Basic properties
| Modulus: | \(10009\) | |
| Conductor: | \(10009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1668\) | 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 10009.t
\(\chi_{10009}(2,\cdot)\) \(\chi_{10009}(13,\cdot)\) \(\chi_{10009}(15,\cdot)\) \(\chi_{10009}(27,\cdot)\) \(\chi_{10009}(32,\cdot)\) \(\chi_{10009}(41,\cdot)\) \(\chi_{10009}(52,\cdot)\) \(\chi_{10009}(83,\cdot)\) \(\chi_{10009}(102,\cdot)\) \(\chi_{10009}(128,\cdot)\) \(\chi_{10009}(131,\cdot)\) \(\chi_{10009}(133,\cdot)\) \(\chi_{10009}(138,\cdot)\) \(\chi_{10009}(164,\cdot)\) \(\chi_{10009}(173,\cdot)\) \(\chi_{10009}(196,\cdot)\) \(\chi_{10009}(219,\cdot)\) \(\chi_{10009}(240,\cdot)\) \(\chi_{10009}(332,\cdot)\) \(\chi_{10009}(338,\cdot)\) \(\chi_{10009}(361,\cdot)\) \(\chi_{10009}(366,\cdot)\) \(\chi_{10009}(386,\cdot)\) \(\chi_{10009}(390,\cdot)\) \(\chi_{10009}(425,\cdot)\) \(\chi_{10009}(432,\cdot)\) \(\chi_{10009}(453,\cdot)\) \(\chi_{10009}(487,\cdot)\) \(\chi_{10009}(493,\cdot)\) \(\chi_{10009}(532,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1668})$ |
| Fixed field: | Number field defined by a degree 1668 polynomial (not computed) |
Values on generators
\(11\) → \(e\left(\frac{239}{1668}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 10009 }(15, a) \) | \(1\) | \(1\) | \(e\left(\frac{159}{278}\right)\) | \(e\left(\frac{163}{834}\right)\) | \(e\left(\frac{20}{139}\right)\) | \(e\left(\frac{115}{417}\right)\) | \(e\left(\frac{320}{417}\right)\) | \(e\left(\frac{127}{556}\right)\) | \(e\left(\frac{199}{278}\right)\) | \(e\left(\frac{163}{417}\right)\) | \(e\left(\frac{707}{834}\right)\) | \(e\left(\frac{239}{1668}\right)\) |