↑

Properties

Label 17425.13918
Modulus $17425$
Conductor $3485$
Order $80$
Real no
Primitive no
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(17425, base_ring=CyclotomicField(80)) M = H._module chi = DirichletCharacter(H, M([60,65,18]))
 
Copy content gp:[g,chi] = znchar(Mod(13918, 17425))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("17425.13918");
 

Basic properties

Modulus: \(17425\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(3485\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(80\)
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: no, induced from \(\chi_{3485}(3463,\cdot)\)
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 17425.bcw

\(\chi_{17425}(7,\cdot)\) \(\chi_{17425}(343,\cdot)\) \(\chi_{17425}(2407,\cdot)\) \(\chi_{17425}(2982,\cdot)\) \(\chi_{17425}(3882,\cdot)\) \(\chi_{17425}(4107,\cdot)\) \(\chi_{17425}(4568,\cdot)\) \(\chi_{17425}(4907,\cdot)\) \(\chi_{17425}(5418,\cdot)\) \(\chi_{17425}(6618,\cdot)\) \(\chi_{17425}(6718,\cdot)\) \(\chi_{17425}(7082,\cdot)\) \(\chi_{17425}(7443,\cdot)\) \(\chi_{17425}(7468,\cdot)\) \(\chi_{17425}(7568,\cdot)\) \(\chi_{17425}(9568,\cdot)\) \(\chi_{17425}(10632,\cdot)\) \(\chi_{17425}(11532,\cdot)\) \(\chi_{17425}(11793,\cdot)\) \(\chi_{17425}(12557,\cdot)\) \(\chi_{17425}(13843,\cdot)\) \(\chi_{17425}(13918,\cdot)\) \(\chi_{17425}(14507,\cdot)\) \(\chi_{17425}(14732,\cdot)\) \(\chi_{17425}(15532,\cdot)\) \(\chi_{17425}(15643,\cdot)\) \(\chi_{17425}(15732,\cdot)\) \(\chi_{17425}(15943,\cdot)\) \(\chi_{17425}(15968,\cdot)\) \(\chi_{17425}(16207,\cdot)\) ...

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: $\Q(\zeta_{80})$
Fixed field: Number field defined by a degree 80 polynomial

Values on generators

\((5577,14351,5951)\) → \((-i,e\left(\frac{13}{16}\right),e\left(\frac{9}{40}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\( \chi_{ 17425 }(13918, a) \) \(-1\)\(1\)\(e\left(\frac{39}{40}\right)\)\(e\left(\frac{7}{16}\right)\)\(e\left(\frac{19}{20}\right)\)\(e\left(\frac{33}{80}\right)\)\(e\left(\frac{37}{80}\right)\)\(e\left(\frac{37}{40}\right)\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{29}{80}\right)\)\(e\left(\frac{31}{80}\right)\)\(e\left(\frac{19}{40}\right)\)
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)
 
\( \chi_{ 17425 }(13918,a) \;\) at \(\;a = \) e.g. 2