![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1848, base_ring=CyclotomicField(30))
M = H._module
chi = DirichletCharacter(H, M([0,15,15,20,12]))
![Copy content]()
pari:[g,chi] = znchar(Mod(1061,1848))
| Modulus: | \(1848\) | |
| Conductor: | \(1848\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(30\) |
![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: | odd |
![Copy content]()
sage:chi.is_odd()
![Copy content]()
pari:zncharisodd(g,chi)
|
\(\chi_{1848}(53,\cdot)\)
\(\chi_{1848}(317,\cdot)\)
\(\chi_{1848}(389,\cdot)\)
\(\chi_{1848}(653,\cdot)\)
\(\chi_{1848}(1061,\cdot)\)
\(\chi_{1848}(1325,\cdot)\)
\(\chi_{1848}(1565,\cdot)\)
\(\chi_{1848}(1829,\cdot)\)
![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 ]
\((463,925,617,1585,673)\) → \((1,-1,-1,e\left(\frac{2}{3}\right),e\left(\frac{2}{5}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 1848 }(1061, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
