LMFDB - Dirichlet character orbit 18225.ce

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(18225, base_ring=CyclotomicField(486)) M = H._module chi = DirichletCharacter(H, M([302,243])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(49,18225)) 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:	$486$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 3645.bh	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{243})$
Fixed field:	Number field defined by a degree 486 polynomial (not computed)

First 31 of 162 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{18225}(49,\cdot)$	$1$	$1$	$e\left(\frac{59}{486}\right)$	$e\left(\frac{59}{243}\right)$	$e\left(\frac{161}{486}\right)$	$e\left(\frac{59}{162}\right)$	$e\left(\frac{208}{243}\right)$	$e\left(\frac{391}{486}\right)$	$e\left(\frac{110}{243}\right)$	$e\left(\frac{118}{243}\right)$	$e\left(\frac{1}{162}\right)$	$e\left(\frac{49}{81}\right)$
$\chi_{18225}(124,\cdot)$	$1$	$1$	$e\left(\frac{103}{486}\right)$	$e\left(\frac{103}{243}\right)$	$e\left(\frac{1}{486}\right)$	$e\left(\frac{103}{162}\right)$	$e\left(\frac{116}{243}\right)$	$e\left(\frac{419}{486}\right)$	$e\left(\frac{52}{243}\right)$	$e\left(\frac{206}{243}\right)$	$e\left(\frac{161}{162}\right)$	$e\left(\frac{32}{81}\right)$
$\chi_{18225}(274,\cdot)$	$1$	$1$	$e\left(\frac{263}{486}\right)$	$e\left(\frac{20}{243}\right)$	$e\left(\frac{347}{486}\right)$	$e\left(\frac{101}{162}\right)$	$e\left(\frac{157}{243}\right)$	$e\left(\frac{79}{486}\right)$	$e\left(\frac{62}{243}\right)$	$e\left(\frac{40}{243}\right)$	$e\left(\frac{139}{162}\right)$	$e\left(\frac{7}{81}\right)$
$\chi_{18225}(349,\cdot)$	$1$	$1$	$e\left(\frac{343}{486}\right)$	$e\left(\frac{100}{243}\right)$	$e\left(\frac{277}{486}\right)$	$e\left(\frac{19}{162}\right)$	$e\left(\frac{56}{243}\right)$	$e\left(\frac{395}{486}\right)$	$e\left(\frac{67}{243}\right)$	$e\left(\frac{200}{243}\right)$	$e\left(\frac{47}{162}\right)$	$e\left(\frac{35}{81}\right)$
$\chi_{18225}(499,\cdot)$	$1$	$1$	$e\left(\frac{413}{486}\right)$	$e\left(\frac{170}{243}\right)$	$e\left(\frac{155}{486}\right)$	$e\left(\frac{89}{162}\right)$	$e\left(\frac{241}{243}\right)$	$e\left(\frac{307}{486}\right)$	$e\left(\frac{41}{243}\right)$	$e\left(\frac{97}{243}\right)$	$e\left(\frac{7}{162}\right)$	$e\left(\frac{19}{81}\right)$
$\chi_{18225}(574,\cdot)$	$1$	$1$	$e\left(\frac{367}{486}\right)$	$e\left(\frac{124}{243}\right)$	$e\left(\frac{13}{486}\right)$	$e\left(\frac{43}{162}\right)$	$e\left(\frac{50}{243}\right)$	$e\left(\frac{101}{486}\right)$	$e\left(\frac{190}{243}\right)$	$e\left(\frac{5}{243}\right)$	$e\left(\frac{149}{162}\right)$	$e\left(\frac{11}{81}\right)$
$\chi_{18225}(724,\cdot)$	$1$	$1$	$e\left(\frac{23}{486}\right)$	$e\left(\frac{23}{243}\right)$	$e\left(\frac{71}{486}\right)$	$e\left(\frac{23}{162}\right)$	$e\left(\frac{217}{243}\right)$	$e\left(\frac{103}{486}\right)$	$e\left(\frac{47}{243}\right)$	$e\left(\frac{46}{243}\right)$	$e\left(\frac{91}{162}\right)$	$e\left(\frac{4}{81}\right)$
$\chi_{18225}(799,\cdot)$	$1$	$1$	$e\left(\frac{175}{486}\right)$	$e\left(\frac{175}{243}\right)$	$e\left(\frac{181}{486}\right)$	$e\left(\frac{13}{162}\right)$	$e\left(\frac{98}{243}\right)$	$e\left(\frac{23}{486}\right)$	$e\left(\frac{178}{243}\right)$	$e\left(\frac{107}{243}\right)$	$e\left(\frac{143}{162}\right)$	$e\left(\frac{41}{81}\right)$
$\chi_{18225}(949,\cdot)$	$1$	$1$	$e\left(\frac{65}{486}\right)$	$e\left(\frac{65}{243}\right)$	$e\left(\frac{95}{486}\right)$	$e\left(\frac{65}{162}\right)$	$e\left(\frac{85}{243}\right)$	$e\left(\frac{439}{486}\right)$	$e\left(\frac{80}{243}\right)$	$e\left(\frac{130}{243}\right)$	$e\left(\frac{67}{162}\right)$	$e\left(\frac{43}{81}\right)$
$\chi_{18225}(1024,\cdot)$	$1$	$1$	$e\left(\frac{253}{486}\right)$	$e\left(\frac{10}{243}\right)$	$e\left(\frac{295}{486}\right)$	$e\left(\frac{91}{162}\right)$	$e\left(\frac{200}{243}\right)$	$e\left(\frac{161}{486}\right)$	$e\left(\frac{31}{243}\right)$	$e\left(\frac{20}{243}\right)$	$e\left(\frac{29}{162}\right)$	$e\left(\frac{44}{81}\right)$
$\chi_{18225}(1174,\cdot)$	$1$	$1$	$e\left(\frac{53}{486}\right)$	$e\left(\frac{53}{243}\right)$	$e\left(\frac{227}{486}\right)$	$e\left(\frac{53}{162}\right)$	$e\left(\frac{88}{243}\right)$	$e\left(\frac{343}{486}\right)$	$e\left(\frac{140}{243}\right)$	$e\left(\frac{106}{243}\right)$	$e\left(\frac{97}{162}\right)$	$e\left(\frac{55}{81}\right)$
$\chi_{18225}(1249,\cdot)$	$1$	$1$	$e\left(\frac{115}{486}\right)$	$e\left(\frac{115}{243}\right)$	$e\left(\frac{355}{486}\right)$	$e\left(\frac{115}{162}\right)$	$e\left(\frac{113}{243}\right)$	$e\left(\frac{29}{486}\right)$	$e\left(\frac{235}{243}\right)$	$e\left(\frac{230}{243}\right)$	$e\left(\frac{131}{162}\right)$	$e\left(\frac{20}{81}\right)$
$\chi_{18225}(1399,\cdot)$	$1$	$1$	$e\left(\frac{473}{486}\right)$	$e\left(\frac{230}{243}\right)$	$e\left(\frac{467}{486}\right)$	$e\left(\frac{149}{162}\right)$	$e\left(\frac{226}{243}\right)$	$e\left(\frac{301}{486}\right)$	$e\left(\frac{227}{243}\right)$	$e\left(\frac{217}{243}\right)$	$e\left(\frac{19}{162}\right)$	$e\left(\frac{40}{81}\right)$
$\chi_{18225}(1474,\cdot)$	$1$	$1$	$e\left(\frac{247}{486}\right)$	$e\left(\frac{4}{243}\right)$	$e\left(\frac{361}{486}\right)$	$e\left(\frac{85}{162}\right)$	$e\left(\frac{80}{243}\right)$	$e\left(\frac{113}{486}\right)$	$e\left(\frac{61}{243}\right)$	$e\left(\frac{8}{243}\right)$	$e\left(\frac{125}{162}\right)$	$e\left(\frac{50}{81}\right)$
$\chi_{18225}(1624,\cdot)$	$1$	$1$	$e\left(\frac{353}{486}\right)$	$e\left(\frac{110}{243}\right)$	$e\left(\frac{329}{486}\right)$	$e\left(\frac{29}{162}\right)$	$e\left(\frac{13}{243}\right)$	$e\left(\frac{313}{486}\right)$	$e\left(\frac{98}{243}\right)$	$e\left(\frac{220}{243}\right)$	$e\left(\frac{157}{162}\right)$	$e\left(\frac{79}{81}\right)$
$\chi_{18225}(1699,\cdot)$	$1$	$1$	$e\left(\frac{163}{486}\right)$	$e\left(\frac{163}{243}\right)$	$e\left(\frac{313}{486}\right)$	$e\left(\frac{1}{162}\right)$	$e\left(\frac{101}{243}\right)$	$e\left(\frac{413}{486}\right)$	$e\left(\frac{238}{243}\right)$	$e\left(\frac{83}{243}\right)$	$e\left(\frac{11}{162}\right)$	$e\left(\frac{53}{81}\right)$
$\chi_{18225}(1849,\cdot)$	$1$	$1$	$e\left(\frac{179}{486}\right)$	$e\left(\frac{179}{243}\right)$	$e\left(\frac{299}{486}\right)$	$e\left(\frac{17}{162}\right)$	$e\left(\frac{178}{243}\right)$	$e\left(\frac{379}{486}\right)$	$e\left(\frac{239}{243}\right)$	$e\left(\frac{115}{243}\right)$	$e\left(\frac{25}{162}\right)$	$e\left(\frac{10}{81}\right)$
$\chi_{18225}(1924,\cdot)$	$1$	$1$	$e\left(\frac{349}{486}\right)$	$e\left(\frac{106}{243}\right)$	$e\left(\frac{211}{486}\right)$	$e\left(\frac{25}{162}\right)$	$e\left(\frac{176}{243}\right)$	$e\left(\frac{443}{486}\right)$	$e\left(\frac{37}{243}\right)$	$e\left(\frac{212}{243}\right)$	$e\left(\frac{113}{162}\right)$	$e\left(\frac{29}{81}\right)$
$\chi_{18225}(2074,\cdot)$	$1$	$1$	$e\left(\frac{437}{486}\right)$	$e\left(\frac{194}{243}\right)$	$e\left(\frac{377}{486}\right)$	$e\left(\frac{113}{162}\right)$	$e\left(\frac{235}{243}\right)$	$e\left(\frac{13}{486}\right)$	$e\left(\frac{164}{243}\right)$	$e\left(\frac{145}{243}\right)$	$e\left(\frac{109}{162}\right)$	$e\left(\frac{76}{81}\right)$
$\chi_{18225}(2149,\cdot)$	$1$	$1$	$e\left(\frac{319}{486}\right)$	$e\left(\frac{76}{243}\right)$	$e\left(\frac{55}{486}\right)$	$e\left(\frac{157}{162}\right)$	$e\left(\frac{62}{243}\right)$	$e\left(\frac{203}{486}\right)$	$e\left(\frac{187}{243}\right)$	$e\left(\frac{152}{243}\right)$	$e\left(\frac{107}{162}\right)$	$e\left(\frac{59}{81}\right)$
$\chi_{18225}(2299,\cdot)$	$1$	$1$	$e\left(\frac{155}{486}\right)$	$e\left(\frac{155}{243}\right)$	$e\left(\frac{77}{486}\right)$	$e\left(\frac{155}{162}\right)$	$e\left(\frac{184}{243}\right)$	$e\left(\frac{187}{486}\right)$	$e\left(\frac{116}{243}\right)$	$e\left(\frac{67}{243}\right)$	$e\left(\frac{85}{162}\right)$	$e\left(\frac{34}{81}\right)$
$\chi_{18225}(2374,\cdot)$	$1$	$1$	$e\left(\frac{73}{486}\right)$	$e\left(\frac{73}{243}\right)$	$e\left(\frac{331}{486}\right)$	$e\left(\frac{73}{162}\right)$	$e\left(\frac{2}{243}\right)$	$e\left(\frac{179}{486}\right)$	$e\left(\frac{202}{243}\right)$	$e\left(\frac{146}{243}\right)$	$e\left(\frac{155}{162}\right)$	$e\left(\frac{62}{81}\right)$
$\chi_{18225}(2524,\cdot)$	$1$	$1$	$e\left(\frac{305}{486}\right)$	$e\left(\frac{62}{243}\right)$	$e\left(\frac{371}{486}\right)$	$e\left(\frac{143}{162}\right)$	$e\left(\frac{25}{243}\right)$	$e\left(\frac{415}{486}\right)$	$e\left(\frac{95}{243}\right)$	$e\left(\frac{124}{243}\right)$	$e\left(\frac{115}{162}\right)$	$e\left(\frac{46}{81}\right)$
$\chi_{18225}(2599,\cdot)$	$1$	$1$	$e\left(\frac{97}{486}\right)$	$e\left(\frac{97}{243}\right)$	$e\left(\frac{67}{486}\right)$	$e\left(\frac{97}{162}\right)$	$e\left(\frac{239}{243}\right)$	$e\left(\frac{371}{486}\right)$	$e\left(\frac{82}{243}\right)$	$e\left(\frac{194}{243}\right)$	$e\left(\frac{95}{162}\right)$	$e\left(\frac{38}{81}\right)$
$\chi_{18225}(2749,\cdot)$	$1$	$1$	$e\left(\frac{401}{486}\right)$	$e\left(\frac{158}{243}\right)$	$e\left(\frac{287}{486}\right)$	$e\left(\frac{77}{162}\right)$	$e\left(\frac{1}{243}\right)$	$e\left(\frac{211}{486}\right)$	$e\left(\frac{101}{243}\right)$	$e\left(\frac{73}{243}\right)$	$e\left(\frac{37}{162}\right)$	$e\left(\frac{31}{81}\right)$
$\chi_{18225}(2824,\cdot)$	$1$	$1$	$e\left(\frac{391}{486}\right)$	$e\left(\frac{148}{243}\right)$	$e\left(\frac{235}{486}\right)$	$e\left(\frac{67}{162}\right)$	$e\left(\frac{44}{243}\right)$	$e\left(\frac{293}{486}\right)$	$e\left(\frac{70}{243}\right)$	$e\left(\frac{53}{243}\right)$	$e\left(\frac{89}{162}\right)$	$e\left(\frac{68}{81}\right)$
$\chi_{18225}(2974,\cdot)$	$1$	$1$	$e\left(\frac{443}{486}\right)$	$e\left(\frac{200}{243}\right)$	$e\left(\frac{311}{486}\right)$	$e\left(\frac{119}{162}\right)$	$e\left(\frac{112}{243}\right)$	$e\left(\frac{61}{486}\right)$	$e\left(\frac{134}{243}\right)$	$e\left(\frac{157}{243}\right)$	$e\left(\frac{13}{162}\right)$	$e\left(\frac{70}{81}\right)$
$\chi_{18225}(3049,\cdot)$	$1$	$1$	$e\left(\frac{469}{486}\right)$	$e\left(\frac{226}{243}\right)$	$e\left(\frac{349}{486}\right)$	$e\left(\frac{145}{162}\right)$	$e\left(\frac{146}{243}\right)$	$e\left(\frac{431}{486}\right)$	$e\left(\frac{166}{243}\right)$	$e\left(\frac{209}{243}\right)$	$e\left(\frac{137}{162}\right)$	$e\left(\frac{71}{81}\right)$
$\chi_{18225}(3199,\cdot)$	$1$	$1$	$e\left(\frac{431}{486}\right)$	$e\left(\frac{188}{243}\right)$	$e\left(\frac{443}{486}\right)$	$e\left(\frac{107}{162}\right)$	$e\left(\frac{115}{243}\right)$	$e\left(\frac{451}{486}\right)$	$e\left(\frac{194}{243}\right)$	$e\left(\frac{133}{243}\right)$	$e\left(\frac{43}{162}\right)$	$e\left(\frac{1}{81}\right)$
$\chi_{18225}(3274,\cdot)$	$1$	$1$	$e\left(\frac{331}{486}\right)$	$e\left(\frac{88}{243}\right)$	$e\left(\frac{409}{486}\right)$	$e\left(\frac{7}{162}\right)$	$e\left(\frac{59}{243}\right)$	$e\left(\frac{299}{486}\right)$	$e\left(\frac{127}{243}\right)$	$e\left(\frac{176}{243}\right)$	$e\left(\frac{77}{162}\right)$	$e\left(\frac{47}{81}\right)$
$\chi_{18225}(3424,\cdot)$	$1$	$1$	$e\left(\frac{365}{486}\right)$	$e\left(\frac{122}{243}\right)$	$e\left(\frac{197}{486}\right)$	$e\left(\frac{41}{162}\right)$	$e\left(\frac{10}{243}\right)$	$e\left(\frac{409}{486}\right)$	$e\left(\frac{38}{243}\right)$	$e\left(\frac{1}{243}\right)$	$e\left(\frac{127}{162}\right)$	$e\left(\frac{67}{81}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{18225}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{486}\right)\)	\(e\left(\frac{59}{243}\right)\)	\(e\left(\frac{161}{486}\right)\)	\(e\left(\frac{59}{162}\right)\)	\(e\left(\frac{208}{243}\right)\)	\(e\left(\frac{391}{486}\right)\)	\(e\left(\frac{110}{243}\right)\)	\(e\left(\frac{118}{243}\right)\)	\(e\left(\frac{1}{162}\right)\)	\(e\left(\frac{49}{81}\right)\)
\(\chi_{18225}(124,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{486}\right)\)	\(e\left(\frac{103}{243}\right)\)	\(e\left(\frac{1}{486}\right)\)	\(e\left(\frac{103}{162}\right)\)	\(e\left(\frac{116}{243}\right)\)	\(e\left(\frac{419}{486}\right)\)	\(e\left(\frac{52}{243}\right)\)	\(e\left(\frac{206}{243}\right)\)	\(e\left(\frac{161}{162}\right)\)	\(e\left(\frac{32}{81}\right)\)
\(\chi_{18225}(274,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{263}{486}\right)\)	\(e\left(\frac{20}{243}\right)\)	\(e\left(\frac{347}{486}\right)\)	\(e\left(\frac{101}{162}\right)\)	\(e\left(\frac{157}{243}\right)\)	\(e\left(\frac{79}{486}\right)\)	\(e\left(\frac{62}{243}\right)\)	\(e\left(\frac{40}{243}\right)\)	\(e\left(\frac{139}{162}\right)\)	\(e\left(\frac{7}{81}\right)\)
\(\chi_{18225}(349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{343}{486}\right)\)	\(e\left(\frac{100}{243}\right)\)	\(e\left(\frac{277}{486}\right)\)	\(e\left(\frac{19}{162}\right)\)	\(e\left(\frac{56}{243}\right)\)	\(e\left(\frac{395}{486}\right)\)	\(e\left(\frac{67}{243}\right)\)	\(e\left(\frac{200}{243}\right)\)	\(e\left(\frac{47}{162}\right)\)	\(e\left(\frac{35}{81}\right)\)
\(\chi_{18225}(499,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{413}{486}\right)\)	\(e\left(\frac{170}{243}\right)\)	\(e\left(\frac{155}{486}\right)\)	\(e\left(\frac{89}{162}\right)\)	\(e\left(\frac{241}{243}\right)\)	\(e\left(\frac{307}{486}\right)\)	\(e\left(\frac{41}{243}\right)\)	\(e\left(\frac{97}{243}\right)\)	\(e\left(\frac{7}{162}\right)\)	\(e\left(\frac{19}{81}\right)\)
\(\chi_{18225}(574,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{367}{486}\right)\)	\(e\left(\frac{124}{243}\right)\)	\(e\left(\frac{13}{486}\right)\)	\(e\left(\frac{43}{162}\right)\)	\(e\left(\frac{50}{243}\right)\)	\(e\left(\frac{101}{486}\right)\)	\(e\left(\frac{190}{243}\right)\)	\(e\left(\frac{5}{243}\right)\)	\(e\left(\frac{149}{162}\right)\)	\(e\left(\frac{11}{81}\right)\)
\(\chi_{18225}(724,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{486}\right)\)	\(e\left(\frac{23}{243}\right)\)	\(e\left(\frac{71}{486}\right)\)	\(e\left(\frac{23}{162}\right)\)	\(e\left(\frac{217}{243}\right)\)	\(e\left(\frac{103}{486}\right)\)	\(e\left(\frac{47}{243}\right)\)	\(e\left(\frac{46}{243}\right)\)	\(e\left(\frac{91}{162}\right)\)	\(e\left(\frac{4}{81}\right)\)
\(\chi_{18225}(799,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{175}{486}\right)\)	\(e\left(\frac{175}{243}\right)\)	\(e\left(\frac{181}{486}\right)\)	\(e\left(\frac{13}{162}\right)\)	\(e\left(\frac{98}{243}\right)\)	\(e\left(\frac{23}{486}\right)\)	\(e\left(\frac{178}{243}\right)\)	\(e\left(\frac{107}{243}\right)\)	\(e\left(\frac{143}{162}\right)\)	\(e\left(\frac{41}{81}\right)\)
\(\chi_{18225}(949,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{486}\right)\)	\(e\left(\frac{65}{243}\right)\)	\(e\left(\frac{95}{486}\right)\)	\(e\left(\frac{65}{162}\right)\)	\(e\left(\frac{85}{243}\right)\)	\(e\left(\frac{439}{486}\right)\)	\(e\left(\frac{80}{243}\right)\)	\(e\left(\frac{130}{243}\right)\)	\(e\left(\frac{67}{162}\right)\)	\(e\left(\frac{43}{81}\right)\)
\(\chi_{18225}(1024,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{253}{486}\right)\)	\(e\left(\frac{10}{243}\right)\)	\(e\left(\frac{295}{486}\right)\)	\(e\left(\frac{91}{162}\right)\)	\(e\left(\frac{200}{243}\right)\)	\(e\left(\frac{161}{486}\right)\)	\(e\left(\frac{31}{243}\right)\)	\(e\left(\frac{20}{243}\right)\)	\(e\left(\frac{29}{162}\right)\)	\(e\left(\frac{44}{81}\right)\)
\(\chi_{18225}(1174,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{486}\right)\)	\(e\left(\frac{53}{243}\right)\)	\(e\left(\frac{227}{486}\right)\)	\(e\left(\frac{53}{162}\right)\)	\(e\left(\frac{88}{243}\right)\)	\(e\left(\frac{343}{486}\right)\)	\(e\left(\frac{140}{243}\right)\)	\(e\left(\frac{106}{243}\right)\)	\(e\left(\frac{97}{162}\right)\)	\(e\left(\frac{55}{81}\right)\)
\(\chi_{18225}(1249,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{486}\right)\)	\(e\left(\frac{115}{243}\right)\)	\(e\left(\frac{355}{486}\right)\)	\(e\left(\frac{115}{162}\right)\)	\(e\left(\frac{113}{243}\right)\)	\(e\left(\frac{29}{486}\right)\)	\(e\left(\frac{235}{243}\right)\)	\(e\left(\frac{230}{243}\right)\)	\(e\left(\frac{131}{162}\right)\)	\(e\left(\frac{20}{81}\right)\)
\(\chi_{18225}(1399,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{473}{486}\right)\)	\(e\left(\frac{230}{243}\right)\)	\(e\left(\frac{467}{486}\right)\)	\(e\left(\frac{149}{162}\right)\)	\(e\left(\frac{226}{243}\right)\)	\(e\left(\frac{301}{486}\right)\)	\(e\left(\frac{227}{243}\right)\)	\(e\left(\frac{217}{243}\right)\)	\(e\left(\frac{19}{162}\right)\)	\(e\left(\frac{40}{81}\right)\)
\(\chi_{18225}(1474,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{247}{486}\right)\)	\(e\left(\frac{4}{243}\right)\)	\(e\left(\frac{361}{486}\right)\)	\(e\left(\frac{85}{162}\right)\)	\(e\left(\frac{80}{243}\right)\)	\(e\left(\frac{113}{486}\right)\)	\(e\left(\frac{61}{243}\right)\)	\(e\left(\frac{8}{243}\right)\)	\(e\left(\frac{125}{162}\right)\)	\(e\left(\frac{50}{81}\right)\)
\(\chi_{18225}(1624,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{353}{486}\right)\)	\(e\left(\frac{110}{243}\right)\)	\(e\left(\frac{329}{486}\right)\)	\(e\left(\frac{29}{162}\right)\)	\(e\left(\frac{13}{243}\right)\)	\(e\left(\frac{313}{486}\right)\)	\(e\left(\frac{98}{243}\right)\)	\(e\left(\frac{220}{243}\right)\)	\(e\left(\frac{157}{162}\right)\)	\(e\left(\frac{79}{81}\right)\)
\(\chi_{18225}(1699,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{486}\right)\)	\(e\left(\frac{163}{243}\right)\)	\(e\left(\frac{313}{486}\right)\)	\(e\left(\frac{1}{162}\right)\)	\(e\left(\frac{101}{243}\right)\)	\(e\left(\frac{413}{486}\right)\)	\(e\left(\frac{238}{243}\right)\)	\(e\left(\frac{83}{243}\right)\)	\(e\left(\frac{11}{162}\right)\)	\(e\left(\frac{53}{81}\right)\)
\(\chi_{18225}(1849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{486}\right)\)	\(e\left(\frac{179}{243}\right)\)	\(e\left(\frac{299}{486}\right)\)	\(e\left(\frac{17}{162}\right)\)	\(e\left(\frac{178}{243}\right)\)	\(e\left(\frac{379}{486}\right)\)	\(e\left(\frac{239}{243}\right)\)	\(e\left(\frac{115}{243}\right)\)	\(e\left(\frac{25}{162}\right)\)	\(e\left(\frac{10}{81}\right)\)
\(\chi_{18225}(1924,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{349}{486}\right)\)	\(e\left(\frac{106}{243}\right)\)	\(e\left(\frac{211}{486}\right)\)	\(e\left(\frac{25}{162}\right)\)	\(e\left(\frac{176}{243}\right)\)	\(e\left(\frac{443}{486}\right)\)	\(e\left(\frac{37}{243}\right)\)	\(e\left(\frac{212}{243}\right)\)	\(e\left(\frac{113}{162}\right)\)	\(e\left(\frac{29}{81}\right)\)
\(\chi_{18225}(2074,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{437}{486}\right)\)	\(e\left(\frac{194}{243}\right)\)	\(e\left(\frac{377}{486}\right)\)	\(e\left(\frac{113}{162}\right)\)	\(e\left(\frac{235}{243}\right)\)	\(e\left(\frac{13}{486}\right)\)	\(e\left(\frac{164}{243}\right)\)	\(e\left(\frac{145}{243}\right)\)	\(e\left(\frac{109}{162}\right)\)	\(e\left(\frac{76}{81}\right)\)
\(\chi_{18225}(2149,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{319}{486}\right)\)	\(e\left(\frac{76}{243}\right)\)	\(e\left(\frac{55}{486}\right)\)	\(e\left(\frac{157}{162}\right)\)	\(e\left(\frac{62}{243}\right)\)	\(e\left(\frac{203}{486}\right)\)	\(e\left(\frac{187}{243}\right)\)	\(e\left(\frac{152}{243}\right)\)	\(e\left(\frac{107}{162}\right)\)	\(e\left(\frac{59}{81}\right)\)
\(\chi_{18225}(2299,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{155}{486}\right)\)	\(e\left(\frac{155}{243}\right)\)	\(e\left(\frac{77}{486}\right)\)	\(e\left(\frac{155}{162}\right)\)	\(e\left(\frac{184}{243}\right)\)	\(e\left(\frac{187}{486}\right)\)	\(e\left(\frac{116}{243}\right)\)	\(e\left(\frac{67}{243}\right)\)	\(e\left(\frac{85}{162}\right)\)	\(e\left(\frac{34}{81}\right)\)
\(\chi_{18225}(2374,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{486}\right)\)	\(e\left(\frac{73}{243}\right)\)	\(e\left(\frac{331}{486}\right)\)	\(e\left(\frac{73}{162}\right)\)	\(e\left(\frac{2}{243}\right)\)	\(e\left(\frac{179}{486}\right)\)	\(e\left(\frac{202}{243}\right)\)	\(e\left(\frac{146}{243}\right)\)	\(e\left(\frac{155}{162}\right)\)	\(e\left(\frac{62}{81}\right)\)
\(\chi_{18225}(2524,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{305}{486}\right)\)	\(e\left(\frac{62}{243}\right)\)	\(e\left(\frac{371}{486}\right)\)	\(e\left(\frac{143}{162}\right)\)	\(e\left(\frac{25}{243}\right)\)	\(e\left(\frac{415}{486}\right)\)	\(e\left(\frac{95}{243}\right)\)	\(e\left(\frac{124}{243}\right)\)	\(e\left(\frac{115}{162}\right)\)	\(e\left(\frac{46}{81}\right)\)
\(\chi_{18225}(2599,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{486}\right)\)	\(e\left(\frac{97}{243}\right)\)	\(e\left(\frac{67}{486}\right)\)	\(e\left(\frac{97}{162}\right)\)	\(e\left(\frac{239}{243}\right)\)	\(e\left(\frac{371}{486}\right)\)	\(e\left(\frac{82}{243}\right)\)	\(e\left(\frac{194}{243}\right)\)	\(e\left(\frac{95}{162}\right)\)	\(e\left(\frac{38}{81}\right)\)
\(\chi_{18225}(2749,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{401}{486}\right)\)	\(e\left(\frac{158}{243}\right)\)	\(e\left(\frac{287}{486}\right)\)	\(e\left(\frac{77}{162}\right)\)	\(e\left(\frac{1}{243}\right)\)	\(e\left(\frac{211}{486}\right)\)	\(e\left(\frac{101}{243}\right)\)	\(e\left(\frac{73}{243}\right)\)	\(e\left(\frac{37}{162}\right)\)	\(e\left(\frac{31}{81}\right)\)
\(\chi_{18225}(2824,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{391}{486}\right)\)	\(e\left(\frac{148}{243}\right)\)	\(e\left(\frac{235}{486}\right)\)	\(e\left(\frac{67}{162}\right)\)	\(e\left(\frac{44}{243}\right)\)	\(e\left(\frac{293}{486}\right)\)	\(e\left(\frac{70}{243}\right)\)	\(e\left(\frac{53}{243}\right)\)	\(e\left(\frac{89}{162}\right)\)	\(e\left(\frac{68}{81}\right)\)
\(\chi_{18225}(2974,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{443}{486}\right)\)	\(e\left(\frac{200}{243}\right)\)	\(e\left(\frac{311}{486}\right)\)	\(e\left(\frac{119}{162}\right)\)	\(e\left(\frac{112}{243}\right)\)	\(e\left(\frac{61}{486}\right)\)	\(e\left(\frac{134}{243}\right)\)	\(e\left(\frac{157}{243}\right)\)	\(e\left(\frac{13}{162}\right)\)	\(e\left(\frac{70}{81}\right)\)
\(\chi_{18225}(3049,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{469}{486}\right)\)	\(e\left(\frac{226}{243}\right)\)	\(e\left(\frac{349}{486}\right)\)	\(e\left(\frac{145}{162}\right)\)	\(e\left(\frac{146}{243}\right)\)	\(e\left(\frac{431}{486}\right)\)	\(e\left(\frac{166}{243}\right)\)	\(e\left(\frac{209}{243}\right)\)	\(e\left(\frac{137}{162}\right)\)	\(e\left(\frac{71}{81}\right)\)
\(\chi_{18225}(3199,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{431}{486}\right)\)	\(e\left(\frac{188}{243}\right)\)	\(e\left(\frac{443}{486}\right)\)	\(e\left(\frac{107}{162}\right)\)	\(e\left(\frac{115}{243}\right)\)	\(e\left(\frac{451}{486}\right)\)	\(e\left(\frac{194}{243}\right)\)	\(e\left(\frac{133}{243}\right)\)	\(e\left(\frac{43}{162}\right)\)	\(e\left(\frac{1}{81}\right)\)
\(\chi_{18225}(3274,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{331}{486}\right)\)	\(e\left(\frac{88}{243}\right)\)	\(e\left(\frac{409}{486}\right)\)	\(e\left(\frac{7}{162}\right)\)	\(e\left(\frac{59}{243}\right)\)	\(e\left(\frac{299}{486}\right)\)	\(e\left(\frac{127}{243}\right)\)	\(e\left(\frac{176}{243}\right)\)	\(e\left(\frac{77}{162}\right)\)	\(e\left(\frac{47}{81}\right)\)
\(\chi_{18225}(3424,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{365}{486}\right)\)	\(e\left(\frac{122}{243}\right)\)	\(e\left(\frac{197}{486}\right)\)	\(e\left(\frac{41}{162}\right)\)	\(e\left(\frac{10}{243}\right)\)	\(e\left(\frac{409}{486}\right)\)	\(e\left(\frac{38}{243}\right)\)	\(e\left(\frac{1}{243}\right)\)	\(e\left(\frac{127}{162}\right)\)	\(e\left(\frac{67}{81}\right)\)

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First 31 of 162 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.ce
Modulus	$18225$
Conductor	$3645$
Order	$486$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(18225\)
Conductor:	\(3645\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(486\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 3645.bh	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)