![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(97693, base_ring=CyclotomicField(462))
M = H._module
chi = DirichletCharacter(H, M([88,399]))
![Copy content]()
gp:[g,chi] = znchar(Mod(5038, 97693))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("97693.5038");
| Modulus: | \(97693\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(97693\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(462\) |
![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);
|
\(\chi_{97693}(101,\cdot)\)
\(\chi_{97693}(1427,\cdot)\)
\(\chi_{97693}(1953,\cdot)\)
\(\chi_{97693}(2422,\cdot)\)
\(\chi_{97693}(2816,\cdot)\)
\(\chi_{97693}(2904,\cdot)\)
\(\chi_{97693}(4274,\cdot)\)
\(\chi_{97693}(4293,\cdot)\)
\(\chi_{97693}(4405,\cdot)\)
\(\chi_{97693}(5038,\cdot)\)
\(\chi_{97693}(5309,\cdot)\)
\(\chi_{97693}(6720,\cdot)\)
\(\chi_{97693}(6930,\cdot)\)
\(\chi_{97693}(7353,\cdot)\)
\(\chi_{97693}(7713,\cdot)\)
\(\chi_{97693}(9035,\cdot)\)
\(\chi_{97693}(9668,\cdot)\)
\(\chi_{97693}(10171,\cdot)\)
\(\chi_{97693}(11150,\cdot)\)
\(\chi_{97693}(12627,\cdot)\)
\(\chi_{97693}(13665,\cdot)\)
\(\chi_{97693}(14106,\cdot)\)
\(\chi_{97693}(14298,\cdot)\)
\(\chi_{97693}(14391,\cdot)\)
\(\chi_{97693}(15054,\cdot)\)
\(\chi_{97693}(15687,\cdot)\)
\(\chi_{97693}(15868,\cdot)\)
\(\chi_{97693}(16997,\cdot)\)
\(\chi_{97693}(20357,\cdot)\)
\(\chi_{97693}(22209,\cdot)\)
...
![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 };
\((81026,33339)\) → \((e\left(\frac{4}{21}\right),e\left(\frac{19}{22}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 97693 }(5038, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{128}{231}\right)\) | \(e\left(\frac{25}{462}\right)\) | \(e\left(\frac{25}{231}\right)\) | \(e\left(\frac{15}{154}\right)\) | \(e\left(\frac{281}{462}\right)\) | \(e\left(\frac{283}{462}\right)\) | \(e\left(\frac{51}{77}\right)\) | \(e\left(\frac{25}{231}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{153}{154}\right)\) |
![Copy content]()
sage:chi(x)
![Copy content]()
gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
![Copy content]()
magma:chi(x)
