Properties

Label 7260.3191
Modulus $7260$
Conductor $1452$
Order $22$
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(7260, base_ring=CyclotomicField(22)) M = H._module chi = DirichletCharacter(H, M([11,11,0,6]))
 
Copy content pari:[g,chi] = znchar(Mod(3191,7260))
 

Basic properties

Modulus: \(7260\)
Conductor: \(1452\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(22\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1452}(287,\cdot)\)
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)
 

Galois orbit 7260.ch

\(\chi_{7260}(551,\cdot)\) \(\chi_{7260}(1871,\cdot)\) \(\chi_{7260}(2531,\cdot)\) \(\chi_{7260}(3191,\cdot)\) \(\chi_{7260}(3851,\cdot)\) \(\chi_{7260}(4511,\cdot)\) \(\chi_{7260}(5171,\cdot)\) \(\chi_{7260}(5831,\cdot)\) \(\chi_{7260}(6491,\cdot)\) \(\chi_{7260}(7151,\cdot)\)

Copy content sage:chi.galois_orbit()
 
Copy content pari:order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: \(\Q(\zeta_{11})\)
Fixed field: Number field defined by a degree 22 polynomial

Values on generators

\((3631,4841,4357,7141)\) → \((-1,-1,1,e\left(\frac{3}{11}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 7260 }(3191, a) \) \(1\)\(1\)\(e\left(\frac{9}{22}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{19}{22}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{21}{22}\right)\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{7}{22}\right)\)
Copy content sage:chi.jacobi_sum(n)
 
\( \chi_{ 7260 }(3191,a) \;\) at \(\;a = \) e.g. 2