↑

Properties

Label 29435.832
Modulus $29435$
Conductor $29435$
Order $812$
Real no
Primitive yes
Minimal yes
Parity even

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(29435, base_ring=CyclotomicField(812)) M = H._module chi = DirichletCharacter(H, M([203,406,668]))
 
Copy content gp:[g,chi] = znchar(Mod(832, 29435))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("29435.832");
 

Basic properties

Modulus: \(29435\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(29435\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(812\)
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: even
Copy content comment:Parity
 
Copy content sage:chi.is_odd()
 
Copy content gp:zncharisodd(g,chi)
 
Copy content magma:IsOdd(chi);
 

Galois orbit 29435.fe

\(\chi_{29435}(83,\cdot)\) \(\chi_{29435}(132,\cdot)\) \(\chi_{29435}(223,\cdot)\) \(\chi_{29435}(342,\cdot)\) \(\chi_{29435}(517,\cdot)\) \(\chi_{29435}(538,\cdot)\) \(\chi_{29435}(587,\cdot)\) \(\chi_{29435}(692,\cdot)\) \(\chi_{29435}(748,\cdot)\) \(\chi_{29435}(832,\cdot)\) \(\chi_{29435}(923,\cdot)\) \(\chi_{29435}(993,\cdot)\) \(\chi_{29435}(1098,\cdot)\) \(\chi_{29435}(1147,\cdot)\) \(\chi_{29435}(1238,\cdot)\) \(\chi_{29435}(1357,\cdot)\) \(\chi_{29435}(1532,\cdot)\) \(\chi_{29435}(1553,\cdot)\) \(\chi_{29435}(1602,\cdot)\) \(\chi_{29435}(1707,\cdot)\) \(\chi_{29435}(1763,\cdot)\) \(\chi_{29435}(1847,\cdot)\) \(\chi_{29435}(1938,\cdot)\) \(\chi_{29435}(2008,\cdot)\) \(\chi_{29435}(2113,\cdot)\) \(\chi_{29435}(2162,\cdot)\) \(\chi_{29435}(2372,\cdot)\) \(\chi_{29435}(2547,\cdot)\) \(\chi_{29435}(2568,\cdot)\) \(\chi_{29435}(2617,\cdot)\) ...

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: $\Q(\zeta_{812})$
Fixed field: Number field defined by a degree 812 polynomial (not computed)

Values on generators

\((17662,25231,28596)\) → \((i,-1,e\left(\frac{167}{203}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(8\)\(9\)\(11\)\(12\)\(13\)\(16\)
\( \chi_{ 29435 }(832, a) \) \(1\)\(1\)\(e\left(\frac{59}{812}\right)\)\(e\left(\frac{15}{812}\right)\)\(e\left(\frac{59}{406}\right)\)\(e\left(\frac{37}{406}\right)\)\(e\left(\frac{177}{812}\right)\)\(e\left(\frac{15}{406}\right)\)\(e\left(\frac{129}{203}\right)\)\(e\left(\frac{19}{116}\right)\)\(e\left(\frac{691}{812}\right)\)\(e\left(\frac{59}{203}\right)\)
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)
 
\( \chi_{ 29435 }(832,a) \;\) at \(\;a = \) e.g. 2