↑

Properties

Label 7260.457
Modulus $7260$
Conductor $55$
Order $20$
Real no
Primitive no
Minimal no
Parity even

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7260, base_ring=CyclotomicField(20)) M = H._module chi = DirichletCharacter(H, M([0,0,5,18]))
 
Copy content pari:[g,chi] = znchar(Mod(457,7260))
 

Basic properties

Modulus: \(7260\)
Conductor: \(55\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(20\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{55}(17,\cdot)\)
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 7260.bp

\(\chi_{7260}(457,\cdot)\) \(\chi_{7260}(1933,\cdot)\) \(\chi_{7260}(2653,\cdot)\) \(\chi_{7260}(4033,\cdot)\) \(\chi_{7260}(4813,\cdot)\) \(\chi_{7260}(4837,\cdot)\) \(\chi_{7260}(5557,\cdot)\) \(\chi_{7260}(6937,\cdot)\)

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: \(\Q(\zeta_{20})\)
Fixed field: \(\Q(\zeta_{55})^+\)

Values on generators

\((3631,4841,4357,7141)\) → \((1,1,i,e\left(\frac{9}{10}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 7260 }(457, a) \) \(1\)\(1\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{1}{5}\right)\)\(-i\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{7}{10}\right)\)\(i\)
Copy content sage:chi.jacobi_sum(n)
 
\( \chi_{ 7260 }(457,a) \;\) at \(\;a = \) e.g. 2