Basic properties
| Modulus: | \(1009\) | |
| Conductor: | \(1009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(168\) | 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 1009.z
\(\chi_{1009}(3,\cdot)\) \(\chi_{1009}(8,\cdot)\) \(\chi_{1009}(35,\cdot)\) \(\chi_{1009}(50,\cdot)\) \(\chi_{1009}(103,\cdot)\) \(\chi_{1009}(113,\cdot)\) \(\chi_{1009}(125,\cdot)\) \(\chi_{1009}(126,\cdot)\) \(\chi_{1009}(173,\cdot)\) \(\chi_{1009}(180,\cdot)\) \(\chi_{1009}(191,\cdot)\) \(\chi_{1009}(205,\cdot)\) \(\chi_{1009}(222,\cdot)\) \(\chi_{1009}(243,\cdot)\) \(\chi_{1009}(271,\cdot)\) \(\chi_{1009}(284,\cdot)\) \(\chi_{1009}(290,\cdot)\) \(\chi_{1009}(315,\cdot)\) \(\chi_{1009}(336,\cdot)\) \(\chi_{1009}(398,\cdot)\) \(\chi_{1009}(417,\cdot)\) \(\chi_{1009}(421,\cdot)\) \(\chi_{1009}(437,\cdot)\) \(\chi_{1009}(480,\cdot)\) \(\chi_{1009}(529,\cdot)\) \(\chi_{1009}(572,\cdot)\) \(\chi_{1009}(588,\cdot)\) \(\chi_{1009}(592,\cdot)\) \(\chi_{1009}(611,\cdot)\) \(\chi_{1009}(673,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{168})$ |
| Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\(11\) → \(e\left(\frac{17}{168}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1009 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{84}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{17}{168}\right)\) |