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.eo
\(\chi_{4009}(47,\cdot)\) \(\chi_{4009}(62,\cdot)\) \(\chi_{4009}(80,\cdot)\) \(\chi_{4009}(93,\cdot)\) \(\chi_{4009}(119,\cdot)\) \(\chi_{4009}(120,\cdot)\) \(\chi_{4009}(194,\cdot)\) \(\chi_{4009}(263,\cdot)\) \(\chi_{4009}(270,\cdot)\) \(\chi_{4009}(291,\cdot)\) \(\chi_{4009}(405,\cdot)\) \(\chi_{4009}(442,\cdot)\) \(\chi_{4009}(446,\cdot)\) \(\chi_{4009}(473,\cdot)\) \(\chi_{4009}(481,\cdot)\) \(\chi_{4009}(492,\cdot)\) \(\chi_{4009}(503,\cdot)\) \(\chi_{4009}(517,\cdot)\) \(\chi_{4009}(598,\cdot)\) \(\chi_{4009}(631,\cdot)\) \(\chi_{4009}(663,\cdot)\) \(\chi_{4009}(669,\cdot)\) \(\chi_{4009}(682,\cdot)\) \(\chi_{4009}(728,\cdot)\) \(\chi_{4009}(738,\cdot)\) \(\chi_{4009}(769,\cdot)\) \(\chi_{4009}(796,\cdot)\) \(\chi_{4009}(803,\cdot)\) \(\chi_{4009}(815,\cdot)\) \(\chi_{4009}(842,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{315})$ |
| Fixed field: | Number field defined by a degree 315 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{4}{9}\right),e\left(\frac{41}{105}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4009 }(1016, a) \) | \(1\) | \(1\) | \(e\left(\frac{263}{315}\right)\) | \(e\left(\frac{179}{315}\right)\) | \(e\left(\frac{211}{315}\right)\) | \(e\left(\frac{206}{315}\right)\) | \(e\left(\frac{127}{315}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{43}{315}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{62}{105}\right)\) |