![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(417, base_ring=CyclotomicField(46))
M = H._module
chi = DirichletCharacter(H, M([23,22]))
![Copy content]()
pari:[g,chi] = znchar(Mod(191,417))
| Modulus: | \(417\) | |
| Conductor: | \(417\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(46\) |
![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)
|
\(\chi_{417}(44,\cdot)\)
\(\chi_{417}(65,\cdot)\)
\(\chi_{417}(77,\cdot)\)
\(\chi_{417}(80,\cdot)\)
\(\chi_{417}(116,\cdot)\)
\(\chi_{417}(125,\cdot)\)
\(\chi_{417}(131,\cdot)\)
\(\chi_{417}(173,\cdot)\)
\(\chi_{417}(191,\cdot)\)
\(\chi_{417}(194,\cdot)\)
\(\chi_{417}(203,\cdot)\)
\(\chi_{417}(218,\cdot)\)
\(\chi_{417}(230,\cdot)\)
\(\chi_{417}(239,\cdot)\)
\(\chi_{417}(245,\cdot)\)
\(\chi_{417}(251,\cdot)\)
\(\chi_{417}(284,\cdot)\)
\(\chi_{417}(314,\cdot)\)
\(\chi_{417}(323,\cdot)\)
\(\chi_{417}(335,\cdot)\)
\(\chi_{417}(341,\cdot)\)
\(\chi_{417}(407,\cdot)\)
![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 ]
\((140,280)\) → \((-1,e\left(\frac{11}{23}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 417 }(191, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{45}{46}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{14}{23}\right)\) | \(e\left(\frac{41}{46}\right)\) | \(e\left(\frac{21}{23}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
![Copy content]()
sage:chi.gauss_sum(a)
![Copy content]()
pari:znchargauss(g,chi,a)
![Copy content]()
sage:chi.jacobi_sum(n)
![Copy content]()
sage:chi.kloosterman_sum(a,b)
