LMFDB - Dirichlet character orbit 18225.cg

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(18225, base_ring=CyclotomicField(540)) M = H._module chi = DirichletCharacter(H, M([470,189])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(53,18225)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$18225$
Conductor:	$2025$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$540$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2025.bv	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:	$\Q(\zeta_{540})$
Fixed field:	Number field defined by a degree 540 polynomial (not computed)

First 31 of 144 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{18225}(53,\cdot)$	$1$	$1$	$e\left(\frac{119}{540}\right)$	$e\left(\frac{119}{270}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{247}{270}\right)$	$e\left(\frac{331}{540}\right)$	$e\left(\frac{121}{135}\right)$	$e\left(\frac{119}{135}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{7}{90}\right)$
$\chi_{18225}(188,\cdot)$	$1$	$1$	$e\left(\frac{403}{540}\right)$	$e\left(\frac{133}{270}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{149}{270}\right)$	$e\left(\frac{227}{540}\right)$	$e\left(\frac{32}{135}\right)$	$e\left(\frac{133}{135}\right)$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{29}{90}\right)$
$\chi_{18225}(377,\cdot)$	$1$	$1$	$e\left(\frac{77}{540}\right)$	$e\left(\frac{77}{270}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{1}{270}\right)$	$e\left(\frac{373}{540}\right)$	$e\left(\frac{118}{135}\right)$	$e\left(\frac{77}{135}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{31}{90}\right)$
$\chi_{18225}(458,\cdot)$	$1$	$1$	$e\left(\frac{431}{540}\right)$	$e\left(\frac{161}{270}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{223}{270}\right)$	$e\left(\frac{19}{540}\right)$	$e\left(\frac{124}{135}\right)$	$e\left(\frac{26}{135}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{73}{90}\right)$
$\chi_{18225}(512,\cdot)$	$1$	$1$	$e\left(\frac{253}{540}\right)$	$e\left(\frac{253}{270}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{119}{270}\right)$	$e\left(\frac{377}{540}\right)$	$e\left(\frac{2}{135}\right)$	$e\left(\frac{118}{135}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{89}{90}\right)$
$\chi_{18225}(863,\cdot)$	$1$	$1$	$e\left(\frac{203}{540}\right)$	$e\left(\frac{203}{270}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{199}{270}\right)$	$e\left(\frac{247}{540}\right)$	$e\left(\frac{127}{135}\right)$	$e\left(\frac{68}{135}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{49}{90}\right)$
$\chi_{18225}(917,\cdot)$	$1$	$1$	$e\left(\frac{241}{540}\right)$	$e\left(\frac{241}{270}\right)$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{203}{270}\right)$	$e\left(\frac{389}{540}\right)$	$e\left(\frac{59}{135}\right)$	$e\left(\frac{106}{135}\right)$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{83}{90}\right)$
$\chi_{18225}(998,\cdot)$	$1$	$1$	$e\left(\frac{487}{540}\right)$	$e\left(\frac{217}{270}\right)$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{101}{270}\right)$	$e\left(\frac{143}{540}\right)$	$e\left(\frac{38}{135}\right)$	$e\left(\frac{82}{135}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{71}{90}\right)$
$\chi_{18225}(1187,\cdot)$	$1$	$1$	$e\left(\frac{53}{540}\right)$	$e\left(\frac{53}{270}\right)$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{169}{270}\right)$	$e\left(\frac{397}{540}\right)$	$e\left(\frac{97}{135}\right)$	$e\left(\frac{53}{135}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{19}{90}\right)$
$\chi_{18225}(1322,\cdot)$	$1$	$1$	$e\left(\frac{229}{540}\right)$	$e\left(\frac{229}{270}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{17}{270}\right)$	$e\left(\frac{401}{540}\right)$	$e\left(\frac{116}{135}\right)$	$e\left(\frac{94}{135}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{77}{90}\right)$
$\chi_{18225}(1403,\cdot)$	$1$	$1$	$e\left(\frac{259}{540}\right)$	$e\left(\frac{259}{270}\right)$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{77}{270}\right)$	$e\left(\frac{371}{540}\right)$	$e\left(\frac{41}{135}\right)$	$e\left(\frac{124}{135}\right)$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{47}{90}\right)$
$\chi_{18225}(1592,\cdot)$	$1$	$1$	$e\left(\frac{41}{540}\right)$	$e\left(\frac{41}{270}\right)$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{253}{270}\right)$	$e\left(\frac{409}{540}\right)$	$e\left(\frac{19}{135}\right)$	$e\left(\frac{41}{135}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{13}{90}\right)$
$\chi_{18225}(1673,\cdot)$	$1$	$1$	$e\left(\frac{287}{540}\right)$	$e\left(\frac{17}{270}\right)$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{151}{270}\right)$	$e\left(\frac{163}{540}\right)$	$e\left(\frac{133}{135}\right)$	$e\left(\frac{17}{135}\right)$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{1}{90}\right)$
$\chi_{18225}(1727,\cdot)$	$1$	$1$	$e\left(\frac{217}{540}\right)$	$e\left(\frac{217}{270}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{101}{270}\right)$	$e\left(\frac{413}{540}\right)$	$e\left(\frac{38}{135}\right)$	$e\left(\frac{82}{135}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{71}{90}\right)$
$\chi_{18225}(1808,\cdot)$	$1$	$1$	$e\left(\frac{31}{540}\right)$	$e\left(\frac{31}{270}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{53}{270}\right)$	$e\left(\frac{59}{540}\right)$	$e\left(\frac{44}{135}\right)$	$e\left(\frac{31}{135}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{23}{90}\right)$
$\chi_{18225}(1997,\cdot)$	$1$	$1$	$e\left(\frac{29}{540}\right)$	$e\left(\frac{29}{270}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{67}{270}\right)$	$e\left(\frac{421}{540}\right)$	$e\left(\frac{76}{135}\right)$	$e\left(\frac{29}{135}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{7}{90}\right)$
$\chi_{18225}(2078,\cdot)$	$1$	$1$	$e\left(\frac{59}{540}\right)$	$e\left(\frac{59}{270}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{127}{270}\right)$	$e\left(\frac{391}{540}\right)$	$e\left(\frac{1}{135}\right)$	$e\left(\frac{59}{135}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{67}{90}\right)$
$\chi_{18225}(2213,\cdot)$	$1$	$1$	$e\left(\frac{343}{540}\right)$	$e\left(\frac{73}{270}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{29}{270}\right)$	$e\left(\frac{287}{540}\right)$	$e\left(\frac{47}{135}\right)$	$e\left(\frac{73}{135}\right)$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{89}{90}\right)$
$\chi_{18225}(2402,\cdot)$	$1$	$1$	$e\left(\frac{17}{540}\right)$	$e\left(\frac{17}{270}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{151}{270}\right)$	$e\left(\frac{433}{540}\right)$	$e\left(\frac{133}{135}\right)$	$e\left(\frac{17}{135}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{1}{90}\right)$
$\chi_{18225}(2483,\cdot)$	$1$	$1$	$e\left(\frac{371}{540}\right)$	$e\left(\frac{101}{270}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{103}{270}\right)$	$e\left(\frac{79}{540}\right)$	$e\left(\frac{4}{135}\right)$	$e\left(\frac{101}{135}\right)$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{43}{90}\right)$
$\chi_{18225}(2537,\cdot)$	$1$	$1$	$e\left(\frac{193}{540}\right)$	$e\left(\frac{193}{270}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{269}{270}\right)$	$e\left(\frac{437}{540}\right)$	$e\left(\frac{17}{135}\right)$	$e\left(\frac{58}{135}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{59}{90}\right)$
$\chi_{18225}(2888,\cdot)$	$1$	$1$	$e\left(\frac{143}{540}\right)$	$e\left(\frac{143}{270}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{79}{270}\right)$	$e\left(\frac{307}{540}\right)$	$e\left(\frac{7}{135}\right)$	$e\left(\frac{8}{135}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{19}{90}\right)$
$\chi_{18225}(2942,\cdot)$	$1$	$1$	$e\left(\frac{181}{540}\right)$	$e\left(\frac{181}{270}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{83}{270}\right)$	$e\left(\frac{449}{540}\right)$	$e\left(\frac{74}{135}\right)$	$e\left(\frac{46}{135}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{53}{90}\right)$
$\chi_{18225}(3023,\cdot)$	$1$	$1$	$e\left(\frac{427}{540}\right)$	$e\left(\frac{157}{270}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{251}{270}\right)$	$e\left(\frac{203}{540}\right)$	$e\left(\frac{53}{135}\right)$	$e\left(\frac{22}{135}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{41}{90}\right)$
$\chi_{18225}(3212,\cdot)$	$1$	$1$	$e\left(\frac{533}{540}\right)$	$e\left(\frac{263}{270}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{49}{270}\right)$	$e\left(\frac{457}{540}\right)$	$e\left(\frac{112}{135}\right)$	$e\left(\frac{128}{135}\right)$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{79}{90}\right)$
$\chi_{18225}(3347,\cdot)$	$1$	$1$	$e\left(\frac{169}{540}\right)$	$e\left(\frac{169}{270}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{167}{270}\right)$	$e\left(\frac{461}{540}\right)$	$e\left(\frac{131}{135}\right)$	$e\left(\frac{34}{135}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{47}{90}\right)$
$\chi_{18225}(3428,\cdot)$	$1$	$1$	$e\left(\frac{199}{540}\right)$	$e\left(\frac{199}{270}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{227}{270}\right)$	$e\left(\frac{431}{540}\right)$	$e\left(\frac{56}{135}\right)$	$e\left(\frac{64}{135}\right)$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{17}{90}\right)$
$\chi_{18225}(3617,\cdot)$	$1$	$1$	$e\left(\frac{521}{540}\right)$	$e\left(\frac{251}{270}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{133}{270}\right)$	$e\left(\frac{469}{540}\right)$	$e\left(\frac{34}{135}\right)$	$e\left(\frac{116}{135}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{73}{90}\right)$
$\chi_{18225}(3698,\cdot)$	$1$	$1$	$e\left(\frac{227}{540}\right)$	$e\left(\frac{227}{270}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{31}{270}\right)$	$e\left(\frac{223}{540}\right)$	$e\left(\frac{13}{135}\right)$	$e\left(\frac{92}{135}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{61}{90}\right)$
$\chi_{18225}(3752,\cdot)$	$1$	$1$	$e\left(\frac{157}{540}\right)$	$e\left(\frac{157}{270}\right)$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{251}{270}\right)$	$e\left(\frac{473}{540}\right)$	$e\left(\frac{53}{135}\right)$	$e\left(\frac{22}{135}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{41}{90}\right)$
$\chi_{18225}(3833,\cdot)$	$1$	$1$	$e\left(\frac{511}{540}\right)$	$e\left(\frac{241}{270}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{203}{270}\right)$	$e\left(\frac{119}{540}\right)$	$e\left(\frac{59}{135}\right)$	$e\left(\frac{106}{135}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{83}{90}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{18225}(53,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{540}\right)\)	\(e\left(\frac{119}{270}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{247}{270}\right)\)	\(e\left(\frac{331}{540}\right)\)	\(e\left(\frac{121}{135}\right)\)	\(e\left(\frac{119}{135}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{7}{90}\right)\)
\(\chi_{18225}(188,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{403}{540}\right)\)	\(e\left(\frac{133}{270}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{149}{270}\right)\)	\(e\left(\frac{227}{540}\right)\)	\(e\left(\frac{32}{135}\right)\)	\(e\left(\frac{133}{135}\right)\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{29}{90}\right)\)
\(\chi_{18225}(377,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{540}\right)\)	\(e\left(\frac{77}{270}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{1}{270}\right)\)	\(e\left(\frac{373}{540}\right)\)	\(e\left(\frac{118}{135}\right)\)	\(e\left(\frac{77}{135}\right)\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{31}{90}\right)\)
\(\chi_{18225}(458,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{431}{540}\right)\)	\(e\left(\frac{161}{270}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{223}{270}\right)\)	\(e\left(\frac{19}{540}\right)\)	\(e\left(\frac{124}{135}\right)\)	\(e\left(\frac{26}{135}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{73}{90}\right)\)
\(\chi_{18225}(512,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{253}{540}\right)\)	\(e\left(\frac{253}{270}\right)\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{119}{270}\right)\)	\(e\left(\frac{377}{540}\right)\)	\(e\left(\frac{2}{135}\right)\)	\(e\left(\frac{118}{135}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{89}{90}\right)\)
\(\chi_{18225}(863,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{203}{540}\right)\)	\(e\left(\frac{203}{270}\right)\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{199}{270}\right)\)	\(e\left(\frac{247}{540}\right)\)	\(e\left(\frac{127}{135}\right)\)	\(e\left(\frac{68}{135}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{49}{90}\right)\)
\(\chi_{18225}(917,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{241}{540}\right)\)	\(e\left(\frac{241}{270}\right)\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{203}{270}\right)\)	\(e\left(\frac{389}{540}\right)\)	\(e\left(\frac{59}{135}\right)\)	\(e\left(\frac{106}{135}\right)\)	\(e\left(\frac{131}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)
\(\chi_{18225}(998,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{487}{540}\right)\)	\(e\left(\frac{217}{270}\right)\)	\(e\left(\frac{41}{108}\right)\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{101}{270}\right)\)	\(e\left(\frac{143}{540}\right)\)	\(e\left(\frac{38}{135}\right)\)	\(e\left(\frac{82}{135}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{71}{90}\right)\)
\(\chi_{18225}(1187,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{540}\right)\)	\(e\left(\frac{53}{270}\right)\)	\(e\left(\frac{67}{108}\right)\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{169}{270}\right)\)	\(e\left(\frac{397}{540}\right)\)	\(e\left(\frac{97}{135}\right)\)	\(e\left(\frac{53}{135}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{19}{90}\right)\)
\(\chi_{18225}(1322,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{229}{540}\right)\)	\(e\left(\frac{229}{270}\right)\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{17}{270}\right)\)	\(e\left(\frac{401}{540}\right)\)	\(e\left(\frac{116}{135}\right)\)	\(e\left(\frac{94}{135}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{77}{90}\right)\)
\(\chi_{18225}(1403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{259}{540}\right)\)	\(e\left(\frac{259}{270}\right)\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{77}{270}\right)\)	\(e\left(\frac{371}{540}\right)\)	\(e\left(\frac{41}{135}\right)\)	\(e\left(\frac{124}{135}\right)\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{47}{90}\right)\)
\(\chi_{18225}(1592,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{540}\right)\)	\(e\left(\frac{41}{270}\right)\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{253}{270}\right)\)	\(e\left(\frac{409}{540}\right)\)	\(e\left(\frac{19}{135}\right)\)	\(e\left(\frac{41}{135}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{13}{90}\right)\)
\(\chi_{18225}(1673,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{287}{540}\right)\)	\(e\left(\frac{17}{270}\right)\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{151}{270}\right)\)	\(e\left(\frac{163}{540}\right)\)	\(e\left(\frac{133}{135}\right)\)	\(e\left(\frac{17}{135}\right)\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{1}{90}\right)\)
\(\chi_{18225}(1727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{217}{540}\right)\)	\(e\left(\frac{217}{270}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{101}{270}\right)\)	\(e\left(\frac{413}{540}\right)\)	\(e\left(\frac{38}{135}\right)\)	\(e\left(\frac{82}{135}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{71}{90}\right)\)
\(\chi_{18225}(1808,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{540}\right)\)	\(e\left(\frac{31}{270}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{53}{270}\right)\)	\(e\left(\frac{59}{540}\right)\)	\(e\left(\frac{44}{135}\right)\)	\(e\left(\frac{31}{135}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{23}{90}\right)\)
\(\chi_{18225}(1997,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{540}\right)\)	\(e\left(\frac{29}{270}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{67}{270}\right)\)	\(e\left(\frac{421}{540}\right)\)	\(e\left(\frac{76}{135}\right)\)	\(e\left(\frac{29}{135}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{7}{90}\right)\)
\(\chi_{18225}(2078,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{540}\right)\)	\(e\left(\frac{59}{270}\right)\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{127}{270}\right)\)	\(e\left(\frac{391}{540}\right)\)	\(e\left(\frac{1}{135}\right)\)	\(e\left(\frac{59}{135}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)
\(\chi_{18225}(2213,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{343}{540}\right)\)	\(e\left(\frac{73}{270}\right)\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{29}{270}\right)\)	\(e\left(\frac{287}{540}\right)\)	\(e\left(\frac{47}{135}\right)\)	\(e\left(\frac{73}{135}\right)\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{89}{90}\right)\)
\(\chi_{18225}(2402,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{540}\right)\)	\(e\left(\frac{17}{270}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{151}{270}\right)\)	\(e\left(\frac{433}{540}\right)\)	\(e\left(\frac{133}{135}\right)\)	\(e\left(\frac{17}{135}\right)\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{1}{90}\right)\)
\(\chi_{18225}(2483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{371}{540}\right)\)	\(e\left(\frac{101}{270}\right)\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{103}{270}\right)\)	\(e\left(\frac{79}{540}\right)\)	\(e\left(\frac{4}{135}\right)\)	\(e\left(\frac{101}{135}\right)\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{43}{90}\right)\)
\(\chi_{18225}(2537,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{540}\right)\)	\(e\left(\frac{193}{270}\right)\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{269}{270}\right)\)	\(e\left(\frac{437}{540}\right)\)	\(e\left(\frac{17}{135}\right)\)	\(e\left(\frac{58}{135}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{59}{90}\right)\)
\(\chi_{18225}(2888,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{143}{540}\right)\)	\(e\left(\frac{143}{270}\right)\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{79}{270}\right)\)	\(e\left(\frac{307}{540}\right)\)	\(e\left(\frac{7}{135}\right)\)	\(e\left(\frac{8}{135}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{19}{90}\right)\)
\(\chi_{18225}(2942,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{540}\right)\)	\(e\left(\frac{181}{270}\right)\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{83}{270}\right)\)	\(e\left(\frac{449}{540}\right)\)	\(e\left(\frac{74}{135}\right)\)	\(e\left(\frac{46}{135}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{53}{90}\right)\)
\(\chi_{18225}(3023,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{427}{540}\right)\)	\(e\left(\frac{157}{270}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{251}{270}\right)\)	\(e\left(\frac{203}{540}\right)\)	\(e\left(\frac{53}{135}\right)\)	\(e\left(\frac{22}{135}\right)\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{41}{90}\right)\)
\(\chi_{18225}(3212,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{533}{540}\right)\)	\(e\left(\frac{263}{270}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{49}{270}\right)\)	\(e\left(\frac{457}{540}\right)\)	\(e\left(\frac{112}{135}\right)\)	\(e\left(\frac{128}{135}\right)\)	\(e\left(\frac{103}{180}\right)\)	\(e\left(\frac{79}{90}\right)\)
\(\chi_{18225}(3347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{540}\right)\)	\(e\left(\frac{169}{270}\right)\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{167}{270}\right)\)	\(e\left(\frac{461}{540}\right)\)	\(e\left(\frac{131}{135}\right)\)	\(e\left(\frac{34}{135}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{47}{90}\right)\)
\(\chi_{18225}(3428,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{540}\right)\)	\(e\left(\frac{199}{270}\right)\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{227}{270}\right)\)	\(e\left(\frac{431}{540}\right)\)	\(e\left(\frac{56}{135}\right)\)	\(e\left(\frac{64}{135}\right)\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{17}{90}\right)\)
\(\chi_{18225}(3617,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{521}{540}\right)\)	\(e\left(\frac{251}{270}\right)\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{133}{270}\right)\)	\(e\left(\frac{469}{540}\right)\)	\(e\left(\frac{34}{135}\right)\)	\(e\left(\frac{116}{135}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{73}{90}\right)\)
\(\chi_{18225}(3698,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{227}{540}\right)\)	\(e\left(\frac{227}{270}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{31}{270}\right)\)	\(e\left(\frac{223}{540}\right)\)	\(e\left(\frac{13}{135}\right)\)	\(e\left(\frac{92}{135}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{61}{90}\right)\)
\(\chi_{18225}(3752,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{540}\right)\)	\(e\left(\frac{157}{270}\right)\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{251}{270}\right)\)	\(e\left(\frac{473}{540}\right)\)	\(e\left(\frac{53}{135}\right)\)	\(e\left(\frac{22}{135}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{41}{90}\right)\)
\(\chi_{18225}(3833,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{511}{540}\right)\)	\(e\left(\frac{241}{270}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{203}{270}\right)\)	\(e\left(\frac{119}{540}\right)\)	\(e\left(\frac{59}{135}\right)\)	\(e\left(\frac{106}{135}\right)\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)

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First 31 of 144 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.cg
Modulus	$18225$
Conductor	$2025$
Order	$540$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(18225\)
Conductor:	\(2025\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(540\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2025.bv	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)