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Properties

Label 2880.73
Modulus $2880$
Conductor $160$
Order $8$
Real no
Primitive no
Minimal no
Parity odd

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2880, base_ring=CyclotomicField(8)) M = H._module chi = DirichletCharacter(H, M([0,3,0,6]))
 
Copy content pari:[g,chi] = znchar(Mod(73,2880))
 

Basic properties

Modulus: \(2880\)
Conductor: \(160\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(8\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{160}(93,\cdot)\)
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 2880.cf

\(\chi_{2880}(73,\cdot)\) \(\chi_{2880}(217,\cdot)\) \(\chi_{2880}(1513,\cdot)\) \(\chi_{2880}(1657,\cdot)\)

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: \(\Q(\zeta_{8})\)
Fixed field: 8.0.33554432000000.1

Values on generators

\((2431,901,641,577)\) → \((1,e\left(\frac{3}{8}\right),1,-i)\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\( \chi_{ 2880 }(73, a) \) \(-1\)\(1\)\(-1\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{7}{8}\right)\)\(i\)\(e\left(\frac{1}{8}\right)\)\(-1\)\(e\left(\frac{5}{8}\right)\)\(1\)\(e\left(\frac{1}{8}\right)\)\(i\)
Copy content sage:chi.jacobi_sum(n)
 
\( \chi_{ 2880 }(73,a) \;\) at \(\;a = \) e.g. 2