![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(59168, base_ring=CyclotomicField(1032))
M = H._module
chi = DirichletCharacter(H, M([516,387,340]))
![Copy content]()
gp:[g,chi] = znchar(Mod(24547, 59168))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("59168.24547");
| Modulus: | \(59168\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(59168\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(1032\) |
![Copy content]()
sage:chi.multiplicative_order()
![Copy content]()
gp:charorder(g,chi)
![Copy content]()
magma:Order(chi);
|
| Real: | no |
![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]()
sage:chi.is_primitive()
![Copy content]()
gp:#znconreyconductor(g,chi)==1
![Copy content]()
magma:IsPrimitive(chi);
|
| Minimal: | yes |
| Parity: | even |
![Copy content]()
sage:chi.is_odd()
![Copy content]()
gp:zncharisodd(g,chi)
![Copy content]()
magma:IsOdd(chi);
|
\(\chi_{59168}(123,\cdot)\)
\(\chi_{59168}(179,\cdot)\)
\(\chi_{59168}(467,\cdot)\)
\(\chi_{59168}(523,\cdot)\)
\(\chi_{59168}(811,\cdot)\)
\(\chi_{59168}(867,\cdot)\)
\(\chi_{59168}(1155,\cdot)\)
\(\chi_{59168}(1211,\cdot)\)
\(\chi_{59168}(1499,\cdot)\)
\(\chi_{59168}(1555,\cdot)\)
\(\chi_{59168}(1843,\cdot)\)
\(\chi_{59168}(1899,\cdot)\)
\(\chi_{59168}(2187,\cdot)\)
\(\chi_{59168}(2243,\cdot)\)
\(\chi_{59168}(2531,\cdot)\)
\(\chi_{59168}(2587,\cdot)\)
\(\chi_{59168}(2875,\cdot)\)
\(\chi_{59168}(2931,\cdot)\)
\(\chi_{59168}(3219,\cdot)\)
\(\chi_{59168}(3563,\cdot)\)
\(\chi_{59168}(3619,\cdot)\)
\(\chi_{59168}(3907,\cdot)\)
\(\chi_{59168}(3963,\cdot)\)
\(\chi_{59168}(4251,\cdot)\)
\(\chi_{59168}(4307,\cdot)\)
\(\chi_{59168}(4595,\cdot)\)
\(\chi_{59168}(4651,\cdot)\)
\(\chi_{59168}(4939,\cdot)\)
\(\chi_{59168}(4995,\cdot)\)
\(\chi_{59168}(5283,\cdot)\)
...
![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 };
| Field of values: |
$\Q(\zeta_{1032})$ |
![Copy content]()
sage:CyclotomicField(chi.multiplicative_order())
![Copy content]()
gp:nfinit(polcyclo(charorder(g,chi)))
![Copy content]()
magma:CyclotomicField(Order(chi));
|
| Fixed field: |
Number field defined by a degree 1032 polynomial (not computed) |
![Copy content]()
sage:chi.fixed_field()
|
\((25887,7397,25889)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{85}{258}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 59168 }(24547, a) \) |
\(1\) | \(1\) | \(e\left(\frac{985}{1032}\right)\) | \(e\left(\frac{991}{1032}\right)\) | \(e\left(\frac{499}{516}\right)\) | \(e\left(\frac{469}{516}\right)\) | \(e\left(\frac{249}{344}\right)\) | \(e\left(\frac{269}{1032}\right)\) | \(e\left(\frac{118}{129}\right)\) | \(e\left(\frac{149}{258}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{317}{344}\right)\) |
![Copy content]()
sage:chi(x) # x integer
![Copy content]()
gp:chareval(g,chi,x) \\ x integer, value in Q/Z
![Copy content]()
magma:chi(x)
