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.br
\(\chi_{2009}(209,\cdot)\) \(\chi_{2009}(230,\cdot)\) \(\chi_{2009}(433,\cdot)\) \(\chi_{2009}(482,\cdot)\) \(\chi_{2009}(496,\cdot)\) \(\chi_{2009}(517,\cdot)\) \(\chi_{2009}(720,\cdot)\) \(\chi_{2009}(769,\cdot)\) \(\chi_{2009}(804,\cdot)\) \(\chi_{2009}(1007,\cdot)\) \(\chi_{2009}(1056,\cdot)\) \(\chi_{2009}(1070,\cdot)\) \(\chi_{2009}(1091,\cdot)\) \(\chi_{2009}(1294,\cdot)\) \(\chi_{2009}(1343,\cdot)\) \(\chi_{2009}(1357,\cdot)\) \(\chi_{2009}(1378,\cdot)\) \(\chi_{2009}(1581,\cdot)\) \(\chi_{2009}(1630,\cdot)\) \(\chi_{2009}(1644,\cdot)\) \(\chi_{2009}(1868,\cdot)\) \(\chi_{2009}(1917,\cdot)\) \(\chi_{2009}(1931,\cdot)\) \(\chi_{2009}(1952,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((493,785)\) → \((e\left(\frac{11}{14}\right),e\left(\frac{3}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2009 }(209, a) \) | \(-1\) | \(1\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{18}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{26}{35}\right)\) |