LMFDB - Dirichlet character orbit 5057.bl

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5057, base_ring=CyclotomicField(1164)) M = H._module chi = DirichletCharacter(H, M([970,255])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(10, 5057)) 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("5057.10"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$5057$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$5057$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$1164$	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:	$\Q(\zeta_{1164})$
Fixed field:	Number field defined by a degree 1164 polynomial (not computed)

First 31 of 384 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{5057}(10,\cdot)$	$-1$	$1$	$e\left(\frac{61}{1164}\right)$	$e\left(\frac{817}{1164}\right)$	$e\left(\frac{61}{582}\right)$	$e\left(\frac{175}{194}\right)$	$e\left(\frac{439}{582}\right)$	$e\left(\frac{13}{582}\right)$	$e\left(\frac{61}{388}\right)$	$e\left(\frac{235}{582}\right)$	$e\left(\frac{1111}{1164}\right)$	$e\left(\frac{299}{582}\right)$
$\chi_{5057}(23,\cdot)$	$-1$	$1$	$e\left(\frac{1009}{1164}\right)$	$e\left(\frac{481}{1164}\right)$	$e\left(\frac{427}{582}\right)$	$e\left(\frac{61}{194}\right)$	$e\left(\frac{163}{582}\right)$	$e\left(\frac{91}{582}\right)$	$e\left(\frac{233}{388}\right)$	$e\left(\frac{481}{582}\right)$	$e\left(\frac{211}{1164}\right)$	$e\left(\frac{347}{582}\right)$
$\chi_{5057}(43,\cdot)$	$-1$	$1$	$e\left(\frac{317}{1164}\right)$	$e\left(\frac{353}{1164}\right)$	$e\left(\frac{317}{582}\right)$	$e\left(\frac{73}{194}\right)$	$e\left(\frac{335}{582}\right)$	$e\left(\frac{287}{582}\right)$	$e\left(\frac{317}{388}\right)$	$e\left(\frac{353}{582}\right)$	$e\left(\frac{755}{1164}\right)$	$e\left(\frac{199}{582}\right)$
$\chi_{5057}(56,\cdot)$	$-1$	$1$	$e\left(\frac{23}{1164}\right)$	$e\left(\frac{995}{1164}\right)$	$e\left(\frac{23}{582}\right)$	$e\left(\frac{31}{194}\right)$	$e\left(\frac{509}{582}\right)$	$e\left(\frac{377}{582}\right)$	$e\left(\frac{23}{388}\right)$	$e\left(\frac{413}{582}\right)$	$e\left(\frac{209}{1164}\right)$	$e\left(\frac{523}{582}\right)$
$\chi_{5057}(75,\cdot)$	$-1$	$1$	$e\left(\frac{1123}{1164}\right)$	$e\left(\frac{1111}{1164}\right)$	$e\left(\frac{541}{582}\right)$	$e\left(\frac{105}{194}\right)$	$e\left(\frac{535}{582}\right)$	$e\left(\frac{163}{582}\right)$	$e\left(\frac{347}{388}\right)$	$e\left(\frac{529}{582}\right)$	$e\left(\frac{589}{1164}\right)$	$e\left(\frac{257}{582}\right)$
$\chi_{5057}(82,\cdot)$	$-1$	$1$	$e\left(\frac{575}{1164}\right)$	$e\left(\frac{431}{1164}\right)$	$e\left(\frac{575}{582}\right)$	$e\left(\frac{193}{194}\right)$	$e\left(\frac{503}{582}\right)$	$e\left(\frac{113}{582}\right)$	$e\left(\frac{187}{388}\right)$	$e\left(\frac{431}{582}\right)$	$e\left(\frac{569}{1164}\right)$	$e\left(\frac{271}{582}\right)$
$\chi_{5057}(88,\cdot)$	$-1$	$1$	$e\left(\frac{331}{1164}\right)$	$e\left(\frac{655}{1164}\right)$	$e\left(\frac{331}{582}\right)$	$e\left(\frac{75}{194}\right)$	$e\left(\frac{493}{582}\right)$	$e\left(\frac{61}{582}\right)$	$e\left(\frac{331}{388}\right)$	$e\left(\frac{73}{582}\right)$	$e\left(\frac{781}{1164}\right)$	$e\left(\frac{239}{582}\right)$
$\chi_{5057}(101,\cdot)$	$-1$	$1$	$e\left(\frac{865}{1164}\right)$	$e\left(\frac{1033}{1164}\right)$	$e\left(\frac{283}{582}\right)$	$e\left(\frac{179}{194}\right)$	$e\left(\frac{367}{582}\right)$	$e\left(\frac{337}{582}\right)$	$e\left(\frac{89}{388}\right)$	$e\left(\frac{451}{582}\right)$	$e\left(\frac{775}{1164}\right)$	$e\left(\frac{185}{582}\right)$
$\chi_{5057}(108,\cdot)$	$-1$	$1$	$e\left(\frac{311}{1164}\right)$	$e\left(\frac{1055}{1164}\right)$	$e\left(\frac{311}{582}\right)$	$e\left(\frac{183}{194}\right)$	$e\left(\frac{101}{582}\right)$	$e\left(\frac{467}{582}\right)$	$e\left(\frac{311}{388}\right)$	$e\left(\frac{473}{582}\right)$	$e\left(\frac{245}{1164}\right)$	$e\left(\frac{265}{582}\right)$
$\chi_{5057}(134,\cdot)$	$-1$	$1$	$e\left(\frac{641}{1164}\right)$	$e\left(\frac{857}{1164}\right)$	$e\left(\frac{59}{582}\right)$	$e\left(\frac{147}{194}\right)$	$e\left(\frac{167}{582}\right)$	$e\left(\frac{461}{582}\right)$	$e\left(\frac{253}{388}\right)$	$e\left(\frac{275}{582}\right)$	$e\left(\frac{359}{1164}\right)$	$e\left(\frac{127}{582}\right)$
$\chi_{5057}(147,\cdot)$	$-1$	$1$	$e\left(\frac{647}{1164}\right)$	$e\left(\frac{155}{1164}\right)$	$e\left(\frac{65}{582}\right)$	$e\left(\frac{37}{194}\right)$	$e\left(\frac{401}{582}\right)$	$e\left(\frac{281}{582}\right)$	$e\left(\frac{259}{388}\right)$	$e\left(\frac{155}{582}\right)$	$e\left(\frac{869}{1164}\right)$	$e\left(\frac{61}{582}\right)$
$\chi_{5057}(160,\cdot)$	$-1$	$1$	$e\left(\frac{461}{1164}\right)$	$e\left(\frac{965}{1164}\right)$	$e\left(\frac{461}{582}\right)$	$e\left(\frac{149}{194}\right)$	$e\left(\frac{131}{582}\right)$	$e\left(\frac{41}{582}\right)$	$e\left(\frac{73}{388}\right)$	$e\left(\frac{383}{582}\right)$	$e\left(\frac{191}{1164}\right)$	$e\left(\frac{361}{582}\right)$
$\chi_{5057}(186,\cdot)$	$-1$	$1$	$e\left(\frac{737}{1164}\right)$	$e\left(\frac{101}{1164}\right)$	$e\left(\frac{155}{582}\right)$	$e\left(\frac{133}{194}\right)$	$e\left(\frac{419}{582}\right)$	$e\left(\frac{491}{582}\right)$	$e\left(\frac{349}{388}\right)$	$e\left(\frac{101}{582}\right)$	$e\left(\frac{371}{1164}\right)$	$e\left(\frac{235}{582}\right)$
$\chi_{5057}(192,\cdot)$	$-1$	$1$	$e\left(\frac{637}{1164}\right)$	$e\left(\frac{937}{1164}\right)$	$e\left(\frac{55}{582}\right)$	$e\left(\frac{91}{194}\right)$	$e\left(\frac{205}{582}\right)$	$e\left(\frac{193}{582}\right)$	$e\left(\frac{249}{388}\right)$	$e\left(\frac{355}{582}\right)$	$e\left(\frac{19}{1164}\right)$	$e\left(\frac{365}{582}\right)$
$\chi_{5057}(199,\cdot)$	$-1$	$1$	$e\left(\frac{653}{1164}\right)$	$e\left(\frac{617}{1164}\right)$	$e\left(\frac{71}{582}\right)$	$e\left(\frac{121}{194}\right)$	$e\left(\frac{53}{582}\right)$	$e\left(\frac{101}{582}\right)$	$e\left(\frac{265}{388}\right)$	$e\left(\frac{35}{582}\right)$	$e\left(\frac{215}{1164}\right)$	$e\left(\frac{577}{582}\right)$
$\chi_{5057}(212,\cdot)$	$-1$	$1$	$e\left(\frac{263}{1164}\right)$	$e\left(\frac{851}{1164}\right)$	$e\left(\frac{263}{582}\right)$	$e\left(\frac{93}{194}\right)$	$e\left(\frac{557}{582}\right)$	$e\left(\frac{161}{582}\right)$	$e\left(\frac{263}{388}\right)$	$e\left(\frac{269}{582}\right)$	$e\left(\frac{821}{1164}\right)$	$e\left(\frac{211}{582}\right)$
$\chi_{5057}(231,\cdot)$	$-1$	$1$	$e\left(\frac{955}{1164}\right)$	$e\left(\frac{979}{1164}\right)$	$e\left(\frac{373}{582}\right)$	$e\left(\frac{81}{194}\right)$	$e\left(\frac{385}{582}\right)$	$e\left(\frac{547}{582}\right)$	$e\left(\frac{179}{388}\right)$	$e\left(\frac{397}{582}\right)$	$e\left(\frac{277}{1164}\right)$	$e\left(\frac{359}{582}\right)$
$\chi_{5057}(238,\cdot)$	$-1$	$1$	$e\left(\frac{1145}{1164}\right)$	$e\left(\frac{89}{1164}\right)$	$e\left(\frac{563}{582}\right)$	$e\left(\frac{25}{194}\right)$	$e\left(\frac{35}{582}\right)$	$e\left(\frac{473}{582}\right)$	$e\left(\frac{369}{388}\right)$	$e\left(\frac{89}{582}\right)$	$e\left(\frac{131}{1164}\right)$	$e\left(\frac{403}{582}\right)$
$\chi_{5057}(244,\cdot)$	$-1$	$1$	$e\left(\frac{781}{1164}\right)$	$e\left(\frac{385}{1164}\right)$	$e\left(\frac{199}{582}\right)$	$e\left(\frac{167}{194}\right)$	$e\left(\frac{1}{582}\right)$	$e\left(\frac{529}{582}\right)$	$e\left(\frac{5}{388}\right)$	$e\left(\frac{385}{582}\right)$	$e\left(\frac{619}{1164}\right)$	$e\left(\frac{527}{582}\right)$
$\chi_{5057}(251,\cdot)$	$-1$	$1$	$e\left(\frac{467}{1164}\right)$	$e\left(\frac{263}{1164}\right)$	$e\left(\frac{467}{582}\right)$	$e\left(\frac{39}{194}\right)$	$e\left(\frac{365}{582}\right)$	$e\left(\frac{443}{582}\right)$	$e\left(\frac{79}{388}\right)$	$e\left(\frac{263}{582}\right)$	$e\left(\frac{701}{1164}\right)$	$e\left(\frac{295}{582}\right)$
$\chi_{5057}(257,\cdot)$	$-1$	$1$	$e\left(\frac{559}{1164}\right)$	$e\left(\frac{751}{1164}\right)$	$e\left(\frac{559}{582}\right)$	$e\left(\frac{163}{194}\right)$	$e\left(\frac{73}{582}\right)$	$e\left(\frac{205}{582}\right)$	$e\left(\frac{171}{388}\right)$	$e\left(\frac{169}{582}\right)$	$e\left(\frac{373}{1164}\right)$	$e\left(\frac{59}{582}\right)$
$\chi_{5057}(329,\cdot)$	$-1$	$1$	$e\left(\frac{683}{1164}\right)$	$e\left(\frac{599}{1164}\right)$	$e\left(\frac{101}{582}\right)$	$e\left(\frac{153}{194}\right)$	$e\left(\frac{59}{582}\right)$	$e\left(\frac{365}{582}\right)$	$e\left(\frac{295}{388}\right)$	$e\left(\frac{17}{582}\right)$	$e\left(\frac{437}{1164}\right)$	$e\left(\frac{247}{582}\right)$
$\chi_{5057}(342,\cdot)$	$-1$	$1$	$e\left(\frac{281}{1164}\right)$	$e\left(\frac{1073}{1164}\right)$	$e\left(\frac{281}{582}\right)$	$e\left(\frac{151}{194}\right)$	$e\left(\frac{95}{582}\right)$	$e\left(\frac{203}{582}\right)$	$e\left(\frac{281}{388}\right)$	$e\left(\frac{491}{582}\right)$	$e\left(\frac{23}{1164}\right)$	$e\left(\frac{13}{582}\right)$
$\chi_{5057}(355,\cdot)$	$-1$	$1$	$e\left(\frac{743}{1164}\right)$	$e\left(\frac{563}{1164}\right)$	$e\left(\frac{161}{582}\right)$	$e\left(\frac{23}{194}\right)$	$e\left(\frac{71}{582}\right)$	$e\left(\frac{311}{582}\right)$	$e\left(\frac{355}{388}\right)$	$e\left(\frac{563}{582}\right)$	$e\left(\frac{881}{1164}\right)$	$e\left(\frac{169}{582}\right)$
$\chi_{5057}(368,\cdot)$	$-1$	$1$	$e\left(\frac{245}{1164}\right)$	$e\left(\frac{629}{1164}\right)$	$e\left(\frac{245}{582}\right)$	$e\left(\frac{35}{194}\right)$	$e\left(\frac{437}{582}\right)$	$e\left(\frac{119}{582}\right)$	$e\left(\frac{245}{388}\right)$	$e\left(\frac{47}{582}\right)$	$e\left(\frac{455}{1164}\right)$	$e\left(\frac{409}{582}\right)$
$\chi_{5057}(374,\cdot)$	$-1$	$1$	$e\left(\frac{289}{1164}\right)$	$e\left(\frac{913}{1164}\right)$	$e\left(\frac{289}{582}\right)$	$e\left(\frac{69}{194}\right)$	$e\left(\frac{19}{582}\right)$	$e\left(\frac{157}{582}\right)$	$e\left(\frac{289}{388}\right)$	$e\left(\frac{331}{582}\right)$	$e\left(\frac{703}{1164}\right)$	$e\left(\frac{119}{582}\right)$
$\chi_{5057}(381,\cdot)$	$-1$	$1$	$e\left(\frac{785}{1164}\right)$	$e\left(\frac{305}{1164}\right)$	$e\left(\frac{203}{582}\right)$	$e\left(\frac{29}{194}\right)$	$e\left(\frac{545}{582}\right)$	$e\left(\frac{215}{582}\right)$	$e\left(\frac{9}{388}\right)$	$e\left(\frac{305}{582}\right)$	$e\left(\frac{959}{1164}\right)$	$e\left(\frac{289}{582}\right)$
$\chi_{5057}(387,\cdot)$	$-1$	$1$	$e\left(\frac{391}{1164}\right)$	$e\left(\frac{619}{1164}\right)$	$e\left(\frac{391}{582}\right)$	$e\left(\frac{139}{194}\right)$	$e\left(\frac{505}{582}\right)$	$e\left(\frac{7}{582}\right)$	$e\left(\frac{3}{388}\right)$	$e\left(\frac{37}{582}\right)$	$e\left(\frac{61}{1164}\right)$	$e\left(\frac{161}{582}\right)$
$\chi_{5057}(407,\cdot)$	$-1$	$1$	$e\left(\frac{659}{1164}\right)$	$e\left(\frac{1079}{1164}\right)$	$e\left(\frac{77}{582}\right)$	$e\left(\frac{11}{194}\right)$	$e\left(\frac{287}{582}\right)$	$e\left(\frac{503}{582}\right)$	$e\left(\frac{271}{388}\right)$	$e\left(\frac{497}{582}\right)$	$e\left(\frac{725}{1164}\right)$	$e\left(\frac{511}{582}\right)$
$\chi_{5057}(420,\cdot)$	$-1$	$1$	$e\left(\frac{1085}{1164}\right)$	$e\left(\frac{125}{1164}\right)$	$e\left(\frac{503}{582}\right)$	$e\left(\frac{155}{194}\right)$	$e\left(\frac{23}{582}\right)$	$e\left(\frac{527}{582}\right)$	$e\left(\frac{309}{388}\right)$	$e\left(\frac{125}{582}\right)$	$e\left(\frac{851}{1164}\right)$	$e\left(\frac{481}{582}\right)$
$\chi_{5057}(426,\cdot)$	$-1$	$1$	$e\left(\frac{919}{1164}\right)$	$e\left(\frac{535}{1164}\right)$	$e\left(\frac{337}{582}\right)$	$e\left(\frac{159}{194}\right)$	$e\left(\frac{145}{582}\right)$	$e\left(\frac{463}{582}\right)$	$e\left(\frac{143}{388}\right)$	$e\left(\frac{535}{582}\right)$	$e\left(\frac{709}{1164}\right)$	$e\left(\frac{173}{582}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{5057}(10,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{1164}\right)\)	\(e\left(\frac{817}{1164}\right)\)	\(e\left(\frac{61}{582}\right)\)	\(e\left(\frac{175}{194}\right)\)	\(e\left(\frac{439}{582}\right)\)	\(e\left(\frac{13}{582}\right)\)	\(e\left(\frac{61}{388}\right)\)	\(e\left(\frac{235}{582}\right)\)	\(e\left(\frac{1111}{1164}\right)\)	\(e\left(\frac{299}{582}\right)\)
\(\chi_{5057}(23,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1009}{1164}\right)\)	\(e\left(\frac{481}{1164}\right)\)	\(e\left(\frac{427}{582}\right)\)	\(e\left(\frac{61}{194}\right)\)	\(e\left(\frac{163}{582}\right)\)	\(e\left(\frac{91}{582}\right)\)	\(e\left(\frac{233}{388}\right)\)	\(e\left(\frac{481}{582}\right)\)	\(e\left(\frac{211}{1164}\right)\)	\(e\left(\frac{347}{582}\right)\)
\(\chi_{5057}(43,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{317}{1164}\right)\)	\(e\left(\frac{353}{1164}\right)\)	\(e\left(\frac{317}{582}\right)\)	\(e\left(\frac{73}{194}\right)\)	\(e\left(\frac{335}{582}\right)\)	\(e\left(\frac{287}{582}\right)\)	\(e\left(\frac{317}{388}\right)\)	\(e\left(\frac{353}{582}\right)\)	\(e\left(\frac{755}{1164}\right)\)	\(e\left(\frac{199}{582}\right)\)
\(\chi_{5057}(56,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{1164}\right)\)	\(e\left(\frac{995}{1164}\right)\)	\(e\left(\frac{23}{582}\right)\)	\(e\left(\frac{31}{194}\right)\)	\(e\left(\frac{509}{582}\right)\)	\(e\left(\frac{377}{582}\right)\)	\(e\left(\frac{23}{388}\right)\)	\(e\left(\frac{413}{582}\right)\)	\(e\left(\frac{209}{1164}\right)\)	\(e\left(\frac{523}{582}\right)\)
\(\chi_{5057}(75,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1123}{1164}\right)\)	\(e\left(\frac{1111}{1164}\right)\)	\(e\left(\frac{541}{582}\right)\)	\(e\left(\frac{105}{194}\right)\)	\(e\left(\frac{535}{582}\right)\)	\(e\left(\frac{163}{582}\right)\)	\(e\left(\frac{347}{388}\right)\)	\(e\left(\frac{529}{582}\right)\)	\(e\left(\frac{589}{1164}\right)\)	\(e\left(\frac{257}{582}\right)\)
\(\chi_{5057}(82,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{575}{1164}\right)\)	\(e\left(\frac{431}{1164}\right)\)	\(e\left(\frac{575}{582}\right)\)	\(e\left(\frac{193}{194}\right)\)	\(e\left(\frac{503}{582}\right)\)	\(e\left(\frac{113}{582}\right)\)	\(e\left(\frac{187}{388}\right)\)	\(e\left(\frac{431}{582}\right)\)	\(e\left(\frac{569}{1164}\right)\)	\(e\left(\frac{271}{582}\right)\)
\(\chi_{5057}(88,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{331}{1164}\right)\)	\(e\left(\frac{655}{1164}\right)\)	\(e\left(\frac{331}{582}\right)\)	\(e\left(\frac{75}{194}\right)\)	\(e\left(\frac{493}{582}\right)\)	\(e\left(\frac{61}{582}\right)\)	\(e\left(\frac{331}{388}\right)\)	\(e\left(\frac{73}{582}\right)\)	\(e\left(\frac{781}{1164}\right)\)	\(e\left(\frac{239}{582}\right)\)
\(\chi_{5057}(101,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{865}{1164}\right)\)	\(e\left(\frac{1033}{1164}\right)\)	\(e\left(\frac{283}{582}\right)\)	\(e\left(\frac{179}{194}\right)\)	\(e\left(\frac{367}{582}\right)\)	\(e\left(\frac{337}{582}\right)\)	\(e\left(\frac{89}{388}\right)\)	\(e\left(\frac{451}{582}\right)\)	\(e\left(\frac{775}{1164}\right)\)	\(e\left(\frac{185}{582}\right)\)
\(\chi_{5057}(108,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{311}{1164}\right)\)	\(e\left(\frac{1055}{1164}\right)\)	\(e\left(\frac{311}{582}\right)\)	\(e\left(\frac{183}{194}\right)\)	\(e\left(\frac{101}{582}\right)\)	\(e\left(\frac{467}{582}\right)\)	\(e\left(\frac{311}{388}\right)\)	\(e\left(\frac{473}{582}\right)\)	\(e\left(\frac{245}{1164}\right)\)	\(e\left(\frac{265}{582}\right)\)
\(\chi_{5057}(134,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{641}{1164}\right)\)	\(e\left(\frac{857}{1164}\right)\)	\(e\left(\frac{59}{582}\right)\)	\(e\left(\frac{147}{194}\right)\)	\(e\left(\frac{167}{582}\right)\)	\(e\left(\frac{461}{582}\right)\)	\(e\left(\frac{253}{388}\right)\)	\(e\left(\frac{275}{582}\right)\)	\(e\left(\frac{359}{1164}\right)\)	\(e\left(\frac{127}{582}\right)\)
\(\chi_{5057}(147,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{647}{1164}\right)\)	\(e\left(\frac{155}{1164}\right)\)	\(e\left(\frac{65}{582}\right)\)	\(e\left(\frac{37}{194}\right)\)	\(e\left(\frac{401}{582}\right)\)	\(e\left(\frac{281}{582}\right)\)	\(e\left(\frac{259}{388}\right)\)	\(e\left(\frac{155}{582}\right)\)	\(e\left(\frac{869}{1164}\right)\)	\(e\left(\frac{61}{582}\right)\)
\(\chi_{5057}(160,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{461}{1164}\right)\)	\(e\left(\frac{965}{1164}\right)\)	\(e\left(\frac{461}{582}\right)\)	\(e\left(\frac{149}{194}\right)\)	\(e\left(\frac{131}{582}\right)\)	\(e\left(\frac{41}{582}\right)\)	\(e\left(\frac{73}{388}\right)\)	\(e\left(\frac{383}{582}\right)\)	\(e\left(\frac{191}{1164}\right)\)	\(e\left(\frac{361}{582}\right)\)
\(\chi_{5057}(186,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{737}{1164}\right)\)	\(e\left(\frac{101}{1164}\right)\)	\(e\left(\frac{155}{582}\right)\)	\(e\left(\frac{133}{194}\right)\)	\(e\left(\frac{419}{582}\right)\)	\(e\left(\frac{491}{582}\right)\)	\(e\left(\frac{349}{388}\right)\)	\(e\left(\frac{101}{582}\right)\)	\(e\left(\frac{371}{1164}\right)\)	\(e\left(\frac{235}{582}\right)\)
\(\chi_{5057}(192,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{637}{1164}\right)\)	\(e\left(\frac{937}{1164}\right)\)	\(e\left(\frac{55}{582}\right)\)	\(e\left(\frac{91}{194}\right)\)	\(e\left(\frac{205}{582}\right)\)	\(e\left(\frac{193}{582}\right)\)	\(e\left(\frac{249}{388}\right)\)	\(e\left(\frac{355}{582}\right)\)	\(e\left(\frac{19}{1164}\right)\)	\(e\left(\frac{365}{582}\right)\)
\(\chi_{5057}(199,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{653}{1164}\right)\)	\(e\left(\frac{617}{1164}\right)\)	\(e\left(\frac{71}{582}\right)\)	\(e\left(\frac{121}{194}\right)\)	\(e\left(\frac{53}{582}\right)\)	\(e\left(\frac{101}{582}\right)\)	\(e\left(\frac{265}{388}\right)\)	\(e\left(\frac{35}{582}\right)\)	\(e\left(\frac{215}{1164}\right)\)	\(e\left(\frac{577}{582}\right)\)
\(\chi_{5057}(212,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{263}{1164}\right)\)	\(e\left(\frac{851}{1164}\right)\)	\(e\left(\frac{263}{582}\right)\)	\(e\left(\frac{93}{194}\right)\)	\(e\left(\frac{557}{582}\right)\)	\(e\left(\frac{161}{582}\right)\)	\(e\left(\frac{263}{388}\right)\)	\(e\left(\frac{269}{582}\right)\)	\(e\left(\frac{821}{1164}\right)\)	\(e\left(\frac{211}{582}\right)\)
\(\chi_{5057}(231,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{955}{1164}\right)\)	\(e\left(\frac{979}{1164}\right)\)	\(e\left(\frac{373}{582}\right)\)	\(e\left(\frac{81}{194}\right)\)	\(e\left(\frac{385}{582}\right)\)	\(e\left(\frac{547}{582}\right)\)	\(e\left(\frac{179}{388}\right)\)	\(e\left(\frac{397}{582}\right)\)	\(e\left(\frac{277}{1164}\right)\)	\(e\left(\frac{359}{582}\right)\)
\(\chi_{5057}(238,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1145}{1164}\right)\)	\(e\left(\frac{89}{1164}\right)\)	\(e\left(\frac{563}{582}\right)\)	\(e\left(\frac{25}{194}\right)\)	\(e\left(\frac{35}{582}\right)\)	\(e\left(\frac{473}{582}\right)\)	\(e\left(\frac{369}{388}\right)\)	\(e\left(\frac{89}{582}\right)\)	\(e\left(\frac{131}{1164}\right)\)	\(e\left(\frac{403}{582}\right)\)
\(\chi_{5057}(244,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{781}{1164}\right)\)	\(e\left(\frac{385}{1164}\right)\)	\(e\left(\frac{199}{582}\right)\)	\(e\left(\frac{167}{194}\right)\)	\(e\left(\frac{1}{582}\right)\)	\(e\left(\frac{529}{582}\right)\)	\(e\left(\frac{5}{388}\right)\)	\(e\left(\frac{385}{582}\right)\)	\(e\left(\frac{619}{1164}\right)\)	\(e\left(\frac{527}{582}\right)\)
\(\chi_{5057}(251,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{467}{1164}\right)\)	\(e\left(\frac{263}{1164}\right)\)	\(e\left(\frac{467}{582}\right)\)	\(e\left(\frac{39}{194}\right)\)	\(e\left(\frac{365}{582}\right)\)	\(e\left(\frac{443}{582}\right)\)	\(e\left(\frac{79}{388}\right)\)	\(e\left(\frac{263}{582}\right)\)	\(e\left(\frac{701}{1164}\right)\)	\(e\left(\frac{295}{582}\right)\)
\(\chi_{5057}(257,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{559}{1164}\right)\)	\(e\left(\frac{751}{1164}\right)\)	\(e\left(\frac{559}{582}\right)\)	\(e\left(\frac{163}{194}\right)\)	\(e\left(\frac{73}{582}\right)\)	\(e\left(\frac{205}{582}\right)\)	\(e\left(\frac{171}{388}\right)\)	\(e\left(\frac{169}{582}\right)\)	\(e\left(\frac{373}{1164}\right)\)	\(e\left(\frac{59}{582}\right)\)
\(\chi_{5057}(329,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{683}{1164}\right)\)	\(e\left(\frac{599}{1164}\right)\)	\(e\left(\frac{101}{582}\right)\)	\(e\left(\frac{153}{194}\right)\)	\(e\left(\frac{59}{582}\right)\)	\(e\left(\frac{365}{582}\right)\)	\(e\left(\frac{295}{388}\right)\)	\(e\left(\frac{17}{582}\right)\)	\(e\left(\frac{437}{1164}\right)\)	\(e\left(\frac{247}{582}\right)\)
\(\chi_{5057}(342,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{281}{1164}\right)\)	\(e\left(\frac{1073}{1164}\right)\)	\(e\left(\frac{281}{582}\right)\)	\(e\left(\frac{151}{194}\right)\)	\(e\left(\frac{95}{582}\right)\)	\(e\left(\frac{203}{582}\right)\)	\(e\left(\frac{281}{388}\right)\)	\(e\left(\frac{491}{582}\right)\)	\(e\left(\frac{23}{1164}\right)\)	\(e\left(\frac{13}{582}\right)\)
\(\chi_{5057}(355,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{743}{1164}\right)\)	\(e\left(\frac{563}{1164}\right)\)	\(e\left(\frac{161}{582}\right)\)	\(e\left(\frac{23}{194}\right)\)	\(e\left(\frac{71}{582}\right)\)	\(e\left(\frac{311}{582}\right)\)	\(e\left(\frac{355}{388}\right)\)	\(e\left(\frac{563}{582}\right)\)	\(e\left(\frac{881}{1164}\right)\)	\(e\left(\frac{169}{582}\right)\)
\(\chi_{5057}(368,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{245}{1164}\right)\)	\(e\left(\frac{629}{1164}\right)\)	\(e\left(\frac{245}{582}\right)\)	\(e\left(\frac{35}{194}\right)\)	\(e\left(\frac{437}{582}\right)\)	\(e\left(\frac{119}{582}\right)\)	\(e\left(\frac{245}{388}\right)\)	\(e\left(\frac{47}{582}\right)\)	\(e\left(\frac{455}{1164}\right)\)	\(e\left(\frac{409}{582}\right)\)
\(\chi_{5057}(374,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{289}{1164}\right)\)	\(e\left(\frac{913}{1164}\right)\)	\(e\left(\frac{289}{582}\right)\)	\(e\left(\frac{69}{194}\right)\)	\(e\left(\frac{19}{582}\right)\)	\(e\left(\frac{157}{582}\right)\)	\(e\left(\frac{289}{388}\right)\)	\(e\left(\frac{331}{582}\right)\)	\(e\left(\frac{703}{1164}\right)\)	\(e\left(\frac{119}{582}\right)\)
\(\chi_{5057}(381,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{785}{1164}\right)\)	\(e\left(\frac{305}{1164}\right)\)	\(e\left(\frac{203}{582}\right)\)	\(e\left(\frac{29}{194}\right)\)	\(e\left(\frac{545}{582}\right)\)	\(e\left(\frac{215}{582}\right)\)	\(e\left(\frac{9}{388}\right)\)	\(e\left(\frac{305}{582}\right)\)	\(e\left(\frac{959}{1164}\right)\)	\(e\left(\frac{289}{582}\right)\)
\(\chi_{5057}(387,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{391}{1164}\right)\)	\(e\left(\frac{619}{1164}\right)\)	\(e\left(\frac{391}{582}\right)\)	\(e\left(\frac{139}{194}\right)\)	\(e\left(\frac{505}{582}\right)\)	\(e\left(\frac{7}{582}\right)\)	\(e\left(\frac{3}{388}\right)\)	\(e\left(\frac{37}{582}\right)\)	\(e\left(\frac{61}{1164}\right)\)	\(e\left(\frac{161}{582}\right)\)
\(\chi_{5057}(407,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{659}{1164}\right)\)	\(e\left(\frac{1079}{1164}\right)\)	\(e\left(\frac{77}{582}\right)\)	\(e\left(\frac{11}{194}\right)\)	\(e\left(\frac{287}{582}\right)\)	\(e\left(\frac{503}{582}\right)\)	\(e\left(\frac{271}{388}\right)\)	\(e\left(\frac{497}{582}\right)\)	\(e\left(\frac{725}{1164}\right)\)	\(e\left(\frac{511}{582}\right)\)
\(\chi_{5057}(420,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1085}{1164}\right)\)	\(e\left(\frac{125}{1164}\right)\)	\(e\left(\frac{503}{582}\right)\)	\(e\left(\frac{155}{194}\right)\)	\(e\left(\frac{23}{582}\right)\)	\(e\left(\frac{527}{582}\right)\)	\(e\left(\frac{309}{388}\right)\)	\(e\left(\frac{125}{582}\right)\)	\(e\left(\frac{851}{1164}\right)\)	\(e\left(\frac{481}{582}\right)\)
\(\chi_{5057}(426,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{919}{1164}\right)\)	\(e\left(\frac{535}{1164}\right)\)	\(e\left(\frac{337}{582}\right)\)	\(e\left(\frac{159}{194}\right)\)	\(e\left(\frac{145}{582}\right)\)	\(e\left(\frac{463}{582}\right)\)	\(e\left(\frac{143}{388}\right)\)	\(e\left(\frac{535}{582}\right)\)	\(e\left(\frac{709}{1164}\right)\)	\(e\left(\frac{173}{582}\right)\)

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First 31 of 384 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	5057.bl
Modulus	$5057$
Conductor	$5057$
Order	$1164$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(5057\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(5057\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(1164\)	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);