![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3667, base_ring=CyclotomicField(192))
M = H._module
chi = DirichletCharacter(H, M([64,127]))
![Copy content]()
gp:[g,chi] = znchar(Mod(1527, 3667))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3667.1527");
| Modulus: | \(3667\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(3667\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(192\) |
![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);
|
\(\chi_{3667}(26,\cdot)\)
\(\chi_{3667}(30,\cdot)\)
\(\chi_{3667}(45,\cdot)\)
\(\chi_{3667}(163,\cdot)\)
\(\chi_{3667}(178,\cdot)\)
\(\chi_{3667}(296,\cdot)\)
\(\chi_{3667}(334,\cdot)\)
\(\chi_{3667}(444,\cdot)\)
\(\chi_{3667}(501,\cdot)\)
\(\chi_{3667}(539,\cdot)\)
\(\chi_{3667}(596,\cdot)\)
\(\chi_{3667}(695,\cdot)\)
\(\chi_{3667}(767,\cdot)\)
\(\chi_{3667}(809,\cdot)\)
\(\chi_{3667}(885,\cdot)\)
\(\chi_{3667}(904,\cdot)\)
\(\chi_{3667}(999,\cdot)\)
\(\chi_{3667}(1018,\cdot)\)
\(\chi_{3667}(1056,\cdot)\)
\(\chi_{3667}(1341,\cdot)\)
\(\chi_{3667}(1356,\cdot)\)
\(\chi_{3667}(1398,\cdot)\)
\(\chi_{3667}(1527,\cdot)\)
\(\chi_{3667}(1584,\cdot)\)
\(\chi_{3667}(1588,\cdot)\)
\(\chi_{3667}(1622,\cdot)\)
\(\chi_{3667}(1626,\cdot)\)
\(\chi_{3667}(1679,\cdot)\)
\(\chi_{3667}(1816,\cdot)\)
\(\chi_{3667}(1892,\cdot)\)
...
![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 };
\((2510,970)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{127}{192}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 3667 }(1527, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{79}{96}\right)\) | \(e\left(\frac{43}{48}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{191}{192}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{15}{32}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{157}{192}\right)\) | \(e\left(\frac{3}{64}\right)\) |
![Copy content]()
sage:chi(x)
![Copy content]()
gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
![Copy content]()
magma:chi(x)
