Basic properties
| Modulus: | \(2299\) | |
| Conductor: | \(2299\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(990\) | 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 2299.bt
\(\chi_{2299}(14,\cdot)\) \(\chi_{2299}(15,\cdot)\) \(\chi_{2299}(48,\cdot)\) \(\chi_{2299}(53,\cdot)\) \(\chi_{2299}(59,\cdot)\) \(\chi_{2299}(60,\cdot)\) \(\chi_{2299}(70,\cdot)\) \(\chi_{2299}(71,\cdot)\) \(\chi_{2299}(86,\cdot)\) \(\chi_{2299}(91,\cdot)\) \(\chi_{2299}(97,\cdot)\) \(\chi_{2299}(108,\cdot)\) \(\chi_{2299}(135,\cdot)\) \(\chi_{2299}(136,\cdot)\) \(\chi_{2299}(146,\cdot)\) \(\chi_{2299}(147,\cdot)\) \(\chi_{2299}(174,\cdot)\) \(\chi_{2299}(181,\cdot)\) \(\chi_{2299}(185,\cdot)\) \(\chi_{2299}(192,\cdot)\) \(\chi_{2299}(203,\cdot)\) \(\chi_{2299}(212,\cdot)\) \(\chi_{2299}(223,\cdot)\) \(\chi_{2299}(224,\cdot)\) \(\chi_{2299}(257,\cdot)\) \(\chi_{2299}(262,\cdot)\) \(\chi_{2299}(268,\cdot)\) \(\chi_{2299}(279,\cdot)\) \(\chi_{2299}(280,\cdot)\) \(\chi_{2299}(295,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{495})$ |
| Fixed field: | Number field defined by a degree 990 polynomial (not computed) |
Values on generators
\((970,1332)\) → \((e\left(\frac{53}{55}\right),e\left(\frac{11}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 2299 }(53, a) \) | \(-1\) | \(1\) | \(e\left(\frac{569}{990}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{74}{495}\right)\) | \(e\left(\frac{43}{495}\right)\) | \(e\left(\frac{158}{495}\right)\) | \(e\left(\frac{68}{165}\right)\) | \(e\left(\frac{239}{330}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{131}{198}\right)\) | \(e\left(\frac{59}{66}\right)\) |