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
\((493,785)\) → \((e\left(\frac{5}{21}\right),e\left(\frac{3}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 2009 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{104}{105}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{89}{210}\right)\) | \(e\left(\frac{151}{210}\right)\) |