![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(54))
M = H._module
chi = DirichletCharacter(H, M([27,1,36]))
![Copy content]()
pari:[g,chi] = znchar(Mod(2027,2268))
| Modulus: | \(2268\) | |
| Conductor: | \(2268\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(54\) |
![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)
|
\(\chi_{2268}(11,\cdot)\)
\(\chi_{2268}(23,\cdot)\)
\(\chi_{2268}(263,\cdot)\)
\(\chi_{2268}(275,\cdot)\)
\(\chi_{2268}(515,\cdot)\)
\(\chi_{2268}(527,\cdot)\)
\(\chi_{2268}(767,\cdot)\)
\(\chi_{2268}(779,\cdot)\)
\(\chi_{2268}(1019,\cdot)\)
\(\chi_{2268}(1031,\cdot)\)
\(\chi_{2268}(1271,\cdot)\)
\(\chi_{2268}(1283,\cdot)\)
\(\chi_{2268}(1523,\cdot)\)
\(\chi_{2268}(1535,\cdot)\)
\(\chi_{2268}(1775,\cdot)\)
\(\chi_{2268}(1787,\cdot)\)
\(\chi_{2268}(2027,\cdot)\)
\(\chi_{2268}(2039,\cdot)\)
![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 ]
\((1135,1541,325)\) → \((-1,e\left(\frac{1}{54}\right),e\left(\frac{2}{3}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 2268 }(2027, a) \) |
\(1\) | \(1\) | \(e\left(\frac{41}{54}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{1}{27}\right)\) | \(e\left(\frac{14}{27}\right)\) | \(e\left(\frac{37}{54}\right)\) | \(e\left(\frac{29}{54}\right)\) | \(e\left(\frac{1}{9}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
