sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2183, base_ring=CyclotomicField(1044))
M = H._module
chi = DirichletCharacter(H, M([377,450]))
pari:[g,chi] = znchar(Mod(1014,2183))
Modulus: | \(2183\) | |
Conductor: | \(2183\) |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | \(1044\) |
sage:chi.multiplicative_order()
pari:charorder(g,chi)
|
Real: | no |
Primitive: | yes |
sage:chi.is_primitive()
pari:#znconreyconductor(g,chi)==1
|
Minimal: | yes |
Parity: | even |
sage:chi.is_odd()
pari:zncharisodd(g,chi)
|
\(\chi_{2183}(2,\cdot)\)
\(\chi_{2183}(13,\cdot)\)
\(\chi_{2183}(18,\cdot)\)
\(\chi_{2183}(24,\cdot)\)
\(\chi_{2183}(32,\cdot)\)
\(\chi_{2183}(39,\cdot)\)
\(\chi_{2183}(42,\cdot)\)
\(\chi_{2183}(50,\cdot)\)
\(\chi_{2183}(52,\cdot)\)
\(\chi_{2183}(54,\cdot)\)
\(\chi_{2183}(55,\cdot)\)
\(\chi_{2183}(56,\cdot)\)
\(\chi_{2183}(61,\cdot)\)
\(\chi_{2183}(69,\cdot)\)
\(\chi_{2183}(72,\cdot)\)
\(\chi_{2183}(89,\cdot)\)
\(\chi_{2183}(91,\cdot)\)
\(\chi_{2183}(92,\cdot)\)
\(\chi_{2183}(93,\cdot)\)
\(\chi_{2183}(96,\cdot)\)
\(\chi_{2183}(98,\cdot)\)
\(\chi_{2183}(106,\cdot)\)
\(\chi_{2183}(109,\cdot)\)
\(\chi_{2183}(113,\cdot)\)
\(\chi_{2183}(124,\cdot)\)
\(\chi_{2183}(126,\cdot)\)
\(\chi_{2183}(128,\cdot)\)
\(\chi_{2183}(129,\cdot)\)
\(\chi_{2183}(131,\cdot)\)
\(\chi_{2183}(150,\cdot)\)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\((1889,297)\) → \((e\left(\frac{13}{36}\right),e\left(\frac{25}{58}\right))\)
\(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 2183 }(1014, a) \) |
\(1\) | \(1\) | \(e\left(\frac{827}{1044}\right)\) | \(e\left(\frac{491}{522}\right)\) | \(e\left(\frac{305}{522}\right)\) | \(e\left(\frac{931}{1044}\right)\) | \(e\left(\frac{85}{116}\right)\) | \(e\left(\frac{82}{261}\right)\) | \(e\left(\frac{131}{348}\right)\) | \(e\left(\frac{230}{261}\right)\) | \(e\left(\frac{119}{174}\right)\) | \(e\left(\frac{53}{87}\right)\) |
sage:chi.jacobi_sum(n)