left(\frac{155}{162}\right)$
$\chi_{18225}(857,\cdot)$	$1$	$1$	$e\left(\frac{257}{972}\right)$	$e\left(\frac{257}{486}\right)$	$e\left(\frac{899}{972}\right)$	$e\left(\frac{257}{324}\right)$	$e\left(\frac{37}{486}\right)$	$e\left(\frac{517}{972}\right)$	$e\left(\frac{46}{243}\right)$	$e\left(\frac{14}{243}\right)$	$e\left(\frac{235}{324}\right)$	$e\left(\frac{13}{162}\right)$
$\chi_{18225}(893,\cdot)$	$1$	$1$	$e\left(\frac{191}{972}\right)$	$e\left(\frac{191}{486}\right)$	$e\left(\frac{653}{972}\right)$	$e\left(\frac{191}{324}\right)$	$e\left(\frac{175}{486}\right)$	$e\left(\frac{475}{972}\right)$	$e\left(\frac{211}{243}\right)$	$e\left(\frac{191}{243}\right)$	$e\left(\frac{157}{324}\right)$	$e\left(\frac{79}{162}\right)$
$\chi_{18225}(932,\cdot)$	$1$	$1$	$e\left(\frac{457}{972}\right)$	$e\left(\frac{457}{486}\right)$	$e\left(\frac{967}{972}\right)$	$e\left(\frac{133}{324}\right)$	$e\left(\frac{149}{486}\right)$	$e\left(\frac{821}{972}\right)$	$e\left(\frac{113}{243}\right)$	$e\left(\frac{214}{243}\right)$	$e\left(\frac{167}{324}\right)$	$e\left(\frac{83}{162}\right)$
$\chi_{18225}(968,\cdot)$	$1$	$1$	$e\left(\frac{895}{972}\right)$	$e\left(\frac{409}{486}\right)$	$e\left(\frac{37}{972}\right)$	$e\left(\frac{247}{324}\right)$	$e\left(\frac{161}{486}\right)$	$e\left(\frac{923}{972}\right)$	$e\left(\frac{233}{243}\right)$	$e\left(\frac{166}{243}\right)$	$e\left(\frac{125}{324}\right)$	$e\left(\frac{131}{162}\right)$
$\chi_{18225}(1082,\cdot)$	$1$	$1$	$e\left(\frac{533}{972}\right)$	$e\left(\frac{47}{486}\right)$	$e\left(\frac{779}{972}\right)$	$e\left(\frac{209}{324}\right)$	$e\left(\frac{211}{486}\right)$	$e\left(\frac{781}{972}\right)$	$e\left(\frac{85}{243}\right)$	$e\left(\frac{47}{243}\right)$	$e\left(\frac{31}{324}\right)$	$e\left(\frac{61}{162}\right)$
$\chi_{18225}(1118,\cdot)$	$1$	$1$	$e\left(\frac{359}{972}\right)$	$e\left(\frac{359}{486}\right)$	$e\left(\frac{749}{972}\right)$	$e\left(\frac{35}{324}\right)$	$e\left(\frac{133}{486}\right)$	$e\left(\frac{847}{972}\right)$	$e\left(\frac{34}{243}\right)$	$e\left(\frac{116}{243}\right)$	$e\left(\frac{61}{324}\right)$	$e\left(\frac{73}{162}\right)$
$\chi_{18225}(1157,\cdot)$	$1$	$1$	$e\left(\frac{481}{972}\right)$	$e\left(\frac{481}{486}\right)$	$e\left(\frac{703}{972}\right)$	$e\left(\frac{157}{324}\right)$	$e\left(\frac{143}{486}\right)$	$e\left(\frac{41}{972}\right)$	$e\left(\frac{53}{243}\right)$	$e\left(\frac{238}{243}\right)$	$e\left(\frac{107}{324}\right)$	$e\left(\frac{59}{162}\right)$
$\chi_{18225}(1193,\cdot)$	$1$	$1$	$e\left(\frac{163}{972}\right)$	$e\left(\frac{163}{486}\right)$	$e\left(\frac{313}{972}\right)$	$e\left(\frac{163}{324}\right)$	$e\left(\frac{101}{486}\right)$	$e\left(\frac{899}{972}\right)$	$e\left(\frac{119}{243}\right)$	$e\left(\frac{163}{243}\right)$	$e\left(\frac{173}{324}\right)$	$e\left(\frac{53}{162}\right)$
$\chi_{18225}(1307,\cdot)$	$1$	$1$	$e\left(\frac{377}{972}\right)$	$e\left(\frac{377}{486}\right)$	$e\left(\frac{551}{972}\right)$	$e\left(\frac{53}{324}\right)$	$e\left(\frac{7}{486}\right)$	$e\left(\frac{505}{972}\right)$	$e\left(\frac{232}{243}\right)$	$e\left(\frac{134}{243}\right)$	$e\left(\frac{259}{324}\right)$	$e\left(\frac{55}{162}\right)$
$\chi_{18225}(1343,\cdot)$	$1$	$1$	$e\left(\frac{95}{972}\right)$	$e\left(\frac{95}{486}\right)$	$e\left(\frac{737}{972}\right)$	$e\left(\frac{95}{324}\right)$	$e\left(\frac{199}{486}\right)$	$e\left(\frac{679}{972}\right)$	$e\left(\frac{208}{243}\right)$	$e\left(\frac{95}{243}\right)$	$e\left(\frac{73}{324}\right)$	$e\left(\frac{13}{162}\right)$
$\chi_{18225}(1382,\cdot)$	$1$	$1$	$e\left(\frac{397}{972}\right)$	$e\left(\frac{397}{486}\right)$	$e\left(\frac{655}{972}\right)$	$e\left(\frac{73}{324}\right)$	$e\left(\frac{407}{486}\right)$	$e\left(\frac{341}{972}\right)$	$e\left(\frac{20}{243}\right)$	$e\left(\frac{154}{243}\right)$	$e\left(\frac{155}{324}\right)$	$e\left(\frac{143}{162}\right)$
$\chi_{18225}(1418,\cdot)$	$1$	$1$	$e\left(\frac{295}{972}\right)$	$e\left(\frac{295}{486}\right)$	$e\left(\frac{805}{972}\right)$	$e\left(\frac{295}{324}\right)$	$e\left(\frac{311}{486}\right)$	$e\left(\frac{11}{972}\right)$	$e\left(\frac{32}{243}\right)$	$e\left(\frac{52}{243}\right)$	$e\left(\frac{5}{324}\right)$	$e\left(\frac{83}{162}\right)$
$\chi_{18225}(1532,\cdot)$	$1$	$1$	$e\left(\frac{761}{972}\right)$	$e\left(\frac{275}{486}\right)$	$e\left(\frac{215}{972}\right)$	$e\left(\frac{113}{324}\right)$	$e\left(\frac{397}{486}\right)$	$e\left(\frac{661}{972}\right)$	$e\left(\frac{1}{243}\right)$	$e\left(\frac{32}{243}\right)$	$e\left(\frac{271}{324}\right)$	$e\left(\frac{157}{162}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{18225}(32,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{253}{972}\right)\)	\(e\left(\frac{253}{486}\right)\)	\(e\left(\frac{295}{972}\right)\)	\(e\left(\frac{253}{324}\right)\)	\(e\left(\frac{443}{486}\right)\)	\(e\left(\frac{161}{972}\right)\)	\(e\left(\frac{137}{243}\right)\)	\(e\left(\frac{10}{243}\right)\)	\(e\left(\frac{191}{324}\right)\)	\(e\left(\frac{125}{162}\right)\)
\(\chi_{18225}(68,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{799}{972}\right)\)	\(e\left(\frac{313}{486}\right)\)	\(e\left(\frac{121}{972}\right)\)	\(e\left(\frac{151}{324}\right)\)	\(e\left(\frac{185}{486}\right)\)	\(e\left(\frac{155}{972}\right)\)	\(e\left(\frac{230}{243}\right)\)	\(e\left(\frac{70}{243}\right)\)	\(e\left(\frac{41}{324}\right)\)	\(e\left(\frac{65}{162}\right)\)
\(\chi_{18225}(182,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{725}{972}\right)\)	\(e\left(\frac{239}{486}\right)\)	\(e\left(\frac{611}{972}\right)\)	\(e\left(\frac{77}{324}\right)\)	\(e\left(\frac{163}{486}\right)\)	\(e\left(\frac{373}{972}\right)\)	\(e\left(\frac{91}{243}\right)\)	\(e\left(\frac{239}{243}\right)\)	\(e\left(\frac{199}{324}\right)\)	\(e\left(\frac{31}{162}\right)\)
\(\chi_{18225}(218,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{972}\right)\)	\(e\left(\frac{11}{486}\right)\)	\(e\left(\frac{689}{972}\right)\)	\(e\left(\frac{11}{324}\right)\)	\(e\left(\frac{463}{486}\right)\)	\(e\left(\frac{7}{972}\right)\)	\(e\left(\frac{175}{243}\right)\)	\(e\left(\frac{11}{243}\right)\)	\(e\left(\frac{121}{324}\right)\)	\(e\left(\frac{97}{162}\right)\)
\(\chi_{18225}(257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{709}{972}\right)\)	\(e\left(\frac{223}{486}\right)\)	\(e\left(\frac{139}{972}\right)\)	\(e\left(\frac{61}{324}\right)\)	\(e\left(\frac{329}{486}\right)\)	\(e\left(\frac{893}{972}\right)\)	\(e\left(\frac{212}{243}\right)\)	\(e\left(\frac{223}{243}\right)\)	\(e\left(\frac{23}{324}\right)\)	\(e\left(\frac{155}{162}\right)\)
\(\chi_{18225}(293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{499}{972}\right)\)	\(e\left(\frac{13}{486}\right)\)	\(e\left(\frac{505}{972}\right)\)	\(e\left(\frac{175}{324}\right)\)	\(e\left(\frac{17}{486}\right)\)	\(e\left(\frac{671}{972}\right)\)	\(e\left(\frac{8}{243}\right)\)	\(e\left(\frac{13}{243}\right)\)	\(e\left(\frac{305}{324}\right)\)	\(e\left(\frac{41}{162}\right)\)
\(\chi_{18225}(407,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{353}{972}\right)\)	\(e\left(\frac{353}{486}\right)\)	\(e\left(\frac{815}{972}\right)\)	\(e\left(\frac{29}{324}\right)\)	\(e\left(\frac{13}{486}\right)\)	\(e\left(\frac{313}{972}\right)\)	\(e\left(\frac{49}{243}\right)\)	\(e\left(\frac{110}{243}\right)\)	\(e\left(\frac{319}{324}\right)\)	\(e\left(\frac{79}{162}\right)\)
\(\chi_{18225}(443,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{503}{972}\right)\)	\(e\left(\frac{17}{486}\right)\)	\(e\left(\frac{137}{972}\right)\)	\(e\left(\frac{179}{324}\right)\)	\(e\left(\frac{97}{486}\right)\)	\(e\left(\frac{55}{972}\right)\)	\(e\left(\frac{160}{243}\right)\)	\(e\left(\frac{17}{243}\right)\)	\(e\left(\frac{25}{324}\right)\)	\(e\left(\frac{91}{162}\right)\)
\(\chi_{18225}(482,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{972}\right)\)	\(e\left(\frac{85}{486}\right)\)	\(e\left(\frac{199}{972}\right)\)	\(e\left(\frac{85}{324}\right)\)	\(e\left(\frac{485}{486}\right)\)	\(e\left(\frac{761}{972}\right)\)	\(e\left(\frac{71}{243}\right)\)	\(e\left(\frac{85}{243}\right)\)	\(e\left(\frac{287}{324}\right)\)	\(e\left(\frac{131}{162}\right)\)
\(\chi_{18225}(518,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{972}\right)\)	\(e\left(\frac{91}{486}\right)\)	\(e\left(\frac{133}{972}\right)\)	\(e\left(\frac{91}{324}\right)\)	\(e\left(\frac{119}{486}\right)\)	\(e\left(\frac{323}{972}\right)\)	\(e\left(\frac{56}{243}\right)\)	\(e\left(\frac{91}{243}\right)\)	\(e\left(\frac{29}{324}\right)\)	\(e\left(\frac{125}{162}\right)\)
\(\chi_{18225}(632,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{521}{972}\right)\)	\(e\left(\frac{35}{486}\right)\)	\(e\left(\frac{911}{972}\right)\)	\(e\left(\frac{197}{324}\right)\)	\(e\left(\frac{457}{486}\right)\)	\(e\left(\frac{685}{972}\right)\)	\(e\left(\frac{115}{243}\right)\)	\(e\left(\frac{35}{243}\right)\)	\(e\left(\frac{223}{324}\right)\)	\(e\left(\frac{73}{162}\right)\)
\(\chi_{18225}(668,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{563}{972}\right)\)	\(e\left(\frac{77}{486}\right)\)	\(e\left(\frac{449}{972}\right)\)	\(e\left(\frac{239}{324}\right)\)	\(e\left(\frac{325}{486}\right)\)	\(e\left(\frac{535}{972}\right)\)	\(e\left(\frac{10}{243}\right)\)	\(e\left(\frac{77}{243}\right)\)	\(e\left(\frac{37}{324}\right)\)	\(e\left(\frac{31}{162}\right)\)
\(\chi_{18225}(707,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{325}{972}\right)\)	\(e\left(\frac{325}{486}\right)\)	\(e\left(\frac{475}{972}\right)\)	\(e\left(\frac{1}{324}\right)\)	\(e\left(\frac{425}{486}\right)\)	\(e\left(\frac{737}{972}\right)\)	\(e\left(\frac{200}{243}\right)\)	\(e\left(\frac{82}{243}\right)\)	\(e\left(\frac{11}{324}\right)\)	\(e\left(\frac{53}{162}\right)\)
\(\chi_{18225}(743,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{547}{972}\right)\)	\(e\left(\frac{61}{486}\right)\)	\(e\left(\frac{949}{972}\right)\)	\(e\left(\frac{223}{324}\right)\)	\(e\left(\frac{5}{486}\right)\)	\(e\left(\frac{83}{972}\right)\)	\(e\left(\frac{131}{243}\right)\)	\(e\left(\frac{61}{243}\right)\)	\(e\left(\frac{185}{324}\right)\)	\(e\left(\frac{155}{162}\right)\)
\(\chi_{18225}(857,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{257}{972}\right)\)	\(e\left(\frac{257}{486}\right)\)	\(e\left(\frac{899}{972}\right)\)	\(e\left(\frac{257}{324}\right)\)	\(e\left(\frac{37}{486}\right)\)	\(e\left(\frac{517}{972}\right)\)	\(e\left(\frac{46}{243}\right)\)	\(e\left(\frac{14}{243}\right)\)	\(e\left(\frac{235}{324}\right)\)	\(e\left(\frac{13}{162}\right)\)
\(\chi_{18225}(893,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{972}\right)\)	\(e\left(\frac{191}{486}\right)\)	\(e\left(\frac{653}{972}\right)\)	\(e\left(\frac{191}{324}\right)\)	\(e\left(\frac{175}{486}\right)\)	\(e\left(\frac{475}{972}\right)\)	\(e\left(\frac{211}{243}\right)\)	\(e\left(\frac{191}{243}\right)\)	\(e\left(\frac{157}{324}\right)\)	\(e\left(\frac{79}{162}\right)\)
\(\chi_{18225}(932,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{457}{972}\right)\)	\(e\left(\frac{457}{486}\right)\)	\(e\left(\frac{967}{972}\right)\)	\(e\left(\frac{133}{324}\right)\)	\(e\left(\frac{149}{486}\right)\)	\(e\left(\frac{821}{972}\right)\)	\(e\left(\frac{113}{243}\right)\)	\(e\left(\frac{214}{243}\right)\)	\(e\left(\frac{167}{324}\right)\)	\(e\left(\frac{83}{162}\right)\)
\(\chi_{18225}(968,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{895}{972}\right)\)	\(e\left(\frac{409}{486}\right)\)	\(e\left(\frac{37}{972}\right)\)	\(e\left(\frac{247}{324}\right)\)	\(e\left(\frac{161}{486}\right)\)	\(e\left(\frac{923}{972}\right)\)	\(e\left(\frac{233}{243}\right)\)	\(e\left(\frac{166}{243}\right)\)	\(e\left(\frac{125}{324}\right)\)	\(e\left(\frac{131}{162}\right)\)
\(\chi_{18225}(1082,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{533}{972}\right)\)	\(e\left(\frac{47}{486}\right)\)	\(e\left(\frac{779}{972}\right)\)	\(e\left(\frac{209}{324}\right)\)	\(e\left(\frac{211}{486}\right)\)	\(e\left(\frac{781}{972}\right)\)	\(e\left(\frac{85}{243}\right)\)	\(e\left(\frac{47}{243}\right)\)	\(e\left(\frac{31}{324}\right)\)	\(e\left(\frac{61}{162}\right)\)
\(\chi_{18225}(1118,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{359}{972}\right)\)	\(e\left(\frac{359}{486}\right)\)	\(e\left(\frac{749}{972}\right)\)	\(e\left(\frac{35}{324}\right)\)	\(e\left(\frac{133}{486}\right)\)	\(e\left(\frac{847}{972}\right)\)	\(e\left(\frac{34}{243}\right)\)	\(e\left(\frac{116}{243}\right)\)	\(e\left(\frac{61}{324}\right)\)	\(e\left(\frac{73}{162}\right)\)
\(\chi_{18225}(1157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{481}{972}\right)\)	\(e\left(\frac{481}{486}\right)\)	\(e\left(\frac{703}{972}\right)\)	\(e\left(\frac{157}{324}\right)\)	\(e\left(\frac{143}{486}\right)\)	\(e\left(\frac{41}{972}\right)\)	\(e\left(\frac{53}{243}\right)\)	\(e\left(\frac{238}{243}\right)\)	\(e\left(\frac{107}{324}\right)\)	\(e\left(\frac{59}{162}\right)\)
\(\chi_{18225}(1193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{972}\right)\)	\(e\left(\frac{163}{486}\right)\)	\(e\left(\frac{313}{972}\right)\)	\(e\left(\frac{163}{324}\right)\)	\(e\left(\frac{101}{486}\right)\)	\(e\left(\frac{899}{972}\right)\)	\(e\left(\frac{119}{243}\right)\)	\(e\left(\frac{163}{243}\right)\)	\(e\left(\frac{173}{324}\right)\)	\(e\left(\frac{53}{162}\right)\)
\(\chi_{18225}(1307,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{377}{972}\right)\)	\(e\left(\frac{377}{486}\right)\)	\(e\left(\frac{551}{972}\right)\)	\(e\left(\frac{53}{324}\right)\)	\(e\left(\frac{7}{486}\right)\)	\(e\left(\frac{505}{972}\right)\)	\(e\left(\frac{232}{243}\right)\)	\(e\left(\frac{134}{243}\right)\)	\(e\left(\frac{259}{324}\right)\)	\(e\left(\frac{55}{162}\right)\)
\(\chi_{18225}(1343,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{972}\right)\)	\(e\left(\frac{95}{486}\right)\)	\(e\left(\frac{737}{972}\right)\)	\(e\left(\frac{95}{324}\right)\)	\(e\left(\frac{199}{486}\right)\)	\(e\left(\frac{679}{972}\right)\)	\(e\left(\frac{208}{243}\right)\)	\(e\left(\frac{95}{243}\right)\)	\(e\left(\frac{73}{324}\right)\)	\(e\left(\frac{13}{162}\right)\)
\(\chi_{18225}(1382,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{397}{972}\right)\)	\(e\left(\frac{397}{486}\right)\)	\(e\left(\frac{655}{972}\right)\)	\(e\left(\frac{73}{324}\right)\)	\(e\left(\frac{407}{486}\right)\)	\(e\left(\frac{341}{972}\right)\)	\(e\left(\frac{20}{243}\right)\)	\(e\left(\frac{154}{243}\right)\)	\(e\left(\frac{155}{324}\right)\)	\(e\left(\frac{143}{162}\right)\)
\(\chi_{18225}(1418,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{295}{972}\right)\)	\(e\left(\frac{295}{486}\right)\)	\(e\left(\frac{805}{972}\right)\)	\(e\left(\frac{295}{324}\right)\)	\(e\left(\frac{311}{486}\right)\)	\(e\left(\frac{11}{972}\right)\)	\(e\left(\frac{32}{243}\right)\)	\(e\left(\frac{52}{243}\right)\)	\(e\left(\frac{5}{324}\right)\)	\(e\left(\frac{83}{162}\right)\)
\(\chi_{18225}(1532,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{761}{972}\right)\)	\(e\left(\frac{275}{486}\right)\)	\(e\left(\frac{215}{972}\right)\)	\(e\left(\frac{113}{324}\right)\)	\(e\left(\frac{397}{486}\right)\)	\(e\left(\frac{661}{972}\right)\)	\(e\left(\frac{1}{243}\right)\)	\(e\left(\frac{32}{243}\right)\)	\(e\left(\frac{271}{324}\right)\)	\(e\left(\frac{157}{162}\right)\)

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First 27 of 324 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.cl
Modulus	$18225$
Conductor	$3645$
Order	$972$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(18225\)
Conductor:	\(3645\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(972\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 3645.bj	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)