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Properties

Label 8450.y
Modulus $8450$
Conductor $169$
Order $13$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8450, base_ring=CyclotomicField(26)) M = H._module chi = DirichletCharacter(H, M([0,16])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(651,8450)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(8450\)
Conductor: \(169\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(13\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 169.g
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{13})\)
Fixed field: 13.13.542800770374370512771595361.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(17\) \(19\) \(21\) \(23\) \(27\) \(29\)
\(\chi_{8450}(651,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(1\) \(e\left(\frac{2}{13}\right)\) \(1\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{8}{13}\right)\)
\(\chi_{8450}(1301,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(1\) \(e\left(\frac{4}{13}\right)\) \(1\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{3}{13}\right)\)
\(\chi_{8450}(1951,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(1\) \(e\left(\frac{6}{13}\right)\) \(1\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{11}{13}\right)\)
\(\chi_{8450}(2601,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(1\) \(e\left(\frac{8}{13}\right)\) \(1\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{6}{13}\right)\)
\(\chi_{8450}(3251,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(1\) \(e\left(\frac{10}{13}\right)\) \(1\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{1}{13}\right)\)
\(\chi_{8450}(3901,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(1\) \(e\left(\frac{12}{13}\right)\) \(1\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{9}{13}\right)\)
\(\chi_{8450}(4551,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(1\) \(e\left(\frac{1}{13}\right)\) \(1\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{4}{13}\right)\)
\(\chi_{8450}(5201,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(1\) \(e\left(\frac{3}{13}\right)\) \(1\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{12}{13}\right)\)
\(\chi_{8450}(5851,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(1\) \(e\left(\frac{5}{13}\right)\) \(1\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{7}{13}\right)\)
\(\chi_{8450}(6501,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(1\) \(e\left(\frac{7}{13}\right)\) \(1\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{2}{13}\right)\)
\(\chi_{8450}(7151,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(1\) \(e\left(\frac{9}{13}\right)\) \(1\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{10}{13}\right)\)
\(\chi_{8450}(7801,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(1\) \(e\left(\frac{11}{13}\right)\) \(1\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{5}{13}\right)\)