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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2009.ce
\(\chi_{2009}(10,\cdot)\) \(\chi_{2009}(59,\cdot)\) \(\chi_{2009}(180,\cdot)\) \(\chi_{2009}(201,\cdot)\) \(\chi_{2009}(262,\cdot)\) \(\chi_{2009}(283,\cdot)\) \(\chi_{2009}(297,\cdot)\) \(\chi_{2009}(346,\cdot)\) \(\chi_{2009}(467,\cdot)\) \(\chi_{2009}(488,\cdot)\) \(\chi_{2009}(502,\cdot)\) \(\chi_{2009}(549,\cdot)\) \(\chi_{2009}(551,\cdot)\) \(\chi_{2009}(584,\cdot)\) \(\chi_{2009}(633,\cdot)\) \(\chi_{2009}(775,\cdot)\) \(\chi_{2009}(789,\cdot)\) \(\chi_{2009}(836,\cdot)\) \(\chi_{2009}(838,\cdot)\) \(\chi_{2009}(857,\cdot)\) \(\chi_{2009}(871,\cdot)\) \(\chi_{2009}(920,\cdot)\) \(\chi_{2009}(1041,\cdot)\) \(\chi_{2009}(1062,\cdot)\) \(\chi_{2009}(1076,\cdot)\) \(\chi_{2009}(1123,\cdot)\) \(\chi_{2009}(1125,\cdot)\) \(\chi_{2009}(1144,\cdot)\) \(\chi_{2009}(1328,\cdot)\) \(\chi_{2009}(1349,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((493,785)\) → \((e\left(\frac{13}{42}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2009 }(10, a) \) | \(-1\) | \(1\) | \(e\left(\frac{26}{105}\right)\) | \(e\left(\frac{13}{42}\right)\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{79}{210}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{131}{210}\right)\) | \(e\left(\frac{103}{105}\right)\) | \(e\left(\frac{169}{210}\right)\) |