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Properties

Label 96195.16336
Modulus $96195$
Conductor $53$
Order $52$
Real no
Primitive no
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(96195, base_ring=CyclotomicField(52)) M = H._module chi = DirichletCharacter(H, M([0,0,0,19]))
 
Copy content gp:[g,chi] = znchar(Mod(16336, 96195))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("96195.16336");
 

Basic properties

Modulus: \(96195\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(53\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(52\)
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 \(\chi_{53}(12,\cdot)\)
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 96195.fz

\(\chi_{96195}(1816,\cdot)\) \(\chi_{96195}(3631,\cdot)\) \(\chi_{96195}(10891,\cdot)\) \(\chi_{96195}(12706,\cdot)\) \(\chi_{96195}(16336,\cdot)\) \(\chi_{96195}(21781,\cdot)\) \(\chi_{96195}(29041,\cdot)\) \(\chi_{96195}(39931,\cdot)\) \(\chi_{96195}(41746,\cdot)\) \(\chi_{96195}(43561,\cdot)\) \(\chi_{96195}(45376,\cdot)\) \(\chi_{96195}(47191,\cdot)\) \(\chi_{96195}(49006,\cdot)\) \(\chi_{96195}(54451,\cdot)\) \(\chi_{96195}(56266,\cdot)\) \(\chi_{96195}(61711,\cdot)\) \(\chi_{96195}(63526,\cdot)\) \(\chi_{96195}(65341,\cdot)\) \(\chi_{96195}(67156,\cdot)\) \(\chi_{96195}(68971,\cdot)\) \(\chi_{96195}(70786,\cdot)\) \(\chi_{96195}(81676,\cdot)\) \(\chi_{96195}(88936,\cdot)\) \(\chi_{96195}(94381,\cdot)\)

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: $\Q(\zeta_{52})$
Fixed field: Number field defined by a degree 52 polynomial

Values on generators

\((32066,76957,90631,88936)\) → \((1,1,1,e\left(\frac{19}{52}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(4\)\(7\)\(8\)\(13\)\(14\)\(16\)\(17\)\(19\)\(23\)
\( \chi_{ 96195 }(16336, a) \) \(-1\)\(1\)\(e\left(\frac{19}{52}\right)\)\(e\left(\frac{19}{26}\right)\)\(e\left(\frac{3}{26}\right)\)\(e\left(\frac{5}{52}\right)\)\(e\left(\frac{10}{13}\right)\)\(e\left(\frac{25}{52}\right)\)\(e\left(\frac{6}{13}\right)\)\(e\left(\frac{17}{26}\right)\)\(e\left(\frac{27}{52}\right)\)\(i\)
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)
 
\( \chi_{ 96195 }(16336,a) \;\) at \(\;a = \) e.g. 2