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Properties

Label 1880.1039
Modulus $1880$
Conductor $940$
Order $46$
Real no
Primitive no
Minimal no
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(1880, base_ring=CyclotomicField(46)) M = H._module chi = DirichletCharacter(H, M([23,0,23,1]))
 
Copy content gp:[g,chi] = znchar(Mod(1039, 1880))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1880.1039");
 

Basic properties

Modulus: \(1880\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(940\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(46\)
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 \(\chi_{940}(99,\cdot)\)
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: no
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 1880.z

\(\chi_{1880}(39,\cdot)\) \(\chi_{1880}(199,\cdot)\) \(\chi_{1880}(279,\cdot)\) \(\chi_{1880}(359,\cdot)\) \(\chi_{1880}(399,\cdot)\) \(\chi_{1880}(599,\cdot)\) \(\chi_{1880}(839,\cdot)\) \(\chi_{1880}(879,\cdot)\) \(\chi_{1880}(919,\cdot)\) \(\chi_{1880}(959,\cdot)\) \(\chi_{1880}(1039,\cdot)\) \(\chi_{1880}(1079,\cdot)\) \(\chi_{1880}(1119,\cdot)\) \(\chi_{1880}(1159,\cdot)\) \(\chi_{1880}(1279,\cdot)\) \(\chi_{1880}(1359,\cdot)\) \(\chi_{1880}(1439,\cdot)\) \(\chi_{1880}(1479,\cdot)\) \(\chi_{1880}(1519,\cdot)\) \(\chi_{1880}(1639,\cdot)\) \(\chi_{1880}(1759,\cdot)\) \(\chi_{1880}(1799,\cdot)\)

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: \(\Q(\zeta_{23})\)
Fixed field: 46.46.1472629538247713057115908841446795301275975338441612336549649339098854081833834905600000000000000000000000.1

Values on generators

\((471,941,377,1321)\) → \((-1,1,-1,e\left(\frac{1}{46}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(19\)\(21\)\(23\)\(27\)
\( \chi_{ 1880 }(1039, a) \) \(1\)\(1\)\(e\left(\frac{10}{23}\right)\)\(e\left(\frac{16}{23}\right)\)\(e\left(\frac{20}{23}\right)\)\(e\left(\frac{15}{23}\right)\)\(e\left(\frac{17}{23}\right)\)\(e\left(\frac{39}{46}\right)\)\(e\left(\frac{11}{23}\right)\)\(e\left(\frac{3}{23}\right)\)\(e\left(\frac{5}{46}\right)\)\(e\left(\frac{7}{23}\right)\)
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)
 
\( \chi_{ 1880 }(1039,a) \;\) at \(\;a = \) e.g. 2