Basic properties
| Modulus: | \(2009\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(840\) | 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 2009.ck
\(\chi_{2009}(11,\cdot)\) \(\chi_{2009}(53,\cdot)\) \(\chi_{2009}(58,\cdot)\) \(\chi_{2009}(60,\cdot)\) \(\chi_{2009}(65,\cdot)\) \(\chi_{2009}(88,\cdot)\) \(\chi_{2009}(93,\cdot)\) \(\chi_{2009}(95,\cdot)\) \(\chi_{2009}(130,\cdot)\) \(\chi_{2009}(135,\cdot)\) \(\chi_{2009}(142,\cdot)\) \(\chi_{2009}(149,\cdot)\) \(\chi_{2009}(151,\cdot)\) \(\chi_{2009}(158,\cdot)\) \(\chi_{2009}(170,\cdot)\) \(\chi_{2009}(179,\cdot)\) \(\chi_{2009}(186,\cdot)\) \(\chi_{2009}(193,\cdot)\) \(\chi_{2009}(198,\cdot)\) \(\chi_{2009}(212,\cdot)\) \(\chi_{2009}(233,\cdot)\) \(\chi_{2009}(235,\cdot)\) \(\chi_{2009}(240,\cdot)\) \(\chi_{2009}(261,\cdot)\) \(\chi_{2009}(268,\cdot)\) \(\chi_{2009}(270,\cdot)\) \(\chi_{2009}(298,\cdot)\) \(\chi_{2009}(317,\cdot)\) \(\chi_{2009}(340,\cdot)\) \(\chi_{2009}(345,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{840})$ |
| Fixed field: | Number field defined by a degree 840 polynomial (not computed) |
Values on generators
\((493,785)\) → \((e\left(\frac{20}{21}\right),e\left(\frac{3}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2009 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{299}{420}\right)\) | \(e\left(\frac{13}{168}\right)\) | \(e\left(\frac{89}{210}\right)\) | \(e\left(\frac{113}{420}\right)\) | \(e\left(\frac{221}{280}\right)\) | \(e\left(\frac{19}{140}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{269}{840}\right)\) | \(e\left(\frac{421}{840}\right)\) |