LMFDB - Dirichlet character orbit 101695.gg

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(101695, base_ring=CyclotomicField(2580)) M = H._module chi = DirichletCharacter(H, M([645,516,2410])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(37, 101695)) 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("101695.37"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$101695$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$101695$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$2580$	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:	$\Q(\zeta_{2580})$
Fixed field:	Number field defined by a degree 2580 polynomial (not computed)

First 11 of 672 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$12$	$13$	$14$
$\chi_{101695}(37,\cdot)$	$1$	$1$	$e\left(\frac{37}{860}\right)$	$e\left(\frac{733}{2580}\right)$	$e\left(\frac{37}{430}\right)$	$e\left(\frac{211}{645}\right)$	$e\left(\frac{1307}{2580}\right)$	$e\left(\frac{111}{860}\right)$	$e\left(\frac{733}{1290}\right)$	$e\left(\frac{191}{516}\right)$	$e\left(\frac{1091}{2580}\right)$	$e\left(\frac{709}{1290}\right)$
$\chi_{101695}(93,\cdot)$	$1$	$1$	$e\left(\frac{159}{860}\right)$	$e\left(\frac{1151}{2580}\right)$	$e\left(\frac{159}{430}\right)$	$e\left(\frac{407}{645}\right)$	$e\left(\frac{1549}{2580}\right)$	$e\left(\frac{477}{860}\right)$	$e\left(\frac{1151}{1290}\right)$	$e\left(\frac{421}{516}\right)$	$e\left(\frac{1597}{2580}\right)$	$e\left(\frac{1013}{1290}\right)$
$\chi_{101695}(467,\cdot)$	$1$	$1$	$e\left(\frac{789}{860}\right)$	$e\left(\frac{1801}{2580}\right)$	$e\left(\frac{359}{430}\right)$	$e\left(\frac{397}{645}\right)$	$e\left(\frac{839}{2580}\right)$	$e\left(\frac{647}{860}\right)$	$e\left(\frac{511}{1290}\right)$	$e\left(\frac{275}{516}\right)$	$e\left(\frac{347}{2580}\right)$	$e\left(\frac{313}{1290}\right)$
$\chi_{101695}(553,\cdot)$	$1$	$1$	$e\left(\frac{303}{860}\right)$	$e\left(\frac{1447}{2580}\right)$	$e\left(\frac{303}{430}\right)$	$e\left(\frac{589}{645}\right)$	$e\left(\frac{1313}{2580}\right)$	$e\left(\frac{49}{860}\right)$	$e\left(\frac{157}{1290}\right)$	$e\left(\frac{137}{516}\right)$	$e\left(\frac{869}{2580}\right)$	$e\left(\frac{1111}{1290}\right)$
$\chi_{101695}(652,\cdot)$	$1$	$1$	$e\left(\frac{213}{860}\right)$	$e\left(\frac{617}{2580}\right)$	$e\left(\frac{213}{430}\right)$	$e\left(\frac{314}{645}\right)$	$e\left(\frac{1783}{2580}\right)$	$e\left(\frac{639}{860}\right)$	$e\left(\frac{617}{1290}\right)$	$e\left(\frac{379}{516}\right)$	$e\left(\frac{679}{2580}\right)$	$e\left(\frac{1211}{1290}\right)$
$\chi_{101695}(768,\cdot)$	$1$	$1$	$e\left(\frac{851}{860}\right)$	$e\left(\frac{2239}{2580}\right)$	$e\left(\frac{421}{430}\right)$	$e\left(\frac{553}{645}\right)$	$e\left(\frac{821}{2580}\right)$	$e\left(\frac{833}{860}\right)$	$e\left(\frac{949}{1290}\right)$	$e\left(\frac{437}{516}\right)$	$e\left(\frac{1013}{2580}\right)$	$e\left(\frac{397}{1290}\right)$
$\chi_{101695}(867,\cdot)$	$1$	$1$	$e\left(\frac{161}{860}\right)$	$e\left(\frac{749}{2580}\right)$	$e\left(\frac{161}{430}\right)$	$e\left(\frac{308}{645}\right)$	$e\left(\frac{2131}{2580}\right)$	$e\left(\frac{483}{860}\right)$	$e\left(\frac{749}{1290}\right)$	$e\left(\frac{343}{516}\right)$	$e\left(\frac{703}{2580}\right)$	$e\left(\frac{17}{1290}\right)$
$\chi_{101695}(983,\cdot)$	$1$	$1$	$e\left(\frac{367}{860}\right)$	$e\left(\frac{1483}{2580}\right)$	$e\left(\frac{367}{430}\right)$	$e\left(\frac{1}{645}\right)$	$e\left(\frac{1877}{2580}\right)$	$e\left(\frac{241}{860}\right)$	$e\left(\frac{193}{1290}\right)$	$e\left(\frac{221}{516}\right)$	$e\left(\frac{641}{2580}\right)$	$e\left(\frac{199}{1290}\right)$
$\chi_{101695}(1082,\cdot)$	$1$	$1$	$e\left(\frac{797}{860}\right)$	$e\left(\frac{1913}{2580}\right)$	$e\left(\frac{367}{430}\right)$	$e\left(\frac{431}{645}\right)$	$e\left(\frac{1447}{2580}\right)$	$e\left(\frac{671}{860}\right)$	$e\left(\frac{623}{1290}\right)$	$e\left(\frac{307}{516}\right)$	$e\left(\frac{211}{2580}\right)$	$e\left(\frac{629}{1290}\right)$
$\chi_{101695}(1413,\cdot)$	$1$	$1$	$e\left(\frac{259}{860}\right)$	$e\left(\frac{2551}{2580}\right)$	$e\left(\frac{259}{430}\right)$	$e\left(\frac{187}{645}\right)$	$e\left(\frac{1409}{2580}\right)$	$e\left(\frac{777}{860}\right)$	$e\left(\frac{1261}{1290}\right)$	$e\left(\frac{305}{516}\right)$	$e\left(\frac{2477}{2580}\right)$	$e\left(\frac{1093}{1290}\right)$
$\chi_{101695}(1512,\cdot)$	$1$	$1$	$e\left(\frac{349}{860}\right)$	$e\left(\frac{1661}{2580}\right)$	$e\left(\frac{349}{430}\right)$	$e\left(\frac{32}{645}\right)$	$e\left(\frac{79}{2580}\right)$	$e\left(\frac{187}{860}\right)$	$e\left(\frac{371}{1290}\right)$	$e\left(\frac{235}{516}\right)$	$e\left(\frac{1807}{2580}\right)$	$e\left(\frac{563}{1290}\right)$

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Character	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(13\)	\(14\)
\(\chi_{101695}(37,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{860}\right)\)	\(e\left(\frac{733}{2580}\right)\)	\(e\left(\frac{37}{430}\right)\)	\(e\left(\frac{211}{645}\right)\)	\(e\left(\frac{1307}{2580}\right)\)	\(e\left(\frac{111}{860}\right)\)	\(e\left(\frac{733}{1290}\right)\)	\(e\left(\frac{191}{516}\right)\)	\(e\left(\frac{1091}{2580}\right)\)	\(e\left(\frac{709}{1290}\right)\)
\(\chi_{101695}(93,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{159}{860}\right)\)	\(e\left(\frac{1151}{2580}\right)\)	\(e\left(\frac{159}{430}\right)\)	\(e\left(\frac{407}{645}\right)\)	\(e\left(\frac{1549}{2580}\right)\)	\(e\left(\frac{477}{860}\right)\)	\(e\left(\frac{1151}{1290}\right)\)	\(e\left(\frac{421}{516}\right)\)	\(e\left(\frac{1597}{2580}\right)\)	\(e\left(\frac{1013}{1290}\right)\)
\(\chi_{101695}(467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{789}{860}\right)\)	\(e\left(\frac{1801}{2580}\right)\)	\(e\left(\frac{359}{430}\right)\)	\(e\left(\frac{397}{645}\right)\)	\(e\left(\frac{839}{2580}\right)\)	\(e\left(\frac{647}{860}\right)\)	\(e\left(\frac{511}{1290}\right)\)	\(e\left(\frac{275}{516}\right)\)	\(e\left(\frac{347}{2580}\right)\)	\(e\left(\frac{313}{1290}\right)\)
\(\chi_{101695}(553,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{303}{860}\right)\)	\(e\left(\frac{1447}{2580}\right)\)	\(e\left(\frac{303}{430}\right)\)	\(e\left(\frac{589}{645}\right)\)	\(e\left(\frac{1313}{2580}\right)\)	\(e\left(\frac{49}{860}\right)\)	\(e\left(\frac{157}{1290}\right)\)	\(e\left(\frac{137}{516}\right)\)	\(e\left(\frac{869}{2580}\right)\)	\(e\left(\frac{1111}{1290}\right)\)
\(\chi_{101695}(652,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{213}{860}\right)\)	\(e\left(\frac{617}{2580}\right)\)	\(e\left(\frac{213}{430}\right)\)	\(e\left(\frac{314}{645}\right)\)	\(e\left(\frac{1783}{2580}\right)\)	\(e\left(\frac{639}{860}\right)\)	\(e\left(\frac{617}{1290}\right)\)	\(e\left(\frac{379}{516}\right)\)	\(e\left(\frac{679}{2580}\right)\)	\(e\left(\frac{1211}{1290}\right)\)
\(\chi_{101695}(768,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{851}{860}\right)\)	\(e\left(\frac{2239}{2580}\right)\)	\(e\left(\frac{421}{430}\right)\)	\(e\left(\frac{553}{645}\right)\)	\(e\left(\frac{821}{2580}\right)\)	\(e\left(\frac{833}{860}\right)\)	\(e\left(\frac{949}{1290}\right)\)	\(e\left(\frac{437}{516}\right)\)	\(e\left(\frac{1013}{2580}\right)\)	\(e\left(\frac{397}{1290}\right)\)
\(\chi_{101695}(867,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{860}\right)\)	\(e\left(\frac{749}{2580}\right)\)	\(e\left(\frac{161}{430}\right)\)	\(e\left(\frac{308}{645}\right)\)	\(e\left(\frac{2131}{2580}\right)\)	\(e\left(\frac{483}{860}\right)\)	\(e\left(\frac{749}{1290}\right)\)	\(e\left(\frac{343}{516}\right)\)	\(e\left(\frac{703}{2580}\right)\)	\(e\left(\frac{17}{1290}\right)\)
\(\chi_{101695}(983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{367}{860}\right)\)	\(e\left(\frac{1483}{2580}\right)\)	\(e\left(\frac{367}{430}\right)\)	\(e\left(\frac{1}{645}\right)\)	\(e\left(\frac{1877}{2580}\right)\)	\(e\left(\frac{241}{860}\right)\)	\(e\left(\frac{193}{1290}\right)\)	\(e\left(\frac{221}{516}\right)\)	\(e\left(\frac{641}{2580}\right)\)	\(e\left(\frac{199}{1290}\right)\)
\(\chi_{101695}(1082,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{797}{860}\right)\)	\(e\left(\frac{1913}{2580}\right)\)	\(e\left(\frac{367}{430}\right)\)	\(e\left(\frac{431}{645}\right)\)	\(e\left(\frac{1447}{2580}\right)\)	\(e\left(\frac{671}{860}\right)\)	\(e\left(\frac{623}{1290}\right)\)	\(e\left(\frac{307}{516}\right)\)	\(e\left(\frac{211}{2580}\right)\)	\(e\left(\frac{629}{1290}\right)\)
\(\chi_{101695}(1413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{259}{860}\right)\)	\(e\left(\frac{2551}{2580}\right)\)	\(e\left(\frac{259}{430}\right)\)	\(e\left(\frac{187}{645}\right)\)	\(e\left(\frac{1409}{2580}\right)\)	\(e\left(\frac{777}{860}\right)\)	\(e\left(\frac{1261}{1290}\right)\)	\(e\left(\frac{305}{516}\right)\)	\(e\left(\frac{2477}{2580}\right)\)	\(e\left(\frac{1093}{1290}\right)\)
\(\chi_{101695}(1512,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{349}{860}\right)\)	\(e\left(\frac{1661}{2580}\right)\)	\(e\left(\frac{349}{430}\right)\)	\(e\left(\frac{32}{645}\right)\)	\(e\left(\frac{79}{2580}\right)\)	\(e\left(\frac{187}{860}\right)\)	\(e\left(\frac{371}{1290}\right)\)	\(e\left(\frac{235}{516}\right)\)	\(e\left(\frac{1807}{2580}\right)\)	\(e\left(\frac{563}{1290}\right)\)

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First 11 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	101695.gg
Modulus	$101695$
Conductor	$101695$
Order	$2580$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(101695\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(101695\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(2580\)	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);