↑

Properties

Label 46208.357
Modulus $46208$
Conductor $46208$
Order $5472$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath
Copy content comment:Define the Dirichlet character
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(46208, base_ring=CyclotomicField(5472)) M = H._module chi = DirichletCharacter(H, M([0,1539,2768]))
 
Copy content gp:[g,chi] = znchar(Mod(357, 46208))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("46208.357");
 

Basic properties

Modulus: \(46208\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(46208\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(5472\)
Copy content comment:Order
 
Copy content sage:chi.multiplicative_order()
 
Copy content gp:charorder(g,chi)
 
Copy content magma:Order(chi);
 
Real: no
Copy content comment:Whether the character is real
 
Copy content sage:chi.multiplicative_order() <= 2
 
Copy content gp:charorder(g,chi) <= 2
 
Copy content magma:Order(chi) le 2;
 
Primitive: yes
Copy content comment:If the character is primitive
 
Copy content sage:chi.is_primitive()
 
Copy content gp:#znconreyconductor(g,chi)==1
 
Copy content magma:IsPrimitive(chi);
 
Minimal: yes
Parity: odd
Copy content comment:Parity
 
Copy content sage:chi.is_odd()
 
Copy content gp:zncharisodd(g,chi)
 
Copy content magma:IsOdd(chi);
 

Galois orbit 46208.fn

\(\chi_{46208}(13,\cdot)\) \(\chi_{46208}(21,\cdot)\) \(\chi_{46208}(29,\cdot)\) \(\chi_{46208}(53,\cdot)\) \(\chi_{46208}(109,\cdot)\) \(\chi_{46208}(117,\cdot)\) \(\chi_{46208}(165,\cdot)\) \(\chi_{46208}(173,\cdot)\) \(\chi_{46208}(181,\cdot)\) \(\chi_{46208}(205,\cdot)\) \(\chi_{46208}(261,\cdot)\) \(\chi_{46208}(269,\cdot)\) \(\chi_{46208}(317,\cdot)\) \(\chi_{46208}(325,\cdot)\) \(\chi_{46208}(357,\cdot)\) \(\chi_{46208}(413,\cdot)\) \(\chi_{46208}(421,\cdot)\) \(\chi_{46208}(469,\cdot)\) \(\chi_{46208}(485,\cdot)\) \(\chi_{46208}(509,\cdot)\) \(\chi_{46208}(565,\cdot)\) \(\chi_{46208}(573,\cdot)\) \(\chi_{46208}(621,\cdot)\) \(\chi_{46208}(629,\cdot)\) \(\chi_{46208}(637,\cdot)\) \(\chi_{46208}(661,\cdot)\) \(\chi_{46208}(717,\cdot)\) \(\chi_{46208}(725,\cdot)\) \(\chi_{46208}(773,\cdot)\) \(\chi_{46208}(781,\cdot)\) ...

Copy content comment:Galois orbit
 
Copy content sage:chi.galois_orbit()
 
Copy content gp:order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 
Copy content magma:order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };
 

Related number fields

Field of values: $\Q(\zeta_{5472})$
Fixed field: Number field defined by a degree 5472 polynomial (not computed)

Values on generators

\((28159,36101,14081)\) → \((1,e\left(\frac{9}{32}\right),e\left(\frac{173}{342}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(11\)\(13\)\(15\)\(17\)\(21\)\(23\)
\( \chi_{ 46208 }(357, a) \) \(-1\)\(1\)\(e\left(\frac{857}{5472}\right)\)\(e\left(\frac{3491}{5472}\right)\)\(e\left(\frac{629}{912}\right)\)\(e\left(\frac{857}{2736}\right)\)\(e\left(\frac{917}{1824}\right)\)\(e\left(\frac{3517}{5472}\right)\)\(e\left(\frac{1087}{1368}\right)\)\(e\left(\frac{269}{1368}\right)\)\(e\left(\frac{4631}{5472}\right)\)\(e\left(\frac{2165}{2736}\right)\)
Copy content comment:Value of chi at x
 
Copy content sage:chi(x)
 
Copy content gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
 
Copy content magma:chi(x)
 
\( \chi_{ 46208 }(357,a) \;\) at \(\;a = \) e.g. 2