![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4553, base_ring=CyclotomicField(546))
M = H._module
chi = DirichletCharacter(H, M([390,28]))
![Copy content]()
gp:[g,chi] = znchar(Mod(951, 4553))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4553.951");
| Modulus: | \(4553\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(4553\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(273\) |
![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);
|
\(\chi_{4553}(52,\cdot)\)
\(\chi_{4553}(81,\cdot)\)
\(\chi_{4553}(132,\cdot)\)
\(\chi_{4553}(168,\cdot)\)
\(\chi_{4553}(194,\cdot)\)
\(\chi_{4553}(197,\cdot)\)
\(\chi_{4553}(228,\cdot)\)
\(\chi_{4553}(257,\cdot)\)
\(\chi_{4553}(281,\cdot)\)
\(\chi_{4553}(344,\cdot)\)
\(\chi_{4553}(429,\cdot)\)
\(\chi_{4553}(480,\cdot)\)
\(\chi_{4553}(488,\cdot)\)
\(\chi_{4553}(518,\cdot)\)
\(\chi_{4553}(542,\cdot)\)
\(\chi_{4553}(571,\cdot)\)
\(\chi_{4553}(603,\cdot)\)
\(\chi_{4553}(625,\cdot)\)
\(\chi_{4553}(645,\cdot)\)
\(\chi_{4553}(658,\cdot)\)
\(\chi_{4553}(663,\cdot)\)
\(\chi_{4553}(741,\cdot)\)
\(\chi_{4553}(749,\cdot)\)
\(\chi_{4553}(832,\cdot)\)
\(\chi_{4553}(837,\cdot)\)
\(\chi_{4553}(866,\cdot)\)
\(\chi_{4553}(894,\cdot)\)
\(\chi_{4553}(906,\cdot)\)
\(\chi_{4553}(951,\cdot)\)
\(\chi_{4553}(953,\cdot)\)
...
![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 };
\((2670,2988)\) → \((e\left(\frac{5}{7}\right),e\left(\frac{2}{39}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4553 }(951, a) \) |
\(1\) | \(1\) | \(e\left(\frac{86}{91}\right)\) | \(e\left(\frac{212}{273}\right)\) | \(e\left(\frac{81}{91}\right)\) | \(e\left(\frac{209}{273}\right)\) | \(e\left(\frac{197}{273}\right)\) | \(e\left(\frac{10}{91}\right)\) | \(e\left(\frac{76}{91}\right)\) | \(e\left(\frac{151}{273}\right)\) | \(e\left(\frac{194}{273}\right)\) | \(e\left(\frac{80}{273}\right)\) |
![Copy content]()
sage:chi(x)
![Copy content]()
gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
![Copy content]()
magma:chi(x)
