Basic properties
| Modulus: | \(10009\) | |
| Conductor: | \(10009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(10008\) | 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 10009.x
\(\chi_{10009}(11,\cdot)\) \(\chi_{10009}(21,\cdot)\) \(\chi_{10009}(22,\cdot)\) \(\chi_{10009}(31,\cdot)\) \(\chi_{10009}(33,\cdot)\) \(\chi_{10009}(35,\cdot)\) \(\chi_{10009}(37,\cdot)\) \(\chi_{10009}(42,\cdot)\) \(\chi_{10009}(43,\cdot)\) \(\chi_{10009}(44,\cdot)\) \(\chi_{10009}(47,\cdot)\) \(\chi_{10009}(57,\cdot)\) \(\chi_{10009}(62,\cdot)\) \(\chi_{10009}(63,\cdot)\) \(\chi_{10009}(66,\cdot)\) \(\chi_{10009}(70,\cdot)\) \(\chi_{10009}(71,\cdot)\) \(\chi_{10009}(74,\cdot)\) \(\chi_{10009}(84,\cdot)\) \(\chi_{10009}(86,\cdot)\) \(\chi_{10009}(88,\cdot)\) \(\chi_{10009}(93,\cdot)\) \(\chi_{10009}(94,\cdot)\) \(\chi_{10009}(95,\cdot)\) \(\chi_{10009}(101,\cdot)\) \(\chi_{10009}(107,\cdot)\) \(\chi_{10009}(109,\cdot)\) \(\chi_{10009}(111,\cdot)\) \(\chi_{10009}(113,\cdot)\) \(\chi_{10009}(114,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{10008})$ |
| Fixed field: | Number field defined by a degree 10008 polynomial (not computed) |
Values on generators
\(11\) → \(e\left(\frac{1}{10008}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 10009 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{167}{1668}\right)\) | \(e\left(\frac{2063}{5004}\right)\) | \(e\left(\frac{167}{834}\right)\) | \(e\left(\frac{1829}{2502}\right)\) | \(e\left(\frac{641}{1251}\right)\) | \(e\left(\frac{467}{1112}\right)\) | \(e\left(\frac{167}{556}\right)\) | \(e\left(\frac{2063}{2502}\right)\) | \(e\left(\frac{4159}{5004}\right)\) | \(e\left(\frac{1}{10008}\right)\) |