Basic properties
| Modulus: | \(10009\) | |
| Conductor: | \(10009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1251\) | 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.s
\(\chi_{10009}(6,\cdot)\) \(\chi_{10009}(20,\cdot)\) \(\chi_{10009}(25,\cdot)\) \(\chi_{10009}(29,\cdot)\) \(\chi_{10009}(36,\cdot)\) \(\chi_{10009}(46,\cdot)\) \(\chi_{10009}(79,\cdot)\) \(\chi_{10009}(81,\cdot)\) \(\chi_{10009}(96,\cdot)\) \(\chi_{10009}(122,\cdot)\) \(\chi_{10009}(134,\cdot)\) \(\chi_{10009}(136,\cdot)\) \(\chi_{10009}(150,\cdot)\) \(\chi_{10009}(151,\cdot)\) \(\chi_{10009}(156,\cdot)\) \(\chi_{10009}(157,\cdot)\) \(\chi_{10009}(170,\cdot)\) \(\chi_{10009}(174,\cdot)\) \(\chi_{10009}(206,\cdot)\) \(\chi_{10009}(209,\cdot)\) \(\chi_{10009}(221,\cdot)\) \(\chi_{10009}(223,\cdot)\) \(\chi_{10009}(249,\cdot)\) \(\chi_{10009}(270,\cdot)\) \(\chi_{10009}(274,\cdot)\) \(\chi_{10009}(292,\cdot)\) \(\chi_{10009}(298,\cdot)\) \(\chi_{10009}(301,\cdot)\) \(\chi_{10009}(306,\cdot)\) \(\chi_{10009}(308,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1251})$ |
| Fixed field: | Number field defined by a degree 1251 polynomial (not computed) |
Values on generators
\(11\) → \(e\left(\frac{31}{1251}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 10009 }(36, a) \) | \(1\) | \(1\) | \(e\left(\frac{346}{417}\right)\) | \(e\left(\frac{304}{1251}\right)\) | \(e\left(\frac{275}{417}\right)\) | \(e\left(\frac{365}{1251}\right)\) | \(e\left(\frac{91}{1251}\right)\) | \(e\left(\frac{21}{139}\right)\) | \(e\left(\frac{68}{139}\right)\) | \(e\left(\frac{608}{1251}\right)\) | \(e\left(\frac{152}{1251}\right)\) | \(e\left(\frac{31}{1251}\right)\) |