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Properties

Label 3234.r
Modulus $3234$
Conductor $49$
Order $7$
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(3234, base_ring=CyclotomicField(14)) M = H._module chi = DirichletCharacter(H, M([0,8,0])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(463,3234)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(3234\)
Conductor: \(49\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(7\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 49.e
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: \(\Q(\zeta_{7})\)
Fixed field: 7.7.13841287201.1

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{3234}(463,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\)
\(\chi_{3234}(925,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\)
\(\chi_{3234}(1387,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{7}\right)\)
\(\chi_{3234}(1849,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{3234}(2311,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{6}{7}\right)\)
\(\chi_{3234}(2773,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\)