![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7081, base_ring=CyclotomicField(288))
M = H._module
chi = DirichletCharacter(H, M([112,237]))
![Copy content]()
gp:[g,chi] = znchar(Mod(1642, 7081))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7081.1642");
| Modulus: | \(7081\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(7081\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(288\) |
![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);
|
\(\chi_{7081}(41,\cdot)\)
\(\chi_{7081}(71,\cdot)\)
\(\chi_{7081}(187,\cdot)\)
\(\chi_{7081}(217,\cdot)\)
\(\chi_{7081}(276,\cdot)\)
\(\chi_{7081}(328,\cdot)\)
\(\chi_{7081}(349,\cdot)\)
\(\chi_{7081}(401,\cdot)\)
\(\chi_{7081}(495,\cdot)\)
\(\chi_{7081}(568,\cdot)\)
\(\chi_{7081}(620,\cdot)\)
\(\chi_{7081}(771,\cdot)\)
\(\chi_{7081}(844,\cdot)\)
\(\chi_{7081}(894,\cdot)\)
\(\chi_{7081}(947,\cdot)\)
\(\chi_{7081}(1093,\cdot)\)
\(\chi_{7081}(1204,\cdot)\)
\(\chi_{7081}(1332,\cdot)\)
\(\chi_{7081}(1478,\cdot)\)
\(\chi_{7081}(1496,\cdot)\)
\(\chi_{7081}(1531,\cdot)\)
\(\chi_{7081}(1642,\cdot)\)
\(\chi_{7081}(1663,\cdot)\)
\(\chi_{7081}(1736,\cdot)\)
\(\chi_{7081}(1882,\cdot)\)
\(\chi_{7081}(1955,\cdot)\)
\(\chi_{7081}(2208,\cdot)\)
\(\chi_{7081}(2226,\cdot)\)
\(\chi_{7081}(2299,\cdot)\)
\(\chi_{7081}(2354,\cdot)\)
...
![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 };
\((5918,1169)\) → \((e\left(\frac{7}{18}\right),e\left(\frac{79}{96}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 7081 }(1642, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{13}{144}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{13}{72}\right)\) | \(e\left(\frac{61}{288}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{29}{96}\right)\) | \(e\left(\frac{23}{144}\right)\) |
![Copy content]()
sage:chi(x)
![Copy content]()
gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
![Copy content]()
magma:chi(x)
