Basic properties
| Modulus: | \(269\) | |
| Conductor: | \(269\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(268\) | 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 269.f
\(\chi_{269}(2,\cdot)\) \(\chi_{269}(3,\cdot)\) \(\chi_{269}(7,\cdot)\) \(\chi_{269}(8,\cdot)\) \(\chi_{269}(10,\cdot)\) \(\chi_{269}(12,\cdot)\) \(\chi_{269}(15,\cdot)\) \(\chi_{269}(17,\cdot)\) \(\chi_{269}(18,\cdot)\) \(\chi_{269}(19,\cdot)\) \(\chi_{269}(22,\cdot)\) \(\chi_{269}(26,\cdot)\) \(\chi_{269}(27,\cdot)\) \(\chi_{269}(28,\cdot)\) \(\chi_{269}(29,\cdot)\) \(\chi_{269}(31,\cdot)\) \(\chi_{269}(32,\cdot)\) \(\chi_{269}(33,\cdot)\) \(\chi_{269}(35,\cdot)\) \(\chi_{269}(39,\cdot)\) \(\chi_{269}(40,\cdot)\) \(\chi_{269}(42,\cdot)\) \(\chi_{269}(46,\cdot)\) \(\chi_{269}(48,\cdot)\) \(\chi_{269}(50,\cdot)\) \(\chi_{269}(59,\cdot)\) \(\chi_{269}(60,\cdot)\) \(\chi_{269}(63,\cdot)\) \(\chi_{269}(68,\cdot)\) \(\chi_{269}(69,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{268})$ |
| Fixed field: | Number field defined by a degree 268 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{59}{268}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 269 }(27, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{268}\right)\) | \(e\left(\frac{267}{268}\right)\) | \(e\left(\frac{59}{134}\right)\) | \(e\left(\frac{53}{67}\right)\) | \(e\left(\frac{29}{134}\right)\) | \(e\left(\frac{49}{268}\right)\) | \(e\left(\frac{177}{268}\right)\) | \(e\left(\frac{133}{134}\right)\) | \(e\left(\frac{3}{268}\right)\) | \(e\left(\frac{85}{134}\right)\) |