![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(373527, base_ring=CyclotomicField(16170))
M = H._module
chi = DirichletCharacter(H, M([13475,5225,9408]))
![Copy content]()
pari:[g,chi] = znchar(Mod(698,373527))
| 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)
|
\(\chi_{373527}(5,\cdot)\)
\(\chi_{373527}(38,\cdot)\)
\(\chi_{373527}(257,\cdot)\)
\(\chi_{373527}(290,\cdot)\)
\(\chi_{373527}(383,\cdot)\)
\(\chi_{373527}(416,\cdot)\)
\(\chi_{373527}(542,\cdot)\)
\(\chi_{373527}(698,\cdot)\)
\(\chi_{373527}(731,\cdot)\)
\(\chi_{373527}(983,\cdot)\)
\(\chi_{373527}(1076,\cdot)\)
\(\chi_{373527}(1202,\cdot)\)
\(\chi_{373527}(1235,\cdot)\)
\(\chi_{373527}(1424,\cdot)\)
![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 ]
\((290522,286408,126568)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{95}{294}\right),e\left(\frac{32}{55}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 373527 }(698, a) \) |
\(1\) | \(1\) | \(e\left(\frac{551}{5390}\right)\) | \(e\left(\frac{551}{2695}\right)\) | \(e\left(\frac{4786}{8085}\right)\) | \(e\left(\frac{1653}{5390}\right)\) | \(e\left(\frac{2245}{3234}\right)\) | \(e\left(\frac{8443}{16170}\right)\) | \(e\left(\frac{1102}{2695}\right)\) | \(e\left(\frac{706}{8085}\right)\) | \(e\left(\frac{151}{330}\right)\) | \(e\left(\frac{6439}{8085}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
