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Properties

Label 529.e
Modulus $529$
Conductor $529$
Order $23$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: Magma / Pari/GP / SageMath
Copy content comment:Define the Dirichlet character orbit
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(529, base_ring=CyclotomicField(46)) M = H._module chi = DirichletCharacter(H, M([10])) chi.galois_orbit()
 
Copy content gp:[g,chi] = znchar(Mod(24, 529)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("529.24"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };
 

Basic properties

Modulus: \(529\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(529\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(23\)
Copy content comment:Order
 
Copy content sage:chi.multiplicative_order()
 
Copy content gp:charorder(g,chi)
 
Copy content magma:Order(chi);
 
Real: no
Copy content comment:Whether the character is real
 
Copy content sage:chi.multiplicative_order() <= 2
 
Copy content gp:charorder(g,chi) <= 2
 
Copy content magma:Order(chi) le 2;
 
Primitive: yes
Copy content comment:If the character is primitive
 
Copy content sage:chi.is_primitive()
 
Copy content gp:#znconreyconductor(g,chi)==1
 
Copy content magma:IsPrimitive(chi);
 
Minimal: yes
Parity: even
Copy content comment:Parity
 
Copy content sage:chi.is_odd()
 
Copy content gp:zncharisodd(g,chi)
 
Copy content magma:IsOdd(chi);
 

Related number fields

Field of values: \(\Q(\zeta_{23})\)
Copy content comment:Field of values of chi
 
Copy content sage:CyclotomicField(chi.multiplicative_order())
 
Copy content gp:nfinit(polcyclo(charorder(g,chi)))
 
Copy content magma:CyclotomicField(Order(chi));
 
Fixed field: Number field defined by a degree 23 polynomial
Copy content comment:Fixed field
 
Copy content sage:chi.fixed_field()
 

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{529}(24,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{14}{23}\right)\)
\(\chi_{529}(47,\cdot)\) \(1\) \(1\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{5}{23}\right)\)
\(\chi_{529}(70,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{19}{23}\right)\)
\(\chi_{529}(93,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{10}{23}\right)\)
\(\chi_{529}(116,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{1}{23}\right)\)
\(\chi_{529}(139,\cdot)\) \(1\) \(1\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{15}{23}\right)\)
\(\chi_{529}(162,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{6}{23}\right)\)
\(\chi_{529}(185,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{20}{23}\right)\)
\(\chi_{529}(208,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{11}{23}\right)\)
\(\chi_{529}(231,\cdot)\) \(1\) \(1\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{2}{23}\right)\)
\(\chi_{529}(254,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{16}{23}\right)\)
\(\chi_{529}(277,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{7}{23}\right)\)
\(\chi_{529}(300,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{21}{23}\right)\)
\(\chi_{529}(323,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{12}{23}\right)\)
\(\chi_{529}(346,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{10}{23}\right)\) \(e\left(\frac{3}{23}\right)\)
\(\chi_{529}(369,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{15}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{11}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{17}{23}\right)\)
\(\chi_{529}(392,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{17}{23}\right)\) \(e\left(\frac{9}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{8}{23}\right)\)
\(\chi_{529}(415,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{22}{23}\right)\)
\(\chi_{529}(438,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{19}{23}\right)\) \(e\left(\frac{6}{23}\right)\) \(e\left(\frac{4}{23}\right)\) \(e\left(\frac{5}{23}\right)\) \(e\left(\frac{13}{23}\right)\)
\(\chi_{529}(461,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{8}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{20}{23}\right)\) \(e\left(\frac{16}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{4}{23}\right)\)
\(\chi_{529}(484,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{21}{23}\right)\) \(e\left(\frac{3}{23}\right)\) \(e\left(\frac{2}{23}\right)\) \(e\left(\frac{14}{23}\right)\) \(e\left(\frac{18}{23}\right)\)
\(\chi_{529}(507,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{12}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{18}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{22}{23}\right)\) \(e\left(\frac{13}{23}\right)\) \(e\left(\frac{1}{23}\right)\) \(e\left(\frac{7}{23}\right)\) \(e\left(\frac{9}{23}\right)\)