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Properties

Label 7260.6077
Modulus $7260$
Conductor $165$
Order $20$
Real no
Primitive no
Minimal no
Parity even

Related objects

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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([0,10,5,8]))
 
Copy content pari:[g,chi] = znchar(Mod(6077,7260))
 

Basic properties

Modulus: \(7260\)
Conductor: \(165\)
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 \(\chi_{165}(137,\cdot)\)
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.bt

\(\chi_{7260}(977,\cdot)\) \(\chi_{7260}(1697,\cdot)\) \(\chi_{7260}(3173,\cdot)\) \(\chi_{7260}(3953,\cdot)\) \(\chi_{7260}(5333,\cdot)\) \(\chi_{7260}(6053,\cdot)\) \(\chi_{7260}(6077,\cdot)\) \(\chi_{7260}(6857,\cdot)\)

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: Number field defined by a degree 20 polynomial

Values on generators

\((3631,4841,4357,7141)\) → \((1,-1,i,e\left(\frac{2}{5}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 7260 }(6077, a) \) \(1\)\(1\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{7}{10}\right)\)\(i\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{7}{10}\right)\)\(-i\)
Copy content sage:chi.jacobi_sum(n)
 
\( \chi_{ 7260 }(6077,a) \;\) at \(\;a = \) e.g. 2