Basic properties
| Modulus: | \(2009\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(56\) | 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.bn
\(\chi_{2009}(85,\cdot)\) \(\chi_{2009}(120,\cdot)\) \(\chi_{2009}(232,\cdot)\) \(\chi_{2009}(260,\cdot)\) \(\chi_{2009}(372,\cdot)\) \(\chi_{2009}(407,\cdot)\) \(\chi_{2009}(519,\cdot)\) \(\chi_{2009}(547,\cdot)\) \(\chi_{2009}(659,\cdot)\) \(\chi_{2009}(694,\cdot)\) \(\chi_{2009}(806,\cdot)\) \(\chi_{2009}(946,\cdot)\) \(\chi_{2009}(1093,\cdot)\) \(\chi_{2009}(1121,\cdot)\) \(\chi_{2009}(1233,\cdot)\) \(\chi_{2009}(1268,\cdot)\) \(\chi_{2009}(1380,\cdot)\) \(\chi_{2009}(1408,\cdot)\) \(\chi_{2009}(1555,\cdot)\) \(\chi_{2009}(1695,\cdot)\) \(\chi_{2009}(1807,\cdot)\) \(\chi_{2009}(1842,\cdot)\) \(\chi_{2009}(1954,\cdot)\) \(\chi_{2009}(1982,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((493,785)\) → \((e\left(\frac{2}{7}\right),e\left(\frac{3}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2009 }(85, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{51}{56}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{5}{56}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{31}{56}\right)\) | \(e\left(\frac{15}{56}\right)\) |