![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(373527, base_ring=CyclotomicField(16170))
M = H._module
chi = DirichletCharacter(H, M([5390,10835,6909]))
![Copy content]()
pari:[g,chi] = znchar(Mod(1426,373527))
| Modulus: | \(373527\) | |
| Conductor: | \(373527\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(16170\) |
![Copy content]()
sage:chi.multiplicative_order()
![Copy content]()
pari:charorder(g,chi)
|
| Real: | no |
| Primitive: | yes |
![Copy content]()
sage:chi.is_primitive()
![Copy content]()
pari:#znconreyconductor(g,chi)==1
|
| Minimal: | yes |
| Parity: | even |
![Copy content]()
sage:chi.is_odd()
![Copy content]()
pari:zncharisodd(g,chi)
|
\(\chi_{373527}(52,\cdot)\)
\(\chi_{373527}(292,\cdot)\)
\(\chi_{373527}(304,\cdot)\)
\(\chi_{373527}(556,\cdot)\)
\(\chi_{373527}(733,\cdot)\)
\(\chi_{373527}(745,\cdot)\)
\(\chi_{373527}(871,\cdot)\)
\(\chi_{373527}(985,\cdot)\)
\(\chi_{373527}(997,\cdot)\)
\(\chi_{373527}(1174,\cdot)\)
\(\chi_{373527}(1249,\cdot)\)
\(\chi_{373527}(1300,\cdot)\)
\(\chi_{373527}(1426,\cdot)\)
\(\chi_{373527}(1438,\cdot)\)
![Copy content]()
sage:chi.galois_orbit()
![Copy content]()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\((290522,286408,126568)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{197}{294}\right),e\left(\frac{47}{110}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 373527 }(1426, a) \) |
\(1\) | \(1\) | \(e\left(\frac{4063}{5390}\right)\) | \(e\left(\frac{1368}{2695}\right)\) | \(e\left(\frac{11591}{16170}\right)\) | \(e\left(\frac{1409}{5390}\right)\) | \(e\left(\frac{761}{1617}\right)\) | \(e\left(\frac{6392}{8085}\right)\) | \(e\left(\frac{41}{2695}\right)\) | \(e\left(\frac{5563}{8085}\right)\) | \(e\left(\frac{104}{165}\right)\) | \(e\left(\frac{3629}{16170}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
