Basic properties
| Modulus: | \(4009\) | |
| Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(315\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4009.en
\(\chi_{4009}(5,\cdot)\) \(\chi_{4009}(25,\cdot)\) \(\chi_{4009}(82,\cdot)\) \(\chi_{4009}(169,\cdot)\) \(\chi_{4009}(275,\cdot)\) \(\chi_{4009}(290,\cdot)\) \(\chi_{4009}(320,\cdot)\) \(\chi_{4009}(332,\cdot)\) \(\chi_{4009}(404,\cdot)\) \(\chi_{4009}(427,\cdot)\) \(\chi_{4009}(435,\cdot)\) \(\chi_{4009}(498,\cdot)\) \(\chi_{4009}(518,\cdot)\) \(\chi_{4009}(536,\cdot)\) \(\chi_{4009}(605,\cdot)\) \(\chi_{4009}(606,\cdot)\) \(\chi_{4009}(625,\cdot)\) \(\chi_{4009}(644,\cdot)\) \(\chi_{4009}(709,\cdot)\) \(\chi_{4009}(712,\cdot)\) \(\chi_{4009}(720,\cdot)\) \(\chi_{4009}(746,\cdot)\) \(\chi_{4009}(747,\cdot)\) \(\chi_{4009}(758,\cdot)\) \(\chi_{4009}(776,\cdot)\) \(\chi_{4009}(784,\cdot)\) \(\chi_{4009}(802,\cdot)\) \(\chi_{4009}(826,\cdot)\) \(\chi_{4009}(909,\cdot)\) \(\chi_{4009}(940,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{315})$ |
| Fixed field: | Number field defined by a degree 315 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{22}{35}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4009 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{163}{315}\right)\) | \(e\left(\frac{184}{315}\right)\) | \(e\left(\frac{11}{315}\right)\) | \(e\left(\frac{61}{315}\right)\) | \(e\left(\frac{32}{315}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{58}{105}\right)\) | \(e\left(\frac{53}{315}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{52}{105}\right)\) |