LMFDB - Dirichlet character orbit 58492.jo

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(58492, base_ring=CyclotomicField(2088)) M = H._module chi = DirichletCharacter(H, M([1044,348,1325])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(31, 58492)) 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("58492.31"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$58492$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$58492$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$2088$	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:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{2088})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 2088 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 21 of 672 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{58492}(31,\cdot)$	$-1$	$1$	$e\left(\frac{263}{1044}\right)$	$e\left(\frac{935}{1044}\right)$	$e\left(\frac{263}{522}\right)$	$e\left(\frac{347}{2088}\right)$	$e\left(\frac{1013}{1044}\right)$	$e\left(\frac{77}{522}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{103}{232}\right)$	$e\left(\frac{89}{232}\right)$	$e\left(\frac{413}{522}\right)$
$\chi_{58492}(59,\cdot)$	$-1$	$1$	$e\left(\frac{689}{1044}\right)$	$e\left(\frac{425}{1044}\right)$	$e\left(\frac{167}{522}\right)$	$e\left(\frac{1961}{2088}\right)$	$e\left(\frac{935}{1044}\right)$	$e\left(\frac{35}{522}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{205}{232}\right)$	$e\left(\frac{51}{232}\right)$	$e\left(\frac{425}{522}\right)$
$\chi_{58492}(115,\cdot)$	$-1$	$1$	$e\left(\frac{869}{1044}\right)$	$e\left(\frac{533}{1044}\right)$	$e\left(\frac{347}{522}\right)$	$e\left(\frac{1349}{2088}\right)$	$e\left(\frac{755}{1044}\right)$	$e\left(\frac{179}{522}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{137}{232}\right)$	$e\left(\frac{231}{232}\right)$	$e\left(\frac{11}{522}\right)$
$\chi_{58492}(131,\cdot)$	$-1$	$1$	$e\left(\frac{451}{1044}\right)$	$e\left(\frac{607}{1044}\right)$	$e\left(\frac{451}{522}\right)$	$e\left(\frac{79}{2088}\right)$	$e\left(\frac{709}{1044}\right)$	$e\left(\frac{7}{522}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{99}{232}\right)$	$e\left(\frac{45}{232}\right)$	$e\left(\frac{85}{522}\right)$
$\chi_{58492}(227,\cdot)$	$-1$	$1$	$e\left(\frac{455}{1044}\right)$	$e\left(\frac{911}{1044}\right)$	$e\left(\frac{455}{522}\right)$	$e\left(\frac{1295}{2088}\right)$	$e\left(\frac{125}{1044}\right)$	$e\left(\frac{161}{522}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{131}{232}\right)$	$e\left(\frac{165}{232}\right)$	$e\left(\frac{389}{522}\right)$
$\chi_{58492}(271,\cdot)$	$-1$	$1$	$e\left(\frac{619}{1044}\right)$	$e\left(\frac{847}{1044}\right)$	$e\left(\frac{97}{522}\right)$	$e\left(\frac{1039}{2088}\right)$	$e\left(\frac{193}{1044}\right)$	$e\left(\frac{211}{522}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{51}{232}\right)$	$e\left(\frac{213}{232}\right)$	$e\left(\frac{325}{522}\right)$
$\chi_{58492}(283,\cdot)$	$-1$	$1$	$e\left(\frac{59}{1044}\right)$	$e\left(\frac{47}{1044}\right)$	$e\left(\frac{59}{522}\right)$	$e\left(\frac{971}{2088}\right)$	$e\left(\frac{521}{1044}\right)$	$e\left(\frac{53}{522}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{95}{232}\right)$	$e\left(\frac{1}{232}\right)$	$e\left(\frac{47}{522}\right)$
$\chi_{58492}(439,\cdot)$	$-1$	$1$	$e\left(\frac{187}{1044}\right)$	$e\left(\frac{379}{1044}\right)$	$e\left(\frac{187}{522}\right)$	$e\left(\frac{1255}{2088}\right)$	$e\left(\frac{625}{1044}\right)$	$e\left(\frac{283}{522}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{75}{232}\right)$	$e\left(\frac{13}{232}\right)$	$e\left(\frac{379}{522}\right)$
$\chi_{58492}(495,\cdot)$	$-1$	$1$	$e\left(\frac{283}{1044}\right)$	$e\left(\frac{367}{1044}\right)$	$e\left(\frac{283}{522}\right)$	$e\left(\frac{1207}{2088}\right)$	$e\left(\frac{181}{1044}\right)$	$e\left(\frac{325}{522}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{147}{232}\right)$	$e\left(\frac{109}{232}\right)$	$e\left(\frac{367}{522}\right)$
$\chi_{58492}(591,\cdot)$	$-1$	$1$	$e\left(\frac{737}{1044}\right)$	$e\left(\frac{941}{1044}\right)$	$e\left(\frac{215}{522}\right)$	$e\left(\frac{1937}{2088}\right)$	$e\left(\frac{191}{1044}\right)$	$e\left(\frac{317}{522}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{125}{232}\right)$	$e\left(\frac{99}{232}\right)$	$e\left(\frac{419}{522}\right)$
$\chi_{58492}(607,\cdot)$	$-1$	$1$	$e\left(\frac{565}{1044}\right)$	$e\left(\frac{397}{1044}\right)$	$e\left(\frac{43}{522}\right)$	$e\left(\frac{805}{2088}\right)$	$e\left(\frac{247}{1044}\right)$	$e\left(\frac{481}{522}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{25}{232}\right)$	$e\left(\frac{159}{232}\right)$	$e\left(\frac{397}{522}\right)$
$\chi_{58492}(635,\cdot)$	$-1$	$1$	$e\left(\frac{481}{1044}\right)$	$e\left(\frac{277}{1044}\right)$	$e\left(\frac{481}{522}\right)$	$e\left(\frac{1369}{2088}\right)$	$e\left(\frac{1027}{1044}\right)$	$e\left(\frac{379}{522}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{165}{232}\right)$	$e\left(\frac{75}{232}\right)$	$e\left(\frac{277}{522}\right)$
$\chi_{58492}(747,\cdot)$	$-1$	$1$	$e\left(\frac{787}{1044}\right)$	$e\left(\frac{43}{1044}\right)$	$e\left(\frac{265}{522}\right)$	$e\left(\frac{955}{2088}\right)$	$e\left(\frac{721}{1044}\right)$	$e\left(\frac{415}{522}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{119}{232}\right)$	$e\left(\frac{33}{232}\right)$	$e\left(\frac{43}{522}\right)$
$\chi_{58492}(831,\cdot)$	$-1$	$1$	$e\left(\frac{685}{1044}\right)$	$e\left(\frac{121}{1044}\right)$	$e\left(\frac{163}{522}\right)$	$e\left(\frac{1789}{2088}\right)$	$e\left(\frac{475}{1044}\right)$	$e\left(\frac{403}{522}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{57}{232}\right)$	$e\left(\frac{47}{232}\right)$	$e\left(\frac{121}{522}\right)$
$\chi_{58492}(871,\cdot)$	$-1$	$1$	$e\left(\frac{209}{1044}\right)$	$e\left(\frac{485}{1044}\right)$	$e\left(\frac{209}{522}\right)$	$e\left(\frac{1157}{2088}\right)$	$e\left(\frac{23}{1044}\right)$	$e\left(\frac{347}{522}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{193}{232}\right)$	$e\left(\frac{151}{232}\right)$	$e\left(\frac{485}{522}\right)$
$\chi_{58492}(887,\cdot)$	$-1$	$1$	$e\left(\frac{649}{1044}\right)$	$e\left(\frac{517}{1044}\right)$	$e\left(\frac{127}{522}\right)$	$e\left(\frac{1285}{2088}\right)$	$e\left(\frac{511}{1044}\right)$	$e\left(\frac{61}{522}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{232}\right)$	$e\left(\frac{127}{232}\right)$	$e\left(\frac{517}{522}\right)$
$\chi_{58492}(1139,\cdot)$	$-1$	$1$	$e\left(\frac{169}{1044}\right)$	$e\left(\frac{577}{1044}\right)$	$e\left(\frac{169}{522}\right)$	$e\left(\frac{1525}{2088}\right)$	$e\left(\frac{643}{1044}\right)$	$e\left(\frac{373}{522}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{105}{232}\right)$	$e\left(\frac{111}{232}\right)$	$e\left(\frac{55}{522}\right)$
$\chi_{58492}(1179,\cdot)$	$-1$	$1$	$e\left(\frac{719}{1044}\right)$	$e\left(\frac{95}{1044}\right)$	$e\left(\frac{197}{522}\right)$	$e\left(\frac{1163}{2088}\right)$	$e\left(\frac{209}{1044}\right)$	$e\left(\frac{407}{522}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{39}{232}\right)$	$e\left(\frac{81}{232}\right)$	$e\left(\frac{95}{522}\right)$
$\chi_{58492}(1223,\cdot)$	$-1$	$1$	$e\left(\frac{307}{1044}\right)$	$e\left(\frac{103}{1044}\right)$	$e\left(\frac{307}{522}\right)$	$e\left(\frac{1195}{2088}\right)$	$e\left(\frac{853}{1044}\right)$	$e\left(\frac{205}{522}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{223}{232}\right)$	$e\left(\frac{17}{232}\right)$	$e\left(\frac{103}{522}\right)$
$\chi_{58492}(1307,\cdot)$	$-1$	$1$	$e\left(\frac{85}{1044}\right)$	$e\left(\frac{457}{1044}\right)$	$e\left(\frac{85}{522}\right)$	$e\left(\frac{1045}{2088}\right)$	$e\left(\frac{379}{1044}\right)$	$e\left(\frac{271}{522}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{129}{232}\right)$	$e\left(\frac{143}{232}\right)$	$e\left(\frac{457}{522}\right)$
$\chi_{58492}(1543,\cdot)$	$-1$	$1$	$e\left(\frac{239}{1044}\right)$	$e\left(\frac{155}{1044}\right)$	$e\left(\frac{239}{522}\right)$	$e\left(\frac{359}{2088}\right)$	$e\left(\frac{341}{1044}\right)$	$e\left(\frac{197}{522}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{27}{232}\right)$	$e\left(\frac{181}{232}\right)$	$e\left(\frac{155}{522}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{58492}(31,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{263}{1044}\right)\)	\(e\left(\frac{935}{1044}\right)\)	\(e\left(\frac{263}{522}\right)\)	\(e\left(\frac{347}{2088}\right)\)	\(e\left(\frac{1013}{1044}\right)\)	\(e\left(\frac{77}{522}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{103}{232}\right)\)	\(e\left(\frac{89}{232}\right)\)	\(e\left(\frac{413}{522}\right)\)
\(\chi_{58492}(59,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{689}{1044}\right)\)	\(e\left(\frac{425}{1044}\right)\)	\(e\left(\frac{167}{522}\right)\)	\(e\left(\frac{1961}{2088}\right)\)	\(e\left(\frac{935}{1044}\right)\)	\(e\left(\frac{35}{522}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{205}{232}\right)\)	\(e\left(\frac{51}{232}\right)\)	\(e\left(\frac{425}{522}\right)\)
\(\chi_{58492}(115,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{869}{1044}\right)\)	\(e\left(\frac{533}{1044}\right)\)	\(e\left(\frac{347}{522}\right)\)	\(e\left(\frac{1349}{2088}\right)\)	\(e\left(\frac{755}{1044}\right)\)	\(e\left(\frac{179}{522}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{137}{232}\right)\)	\(e\left(\frac{231}{232}\right)\)	\(e\left(\frac{11}{522}\right)\)
\(\chi_{58492}(131,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{451}{1044}\right)\)	\(e\left(\frac{607}{1044}\right)\)	\(e\left(\frac{451}{522}\right)\)	\(e\left(\frac{79}{2088}\right)\)	\(e\left(\frac{709}{1044}\right)\)	\(e\left(\frac{7}{522}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{99}{232}\right)\)	\(e\left(\frac{45}{232}\right)\)	\(e\left(\frac{85}{522}\right)\)
\(\chi_{58492}(227,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{455}{1044}\right)\)	\(e\left(\frac{911}{1044}\right)\)	\(e\left(\frac{455}{522}\right)\)	\(e\left(\frac{1295}{2088}\right)\)	\(e\left(\frac{125}{1044}\right)\)	\(e\left(\frac{161}{522}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{131}{232}\right)\)	\(e\left(\frac{165}{232}\right)\)	\(e\left(\frac{389}{522}\right)\)
\(\chi_{58492}(271,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{619}{1044}\right)\)	\(e\left(\frac{847}{1044}\right)\)	\(e\left(\frac{97}{522}\right)\)	\(e\left(\frac{1039}{2088}\right)\)	\(e\left(\frac{193}{1044}\right)\)	\(e\left(\frac{211}{522}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{51}{232}\right)\)	\(e\left(\frac{213}{232}\right)\)	\(e\left(\frac{325}{522}\right)\)
\(\chi_{58492}(283,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{1044}\right)\)	\(e\left(\frac{47}{1044}\right)\)	\(e\left(\frac{59}{522}\right)\)	\(e\left(\frac{971}{2088}\right)\)	\(e\left(\frac{521}{1044}\right)\)	\(e\left(\frac{53}{522}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{95}{232}\right)\)	\(e\left(\frac{1}{232}\right)\)	\(e\left(\frac{47}{522}\right)\)
\(\chi_{58492}(439,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{187}{1044}\right)\)	\(e\left(\frac{379}{1044}\right)\)	\(e\left(\frac{187}{522}\right)\)	\(e\left(\frac{1255}{2088}\right)\)	\(e\left(\frac{625}{1044}\right)\)	\(e\left(\frac{283}{522}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{75}{232}\right)\)	\(e\left(\frac{13}{232}\right)\)	\(e\left(\frac{379}{522}\right)\)
\(\chi_{58492}(495,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{283}{1044}\right)\)	\(e\left(\frac{367}{1044}\right)\)	\(e\left(\frac{283}{522}\right)\)	\(e\left(\frac{1207}{2088}\right)\)	\(e\left(\frac{181}{1044}\right)\)	\(e\left(\frac{325}{522}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{147}{232}\right)\)	\(e\left(\frac{109}{232}\right)\)	\(e\left(\frac{367}{522}\right)\)
\(\chi_{58492}(591,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{737}{1044}\right)\)	\(e\left(\frac{941}{1044}\right)\)	\(e\left(\frac{215}{522}\right)\)	\(e\left(\frac{1937}{2088}\right)\)	\(e\left(\frac{191}{1044}\right)\)	\(e\left(\frac{317}{522}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{125}{232}\right)\)	\(e\left(\frac{99}{232}\right)\)	\(e\left(\frac{419}{522}\right)\)
\(\chi_{58492}(607,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{565}{1044}\right)\)	\(e\left(\frac{397}{1044}\right)\)	\(e\left(\frac{43}{522}\right)\)	\(e\left(\frac{805}{2088}\right)\)	\(e\left(\frac{247}{1044}\right)\)	\(e\left(\frac{481}{522}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{25}{232}\right)\)	\(e\left(\frac{159}{232}\right)\)	\(e\left(\frac{397}{522}\right)\)
\(\chi_{58492}(635,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{481}{1044}\right)\)	\(e\left(\frac{277}{1044}\right)\)	\(e\left(\frac{481}{522}\right)\)	\(e\left(\frac{1369}{2088}\right)\)	\(e\left(\frac{1027}{1044}\right)\)	\(e\left(\frac{379}{522}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{165}{232}\right)\)	\(e\left(\frac{75}{232}\right)\)	\(e\left(\frac{277}{522}\right)\)
\(\chi_{58492}(747,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{787}{1044}\right)\)	\(e\left(\frac{43}{1044}\right)\)	\(e\left(\frac{265}{522}\right)\)	\(e\left(\frac{955}{2088}\right)\)	\(e\left(\frac{721}{1044}\right)\)	\(e\left(\frac{415}{522}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{119}{232}\right)\)	\(e\left(\frac{33}{232}\right)\)	\(e\left(\frac{43}{522}\right)\)
\(\chi_{58492}(831,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{685}{1044}\right)\)	\(e\left(\frac{121}{1044}\right)\)	\(e\left(\frac{163}{522}\right)\)	\(e\left(\frac{1789}{2088}\right)\)	\(e\left(\frac{475}{1044}\right)\)	\(e\left(\frac{403}{522}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{57}{232}\right)\)	\(e\left(\frac{47}{232}\right)\)	\(e\left(\frac{121}{522}\right)\)
\(\chi_{58492}(871,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{209}{1044}\right)\)	\(e\left(\frac{485}{1044}\right)\)	\(e\left(\frac{209}{522}\right)\)	\(e\left(\frac{1157}{2088}\right)\)	\(e\left(\frac{23}{1044}\right)\)	\(e\left(\frac{347}{522}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{193}{232}\right)\)	\(e\left(\frac{151}{232}\right)\)	\(e\left(\frac{485}{522}\right)\)
\(\chi_{58492}(887,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{649}{1044}\right)\)	\(e\left(\frac{517}{1044}\right)\)	\(e\left(\frac{127}{522}\right)\)	\(e\left(\frac{1285}{2088}\right)\)	\(e\left(\frac{511}{1044}\right)\)	\(e\left(\frac{61}{522}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{1}{232}\right)\)	\(e\left(\frac{127}{232}\right)\)	\(e\left(\frac{517}{522}\right)\)
\(\chi_{58492}(1139,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{169}{1044}\right)\)	\(e\left(\frac{577}{1044}\right)\)	\(e\left(\frac{169}{522}\right)\)	\(e\left(\frac{1525}{2088}\right)\)	\(e\left(\frac{643}{1044}\right)\)	\(e\left(\frac{373}{522}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{105}{232}\right)\)	\(e\left(\frac{111}{232}\right)\)	\(e\left(\frac{55}{522}\right)\)
\(\chi_{58492}(1179,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{719}{1044}\right)\)	\(e\left(\frac{95}{1044}\right)\)	\(e\left(\frac{197}{522}\right)\)	\(e\left(\frac{1163}{2088}\right)\)	\(e\left(\frac{209}{1044}\right)\)	\(e\left(\frac{407}{522}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{39}{232}\right)\)	\(e\left(\frac{81}{232}\right)\)	\(e\left(\frac{95}{522}\right)\)
\(\chi_{58492}(1223,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{307}{1044}\right)\)	\(e\left(\frac{103}{1044}\right)\)	\(e\left(\frac{307}{522}\right)\)	\(e\left(\frac{1195}{2088}\right)\)	\(e\left(\frac{853}{1044}\right)\)	\(e\left(\frac{205}{522}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{223}{232}\right)\)	\(e\left(\frac{17}{232}\right)\)	\(e\left(\frac{103}{522}\right)\)
\(\chi_{58492}(1307,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{85}{1044}\right)\)	\(e\left(\frac{457}{1044}\right)\)	\(e\left(\frac{85}{522}\right)\)	\(e\left(\frac{1045}{2088}\right)\)	\(e\left(\frac{379}{1044}\right)\)	\(e\left(\frac{271}{522}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{129}{232}\right)\)	\(e\left(\frac{143}{232}\right)\)	\(e\left(\frac{457}{522}\right)\)
\(\chi_{58492}(1543,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{239}{1044}\right)\)	\(e\left(\frac{155}{1044}\right)\)	\(e\left(\frac{239}{522}\right)\)	\(e\left(\frac{359}{2088}\right)\)	\(e\left(\frac{341}{1044}\right)\)	\(e\left(\frac{197}{522}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{27}{232}\right)\)	\(e\left(\frac{181}{232}\right)\)	\(e\left(\frac{155}{522}\right)\)

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First 21 of 672 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	58492.jo
Modulus	$58492$
Conductor	$58492$
Order	$2088$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(58492\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(58492\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(2088\)	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:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);