LMFDB - Dirichlet character orbit 54000.nl

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(54000, base_ring=CyclotomicField(900)) M = H._module chi = DirichletCharacter(H, M([450,0,350,873])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(47,54000)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$54000$
Conductor:	$13500$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$900$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 13500.ec	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:	$\Q(\zeta_{900})$
Fixed field:	Number field defined by a degree 900 polynomial (not computed)

First 31 of 240 characters in Galois orbit

Character	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{54000}(47,\cdot)$	$-1$	$1$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{62}{225}\right)$	$e\left(\frac{847}{900}\right)$	$e\left(\frac{193}{300}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{763}{900}\right)$	$e\left(\frac{119}{225}\right)$	$e\left(\frac{377}{450}\right)$	$e\left(\frac{139}{300}\right)$	$e\left(\frac{131}{450}\right)$
$\chi_{54000}(383,\cdot)$	$-1$	$1$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{88}{225}\right)$	$e\left(\frac{353}{900}\right)$	$e\left(\frac{107}{300}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{437}{900}\right)$	$e\left(\frac{31}{225}\right)$	$e\left(\frac{223}{450}\right)$	$e\left(\frac{161}{300}\right)$	$e\left(\frac{19}{450}\right)$
$\chi_{54000}(527,\cdot)$	$-1$	$1$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{166}{225}\right)$	$e\left(\frac{671}{900}\right)$	$e\left(\frac{149}{300}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{359}{900}\right)$	$e\left(\frac{217}{225}\right)$	$e\left(\frac{211}{450}\right)$	$e\left(\frac{227}{300}\right)$	$e\left(\frac{133}{450}\right)$
$\chi_{54000}(623,\cdot)$	$-1$	$1$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{221}{225}\right)$	$e\left(\frac{301}{900}\right)$	$e\left(\frac{19}{300}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{829}{900}\right)$	$e\left(\frac{152}{225}\right)$	$e\left(\frac{41}{450}\right)$	$e\left(\frac{37}{300}\right)$	$e\left(\frac{173}{450}\right)$
$\chi_{54000}(767,\cdot)$	$-1$	$1$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{83}{225}\right)$	$e\left(\frac{223}{900}\right)$	$e\left(\frac{37}{300}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{67}{900}\right)$	$e\left(\frac{221}{225}\right)$	$e\left(\frac{443}{450}\right)$	$e\left(\frac{151}{300}\right)$	$e\left(\frac{179}{450}\right)$
$\chi_{54000}(1103,\cdot)$	$-1$	$1$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{217}{225}\right)$	$e\left(\frac{377}{900}\right)$	$e\left(\frac{263}{300}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{533}{900}\right)$	$e\left(\frac{79}{225}\right)$	$e\left(\frac{307}{450}\right)$	$e\left(\frac{149}{300}\right)$	$e\left(\frac{121}{450}\right)$
$\chi_{54000}(1247,\cdot)$	$-1$	$1$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{97}{225}\right)$	$e\left(\frac{407}{900}\right)$	$e\left(\frac{233}{300}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{203}{900}\right)$	$e\left(\frac{139}{225}\right)$	$e\left(\frac{187}{450}\right)$	$e\left(\frac{59}{300}\right)$	$e\left(\frac{361}{450}\right)$
$\chi_{54000}(1487,\cdot)$	$-1$	$1$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{194}{225}\right)$	$e\left(\frac{139}{900}\right)$	$e\left(\frac{241}{300}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{631}{900}\right)$	$e\left(\frac{53}{225}\right)$	$e\left(\frac{149}{450}\right)$	$e\left(\frac{43}{300}\right)$	$e\left(\frac{47}{450}\right)$
$\chi_{54000}(1823,\cdot)$	$-1$	$1$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{211}{225}\right)$	$e\left(\frac{41}{900}\right)$	$e\left(\frac{179}{300}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{89}{900}\right)$	$e\left(\frac{82}{225}\right)$	$e\left(\frac{31}{450}\right)$	$e\left(\frac{17}{300}\right)$	$e\left(\frac{43}{450}\right)$
$\chi_{54000}(1967,\cdot)$	$-1$	$1$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{118}{225}\right)$	$e\left(\frac{683}{900}\right)$	$e\left(\frac{77}{300}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{407}{900}\right)$	$e\left(\frac{16}{225}\right)$	$e\left(\frac{253}{450}\right)$	$e\left(\frac{71}{300}\right)$	$e\left(\frac{409}{450}\right)$
$\chi_{54000}(2063,\cdot)$	$-1$	$1$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{29}{225}\right)$	$e\left(\frac{349}{900}\right)$	$e\left(\frac{31}{300}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{121}{900}\right)$	$e\left(\frac{23}{225}\right)$	$e\left(\frac{209}{450}\right)$	$e\left(\frac{13}{300}\right)$	$e\left(\frac{377}{450}\right)$
$\chi_{54000}(2687,\cdot)$	$-1$	$1$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{4}{225}\right)$	$e\left(\frac{599}{900}\right)$	$e\left(\frac{281}{300}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{71}{900}\right)$	$e\left(\frac{73}{225}\right)$	$e\left(\frac{409}{450}\right)$	$e\left(\frac{263}{300}\right)$	$e\left(\frac{277}{450}\right)$
$\chi_{54000}(2783,\cdot)$	$-1$	$1$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{68}{225}\right)$	$e\left(\frac{733}{900}\right)$	$e\left(\frac{127}{300}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{757}{900}\right)$	$e\left(\frac{116}{225}\right)$	$e\left(\frac{203}{450}\right)$	$e\left(\frac{121}{300}\right)$	$e\left(\frac{209}{450}\right)$
$\chi_{54000}(2927,\cdot)$	$-1$	$1$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{11}{225}\right)$	$e\left(\frac{691}{900}\right)$	$e\left(\frac{229}{300}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{139}{900}\right)$	$e\left(\frac{32}{225}\right)$	$e\left(\frac{281}{450}\right)$	$e\left(\frac{67}{300}\right)$	$e\left(\frac{143}{450}\right)$
$\chi_{54000}(3263,\cdot)$	$-1$	$1$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{19}{225}\right)$	$e\left(\frac{89}{900}\right)$	$e\left(\frac{191}{300}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{281}{900}\right)$	$e\left(\frac{178}{225}\right)$	$e\left(\frac{199}{450}\right)$	$e\left(\frac{293}{300}\right)$	$e\left(\frac{247}{450}\right)$
$\chi_{54000}(3503,\cdot)$	$-1$	$1$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{197}{225}\right)$	$e\left(\frac{757}{900}\right)$	$e\left(\frac{283}{300}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{853}{900}\right)$	$e\left(\frac{164}{225}\right)$	$e\left(\frac{287}{450}\right)$	$e\left(\frac{109}{300}\right)$	$e\left(\frac{311}{450}\right)$
$\chi_{54000}(3647,\cdot)$	$-1$	$1$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{167}{225}\right)$	$e\left(\frac{427}{900}\right)$	$e\left(\frac{13}{300}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{883}{900}\right)$	$e\left(\frac{179}{225}\right)$	$e\left(\frac{257}{450}\right)$	$e\left(\frac{199}{300}\right)$	$e\left(\frac{371}{450}\right)$
$\chi_{54000}(3983,\cdot)$	$-1$	$1$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{58}{225}\right)$	$e\left(\frac{473}{900}\right)$	$e\left(\frac{287}{300}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{17}{900}\right)$	$e\left(\frac{46}{225}\right)$	$e\left(\frac{193}{450}\right)$	$e\left(\frac{101}{300}\right)$	$e\left(\frac{79}{450}\right)$
$\chi_{54000}(4127,\cdot)$	$-1$	$1$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{46}{225}\right)$	$e\left(\frac{251}{900}\right)$	$e\left(\frac{269}{300}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{479}{900}\right)$	$e\left(\frac{52}{225}\right)$	$e\left(\frac{91}{450}\right)$	$e\left(\frac{287}{300}\right)$	$e\left(\frac{373}{450}\right)$
$\chi_{54000}(4223,\cdot)$	$-1$	$1$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{191}{225}\right)$	$e\left(\frac{421}{900}\right)$	$e\left(\frac{199}{300}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{409}{900}\right)$	$e\left(\frac{167}{225}\right)$	$e\left(\frac{11}{450}\right)$	$e\left(\frac{277}{300}\right)$	$e\left(\frac{233}{450}\right)$
$\chi_{54000}(4367,\cdot)$	$-1$	$1$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{188}{225}\right)$	$e\left(\frac{703}{900}\right)$	$e\left(\frac{157}{300}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{187}{900}\right)$	$e\left(\frac{56}{225}\right)$	$e\left(\frac{323}{450}\right)$	$e\left(\frac{211}{300}\right)$	$e\left(\frac{419}{450}\right)$
$\chi_{54000}(4703,\cdot)$	$-1$	$1$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{187}{225}\right)$	$e\left(\frac{497}{900}\right)$	$e\left(\frac{143}{300}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{113}{900}\right)$	$e\left(\frac{94}{225}\right)$	$e\left(\frac{277}{450}\right)$	$e\left(\frac{89}{300}\right)$	$e\left(\frac{181}{450}\right)$
$\chi_{54000}(4847,\cdot)$	$-1$	$1$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{202}{225}\right)$	$e\left(\frac{887}{900}\right)$	$e\left(\frac{53}{300}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{323}{900}\right)$	$e\left(\frac{199}{225}\right)$	$e\left(\frac{67}{450}\right)$	$e\left(\frac{119}{300}\right)$	$e\left(\frac{151}{450}\right)$
$\chi_{54000}(5087,\cdot)$	$-1$	$1$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{74}{225}\right)$	$e\left(\frac{619}{900}\right)$	$e\left(\frac{61}{300}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{751}{900}\right)$	$e\left(\frac{113}{225}\right)$	$e\left(\frac{29}{450}\right)$	$e\left(\frac{103}{300}\right)$	$e\left(\frac{287}{450}\right)$
$\chi_{54000}(5423,\cdot)$	$-1$	$1$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{181}{225}\right)$	$e\left(\frac{161}{900}\right)$	$e\left(\frac{59}{300}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{569}{900}\right)$	$e\left(\frac{97}{225}\right)$	$e\left(\frac{1}{450}\right)$	$e\left(\frac{257}{300}\right)$	$e\left(\frac{103}{450}\right)$
$\chi_{54000}(5567,\cdot)$	$-1$	$1$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{223}{225}\right)$	$e\left(\frac{263}{900}\right)$	$e\left(\frac{197}{300}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{527}{900}\right)$	$e\left(\frac{76}{225}\right)$	$e\left(\frac{133}{450}\right)$	$e\left(\frac{131}{300}\right)$	$e\left(\frac{199}{450}\right)$
$\chi_{54000}(5663,\cdot)$	$-1$	$1$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{224}{225}\right)$	$e\left(\frac{469}{900}\right)$	$e\left(\frac{211}{300}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{601}{900}\right)$	$e\left(\frac{38}{225}\right)$	$e\left(\frac{179}{450}\right)$	$e\left(\frac{253}{300}\right)$	$e\left(\frac{437}{450}\right)$
$\chi_{54000}(6287,\cdot)$	$-1$	$1$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{109}{225}\right)$	$e\left(\frac{179}{900}\right)$	$e\left(\frac{101}{300}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{191}{900}\right)$	$e\left(\frac{133}{225}\right)$	$e\left(\frac{289}{450}\right)$	$e\left(\frac{23}{300}\right)$	$e\left(\frac{67}{450}\right)$
$\chi_{54000}(6383,\cdot)$	$-1$	$1$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{38}{225}\right)$	$e\left(\frac{853}{900}\right)$	$e\left(\frac{7}{300}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{337}{900}\right)$	$e\left(\frac{131}{225}\right)$	$e\left(\frac{173}{450}\right)$	$e\left(\frac{61}{300}\right)$	$e\left(\frac{269}{450}\right)$
$\chi_{54000}(6527,\cdot)$	$-1$	$1$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{116}{225}\right)$	$e\left(\frac{271}{900}\right)$	$e\left(\frac{49}{300}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{259}{900}\right)$	$e\left(\frac{92}{225}\right)$	$e\left(\frac{161}{450}\right)$	$e\left(\frac{127}{300}\right)$	$e\left(\frac{383}{450}\right)$
$\chi_{54000}(6863,\cdot)$	$-1$	$1$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{214}{225}\right)$	$e\left(\frac{209}{900}\right)$	$e\left(\frac{71}{300}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{761}{900}\right)$	$e\left(\frac{193}{225}\right)$	$e\left(\frac{169}{450}\right)$	$e\left(\frac{233}{300}\right)$	$e\left(\frac{307}{450}\right)$

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	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{54000}(47,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{62}{225}\right)\)	\(e\left(\frac{847}{900}\right)\)	\(e\left(\frac{193}{300}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{763}{900}\right)\)	\(e\left(\frac{119}{225}\right)\)	\(e\left(\frac{377}{450}\right)\)	\(e\left(\frac{139}{300}\right)\)	\(e\left(\frac{131}{450}\right)\)
\(\chi_{54000}(383,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{88}{225}\right)\)	\(e\left(\frac{353}{900}\right)\)	\(e\left(\frac{107}{300}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{437}{900}\right)\)	\(e\left(\frac{31}{225}\right)\)	\(e\left(\frac{223}{450}\right)\)	\(e\left(\frac{161}{300}\right)\)	\(e\left(\frac{19}{450}\right)\)
\(\chi_{54000}(527,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{166}{225}\right)\)	\(e\left(\frac{671}{900}\right)\)	\(e\left(\frac{149}{300}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{359}{900}\right)\)	\(e\left(\frac{217}{225}\right)\)	\(e\left(\frac{211}{450}\right)\)	\(e\left(\frac{227}{300}\right)\)	\(e\left(\frac{133}{450}\right)\)
\(\chi_{54000}(623,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{221}{225}\right)\)	\(e\left(\frac{301}{900}\right)\)	\(e\left(\frac{19}{300}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{829}{900}\right)\)	\(e\left(\frac{152}{225}\right)\)	\(e\left(\frac{41}{450}\right)\)	\(e\left(\frac{37}{300}\right)\)	\(e\left(\frac{173}{450}\right)\)
\(\chi_{54000}(767,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{83}{225}\right)\)	\(e\left(\frac{223}{900}\right)\)	\(e\left(\frac{37}{300}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{67}{900}\right)\)	\(e\left(\frac{221}{225}\right)\)	\(e\left(\frac{443}{450}\right)\)	\(e\left(\frac{151}{300}\right)\)	\(e\left(\frac{179}{450}\right)\)
\(\chi_{54000}(1103,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{217}{225}\right)\)	\(e\left(\frac{377}{900}\right)\)	\(e\left(\frac{263}{300}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{533}{900}\right)\)	\(e\left(\frac{79}{225}\right)\)	\(e\left(\frac{307}{450}\right)\)	\(e\left(\frac{149}{300}\right)\)	\(e\left(\frac{121}{450}\right)\)
\(\chi_{54000}(1247,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{97}{225}\right)\)	\(e\left(\frac{407}{900}\right)\)	\(e\left(\frac{233}{300}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{203}{900}\right)\)	\(e\left(\frac{139}{225}\right)\)	\(e\left(\frac{187}{450}\right)\)	\(e\left(\frac{59}{300}\right)\)	\(e\left(\frac{361}{450}\right)\)
\(\chi_{54000}(1487,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{194}{225}\right)\)	\(e\left(\frac{139}{900}\right)\)	\(e\left(\frac{241}{300}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{631}{900}\right)\)	\(e\left(\frac{53}{225}\right)\)	\(e\left(\frac{149}{450}\right)\)	\(e\left(\frac{43}{300}\right)\)	\(e\left(\frac{47}{450}\right)\)
\(\chi_{54000}(1823,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{211}{225}\right)\)	\(e\left(\frac{41}{900}\right)\)	\(e\left(\frac{179}{300}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{89}{900}\right)\)	\(e\left(\frac{82}{225}\right)\)	\(e\left(\frac{31}{450}\right)\)	\(e\left(\frac{17}{300}\right)\)	\(e\left(\frac{43}{450}\right)\)
\(\chi_{54000}(1967,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{118}{225}\right)\)	\(e\left(\frac{683}{900}\right)\)	\(e\left(\frac{77}{300}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{407}{900}\right)\)	\(e\left(\frac{16}{225}\right)\)	\(e\left(\frac{253}{450}\right)\)	\(e\left(\frac{71}{300}\right)\)	\(e\left(\frac{409}{450}\right)\)
\(\chi_{54000}(2063,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{29}{225}\right)\)	\(e\left(\frac{349}{900}\right)\)	\(e\left(\frac{31}{300}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{121}{900}\right)\)	\(e\left(\frac{23}{225}\right)\)	\(e\left(\frac{209}{450}\right)\)	\(e\left(\frac{13}{300}\right)\)	\(e\left(\frac{377}{450}\right)\)
\(\chi_{54000}(2687,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{4}{225}\right)\)	\(e\left(\frac{599}{900}\right)\)	\(e\left(\frac{281}{300}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{71}{900}\right)\)	\(e\left(\frac{73}{225}\right)\)	\(e\left(\frac{409}{450}\right)\)	\(e\left(\frac{263}{300}\right)\)	\(e\left(\frac{277}{450}\right)\)
\(\chi_{54000}(2783,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{68}{225}\right)\)	\(e\left(\frac{733}{900}\right)\)	\(e\left(\frac{127}{300}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{757}{900}\right)\)	\(e\left(\frac{116}{225}\right)\)	\(e\left(\frac{203}{450}\right)\)	\(e\left(\frac{121}{300}\right)\)	\(e\left(\frac{209}{450}\right)\)
\(\chi_{54000}(2927,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{11}{225}\right)\)	\(e\left(\frac{691}{900}\right)\)	\(e\left(\frac{229}{300}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{139}{900}\right)\)	\(e\left(\frac{32}{225}\right)\)	\(e\left(\frac{281}{450}\right)\)	\(e\left(\frac{67}{300}\right)\)	\(e\left(\frac{143}{450}\right)\)
\(\chi_{54000}(3263,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{19}{225}\right)\)	\(e\left(\frac{89}{900}\right)\)	\(e\left(\frac{191}{300}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{281}{900}\right)\)	\(e\left(\frac{178}{225}\right)\)	\(e\left(\frac{199}{450}\right)\)	\(e\left(\frac{293}{300}\right)\)	\(e\left(\frac{247}{450}\right)\)
\(\chi_{54000}(3503,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{197}{225}\right)\)	\(e\left(\frac{757}{900}\right)\)	\(e\left(\frac{283}{300}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{853}{900}\right)\)	\(e\left(\frac{164}{225}\right)\)	\(e\left(\frac{287}{450}\right)\)	\(e\left(\frac{109}{300}\right)\)	\(e\left(\frac{311}{450}\right)\)
\(\chi_{54000}(3647,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{167}{225}\right)\)	\(e\left(\frac{427}{900}\right)\)	\(e\left(\frac{13}{300}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{883}{900}\right)\)	\(e\left(\frac{179}{225}\right)\)	\(e\left(\frac{257}{450}\right)\)	\(e\left(\frac{199}{300}\right)\)	\(e\left(\frac{371}{450}\right)\)
\(\chi_{54000}(3983,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{58}{225}\right)\)	\(e\left(\frac{473}{900}\right)\)	\(e\left(\frac{287}{300}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{17}{900}\right)\)	\(e\left(\frac{46}{225}\right)\)	\(e\left(\frac{193}{450}\right)\)	\(e\left(\frac{101}{300}\right)\)	\(e\left(\frac{79}{450}\right)\)
\(\chi_{54000}(4127,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{46}{225}\right)\)	\(e\left(\frac{251}{900}\right)\)	\(e\left(\frac{269}{300}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{479}{900}\right)\)	\(e\left(\frac{52}{225}\right)\)	\(e\left(\frac{91}{450}\right)\)	\(e\left(\frac{287}{300}\right)\)	\(e\left(\frac{373}{450}\right)\)
\(\chi_{54000}(4223,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{191}{225}\right)\)	\(e\left(\frac{421}{900}\right)\)	\(e\left(\frac{199}{300}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{409}{900}\right)\)	\(e\left(\frac{167}{225}\right)\)	\(e\left(\frac{11}{450}\right)\)	\(e\left(\frac{277}{300}\right)\)	\(e\left(\frac{233}{450}\right)\)
\(\chi_{54000}(4367,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{188}{225}\right)\)	\(e\left(\frac{703}{900}\right)\)	\(e\left(\frac{157}{300}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{187}{900}\right)\)	\(e\left(\frac{56}{225}\right)\)	\(e\left(\frac{323}{450}\right)\)	\(e\left(\frac{211}{300}\right)\)	\(e\left(\frac{419}{450}\right)\)
\(\chi_{54000}(4703,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{187}{225}\right)\)	\(e\left(\frac{497}{900}\right)\)	\(e\left(\frac{143}{300}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{113}{900}\right)\)	\(e\left(\frac{94}{225}\right)\)	\(e\left(\frac{277}{450}\right)\)	\(e\left(\frac{89}{300}\right)\)	\(e\left(\frac{181}{450}\right)\)
\(\chi_{54000}(4847,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{202}{225}\right)\)	\(e\left(\frac{887}{900}\right)\)	\(e\left(\frac{53}{300}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{323}{900}\right)\)	\(e\left(\frac{199}{225}\right)\)	\(e\left(\frac{67}{450}\right)\)	\(e\left(\frac{119}{300}\right)\)	\(e\left(\frac{151}{450}\right)\)
\(\chi_{54000}(5087,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{74}{225}\right)\)	\(e\left(\frac{619}{900}\right)\)	\(e\left(\frac{61}{300}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{751}{900}\right)\)	\(e\left(\frac{113}{225}\right)\)	\(e\left(\frac{29}{450}\right)\)	\(e\left(\frac{103}{300}\right)\)	\(e\left(\frac{287}{450}\right)\)
\(\chi_{54000}(5423,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{181}{225}\right)\)	\(e\left(\frac{161}{900}\right)\)	\(e\left(\frac{59}{300}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{569}{900}\right)\)	\(e\left(\frac{97}{225}\right)\)	\(e\left(\frac{1}{450}\right)\)	\(e\left(\frac{257}{300}\right)\)	\(e\left(\frac{103}{450}\right)\)
\(\chi_{54000}(5567,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{223}{225}\right)\)	\(e\left(\frac{263}{900}\right)\)	\(e\left(\frac{197}{300}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{527}{900}\right)\)	\(e\left(\frac{76}{225}\right)\)	\(e\left(\frac{133}{450}\right)\)	\(e\left(\frac{131}{300}\right)\)	\(e\left(\frac{199}{450}\right)\)
\(\chi_{54000}(5663,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{224}{225}\right)\)	\(e\left(\frac{469}{900}\right)\)	\(e\left(\frac{211}{300}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{601}{900}\right)\)	\(e\left(\frac{38}{225}\right)\)	\(e\left(\frac{179}{450}\right)\)	\(e\left(\frac{253}{300}\right)\)	\(e\left(\frac{437}{450}\right)\)
\(\chi_{54000}(6287,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{167}{180}\right)\)	\(e\left(\frac{109}{225}\right)\)	\(e\left(\frac{179}{900}\right)\)	\(e\left(\frac{101}{300}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{191}{900}\right)\)	\(e\left(\frac{133}{225}\right)\)	\(e\left(\frac{289}{450}\right)\)	\(e\left(\frac{23}{300}\right)\)	\(e\left(\frac{67}{450}\right)\)
\(\chi_{54000}(6383,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{38}{225}\right)\)	\(e\left(\frac{853}{900}\right)\)	\(e\left(\frac{7}{300}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{337}{900}\right)\)	\(e\left(\frac{131}{225}\right)\)	\(e\left(\frac{173}{450}\right)\)	\(e\left(\frac{61}{300}\right)\)	\(e\left(\frac{269}{450}\right)\)
\(\chi_{54000}(6527,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{103}{180}\right)\)	\(e\left(\frac{116}{225}\right)\)	\(e\left(\frac{271}{900}\right)\)	\(e\left(\frac{49}{300}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{259}{900}\right)\)	\(e\left(\frac{92}{225}\right)\)	\(e\left(\frac{161}{450}\right)\)	\(e\left(\frac{127}{300}\right)\)	\(e\left(\frac{383}{450}\right)\)
\(\chi_{54000}(6863,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{214}{225}\right)\)	\(e\left(\frac{209}{900}\right)\)	\(e\left(\frac{71}{300}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{761}{900}\right)\)	\(e\left(\frac{193}{225}\right)\)	\(e\left(\frac{169}{450}\right)\)	\(e\left(\frac{233}{300}\right)\)	\(e\left(\frac{307}{450}\right)\)

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First 31 of 240 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	54000.nl
Modulus	$54000$
Conductor	$13500$
Order	$900$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(54000\)
Conductor:	\(13500\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(900\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 13500.ec	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)