↑

Properties

Label 19425.13439
Modulus $19425$
Conductor $19425$
Order $60$
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(19425, base_ring=CyclotomicField(60)) M = H._module chi = DirichletCharacter(H, M([30,18,30,5]))
 
Copy content gp:[g,chi] = znchar(Mod(13439, 19425))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("19425.13439");
 

Basic properties

Modulus: \(19425\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(19425\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(60\)
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 19425.rg

\(\chi_{19425}(1679,\cdot)\) \(\chi_{19425}(1784,\cdot)\) \(\chi_{19425}(3359,\cdot)\) \(\chi_{19425}(3464,\cdot)\) \(\chi_{19425}(5564,\cdot)\) \(\chi_{19425}(5669,\cdot)\) \(\chi_{19425}(7244,\cdot)\) \(\chi_{19425}(9554,\cdot)\) \(\chi_{19425}(11129,\cdot)\) \(\chi_{19425}(11234,\cdot)\) \(\chi_{19425}(13334,\cdot)\) \(\chi_{19425}(13439,\cdot)\) \(\chi_{19425}(15014,\cdot)\) \(\chi_{19425}(15119,\cdot)\) \(\chi_{19425}(17219,\cdot)\) \(\chi_{19425}(19004,\cdot)\)

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: \(\Q(\zeta_{60})\)
Fixed field: Number field defined by a degree 60 polynomial

Values on generators

\((6476,10102,8326,8401)\) → \((-1,e\left(\frac{3}{10}\right),-1,e\left(\frac{1}{12}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(4\)\(8\)\(11\)\(13\)\(16\)\(17\)\(19\)\(22\)\(23\)
\( \chi_{ 19425 }(13439, a) \) \(-1\)\(1\)\(e\left(\frac{53}{60}\right)\)\(e\left(\frac{23}{30}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{7}{60}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{29}{60}\right)\)\(e\left(\frac{49}{60}\right)\)\(e\left(\frac{41}{60}\right)\)\(e\left(\frac{1}{20}\right)\)
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)
 
\( \chi_{ 19425 }(13439,a) \;\) at \(\;a = \) e.g. 2