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Properties

Label 1832.1347
Modulus $1832$
Conductor $1832$
Order $38$
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(1832, base_ring=CyclotomicField(38)) M = H._module chi = DirichletCharacter(H, M([19,19,9]))
 
Copy content gp:[g,chi] = znchar(Mod(1347, 1832))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1832.1347");
 

Basic properties

Modulus: \(1832\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(1832\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(38\)
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 1832.ba

\(\chi_{1832}(11,\cdot)\) \(\chi_{1832}(187,\cdot)\) \(\chi_{1832}(627,\cdot)\) \(\chi_{1832}(643,\cdot)\) \(\chi_{1832}(691,\cdot)\) \(\chi_{1832}(755,\cdot)\) \(\chi_{1832}(795,\cdot)\) \(\chi_{1832}(859,\cdot)\) \(\chi_{1832}(899,\cdot)\) \(\chi_{1832}(931,\cdot)\) \(\chi_{1832}(1171,\cdot)\) \(\chi_{1832}(1331,\cdot)\) \(\chi_{1832}(1347,\cdot)\) \(\chi_{1832}(1499,\cdot)\) \(\chi_{1832}(1587,\cdot)\) \(\chi_{1832}(1667,\cdot)\) \(\chi_{1832}(1771,\cdot)\) \(\chi_{1832}(1779,\cdot)\)

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: \(\Q(\zeta_{19})\)
Fixed field: Number field defined by a degree 38 polynomial

Values on generators

\((1375,917,1609)\) → \((-1,-1,e\left(\frac{9}{38}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(11\)\(13\)\(15\)\(17\)\(19\)\(21\)
\( \chi_{ 1832 }(1347, a) \) \(-1\)\(1\)\(e\left(\frac{5}{19}\right)\)\(e\left(\frac{27}{38}\right)\)\(e\left(\frac{16}{19}\right)\)\(e\left(\frac{10}{19}\right)\)\(e\left(\frac{7}{19}\right)\)\(e\left(\frac{4}{19}\right)\)\(e\left(\frac{37}{38}\right)\)\(e\left(\frac{4}{19}\right)\)\(e\left(\frac{15}{19}\right)\)\(e\left(\frac{2}{19}\right)\)
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)
 
\( \chi_{ 1832 }(1347,a) \;\) at \(\;a = \) e.g. 2