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Properties

Label 7595.2019
Modulus $7595$
Conductor $7595$
Order $210$
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(7595, base_ring=CyclotomicField(210)) M = H._module chi = DirichletCharacter(H, M([105,65,126]))
 
Copy content gp:[g,chi] = znchar(Mod(2019, 7595))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("7595.2019");
 

Basic properties

Modulus: \(7595\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(7595\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(210\)
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 7595.if

\(\chi_{7595}(159,\cdot)\) \(\chi_{7595}(194,\cdot)\) \(\chi_{7595}(684,\cdot)\) \(\chi_{7595}(934,\cdot)\) \(\chi_{7595}(969,\cdot)\) \(\chi_{7595}(1039,\cdot)\) \(\chi_{7595}(1279,\cdot)\) \(\chi_{7595}(1349,\cdot)\) \(\chi_{7595}(1459,\cdot)\) \(\chi_{7595}(1769,\cdot)\) \(\chi_{7595}(2019,\cdot)\) \(\chi_{7595}(2054,\cdot)\) \(\chi_{7595}(2124,\cdot)\) \(\chi_{7595}(2329,\cdot)\) \(\chi_{7595}(2364,\cdot)\) \(\chi_{7595}(2434,\cdot)\) \(\chi_{7595}(2544,\cdot)\) \(\chi_{7595}(2854,\cdot)\) \(\chi_{7595}(3104,\cdot)\) \(\chi_{7595}(3139,\cdot)\) \(\chi_{7595}(3209,\cdot)\) \(\chi_{7595}(3414,\cdot)\) \(\chi_{7595}(3519,\cdot)\) \(\chi_{7595}(3629,\cdot)\) \(\chi_{7595}(4189,\cdot)\) \(\chi_{7595}(4224,\cdot)\) \(\chi_{7595}(4499,\cdot)\) \(\chi_{7595}(4534,\cdot)\) \(\chi_{7595}(4604,\cdot)\) \(\chi_{7595}(4714,\cdot)\) ...

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: $\Q(\zeta_{105})$
Fixed field: Number field defined by a degree 210 polynomial (not computed)

Values on generators

\((6077,5736,4901)\) → \((-1,e\left(\frac{13}{42}\right),e\left(\frac{3}{5}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(8\)\(9\)\(11\)\(12\)\(13\)\(16\)
\( \chi_{ 7595 }(2019, a) \) \(-1\)\(1\)\(e\left(\frac{199}{210}\right)\)\(e\left(\frac{43}{105}\right)\)\(e\left(\frac{94}{105}\right)\)\(e\left(\frac{5}{14}\right)\)\(e\left(\frac{59}{70}\right)\)\(e\left(\frac{86}{105}\right)\)\(e\left(\frac{19}{105}\right)\)\(e\left(\frac{32}{105}\right)\)\(e\left(\frac{11}{35}\right)\)\(e\left(\frac{83}{105}\right)\)
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)
 
\( \chi_{ 7595 }(2019,a) \;\) at \(\;a = \) e.g. 2