![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2183, base_ring=CyclotomicField(174))
M = H._module
chi = DirichletCharacter(H, M([145,78]))
![Copy content]()
pari:[g,chi] = znchar(Mod(1084,2183))
| Modulus: | \(2183\) | |
| Conductor: | \(2183\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(174\) |
![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)
|
\(\chi_{2183}(27,\cdot)\)
\(\chi_{2183}(48,\cdot)\)
\(\chi_{2183}(64,\cdot)\)
\(\chi_{2183}(85,\cdot)\)
\(\chi_{2183}(122,\cdot)\)
\(\chi_{2183}(138,\cdot)\)
\(\chi_{2183}(159,\cdot)\)
\(\chi_{2183}(175,\cdot)\)
\(\chi_{2183}(196,\cdot)\)
\(\chi_{2183}(212,\cdot)\)
\(\chi_{2183}(307,\cdot)\)
\(\chi_{2183}(323,\cdot)\)
\(\chi_{2183}(344,\cdot)\)
\(\chi_{2183}(381,\cdot)\)
\(\chi_{2183}(418,\cdot)\)
\(\chi_{2183}(434,\cdot)\)
\(\chi_{2183}(492,\cdot)\)
\(\chi_{2183}(508,\cdot)\)
\(\chi_{2183}(529,\cdot)\)
\(\chi_{2183}(566,\cdot)\)
\(\chi_{2183}(582,\cdot)\)
\(\chi_{2183}(619,\cdot)\)
\(\chi_{2183}(656,\cdot)\)
\(\chi_{2183}(677,\cdot)\)
\(\chi_{2183}(730,\cdot)\)
\(\chi_{2183}(788,\cdot)\)
\(\chi_{2183}(841,\cdot)\)
\(\chi_{2183}(862,\cdot)\)
\(\chi_{2183}(936,\cdot)\)
\(\chi_{2183}(973,\cdot)\)
...
![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 ]
\((1889,297)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{13}{29}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2183 }(1084, a) \) |
\(1\) | \(1\) | \(e\left(\frac{49}{174}\right)\) | \(e\left(\frac{7}{87}\right)\) | \(e\left(\frac{49}{87}\right)\) | \(e\left(\frac{149}{174}\right)\) | \(e\left(\frac{21}{58}\right)\) | \(e\left(\frac{64}{87}\right)\) | \(e\left(\frac{49}{58}\right)\) | \(e\left(\frac{14}{87}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
