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Properties

Label 35476.14811
Modulus $35476$
Conductor $35476$
Order $140$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

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Show commands: Magma / Pari/GP / SageMath
Copy content comment:Define the Dirichlet character
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(35476, base_ring=CyclotomicField(140)) M = H._module chi = DirichletCharacter(H, M([70,110,7]))
 
Copy content gp:[g,chi] = znchar(Mod(14811, 35476))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("35476.14811");
 

Basic properties

Modulus: \(35476\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(35476\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(140\)
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 35476.ks

\(\chi_{35476}(755,\cdot)\) \(\chi_{35476}(1483,\cdot)\) \(\chi_{35476}(1651,\cdot)\) \(\chi_{35476}(3779,\cdot)\) \(\chi_{35476}(3947,\cdot)\) \(\chi_{35476}(4451,\cdot)\) \(\chi_{35476}(4675,\cdot)\) \(\chi_{35476}(5823,\cdot)\) \(\chi_{35476}(6047,\cdot)\) \(\chi_{35476}(6551,\cdot)\) \(\chi_{35476}(6719,\cdot)\) \(\chi_{35476}(8847,\cdot)\) \(\chi_{35476}(9519,\cdot)\) \(\chi_{35476}(9743,\cdot)\) \(\chi_{35476}(10891,\cdot)\) \(\chi_{35476}(11115,\cdot)\) \(\chi_{35476}(11619,\cdot)\) \(\chi_{35476}(11787,\cdot)\) \(\chi_{35476}(14083,\cdot)\) \(\chi_{35476}(14587,\cdot)\) \(\chi_{35476}(14811,\cdot)\) \(\chi_{35476}(15959,\cdot)\) \(\chi_{35476}(16183,\cdot)\) \(\chi_{35476}(16687,\cdot)\) \(\chi_{35476}(18983,\cdot)\) \(\chi_{35476}(19151,\cdot)\) \(\chi_{35476}(19655,\cdot)\) \(\chi_{35476}(19879,\cdot)\) \(\chi_{35476}(21027,\cdot)\) \(\chi_{35476}(21251,\cdot)\) ...

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: $\Q(\zeta_{140})$
Fixed field: Number field defined by a degree 140 polynomial (not computed)

Values on generators

\((17739,22445,33125)\) → \((-1,e\left(\frac{11}{14}\right),e\left(\frac{1}{20}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(9\)\(11\)\(13\)\(15\)\(17\)\(19\)\(23\)\(25\)
\( \chi_{ 35476 }(14811, a) \) \(-1\)\(1\)\(e\left(\frac{3}{35}\right)\)\(e\left(\frac{41}{70}\right)\)\(e\left(\frac{6}{35}\right)\)\(e\left(\frac{1}{35}\right)\)\(e\left(\frac{9}{70}\right)\)\(e\left(\frac{47}{70}\right)\)\(e\left(\frac{11}{28}\right)\)\(-i\)\(e\left(\frac{1}{140}\right)\)\(e\left(\frac{6}{35}\right)\)
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)
 
\( \chi_{ 35476 }(14811,a) \;\) at \(\;a = \) e.g. 2