![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3600, base_ring=CyclotomicField(60))
M = H._module
chi = DirichletCharacter(H, M([0,15,50,42]))
![Copy content]()
pari:[g,chi] = znchar(Mod(2309,3600))
| Modulus: | \(3600\) | |
| Conductor: | \(3600\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(60\) |
![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)
|
\(\chi_{3600}(29,\cdot)\)
\(\chi_{3600}(389,\cdot)\)
\(\chi_{3600}(509,\cdot)\)
\(\chi_{3600}(869,\cdot)\)
\(\chi_{3600}(1109,\cdot)\)
\(\chi_{3600}(1229,\cdot)\)
\(\chi_{3600}(1469,\cdot)\)
\(\chi_{3600}(1589,\cdot)\)
\(\chi_{3600}(1829,\cdot)\)
\(\chi_{3600}(2189,\cdot)\)
\(\chi_{3600}(2309,\cdot)\)
\(\chi_{3600}(2669,\cdot)\)
\(\chi_{3600}(2909,\cdot)\)
\(\chi_{3600}(3029,\cdot)\)
\(\chi_{3600}(3269,\cdot)\)
\(\chi_{3600}(3389,\cdot)\)
![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 ]
\((3151,901,2801,577)\) → \((1,i,e\left(\frac{5}{6}\right),e\left(\frac{7}{10}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 3600 }(2309, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{7}{15}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
