![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2230, base_ring=CyclotomicField(148))
M = H._module
chi = DirichletCharacter(H, M([37,86]))
![Copy content]()
gp:[g,chi] = znchar(Mod(87, 2230))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2230.87");
| Modulus: | \(2230\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(1115\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(148\) |
![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 \(\chi_{1115}(87,\cdot)\) |
![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);
|
\(\chi_{2230}(13,\cdot)\)
\(\chi_{2230}(27,\cdot)\)
\(\chi_{2230}(87,\cdot)\)
\(\chi_{2230}(103,\cdot)\)
\(\chi_{2230}(157,\cdot)\)
\(\chi_{2230}(163,\cdot)\)
\(\chi_{2230}(167,\cdot)\)
\(\chi_{2230}(193,\cdot)\)
\(\chi_{2230}(207,\cdot)\)
\(\chi_{2230}(277,\cdot)\)
\(\chi_{2230}(327,\cdot)\)
\(\chi_{2230}(397,\cdot)\)
\(\chi_{2230}(413,\cdot)\)
\(\chi_{2230}(473,\cdot)\)
\(\chi_{2230}(533,\cdot)\)
\(\chi_{2230}(537,\cdot)\)
\(\chi_{2230}(557,\cdot)\)
\(\chi_{2230}(587,\cdot)\)
\(\chi_{2230}(603,\cdot)\)
\(\chi_{2230}(613,\cdot)\)
\(\chi_{2230}(637,\cdot)\)
\(\chi_{2230}(653,\cdot)\)
\(\chi_{2230}(667,\cdot)\)
\(\chi_{2230}(723,\cdot)\)
\(\chi_{2230}(773,\cdot)\)
\(\chi_{2230}(777,\cdot)\)
\(\chi_{2230}(787,\cdot)\)
\(\chi_{2230}(843,\cdot)\)
\(\chi_{2230}(877,\cdot)\)
\(\chi_{2230}(983,\cdot)\)
...
![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 };
\((447,1341)\) → \((i,e\left(\frac{43}{74}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 2230 }(87, a) \) |
\(1\) | \(1\) | \(e\left(\frac{49}{148}\right)\) | \(e\left(\frac{41}{148}\right)\) | \(e\left(\frac{49}{74}\right)\) | \(e\left(\frac{13}{74}\right)\) | \(e\left(\frac{25}{148}\right)\) | \(e\left(\frac{137}{148}\right)\) | \(e\left(\frac{33}{74}\right)\) | \(e\left(\frac{45}{74}\right)\) | \(e\left(\frac{69}{148}\right)\) | \(e\left(\frac{147}{148}\right)\) |
![Copy content]()
sage:chi(x)
![Copy content]()
gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
![Copy content]()
magma:chi(x)
