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Properties

Label 1453.1334
Modulus $1453$
Conductor $1453$
Order $33$
Real no
Primitive yes
Minimal yes
Parity even

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(1453, base_ring=CyclotomicField(66)) M = H._module chi = DirichletCharacter(H, M([10]))
 
Copy content gp:[g,chi] = znchar(Mod(1334, 1453))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1453.1334");
 

Basic properties

Modulus: \(1453\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(1453\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(33\)
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: even
Copy content comment:Parity
 
Copy content sage:chi.is_odd()
 
Copy content gp:zncharisodd(g,chi)
 
Copy content magma:IsOdd(chi);
 

Galois orbit 1453.i

\(\chi_{1453}(11,\cdot)\) \(\chi_{1453}(63,\cdot)\) \(\chi_{1453}(111,\cdot)\) \(\chi_{1453}(121,\cdot)\) \(\chi_{1453}(144,\cdot)\) \(\chi_{1453}(394,\cdot)\) \(\chi_{1453}(507,\cdot)\) \(\chi_{1453}(625,\cdot)\) \(\chi_{1453}(697,\cdot)\) \(\chi_{1453}(988,\cdot)\) \(\chi_{1453}(1032,\cdot)\) \(\chi_{1453}(1063,\cdot)\) \(\chi_{1453}(1084,\cdot)\) \(\chi_{1453}(1181,\cdot)\) \(\chi_{1453}(1218,\cdot)\) \(\chi_{1453}(1221,\cdot)\) \(\chi_{1453}(1321,\cdot)\) \(\chi_{1453}(1334,\cdot)\) \(\chi_{1453}(1428,\cdot)\) \(\chi_{1453}(1441,\cdot)\)

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: \(\Q(\zeta_{33})\)
Fixed field: Number field defined by a degree 33 polynomial

Values on generators

\(2\) → \(e\left(\frac{5}{33}\right)\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\( \chi_{ 1453 }(1334, a) \) \(1\)\(1\)\(e\left(\frac{5}{33}\right)\)\(e\left(\frac{1}{33}\right)\)\(e\left(\frac{10}{33}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{2}{33}\right)\)\(e\left(\frac{16}{33}\right)\)\(e\left(\frac{1}{3}\right)\)
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)
 
\( \chi_{ 1453 }(1334,a) \;\) at \(\;a = \) e.g. 2