Basic properties
| Modulus: | \(10009\) | |
| Conductor: | \(10009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(834\) | 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.q
\(\chi_{10009}(4,\cdot)\) \(\chi_{10009}(30,\cdot)\) \(\chi_{10009}(54,\cdot)\) \(\chi_{10009}(104,\cdot)\) \(\chi_{10009}(125,\cdot)\) \(\chi_{10009}(127,\cdot)\) \(\chi_{10009}(145,\cdot)\) \(\chi_{10009}(169,\cdot)\) \(\chi_{10009}(204,\cdot)\) \(\chi_{10009}(225,\cdot)\) \(\chi_{10009}(241,\cdot)\) \(\chi_{10009}(261,\cdot)\) \(\chi_{10009}(262,\cdot)\) \(\chi_{10009}(328,\cdot)\) \(\chi_{10009}(371,\cdot)\) \(\chi_{10009}(395,\cdot)\) \(\chi_{10009}(405,\cdot)\) \(\chi_{10009}(413,\cdot)\) \(\chi_{10009}(447,\cdot)\) \(\chi_{10009}(463,\cdot)\) \(\chi_{10009}(521,\cdot)\) \(\chi_{10009}(533,\cdot)\) \(\chi_{10009}(557,\cdot)\) \(\chi_{10009}(571,\cdot)\) \(\chi_{10009}(637,\cdot)\) \(\chi_{10009}(670,\cdot)\) \(\chi_{10009}(711,\cdot)\) \(\chi_{10009}(729,\cdot)\) \(\chi_{10009}(772,\cdot)\) \(\chi_{10009}(780,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{417})$ |
| Fixed field: | Number field defined by a degree 834 polynomial (not computed) |
Values on generators
\(11\) → \(e\left(\frac{203}{834}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 10009 }(30, a) \) | \(1\) | \(1\) | \(e\left(\frac{124}{139}\right)\) | \(e\left(\frac{121}{417}\right)\) | \(e\left(\frac{109}{139}\right)\) | \(e\left(\frac{314}{417}\right)\) | \(e\left(\frac{76}{417}\right)\) | \(e\left(\frac{9}{278}\right)\) | \(e\left(\frac{94}{139}\right)\) | \(e\left(\frac{242}{417}\right)\) | \(e\left(\frac{269}{417}\right)\) | \(e\left(\frac{203}{834}\right)\) |