Basic properties
| Modulus: | \(4009\) | |
| Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(630\) | 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.ev
\(\chi_{4009}(17,\cdot)\) \(\chi_{4009}(35,\cdot)\) \(\chi_{4009}(118,\cdot)\) \(\chi_{4009}(130,\cdot)\) \(\chi_{4009}(131,\cdot)\) \(\chi_{4009}(187,\cdot)\) \(\chi_{4009}(195,\cdot)\) \(\chi_{4009}(214,\cdot)\) \(\chi_{4009}(233,\cdot)\) \(\chi_{4009}(302,\cdot)\) \(\chi_{4009}(329,\cdot)\) \(\chi_{4009}(366,\cdot)\) \(\chi_{4009}(370,\cdot)\) \(\chi_{4009}(385,\cdot)\) \(\chi_{4009}(461,\cdot)\) \(\chi_{4009}(479,\cdot)\) \(\chi_{4009}(549,\cdot)\) \(\chi_{4009}(555,\cdot)\) \(\chi_{4009}(586,\cdot)\) \(\chi_{4009}(587,\cdot)\) \(\chi_{4009}(674,\cdot)\) \(\chi_{4009}(690,\cdot)\) \(\chi_{4009}(708,\cdot)\) \(\chi_{4009}(745,\cdot)\) \(\chi_{4009}(766,\cdot)\) \(\chi_{4009}(840,\cdot)\) \(\chi_{4009}(879,\cdot)\) \(\chi_{4009}(916,\cdot)\) \(\chi_{4009}(929,\cdot)\) \(\chi_{4009}(956,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{315})$ |
| Fixed field: | Number field defined by a degree 630 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{199}{210}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4009 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{317}{630}\right)\) | \(e\left(\frac{611}{630}\right)\) | \(e\left(\frac{2}{315}\right)\) | \(e\left(\frac{307}{315}\right)\) | \(e\left(\frac{149}{315}\right)\) | \(e\left(\frac{11}{210}\right)\) | \(e\left(\frac{107}{210}\right)\) | \(e\left(\frac{296}{315}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{19}{105}\right)\) |