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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4009.el
\(\chi_{4009}(145,\cdot)\) \(\chi_{4009}(202,\cdot)\) \(\chi_{4009}(240,\cdot)\) \(\chi_{4009}(259,\cdot)\) \(\chi_{4009}(369,\cdot)\) \(\chi_{4009}(373,\cdot)\) \(\chi_{4009}(392,\cdot)\) \(\chi_{4009}(563,\cdot)\) \(\chi_{4009}(582,\cdot)\) \(\chi_{4009}(597,\cdot)\) \(\chi_{4009}(635,\cdot)\) \(\chi_{4009}(749,\cdot)\) \(\chi_{4009}(962,\cdot)\) \(\chi_{4009}(996,\cdot)\) \(\chi_{4009}(1072,\cdot)\) \(\chi_{4009}(1186,\cdot)\) \(\chi_{4009}(1323,\cdot)\) \(\chi_{4009}(1357,\cdot)\) \(\chi_{4009}(1399,\cdot)\) \(\chi_{4009}(1589,\cdot)\) \(\chi_{4009}(1604,\cdot)\) \(\chi_{4009}(1642,\cdot)\) \(\chi_{4009}(1684,\cdot)\) \(\chi_{4009}(1760,\cdot)\) \(\chi_{4009}(1855,\cdot)\) \(\chi_{4009}(1893,\cdot)\) \(\chi_{4009}(1984,\cdot)\) \(\chi_{4009}(2007,\cdot)\) \(\chi_{4009}(2041,\cdot)\) \(\chi_{4009}(2117,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{191}{210}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4009 }(202, a) \) | \(1\) | \(1\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{41}{105}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{89}{210}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{12}{35}\right)\) |