Basic properties
Modulus: | \(1279\) | |
Conductor: | \(1279\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1278\) | 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 1279.l
\(\chi_{1279}(3,\cdot)\) \(\chi_{1279}(6,\cdot)\) \(\chi_{1279}(13,\cdot)\) \(\chi_{1279}(15,\cdot)\) \(\chi_{1279}(21,\cdot)\) \(\chi_{1279}(22,\cdot)\) \(\chi_{1279}(24,\cdot)\) \(\chi_{1279}(26,\cdot)\) \(\chi_{1279}(29,\cdot)\) \(\chi_{1279}(31,\cdot)\) \(\chi_{1279}(38,\cdot)\) \(\chi_{1279}(44,\cdot)\) \(\chi_{1279}(48,\cdot)\) \(\chi_{1279}(54,\cdot)\) \(\chi_{1279}(55,\cdot)\) \(\chi_{1279}(60,\cdot)\) \(\chi_{1279}(61,\cdot)\) \(\chi_{1279}(62,\cdot)\) \(\chi_{1279}(65,\cdot)\) \(\chi_{1279}(67,\cdot)\) \(\chi_{1279}(69,\cdot)\) \(\chi_{1279}(76,\cdot)\) \(\chi_{1279}(77,\cdot)\) \(\chi_{1279}(84,\cdot)\) \(\chi_{1279}(89,\cdot)\) \(\chi_{1279}(91,\cdot)\) \(\chi_{1279}(95,\cdot)\) \(\chi_{1279}(99,\cdot)\) \(\chi_{1279}(101,\cdot)\) \(\chi_{1279}(102,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{639})$ |
Fixed field: | Number field defined by a degree 1278 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{1}{1278}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1279 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{639}\right)\) | \(e\left(\frac{1}{1278}\right)\) | \(e\left(\frac{46}{639}\right)\) | \(e\left(\frac{455}{639}\right)\) | \(e\left(\frac{47}{1278}\right)\) | \(e\left(\frac{356}{639}\right)\) | \(e\left(\frac{23}{213}\right)\) | \(e\left(\frac{1}{639}\right)\) | \(e\left(\frac{478}{639}\right)\) | \(e\left(\frac{19}{426}\right)\) |