![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2607, base_ring=CyclotomicField(390))
M = H._module
chi = DirichletCharacter(H, M([195,117,280]))
![Copy content]()
gp:[g,chi] = znchar(Mod(1295, 2607))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2607.1295");
| Modulus: | \(2607\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(2607\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(390\) |
![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);
|
\(\chi_{2607}(2,\cdot)\)
\(\chi_{2607}(50,\cdot)\)
\(\chi_{2607}(83,\cdot)\)
\(\chi_{2607}(95,\cdot)\)
\(\chi_{2607}(128,\cdot)\)
\(\chi_{2607}(167,\cdot)\)
\(\chi_{2607}(194,\cdot)\)
\(\chi_{2607}(200,\cdot)\)
\(\chi_{2607}(239,\cdot)\)
\(\chi_{2607}(248,\cdot)\)
\(\chi_{2607}(281,\cdot)\)
\(\chi_{2607}(332,\cdot)\)
\(\chi_{2607}(347,\cdot)\)
\(\chi_{2607}(365,\cdot)\)
\(\chi_{2607}(392,\cdot)\)
\(\chi_{2607}(404,\cdot)\)
\(\chi_{2607}(431,\cdot)\)
\(\chi_{2607}(437,\cdot)\)
\(\chi_{2607}(446,\cdot)\)
\(\chi_{2607}(479,\cdot)\)
\(\chi_{2607}(524,\cdot)\)
\(\chi_{2607}(557,\cdot)\)
\(\chi_{2607}(569,\cdot)\)
\(\chi_{2607}(578,\cdot)\)
\(\chi_{2607}(602,\cdot)\)
\(\chi_{2607}(629,\cdot)\)
\(\chi_{2607}(668,\cdot)\)
\(\chi_{2607}(677,\cdot)\)
\(\chi_{2607}(722,\cdot)\)
\(\chi_{2607}(743,\cdot)\)
...
![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 };
\((1739,475,793)\) → \((-1,e\left(\frac{3}{10}\right),e\left(\frac{28}{39}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 2607 }(1295, a) \) |
\(1\) | \(1\) | \(e\left(\frac{131}{195}\right)\) | \(e\left(\frac{67}{195}\right)\) | \(e\left(\frac{83}{390}\right)\) | \(e\left(\frac{59}{390}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{277}{390}\right)\) | \(e\left(\frac{107}{130}\right)\) | \(e\left(\frac{134}{195}\right)\) | \(e\left(\frac{18}{65}\right)\) |
![Copy content]()
sage:chi(x)
![Copy content]()
gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
![Copy content]()
magma:chi(x)
