![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(44100, base_ring=CyclotomicField(42))
M = H._module
chi = DirichletCharacter(H, M([0,7,0,1]))
![Copy content]()
pari:[g,chi] = znchar(Mod(101,44100))
\(\chi_{44100}(101,\cdot)\)
\(\chi_{44100}(12101,\cdot)\)
\(\chi_{44100}(12701,\cdot)\)
\(\chi_{44100}(18401,\cdot)\)
\(\chi_{44100}(19001,\cdot)\)
\(\chi_{44100}(24701,\cdot)\)
\(\chi_{44100}(25301,\cdot)\)
\(\chi_{44100}(31001,\cdot)\)
\(\chi_{44100}(31601,\cdot)\)
\(\chi_{44100}(37301,\cdot)\)
\(\chi_{44100}(37901,\cdot)\)
\(\chi_{44100}(43601,\cdot)\)
![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 ]
\((22051,34301,15877,9901)\) → \((1,e\left(\frac{1}{6}\right),1,e\left(\frac{1}{42}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 44100 }(101, a) \) |
\(1\) | \(1\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(-1\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{17}{21}\right)\) |
![Copy content]()
sage:chi.jacobi_sum(n)
