Basic properties
| Modulus: | \(4009\) | |
| Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(105\) | 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.do
\(\chi_{4009}(11,\cdot)\) \(\chi_{4009}(64,\cdot)\) \(\chi_{4009}(87,\cdot)\) \(\chi_{4009}(121,\cdot)\) \(\chi_{4009}(125,\cdot)\) \(\chi_{4009}(216,\cdot)\) \(\chi_{4009}(486,\cdot)\) \(\chi_{4009}(501,\cdot)\) \(\chi_{4009}(543,\cdot)\) \(\chi_{4009}(615,\cdot)\) \(\chi_{4009}(638,\cdot)\) \(\chi_{4009}(729,\cdot)\) \(\chi_{4009}(923,\cdot)\) \(\chi_{4009}(957,\cdot)\) \(\chi_{4009}(995,\cdot)\) \(\chi_{4009}(1037,\cdot)\) \(\chi_{4009}(1151,\cdot)\) \(\chi_{4009}(1375,\cdot)\) \(\chi_{4009}(1379,\cdot)\) \(\chi_{4009}(1417,\cdot)\) \(\chi_{4009}(1660,\cdot)\) \(\chi_{4009}(1797,\cdot)\) \(\chi_{4009}(1831,\cdot)\) \(\chi_{4009}(1964,\cdot)\) \(\chi_{4009}(2021,\cdot)\) \(\chi_{4009}(2082,\cdot)\) \(\chi_{4009}(2135,\cdot)\) \(\chi_{4009}(2192,\cdot)\) \(\chi_{4009}(2253,\cdot)\) \(\chi_{4009}(2386,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{27}{35}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4009 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{46}{105}\right)\) | \(e\left(\frac{88}{105}\right)\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{52}{105}\right)\) | \(e\left(\frac{29}{105}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{71}{105}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{34}{35}\right)\) |