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Properties

Label 24200.3379
Modulus $24200$
Conductor $2200$
Order $10$
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(24200, base_ring=CyclotomicField(10)) M = H._module chi = DirichletCharacter(H, M([5,5,1,1]))
 
Copy content pari:[g,chi] = znchar(Mod(3379,24200))
 

Basic properties

Modulus: \(24200\)
Conductor: \(2200\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(10\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{2200}(1179,\cdot)\)
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 24200.bi

\(\chi_{24200}(3379,\cdot)\) \(\chi_{24200}(12339,\cdot)\) \(\chi_{24200}(15219,\cdot)\) \(\chi_{24200}(16859,\cdot)\)

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: \(\Q(\zeta_{5})\)
Fixed field: 10.10.58948692275000000000000000.4

Values on generators

\((18151,12101,6777,14401)\) → \((-1,-1,e\left(\frac{1}{10}\right),e\left(\frac{1}{10}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(7\)\(9\)\(13\)\(17\)\(19\)\(21\)\(23\)\(27\)\(29\)
\( \chi_{ 24200 }(3379, a) \) \(1\)\(1\)\(-1\)\(e\left(\frac{7}{10}\right)\)\(1\)\(-1\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{3}{5}\right)\)\(-1\)\(e\left(\frac{2}{5}\right)\)
Copy content sage:chi.jacobi_sum(n)
 
\( \chi_{ 24200 }(3379,a) \;\) at \(\;a = \) e.g. 2