↑

Properties

Label 7832.1763
Modulus $7832$
Conductor $7832$
Order $220$
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(7832, base_ring=CyclotomicField(220)) M = H._module chi = DirichletCharacter(H, M([110,110,176,125]))
 
Copy content gp:[g,chi] = znchar(Mod(1763, 7832))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("7832.1763");
 

Basic properties

Modulus: \(7832\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(7832\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(220\)
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 7832.em

\(\chi_{7832}(339,\cdot)\) \(\chi_{7832}(427,\cdot)\) \(\chi_{7832}(555,\cdot)\) \(\chi_{7832}(587,\cdot)\) \(\chi_{7832}(603,\cdot)\) \(\chi_{7832}(643,\cdot)\) \(\chi_{7832}(691,\cdot)\) \(\chi_{7832}(707,\cdot)\) \(\chi_{7832}(819,\cdot)\) \(\chi_{7832}(907,\cdot)\) \(\chi_{7832}(939,\cdot)\) \(\chi_{7832}(1059,\cdot)\) \(\chi_{7832}(1115,\cdot)\) \(\chi_{7832}(1147,\cdot)\) \(\chi_{7832}(1523,\cdot)\) \(\chi_{7832}(1555,\cdot)\) \(\chi_{7832}(1611,\cdot)\) \(\chi_{7832}(1731,\cdot)\) \(\chi_{7832}(1763,\cdot)\) \(\chi_{7832}(1851,\cdot)\) \(\chi_{7832}(1963,\cdot)\) \(\chi_{7832}(2011,\cdot)\) \(\chi_{7832}(2027,\cdot)\) \(\chi_{7832}(2083,\cdot)\) \(\chi_{7832}(2115,\cdot)\) \(\chi_{7832}(2363,\cdot)\) \(\chi_{7832}(2539,\cdot)\) \(\chi_{7832}(2843,\cdot)\) \(\chi_{7832}(2979,\cdot)\) \(\chi_{7832}(3155,\cdot)\) ...

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: $\Q(\zeta_{220})$
Fixed field: Number field defined by a degree 220 polynomial (not computed)

Values on generators

\((1959,3917,4985,7657)\) → \((-1,-1,e\left(\frac{4}{5}\right),e\left(\frac{25}{44}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(13\)\(15\)\(17\)\(19\)\(21\)\(23\)
\( \chi_{ 7832 }(1763, a) \) \(-1\)\(1\)\(e\left(\frac{213}{220}\right)\)\(e\left(\frac{26}{55}\right)\)\(e\left(\frac{27}{220}\right)\)\(e\left(\frac{103}{110}\right)\)\(e\left(\frac{81}{220}\right)\)\(e\left(\frac{97}{220}\right)\)\(e\left(\frac{67}{110}\right)\)\(e\left(\frac{63}{220}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{39}{44}\right)\)
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)
 
\( \chi_{ 7832 }(1763,a) \;\) at \(\;a = \) e.g. 2