Basic properties
Modulus: | \(709\) | |
Conductor: | \(709\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(708\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 709.l
\(\chi_{709}(2,\cdot)\) \(\chi_{709}(6,\cdot)\) \(\chi_{709}(10,\cdot)\) \(\chi_{709}(14,\cdot)\) \(\chi_{709}(17,\cdot)\) \(\chi_{709}(22,\cdot)\) \(\chi_{709}(23,\cdot)\) \(\chi_{709}(24,\cdot)\) \(\chi_{709}(31,\cdot)\) \(\chi_{709}(32,\cdot)\) \(\chi_{709}(37,\cdot)\) \(\chi_{709}(38,\cdot)\) \(\chi_{709}(39,\cdot)\) \(\chi_{709}(40,\cdot)\) \(\chi_{709}(41,\cdot)\) \(\chi_{709}(51,\cdot)\) \(\chi_{709}(52,\cdot)\) \(\chi_{709}(54,\cdot)\) \(\chi_{709}(56,\cdot)\) \(\chi_{709}(61,\cdot)\) \(\chi_{709}(65,\cdot)\) \(\chi_{709}(69,\cdot)\) \(\chi_{709}(71,\cdot)\) \(\chi_{709}(72,\cdot)\) \(\chi_{709}(79,\cdot)\) \(\chi_{709}(85,\cdot)\) \(\chi_{709}(86,\cdot)\) \(\chi_{709}(88,\cdot)\) \(\chi_{709}(89,\cdot)\) \(\chi_{709}(90,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{708})$ |
Fixed field: | Number field defined by a degree 708 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{169}{708}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 709 }(89, a) \) | \(-1\) | \(1\) | \(e\left(\frac{169}{708}\right)\) | \(e\left(\frac{10}{177}\right)\) | \(e\left(\frac{169}{354}\right)\) | \(e\left(\frac{305}{354}\right)\) | \(e\left(\frac{209}{708}\right)\) | \(e\left(\frac{73}{177}\right)\) | \(e\left(\frac{169}{236}\right)\) | \(e\left(\frac{20}{177}\right)\) | \(e\left(\frac{71}{708}\right)\) | \(e\left(\frac{329}{354}\right)\) |