Basic properties
| Modulus: | \(2009\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | 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 2009.cd
\(\chi_{2009}(4,\cdot)\) \(\chi_{2009}(23,\cdot)\) \(\chi_{2009}(25,\cdot)\) \(\chi_{2009}(72,\cdot)\) \(\chi_{2009}(86,\cdot)\) \(\chi_{2009}(107,\cdot)\) \(\chi_{2009}(228,\cdot)\) \(\chi_{2009}(277,\cdot)\) \(\chi_{2009}(291,\cdot)\) \(\chi_{2009}(310,\cdot)\) \(\chi_{2009}(359,\cdot)\) \(\chi_{2009}(394,\cdot)\) \(\chi_{2009}(515,\cdot)\) \(\chi_{2009}(564,\cdot)\) \(\chi_{2009}(578,\cdot)\) \(\chi_{2009}(597,\cdot)\) \(\chi_{2009}(599,\cdot)\) \(\chi_{2009}(646,\cdot)\) \(\chi_{2009}(660,\cdot)\) \(\chi_{2009}(681,\cdot)\) \(\chi_{2009}(865,\cdot)\) \(\chi_{2009}(884,\cdot)\) \(\chi_{2009}(886,\cdot)\) \(\chi_{2009}(933,\cdot)\) \(\chi_{2009}(947,\cdot)\) \(\chi_{2009}(968,\cdot)\) \(\chi_{2009}(1089,\cdot)\) \(\chi_{2009}(1138,\cdot)\) \(\chi_{2009}(1152,\cdot)\) \(\chi_{2009}(1171,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((493,785)\) → \((e\left(\frac{2}{21}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2009 }(277, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{37}{105}\right)\) | \(e\left(\frac{17}{105}\right)\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{191}{210}\right)\) | \(e\left(\frac{199}{210}\right)\) |