![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(93025, base_ring=CyclotomicField(122))
M = H._module
chi = DirichletCharacter(H, M([61,93]))
![Copy content]()
gp:[g,chi] = znchar(Mod(24399, 93025))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("93025.24399");
| Modulus: | \(93025\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(18605\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(122\) |
![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 \(\chi_{18605}(5794,\cdot)\) |
![Copy content]()
sage:chi.is_primitive()
![Copy content]()
gp:#znconreyconductor(g,chi)==1
![Copy content]()
magma:IsPrimitive(chi);
|
| Minimal: | no |
| Parity: | even |
![Copy content]()
sage:chi.is_odd()
![Copy content]()
gp:zncharisodd(g,chi)
![Copy content]()
magma:IsOdd(chi);
|
\(\chi_{93025}(1524,\cdot)\)
\(\chi_{93025}(3049,\cdot)\)
\(\chi_{93025}(4574,\cdot)\)
\(\chi_{93025}(6099,\cdot)\)
\(\chi_{93025}(7624,\cdot)\)
\(\chi_{93025}(9149,\cdot)\)
\(\chi_{93025}(10674,\cdot)\)
\(\chi_{93025}(12199,\cdot)\)
\(\chi_{93025}(13724,\cdot)\)
\(\chi_{93025}(15249,\cdot)\)
\(\chi_{93025}(16774,\cdot)\)
\(\chi_{93025}(18299,\cdot)\)
\(\chi_{93025}(19824,\cdot)\)
\(\chi_{93025}(21349,\cdot)\)
\(\chi_{93025}(22874,\cdot)\)
\(\chi_{93025}(24399,\cdot)\)
\(\chi_{93025}(25924,\cdot)\)
\(\chi_{93025}(27449,\cdot)\)
\(\chi_{93025}(28974,\cdot)\)
\(\chi_{93025}(30499,\cdot)\)
\(\chi_{93025}(32024,\cdot)\)
\(\chi_{93025}(33549,\cdot)\)
\(\chi_{93025}(35074,\cdot)\)
\(\chi_{93025}(36599,\cdot)\)
\(\chi_{93025}(38124,\cdot)\)
\(\chi_{93025}(39649,\cdot)\)
\(\chi_{93025}(41174,\cdot)\)
\(\chi_{93025}(42699,\cdot)\)
\(\chi_{93025}(44224,\cdot)\)
\(\chi_{93025}(45749,\cdot)\)
...
![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 };
\((22327,70701)\) → \((-1,e\left(\frac{93}{122}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 93025 }(24399, a) \) |
\(1\) | \(1\) | \(e\left(\frac{16}{61}\right)\) | \(e\left(\frac{59}{122}\right)\) | \(e\left(\frac{32}{61}\right)\) | \(e\left(\frac{91}{122}\right)\) | \(e\left(\frac{11}{61}\right)\) | \(e\left(\frac{48}{61}\right)\) | \(e\left(\frac{59}{61}\right)\) | \(e\left(\frac{89}{122}\right)\) | \(e\left(\frac{1}{122}\right)\) | \(e\left(\frac{91}{122}\right)\) |
![Copy content]()
sage:chi(x)
![Copy content]()
gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
![Copy content]()
magma:chi(x)
