Basic properties
| Modulus: | \(4009\) | |
| Conductor: | \(4009\) | 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 4009.eh
\(\chi_{4009}(7,\cdot)\) \(\chi_{4009}(106,\cdot)\) \(\chi_{4009}(406,\cdot)\) \(\chi_{4009}(425,\cdot)\) \(\chi_{4009}(444,\cdot)\) \(\chi_{4009}(577,\cdot)\) \(\chi_{4009}(581,\cdot)\) \(\chi_{4009}(596,\cdot)\) \(\chi_{4009}(672,\cdot)\) \(\chi_{4009}(885,\cdot)\) \(\chi_{4009}(919,\cdot)\) \(\chi_{4009}(1090,\cdot)\) \(\chi_{4009}(1185,\cdot)\) \(\chi_{4009}(1242,\cdot)\) \(\chi_{4009}(1246,\cdot)\) \(\chi_{4009}(1569,\cdot)\) \(\chi_{4009}(1626,\cdot)\) \(\chi_{4009}(1641,\cdot)\) \(\chi_{4009}(1854,\cdot)\) \(\chi_{4009}(2044,\cdot)\) \(\chi_{4009}(2101,\cdot)\) \(\chi_{4009}(2139,\cdot)\) \(\chi_{4009}(2158,\cdot)\) \(\chi_{4009}(2268,\cdot)\) \(\chi_{4009}(2272,\cdot)\) \(\chi_{4009}(2291,\cdot)\) \(\chi_{4009}(2462,\cdot)\) \(\chi_{4009}(2481,\cdot)\) \(\chi_{4009}(2496,\cdot)\) \(\chi_{4009}(2534,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{139}{210}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4009 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{209}{210}\right)\) | \(e\left(\frac{167}{210}\right)\) | \(e\left(\frac{104}{105}\right)\) | \(e\left(\frac{74}{105}\right)\) | \(e\left(\frac{83}{105}\right)\) | \(e\left(\frac{1}{210}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{62}{105}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{8}{35}\right)\) |