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Properties

Label 1507.p
Modulus $1507$
Conductor $137$
Order $34$
Real no
Primitive no
Minimal yes
Parity even

Related objects

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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(1507, base_ring=CyclotomicField(34)) M = H._module chi = DirichletCharacter(H, M([0,9])) chi.galois_orbit()
 
Copy content gp:[g,chi] = znchar(Mod(78, 1507)) 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("1507.78"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };
 

Basic properties

Modulus: \(1507\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(137\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(34\)
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: no, induced from 137.f
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: \(\Q(\zeta_{17})\)
Fixed field: Number field defined by a degree 34 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(12\)
\(\chi_{1507}(78,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(-1\) \(e\left(\frac{19}{34}\right)\)
\(\chi_{1507}(155,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(-1\) \(e\left(\frac{29}{34}\right)\)
\(\chi_{1507}(474,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(-1\) \(e\left(\frac{27}{34}\right)\)
\(\chi_{1507}(562,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(-1\) \(e\left(\frac{1}{34}\right)\)
\(\chi_{1507}(749,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(-1\) \(e\left(\frac{9}{34}\right)\)
\(\chi_{1507}(826,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(-1\) \(e\left(\frac{3}{34}\right)\)
\(\chi_{1507}(837,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(-1\) \(e\left(\frac{25}{34}\right)\)
\(\chi_{1507}(903,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(-1\) \(e\left(\frac{21}{34}\right)\)
\(\chi_{1507}(925,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(-1\) \(e\left(\frac{31}{34}\right)\)
\(\chi_{1507}(1024,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(-1\) \(e\left(\frac{15}{34}\right)\)
\(\chi_{1507}(1046,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(-1\) \(e\left(\frac{7}{34}\right)\)
\(\chi_{1507}(1145,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(-1\) \(e\left(\frac{33}{34}\right)\)
\(\chi_{1507}(1255,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(-1\) \(e\left(\frac{13}{34}\right)\)
\(\chi_{1507}(1310,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(-1\) \(e\left(\frac{11}{34}\right)\)
\(\chi_{1507}(1332,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(-1\) \(e\left(\frac{5}{34}\right)\)
\(\chi_{1507}(1354,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(-1\) \(e\left(\frac{23}{34}\right)\)