Basic properties
| Modulus: | \(1297\) | |
| Conductor: | \(1297\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1296\) | 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 1297.y
\(\chi_{1297}(10,\cdot)\) \(\chi_{1297}(15,\cdot)\) \(\chi_{1297}(17,\cdot)\) \(\chi_{1297}(20,\cdot)\) \(\chi_{1297}(22,\cdot)\) \(\chi_{1297}(29,\cdot)\) \(\chi_{1297}(31,\cdot)\) \(\chi_{1297}(33,\cdot)\) \(\chi_{1297}(35,\cdot)\) \(\chi_{1297}(37,\cdot)\) \(\chi_{1297}(43,\cdot)\) \(\chi_{1297}(44,\cdot)\) \(\chi_{1297}(45,\cdot)\) \(\chi_{1297}(51,\cdot)\) \(\chi_{1297}(59,\cdot)\) \(\chi_{1297}(60,\cdot)\) \(\chi_{1297}(62,\cdot)\) \(\chi_{1297}(68,\cdot)\) \(\chi_{1297}(77,\cdot)\) \(\chi_{1297}(79,\cdot)\) \(\chi_{1297}(80,\cdot)\) \(\chi_{1297}(82,\cdot)\) \(\chi_{1297}(87,\cdot)\) \(\chi_{1297}(89,\cdot)\) \(\chi_{1297}(90,\cdot)\) \(\chi_{1297}(95,\cdot)\) \(\chi_{1297}(99,\cdot)\) \(\chi_{1297}(102,\cdot)\) \(\chi_{1297}(105,\cdot)\) \(\chi_{1297}(109,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1296})$ |
| Fixed field: | Number field defined by a degree 1296 polynomial (not computed) |
Values on generators
\(10\) → \(e\left(\frac{649}{1296}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1297 }(1287, a) \) | \(-1\) | \(1\) | \(e\left(\frac{239}{648}\right)\) | \(e\left(\frac{1}{162}\right)\) | \(e\left(\frac{239}{324}\right)\) | \(e\left(\frac{19}{144}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{115}{648}\right)\) | \(e\left(\frac{23}{216}\right)\) | \(e\left(\frac{1}{81}\right)\) | \(e\left(\frac{649}{1296}\right)\) | \(e\left(\frac{425}{432}\right)\) |