Basic properties
| Modulus: | \(2299\) | |
| Conductor: | \(2299\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | 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.bq
\(\chi_{2299}(31,\cdot)\) \(\chi_{2299}(69,\cdot)\) \(\chi_{2299}(103,\cdot)\) \(\chi_{2299}(126,\cdot)\) \(\chi_{2299}(141,\cdot)\) \(\chi_{2299}(179,\cdot)\) \(\chi_{2299}(236,\cdot)\) \(\chi_{2299}(240,\cdot)\) \(\chi_{2299}(278,\cdot)\) \(\chi_{2299}(312,\cdot)\) \(\chi_{2299}(335,\cdot)\) \(\chi_{2299}(350,\cdot)\) \(\chi_{2299}(388,\cdot)\) \(\chi_{2299}(411,\cdot)\) \(\chi_{2299}(445,\cdot)\) \(\chi_{2299}(449,\cdot)\) \(\chi_{2299}(521,\cdot)\) \(\chi_{2299}(544,\cdot)\) \(\chi_{2299}(559,\cdot)\) \(\chi_{2299}(597,\cdot)\) \(\chi_{2299}(620,\cdot)\) \(\chi_{2299}(654,\cdot)\) \(\chi_{2299}(658,\cdot)\) \(\chi_{2299}(696,\cdot)\) \(\chi_{2299}(730,\cdot)\) \(\chi_{2299}(768,\cdot)\) \(\chi_{2299}(806,\cdot)\) \(\chi_{2299}(829,\cdot)\) \(\chi_{2299}(863,\cdot)\) \(\chi_{2299}(867,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((970,1332)\) → \((e\left(\frac{34}{55}\right),e\left(\frac{5}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 2299 }(278, a) \) | \(-1\) | \(1\) | \(e\left(\frac{149}{330}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{149}{165}\right)\) | \(e\left(\frac{13}{165}\right)\) | \(e\left(\frac{113}{165}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{39}{110}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{3}{22}\right)\) |