Basic properties
| Modulus: | \(2009\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | 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.bs
\(\chi_{2009}(139,\cdot)\) \(\chi_{2009}(160,\cdot)\) \(\chi_{2009}(174,\cdot)\) \(\chi_{2009}(223,\cdot)\) \(\chi_{2009}(426,\cdot)\) \(\chi_{2009}(447,\cdot)\) \(\chi_{2009}(461,\cdot)\) \(\chi_{2009}(510,\cdot)\) \(\chi_{2009}(713,\cdot)\) \(\chi_{2009}(748,\cdot)\) \(\chi_{2009}(797,\cdot)\) \(\chi_{2009}(1000,\cdot)\) \(\chi_{2009}(1021,\cdot)\) \(\chi_{2009}(1035,\cdot)\) \(\chi_{2009}(1084,\cdot)\) \(\chi_{2009}(1287,\cdot)\) \(\chi_{2009}(1308,\cdot)\) \(\chi_{2009}(1574,\cdot)\) \(\chi_{2009}(1595,\cdot)\) \(\chi_{2009}(1609,\cdot)\) \(\chi_{2009}(1658,\cdot)\) \(\chi_{2009}(1882,\cdot)\) \(\chi_{2009}(1896,\cdot)\) \(\chi_{2009}(1945,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((493,785)\) → \((e\left(\frac{5}{14}\right),e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2009 }(139, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{9}{70}\right)\) |