from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, base_ring=CyclotomicField(34))
M = H._module
chi = DirichletCharacter(H, M([0,19]))
pari: [g,chi] = znchar(Mod(28,2151))
Basic properties
Modulus: | \(2151\) | |
Conductor: | \(239\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(34\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{239}(28,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2151.o
\(\chi_{2151}(28,\cdot)\) \(\chi_{2151}(73,\cdot)\) \(\chi_{2151}(172,\cdot)\) \(\chi_{2151}(199,\cdot)\) \(\chi_{2151}(217,\cdot)\) \(\chi_{2151}(262,\cdot)\) \(\chi_{2151}(442,\cdot)\) \(\chi_{2151}(793,\cdot)\) \(\chi_{2151}(1063,\cdot)\) \(\chi_{2151}(1144,\cdot)\) \(\chi_{2151}(1189,\cdot)\) \(\chi_{2151}(1306,\cdot)\) \(\chi_{2151}(1333,\cdot)\) \(\chi_{2151}(1486,\cdot)\) \(\chi_{2151}(1837,\cdot)\) \(\chi_{2151}(2080,\cdot)\)
sage: chi.galois_orbit()
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Related number fields
Field of values: | \(\Q(\zeta_{17})\) |
Fixed field: | Number field defined by a degree 34 polynomial |
Values on generators
\((479,1441)\) → \((1,e\left(\frac{19}{34}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 2151 }(28, a) \) | \(-1\) | \(1\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(1\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{9}{17}\right)\) |
sage: chi.jacobi_sum(n)