LMFDB - Dirichlet character orbit 10585.lw

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10585, base_ring=CyclotomicField(504)) M = H._module chi = DirichletCharacter(H, M([252,234,287])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(14, 10585)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("10585.14"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$10585$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$10585$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$504$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{504})$
Fixed field:	Number field defined by a degree 504 polynomial (not computed)

First 31 of 144 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{10585}(14,\cdot)$	$1$	$1$	$e\left(\frac{131}{252}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{191}{252}\right)$	$e\left(\frac{145}{168}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{467}{504}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{229}{504}\right)$
$\chi_{10585}(44,\cdot)$	$1$	$1$	$e\left(\frac{89}{252}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{149}{252}\right)$	$e\left(\frac{103}{168}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{173}{504}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{19}{504}\right)$
$\chi_{10585}(84,\cdot)$	$1$	$1$	$e\left(\frac{73}{252}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{193}{252}\right)$	$e\left(\frac{143}{168}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{493}{504}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{395}{504}\right)$
$\chi_{10585}(214,\cdot)$	$1$	$1$	$e\left(\frac{127}{252}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{139}{252}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{295}{504}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{449}{504}\right)$
$\chi_{10585}(224,\cdot)$	$1$	$1$	$e\left(\frac{55}{252}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{211}{252}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{475}{504}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{125}{504}\right)$
$\chi_{10585}(264,\cdot)$	$1$	$1$	$e\left(\frac{31}{252}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{151}{252}\right)$	$e\left(\frac{101}{168}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{199}{504}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{185}{504}\right)$
$\chi_{10585}(279,\cdot)$	$1$	$1$	$e\left(\frac{113}{252}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{209}{252}\right)$	$e\left(\frac{127}{168}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{197}{504}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{211}{504}\right)$
$\chi_{10585}(334,\cdot)$	$1$	$1$	$e\left(\frac{173}{252}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{233}{252}\right)$	$e\left(\frac{103}{168}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{504}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{187}{504}\right)$
$\chi_{10585}(379,\cdot)$	$1$	$1$	$e\left(\frac{23}{252}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{47}{252}\right)$	$e\left(\frac{121}{168}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{107}{504}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{373}{504}\right)$
$\chi_{10585}(569,\cdot)$	$1$	$1$	$e\left(\frac{169}{252}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{181}{252}\right)$	$e\left(\frac{155}{168}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{337}{504}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{407}{504}\right)$
$\chi_{10585}(704,\cdot)$	$1$	$1$	$e\left(\frac{13}{252}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{169}{252}\right)$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{181}{504}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{419}{504}\right)$
$\chi_{10585}(744,\cdot)$	$1$	$1$	$e\left(\frac{95}{252}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{227}{252}\right)$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{179}{504}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{445}{504}\right)$
$\chi_{10585}(989,\cdot)$	$1$	$1$	$e\left(\frac{115}{252}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{235}{252}\right)$	$e\left(\frac{17}{168}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{283}{504}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{101}{504}\right)$
$\chi_{10585}(1134,\cdot)$	$1$	$1$	$e\left(\frac{227}{252}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{179}{252}\right)$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{59}{504}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{493}{504}\right)$
$\chi_{10585}(1139,\cdot)$	$1$	$1$	$e\left(\frac{125}{252}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{113}{252}\right)$	$e\left(\frac{55}{168}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{461}{504}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{307}{504}\right)$
$\chi_{10585}(1199,\cdot)$	$1$	$1$	$e\left(\frac{137}{252}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{17}{252}\right)$	$e\left(\frac{67}{168}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{473}{504}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{151}{504}\right)$
$\chi_{10585}(1319,\cdot)$	$1$	$1$	$e\left(\frac{19}{252}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{247}{252}\right)$	$e\left(\frac{89}{168}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{187}{504}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{341}{504}\right)$
$\chi_{10585}(1429,\cdot)$	$1$	$1$	$e\left(\frac{209}{252}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{197}{252}\right)$	$e\left(\frac{55}{168}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{293}{504}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{475}{504}\right)$
$\chi_{10585}(1489,\cdot)$	$1$	$1$	$e\left(\frac{53}{252}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{185}{252}\right)$	$e\left(\frac{67}{168}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{137}{504}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{487}{504}\right)$
$\chi_{10585}(1519,\cdot)$	$1$	$1$	$e\left(\frac{239}{252}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{83}{252}\right)$	$e\left(\frac{85}{168}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{71}{504}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{337}{504}\right)$
$\chi_{10585}(1564,\cdot)$	$1$	$1$	$e\left(\frac{65}{252}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{89}{252}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{401}{504}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{79}{504}\right)$
$\chi_{10585}(1674,\cdot)$	$1$	$1$	$e\left(\frac{55}{252}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{211}{252}\right)$	$e\left(\frac{125}{168}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{223}{504}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{377}{504}\right)$
$\chi_{10585}(1684,\cdot)$	$1$	$1$	$e\left(\frac{163}{252}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{103}{252}\right)$	$e\left(\frac{65}{168}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{331}{504}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{485}{504}\right)$
$\chi_{10585}(1854,\cdot)$	$1$	$1$	$e\left(\frac{233}{252}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{5}{252}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{65}{504}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{415}{504}\right)$
$\chi_{10585}(1859,\cdot)$	$1$	$1$	$e\left(\frac{227}{252}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{179}{252}\right)$	$e\left(\frac{157}{168}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{311}{504}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{241}{504}\right)$
$\chi_{10585}(1924,\cdot)$	$1$	$1$	$e\left(\frac{193}{252}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{241}{252}\right)$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{361}{504}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{95}{504}\right)$
$\chi_{10585}(1929,\cdot)$	$1$	$1$	$e\left(\frac{173}{252}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{233}{252}\right)$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{257}{504}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{439}{504}\right)$
$\chi_{10585}(2004,\cdot)$	$1$	$1$	$e\left(\frac{115}{252}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{235}{252}\right)$	$e\left(\frac{101}{168}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{31}{504}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{353}{504}\right)$
$\chi_{10585}(2049,\cdot)$	$1$	$1$	$e\left(\frac{235}{252}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{31}{252}\right)$	$e\left(\frac{137}{168}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{403}{504}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{53}{504}\right)$
$\chi_{10585}(2164,\cdot)$	$1$	$1$	$e\left(\frac{85}{252}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{97}{252}\right)$	$e\left(\frac{71}{168}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{253}{504}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{491}{504}\right)$
$\chi_{10585}(2219,\cdot)$	$1$	$1$	$e\left(\frac{89}{252}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{149}{252}\right)$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{425}{504}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{271}{504}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{10585}(14,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{252}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{191}{252}\right)\)	\(e\left(\frac{145}{168}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{467}{504}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{229}{504}\right)\)
\(\chi_{10585}(44,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{252}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{149}{252}\right)\)	\(e\left(\frac{103}{168}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{173}{504}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{19}{504}\right)\)
\(\chi_{10585}(84,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{252}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{193}{252}\right)\)	\(e\left(\frac{143}{168}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{493}{504}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{395}{504}\right)\)
\(\chi_{10585}(214,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{252}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{139}{252}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{295}{504}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{449}{504}\right)\)
\(\chi_{10585}(224,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{252}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{211}{252}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{475}{504}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{125}{504}\right)\)
\(\chi_{10585}(264,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{252}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{151}{252}\right)\)	\(e\left(\frac{101}{168}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{199}{504}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{185}{504}\right)\)
\(\chi_{10585}(279,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{252}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{209}{252}\right)\)	\(e\left(\frac{127}{168}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{197}{504}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{211}{504}\right)\)
\(\chi_{10585}(334,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{252}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{233}{252}\right)\)	\(e\left(\frac{103}{168}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{504}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{187}{504}\right)\)
\(\chi_{10585}(379,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{252}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{47}{252}\right)\)	\(e\left(\frac{121}{168}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{107}{504}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{373}{504}\right)\)
\(\chi_{10585}(569,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{252}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{181}{252}\right)\)	\(e\left(\frac{155}{168}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{337}{504}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{407}{504}\right)\)
\(\chi_{10585}(704,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{252}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{169}{252}\right)\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{181}{504}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{419}{504}\right)\)
\(\chi_{10585}(744,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{252}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{227}{252}\right)\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{179}{504}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{445}{504}\right)\)
\(\chi_{10585}(989,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{252}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{235}{252}\right)\)	\(e\left(\frac{17}{168}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{283}{504}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{101}{504}\right)\)
\(\chi_{10585}(1134,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{227}{252}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{179}{252}\right)\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{59}{504}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{493}{504}\right)\)
\(\chi_{10585}(1139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{252}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{113}{252}\right)\)	\(e\left(\frac{55}{168}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{461}{504}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{307}{504}\right)\)
\(\chi_{10585}(1199,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{252}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{17}{252}\right)\)	\(e\left(\frac{67}{168}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{473}{504}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{151}{504}\right)\)
\(\chi_{10585}(1319,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{252}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{247}{252}\right)\)	\(e\left(\frac{89}{168}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{187}{504}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{341}{504}\right)\)
\(\chi_{10585}(1429,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{209}{252}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{197}{252}\right)\)	\(e\left(\frac{55}{168}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{293}{504}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{475}{504}\right)\)
\(\chi_{10585}(1489,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{252}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{185}{252}\right)\)	\(e\left(\frac{67}{168}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{137}{504}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{487}{504}\right)\)
\(\chi_{10585}(1519,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{239}{252}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{83}{252}\right)\)	\(e\left(\frac{85}{168}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{71}{504}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{337}{504}\right)\)
\(\chi_{10585}(1564,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{252}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{89}{252}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{401}{504}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{79}{504}\right)\)
\(\chi_{10585}(1674,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{252}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{211}{252}\right)\)	\(e\left(\frac{125}{168}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{223}{504}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{377}{504}\right)\)
\(\chi_{10585}(1684,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{252}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{103}{252}\right)\)	\(e\left(\frac{65}{168}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{331}{504}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{485}{504}\right)\)
\(\chi_{10585}(1854,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{233}{252}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{5}{252}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{65}{504}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{415}{504}\right)\)
\(\chi_{10585}(1859,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{227}{252}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{179}{252}\right)\)	\(e\left(\frac{157}{168}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{311}{504}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{241}{504}\right)\)
\(\chi_{10585}(1924,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{252}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{241}{252}\right)\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{361}{504}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{95}{504}\right)\)
\(\chi_{10585}(1929,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{252}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{233}{252}\right)\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{257}{504}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{439}{504}\right)\)
\(\chi_{10585}(2004,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{252}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{235}{252}\right)\)	\(e\left(\frac{101}{168}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{31}{504}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{353}{504}\right)\)
\(\chi_{10585}(2049,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{235}{252}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{31}{252}\right)\)	\(e\left(\frac{137}{168}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{403}{504}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{53}{504}\right)\)
\(\chi_{10585}(2164,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{252}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{97}{252}\right)\)	\(e\left(\frac{71}{168}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{253}{504}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{491}{504}\right)\)
\(\chi_{10585}(2219,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{252}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{149}{252}\right)\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{425}{504}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{271}{504}\right)\)

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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	10585.lw
Modulus	$10585$
Conductor	$10585$
Order	$504$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(10585\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(10585\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(504\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);