![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10153, base_ring=CyclotomicField(210))
M = H._module
chi = DirichletCharacter(H, M([147,140,45]))
![Copy content]()
gp:[g,chi] = znchar(Mod(3857, 10153))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10153.3857");
| Modulus: | \(10153\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(10153\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(210\) |
![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);
|
\(\chi_{10153}(94,\cdot)\)
\(\chi_{10153}(523,\cdot)\)
\(\chi_{10153}(536,\cdot)\)
\(\chi_{10153}(607,\cdot)\)
\(\chi_{10153}(744,\cdot)\)
\(\chi_{10153}(822,\cdot)\)
\(\chi_{10153}(893,\cdot)\)
\(\chi_{10153}(1459,\cdot)\)
\(\chi_{10153}(1667,\cdot)\)
\(\chi_{10153}(1745,\cdot)\)
\(\chi_{10153}(2252,\cdot)\)
\(\chi_{10153}(2323,\cdot)\)
\(\chi_{10153}(2382,\cdot)\)
\(\chi_{10153}(2668,\cdot)\)
\(\chi_{10153}(2934,\cdot)\)
\(\chi_{10153}(3175,\cdot)\)
\(\chi_{10153}(3363,\cdot)\)
\(\chi_{10153}(3786,\cdot)\)
\(\chi_{10153}(3857,\cdot)\)
\(\chi_{10153}(4098,\cdot)\)
\(\chi_{10153}(4215,\cdot)\)
\(\chi_{10153}(4286,\cdot)\)
\(\chi_{10153}(4507,\cdot)\)
\(\chi_{10153}(4780,\cdot)\)
\(\chi_{10153}(5209,\cdot)\)
\(\chi_{10153}(5222,\cdot)\)
\(\chi_{10153}(5359,\cdot)\)
\(\chi_{10153}(5430,\cdot)\)
\(\chi_{10153}(5508,\cdot)\)
\(\chi_{10153}(6074,\cdot)\)
...
![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 };
\((9231,782,859)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{2}{3}\right),e\left(\frac{3}{14}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 10153 }(3857, a) \) |
\(1\) | \(1\) | \(e\left(\frac{137}{210}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{32}{105}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{103}{210}\right)\) | \(e\left(\frac{47}{105}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{1}{7}\right)\) |
![Copy content]()
sage:chi(x)
![Copy content]()
gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
![Copy content]()
magma:chi(x)
