![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(955, base_ring=CyclotomicField(190))
M = H._module
chi = DirichletCharacter(H, M([0,49]))
![Copy content]()
gp:[g,chi] = znchar(Mod(141, 955))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("955.141");
| Modulus: | \(955\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(191\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(190\) |
![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: | no, induced from \(\chi_{191}(141,\cdot)\) |
![Copy content]()
sage:chi.is_primitive()
![Copy content]()
gp:#znconreyconductor(g,chi)==1
![Copy content]()
magma:IsPrimitive(chi);
|
| Minimal: | yes |
| Parity: | odd |
![Copy content]()
sage:chi.is_odd()
![Copy content]()
gp:zncharisodd(g,chi)
![Copy content]()
magma:IsOdd(chi);
|
\(\chi_{955}(21,\cdot)\)
\(\chi_{955}(56,\cdot)\)
\(\chi_{955}(61,\cdot)\)
\(\chi_{955}(71,\cdot)\)
\(\chi_{955}(76,\cdot)\)
\(\chi_{955}(91,\cdot)\)
\(\chi_{955}(101,\cdot)\)
\(\chi_{955}(106,\cdot)\)
\(\chi_{955}(111,\cdot)\)
\(\chi_{955}(116,\cdot)\)
\(\chi_{955}(126,\cdot)\)
\(\chi_{955}(131,\cdot)\)
\(\chi_{955}(141,\cdot)\)
\(\chi_{955}(146,\cdot)\)
\(\chi_{955}(151,\cdot)\)
\(\chi_{955}(171,\cdot)\)
\(\chi_{955}(176,\cdot)\)
\(\chi_{955}(181,\cdot)\)
\(\chi_{955}(226,\cdot)\)
\(\chi_{955}(286,\cdot)\)
\(\chi_{955}(296,\cdot)\)
\(\chi_{955}(301,\cdot)\)
\(\chi_{955}(331,\cdot)\)
\(\chi_{955}(336,\cdot)\)
\(\chi_{955}(356,\cdot)\)
\(\chi_{955}(366,\cdot)\)
\(\chi_{955}(401,\cdot)\)
\(\chi_{955}(411,\cdot)\)
\(\chi_{955}(426,\cdot)\)
\(\chi_{955}(456,\cdot)\)
...
![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 };
\((192,401)\) → \((1,e\left(\frac{49}{190}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 955 }(141, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{33}{95}\right)\) | \(e\left(\frac{87}{95}\right)\) | \(e\left(\frac{66}{95}\right)\) | \(e\left(\frac{5}{19}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{4}{95}\right)\) | \(e\left(\frac{79}{95}\right)\) | \(e\left(\frac{35}{38}\right)\) | \(e\left(\frac{58}{95}\right)\) | \(e\left(\frac{84}{95}\right)\) |
![Copy content]()
sage:chi(x)
![Copy content]()
gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
![Copy content]()
magma:chi(x)
![Copy content]()
sage:chi.gauss_sum(a)
![Copy content]()
gp:znchargauss(g,chi,a)
![Copy content]()
sage:chi.jacobi_sum(n)
![Copy content]()
sage:chi.kloosterman_sum(a,b)
