![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12095, base_ring=CyclotomicField(1160))
M = H._module
chi = DirichletCharacter(H, M([580,551,1000]))
![Copy content]()
gp:[g,chi] = znchar(Mod(239, 12095))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("12095.239");
| Modulus: | \(12095\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(12095\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(1160\) |
![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: | odd |
![Copy content]()
sage:chi.is_odd()
![Copy content]()
gp:zncharisodd(g,chi)
![Copy content]()
magma:IsOdd(chi);
|
\(\chi_{12095}(19,\cdot)\)
\(\chi_{12095}(29,\cdot)\)
\(\chi_{12095}(94,\cdot)\)
\(\chi_{12095}(104,\cdot)\)
\(\chi_{12095}(134,\cdot)\)
\(\chi_{12095}(194,\cdot)\)
\(\chi_{12095}(199,\cdot)\)
\(\chi_{12095}(234,\cdot)\)
\(\chi_{12095}(239,\cdot)\)
\(\chi_{12095}(299,\cdot)\)
\(\chi_{12095}(304,\cdot)\)
\(\chi_{12095}(399,\cdot)\)
\(\chi_{12095}(429,\cdot)\)
\(\chi_{12095}(434,\cdot)\)
\(\chi_{12095}(439,\cdot)\)
\(\chi_{12095}(464,\cdot)\)
\(\chi_{12095}(479,\cdot)\)
\(\chi_{12095}(499,\cdot)\)
\(\chi_{12095}(559,\cdot)\)
\(\chi_{12095}(609,\cdot)\)
\(\chi_{12095}(639,\cdot)\)
\(\chi_{12095}(669,\cdot)\)
\(\chi_{12095}(684,\cdot)\)
\(\chi_{12095}(744,\cdot)\)
\(\chi_{12095}(749,\cdot)\)
\(\chi_{12095}(794,\cdot)\)
\(\chi_{12095}(854,\cdot)\)
\(\chi_{12095}(874,\cdot)\)
\(\chi_{12095}(889,\cdot)\)
\(\chi_{12095}(914,\cdot)\)
...
![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 };
\((9677,4721,3896)\) → \((-1,e\left(\frac{19}{40}\right),e\left(\frac{25}{29}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 12095 }(239, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{413}{580}\right)\) | \(e\left(\frac{169}{232}\right)\) | \(e\left(\frac{123}{290}\right)\) | \(e\left(\frac{511}{1160}\right)\) | \(e\left(\frac{629}{1160}\right)\) | \(e\left(\frac{79}{580}\right)\) | \(e\left(\frac{53}{116}\right)\) | \(e\left(\frac{1133}{1160}\right)\) | \(e\left(\frac{177}{1160}\right)\) | \(e\left(\frac{21}{1160}\right)\) |
![Copy content]()
sage:chi(x)
![Copy content]()
gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
![Copy content]()
magma:chi(x)
