Basic properties
| Modulus: | \(8009\) | |
| Conductor: | \(8009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(728\) | 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 8009.ba
\(\chi_{8009}(19,\cdot)\) \(\chi_{8009}(23,\cdot)\) \(\chi_{8009}(30,\cdot)\) \(\chi_{8009}(47,\cdot)\) \(\chi_{8009}(107,\cdot)\) \(\chi_{8009}(148,\cdot)\) \(\chi_{8009}(192,\cdot)\) \(\chi_{8009}(231,\cdot)\) \(\chi_{8009}(267,\cdot)\) \(\chi_{8009}(292,\cdot)\) \(\chi_{8009}(294,\cdot)\) \(\chi_{8009}(303,\cdot)\) \(\chi_{8009}(334,\cdot)\) \(\chi_{8009}(349,\cdot)\) \(\chi_{8009}(373,\cdot)\) \(\chi_{8009}(394,\cdot)\) \(\chi_{8009}(414,\cdot)\) \(\chi_{8009}(439,\cdot)\) \(\chi_{8009}(446,\cdot)\) \(\chi_{8009}(481,\cdot)\) \(\chi_{8009}(540,\cdot)\) \(\chi_{8009}(545,\cdot)\) \(\chi_{8009}(554,\cdot)\) \(\chi_{8009}(557,\cdot)\) \(\chi_{8009}(587,\cdot)\) \(\chi_{8009}(604,\cdot)\) \(\chi_{8009}(609,\cdot)\) \(\chi_{8009}(624,\cdot)\) \(\chi_{8009}(649,\cdot)\) \(\chi_{8009}(682,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{728})$ |
| Fixed field: | Number field defined by a degree 728 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{251}{728}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8009 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{265}{364}\right)\) | \(e\left(\frac{251}{728}\right)\) | \(e\left(\frac{83}{182}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{53}{728}\right)\) | \(e\left(\frac{8}{91}\right)\) | \(e\left(\frac{67}{364}\right)\) | \(e\left(\frac{251}{364}\right)\) | \(e\left(\frac{61}{182}\right)\) | \(e\left(\frac{97}{364}\right)\) |