↑

Properties

Label 10143.4157
Modulus $10143$
Conductor $3381$
Order $154$
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(10143, base_ring=CyclotomicField(154)) M = H._module chi = DirichletCharacter(H, M([77,55,49]))
 
Copy content gp:[g,chi] = znchar(Mod(4157, 10143))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("10143.4157");
 

Basic properties

Modulus: \(10143\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(3381\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(154\)
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 \(\chi_{3381}(776,\cdot)\)
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 10143.es

\(\chi_{10143}(125,\cdot)\) \(\chi_{10143}(251,\cdot)\) \(\chi_{10143}(314,\cdot)\) \(\chi_{10143}(503,\cdot)\) \(\chi_{10143}(566,\cdot)\) \(\chi_{10143}(755,\cdot)\) \(\chi_{10143}(1259,\cdot)\) \(\chi_{10143}(1385,\cdot)\) \(\chi_{10143}(1574,\cdot)\) \(\chi_{10143}(1700,\cdot)\) \(\chi_{10143}(1952,\cdot)\) \(\chi_{10143}(2015,\cdot)\) \(\chi_{10143}(2330,\cdot)\) \(\chi_{10143}(2708,\cdot)\) \(\chi_{10143}(2771,\cdot)\) \(\chi_{10143}(2834,\cdot)\) \(\chi_{10143}(3023,\cdot)\) \(\chi_{10143}(3149,\cdot)\) \(\chi_{10143}(3212,\cdot)\) \(\chi_{10143}(3401,\cdot)\) \(\chi_{10143}(3464,\cdot)\) \(\chi_{10143}(3653,\cdot)\) \(\chi_{10143}(3779,\cdot)\) \(\chi_{10143}(4157,\cdot)\) \(\chi_{10143}(4220,\cdot)\) \(\chi_{10143}(4283,\cdot)\) \(\chi_{10143}(4472,\cdot)\) \(\chi_{10143}(4598,\cdot)\) \(\chi_{10143}(4661,\cdot)\) \(\chi_{10143}(4913,\cdot)\) ...

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: $\Q(\zeta_{77})$
Fixed field: Number field defined by a degree 154 polynomial (not computed)

Values on generators

\((5636,3727,442)\) → \((-1,e\left(\frac{5}{14}\right),e\left(\frac{7}{22}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(4\)\(5\)\(8\)\(10\)\(11\)\(13\)\(16\)\(17\)\(19\)
\( \chi_{ 10143 }(4157, a) \) \(-1\)\(1\)\(e\left(\frac{65}{154}\right)\)\(e\left(\frac{65}{77}\right)\)\(e\left(\frac{27}{154}\right)\)\(e\left(\frac{41}{154}\right)\)\(e\left(\frac{46}{77}\right)\)\(e\left(\frac{50}{77}\right)\)\(e\left(\frac{37}{154}\right)\)\(e\left(\frac{53}{77}\right)\)\(e\left(\frac{101}{154}\right)\)\(e\left(\frac{3}{11}\right)\)
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)
 
\( \chi_{ 10143 }(4157,a) \;\) at \(\;a = \) e.g. 2